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SCHEDULE OF DR. XIAOWEI ZHUANG

9:30 a.m. - 10:30 a.m.

11:00 a.m. - 12 noon

2:00 p.m. - 3:00 p.m.

3:00 p.m. - 4:00 p.m.

4:00 p.m. - 5:00 p.m. •

April 3, 1997 Thursday

Professor Doug Osheroff Varian Physics Building, Room 150

SEMINAR Applied Physics, Room 202

723-4228

Title: "Physical Understanding of Surface-Induced Bulk Alignment of Liquid Crystals"

Drs. Osheroff, Harris, Goodman, Marcus, Harrison, Herring, Fejer, Siegman, Schawlow

Professor Steve Harris Ginzton Laboratory, Room 4

Professor Charlie Marcus Varian Physics Building, Room 154

Professor Tony Siegman Ginzton Laboratory, Room 35

723 -0224

723 -4613

723-0223

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SCHEDULE OF DR. XIAOWEI ZHUANG

9:30 a.m. - 10:30 a.m.

11:00 a.m. - 12 noon

2:00 p.m. - 3:00 p.m.

3:00 p.m. - 4:00 p.m.

4:00 p.m. - 5:00 p.m. •

April 3, 1997 Thursday

Professor Doug Osheroff Varian Physics Building, Room 150

SEMINAR Applied Physics, Room 202

723-4228

Title: "Physical Understanding of Surface-Induced Bulk Alignment of Liquid Crystals"

Drs. Osheroff, Harris, Goodman, Marcus, Harrison, Herring, Fejer, Siegman, Schawlow

Professor Steve Harris Ginzton Laboratory, Room 4

Professor Charlie Marcus Varian Physics Building, Room 154

Professor Tony Siegman Ginzton Laboratory, Room 35

723-0224

723-4613

723 -0223

Lecture I-I

, •

Let me start out with a few words on the "why?" and the "what?" of this l~cture series.

To begin with, history in general is a fun thing - at least, it strikes me that way.

It's interesting, and often amusing, to see the problems people of an earlier time wrestled with, the dumb mistakes they made, the fights they got into, and the way they sometimes found very clever ways to forge ahead.

From a more serious point of view, the study of the history of science can give us a perspective on the interplay of observation and insight, and on how the very fallible humans we call scientists make progress by interacting with each other, often by arguIng.

Maybe by understanding how this has worked in the past we can be better scientists today.

I must warn you that I have many lilnitations as a lecturer on the history of solid-state physics.

The field is a huge one, and many of the things I'll try to talk about are things I know only at second hand.

Also, I have no qualifications as a professional historian of science.

My main virtue is that I'm an old man, so I can remember how things felt in the 1930s when I made Iny decision to switch the focus of my graduate studies from astrophysics to solid state.

Coincidentally, this was about the tiine when the words "solid state" were first starting to be used to describe a recognized subdivision of physics.

1-2

In the six plus decades since that time, I've listened to, and often known personally, a sizable number, though far from all, of the people who have made the major discoveries in solid­state physics.

So I can describe some typical examples of how scientists can be confused, argue with each other, and finally come to a clear consensus.

The synthesizers and textbook writers have often done such a good job of making everything simple and transparent - just what they should do, of course - that the modern student can fail to realize what the original creative process was like.

Now let me shift gears and say a few words about the problem of organizing the lectures.

You can see the problem I face.

There are just a huge number of different subfields, lines of thought, experimental techniques, and so on.

All of them have been evolving over time, and also influencing each other as they've done so.

One couldn't follow one topic in time without having to follow a lot of others along with it.

For example, if one tried to follow magnetism, one would have to say a lot about thin films, low temperature techniques, Green's functions, Mossbauer effect, slow neutron physics, etc.

On the other hand, it would be both difficult and boring to describe all the different sub fields as of 1940, then go through the whole list as of 1950, then the same for 1960, etc.

1-3

So I'm going to compromise.

I'm going to show you a little map, the backbone of which describes in a very general way the types of concepts we have tried to use in building up a rational picture of how solids function.

These types of concepts have guided both the design and interpretation of experiments and the development of theories.

My picture will show, with time increasing downward, how the types of concepts have evolved, the major roadblocks that they have encountered, and how they have changed to get around the roadblocks.

In this first lecture, I'm going to focus just on the earliest and most fundamental of the changes in viewpoint, namely, the gradual recognition that solids are not continuous and infinitely divisible, but are made of atoms.

As I'll describe in a minute, the rise of European science in the 17th to 19th centuries put some quantitative truth into the ancient concept of continuous matter, by developing such concepts as stress, strain, and inertia to describe mechanical behavior, and then adding thermodynamics.

But what could be done with this sort of modeling was very limited.

For all the properties that different kinds of solids possess - color, hardness, density, transparency, electrical conductivity, etc. - and for the temperature dependence of these properties, one had no model that could describe or explain them.

They just had to be measured and tabulated, and their study seemed to amount mostly to the sterile recording of tables of data.

1-4

Fortunately, as I'll now recount in detail, a number of scientific developments from the late 17th to early 20th centuries gave such spectacular support to the atomic picture of matter that it gradually became universally accepted.

So let me start now with the centuries-old controversy between the atomists, who thought of matter as made up of discrete units, called "atoms", and the group that might be called "continuumists", who contended that matter had to be subdividable into arbitrarily small pieces, whose specific properties would eventually become uniform.

As you probably know, the very word "atom" comes from the Greek, from the negative prefix "a" and the "tom" root, used for example in "tome", a cutting, or "tomos", a section.

So the idea was something that can't be cut, at least not into smaller pieces with the same properties.

The atomistic concept goes back at least to Democritus, in the 5th century B.C., and it was strongly espoused by Epicurus in the Hellenistic period and systematically expounded by the Roman poet-philosopher Lucretius in the first century B.C.

However, many other philosophers, including Aristotle, strongly denounced it.

Although the ancient atomists thought that the motions and shapes of atoms could account mechanistically for all the properties of different kinds of matter, their ideas seem to us just to be arbitrary speculations, since they didn't relate them to quantitative physical laws.

So you may wonder why I bother to mention them at all.

1-5

Well, just remember that what we call "physics" was called "natural philosophy", even as late as the 19th century.

When Europe climbed out of the Dark Ages and physics began to grow as a modem physical science, many of the people who tried to formulate laws of physics had at least studied under philosophers, and could read Latin and often Greek.

So they probably were aware of the arguments of the two schools of thought, and often developed prejudices of their own for the one or the other side.

Let's turn, then, to a closer look at the progress of the atomistic school since about 1600.

This is a continuation of the historical panorama I just showed you, taking up the progress of the war after a long hiatus in the Middle Ages.

In this Vu-graph, as in a couple more that I'll show on the historical panorama, I've put the important discoveries in boxes of different colors, the colors referring to different fields of science, which are named in boxes of the same colors near the top of the picture.

These discovery boxes are so big they can't be placed very accurately on the vertical time scale, but I've tried to place the names of the individual scientists who made the discoveries as close as possible to the proper times.

I'll continue to put orange boxes around the names of opponents of atomism, but to minimize clutter I'll identify th~ contributors of atomistic insights with half-boxes colored for their scientific diScipline, rather than the green boxes I used in the earlier centuries for atomists.

1-6

As we get into the 1700's, we find a lot more in the way of detailed evidence coming to light as a result of observations and experiments.

On this Vu-graph I've divided the new developments into two categories - those arising from the new science of crystallography, represented by the boxes on the left here, and those from other areas of physics and chemistry, listed in the boxes on the right.

1 call crystallography a new science because serious natural philosophers seem to have written practically nothing on the science of crystals until almost 1700.

Although the ancients did speculate on possible different shapes for atoms of different materials, it was a long time indeed before the theory of atoms started to be put into a quantitative form and related to a science based on the experimental method.

Newton and Boyle, in the 17th century, were attracted to the idea of atoms capable of free motion, and also of mutual attachment, hence useful to understand the properties of gases and phenomena of chemical gases.

Anyone who has taken high school chemistry will remember Boyle's law, which says that the pressure of a given amount of gas increases when it is compressed into a smaller volume.

This accords with the idea that compression should increase the . concentration of moving atoms.

However, the interpretation of pressure as momentum transferred to the container walls by reflection of impinging atoms seems not to have been clearly stated until the time of Bernouilli, in the 1700's.

1-7

But there were also at this time important opponents of atomism, including for example Descartes, who reasoned more from philosophical than experimental considerations.

Now let's take a look at the crystallography side of the picture.

As I mentioned earlier, it was about the time of Newton and Boyle -the late 1600s - that natural philosophers first began to write about crystals.

I've singled out two names for special mention here, Steno, a Danish theologian, and Guglielmini, an Italian professor who noted among other things, that the facets of a crystal of a given substance always make the same angles with each other, even when the crystals as wholes look quite different.

Let me interrupt this historical picture for just a minute to show what this means.

These diagrams show several of the hundred or more different shapes in which crystals of calcite - calcium carbonate - can be found.

At first sight these six forms all look quite different.

But when each one is properly oriented - and of course the appropriate orientations have been chosen for you by the draftsman - you begin to see some common features.

With this choice of orientations, you find time and again that facets that occur with a certain orientation on one crystal occur with an exactly parallel orientation on some of the others.

For example, of the planes with the type label m, the two in Fig. 4 and Fig. 6 that I've connected with a green line.

Similarly, the three of type e in Figs. 2,4 and 6, connected with a purple line, are all paralleL

1-8

Rome de 1'Isle became the first to realize that a universal principle was involved.

This principle he called the "Law of constancy of angle."

Each substance has a small number of special planes on which it likes to cleave 017 facet, and the angles of these planes with each other are always the same, from one specimen of the substance to another.

Haiiy now made a brilliant contribution by studying these angles in more detail.

Suppose we take a particular substance, like the calcite we've just been looking at.

And suppose we've been able to identify a number of crystal planes for it, like the ones labeled with the letters here.

This you'll recognize as a duplicate of one of the crystal forms 1 showed on the previous Vu-graph.

The intersection of any two of these planes, say these two m planes, is a line parallel to one of the possible crystal edges.

Suppose we select three such lines, like the ones I've traced over in orange here that are not all in the same plane, and draw them through a common point, like the corner I've marked with a black dot.

And now suppose we take some other one of the crystal planes, like this e-type plane over here that I've colored purple, and think of it, or a plane parallel to it, since it's only the orientation that matters, just as an unbounded geometrical plane, extending on beyond any crystal boundaries.

Then somewhere this plane will intersect each of the orange lines, unless of course it happens to be parallel to one of the lines.

1-9

I've tried to show this on the right, by extending this purple plane, not all the way to infinity, but far enough to reach its intersection points with each of the orange lines.

I've identified these intersection points by hollow purple circles.

The remarkable thing that Haiiy found was that the distances of the three purple circles from the black dot always turn out to be related to each other by the ratios of small integers, like 2:1 or 1:3:2, etc.

Of course, if the plane is parallel to one of the lines, it won't intersect that line, and we might say that the distance to this particular intersection point is infinity, which certainly won't fit on the small integer scale.

This is what happens if we choose for our plane, in the present example, the c-type plane that I've colored green.

This plane meets two of the orange lines in the two green points I've shown here.

But the third orange line, this one here, it doesn't meet at alL

To take account of cases like this, one can state the law just a little differently.

Suppose that instead of tabulating the distances of the intersection points from the origin, we tabulate instead the reciprocals of these distances.

Then when the line and the plane are parallel, instead of entering the distance infinity, we can enter the reciprocal distance as zero.

The ratios of the three numbers characterizing any crystal plane will then always be ratios of small integers, including zero as a possibility .

1-10

This rule is what is called the law of rational indices, and I've entered it in this box on our history diagram.

Discovery of this law inspired Haiiy to imagine little bricks to be made in the shape of parallelepipeds with edges parallel to a suitably chosen set of reference lines like the three black lines I showed you in the last Vu-graph, then all the characteristic crystal planes could be represented either as parallel to one of the faces of a brick, or as average slopes of a regular staircase of bricks.

This on the left shows one of his drawings.

Here I've identified a single brick by coloring its three exposed faces red, green, and purple.

Now at the bottom you can see a large plane that is just parallel to one of the faces of a single brick - the one I colored red up at the top.

Over on the right here you have a staircase that rises on step this way for each brick-length of progress this way.

On a macroscopic scale this represents an inclined plane.

On the left there's another staircase, rising one brick height this way for every two brick-widths this way.

And so on.

It's not hard to see that each simple staircase of this sort will represent a macroscopic plane whose indices in Haiiy's construction will simply correspond to the step widths and step heights measured in terms of brick dimensions.

C>

1-11

The diagrams on the right show how some of the simple diagonal planes commonly found in crystals of cubic symmetry can arise from a stacking of cubes.

The natural inference from models of this sort is that a crystal always consists of a regular array of identical structural units that repeats itself identically if translated by anyone of three non-coplanar vectors ti, t2, and t3.

In modern language, it has the symmetry of a translation group.

This principle, with one modification that I'll discuss in a later lecture, has been fundamental to crystal physics ever since.

The elementary structural units are of course not bricks, but groups of atoms.

This fact came to be realized within a few decades of Hauy's work, thanks to the work of the French chemist Proust and the English chemist Dalton.

Proust, making improvements on the then-known techniques for quantitative analysis and synthesis, settled the controversy over whether the elements combining to form a given compound always combined in the same ratio of weights.

He found in 1799 that indeed they do, and thus proclaimed what is called the "law of definite proportions."

This work was soon extended in a very important way by Dalton.

Wearing the hat of a theoretical physicist, Dalton had been studying gases, especially gaseous mixtures, and had been impressed by the utility of the atomic picture for the understanding of gases.

1-12

So he had the atomic picture in mind when he started thinking about how to understand the law of definite proportions in chemistry.

By this time there had been trustworthy measurements on enough different compounds so that in a number of cases, one could compare the relative weights of two elements in more than one compound of these same elements (for example, what we now call carbon monoxide and carbon dioxide).

He found that the ratios of element weights in two different compounds were always proportional to two small integers.

This delighted him, as he was already a convinced atomist, and the discovery was just what one would expect if each compound was made up of identical molecules, with each molecule consisting of a definite number of each of the two kinds of atoms.

So, in a book published in 1808, he proclaimed his "law of multiple proportions", which laid the foundation for modern chemistry.

The essence of this law is stated here.

Note that if one interprets this law atomistic ally, a ratio of weights for a particular compound, like the numerator or the denominator here, depends on two types of quantities.

Namely, it depends on the number of A atoms and B atoms in a molecule of the compound, and on the masses of the two types of atoms.

But when we form this ratio of ratios here, the masses of A and B cancel out, and we are left with a ratio depending only on what we would today call the chemical formulas of C1 and C2.

1-13

The law gives us a constraint on the possible subscripts (as we would now call them) in the two formulas, but still doesn't fully determine the formulas, even when one has several pairs to work with.

Fortunately, there is another law, discovered by the French chemist Gay-Lussac at about the same time, that can give information on a single compound, though it was applicable to only a small fraction of the compounds that could be studied at that time.

Gay-Lussac, who was really as much a physicist as a chemist, had a special interest in gases, and had been studying the reactions of gaseous elements to form (usually) gaseous compounds.

He found that when the amounts of the different elements, and of the product if that was gaseous too, were measured in terms of their volumes at some standard temperature and pressure, the ratios of these volumes would always be ratios of small integers.

Unlike Dalton's law here, which involves two compounds together, this law tells us something about a single compound at a time.

However, to scientists of that time, even atomists, this may not have seemed very helpful in revealing the relative numbers of A and B atoms in a molecule of C.

For just as a Dalton ratio of combining weights involved the masses of the A and B atoms as well as their relative numbers, so Gay-Lussac's ratio of combining volumes involved these numbers and also the (unknown) ratio of volumes per atom for A and B.

A crucial step making possible simple molecular interpretation was, however, given in a few years by the Italian physicist Avogadro.

1-14

His reasoning must have been something like this:

Dalton's simple rational ratios follow from the mere fact that a molecule of a compound contains an integral number of atoms of each kind.

Gay-Lussac's rational ratios would require, in addition, some simple rational ratios for the volumes per molecule of different gases.

But wouldn't it be simpler and more plausible, Avogadro must have thought, to just say that the idea of atoms in molecules is the only source of simple rational ratios, and not have to invent a mechanism to make volume per atom, or per molecule, vary from case to case as a ratio of integers?

So he proposed this law: volume per molecule at given T,p, is the same for molecules of all kinds.

Today we regard this as a trivial consequence of the principle of equipartition of kinetic energy in statistical mechanics.

But this principle wasn't derived until the work of Boltzmann and Maxwell around 1860.

So for the first half of the century Avogadro's law continued to be disputed, though it was often invoked by its supporters, as a tool to help in determining formulas of compounds and the relative masses of atoms of different elements.

Playing with these concepts, the atomists of this half-century had a great time.

Q.Q_------------ . -- .-.-,. ........... -_ .... _-----------But even these concepts were unsatisfying in one respect.

What are called "atomic weights" are of course only relative weights of different kinds of atoms.

The absolute weights of atoms, like their sizes, were cOlnpletely unknown in the early 19th century .

1-15

All the things I've mentioned so far as supporting the idea of atolns -gas cOlnpression, formation of compounds out of elements, structure of crystals - will work as well at one size scale as another.

If philosopher A were to think of atOlns as having S0111e specific size, philosopher B could argue that the atoms could just as well be a thousand times smaller, or a million or a trillion, or anything.

So maybe they don't have any size at all, but are just a fictitious construct.

This shows the dilemma, in words.

Returning to the historical panorama, we find ourselves at the bottom of this Vu-graph, having seen a lot of progress, but still in an unsatisfactory situation, with the atOlnists hopeful

_->..., but no] ontent, and the doubters still unconvinced.

So let's scroll the picture to the full 19th century.

Fortunately, the great proliferation of experimental and theoretical physics in the 19th century eventually gave clues to the sizes of atoms, though not everyone accepted the evidence at first.

Some of the strongest pieces of evidence carne from experimental and theoretical studies of some of the properties of gases.

You'll remember I mentioned that Boyle and Newton had been attracted by the idea that the pressure of a gas could be interpreted as the average force exerted on the walls of the container by moving atoms striking them and being reflected.

1-16

Well now, with the growth of interest in atoms and the sophisticated mathematical development of the science of mechanics based on Newton's laws of motion, people began trying to explain not only pressure but all sorts of other properties of gases in terms of the statistical properties of atoms or molecules moving around randomly through mostly empty space, but occasionally bumping into one another.

This new science, called the kinetic theory of gases, tried to explain phenomena like diffusion and viscosity.

Diffusion is perhaps the easiest to explain.

Suppose we have a longish container, like this, filled with a particular kind of gas, say nitrogen, whose molecules I've represented as green dots.

And now suppose that at some instant of time we add a little bit of some other gas, say bromine, in the middle.

Since bromine is reddish brown, I've chosen to represent its molecules as red dots.

If we've been able to do this without any stirring, that is, without making any macroscopic winds, the only thing that will cause the gases to intermingle will be the random motions of the individual molecules, the motions that the atomists believed represented heat energy.

This will cause the bromine molecules to gradually spread out over a wider and wider range, as I've shown here.

We can follow this spreading out just by noting the width of the region with brownish color, or alternatively by some other more sophisticated technique of measuring the distribution of the second gas.

1-17

At the risk of boring any of you that have studied kinetic theory, I'd like to take a few minutes to show how one can get an estimate of the size of the molecules by measuring the mean square distance the one gas spreads into the other, and using a couple of other measurements that are even easier to make.

Suppose for simplicity that gas A is present in dilute concentration in gas B, and consider the motion of a particular molecule of A.

This motion will appear as I've shown here, with a number of rectilinear stretches in random directions and whose lengths vary randomly about a mean free path "A".

In a macroscopic time t there will be on the average vt/A such stretches, where v is an average velocity.

Because the motion is randomized after each collision, the mean square displacement in say the x-direction in time t will be of the order of A2 times the number of stretches.

I write this as Wx = a coefficient G of order unity time A2 times the average vt/A.

A more careful calculation gives G = 2/3, as I've written here.

The macroscopic diffusion equation gives for this same wx2 the value 2Dt, where D is the diffusion coefficient.

Thus the product VA must equal three times the measured D.

By about 1873, when Maxwell published his definitive version of kinetic theory, this and other similar analyses had been worked out for this and several other properties of gases.

I

V&lrJ

I - 18

In particular it turns out that the viscosity 11 of a gas and its thermal conductivity K, are also related to vA by these last two equalities here, where Pg is the ll1ass density of the gas and Cv is its specific heat at constant volume.

To keep my promise I now have to show you how the VA one can obtain in this way can be used to get the molecular sizes.

But before I elubark on this I should reluark that these last equations here already gave a triuluph for kinetic theory, and therefore for atomism, because they relate the independently Iueasurable quantities, self-diffusion coefficients, viscosity, and thermal conductivity, to each other.

And indeed, these relations were actually observed to be pretty much true for simple gases, to within a modest percentage, though the temperature variations suggested that the rigid sphere model was a little too crude.

Considering that the relations were derived frOlu an obviously crude model, they must have seemed like quite a triLuuph for molecular theory.

But let me get back to the matter of relating this VA to Iuolecular SIzes .

As early as 1843 Joule had pointed out that the pressure and density of a gas should yield the 1110lecular velocity.

In the molecular model of a gas, the pressure p should be the net force exerted on unit area of the container wall by Iuany molecules striking against it and being reflected.

So it's roughly the number of impacts per unit area per unit time, times twice the average momentum normal to the surface.

The first factor is the normal velocity V..1 times the number n of molecules per unit volume, while the second is twice the molecular mass times V..1.

1-19

So we have nmv..1 , or since the perpendicular direction is just one of three equivalent directions, we can write this as 1/3 mv2 , where the v2 is obviously a mean square velocity.

Since the density Pg of the gas is just nm, we have finally just mean

v2 =3p / Pg

There's a trivial factor, nearly unity, to convert the root mean square velocity into the average velocity I used in the preceding transparency - it's not really important for my present discussion of orders of magnitude.

So it's trivial to combine the v information we get here with the VA we just get from transport data to get the mean free path A.

Now let's look at what determines 'A.

Consider an atom of diameter d moving in some arbitrary direction through a gas of the same kind of atoms.

It will have a collision as soon as it finds another atom whose center is inside the cylinder of diameter 2d centered on the path of the moving atom.

Since the atomic positions before the collision are essentially uncorrelated, this will happen on the average when the volume of the cylinder swept out is just equal to the volume lin per atom in the gas.

If 'A is much larger than d, the length of this cylinder is essentially the 'A we are interested in, so we have 1td2'An = 1.

1-20

We still have two unknowns, d and n, but there is a trivial relation between them if one is willing to assume, as some of the early atomists were, that when we condense the gas into a solid, the molecules remain essentially unchanged, but are packed together as spheres in contact.

For a close packing of spheres, the volume per sphere of diameter d is (2 3/ 2/ 3)d3, so if m is the molecular mass, the density Ps of the solid is 3m/2 3/2 d3.

Since the density Pg of the gas is nm, we can eliminate m and write

nd3 = (2 ~2 / 3) Pg/ps.

So the complete line of reasoning is: gaseous transport gives VA, Joule's relation gives v, these give A which gives d2n, gas-solid density ratio gives d3n, hence we get d and n.

It's interesting to compare these crude gas-kinetic estimates of molecular sizes with present-day knowledge.

I still have, at home, an 11th Edition Encyclopedia Brittannica, published in 1910, which my parents bought for me when I was in school in the 1920's.

The articles in it on atoms, molecules, etc. were all written before the possibility of accurate measurements by x-ray diffraction had been discovered.

But the authors were all convinced atomists, and in one of the articles I found a table of the molecular diameters of a number of common gases, as derived from kinetic theory.

1-21

Though the author recognized that the hard-sphere model was rather crude, the table was presented with some confidence as a table of "average diameters."

For hydrogen, for example, it gave a diameter of 2.03 Angstroms, somewhat less than the spacing of 3.75 Angstroms now accepted as the nearest neighbor distance in solid hydrogen, but at least in the right ball park.

I'm tempted to guess at the reason for the discrepancy, though I can't be sure since the detailed reasoning behind the figures in the Brittannica table weren't given.

My guess is that since the true intermolecular potential has a long­range attractive part and a short-range repulsive part, like this ----, the spacing in the solid is close to the minimum of this curve, here, while in the gas large-angle scatterings are most often caused by the long range force, at a larger distance.

Introduction of about a 35% difference between the effective diameters d in these two equations would cause the calculation I've sketched here to yield a diameter, in the solid, about 1.8 times as great as the simple calculation assuming both d's the same.

Actually, the idea of intermolecular potential curves like this one I've drawn here came into prominence at about the time the kinetic theory of gases matured.

In 1873 the Dutch physicist van der Waals proposed that the slight departures of the equation of state of real gases from the ideal gas law could be roughly accounted for by force laws of this type.

To approximate their effect, he wrote down his famous equation of state, which I'm sure you've all seen.

I -22

This expresses the relation of the pressure p to the volume V of one mole of materiat at any temperature T.

R is this usual gas constant, and the two new constants introduced by van der Waals are this a and this b, independent of volulne and temperature and characteristic of the type of Inolecule Inaking up the gas.

The rationale, you'll remember, is that p + a/v2 is supposed to approximate that part of the pressure that is due to the translatory motion of the 1110lecules .

.,.-t ~re.

~ This is 1is; than the total pressure p when the molecules are mostly well separated from each other, because just by virtue of their positions they attract their near neighbors and thus create a negative term in the pressure.

Being due to two-body forces, this term is proportional to the square of the concentration of Inolecules, hence the a/v2.

And subtracting a negative pressure gives p plus a/v2.

In the second factor here, the rationale is to use the volulne that is available for a molecule to Inove around in, which is essentially the total volume v minus the volulne the molecules would occupy if they were a close-packed solid.

This equation turned out to be fairly successful in accounting for the departures shown by actual gases frOln the idea gas law.

And the values of b fitted to equations of state were roughly consistent with the rigid-sphere sizes inferred froll1 the kinetic-theory argulnent I've just discussed.

So here was another piece of evidence favorable to the atOlnistic picture .

But van der Waals made an even more important further step.

1-23

He pointed out that an equation of state of this sort could account semi-quantitatively for both the gaseous and the liquid phases.

Consider the shape of the plot of p against v, at any fixed temperature.

It's easy to see that the equation determines a single value of p for any assumed v greater than b.

But if you try to take p as the independent variable, you get a cubic equation for v, which has three roots.

Of course, depending on the parameters, these may either be all real, or one may be real and the other two complex, and conjugate to each other.

It's not hard to show that for different temperatures on gets a family of p-V curves like that shown in this figure.

At high temperatures, the curves look almost like the hyperbolas pV= constant, which is Boyle's law.

As the temperature is decreased, the curves at first continue to descend monotonically but get less steep in the middle.

At still lower temperatures, the curves are no longer monotonous, but have a real hill in the middle.

This is physically impossible for a stable state of a homogeneous real system, because the part of the curve where pressure increases with volume represents a system of negative compressibility .

1-24

If such a system existed, on can easily show, by a simple Gedanken experiment, that one could extract work from the system without changing its total volume or temperature, hence necessarily lowering its free energy and converting the starting state into a more stable state.

Specifically, the Gedanken experiment could consist of dividing the system into two equal halves, expanding the first by a given amount, and compressing the second by the same amount, so as to leave the sum of the two volumes unchanged.

Since the average pressure in the expanded half would be greater than that in the compressed half, because of the positive slope of the p-V curve, a net work would be done by the system on the controlling pistons.

So I color the rising portion of any curve red to brand it as unstable.

And therefore the van der Waals equation implies that at any temperature below the critical temperature at which the down-up-down shape first appears, imposition of any pressure below the critical pressure will allow the system to be stable and homogeneous at two and only two different volumes, here and here, the left-hand one corresponding to the liquid phase, the right-hand one to the gaseous.

For these insights and for his related work on the so-called "principle of corresponding states" van der Waals was awarded the Nobel Prize in Physics in 1910.

Before I leave the main part of the 19th century, I'd like to mention one other area of research that further stimulated thinking about atoms and molecules, and that was destined to lead into some very revolutionary concepts around the turn of the century.

1-25

This was the field of gas discharge physics, which had begun about the middle of the 1800s when Geissler perfected the technique of making partially evacuated glass tubes with electrodes in them.

A lot of people studied the gaseous fluorescence produced by applying voltages to electrodes in such tubes, and the fluorescence of the glass walls that became especially noticeable at low gas pressures.

In the 1870's, special attention focused on the observation that much of this fluorescence seemed to be produced by something coming from the cathode.

This "something" was called "cathode rays" by Goldstein in 1876, who thought of it as some sort of wave in the ether.

It was soon found that cathode rays tended to travel in straight lines, and could cast shadows.

However, they were deflectable by electric and magnetic fields, so some scientists, especially the British ones, pictured them as streams of charged corpuscles.

The crucial experiments were finally done in 1897 by J.J. Thomson, who measured the deflections in electric and magnetic fields quantitatively, and from these extracted the velocity and the charge-to-mass ratio elm of the presumed corpuscles.

And he was able, within a few years, to create his "electrons" by shining light on a metal surface, make gaseous ions with them, and measure their charge, which turned out roughly as he had expected.

This last he did by counting the ions using the cloud-chamber techniques that had just been developed by his student C.T.R. Wilson.

c

1-26

Now it happened that some years before this, the electrochemists had measured the mass of a given metal (say, copper) deposited by passing a given amount of electric charge through an electroplating bath.

And they had found that for all monovalent metals the mass-to­charge ratio was proportional to the atomic weight.

To an atomist, who would be a believer in Avogadro's law, this meant that a positive ion of a monovalent metal always carried the same electric charge.

Indeed, the magnitude of this charge had been roughly determined from Avogadro's number by the Irish electrochemist Stoney in 1874, and he coined the word "electron" for it in 1891.

So it was natural for Thomson to appropriate this name for the cathode-ray particle he had discovered.

He called special attention to the fact that his new particle, while presumably having the same charge e as a monovalent ion, had an enormously larger elm, hence a mass vastly smaller than that of an ion or atom

Though further experiments were obviously needed, and in due time were of course performed, it was starting to become clear that there was such a thing as a basic atom of negative charge and that, quite possibly, charge of all kinds was quantized.

Here as I'm changing Vu-Graphs it's as good a time as any to pause for a few sentences summarizing the state of progress, at around 1900, of what I've been calling "the war."

The atomists seemed to be winning: most thoughtful physicists and chemists were now on their side.

But there were still a few holdouts, some very intelligent and highly respected.

1-27

Two of the most noted of these I've put in orange boxes here.

These were the physicist Ernst Mach, a widely respected thinker and authority on the foundations and history of physics, and Wilhelm Ostwald, the distinguished chemist who was later to receive the 1909 Nobel Prize in Chemistry.

Mach, for example, put these words in his book "The Science of Mechanics" :

So it was still of some importance that a few new areas, which I'll discuss in a minute, were yielding still further support for the atomic picture.

But in parallel with this, the properties of the newly-discovered electron were starting to show that the correct version of atomic theory would have to be much more complicated than anyone in earlier years had realized.

Quantum theory and x-ray physics were being born, and my history of the war will close with a look at where they were leading.

So now I'll turn to the new findings on what 1 might call the classical aspect of atoms.

One very simple experiment that was already tried near the start of the century was the study of things like surface tension.

Thomas Young, an English scientist distinguished in such diverse fields as physics, medicine and archaeology, concluded in 1805 from studies of capillary phenomena that the range of intermolecular forces was somewhere between about 1/4 Angstrom and about a tenth this.

For its time this was a fair estimate, though 1 don't know why it came out so small.

1-28

The conclusion didn't seem to have very much influence on the conversion of scientists to atomism, though, and it wasn't until late in the century that improved versions of the experiment were carried out.

Notable was an experiment by Lord Rayleigh in 1890.

He found that a sensitive indicator of inhomogeneity in the surface tension of water covered by a thin olive oil film was provided by the behavior of a tiny lump of camphor placed on the surface.

If there is no oil on the surface, the camphor dissolves in the water and forms a surface film with altered surface tension.

Since this dissolution normally occurs more rapidly on one side of the camphor than on the other, the camphor is pulled away from this side by the anisotropy of the surface tension forces, and skitters about.

If there is a full monolayer or more of olive oil on the water, the dissolution is blocked, and the camphor remains at rest.

Rayleigh found the former behavior for an oil film of about 8 Angstroms average thickness, and the latter behavior for films 10 Angstroms thick.

Thus this experiment suggests a molecular diameter of the order of 9 Angstroms, which sounds to us to be about the right order of magnitude for a middle-sized organic molecule like the several compounds that make up olive oil.

A couple of further discoveries have to do with solutions and suspenSIons.

Einstein's Ph.D. thesis, one of the publications of his famous year 1905, had to do with the increase of viscosity with concentration in dilute solutions of sugar in water.

1-29

What Einstein did was to infer both Avogadro's number and the size of a sugar molecule, assumed roughly spherical in shape, from two Iueasured properties of the solutions, the viscosity I just mentioned, and the diffusion coefficient of the sugar.

What he did is actually very reluiniscent of the 19th century gas­kinetic work I told you about a few Iuinutes ago, which inferred Avogadro's number and the size of a gas Iuolecule from a gaseous diffusion coefficient and a ratio of gaseous to solid densities.

However, as Einstein was dealing with a liquid rather than a gaseous system, the mathematics had to be rather different.

His major contribution was a scheme for calculating the diffusion coefficient, in a liquid, of an object large compared with molecular dimensions, due to the nudges it gets frolu the random vibrations of the Iuolecules of the liquid.

*** New Material From Tape To Be Inserted Here ****

When accurate measurements of D for spherical colloidal particles ~ were made a few years later by Perr~n, Einstein's fonuula

was indeed found to have predicted correctly.

Actually, credit for this fonuula should be shared between Einstein and the great Polish physicist Smoluchowski, who actually derived it independently slightly before Einstein, but did not publish it until the following year, as he had hoped to complete some experiments on it before publishing.

However, the two men soon developed a very friendly and rewarding correspondence.

1-30

\

At this point I'd like to make a couple of summarizing remarks before turning to a new path of investigation that not only gave spectacular support to the atomic picture, but at the same time showed that making progress in the atomic world was going to be much trickier than anyone had foreseen.

The two developments I've just finished talking about, when added to all that had gone before, made an impressive total of widely different types of measurements that all yielded essentially the same value for Avogadro's number - the number of molecules in a gram mole of anything.

This was perhaps the straw that broke the camel's back in the case of Ostwald, who in a book published in 1908 switched sides and wrote that these results and those on the electron:

"entitle even the cautious scientist to speak of an experimental proof for the atomistic constitution of space-filled matter."

Although Mach never renounced his doubts about atoms, he died in 1916, and no doubters of comparable stature remained.

The war was won.

But ever new demonstrations of the atomic nature of matter continued to be made, and as I've already hinted, some of them were both puzzling and exciting.

So I have to close by saying a few words about these.

A very early consequence of the flurry of research on cathode rays was the accidental discovery, made by Roentgen in 1895, of the x-radiation that was emitted from the walls of the tube as a result of their bombardment by the cathode rays.

It's a familiar story how he found them to penetrate matter opaque to ordinary light, to be uncharged, and to be generated near the point of impact of the cathode rays on some solid body.

,;

"

. .:- ..

. , ~ ..

o'.:-i

oj;"

X-rays of course soon attracted a great deal of attention in the research community.

1-31

It was found within a few years that they could ionize the molecules of a gas and release negative charges, presumably electrons, from the surfaces of solids.

Here a happy confluence of two developments occurred, namely of x-ray physics with quantum theory.

As you know, quantum theory had its origin in the attempt by Max Planck to find a rational explanation for the frequency distribution of light in black-body radiation.

He succeeded in deriving a formula that gave a beautiful agreement with observation by making what seemed at first to be a very puzzling hypothesis.

In its original form this was the hypothesis: that a material harmonic oscillator can have only certain specific energies, namely those that are an integral multiple of a certain constant called h times the frequency of the oscillator.

Various interpretations of this and various attempts to reformulate it were made in the succeeding decade, and even for longer.

One of these was due to Einstein, who pointed out in 1905 that if one made the assumption that light of any particular frequency v could exist only in quanta of energy hv , then one could explain certain newly discovered facts about the emission of electrons from illuminated metal surfaces.

His proposal was, of course, the famous Einstein photoelectric equation, which after many years of doubt and rejection was finally found to be in very accurate accord with careful experiments, and for which Einstein received the 1921 Nobel Prize.

1-32

Within a few years energies of photoelectrons produced by x-rays were interpreted using Einstein's formula to imply that the wave length of the x-rays must be of the order of Angstroms.

Then in 1912, von Laue, having become aware of this fact, pointed out that the regular arrangement of atoms in a crystal should enable the crystal to act as a 3-dimensional diffraction grating, and diffract a collimated x-ray beam and thereby yield information on the ratio of the x-ray wavelength to the lattice spacing in the crystal.

An experiment was soon performed by Friedrich and Knipping in Germany, using a zincblende crystal, and a little later by the Braggs, father and son, in England, using the same material, and providing a more complete analysis of the diffraction pattern.

These experiments, which launched the vast field of x-ray crystallography, at once received great attention, and were rewarded with Nobel Prizes for Laue and for the Braggs.

However, their role in the war between atomism and its opponents is perhaps to be characterized best as a "clean-up" operation - the war had already been won.

Well, this really concludes all 1 have to say on the history of the war itself.

However, I'd like to add one little postscript that shows how it really took many more decades before scientists were able to feel really at home with atoms.

What I've said so far has come from old papers and history books, and now by contrast, I want to share just a few personal remiruscences.

11-32

Although, as you've just seen, the atomic picture of solids was universally accepted from about 1910-1915 onwards, and was taught in all the textbooks, scientists didn't yet feel quite as at

. home with atoms as they did with things they could see and measure directly.

This feeling of awkwardness showed through in the long boring arguments about issues that seemed almost impossible to decide experimentally, issues such as the arrangement of atoms and ions when cesium adsorbs on tungsten.

Or for another example, some theorists proposed that a crystal surface might have a different periodicity from that of the underlying bulk - the phenomenon we now call "reconstruction" - but nobody paid much attention.

At the time I want to focus on, the middle 1950's, electron microscopy, though a wonderful advance over optical microscopy, still didn't have nearly enough resolution to distinguish individual atoms.

The first breakthrough finally came, via field ion microscopy, a technique developed by the late Erwin Mueller, working first in Germany and then at Penn State.

The basic idea, which I'm sure many of you are familiar with, is shown here.

One prepares a sharp point of some metal, like tungsten, that's easily cleaned of adsorbed contaminants by heating it.

The tip is macroscopically smoothly rounded, with a radius of curvature of the order of a few hundred Angstroms, and is mounted at the center of a spherical glass container with a luminescent screen on its inner surface.

1-34

When a high positive voltage is applied to the tip, the field on a macroscopic scale will of course be greater at the end than down on the shank, because of the greater curvature.

For the same reason, the field will be greater at the edges of atom layers - here for example - than in the middle of close-packed flat regions - such as here.

Indeed, it will even be greater over the centers of atoms than over the hollows between atoms.

I've tried to show these field fluctuations roughly by the lengths of these little red lines.

Now if the tube contains only a very low pressure of a light gas, say helium, the neutral gas atoms will approach the metal surface at random, but if the positive voltage on the tip is large enough, the gas atoms will suffer field ionization as they approach the very high-field regions of the tip.

In other words, an electron will tunnel from the atom to the metaL

The slow-moving atom will become a positive ion, and be accelerated rapidly away from the tip.

Since most of the voltage drop occurs very close to the point, the orbit of the ion will be almost perpendicular to the local mean surface - the green curve here, and the points of impingement of the ions on the fluorescent screen will give a reasonably true map of their points of origin just outside the metal surface.

Professor Mueller presented some early results in an invited lecture at the Annual Meeting of the American Physical Society, on Jan. 31, 1956.

I was there.

1-35

The talk was in a large auditorium adjacent to the Hotel New Yorker on 34th Street, and the room was packed.

After explaining his technique, Mueller showed a slide of a photograph he had taken of his luminescent screen when he was drawing ions away from a tungsten point.

To maximize your feeling of identification with the 1956 audience, I'd like to be able to show you an exact copy of the slide Mueller showed then.

Unfortunately, my efforts to locate this slide have failed.

However, I do have a very similar picture taken in the same laboratory only a few years later by Tien Tsong, Mueller's student and successor as director of the laboratory.

I am grateful to Dr. Tsong, who now is Director of the Institute of Physics of the Academia Sinica in Taipei, for sending it to me.

Here it is.

Well when the physicists saw that, they just went wild.

They clapped and clapped and clapped, and finally gave him a standing ovation.

While the people in the room had not had any doubts about the existence of atoms, they would have had to admit that their faith was based on indirect reasoning, based on such things as the theory of x-ray diffraction, chemical valence, collisions in gases, et.

Now they could feel their faith vindicated, and could just say "seeing is believing."

The details of the picture make very good sense.

1-36

In the regions,that are not in or near a low-index facet, you can see every atom.

The low-index facets relnain dark silnply because they are atomically flat, and the electric field over them is much smaller than over the curved regions.

For example, the central facet here is the (110), which is the most closely packed plane for a body-centered cubic crystal.

The (100) type facets, here and here, are also quite flat, and hence dark.

And so on.

But these are stories for another lecture .

I just wanted you to feel the sense of triumph at the ability to see atomic arrangements.

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(

Report of the High Energy Physics Laboratory (HEPL) Visiting Committee

April 1990

The High Energy Physics Laboratory (HEPL) has been a remarkably successful laboratory throughout its existence and is a unique facility for the University and for the nation. This report will concentrate on a review of the science being done in HEPL, a discussion of the ways in which HEPL is a unique resource, and problems and opponunities now facing the Laboratory.

I. The Science

The science being carried out in HEPL is in several subdisciplines of physics: superconducting accelerator/free electron laser research, astrophysics, high energy and particle physics, experimental gravitation and some aspects of condensed matter physics. Although seemingly disparate areas, the common element in the research is the application of advanced technology developed within HEPL to a set of interesting and important problems in science.

Individual members of the committee are expert in the subdisciplines . represented by the HEPL programs. Their evaluation of the research is giyen below.

. The Superconducting AcceleratorlFree Electron Laser Research

Principal Investigators: Schwettman, Smith Visiting Committee Members: Sievers, Sessler

It was at Stanford and HEPL in the 1970's that the free electron laser (PEL) was invented, built, and first made to work. The superconducting accelerator (SCA) was used for this purpose and is, even now, being used to operate the FEL. It is a real breakthrough to have a machine that is available and successful in providing a high quality beam for multiple pulse experiments. This group is on the cutting edge in putting the PEL to solid use.

The SeA is a unique accelerator eminently suitable for an FEL and HEPL is to be congratulated for having developed and improved this fine machine over the last two decades. The laboratory has submitted a large ( 14M) proposal to make a user facility out of the SCNFEL. At present, the Stanford PEL is the best in the world and, coupled with HEPL's tradition ofFEL science, we believe that the Stanford proposal will be supported.

Turning an PEL from a laboratory curiosity into a scientific instrument is a non-trivial task. Further, it is an important task. HEPL is to be congratulated for identifying this need and for being willing to undertake the challenge. We can envision the development work eventually resulting in FEL user facilities quite analogous to present day synchrotron radiation facilities (like the Stanford Synchrotron Radiation Laboratory, SSRL). At present, however, the FEL would only have a few users, although even that will have an impact on HEPL. The close

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1-3

So I'ln going to compromise.

I'm going to show you a little map, the backbone of which describes in a very general way the types of concepts we have tried to use in building up a rational picture of how solids function.

These types of concepts have guided both the design and interpretation of experiments and the development of theories.

My picture will show, with time increasing downward, how the types of concepts have evolved, the major roadblocks that they have encountered, and how they have changed to get around the roadblocks.

In this first lecture, I'm going to focus just on the earliest and most fundamental of the changes in viewpoint, namely, the gradual recognition that solids are not continuous and infinitely divisible, but are made of atoms.

As I'll describe in a Ininute, the rise of European science in the 17th to 19th centuries put some quantitative truth into the ancient concept of continuous matter, by developing such concepts as stress, strain, and inertia to describe mechanical behavior, and then adding thermodynamics.

But what could be done with this sort of modeling was very limited.

For all the properties that different kinds of solids possess - color, hardness, density, transparency, electrical conductivity, etc. - and for the temperature dependence of these properties, one had no model that could describe or explain theln.

VG 1

1-4

They just had to be measured and tabulated, and their study seemed to alnount mostly to the sterile recording of tables of data.

Fortunately, as I'll now recount in detail, a nUlnber of scientific developments from the late 17th to early 20th centuries gave such spectacular support to the atOlnic picture of nl.atter that it gradually became universally accepted.

So let me start now with the centuries-old controversy between the atomists, who thought of matter as Inade up of discrete units, called "atoms", and the group that might be called "continuumists", who contended that matter had to be subdividable into arbitrarily small pieces, whose specific properties would eventually become uniform.

As you probably know, the very word "atOln" COlnes from the Greek, from the negative prefix "a" and the "tom" root, used for example in "tome", a cutting, or "tOlnos", a section.

So the idea was something that can't be cut, at least not into smaller pieces with the SaIne properties.

The atomistic concept goes back at least to Democritus, in the 5th century B.C., and it was strongly espoused by Epicurus in the Hellenistic period and systelnatically expounded by the Roman poet-philosopher Lucretius in the first century B.C.

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the individual scientists who made the discoveries as close as possible to the proper times.

I'll continue to put orange boxes around the names of opponents of atomism, but to minimize clutter i'll identify the Jet cer c.on cr; bl,(-t-.::.'t's of atomistic insights with · boxes colored for then scientific discipline, rather than the green boxes I used in the earlier centuries for atomists.

As we get into the 1700's, we find a lot more in the way of detailed evidence coming to light as a result of observations and experiments.

On this Vu-graph I've divided the new developluents into two categories - those arising frOlu the new science of crystallography, represented by the boxes on the left here, and those from other areas of physics and chemistry, listed in the boxes on the right.

I call crystallography a new science because serious natural philosophers seem to have written practically nothing on the science of crystals until almost 1700.

1-7

Although the ancients did speculate on possible different shapes for atoms of different materials, it was a long tilne indeed before the theory of atoms started to be put into a quantitative form and related to a science based on the experill1entallnethod.

Newton and Bo Ie, in t e 17th century:, were attracterl to the idea of ,.r 11 c().. t«.bu )"~.e. t' ';4?f11AJ-:::~&t-b~4L If#%&nt'l1~ ~HC-.e' atoms/\ mo lOn~1 a 1 ~~~y

fA./,jt(tt) to understand the properties of gases. a.. Yft. p",~n(?m.el1() '1 C h~JH~~1 a-tia . ..-e .... Lt a.-a, ~YrC ,

Anyone who has taken high school chemistry will relnelnber Boyle's law, which says that the pressure of a given amount of gas increases when it is cOlnpressed into a slnaller volull1e.

~ "> f[/'seem~to j30~ ac~~9"te ~a}h c I ~ea~wop~tiojClen~0 ~J 0

-ow let's take a look at the crystallography side of the picture.

As I mentioned earlier, it was about the time of Newton and Boyle­the late 1600s - that natural philosophers first began to write about crystals.

I've singled out two names for special mention here, Steno, a Danish theologian, and Gugliehnini, an Italian profes-t0r who noted among other things, that the facets of a crystal of a given substance always make the saIne angles with each other, even when the crystals as wholes look quite different.

Let me interrupt this historical picture for just a ll1inute to show what this means.

These diagrams show several of the hundred or lnore different shapes in which crystals of calcite - calcium carbonate - can be found.

At first sight these six forms all look quite different.

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So for the first half of the century Avogadro's law continued to be disputed, though it was often invoked by its support]~sas a tool to help in determining formulas of cOlupounds a'nd the relative masses of atOlus of different elements.

Playing with these concepts, the atOluists of this half-century had a great time.

But even these concepts were unsatisfying in one respect.

What are called "atomic weights" are of course only relative weights of different kinds of atoms.

The absolute weights of atoms, like their sizes, were completely unknown in the early 19th century.

All the things I've mentioned so far as supporting the idea of atoms -gas compression, formation of compounds out of elements, structure of crystals - will work as well at one size scale as another.

If philosopher A were to think of atoms as having some specific size, philosopher B could argue that the atoms could just as well be a thousand times slualler, or a million or a trillion, or anything.

So luaybe they don't have any size at all, but are just a fictitious construct.

VG~I TAl ~ 5how~ #Z~ cli)f'Wlma.) lYl W6 Y1d 5 · ",/1 Returning to the historical panorama, we find ourselves at t~e

bottom of this Vu-graph, having seen a lot of progress, but still in an unsatisfactory situation, with the atOluists hopeful but no content, and the doubters still unconvinced.

---------------------------------------------------------------VG-7~ So let's scroll the picture to the full 19th century", \Qolif~ 8:J3ll8@Jlpg­

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•

I - 25

For these insights and for his related work on the so-called "principle of corresponding states" van der Waals was awarded the Nobel Prize in Physics in 1910.

One very simple experiment that was already tried near the start of the century was the study of things like surface tension.

Thomas Young, an English scientist distinguished in such diverse fields as physics, medicine and archaeology, concluded in 1805 from studies of capilllary phenomena that the range of intermolecular forces was somewhere between about 1/4 Angstrom and about a tenth this.

For its time this was a fair estilnate, though I don't know why it came out so small.

The conclusion didn't seeln to have very much influence on the conversion of scientists to atomism, though, and it wasn't until late in the century that improved versions of the experiment were carried out.

Notable was an experiment by Lord Rayleigh in 1890.

He found that a sensitive indicator of inhomogeneity in the surface tension of water covered by a thin olive oil fihn was provided by the behavior of a tiny lump of camphor placed on the surface.

If there is no oil on the surface, the cmnphor dissolves in the water and forms a surface fihn with altered surface tension.

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Since this dissolution normally occurs more rapidly on one side of the camphor than on the other, the camphor is pulled away from this side by the anisotropy of the surface tension forces, and skitters about.

If there is a full monolayer or Inore of olive oil on the water, the dissolution is blocked, and the camphor remains at rest.

Rayleigh found the fonner behavior for an oil film of about 8 Angstroms average thickness, and the latter behavior for films 10 Angstroms thick.

Thus this experiment suggests a 1110lecular dialneter of the order of 9 Angstroms, which sounds to us to be about the right order of magnitude for a Iniddle-sized organic molecule like the several cOlnpounds that Inake up olive oil.

~~~~~~~!,e:!~~ the physicist Ernst Mach, a widely respected thinker and authority on the foundations and history of physics, and Wilhelm Ostwald, the distinguished chemist who was later to receive the 1909 Nobel Prize in Chemistry.

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---;7 -rh t ~ J;:h@ anee~to l!Sef ~(51ne of thm,Q Ll QVl dil'eev~ was the field of gas tlischarge physics, which had begun about the Iniddle of the 1800s when Geissler perfected the technique of l1.1.aking partially evacuated glass tubes with electrodes in them.

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And he was able, within a few years, to create his "electrons" by shining light on a metal surface, make gaseous ions with them, and measure their charge, which turned out roughly as he had expected.

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This last he did by counting the ions using the cloud-chall'lber techniques that had just been developed by his student C.T.R. Wilson.

Now it happened that some years before this, the electro chemists had measured the mass of a given metal (say, copper) deposited by passing a given amount of electric charge through an electroplating bath.

And they had found that for allluonovalent metals the luass-to­charge ratio was proportional to the atoll'lic weight.

To an atomist, who would be a believer in Avogadro's law, this meant that a positive ion of a monovalent luetal always carried the same electric charge.

Indeed, the magnitude of this charge had been roughly detenuined from Avogadro's number by the Irish electrocheluist Stoney in 1874, and he coined the word "electron" for it in 1891.

So it was natural for ThOluson to appropriate this nalue for the cathode-ray particle he had discovered.

He called special attention to the fact that his new particle, while presumably having the same charge e as a luonovalent ion, had an enormously larger elm, hence a mass v astly smaller than that of an ion or atom

Though further experiments were obviously needed, and in due time were of course performed, it was starting to becOlue clear that there was such a thing as a basic atOlu of negative charge and that, quite possibly, charge of all kinds was quantized.

~-~ - - - -- - - .-..:----- ~ ---7 A~very early consequence,-how~n8~ of the flurry of research on

cathode rays was the accidental discovery, lTIade by Roentgen in 1895, of the x-radiation that was eluitted frOlTI the walls of the tube as a result of their bOlubardluent by the cathode rays.

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1-30

His proposal was, of course, the famous Einstein photoelectric equation, which after many years of doubt and rejection was finally found to be in very accurate accord with careful experiments, and for which Einstein received the 1921 Nobel Prize.

Within a few years energies of photoelectrons produced by x-rays were interpreted using Einstein's formula to ilnply that the wave length of the x-rays must be of the order of Angstroms.

Then in 1912, von Laue, having becOlne aware of this fact, pointed out that the regular arrangelnent of atOlns in a crystal should enable the crystal to act as a 3-dimensional diffraction grating, and diffract a collimated x-ray beam and thereby yield information on the ratio of the x-ray wavelength to the lattice spacing in the crystal.

An experiment was soon performed by Friedrich and Knipping in Germany, using a zincblende crystal, and a little later by the Braggs, father and son, in England, using the SaIne Inaterial, and providing a more complete analysis of the diffraction pattern.

These experiments, which launched the vast field of x-ray crystallography, at once received great attention, and were rewarded with Nobel Prizes for Laue and for the Braggs.

However, their role in the war between atomism and its opponents is perhaps to be characterized best as a "clean-up" operation - the war had already been won.

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I - 31

Well, this really concludes all I have to say on the history of the war itself.

However, I'd like to add one little postscript that shows how it really took many more decades before scientists were able to feel really at home with atoms.

What I've said so far has come frOln old papers and history books, and now by contrast, I want to share just a few personal remInIscences.

Although, as you've just seen, the atomic picture of solids was universally accepted from about 1910-1915 onwards, and was taught in all the textbooks, scientists didn't yet feel quite as at home with atoms as they did with things they could see and measure directly.

This feeling of awkwardness showed through in the long boring arguments about issues that seemed ahnost ilnpossible to decide experimentally, issues such as the arrangement of atoms and ions when cesium adsorbs on tungsten.

Or for another example, some theorists proposed that a crystal surface might have a different periodicity from that of the underlying bulk - the phenomenon we now call "reconstruction" - but nobody paid much attention.

Lecture I-I

Let me start out with a few words on the "why?" and the "what?" of this lecture series.

To begin with, history in general is a lim thing - at least, it strikes me that way.

It's interesting, and often amusing, to see the problems people of an earlier time wrestled with, the dumb mistakes they made, the fights they got into, and the way they sometinles fOWld very clever ways to forge ahead.

From a more serious point of view, the s tudy of the history of science can give u s a perspective on the interplay of observation and insight, and on how the very fallible hlunans we call scientists m ake progress by interacting with each other, often by argumg.

Maybe b~lmderstanding how this has worked in the past we can be better scientists today.

I must warn you that I have many limitations as a lecturer on the h.is tory of solid-s tate physics.

The field is a huge one, and many of the things I'll try to talk about are things I know only at second hand.

Also, I h ave no qualifications as a professional historian of science.

My m ain virtue is that I'm an old man, so I can remember how things felt in the 1930s when I m ade my decision to switch the focus of my graduate studies Ii·om astrophysics to solid s tate.

Coincidentally, this was about the time when the words "solid s ta te" were first starting to be used to describe a recognized subdivision of physics.

1-2

In the six plus decades since that time, I've listened to, and often known personally, a sizable number, though far from all, of the people who have made the major discoveries in solid­state physics.

So I can describe some typical examples of how scientists can be confused, argue with each other, and finally come to a clear consensus.

The synthesizers and textbook writers have often done such a good job of making everything simple and transparent - just what they should do, of course - that the modern student can fail to realize what the original creative process was like.

Now let me shift gears and say a few words about the problem of organizing the lectures.

You can see the problem I face.

There are just a huge number of different subfields, lines of thought, experimental techniques, and so on.

All of them have been evolving over time, and also influencing each other as they've done so.

One couldn't follow one topic in time without having to follow a lot of others along with it.

For example, if one tried to follow magnetism, one would have to say a lot about thin films, low temperature techniques, Green's functions, Miissbauer effect, slow neutron physics, etc.

On the other hand, it would be both difficult and boring to describe all the different subfields as of 1940, then go through the whole list as of 1950, then the same for 1960, etc.

1-3

So I'm going to compromise.

I'm going to show you a little map, the backbone of which describes in a very general way the types of concepts we have tried to use in building up a rational picture of how solids function.

These types of concepts have guided both the design and interpretation of experiments and the development of theories.

My picture will show, with time increasing downward, how the types of concepts have evolved, the major roadblocks that they have encountered, and how they have changed to get around the roadblocks.

In this first lecture, I'm going to focus just on the earliest and most fundamental of the changes in viewpoint, namely, the gradual recognition that solids are not continuous and infinitely divisible, but are made of atoms.

As I'll describe in a minute, the rise of European science in the 17th to 19th centuries put some quantitative truth into the ancient concept of continuous matter, by developing such concepts as stress, strain, and inertia to describe mechanical behavior, and then adding thermodynamics.

But what could be done with this sort of modeling was very limited.

For all the properties that different kinds of solids possess - color, hardness, density, transparency, electrical conductivity, etc. - and for the temperature dependence of these properties, one had no model that could describe or explain them.

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1-4

They just had to be measured and tabulated, and their study seemed to amount mostly to the sterile recording of tables of data.

Fortunately, as I'll now recount in detail, a number of scientific developments from the late 17th to early 20th centuries gave such spectacular support to the atomic picture of matter that it gradually became universally accepted.

So let me start now with the centuries-old controversy between the atomists, who thought of matter as made up of discrete units, called "atoms", and the group that might be called "continuumists", who contended that matter had to be subdividable into arbitrarily small pieces, whose specific properties would eventually become uniform.

As you probably know, the very word "atom" comes from the Greek, from the negative prefix "a" and the "tom" root, used for example in "tome", a cutting, or "tomos", a section.

So the idea was something that can't be cut, at least not into smaller pieces with the same properties.

The atomistic concept goes back at least to Democritus, in the 5th century B.C., and it was strongly espoused by Epicurus in the Hellenistic period and systematically expounded by the Roman poet-philosopher Lucretius in the first century B.C.

1-5

However, many other philosophers, including Aris totle, s trongly denolU1ced it.

Although the ancient a tomists thought that the motions and shapes of a toms could account mechanistically for all the properties of different kinds of matter, their ideas seem to us just to be arbitrary specula tions, since they didn't relate them to quantitative physical laws.

So you may wonder w hy I bother to men tion them at all.

Well, jus t remember tha t what we call "physics" was called "natural philosophy", even as la te as the 19th centmy.

Wl1en Emope climbed out of the Dark Ages and physics began to grow as a modern physical science, many of the people who tried to formulate laws of physics had a t least studied w1der philosophers, and could read Latin and often Greek.

So they probably were aware of the argwnents of the two schools of thought, and often developed prej udices of their own for the one or the other side.

Let's tmn, then, to a closer look at the progress of the atomistic school since about 1600.

This is a continua tion of the historical panorama I just showed you, taking up the progress of the war after a long hiatus in the Middle Ages.

In this Vu-graph, as in a couple more that I'll show on the his torical panorama, I' ve put the important discoveries in boxes of different colors, the colors referring to different fields of science, w hich are named in boxes of the sanle colors near the top of the picture.

These discovery boxes are so big they can' t be placed very accurately on the vertical time scale, but I've tried to place the names of

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the individual scientists who made the discoveries as close as possible to the proper times.

I'll continue to put orange boxes around the names of opponents of atomism, but to minimize clutter i'll identify the )",t:er c.Ol1t-,,,;b,,-&>,S

of atomistic insights with· boxes colored for melr scientific discipline, rather than the green boxes I used in the earlier centuries for atomists.

I~~~1600'-~~)Jt-~--BOY~ an~' New~n~re attra~tec;J.><to ato\' sm,/ thbpgh escarte\reJe ed It.\( \ \/ \ .

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Boyle, in particular, noticed that\f one i~terpreted g\,s prf\ssur\,as ./ the statistical effect of'{~domly movmg atoms striking'~e

walls of the container,,~en the atomic picture cO,uld a!(co~ nicely for the pressure bcipg inversely proportional' the vdhune, ,'~s h~ had observed. \ \ \, >\' \" \ ,/

~y'tli numb~r ~~ato' / p gin~:\)n \ ar,e~ , . t ime ~~ e proportio I to e nsity \if the eloci is sum:'ed ~ \

\ end 0 ' ~he t ratur~

As we get into the 1700's, we find a lot more in the way of detailed evidence coming to light as a result of observations and experiments.

On this Vu-graph I've divided the new developments into two categories - those arising from the new science of crystallography, represented by the boxes on the left here, and those from other areas of physics and chemistry, listed in the boxes on the right.

I call crystallography a new science because serious natural philosophers seem to have written practically nothing on the science of crystals until almost 1700.

, ~,

1-7

Although the ancients did speculate on possible different shapes for atoms of different materials, it was a long time indeed before the theory of atoms started to be put into a quantitative form and related to a science based on the experimental method.

Newton and Bo Ie, in t e 17th ceIllUI, v eo- '-H )'Wt.e

atomsl\~fOftSil~"'" mc)ticmrJ... 1A/;6(~) to understand the properties of gases. 4YfJ p"~n(?"'e,,a '1 ct,~"''''«1

o.-Ua-c...}"..., ~. Anyone who has taken high school chemistry will remember Boyle's

'_ law, which says that the pressure of a given amount of gas .,<", increases when it is compressed into a smaller volume.

',~', ~, .... ' \ ........

','.' -" " .• '~:;,. ('hi;' 'seem<lU.to 1l0y~ ac~~fhe ~a) ._:- ~~ -:F>-"_;, ~ea~~opu;atiojCien~.¢ tJre-l

"',4-,-.,~--' c· """'""-" -- -- - ----",:,,~~.,~. Now let's take a look at the crystallography side of the picture. ,~

-, As I mentioned earlier, it was about the time of Newton and Boyle -

" ~ \ , ,-; ? "/ -.... ..

the late 1600s - that natural philosophers first began to write about crystals.

I've singled out two names for special mention here, Steno, a Danish theologian, and Guglielmini, an Italian profes.;;or who noted among other things, that the facets of a crystal of a given substance always make the same angles with each other, even when the crystals as wholes look quite different.

Let me interrupt this historical picture for just a minute to show what this means.

These diagrams show several of the hundred or more different shapes in which crystals of calcite - calcium carbonate - can be found.

At first sight these six forms all look quite different.

1- 8

But when each one is properly oriented - and of course the appropriate orientations have been chosen for you by the draftsman - you begin to see some common fea tures.

With this choice of orien tations, you find time and again that facets that occur w ith a certain orientation on one crystal occur with an exactly parallel orientation on some of the o thers.

For example, of the planes with the type label m, the two in Fig. 4 and Fig. 6 that I've cOimected with a green line v,l-i p«(<1 I;. },

Similarly, the tlu-ee of type e in Figs. 2, 4 and 6, cOlU1ected with a purple line, are all parallel.

Rome de !'Isle became tl1e firs t to rea lize that a universal principle was involved.

This principle he called the "Law of constancy of an gle."

Ead1 substance has a small number of special planes on which it likes to cleave or facet, and the angles of these planes w ith each other are always tl1e sam e, from one specimen of the substance to another.

Haiiy now made a brilliant conh'ibution by studying these angles in more de tail.

Suppose we take a p articular substance, like the calcite we've just been looking at.

And suppose we've been able to identify a mm1ber of crystal planes for it, like the ones labeled with the le tters here.

This you' ll recognize as a duplica te of one of the crystal forms I showed on the previous Vu-graph.

The intersection of any two of these planes, say these two m planes, is a line parallel to one of the possible crystal edges.

1-9

Suppose we select three such lines, like the ones I've traced over in orange here that are not all in the same plane, and draw them through a common point, like the corner I've marked with a black dot.

And now suppose we take some other one of the crystal planes, like this e-type plane over here that I've colored purple, and think of it, or a plane parallel to it, since it's only the orientation that matters, just as an unbounded geometrical plane, extending on beyond any crystal boundaries.

Then somewhere this plane will intersect each of the orange lines, unless of course it happens to be parallel to one of the lines.

I've tried to show this on the right, by extending this purple plane, not all the way to infinity, but far enough to reach its intersection points with each of the orange lines.

I've identified these intersection points by hollow purple circles.

The remarkable thing that Hally found was that the distances of the three purplse circles from the black dot always turn out to be related to each other by the ratios of small integers, like 2:1 or 1:3:2, etc.

Of course, if the plane is parallel to one of the lines, it won't intersect that line, and we might say that the distance to this particular intersection point is infinity, which certainly won't fit on the small integer scale.

This is what happens if we choose for our plane, in the present example, the c-type plane that I've colored green.

This plane meets two of the orange lines in the two green points I've shown here.

But the third orange line, this one here, it doesn't meet at all.

I - 10

To take account of cases like this, one can s tate the law just a little differently.

Suppose that instead of tabulating the dis tances of the intersection points from the origin, we tabulate instead the reciprocals of these dis tances.

Then when the line and the plane are parallel, instead of entering the distance infinity, we can enter the reciprocal dis tance as zero.

The ratios of the three numbers characterizing any crystal plan e will then always be ratios of small integers, including zero as a possibility .

This rule is what is called the law of ra tional indices, and I' ve entered it in this box on om history diagram.

Discovery of this law inspired Haiiy to imagine little bricks to be made in the shape of parallelepipeds wi th edges parallel to a suitably chosen set of reference lines like the three black lines I showed you in the last Vu-graph, then all the characteristic crystal planes could be represented either as parallel to one of tlle faces of a brick, or as average slopes of a regular staircase of bricks.

This on the left shows one of his drawings.

Here I've identified a sing le brick by coloring its three exposed faces red , green, and purple.

Now at the bottom you can see a large plane that is just parallel to one of the faces of a single brick - the one I colored red up at the top.

Over on the right here you have a staircase that rises on s tep this way for each brick-length of progress this way.

On a macroscopic scale this represents an inclined plane.

=

I - 11

On the left there's another staircase, rising one brick height this way for every two brick-widths this way.

And so on.

It's not hard to see that each simple staircase of this sort will represent a macroscopic plane whose indices in Haiiy's construction will simply correspond to the step widths and step heights measured in terms of brick dimensions.

The diagrams on the right show how some of the simple diagonal planes commonly found in crystals of cubic symmetry can arise from a stacking of cubes.

The natural inference from models of this sort is that a crystal always consists of a regular array of identical structural units that repeats itself identically if translated by anyone of three non-coplanar vectors ti, t2, and t3·

In modern language, it has the symmetry of a translation group.

This principle, with one modification that I'll discuss in a later lecture, has been fundamental to crystal physics ever since.

The elementary structural units are of course not bricks, but groups of atoms.

--------'----This fact came to be realized within a few decades of Haiiy's work,

thanks to the work of the French chemist Proust and the English chemist Dalton.

Proust, making improvements on the then-known techniques for quantitative analysis and synthesiS, settled the controversy over whether the elements combining to form a given compound always combined in the same ratio of weights.

He found in 1799 that indeed they do, and thus proclaimed what is called the "law of definite proportions."

.~-.

','. ,

VG(P

[ - 12

This work was soon ex tended in a very important way by Dalton.

Wearing the hat of a theoretical physicist, Dalton had been s tud ying gases, especially gaseous mixtures, and had been impressed by the utility of the atomic picture for the w1derstanding of gases.

So he had the atomic picture in mind when he s tarted thinking about how to understand the law of definite proportions in chemistry.

By this tin1e there had been trustworthy measmements on enough different compOLmds so that in a munber of cases, one could compare the relative weights of two elements in more than one compound of these sam e elem ents (for example, wh at we now call carbon m onoxide and carbon dioxide).

He found that the ratios of elem ent weights in two different compounds were always proportional to two sm all integers.

This delighted hin1, as he was already a convinced atomist, and the discovery was just wha t one would expec t if each compound was made up of identical molecules, with each molecule consisting of a definite number of each of the two kinds of atom s.

So, in a book published in 1808, he proclaimed his "law of multiple proportions", w hich laid the fow1dation for modern chemistry.

The essence of this law is stated here.

Note that if one interprets this law a tomistically, a ra tio of weights for a particular compound, like the nwnerator or the denominator here, depends on two types of quantities.

1-13

Namely, it depends on the number of A atoms and B atoms in a molecule of the compound, and on the masses of the two types of atoms.

But when we form this ratio of ratios here, the masses of A and B cancel out, and we are left with a ratio depending only on what we would today call the chemical formulas of Cl and C2.

The law gives us a constraint on the possible subscripts (as we would now call them) in the two formulas, but still doesn't fully determine the formulas, even when one has several pairs to work with.

Fortunately, there is another law, discovered by the French chemist Gay-Lussac at about the same time, that can give information on a single compound, though it was applicable to only a small fraction of the compounds that could be studied at that time.

Gay-Lussac, who was really as much a physicist as a chemist, had a special interest in gases, and had been studying the reactions of gaseous elements to form (usually) gaseous compounds.

He found that when the amounts of the different elements, and of the product if that was gaseous too, were measured in terms of their volumes at some standard temperature and pressure, the ratios of these volumes would always be ratios of small integers.

Unlike Dalton's law here, which involves two compounds together, this law tells us something about a single compound at a time.

However, to scientists of that time, even atomists, this may not have seemed very helpful in revealing the relative numbers of A and B atoms in a molecule of C.

1-14

For just as a Dalton ratio of combining weights involved the masses of the A and B atoms as well as their relative numbers, so Gay-Lussac's ratio of combining volumes involved these numbers and also the (unknown) ratio of volumes per atom for AandB.

A crucial step making possible simple molecular interpretation was, however, given in a few years by the Italian physicist Avogadro.

His reasoning must have been something like this:

Dalton's simple rational ratios follow from the mere fact that a molecule of a compound contains an integral number of atoms of each kind.

Gay-Lussac's rational ratios would require, in addition, some simple rational ratios for the volumes per molecule of different gases.

But wouldn't it be simpler and more plausible, Avogadro must have thought, to just say that the idea of atoms in molecules is the only source of simple rational ratios, and not have to invent a mechanism to make volume per atom, or per molecule, vary from case to case as a ratio of integers?

So he proposed this law: volume per molecule at given T,p, is the same for molecules of all kinds.

Today we regard this as a trivial consequence of the principle of equipartition of kinetic energy in statistical mechanics.

But this principle wasn't derived until the work of Boltzmann and Maxwell around 1860.

1- 15

So for the first half of the century Avogadro's law continued to be disputed, though it was often invoked by its suppor~~sas a tool to help in determining formulas of compounds a"nd the relative masses of atoms of different elements.

Playing with these concepts, the atomists of this half-century had a great time.

But even these concepts were unsatisfying in one respect.

What are called "atomic weights" are of course only relative weights of different kinds of atoms.

The absolute weights of atoms, like their sizes, were completely unknown in the early 19th century.

All the things I've mentioned so far as supporting the idea of atoms -gas compression, formation of compounds out of elements, structure of crystals - will work as well at one size scale as another.

If philosopher A were to think of atoms as having some specific size, philosopher B could argue that the atoms could just as well be a thousand times smaller, or a million or a trillion, or anything.

So maybe they don't have any size at all, but are just a fictitious construct.

·/G(/ .. Tf.,i $. 5how!S fh.e dc'/f.'mma.l lYl We> Y'd 5· . __ ; Returrung to the histoncal panorama, we fmd ourselves at the

bottom of this Vu-graph, having seen a lot of progress, but still in an unsatisfactory situation, with the atomists hopeful but no content, and the doubters still unconvinced.

So let's scroll the picture to the full 19th century. "'i\1o • ""aBins "IE I' u~,at-ta.~ t i!f' •

1-16

Fortunately, the great proliferation of experimen tal and theoretical physics in the 19th centmy eventually gave clues to the sizes of atoms, though not everyone accepted the evidence a t firs t. -_. --- ---- --- - -----

Some of the strongest pieces of evidence came from experimental and theore tical studies of some of the p roperties of gases.

You'll remember I m entioned that Boy le and New ton had been a ttracted by the idea that the pressure of a gas could be interpreted as the average force exerted on the walls of the container by moving atoms striking them and being refl ec ted .

Well now, w ith the growth of interest in atoms and the sophisticated mathematical development of the science of m echanics based on Newton's laws of m otion, peop le began tryin g to explain not only pressure but all sorts of other properties of gases in terms of the sta tistical properties of atoms or molecules moving around randomly tlu·ough mostly empty space, but occasionally blunping into one another.

This new science, called the kinetic theory of gases, tried to explain phenomena like diffusion and viscosity.

v c,. ~ Diffusion is perhaps the easiest to explain.

Suppose we have a longish container, like this, filled w ith a particular kind of gas, say nitrogen, w hose molecules I've represented as green do ts.

And now suppose that at some instan t of tinle we ad d a little bit of some other gas, say bromine, in the middle.

Since bromine is reddish brown, I've chosen to represent its molecules as red dots.

-.. '0' ~.,. ... ~".

1-17

If we've been able to do this without any stirring, tha t is, without making any macroscopic winds, the only thing that will cause the gases to intermingle will be the random motions of the individual molecules, the motions that U,e atomists believed represented heat energy.

This will cause the bromine molecules to gradually spread out over a w ider and wider range, as I've shown here.

We can follow this spreading out just by noting the widU, of the region with brownish color, or alternatively by some other more sophisticated technique of measuring the distribution of the second gas.

At U,e risk of boring an y of you that have studied kinetic theory, I'd like to take a few minutes to show how one can get an estimate of the size of the molecu les by measuring the mean square dis tance u'e one gas spreads into U,e other, and using a couple of o ther m easurements tha t are even easier to make.

Suppose for sin1plicity that gas A is present in dilute concentra tion in gas B, and consider the motion of a particular molecule of A.

This motion will appear as I've shown here, with a l1LuIl ber of rectilinear stretches in random directions and w hose lengths vary randomly about a mean free path "A".

In a macroscopic time t U,ere will be on the average v t/ Asuch stretches, w here v is an average veloci ty.

Because the motion is randomized after each collision, the mean square displacement in say the x-direc tion in time t will be of the order of A2 times the mmlber of stretches.

I write this as Wx = a coefficient G of order wuty time A2 times the average v t/A.

A more careful calculation gives G = 2/3, as I've written here.

The m acroscopic diffusion equation gives for this same wx2 the value 20t, w here 0 is the diffusion coefficient.

Thus the product VA must equal three times the measured O.

1-18

By about 1873, when Maxwell published his definitive version of kinetic theory, this and other similar analyses had been worked out for this and several other properties of gases.

In particular it turns out that the viscosity '1 of a gas and its thermal conductivity K, are also related to VA by these last two equalities here, where Pg is the mass density of the gas and Cv is its specific heat at constant volume.

To keep m y promise I now have to show you how the v A one can obtain in this way can be used to get the molecular sizes.

But before I embark on this I should remark that these last equations here already gave a trililllph for kinetic theory, and therefore for atomism, because they relate the independently measurable quantities, self-diffusion coefficients, viscosity, and thermal conductivity, to each o ther.

And indeed, these relations were actually observed to be pretty much true for simple gases, to within a modest percentage, though the temperature variations suggested that the rigid sphere model was a Ii ttle too crude.

Considering that the relations were derived from an obviously crude model, they must have seemed like quite a triwnph for molecular theory.

But let me get back to the matter of relating this VA to molecular SIzes.

1-19

As early as 1843 Joule had pointed out that the pressure and density of a gas should yield the molecular velocity.

In the molecular model of a gas, the pressure p should be the net force exerted on unit area of the container wall by many molecules striking against it and being reflected.

So it's roughly the number of impacts per unit area per unit time, times twice the average momentum normal to the surface.

The first factor is the normal velocity v 1- times the number n of molecules per unit volume, while the second is twice the molecular mass times v 1-.

So we have nmv 1- , or since the perpendicular direction is just one of three equivalent directions, we can write this as 1/3 mv2 , where the v2 is obviously a mean square velocity.

Since the density Pg of the gas is just nm, we have finally just mean

v2 =3p / Pg

There's a trivial factor, nearly unity, to convert the root mean square velocity into the average velocity I used in the preceding transparency - it's not really important for my present discussion of orders of magnitude.

So it's trivial to combine the v information we get here with the VA we just get from transport data to get the mean free path A.

Now let's look at what determines A.

Consider an atom of diameter d moving in some arbitrary direction through a gas of the same kind of atoms.

1-20

It will have a collision as soon as it finds another atom whose center is inside the cylinder of diameter 2d centered on the path of the moving atom.

Since the atomic positions before the collision are essentially uncorrelated, this will happen on the average when the volume of the cylinder swept out is just equal to the volume lin per atom in the gas.

If A is much larger than d, the length of this cylinder is essentially the A we are interested in, so we have rrd2An = 1.

We still have two unknowns, d and n, but there is a trivial relation between them if one is willing to assume, as some of the early atomists were, that when we condense the gas into a solid, the molecules remain essentially unchanged, but are packed together as spheres in contact.

For a close packing of spheres, the volume per sphere of diameter d is (23/2/ 3)d3, so if m is the molecular mass, the density Ps of the solid is 3m/2 3/2 d3.

Since the density Pg of the gas is TIm, we can eliminate m and write

nd3 = (2 ~2 I 3) Pg/Ps.

So the complete line of reasoning is: gaseous transport gives vA, Joule's relation gives v, these give A which gives d2n, gas-solid density ratio gives d3n, hence we get d and n.

It·s interesting to compare these crude gas-kinetic estimates of molecular sizes with present-day knowledge.

1- 2l

I still have, at home, an 11th Edition Encyclopedia Brittannica, published in 1910, which my parents bought for me when I was in school in the 1920's.

The articles in it on atoms, molecules, etc. were all written before the possibility of accurate measurements by x-ray diffraction had been discovered.

But the authors were all convinced atomists, and in one of the articles I found a table of the molecular diameters of a number of common gases, as derived from kinetic theory.

Though the author recognized that the hard-sphere model was rather crude, the table was presented with some confidence as a table of "average diameters."

For hydrogen, for example, it gave a diameter of 2.03 Angstroms, somewhat less than the spacing of 3.75 Angstroms now accepted as the nearest neighbor distance in solid hydrogen, but at least in the right ball park.

I'm tempted to guess at the reason for the discrepancy, though I can't be sure since the detailed reasoning behind the figures in the Brittannica table weren't given.

My guess is that since the true intermolecular potential has a long­range attractive part and a short-range repulsive part, like this ----, the spacing in the solid is close to the minimum of this curve, here, while in the gas large-angle scatterings are most often caused by the long range force, at a larger distance.

Introduction of about a 35% difference between the effective diameters d in these two equations would cause the calculation I've sketched here to yield a diameter, in the solid, about 1.8 times as great as the simple calculation assuming both d's the same. -- ---

1-22

Actually, the idea of intermolecular potential curves like this one I've drawn here came into prominence at about the tinl e the kine tic theory of gases ma tured.

In 1873 the Dutch physicist van der Waals proposed that the slight departures of the equation of s tate of real gases from the ideal gas law could be roughly accolmted for by force laws of this type.

To approximate their effect, he wrote down his famous equation of s ta te, which I'm sure you've all seen.

This expresses the relation of the pressm e p to the volume V of one m ole of material, at any temperature T.

R is this usual gas constant, and the two new consta nts introduced by van der Waals are this a and this b, independent of volwne and temperature and characteris tic of the type of m olecule making up the gas.

The rationale, you 'll rem ember, is that p + a/v2 is supposed to approxima te that part of the pressure tha t is due to the transla tory motion of the molecules.

This is less than the total pressure p when the molecules are most! y well sepa rated from each other, because just by virtue of thei.r positions they a ttract their near neighbors and thus create a negative term in the pressure.

Being due to two-body forces, this term is proportional to the square of the concentration of molecules, hence the a/v2

And subtracting a negative pressure gives p plus a/v2.

1-23

In the second factor here, the rationale is to use the volume that is available for a molecule to move around in, which is essentially the total volume v minus the volume the molecules would occupy if they were a dose-packed solid.

This equation turned out to be fairly successful in accounting for the departures shown by actual gases from the idea gas law.

And the values of b fitted to equations of state were roughly consistent with the rigid-sphere sizes inferred from the kinetic-theory argument I've just discussed.

So here was another piece of evidence favorable to the atomistic picture.

But van der Waals made an even more important further step.

He pointed out that an equation of state of this sort could account semi-quantitatively for both the gaseous and the liquid phases.

Consider the shape of the plot of p against v, at any fixed temperature.

It's easy to see that the equation determines a single value of p for any assumed v greater than b.

But if you try to take p as the independent variable, you get a cubic equation for v, which has three roots.

Of course, depending on the parameters, these may either be all real, or one may be real and the other two complex, and conjugate to each other.

It's not hard to show that for different temperatures on gets a family of p-V curves like that shown in this figure.

1-24

At high temperatures, the curves look almost like the hyperbolas pV= constant, which is Boyle's law.

As the temperature is decreased, the curves at first continue to descend monotonically but get less steep in the middle.

At still lower temperatures, the curves are no longer monotonous, but have a real hill in the middle.

This is physically impossible for a stable state of a homogeneous real system, because the part of the curve where pressure increases with volume represents a system of negative compressibility.

If such a system existed, on can easily show, by a simple Gedanken experiment, that one could extract work from the system without changing its total volume or temperature, hence necessarily lowering its free energy and converting the starting state into a more stable state.

Specifically, the Gedanken experiment could consist of dividing the system into two equal halves, expanding the first by a given amount, and compressing the second by the same amount, so as to leave the sum of the two volumes unchanged.

Since the average pressure in the expanded half would be greater than that in the compressed half, because of the positive slope of the p-V curve, a net work would be done by the system on the controlling pistons.

So I color the rising portion of any curve red to brand it as unstable.

And therefore the van der Waals equation implies that at any temperature below the critical temperature at which the down-up-down shape first appears, imposition of any pressure below the critical pressure will allow the system to be stable and homogeneous at two and only two different volumes, here and here, the left-hand one corresponding to the liquid phase, the right-hand one to the gaseous.

1-25

For these insights and for his related work on the so-called "principle of corresponding states" van der Waals was awarded the Nobel Prize in Physics in 1910.

One very simple experiment that was already tried near the start of the century was the study of things like surface tension.

Thomas Young, an English scientist distinguished in such diverse fields as physics, medicine and archaeology, concluded in 1805 from studies of capilllary phenomena that the range of intermolecular forces was somewhere between about 1/4 Angstrom and about a tenth this.

For its time this was a fair estimate, though I don't know why it came out so small.

The conclusion didn't seem to have very much influence on the conversion of scientists to atomism, though, and it wasn't until late in the century that improved versions of the experiment were carried out.

Notable was an experiment by Lord Rayleigh in 1890.

He found that a sensitive indicator of inhomogeneity in the surface tension of water covered by a thin olive oil film was provided by the behavior of a tiny lump of camphor placed on the surface.

If there is no oil on the surface, the camphor dissolves in the water and forms a surface film with altered surface tension.

1-26

Since this dissolution normally occurs more rapidly on one side of the camphor than on the other, the camphor is pulled away from this side by the anisotropy of the surface tension forces, and skitters about.

If there is a full monolayer or more of olive oil on the water, the dissolution is blocked, and the camphor remains at rest.

Rayleigh found the former behavior for an oil film of about 8 Angstroms average thickness, and the latter behavior for films 10 Angstroms thick.

Thus this experiment suggests a molecular diameter of the order of 9 Angstroms, which sounds to us to be about the right order of magnitude for a middle-sized organic molecule like the several compounds that make up olive oil.

-- ---- - - - -'-~----

.~l!1ar1y D@ta~le-Jttere the physicist Ernst Mach, a widel"y-----, ;, ./.. ~=:-i respected thinker and authority on the foundations and " c., '.~!.. . . history of physics, and Wilhelm Ostwald, the distinguished !

,. -,,/_.~ I chemist who was later to receive the 1909 Nobel Prize in ' .'~ 'Chemistry. I

------~.

)

1-27

----- .. ----' -- --- -

~ -rhz? 'ill@ n~geitQr ef some sf thei" OQl'" clis=ovuMt; was the field of gas -- 'discharge physics, which had begun about the middle of the

1800s when Geissler perfected the technique of making partially evacuated glass tubes with electrodes in them.

A lot of people studied the gaseous fluorescence produced by applying voltages to electrodes in such tubes, and the fluorescence of the glass walls that became especially noticeable at low gas pressures.

In the 1870's, special attention focused on the observation that much of this fluorescence seemed to be produced by something coming from the cathode.

This "something" was called "cathode rays" by Goldstein in 1876, who thought of it as some sort of wave in the ether.

It was soon found that cathode rays tended to travel in straight lines, and could cast shadows.

However, they were deflectable by electric and magnetic fields, so some scientists, especially the British ones, pictured them as streams of charged corpuscles.

The crucial experiments were finally done in 1897 by J.J. Thomson, who measured the deflections in electric and magnetic fields quantitatively, and from these extracted the velocity and the charge-to-mass ratio elm of the presumed corpuscles.

And he was able, within a few years, to create his "electrons" by shining light on a metal surface, make gaseous ions with them, and measure their charge, which turned out roughly as he had expected.

1-28

This last he did by counting the ions using the cloud-chamber techniques that had just been developed by his student C.T.R. Wilson.

Now it happened that some years before this, the electrochemists had measured the mass of a given metal (say, copper) deposited by passing a given amount of electric charge through an electroplating bath.

And they had found that for all monovalent metals the mass-to­charge ratio was proportional to the atomic weight.

To an atomist, who would be a believer in Avogadro's law, this meant that a positive ion of a monovalent metal always carried the same electric charge.

Indeed, the magnitude of this charge had been roughly determined from Avogadro's number by the Irish eleclrochemist Stoney in 1874, and he coined the word "electron" for it in 1891.

So it was natural for Thomson to appropriate this name for the cathode-ray particle he had discovered.

He called special attention to the fact that his new particle, while presumably having the same charge e as a monovalent ion, had an enormously larger elm, hence a mass vastly smaller than that of an ion or atom

Though further experiments were obviously needed, and in due time were of course performed, it was starting to become clear that there was such a thing as a basic atom of negative charge and that, quite possibly, charge of all kinds was quantized. ---- ---- ---

_ A~ very early consequence".h"" .. '." .... of the flurry of research on cathode rays was the accidental discovery, made by Roentgen in 1895, of the x-radiation that was emitted from the walls of the tube as a result of their bombardment by the cathode rays.

/

1-29

It's a familiar story how he found them to penetrate matter opaque to ordinary light, to be uncharged, and to be generated near the point of impact of the cathode rays on some solid body.

X-rays of course soon attracted a great deal of attention in the research community.

It was found within a few years that they could ionize the molecules of a gas and release negative charges, presumably electrons, from the surfaces of solids.

- - - -. -- ----Here a happy confluence of two developments occurred, namely of

x-ray physics with quantum theory.

As you know, quantum theory had its origin in the attempt by Max Planck to find a rational explanation for the frequency distribution of light in black-body radiation.

He succeeded in deriving a formula that gave a beautiful agreement with observation by making what seemed at first to be a very puzzling hypothesis.

In its original form this was the hypothesis: that a material harmonic oscillator can have only certain specific energies, namely those that are an integral multiple of a certain constant called h times the frequency of the oscillator.

Various interpretations of this and various attempts to reformulate it were made in the succeeding decade, and even for longer.

One of these was due to Einstein, who pointed out in 1905 that if one made the assumption that light of any particular frequency v could exist only in quanta of energy hv , then one could explain certain newly discovered facts about the emission of electrons from illuminated metal surfaces.

1-30

His proposal was, of course, the famous Einstein photoelectric equation, which after many years of doubt and rejection was finally found to be in very accurate accord with careful experiments, and for which Einstein received the 1921 Nobel Prize.

Within a few years energies of photoelectrons produced by x-rays were interpreted using Einstein's formula to imply that the wave length of the x-rays must be of the order of Angstroms.

---Then in 1912, von Laue, having become aware of this fact, pointed

out that the regular arrangement of atoms in a crystal should enable the crystal to act as a 3-dimensional diffraction grating, and diffract a collimated x-ray beam and thereby yield information on the ratio of the x-ray wavelength to the lattice spacing in the crystal.

An experiment was soon performed by Friedrich and Knipping in Germany, using a zincblende crystal, and a little later by the Braggs, father and son, in England, using the same material, and providing a more complete analysis of the diffraction pattern.

These experiments, which launched the vast field of x-ray crystallography, at once received great attention, and were rewarded with Nobel Prizes for Laue and for the Braggs.

However, their role in the war between atomism and its opponents is perhaps to be characterized best as a "clean-up" operation - the war had already been won.

•

LIC+U.{IL \ (0'),\ II y\ll"-cl

1-31

Well, this really concludes all I have to say on the history of the war itself.

However, I'd like to add one little postscript that shows how it really took many more decades before scientists were able to feel really at home with atoms.

What I've said so far has come from old papers and history books, and now by contrast, I want to share just a few personal rerruruscences.

Although, as you've just seen, the atomic picture of solids was universally accepted from about 1910-1915 onwards, and was taught in all the textbooks, scientists didn't yet feel quite as at home with atoms as they did with things they could see and measure directly.

This feeling of awkwardness showed through in the long boring arguments about issues that seemed almost impossible to decide experimentally, issues such as the arrangement of atoms and ions when cesium adsorbs on tungsten.

Or for another example, some theorists proposed that a crystal surface might have a different periodicity from that of the underlying bulk - the phenomenon we now call "reconstruction" - but nobody paid much attention.

A t the time I want to focus on, the middle 1950's, electron microscopy, though a wonderful advance over optical microscopy, still didn't have nearly enough resolution to dis tinguish indi vidual a toms.

II-32

The first breakthrough finally came via field ion microscopy, a teclmique developed by the late Erwin Mueller, working firs t in Germany and then a t Pelm State.

The basic idea, whicll I'm sure many of you are familiar with, is shown here.

One prepa res a sharp point of some metal, like hmgsten, that's easily cleaned of adsorbed contaminants by hea ting it.

The tip is macroscopically smoothly rounded, w ith a radius of curvature of the order of a few hundred An gstroms, and is mOLmted at the center of a spherical glass container wi th a luminescent screen on its ilmer surface.

When a high p ositive voltage is applied to the tip, the fjeld on a macroscopic scale will of course be greater at the end than down on the shank, because of the greater curvature.

For the same reason, the field will be greater a t the edges of a tom layers - here for example - than in the middle of close-packed flat regions - such as here.

Indeed, it will even be greater over the centers of atoms than over the hollows between atoms.

I' ve tried to show these field fluctuations roughly by the lengths of these little red lines.

Now if the tube contains only a very low pressure of a light gas, say helium, the neutral gas atoms will approach the metal surface at random, but if the positive voltage on the tip is large enough, the gas a toms will suffer field ioniz ation as they approach the very high-field regions of the tip.

Il-33

In other words, an electron will tunnel from the atom to the m etal.

The slow-moving a tom will become a positive ion, and be accelerated rapidly away from the tip.

Since most of the voltage drop occurs very close to the point, the orbit of the ion will be almost perpendicUlar to the local m ean surface - the green curve here, and the points of impingement of the ions on the fluorescent screen will give a reasonably true map of their points of origin just outside the metal surface.

Professor Mueller presented some early results in an invited lecture at the Annual Meeting of the American Physical Society, on Jan. 31, 1956.

I was there.

The talk was in a large auditorium adjacent to the Hotel New Yorker on 34th Street, and the room was packed.

After explaining his teclmique, Mueller showed a slide of a photograph he had taken of his lluninescent screen when he was draw ing ions away frol11 a tungsten point.

To maximize your feeling of identification with the 1956 audience, I'd like to be able to show you an exact copy of the slide Mueller showed then.

UnfortLmately, my efforts to locate this slide have failed.

However, I do have a very similar picture taken in the same laboratory only a few years later by Tien Tsong, Mueller's student and successor as director of the laboratory.

I am grateful to Dr. Tsong, who now is Director of the h,stitute of Physics of the Academia Sinica in Taipei, for sending it to me.

vr; ) (, Here it is.

Well when the physicists saw that, they just went wild.

They clapped and clapped and clapped, and finally gave him a standing ovation.

1-34

While the people in the room had not had any doubts about the existence of atoms, they would have had to admit that their faith was based on indirect reasoning, based on such things as the theory of x-ray diffraction, chemical valence, collisions in gases, et.

Now they could feel their faith vindicated, and could just say "seeing is believing."

The details of the picture make very good sense.

In the regions that are not in or near a low-index facet, you can see every atom.

The low-index facets remain dark simply because they are atomically flat, and the electric field over them is much smaller than over the curved regions.

For example, the central facet here is the (110), which is the most closely packed plane for a body-centered cubic crystal.

The (100) type facets, here and here, are also quite flat, and hence dark.

And so on.

But these are stories for another lecture.

1 just wanted you to feel the sense of triumph at the ability to see atomic arrangements.

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•

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for calculating an E~ from the data of Ref. 5; the above sketch has for brevity made several

oversimplifications.) The diffusional analysis used in the earlier paper· of Myers et al. was

more complicated, since it used among its fitting parameters the characteristics of atomic­

scale traps for hydrogen that appeared to be present in the silicon crystal, and since it

needed to rely on the data of Ref. 5. However, this work, also, made the error of assuming

E9 - EA S - s·

In the preceding paragraphs we have stressed the fact that Ref. 4 assumed the high­

temperature solid-solution hydrogen to be the neutral species HO. However, it is now known

that the donor level of monatomic hydrogen in silicon is of the order of 0.2 eV below the

conduction band12 and that the acceptor level is almost exactly at midgap,t3 so that under

intrinsic conditions practically all the hydrogen will be H+. However, the change from

an HO picture to an H+ picture will not affect the values of EB obtained by the type of

reasoning used in Ref. 4 and discussed in the preceding paragraphs. For Eq. (1) of Ref. 4

remains correct if Es is interpreted as the E~(O) relevant to transfer of an HO between crystal

and molecule, and C as the dissolved concentration C(O) of HO. But C(O) exp(E~(O) / kT) =

C(+) exp(E1+) /kT), where E1+) and C(+) refer to the H+ species, with the charge change

produced by electron exchange with a reservoir at the Fermi level. And of course, our

Eqs. (1)-(5) need no reference at all to the dissolved H species. The analysis of diffusion

used in Refs. 2 and 3 is similarly immune to the difference between the HO and H+ models.

In summary, we have derived a value for the binding energy of Si-H bonds on the Si

surface, based on the experimental data of Ref. 4. We have identified an error in the

analysis of Ref. 4, and presented a simpler but correct thermodynamic formalism. The

obtained result for EB can be considered the most reliable value currently available.

We acknowledge useful discussions with D. Biegelsen and J. E. Northrup. This work is

supported in part by NREL and by AFOSR.

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FIGURE CAPTIONS

Typical profile of the distribution no(x) of mobile HO (a convenient measure

for the density of all monatomic hydrogen, if H+ and/or H- are

equilibrated with Ho) at an arbitrary time during an experiment on a slab­

shaped crystal specimen. The surface boundary conditions at the entrance

and exit surfaces are defined by the diffusion offset lengths dent. and dex.'

respecti vely.

Illustration of the surface peak, probably formed during quenching, in the

depth distribution of total deuterium introduced by heating silicon

samples in the downstream gases from a plasma discharge (Johnson 1dd'~P.~ t:.: ~9871). Upper curve: results of SIMS measurements on a sample doped

with 2 X 1018 Sb atoms per cm3, deuterated 2 hrs at 400°C. Lower curve:

same for an identical sample deuterated 2 hrs. at 500°C. Quenching was I

with piped water.

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If elements A, B can make compounds C1 01

C2 with weights

wA(l) + wB(l) > WCI

W A(2) + wB(2) > WC2,

then oW A (l)/wB (1) W A (2)/WB (2)

is a ratio of small integers.

Gay-Lussac 1808: Empirical Rule:

If A and B are gases that combine to form compound D, the combining volumes obey iV A/VB = ratio of small integers

:Avogadro 1811: Atomist's Intuition:

At any given T, p, the number of molecules per unit volume is the same for all gases.

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EARLY QUESTION

Can one assign specific sizes to atoms?

If "yes", then what

are these sizes?

If "no", then what is the meaning

of the atomic picture?

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~ ~ . ,," • • -..... . . ... " ... ....... .. ..... ,. ... .... .... " .... .. ... ' •• • .: ... ' .. . ...... .. .. ... . .. -.. " .," .. -. ::: .. ..... \ .. ,. ,,"" .. ...... .. .. :,," .:: .. "' ."" ...... " "" ...... .. .... . .' " .. " .. .. "", ". ." · . .. .. ,,".: -:

".. .. .. ' . ':. ....... . · .. " .. .. " .. ,,",,: " .. " -... .. " .. .... .. .. " .. ...... "

..: .. "

:x o -

JL = [f}~(Ea - TSa)] T,N,

(1 - 0) = -Es + Evib - TSvib - kTln -0- . (1)

relative to the isolated-atom ground state. This JLH must be the same as that of the gas

phase

__ ED Hg - TSg kT In p JLH - 2 + 2NA + 2 1 atm (2)

where the first term is half the dissociation energy ED of the H2 molecule, NA is Avogadro's

number, H9 , S9 are respectively the enthalpy and entropy of hydrogen gas at the experi­

mental temperature and one atmosphere pressure, and p is the experimental gas pressure.

Equating (2) to (1) gives for the pressure dependence of the coverage ()

1 o = c(p/l atm)2" 1

1 + c(p/l atm)2" (3)

where

_ [Es - Evib + TSvib - ED/2 + (Hg - TSg )/2NA)] c - exp kT . (4)

Figure 2 of Ref. 4 compares the observed O(p) values with plots of Eq. (3) for three values

of c. The central plot, which gives the best fit to the data, corresponds to c = 5.28 at

800oe, so that, with ED = -4.556 eV, (H9 - TS9)/2NA = -0.85 eV for deuterium at this

temperature,8 one gets

Es - Evib + TSvib = 3.29 eVe (5)

The result (5) is a fairly clean and unambiguous conclusion if one accepts the measure­

ments of Ref. 4 and the approximate validity of a model with chemisorption on a single type

of neutral non-interacting sites. To compare with the ab initio calculations of Ref. 6, we

must make some guesses about adsorbate vibrations, which affect the ground-state energy

EB via their zero-point energy and also determine the last two terms on the left of (5).

Now Ref. 2 reported a set of infrared absorption peaks associated with deuterium on cavity

5

Motion of Green Molecule:

, .

In time t avg. no. of stretches = vt -

random in direction, so <Wx2 ) = mean sq. displacement in x direction

Must

= G A2 V t = 2 A v t A 3

= 2 Dt, so

vA = 3D

(Also = 3 n p

- 3 K )

pC v

(Summarized Maxwell 1873)

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• •

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.'.. . r

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lringia; it w,as ngt un~ ~P9ut ; present sense .. ~ f ; T~e ~neJ;a.I o.er the names calcareous soar

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Crystals of calcite are extremely'varied,in form; but,:8$ ~:ru.!~;~ , they may be referred to:·f()ur;distinct-h~bits;inamely:·rho:Ql,Qo~ . hedral, prismatic, scalenohedral,o and, tabular'~ :. ~!The .p$itive, rhombohedron,i" {-IOO}. (fig.: I); is comparative1yd~ilre e~cept':in combination with other formsl.[ ~:.Afiatter.rhombohedJQni.d (IIQ}I,: is shown·.in·· fig.: 2, and :~ i.more·"acute'; ·on.e,cf, .. Jl~I.}; dn-; ~g~ ;3.~ '1;hesethree rhombohedra are related· in such a ·manner ~h~t,: 'whep: in"combinatioll; the faceS of. ,,:truncate the polar; 'edges:' of.j,j and the faces of e .trunc~te:the'edges·of. .. ,"~,.}.rhe'crystatof.pri~mB:t~c habit shown'~in fig. 4, is ,a ·combination.of..theprism .m:·:t2~},an~ 'the rhombohedron e' {lIe}; fig;:5 is a:c9mbination;of the sGa1eno~ hedron ·v..{:2oi}~ :~d.;the rhombohedron.·"·{.IOOL; 'antl:,thed:;rystal .. of ·tabularhabitr represetlte~k:in fig.;: :~,.is ·a.::cQmbinatiQnJ9f:,~e, basal .. ,piIiacoid·(; JIIli:;c:pruun .. m t2lIJfiandrhombqhed.r~fl~ {I'IOh: i'~;In,these ~es OJllY~' ~tip.ct fO!1D~ (r,; ~;:.f:, .. m.,:f);ft;} l~~~

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IV

Joule 1843

p = impacts (2 x ~ momentum) area x time

= «(nv ~) (2 mv ~» = nm (v2)

2 3

nm = Pgas , so(v2 )= 3p

P as

Combining with v 'A gives 'A.

If 'A »d, l nd2'An ~ 1 --7 d 2n 1 In close-packed solid

volume per sphere = 23/2 d 3

3

P solid = 3m 23/2 d3

2V2: .J2-gas- = d3n

3 P solid

t:~8r gluol

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ch ~\c~ = 919rlqa 19q 9fHuIov C

me = hiloa Q

nCh = -a£~Q... n~ biloe Q C

CHARGE TO THE HEPL VISITING COMMITIEE

The COmmittee will report to the Vice Provost and Dean Robert L. Byer. and is charged to:

I. Evaluate the current and planned research programs in the Laboratory.

1. Are they of the international status appropnate to a major university such as Stanford?

2. What role should current research programs (in space science. astrophysics, condensed matter physics, biophysics, FEL) play in the evolution of HEPL? Are these appropriate research directions for Stanford in the long tenn? Are the scale and long-term commitments of some of the major programs in HEPL appropnate for (a) the university. and (b) the laboratory?

3. What is the educational value -of the programs? How well are the needs of the students met?

4. Offer suggestions. as appropnate. for deepening or broadening the research base of HEPL.

5. Evaluate the current plan for developing and utilizing space and other resources. Advise on the implementation of this program.

II. Assess. in consultation with the chairpersons of Physics, Applied Physics and Aeronautics-Astronautics HEPL's support of the research and teaching in those Departments.

III. Provide recommendations for any ~ctions which would enhance the effectiveness of the Laboratory.

1 ,

van der Waals 1873: For One Mole

~(P +a/v2)· (v-b)\ RT

kinetic pressure available volume = p - (static = v - (volume of

p

pressure) hard spheres)

One p for each V , but three v's (maybe not all real) for each p

v

Curves for various T

:E Sf ~I£6 W 19b fI£V

9IoM 9nO 10l

TJI ('(<i-V). (~V\s+ q)~

9muIov 9Id£Ii£v£ 91uaa91q )if9nbI to 9muIov) - v = )if£ta) - q = {a919.r1qa bl£.rI hnuaa91q

a'v 991.r1t tud ,v n)£9 lot q 9ftO q r1)£9 lOt (1£91 11£ tOft 9d'{£ro)

lot a9V1UJ T aJJOil£V

'. \ ... ........ ,

1 r··.. •• \ ~~ ij ~ .

:::::..---- • " ' 0- - • \

12 B. Bech Nielsen, K. Bonde Nielsen, and J. R. Byberg, Mater. Sci. Forum 143-147, 909

(1994).

13 N. M. Johnson, C. Herring, and C. G. Van de Walle, Phys. Rev. Lett. 73, 130 (1994).

10

· •.•.. ~. ~

E. MACH: "THE SCIENCE OF MECHANICS"

"Thus, chemical, electrical, and optical phenomena are explained by atoms. But the mental artifice atom was not formed by the principle of continuity; on the contrary, it is a product especially devised for the purpose in view , A toms cannot be perceived by the senses; like all substances, they are things of thought. Furthermore, the atoms are invested with properties that absolutely contradict the attributes hitherto observed in bodies. However well fitted atomic theories may be to reproduce certain groups of facts, the physical inquirer who has laid to heart Newton's rules will only admit those theories as provisional helps, and will strive to attain, in some more natural way, a satisfactory substitute."

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n • -I l. • o ~itrid,2{~U:~ 't'(ol~,~J1,~!;~:g £

The Gravity Probe B (GPB), under the direction of Everitt, Parkinson and Turneaure, is a space experiment to measure the dragging of the inertial frame by the rotation of the Earth. It is a new test of Einstein's' General Relativity theorY which has fundamental imponance to establishing the proper theory of relativistic gravitation. Funhennore, it has astrophysical applications in understanding the dynamics of rotating black holes. A prerequisite to the execution of the experiment has been the development of exquisite new experimental techniques in physics (the development of gyroscopes with unprecedented perfonnance, the creation of regions of ultralow magnetic fields, and basic developments in the physics of superconducting devices) coupled to new engineering approaches to spacecraft technology (drag free systems, low thrust propulsion and cryogenic space systems).

The bold effon is precedent breaking in the United States space program. It is the first basic physics experiment of first rank imponance to be perfonned in space and, since it involves such unconventional technology, the scientific requirements have forced a new approach to the management of a scientific/engineering program for space. The successful execution of this project will be a high point for physics as well as the space program and may show a new productive way for universities to carry out space research.

Progress toward the space mission is excellent. The enabling technology is now in hand and the critical work to integrate the experiment for a ground--based test followed by a shuttle test mission is on schedule. Although no definite plan for the science mission has yet been made by NASA, detailed science mission planning has begun. A recently uncovered ancillary benefit from flying the mission is a remarkable improvement in measuring the gravitational figure of the eanh by ranging to GPB in its drag free polar orbit in concert with ranging to other existing satellites.

The GPB project has once again demonstrated how technology development spawns or enables new science. Cabrera's elegant work on measuring the ratio of Planck's constant to the mass of the electron and the interesting upper limits determined on the magnetic monopole flux are direct beneficiaries of the technology developed for GPB.

A new test of the Principle of Equivalence, another fundamental experiment in gravitation, using technology similar to that in GPB, is being planned by Everitt and Warden. The experiment measures the difference in the ratio of the gravitational to inertial mass of two bodies of unlike composition. A basic tenet of general relativity is that this ratio should be the same for all bodies. The experiment will measure or set new limits on the difference by a precision measurement of the relative motion of the two objects as they orbit the Eanh. The experiment holds promise of a six order of magnitude improvement in establishing the principle of equivalence and explores a sensitivity domain where it might be violated

The technology for the experiment has been under development for many years. A joint NASA and ESA scientific mission to carry out the experiment is now being actively considered

4

Dalton 1808: Empirical Rule ;

If elements A, B can make compounds C1 01

C2 with weights

w A (1) + wB(l) , . ,.., wCl w A(2) + wB(2) >- WC2,

then .w A(l)/wB(l) w A (2)/WB (2)

is a ratio of small integers.

Gay-Lussac 1808: Empirical Rule :

If A and B are gases that combine to form compound D, the combining volumes obey V A/VB = ratio of small integers

Avogadro 1811: Atomist's Intuition:

At any given T, p, the number of molecules per unit volume is the same for all gases.

Inter~Office Memorandum

To GSL Date March 21, 1985

From R.Z. Bachrach (x4157) Location Palo Alto

Subject GSL Discussion Survey

Attached is the survey from the GSL meeting today. Please fill it out and return as soon as possible.

The discussion generated the following lists. Since these were not fully completed, perhaps these can be expanded more at the next meeting.

Motivations for Choice of Research 1. Relevance to Xerox 2 Ability to Succeed 3. Availability of human, money

and time resources 4. Personal interest 5. Innovative potential 6. Controversy 7. Recognition 8. Rewards 9. Participation on Frontier 10. Perceived Scientific Importance 11. Career Development 12. Collaborative Potential

Objectives 1. Follow Through 2. Useful Knowledge 3. useful technology 4. participate in corporate decisions

Thanks,

Bob

Objections to Choice Obvious or trivial Squandering of Resources Relative Resource Needs Poor Return on Investment

ties that will naturally develop with condensed matter physics, physical chemistry, and photo--biology, should be most valuable to HEPL.

The FEL facility, in concert with its users, provides the first opponunity to explore the nonlinear dynamics of condensed matter in the infrared (IR) pan of the electromagnetic spectrum. Of fundamental importance as a scientific tool is the unique time structure of the radiation, pulses of a few picosecond width separated by approximately 80 nanoseconds. The large time interval between pulses pennits the use of present day pulse selectors to transfer pulses and pulse sequences to the material under investigation. Professor Fayer of the Department of Chemistry has already used this technique to demonstrate the capability of the FEL to obtain dynamical information about glassy systems.

By tuning the FEL toward longer wavelengths in the infrared, it will be possible to carry out related studies on the nonlinear response of the vibrational dynamics of solids and identify the transfonnation from phonon modes to localize vibrational excitations at high intensities.

Astrophvsics

Principal Investigators: Hofstadter, Scherrer, Timothy, Walker Visiting Committee Members: McDonald, Peterson

Solar and XlN Astrqphvsics

A team of three experimental astrophysicists from the Applied Physics Department are participating in HEPL. Their Solar and Heliospheric Observatory

'. (SOHO) investigation on solar oscillation is a large scale space experiment that will yield imponant new fundamental results in solar physics (such as, information on . the internal structure of the sun) that will have broad applicability in astrophysics. The SOHO project is a major new NASA initiative and was selected from a tough international competition.

The low noise Multi-Anode Microchannel Array (MAMA) detectors of Timothy represent an important new technology development for imaging detector systems that will be used extensively in Earth sciences and astrophysics.

The rocket program of Arthur Walker has been a valuable means of making new astrophysical observations, developing new experiments, and training students. Their investigations constitute a small but very competent and productive experimental astrophysics group.

Gamma Rav AstrQphysics

The group under the direction of Roben Hofstadter and Banie Hughes is doing leading research in high energy astrophysics with their participation in the Gamma­Ray Observatory (GRO). The GRO is the key mission being implemented by NASA in the 1990's to funher explore this field. Stanford, through HEPL, has a significant role in the Energetic Gamma--Ray Experiment Telescope (EGRET) on the GRO, and has supplied a major component of the instrument. The instrument may uncover new astrophysical processes and will detect gamma--rays from energetic phenomena in compact objects such as neutron stars and black holes. These sources will be detected with unprecedented sensitivity, angular resolution and spectral determination. This forefront instrument capitalizes on the HEPL

2

FIELD ION lVlICROSCOPY

H

ygO:J205I::JHA VIOI OJ3FI

Journal Club Wednesday, February 18

Applied Physics Room 200 4:00 P.M.

"Thermal Conductivity in a High Tc Material"

Krishna et al., Science 277, 83 (1997)

Aubin et al., Internet

"Discontinuous Change of Island Shape With Size in Heteroepitaxy: Cause and Effects"

Ross et al., Phys. Rev. Lett. 8Q, 984 (1998)

A. Kapitulnik Applied Physics

20 minutes

c. Herring Applied Physics

15 minutes

J1 DIFFUSION OF A LARGE MOLECULE OR A COLLOID PARTICLE IN A LIQUID

Model as a solid sphere of radius at. whose surface drags the liquid with it.

Imagine a dilute solution of such spheres in thermal equilibrium in the presence of a weak constant force

field F acting on each sphere in the x-direction (pot.en. V=-Fx for a sphere centered at x).

The average concentration c at x will obey

c(x) oc exp (V /kT) = exp (FxlkT)

and to first order in F the diffusive flux must just cancel the drift flux

D ac/ax = Dc F/kT = cF (v drift/F)

By Stokes' law of hydrodynamics (v drift/F) = 1/6TC11 a

so D = kT/6TC11 a = RT/6TC11 Na (Einstein relation) (1)

For sugar solutions D is measured, Rand 11 known, (l j gives Na. Solution of hyd. problem of disturbance of shear flow around a sphere gives 11 (solution)/l1 (pure water) in terms of volume fraction of spheres (ocNa3).

Solve for Nand a.

For BroT,ynian motion a is known, D measured, so (1) alone gives N.

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ELECTRO­CHEMISTRY

Faraday 1833

1840 -

GAS DISCHARGE

PHYSICS

ATOMIC WEIGHTS; Geissler AN ION IN

ELECTROLYSIS DISCHARGE DEPOSITS TUBES

CHARGE oc VALENCE

1860 -

KINETIC THEORY

OF GASES

Joule 1843

MOLECULAR VELOCITIES

Maxwell 1859 Boltzmann 1861

EQUIP ARTITION OF KINETIC ENERGY

.~

~

1870 - Goldstein 1876

CATHODE RAYS

ELECTRON: QUANTIZ. OF

CHARGE, LOW m Thomson

1897 1900 -

Maxwell 1873 ~

THEORY OF TRANSPORT van der

IN GASES Waals 1873

DEPARTURES FROM GAS

BOYLE'S LAW LIQUID TRANSITION

1 Motion of Green Molecule:

o

0- '> -0 , -

In time t avg. no. of stretches = v t

random in direction, so (wx2 ) = mean sq. displacement in x direction

=GA2vt=2 Avt A 3

Must = 2 Dt 1 so

VA =3D

(Also = 3 n p

= 3 K )

pC v

(Summarized Maxwell 1873)

1

1

1

1

1

1

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1

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t6 Joule 1843

p = impacts (2 x ..1 momentum) area x time

= «(nv.l) (2 mv.l» = nm (v2)

2 3

nm = Pgas 1 so (v2 ) = 3p

Combining with v A gives A.

If A »d, nd2An z 1 ~ d2n

In close-packed solid

volume per sphere = 23/2 d3

3

P solid = 3m 23/2 d3

2VJ.: ...J2gas- = d3n 3 P solid

Pgas

van der Waals 1873: For One Mole

/ (P +a/v2) ' (v-b)\ RT

kinetic pressure available volume = p - (static = v - (volume of

p

pressure) hard spheres)

One p for each v, but three v's (maybe not all real) for each p

v

Curves for various T

"

p'

_ ...... -

,/"

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•

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. :. i

1890 - Rayleigh MISC. THICKNESS OF OLIVE OIL MONOLAYERS

Mach 1900 -

Ostwald 1902

.~ \

X-RAYS

Roentgen 1895

X-RAYS RESEMBLE

LIGHT

QUANTUM THEORY

Planck 1900

MATERIAL SHO LIMITED TO

ENERGIES nhV

Einstein 1905 Einstein 1905 BROWNIAN MOTION OF PARTICLES

Smoluchowski 1906 LIGHT ABS.

Ostwald 1908 SIZE OF SUGAR MOLECULES IN

SOLUTIONS

CAN IMPART ONLY ENS. nh V

----~ ?

1910 -

hi

II

von Laue 1912 Friedrich & Knipping 1913 Braggs 1914

X-RAYS HAVE LARGE (~keV)

QUANTUM ENERGIES

CRYSTALS DIFFRACT XRA YS

-----. "'-.1

l~

, -:;-', I -

E. MACH: "THE SCIENCE OF MECHANICS"

"Thus, chemical, electrical, and optical phenomena are explained by atoms. But the mental artifice atom was not formed by the principle of continuity; on the contrary, it is a product especially devised for the purpose in view. Atoms cannot be perceived by the senses; like all substances, they are things of thought. Furthermore, the atoms are invested with properties that absolutely contradict the attributes hitherto observed in bodies. However well fitted atomic theories may be to reproduce certain groups of facts, the physical inquirer who has laid to heart Newton's rules will only admit those theories as provisional helps, and will strive to attain, in some more natural way, a satisfactory substitute."

DIFFUSION OF A LARGE MOLECULE OR A COLLOID PARTICLE IN A LIQUID

Model as a solid sphere of radius a, -whose surface drags the liquid -with it.

Im.agine a dilute solution of such spheres in thennal equilibriull1. in the presence ofa "Weak constant force

field F acting on each sphere in the x-direction (pot.en. V =-Fx for a sphere centered at x).

The average concentration c at x -will obey

c(x) oc exp (V IkT) = exp (FxlkT)

and to first order in F the diffusive flux lllUst just cancel the drift flux

D ac/ax = Dc F/kT = cF (v driWF)

By Stokes' law of hydrodynamics (vdriftlF) = 1/61t1l a

so D = kT/61tT\ a = RT/61t1l Na (Einstein relation) (1)

For sugar solutions D is measured, Rand 11 known, (lJ gives Na. Solution of hyd. problem of disturbance of shear flow around a sphere gives ll(solution)/ll(pure -water) in term.s of volullle fraction of spheres (ocNa3

).

Solve for Nand a.

For Bro-wnian m.otion a is kno-wn, D tneasured, so (1) alone gives N.

Year A.D.

1600 -Descartes

Steno CRYSTALLOGRAPHY Boyle

Newton 1700 - Guglielmini

Rome de l'Isle LAW OF CONSTANCY OF ANGLE

Boscovich

- - .

CHEMISTRY

LAW OF DEFINITE

PROPORTIONS Proust

:.e.t-o ~[f11.: f~1~

•

1800 -

1810 -

\

frt/Jv...t- ;-e

7~ LAW OF

RATIONAL INDICES

LAW OF Dalton Gay-Lussac MULTIPLE

PROPORTIONS

LAW OF COMBINING

VOLUMES

Avogadro

UNIVERSALITY OF MOLECULAR

DENSITY VV7 c v~ ~ /?'1 vvb() Vtt- J I tn--c.

l870 - Goldstein 1876 Maxwell 1873

CATHODE RAYS THEORY OF TRANSPORT van der IN GASES Waals 1873

/f'J ~~~ L ~ 1~/t!P

ELECTRON: ~.J..E-P>--A-R-T-"-U-R-E-S'L ~ QUANTIZ. OF homson 189 FROM ~ \.)0--_....

CHARGE, LOW m . 1 OYLE'S LA GAS-t LIQUID M~~ ( TRANSITIO

fJ1( I ,~~~~

-'ELECTReCIIEl\II1S FRY

GAS

*INETfC TIIJ3'8RY 8FGASES J ~~

J< ) N lfTl c. a;?d . U?~

~ DISCHARGE PHYSICS

T H-Ec>A Y ?-~ OF G/J-SES

Faraday 1833 1840 -

ATOMIC WEIGHTS AN ION IN ~

ELECTROL YSIS DEPOSITS

CHARGE oc VALENCE

1860 -

P1P 5-eb~~ ~ (Geis~ tlJ?e'1r

DISCHARGE TUBES

Joule 1843

MOLECULAR VELOCITIES

Maxwell 1859 Boltzmann 1861

EQUIPARTITION OF KINETIC ENERGY

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/ ' THERMAL EXPANSION ~Ubye 1914)

Expansion coeff. is ex = 1fV (aV faT)p=o

In latter O=dp=(apfaT)v dT + (apfaVh dV

so ex = - 1 (apfaT)v = V (apfaVh

Here the entropy S can be written

S(V,T) = SD 8 (V) SA (V,T) T

Debye approx. Anharm.

and if SA is « SD and not much more sensitive to V, we can neglect aSAfaV and get aSDfaV,

for say a mole of material, from

Cv = T(aSfaT)v ;:::: T [dSDfd (8fT)] (-8fT2)

(aSDfaVh = [aSDfd (8fT)] [d8fdV]fT

= -Cv (d8fdV)f8

So finally ex;:::: K - dln8 Cv dlnV Vm

· r

\ \

-\

THERMAL EXPANSION (Debye 1914)

Expansion coeff. is a = 1/V (aV/aT)p=o

In latter O=dp=(ap/aT)v dT + (ap/aVh dV

~ <" c:sn a= ])1 (ap/aT)v = K(ili!') = K(as~ vnrn>t-5 SJT?J J V (ap/aVh \ aT)v aV)T

Here the entropy S can be written

S(V,T) = SO( 8 iV) + SA (V,T)

Debye approx_ Anharm.

and if SA is « SD and not much more sensitive tc V, we can neglect aSA/aV and get aSD/aV, for say -

~ mole of material)from /l

u;11'J?-1tl ~~ IM,w.e. ~

Cv = T(aS/aT)v ~ T [dSD/d (8/T)] (-8/T2)

(aSD/aVh = [aSD/d (8/T)] [d~/dV]/T fl~ pa~i"'Iu}'·5

= -Cv (d8/dV)/8

So finally a ~ K - dln8 Cv dlnVi Vm

~

I

\

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\ ,) ,Using varIables L1qz and L1qp = ( L1Qx2 + L1Qy2)112

integrate volumes of cylindrical shells

dV1 = 2 rr~qp [(L1qp2 + lL1col )1/2 - L1qp] d~qp (2)

, ~ "e:-- cone ~qp = IL1Qzl

~ /

------.,.,~ c u to ff hyperboloid

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L1Q2pc

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o

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Using variables dqz and dqp = (dQx2 + dQi)1/2

integrate volumes of cylindrical shells

dV 1 = 2 TIdqp [(dqp2 + Idrol )1/2 - dqp] ddqp (2)

..e- cone dqp = Idqzl

I

~- cutoff hyperboloid

dqpc-

dq2pc

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o

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CAUCHY RELATIONS (1837)

If one assumes: En. = L, <?ij (Iij ) atom

pairs if j

and equilibrium at zero p, i.e.,

Let a macroscopic uniform strain u~ v

cause each atom i to be displaced by a vector

Ui ~ = L, u~ v Iiv (often required by symmetry) v

Then one can prove that elastic constants Ca ~ ~ v

defined by

p a ~ = L, Ca ~ ~ v U~l V

~v

have complete symmetry with respect to permutation of a, ~, ~, and v.

(E.g., C1122 = C1212 which in the " ~t~ ~~\\a\ notation is Cn = C l\A)

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