Mineral ChemistryMineral properties = f(structure + chemistry)But not independent: structure = f(chem, T, P)Compositions are conventionally given as wt% oxides(unless sulfides, halides, etc.)I'd prefer mole % actually, but inherited this systemDifference between Fo = Mg2SiO4 and Fo= 51.5% SiO2 and 48.5% MgO

Mineral ChemistryHomework Problem Handout1) 2 PyroxenesConvert wt% oxides to formula. COOKBOOK2) Unit cell dimensions & density of olivineCalculate the Unit Cell Content.Remember ducky/fishy? Z= # of motifs/u.c. Now motif = some "molecule"Use method of Scientific Analysis!

Mineral ChemistryMethod of Scientific AnalysisWrite single equation to get from what have to what want.Have: u. c. Volume (in A3) & formula A = 10-8 cm. Want Z = # formula units/ u.c.Example 8 mi/hr = ? in ft/sec?

If do all on one line with #'s and units, If units work # must!Want formula units/mole (Avocados #)

Composition of the Earths CrustMost common silicates are from theseO alone = 94 vol. % of crustPerhaps good to think of crust as a packed O array with interspersed metal cations in the interstices!Analogy works for minerals too (they make up the crust)

Sheet1

Weight %Atom %Ionic RadiusVolume %

O46.6062.551.4093.8

Si27.7221.220.420.9

Al8.136.470.510.5

Fe5.001.920.740.4

Ca3.631.940.991.0

Na2.832.640.971.3

K2.591.421.331.8

Mg2.091.840.660.3

Total98.59100.00100.00

Sheet2

Sheet3

Chemistry ReviewBohr model for the atomNucleus = p + n Z (Atomic #) Gives elements their identity (properties) (~ all mass)p + n (variable) atomic weight (isotopes)At. Wt. is real # due to average of isotopese- spin around atom and give it it's size (statistical size) Atomic radii in the range 0.5-2.5 Ae- in special shells w/ particular Energy levels Quantized

Chemistry ReviewQuantized energy levels (Fig. 4.12)Relative Energyn = 1 K 2 L 3 M 4 N 5 O 6 P 7 QNote that the energy does not necessarily increase K L M N etc.4s < 3d

Chemistry ReviewShells and SubshellsinnermostK(n = 1)2es(lowest E)L(n = 2)8es, pM(n = 3)18es, p, douter N(n = 4)32es, p, d, f(generally higher E) higher levels not filled

Chemistry ReviewShells and Subshells1s 2s and 3s orbitals

Shells and Subshells2 p orbitalsxzyyxzzyxpxpypz

d orbitals

Table 3.6 p. 51-52 shows the progressive filling of orbitals as energy increases

The Periodic Table

Notation: Al = 1s2 2s2 2p6 3s2 3p1Atoms may not look like thisIt's only a modelBut it's a pretty good oneWe'll see that these subshell shapes explain a lot of macroscopic propertiesCharacteristics of an atom depend a lot on e- configurationThis results in part from # p & electrical neutralityBut atoms with a different # of p & e, but with similar e-configurations have similar properties

It is the outermost shell or valence e- s that are fundamentalSimilar outermost shell configurations Groups in the Periodic Table (Table 4.8 p.188)alkali metals (Ia) have a lonely e- in outer shell halogens (VIIa) have 7 e-inert gases (VIIIa) have 8e- a magic #... filled s & p (He only has s with 2 e-)

Other elements try to gain this stable inert gas config.If have one extra (alkalis) will readily lose it if it can find another way to attain charge balanceThis results in an ion with a +1 valenceGroup II metals will lose 2 e- +2 valenceHalogens will capture an e- inert gas config. -1 Ionization Potential (T 3.7)Electronegativity is the ability of an atom in a crystal structure to attract electrons into its outer shellIn general, electronegativity increases

(except for inert gases which are very low)

Elements are classified as:Metals w/ e-neg < 1.9 thus lose e- and cationsNonmetals> 2.1thus gain e- and anionsMetalloids intermediate (B, Si, Ge, As, Sb, Te, Po..)

Chemical BondsElectrical in nature- responsible for most mineral properties1) Ionic Na: low 1st IP e- Na+ (Ne config)Cl: high e-neg takes e- & = Cl- (Ar config)Now they have opposite charges & attract bond(really a very unequal sharing)Bonding is strong (high melting point)But easily disrupted by polarized solvents (water)Poor electrical conductors.Strength (1/bond length) & valenceAlso non-directional (more later), so symm. is a packing function and thus rather high (isometric common).If e-neg of 2 atoms differs by 2.0 or more will ionic

Chemical Bonds2) CovalentConsider 2 Cl atoms each trying to steal each other's e- = 1s2 2s2 2 p6 3s2 3p5Can't do, but if draw close until overlap an outer orbital, perhaps can share whereby 2 e- "fill" the remaining 3p shell of each ClActually fill it only 1/2 the time for each, but better than nothingIn fact this compulsion to stay overlapped & share results in a strong bond Cl2This is the covalent or shared e- bond (the Socialist bond) Double bonds when 2 orbitals sharedTriple bonds when 3 orbitals shared

Chemical BondsHybrid orbitalsCarbon: | | | 1s 2s 2p 1s 2(sp3)C-C-C angle = 109o 28Fig 8-8 of Bloss, Crystallography and Crystal Chemistry. MSA

Chemical BondsHybrid orbitals2(sp3) is tetrahedrally shaped (energy is identical)Larger overlap strongerDirectional: each C is tetrahedrally coordinated with 4 others (& each of them with 4 others...)C-C-C bond angle fixed at 109o 28' (max. overlap)Note Face-centered Cubic latticeThe directional character lower coordination & symmetry, density

Chemical BondsHybrid orbitalsAlternatively:Carbon: | | | | 1s 2s 2p 1s 2(sp2) 2p

As most organic chemists know, C is a flexible elementIn fact, many atoms in the center of the Periodic Table with partially filled valence shells are variable in how they attain stability (this includes Si)

Chemical BondsThe 3 2(sp2) orbitals are coplanar & 120o apartGraphite structureFig 8-8 of Bloss, Crystallography and Crystal Chemistry. MSA

Chemical BondsThe 3 2(sp2) orbitals are coplanar & 120o apartGraphite structureOverlap similar to diamond w/in sheets (strong too!)Must Hexagonal Crystal ClassNote p-bonding between remaining 2p'sThis results in delocalized e- 's in 2p which results in electrical conductivity only within sheets

Chemical BondsThere are other hybrids as well (dsp2 in CuO- planar X)e- may resonate in bonds of non-identical atoms & give a partial ionic character if one much more e-neg than otherIn fact most ionic crystals share to some extent while covalent may share unequallyThis is a result of De-neg

Chemical Bonds3) Metallic BondingMetals are on the left of the P.T. Have few, loosely held valence e-If closely pack them can get up to 12 "touching" nearest neighborsThis a high density of valence e- around any given atom & also a high density of neighbor atoms around the loose valence e-The effect is to show such a general attraction for these e- that they become free to maintain an electrical neutrality in the xl as a whole... a sea of mobile electronsLet's call it the left-side equivalent of the covalent bond(On the right side the e-neg is high & atoms are trying to take e-)

Chemical Bonds3) Metallic BondingLet's call it the left-side equivalent of the covalent bondOn the right side the e-neg is high & atoms are trying to take e-If can't, must share tightlyOn left, w/ low e-neg & low I.P. they aren't trying to take, but to give, so loosely shareMetallic crystals thus conduct electricity and heat

Chemical Bonds4) Van der Waals BondsWeakest bondUsually between neutral molecules (even large ones like graphite sheets)Aided by polar or partial polar covalent bonds.Even stable A-A bonds like O2 or Cl2 will get slightly polar at low T & condense to liquid & ordered solid as vibration slows & polarityWeakness of the bond is apparent in graphite cleavageCondensed Clcov VdW

Atomic and Ionic RadiiCan't absolutely determine: e- cloud is nebulous & based on probability of encountering an e-In crystalline solids the center-to-center distance = bond length & is accepted to = sum of ionic radiiHow get ionic radius of X & Y in XY compound??

Atomic and Ionic RadiiNeed one pure element firstNative Cu. Atomic radius = 1/2 bond lengthMetals usually FCC or BCCaaX-ray d100 a

Ionic radius = 242a

Atomic and Ionic RadiiWe can do this on our lab!! If can look up lattice type (really space group)BCC uses body diagonal rather than faceWith compounds, don't know what % of bondlength to which atom, but if know one can get otherSo can keep on as accumulate more & more compounds from known setO lots of cations etc.

Atomic and Ionic RadiiHowever there are variations:1) Variations in related to % ionic or covalent character (or VdW)2) Variations in # of closest neighbors (coordination #)

Handout of Atomic and Ionic Radii

Atomic and Ionic RadiiCorrections:Ions- usually for VI coordination (not 6-fold symm!) x 0.94 IV (Si)x 1.03 VIIIx 1.12 XII (metals)Metallic Atoms given for XII (most common) x 0.88 IVx 0.96 VIx 0.98 VIIICovalent bonds given for single bondsCorrect for double, triple (stronger shorter)

Atomic and Ionic Radii

True radius will vary with actual bond-type, resonance (1x 2x in covalent), structural causes (Na in Ab), & coordination #Purpose of all this radii stuff: To understand & predict behavior of atoms in crystalline solidsParticularly Coordination Number

Crystal ChemistryCrystals can be classified into 4 types:1. Molecular CrystalsNeutral molecules held together by weak van der Waals bondsRare as mineralsMostly organicWeak and readliy decompose, melt, etc

Example: graphite

Crystal Chemistry2. Covalent CrystalsAtoms of similar high e-neg and toward right side of PTAlso uncommon as minerals (but less so than molecular)Network of strong covalent bonds with no weak linksDirectional bonds low symmetry and density

Example: diamond

Crystal ChemistryThe diamond structureAll carbon atoms in IV coordinationball-and-stick modelpolyhedral modelblue C onlyhard-sphere modelFCC unit cell

Crystal Chemistry3. Metallic CrystalsAtoms of similar e-neg and toward left side of PTMetallic bonds are directionless bonds high symmetry and densityPure metals have same sized atomsClosest packing 12 nearest mutually-touching neighborsCubic Closest Packing (CCP) abcabcabc stacking = FCC cellHexagonal Closest Packing (HCP) ababab = hexagonal cellAlso BCC in metals, but this is not CP (VII coordination)

More on coordination and closest packing a bit later

Crystal Chemistry4. Ionic CrystalsMost mineralsFirst approximation: Closest-packed array of oxygen atoms Cations fit into interstices between oxygensDifferent types of interstitial sites availableOccupy only certain types where can fitOccupy only enough of them to attain electric neutrality

Again, energy does not increase regularly K L M N etc. Some complications with spin V Cr, etc.