Mineral ChemistryMineral 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 system

Difference between

Fo = Mg2SiO4

and

Fo= 51.5% SiO2 and 48.5% MgO

Mineral ChemistryMineral Chemistry

Homework Problem HandoutHomework Problem Handout

1) 2 Pyroxenes1) 2 PyroxenesConvert wt% oxides to formula. COOKBOOKConvert wt% oxides to formula. COOKBOOK

2) Unit cell dimensions & density of olivine2) Unit cell dimensions & density of olivineCalculate the Unit Cell Content.Calculate the Unit Cell Content.

Remember ducky/fishy? Z= # of motifs/u.c. Remember ducky/fishy? Z= # of motifs/u.c.

Now motif = some "molecule"Now motif = some "molecule"

Use method of Scientific Analysis!Use method of Scientific Analysis!

Mineral ChemistryMineral Chemistry

Method of Scientific AnalysisMethod of Scientific AnalysisWrite single equation to get from what have to what want.Write single equation to get from what have to what want.

Have: u. c. Volume (in AHave: u. c. Volume (in A33) & formula A = 10) & formula A = 10-8-8 cm. cm.

Want Z = # formula units/ u.c.Want Z = # formula units/ u.c.

Example 8 mi/hr = ? in ft/sec?Example 8 mi/hr = ? in ft/sec?

If do all on one line with #'s and units, If do all on one line with #'s and units,

If units work # must!If units work # must!

Want formula units/mole (Avocado’s #)Want formula units/mole (Avocado’s #)

Composition of the Earth’s CrustComposition of the Earth’s CrustWeight % Atom % Ionic Radius Volume %

O 46.60 62.55 1.40 93.8Si 27.72 21.22 0.42 0.9Al 8.13 6.47 0.51 0.5Fe 5.00 1.92 0.74 0.4Ca 3.63 1.94 0.99 1.0Na 2.83 2.64 0.97 1.3K 2.59 1.42 1.33 1.8Mg 2.09 1.84 0.66 0.3

Total 98.59 100.00 100.00

Most common silicates are from theseMost common silicates are from these

O alone = 94 vol. % of crustO alone = 94 vol. % of crust

Perhaps good to think of crust as a packed O array with Perhaps good to think of crust as a packed O array with interspersed metal cations in the interstices!interspersed metal cations in the interstices!

Analogy works for minerals too (they make up the crust)Analogy works for minerals too (they make up the crust)

Chemistry ReviewChemistry Review

Bohr model for the atomBohr model for the atom

Nucleus = p + n Nucleus = p + n Z (Atomic #) Z (Atomic #)

Gives elements their identity (properties) Gives elements their identity (properties) (~ all mass) (~ all mass)

p + n (variable) p + n (variable) atomic weight (isotopes) atomic weight (isotopes)

At. Wt. is real # due to average of isotopesAt. Wt. is real # due to average of isotopes

ee-- spin around atom and give it it's size (statistical size) spin around atom and give it it's size (statistical size) Atomic radii in the range 0.5-2.5 AAtomic radii in the range 0.5-2.5 A

ee-- in special shells w/ particular Energy levels in special shells w/ particular Energy levels QuantizedQuantized

Chemistry ReviewChemistry Review

Quantized energy levels Quantized energy levels (Fig. 4.12)(Fig. 4.12)

Rel

ativ

e E

nerg

yR

elat

ive

Ene

rgy

n = 1 K 2 L 3 M 4 N 5 O 6 P 7 Qn = 1 K 2 L 3 M 4 N 5 O 6 P 7 Q

ss

ss

ss

ss

ssss

ss

pp

pp

pp

pppp

pp

dd

dddd

dd

dd

ff

ffff

Note that the energy Note that the energy does not necessarily does not necessarily increase K increase K L L M M N etc. N etc.4s < 3d4s < 3d

Chemistry ReviewChemistry ReviewShells and SubshellsShells and Subshells

innermostinnermost KK (n = 1)(n = 1) 2e2e ss

(lowest E)(lowest E) LL (n = 2)(n = 2) 8e8e s, ps, p

MM (n = 3)(n = 3) 18e18e s, s, p, dp, d

outer outer NN (n = 4)(n = 4) 32e32e s, p, d, fs, p, d, f

(generally higher E)(generally higher E)

higher levels not filledhigher levels not filled

Chemistry ReviewChemistry ReviewShells and SubshellsShells and Subshells

1s 2s and 3s orbitals1s 2s and 3s orbitals

Shells and SubshellsShells and Subshells

2 p orbitals2 p orbitals xx

zz

yy

yy

xx

zzzz

yy

xx

ppxx

ppyy ppzz

d orbitalsd orbitals

yyxx

zzdd xx22-y-y22

zz

xxyy

dd xzxz zz

yy xx

dd xyxy

xxyy

zzdd yzyz

zz

yy xx

dd zz22

Shell K LSubshell s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 5g1. H 12. He 23. Li 2 14. Be 2 25. B 2 2 16. C 2 2 27. N 2 2 38. O 2 2 49. F 2 2 510. Ne 2 2 611. Na 2 2 6 112. Mg 2 2 6 213. Al 2 2 6 2 114. Si 2 2 6 2 215. P 2 2 6 2 316. S 2 2 6 2 417. Cl 2 2 6 2 518 Ar 2 2 6 2 619. K 2 2 6 2 6 120. Ca 2 2 6 2 6 221. Sc 2 2 6 2 6 1 222. Ti 2 2 6 2 6 2 223. V 2 2 6 2 6 3 224. Cr 2 2 6 2 6 5 125. Mn 2 2 6 2 6 5 226. Fe 2 2 6 2 6 6 227. Co 2 2 6 2 6 7 228. Ni 2 2 6 2 6 8 229. Cu 2 2 6 2 6 10 130. Zn 2 2 6 2 6 10 231. Ga 2 2 6 2 6 10 2 132. Ge 2 2 6 2 6 10 2 233. As 2 2 6 2 6 10 2 334. Se 2 2 6 2 6 10 2 435. Br 2 2 6 2 6 10 2 536. Kr 2 2 6 2 6 10 2 637. Rb 2 2 6 2 6 10 2 6 138. Sr 2 2 6 2 6 10 2 6 239. Y 2 2 6 2 6 10 2 6 1 240. Zr 2 2 6 2 6 10 2 6 2 241. Nb 2 2 6 2 6 10 2 6 4 142. Mo 2 2 6 2 6 10 2 6 5 143. Tc 2 2 6 2 6 10 2 6 5 244. Ru 2 2 6 2 6 10 2 6 7 145. Rh 2 2 6 2 6 10 2 6 8 146. Pd 2 2 6 2 6 10 2 6 1047. Ag 2 2 6 2 6 10 2 6 10 148. Cd 2 2 6 2 6 10 2 6 10 249. In 2 2 6 2 6 10 2 6 10 2 150. Sn 2 2 6 2 6 10 2 6 10 2 251. Sb 2 2 6 2 6 10 2 6 10 2 352. Te 2 2 6 2 6 10 2 6 10 2 453. I 2 2 6 2 6 10 2 6 10 2 5

TABLE 3.6 Electron Configurations of the AtomsM N 0

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

The Periodic TableThe Periodic Table

Notation: Al = 1sNotation: Al = 1s22 2s 2s22 2p 2p66 3s 3s22 3p 3p11

Atoms may not look like thisAtoms may not look like this

It's only a modelIt's only a model

But it's a pretty good oneBut it's a pretty good one

We'll see that these subshell shapes explain a lot of We'll see that these subshell shapes explain a lot of macroscopic propertiesmacroscopic properties

Characteristics of an atom depend a lot on eCharacteristics of an atom depend a lot on e-- configuration configuration

This results in part from # p & electrical neutralityThis results in part from # p & electrical neutrality

But atoms with a different # of p & e, but with similar But atoms with a different # of p & e, but with similar e-configurations have similar propertiese-configurations have similar properties

It is the outermost shell or It is the outermost shell or valencevalence e e-- s that are fundamental s that are fundamental

Similar outermost shell configurations Similar outermost shell configurations GroupsGroups in the in the Periodic Table (Table 4.8 p.188)Periodic Table (Table 4.8 p.188)

alkali metalsalkali metals (Ia) have a lonely e (Ia) have a lonely e-- in outer shell in outer shell

halogenshalogens (VIIa) have 7 e (VIIa) have 7 e--

inert gasesinert gases (VIIIa) have 8e (VIIIa) have 8e-- a magic #... filled s & p a magic #... filled s & p

(He only has s with 2 e(He only has s with 2 e--))

Other elements try to gain this stable inert gas config.Other elements try to gain this stable inert gas config.If have one extra (alkalis) will readily lose it if it can find If have one extra (alkalis) will readily lose it if it can find

another way to attain charge balanceanother way to attain charge balanceThis results in an This results in an ionion with a +1 with a +1 valencevalenceGroup II metals will lose 2 eGroup II metals will lose 2 e-- +2 valence +2 valenceHalogens will capture an eHalogens will capture an e-- inert gas config. inert gas config. -1 -1

Ionization PotentialIonization Potential (T 3.7) (T 3.7)ElectronegativityElectronegativity is the ability of an atom is the ability of an atom in a crystalin a crystal

structurestructure to attract electrons into its outer shell to attract electrons into its outer shellIn general, electronegativity increasesIn general, electronegativity increases

(except for inert gases which are very low)

Elements are classified as:Elements are classified as:MeMetatalsls w/ e-neg < 1.9 thus lose e w/ e-neg < 1.9 thus lose e-- and and cationscations

NonNonmetmetalsals > 2.1> 2.1 thus gain ethus gain e-- and and anionsanions

MetalloidsMetalloids intermediate (B, Si, Ge, As, Sb, Te, Po..) intermediate (B, Si, Ge, As, Sb, Te, Po..)

Chemical BondsChemical BondsElectrical in nature- responsible for most mineral propertiesElectrical in nature- responsible for most mineral properties1) Ionic1) Ionic Na: low 1st IP Na: low 1st IP e e-- Na Na++ (Ne config) (Ne config)

Cl: high e-neg takes e- & = ClCl: high e-neg takes e- & = Cl-- (Ar config) (Ar config)Now they have opposite charges & attract Now they have opposite charges & attract bond bond

(really a very unequal sharing)(really a very unequal sharing)Bonding is strong (high melting point)Bonding is strong (high melting point)But easily disrupted by polarized solvents (water)But easily disrupted by polarized solvents (water)Poor electrical conductors.Poor electrical conductors.Strength Strength (1/bond length) & valence (1/bond length) & valenceAlso Also non-directionalnon-directional (more later), so symm. is a packing (more later), so symm. is a packing

function and thus rather high (isometric common).function and thus rather high (isometric common).If e-neg of 2 atoms differs by 2.0 or more will If e-neg of 2 atoms differs by 2.0 or more will ionic ionic

Chemical BondsChemical Bonds2) Covalent2) Covalent

Consider 2 Cl atoms each trying to steal each other's eConsider 2 Cl atoms each trying to steal each other's e -- = 1s = 1s22 2s 2s22 2 p 2 p66 3s 3s22 3p 3p55

Can't do, but if draw close until overlap an outer orbital, Can't do, but if draw close until overlap an outer orbital, perhaps can share whereby 2 eperhaps can share whereby 2 e-- "fill" the remaining 3p "fill" the remaining 3p shell of each Clshell of each Cl

Actually fill it only 1/2 the time for each, but better than nothingActually fill it only 1/2 the time for each, but better than nothing

In fact this compulsion to stay overlapped & share results In fact this compulsion to stay overlapped & share results in a strong bond in a strong bond Cl Cl22

This is the covalent or shared eThis is the covalent or shared e-- bond (the Socialist bond) bond (the Socialist bond) Double bonds when 2 orbitals sharedDouble bonds when 2 orbitals shared

Triple bonds when 3 orbitals sharedTriple bonds when 3 orbitals shared

Chemical BondsChemical BondsHybrid orbitalsHybrid orbitals

Carbon: Carbon: | | || || 1s 2s 2p1s 2s 2p 1s 1s 2(sp 2(sp33))

C-C-C angle = 109o 28’

Fig 8-8 of Bloss, Crystallography and Crystal Chemistry. © MSA

Chemical BondsChemical BondsHybrid orbitalsHybrid orbitals

2(sp2(sp33) is tetrahedrally shaped ) is tetrahedrally shaped (energy is identical)(energy is identical)

Larger overlap Larger overlap stronger stronger

Directional:Directional: each C is tetrahedrally coordinated each C is tetrahedrally coordinated with 4 others (& each of them with 4 others...)with 4 others (& each of them with 4 others...)

C-C-C bond angle fixed at 109C-C-C bond angle fixed at 109oo 28' (max. overlap) 28' (max. overlap)

Note Face-centered Cubic latticeNote Face-centered Cubic lattice

The directional character The directional character lower coordination & lower coordination & symmetry, densitysymmetry, density

Chemical BondsChemical BondsHybrid orbitalsHybrid orbitals

Alternatively:Alternatively:

Carbon: Carbon: | | || || || 1s 2s 2p1s 2s 2p 1s 2(sp 1s 2(sp22) 2p) 2p

As most organic chemists know, C is a flexible elementAs most organic chemists know, C is a flexible element

In fact, many atoms in the center of the Periodic Table In fact, many atoms in the center of the Periodic Table with partially filled valence shells are variable in how with partially filled valence shells are variable in how they attain stability (this includes Si)they attain stability (this includes Si)

Chemical BondsChemical BondsThe 3 2(spThe 3 2(sp22) orbitals are coplanar & 120) orbitals are coplanar & 120oo apart apart

Graphite structureGraphite structure

Fig 8-8 of Bloss, Crystallography and Crystal Chemistry. © MSA

Chemical BondsChemical BondsThe 3 2(spThe 3 2(sp22) orbitals are coplanar & 120) orbitals are coplanar & 120oo apart apart

Graphite structureGraphite structure

Overlap similar to diamond w/in sheets (strong Overlap similar to diamond w/in sheets (strong too!)too!)

Must Must Hexagonal Crystal Class Hexagonal Crystal Class

Note Note -bonding-bonding between remaining 2p's between remaining 2p's

This results in This results in delocalizeddelocalized e e-- 's in 2p which results 's in 2p which results in electrical conductivity only within sheetsin electrical conductivity only within sheets

Chemical BondsChemical Bonds

There are other hybrids as well There are other hybrids as well (dsp(dsp22 in CuO- planar X) in CuO- planar X) ee-- may resonate in bonds of non-identical may resonate in bonds of non-identical

atoms & give a partial ionic character if one atoms & give a partial ionic character if one much more e-neg than othermuch more e-neg than other

In fact most ionic crystals share to some extent In fact most ionic crystals share to some extent while covalent may share unequallywhile covalent may share unequally

This is a result of This is a result of e-nege-neg

Chemical BondsChemical Bonds3) Metallic Bonding3) Metallic Bonding

Metals are on the left of the P.T. Metals are on the left of the P.T.

Have few, loosely held valence eHave few, loosely held valence e--

If closely pack them can get up to 12 "touching" nearest If closely pack them can get up to 12 "touching" nearest neighborsneighbors

This This a high density of valence e a high density of valence e-- around any given atom & also around any given atom & also a high density of neighbor atoms around the loose valence ea high density of neighbor atoms around the loose valence e--

The effect is to show such a general attraction for these eThe effect is to show such a general attraction for these e -- that that they become free to maintain an electrical neutrality in the xl as they become free to maintain an electrical neutrality in the xl as a whole... a sea of mobile electronsa whole... a sea of mobile electrons

Let's call it the left-side equivalent of the covalent bondLet'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(On the right side the e-neg is high & atoms are trying to take e --))

Chemical BondsChemical Bonds3) Metallic Bonding3) Metallic Bonding

Let's call it the left-side equivalent of the covalent bondLet's call it the left-side equivalent of the covalent bond

On the right side the e-neg is high & atoms are trying On the right side the e-neg is high & atoms are trying to take eto take e--

If can't, must share If can't, must share tightlytightly

On left, w/ low e-neg & low I.P. they aren't trying to On left, w/ low e-neg & low I.P. they aren't trying to take, but to give, so take, but to give, so looselyloosely shareshare

Metallic crystals thus conduct electricity and heatMetallic crystals thus conduct electricity and heat

Chemical BondsChemical Bonds4) Van der Waals Bonds4) Van der Waals Bonds

Weakest bondWeakest bond

Usually between neutral molecules (even large ones like Usually between neutral molecules (even large ones like graphite sheets)graphite sheets)

Aided by polar or partial polar covalent bonds.Aided by polar or partial polar covalent bonds.Even stable A-A bonds like OEven stable A-A bonds like O22 or Cl or Cl22 will get slightly polar at will get slightly polar at

low T & condense to liquid & ordered solid as vibration low T & condense to liquid & ordered solid as vibration slows & slows & polarity polarity

Weakness of the bond is apparent in graphite cleavageWeakness of the bond is apparent in graphite cleavage

Condensed ClCondensed Cl

cov VdWcov VdW

Atomic and Ionic RadiiAtomic and Ionic RadiiCan't absolutely determine: eCan't absolutely determine: e-- cloud is nebulous & cloud is nebulous &

based on probability of encountering an ebased on probability of encountering an e --

In crystalline solids the center-to-center distance = In crystalline solids the center-to-center distance = bond lengthbond length & is accepted to = & is accepted to = sum of ionic radiisum of ionic radii

How get ionic radius of X & Y in XY compound??How get ionic radius of X & Y in XY compound??

Atomic and Ionic RadiiAtomic and Ionic RadiiNeed one pure element firstNeed one pure element first

Native Cu. Atomic radius = 1/2 bond lengthNative Cu. Atomic radius = 1/2 bond length

Metals usually FCC or BCCMetals usually FCC or BCC

a

a

X-ray d100 a

Ionic radius = 24

2a

Atomic and Ionic RadiiAtomic and Ionic RadiiWe can do this on We can do this on ourour lab!! lab!!

If can look up lattice type (really space group)If can look up lattice type (really space group)

BCC uses BCC uses bodybody diagonal rather than face diagonal rather than face

With compounds, don't know what % of bondlength to With compounds, don't know what % of bondlength to which atom, but if know one can get otherwhich atom, but if know one can get other

So can keep on as accumulate more & more compounds So can keep on as accumulate more & more compounds from known setfrom known set

O O lots of cations etc. lots of cations etc.

Atomic and Ionic RadiiAtomic and Ionic RadiiHowever there are variations:However there are variations:

1) Variations in related to % ionic or covalent character 1) Variations in related to % ionic or covalent character (or VdW)(or VdW)

2) Variations in # of closest neighbors (coordination #) 2) Variations in # of closest neighbors (coordination #)

Handout of Atomic and Ionic RadiiHandout of Atomic and Ionic Radii

Atomic and Ionic RadiiAtomic and Ionic RadiiCorrections:Corrections:

Ions- usually for VI coordination (not 6-fold symm!) Ions- usually for VI coordination (not 6-fold symm!) x 0.94 x 0.94 IV (Si) IV (Si) x 1.03 x 1.03 VIII VIII x 1.12 x 1.12 XII (metals) XII (metals)

Metallic Atoms given for XII (most common) Metallic Atoms given for XII (most common) x 0.88 x 0.88 IV IV x 0.96 x 0.96 VI VI x 0.98 x 0.98 VIII VIII

Covalent bonds given for Covalent bonds given for singlesingle bonds bonds Correct for double, triple (stronger Correct for double, triple (stronger shorter) shorter)

Atomic and Ionic RadiiAtomic 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 ChemistryCrystal ChemistryCrystals can be classified into 4 types:Crystals can be classified into 4 types:

1. Molecular Crystals1. Molecular CrystalsNeutral molecules held together by weak van der Waals bondsNeutral molecules held together by weak van der Waals bonds

Rare as mineralsRare as minerals

Mostly organicMostly organic

Weak and readliy Weak and readliy

decompose, melt, etcdecompose, melt, etc

Example: Example: graphitegraphite

Crystal ChemistryCrystal Chemistry2. Covalent Crystals2. Covalent Crystals

Atoms of similar high e-neg and toward right side of PTAtoms of similar high e-neg and toward right side of PT

Also uncommon as minerals (but less so than molecular)Also uncommon as minerals (but less so than molecular)

Network of strong covalentNetwork of strong covalent

bonds with no weak linksbonds with no weak links

Directional bonds Directional bonds low low

symmetry and densitysymmetry and density

Example: Example: diamonddiamond

Crystal ChemistryCrystal Chemistry

The diamond structureThe diamond structureAll carbon atoms in IV coordinationAll carbon atoms in IV coordination

ball-and-stick modelball-and-stick model polyhedral modelpolyhedral model blue C onlyblue C only

hard-sphere modelhard-sphere model

FCC unit cellFCC unit cell

Crystal ChemistryCrystal Chemistry3. Metallic Crystals3. Metallic Crystals

Atoms of similar e-neg and toward left side of PTAtoms of similar e-neg and toward left side of PT

Metallic bonds are directionless bonds Metallic bonds are directionless bonds high high

symmetry and densitysymmetry and density

Pure metals have same sized atomsPure metals have same sized atoms

Closest packingClosest packing 12 nearest mutually-touching neighbors 12 nearest mutually-touching neighbors

Cubic Closest Packing (CCP) abcabcabc stacking = FCC cellCubic Closest Packing (CCP) abcabcabc stacking = FCC cell

Hexagonal Closest Packing (HCP) ababab = hexagonal cellHexagonal Closest Packing (HCP) ababab = hexagonal cell

Also BCC in metals, but this is not CP (VII coordination)Also BCC in metals, but this is not CP (VII coordination)

More on coordination and closest packing a bit laterMore on coordination and closest packing a bit later

Crystal ChemistryCrystal Chemistry4. Ionic Crystals4. Ionic Crystals

Most mineralsMost minerals

First approximation: First approximation: Closest-packed array of oxygen atoms Closest-packed array of oxygen atoms Cations fit into interstices between oxygensCations fit into interstices between oxygens

Different types of interstitial sites availableDifferent types of interstitial sites available Occupy only certain types where can fitOccupy only certain types where can fit Occupy only enough of them to attain electric Occupy only enough of them to attain electric

neutralityneutrality