# Mineral Chemistry Mineral properties = f(structure + chemistry)

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Mineral Chemistry Mineral 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 system Difference between Fo = Mg2SiO4 and Fo= 51.5% SiO2 and 48.5% MgO

Homework Problem Handout
Mineral Chemistry Homework Problem Handout 1) 2 Pyroxenes Convert wt% oxides to formula. COOKBOOK 2) Unit cell dimensions & density of olivine Calculate the Unit Cell Content. Remember ducky/fishy? Z= # of motifs/u.c. Now motif = some "molecule" Use method of Scientific Analysis!

Method of Scientific Analysis
Mineral Chemistry Method of Scientific Analysis Write 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 (Avocado’s #)

Composition of the Earth’s Crust
Most common silicates are from these O alone = 94 vol. % of crust Perhaps 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)

Chemistry Review Bohr model for the atom
Nucleus = 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 isotopes e- spin around atom and give it it's size (statistical size) Atomic radii in the range A e- in special shells w/ particular Energy levels Quantized

Quantized energy levels (Fig. 4.12)
Chemistry Review Quantized energy levels (Fig. 4.12) s p d f Relative Energy Note that the energy does not necessarily increase K  L  M  N etc. 4s < 3d n = 1 K L 3 M N O P Q

Chemistry Review Shells and Subshells innermost K (n = 1) 2e s
(lowest E) L (n = 2) 8e s, p M (n = 3) 18e s, p, d outer N (n = 4) 32e s, p, d, f (generally higher E) higher levels not filled

Shells and Subshells 1s 2s and 3s orbitals
Chemistry Review Shells and Subshells 1s 2s and 3s orbitals

Shells and Subshells 2 p orbitals
px z Shells and Subshells 2 p orbitals x y z z py pz x x y y

d orbitals z x y d xz z y x d xy x y z d yz z y x d z2 y x z d x2-y2

Table 3.6 p. 51-52 shows the progressive filling of orbitals as energy increases
Again, energy does not increase regularly K  L  M  N etc. Some complications with spin V  Cr, etc.

The Periodic Table

Notation: Al = 1s2 2s2 2p6 3s2 3p1 Atoms may not look like this
It's only a model But it's a pretty good one We'll see that these subshell shapes explain a lot of macroscopic properties Characteristics of an atom depend a lot on e- configuration This results in part from # p & electrical neutrality But 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 fundamental
Similar 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 balance This results in an ion with a +1 valence Group II metals will lose 2 e-  +2 valence Halogens 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 shell In 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  cations Nonmetals > 2.1 thus gain e- and  anions Metalloids intermediate (B, Si, Ge, As, Sb, Te, Po..)

Chemical Bonds Electrical in nature- responsible for most mineral properties 1) 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) & valence Also 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 Bonds 2) Covalent
Consider 2 Cl atoms each trying to steal each other's e = 1s2 2s2 2 p6 3s2 3p5 Can't do, but if draw close until overlap an outer orbital, perhaps can share whereby 2 e- "fill" the remaining 3p shell of each Cl Actually fill it only 1/2 the time for each, but better than nothing In fact this compulsion to stay overlapped & share results in a strong bond  Cl2 This is the covalent or shared e- bond (the Socialist bond) Double bonds when 2 orbitals shared Triple bonds when 3 orbitals shared

Chemical Bonds Hybrid orbitals Carbon:  |  |     |    
1s 2s p s (sp3) Fig 8-8 of Bloss, Crystallography and Crystal Chemistry. © MSA C-C-C angle = 109o 28’

Chemical Bonds Hybrid orbitals
2(sp3) is tetrahedrally shaped (energy is identical) Larger overlap  stronger Directional: 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 lattice The directional character  lower coordination & symmetry, density

Chemical Bonds Hybrid orbitals Alternatively:
Carbon:  |  |     |    |  1s 2s p s (sp2) p As most organic chemists know, C is a flexible element In 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 Bonds The 3 2(sp2) orbitals are coplanar & 120o apart
Graphite structure Fig 8-8 of Bloss, Crystallography and Crystal Chemistry. © MSA

Chemical Bonds The 3 2(sp2) orbitals are coplanar & 120o apart
Graphite structure Overlap similar to diamond w/in sheets (strong too!) Must  Hexagonal Crystal Class Note p-bonding between remaining 2p's This results in delocalized e- 's in 2p which results in electrical conductivity only within sheets

Chemical Bonds There 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 other In fact most ionic crystals share to some extent while covalent may share unequally This is a result of De-neg

Chemical Bonds 3) Metallic Bonding Metals 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 neighbors This  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 electrons Let'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 Bonds 3) Metallic Bonding
Let'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- If can't, must share tightly On left, w/ low e-neg & low I.P. they aren't trying to take, but to give, so loosely share Metallic crystals thus conduct electricity and heat

Chemical Bonds 4) Van der Waals Bonds Weakest bond
Usually 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 &  polarity Weakness of the bond is apparent in graphite cleavage cov VdW Condensed Cl

Atomic and Ionic Radii Can'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 radii How get ionic radius of X & Y in XY compound??

Atomic and Ionic Radii a a Need one pure element first
Native Cu. Atomic radius = 1/2 bond length Metals usually FCC or BCC X-ray d100  a Ionic radius = a 2 a 2 a 4

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

Atomic and Ionic Radii However 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

Ions- usually for VI coordination (not 6-fold symm!) x 0.94  IV (Si) x 1.03  VIII x 1.12  XII (metals) Metallic Atoms given for XII (most common) x 0.88  IV x 0.96  VI x 0.98  VIII Covalent bonds given for single bonds Correct 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 solids Particularly Coordination Number

Crystal Chemistry Crystals can be classified into 4 types:
1. Molecular Crystals Neutral molecules held together by weak van der Waals bonds Rare as minerals Mostly organic Weak and readliy decompose, melt, etc Example: graphite

Crystal Chemistry 2. Covalent Crystals
Atoms of similar high e-neg and toward right side of PT Also uncommon as minerals (but less so than molecular) Network of strong covalent bonds with no weak links Directional bonds  low symmetry and density Example: diamond

The diamond structure All carbon atoms in IV coordination
Crystal Chemistry hard-sphere model The diamond structure All carbon atoms in IV coordination FCC unit cell ball-and-stick model polyhedral model blue C only

Crystal Chemistry 3. Metallic Crystals
Atoms of similar e-neg and toward left side of PT Metallic bonds are directionless bonds  high symmetry and density Pure metals have same sized atoms Closest packing  12 nearest mutually-touching neighbors Cubic Closest Packing (CCP) abcabcabc stacking = FCC cell Hexagonal Closest Packing (HCP) ababab = hexagonal cell Also BCC in metals, but this is not CP (VII coordination) More on coordination and closest packing a bit later

Crystal Chemistry 4. Ionic Crystals Most minerals First approximation:
Closest-packed array of oxygen atoms Cations fit into interstices between oxygens Different types of interstitial sites available Occupy only certain types where can fit Occupy only enough of them to attain electric neutrality