1. 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

2. 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!

3. 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 #)

4. 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)

5. 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

6. 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

7. 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

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

9. Shells and Subshells 2 p orbitalspx z
Shells and Subshells
2 p orbitals x y z z py pz x x y y

10. 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

11. 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.

12. The Periodic Table

13. 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

14. 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-)

15. 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)

16. 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..)

17. 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

18. 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

19. 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’

20. 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

21. 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)

22. Chemical Bonds The 3 2(sp2) orbitals are coplanar & 120o apart
Graphite structure
Fig 8-8 of Bloss, Crystallography and Crystal Chemistry. © MSA

23. 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

24. 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

25. 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-)

26. 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

27. 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

28. 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??

29. 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

30. 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.

31. 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

32. Atomic and Ionic Radii Corrections:
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)

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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