tutorial 2 - 1280 from word 2003

8/8/2019 Tutorial 2 - 1280 From Word 2003

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Mech 1280 Tutorial 2

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PLEASE DO NOT GIVE COPIES OF THESE TUTORIAL SHEETS TO THE STUDENTS they will be

distributed soon afterwards _

Q. Draw the exploded view of the atomic arrangement in the unit cell of a face centred

cubic (FCC) crystal structure. Include 3 axes (x, y & z) in the arrangement shown in lecture

and the notes to Unit 3 (Note; we use exploded views because they are simpler to draw

than the true life representation where many atoms are touching).

Note: there is an atom centrally located on each face of the cube, as well as eachcorner, hence the name.

Q. next, on the unit cell indicate the lattice parameter a and give a typical size (the

students should know -> answer - about 0.2 nm).

Q. What are slip planes and why are they important?

A. Slip planes are the pathways by which plastic deformation or plastic flow takes place.

Q. Can you draw the most important slip plane for an FCC crystal structure? Draw it on your

existing drawing 2.


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A.

Q. Can you derive the Miller Indices for this example?

A. To get these, we take the unit cell edge length represent 1 unit of length. Next we look

for where the plane intercepts the various axes if at all (or is parallel to one or two of the

axes). In this specific case, the x, y and z axes are intercepted at one edge length see moredetail in the next drawing.

Q. What next?

A. hen you take the reciprocal of the intercept so this gives us 1/1, 1/1, 1/1

And the result is the Miller Indices for the plane 1 1 1 we surround these numbers by

round brackets this indicates the unique and specific (111) plane.

Q Can you represent the entire family of {111} planes ?

Note: When talking about the 111 family or 111 types of planes we do so by usingcurly brackets - {111}.

A The following all meant to have round brackets left out here for convenience:-


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Q. What does the line over the ones mean?

A. This is a relatively negative direction of the plane intercept. We refer to such numbers as

bar ,for example, when reading the plane on the top of the list we call this the bar 1, bar

1, bar 1 plane (rather than saying -1, -1, -1).

Take a closer look.

Q. Can you identify this plane? (tutor should draw this)

A. To solve this, we have to move the origin or the plane so that the plane intercepts at

least one of the axes or is parallel to one or two of the axes. (It should also not

intercept the origin). In this specific example, after we relocate the plane we see all

three axes are intercepted, the x and y axes are intercepted at -1 and -1 edge

lengths while the z axis is intercepted at +1 but we dont use the +.

A. Next take the reciprocal - this gives -1/1, -1/1 and 1/1 and so the Miller indices are


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Q. Why does plastic deformation take place along the {111} type planes?

A. Because these are the close packed planes (CPPs) and they can carry most stress.

Q. What does this mean

A. These are the planes where the atoms are the most densely packed possible.

Q. Can you prove this? First draw an exploded view of the arrangement of atoms in the

(111) plane.

A. See below

Q. What does this really look like?

A.

Note the gaps in a CPP are very small much less than the diameter of an atom.

Q. Can you draw the following plane:-

A. Do this in TWO stages


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Stage 1 move the plane to a position where it intercepts all 3 axes (in this example) at

the interception positions: -1, -1, -1.

Stage 2 Now you can now move the plane back into the unit cell.

Q. How is this plane related to the (111) plane? Look at both.


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A. It is parallel in other words the same

Note: In such cases, where two miller indices result in parallel planes (in the same unit

cell) we use ONLY one of the miller indices for identification as both planes are of the

same orientation (they are parallel). Further, we always select the most positive of the

possible indices in the last case, just drawn, we never use the bar 1, bar 1, bar 1 miller

indices just (111).

Looking again at our list of the {111} family (types) we see that other negative Miller

indices should also cancelled out (so to speak) since there is a positive equivalent that isparallel (of the same orientation) i.e., although there are 8 Miller Indices of the {111} type

there are only 4 orientations

The following are parallel - (this is new to the students):-

Q. Name some important FCC metals

A. Al, Cu, Ni, -Fe.


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Q. Next, draw the exploded view of the atomic arrangement in the unit cell of a

hexagonal close packed (HCP) structure. Here you need FOUR axes because there are more

planes of symmetry in this structure.

A. Here are the axes

Next comes the basal plane of the unit cell:-

A. Then we can draw the prismatic planes and finish off with the uppermost

(horizontal) basal plane.

A. Then add atoms to the corners and place one atom in the centre of each basal

plane.


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A. Finally add the three centremost atoms midway between the upper and lower basal

planes.

Q. So how many basal planes are there? (We should have picked up part of the answer

during the sketching exercise)

A. We can see 3 actual planes but they all have the same Miller Indices THE SAME

ORIENTATION - since ALL 3 are PARALLEL these planes are all designated (0001). Here, we

use a modified version of the Miller Indices because we are now working with 4 axes (x, y, I,z). BUT we dont need to worry too much about this at this time.


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Q. Where are the close packed planes in this crystal structure?

A. These are the basal planes

Q. Can you indicate where the lattice parameters are in this case?

A. Here we need 2 lattice parameters to quantify the unit cell size, a and c.

Q. Name some important HCP metals

A. Mg (used in low mass structures), -Ti (stable at room temperature & used in aircraft

structures and bio-implants), -Co (stable at room temperature & used in joint

replacements)

Q. NEXT name some important BCC metals

A. -Fe (main phase in steel), -Ti (features in special Ti alloys)

Q. Can you draw the unit cell of a body centred cubic metal?

A.


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Note: there is one atom located in the centre of the cube and one atom at eachcorner, hence the name.

Q. Where are the close packed planes?

A. There are no close packed planes (CPPs). But there are near close packed planes (NCPP).

Q. Show an exploded view of one of the NCPPs in the drawing.

A. (Some atoms removed for clarity)

Q. What are the Miller Indices of this plane?

A. (110)

Q. How many unique {110} planes are there ?

A. Six different orientations

Q. Show how the atoms touch in (110) plane

A.

Q. How does this compare to the CPP in the FCC structure? Can you compare the packing?


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A.

Q. Can you see the close packed directions (CPDs) ? Indicate them on the drawing.

A. The double arrows show the CPDs. There are 2 for NCPPs and 3 for CPPs.

A. The close packed directions are those in which the atoms are touching.

Note: the close packed directions on close packed planes or near close packed planesare the directions along which most stress is carried during plastic deformation that is, the

planes slide over each other, but only in the directions that are close packed.

Q What happens of a force is applied to the near close packed plane in a non-close packed

direction direction A?

A. Although some forces get resolved along the close packed directions some of the force

gets used to split apart the structure

Fracture can be initiated !

Q. Based on your knowledge of slip planes can you draw a series of stress-strain curves to

show what behaviour you would expect for BCC, HCP and FCC metals?


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A. The rationale is in relation to ductility (UNIT 2) which we quantify using f theplastic strain to fracture.

HCP metals have limited ductility only one orientation of close packed plane (the {0001}

basal planes).

BCC metals have better ductility as they have SIX orientations of the NCPPs with 2 CPDs per

plane this provided better ductility BUT fracture is initiated more easily because of the

open nature of the NCPPs.

FCC Metals contain 4 unique orientations of CPPs with 3 CPDs per plane. This enables

greater ductility than for BCC or HCP.

Curves off set for clarity. Strength levels can vary for various reasons like differences instrain hardening index (behavior).

tutorial 2 - 1280 from word 2003

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