Crystal ChemistryCrystal Chemistry

Mineral – “…defined, but generally not Mineral – “…defined, but generally not fixed, chemical composition…”fixed, chemical composition…”

Modern geology – Geochemistry or Modern geology – Geochemistry or GeophysicsGeophysics GeophysicsGeophysics – application of physical – application of physical

principles to study of earthprinciples to study of earth GeochemistryGeochemistry – application of chemical – application of chemical

principles to study of earthprinciples to study of earth high T or low Thigh T or low T

Coming up… a review of basic Coming up… a review of basic chemistrychemistry ElementsElements

protons, neutrons, electronsprotons, neutrons, electrons Bond types and controls on bondsBond types and controls on bonds

Nuclear ChemistryNuclear Chemistry

Atomic number (Z) – number of Atomic number (Z) – number of protonsprotons Specific for particular elements (periodic Specific for particular elements (periodic

table)table) Neutrons – about same mass as Neutrons – about same mass as

protons, different number of neutrons protons, different number of neutrons make isotopesmake isotopes

Atomic weight – sum of weight of Atomic weight – sum of weight of neutrons and protonsneutrons and protons Isotopes - Superscript in front of Isotopes - Superscript in front of

element symbol, atomic weight exact element symbol, atomic weight exact Elements – atomic weight is the average Elements – atomic weight is the average

of abundance of isotopesof abundance of isotopes

Stable IsotopesStable Isotopes Oxygen – Z = 8; three isotopesOxygen – Z = 8; three isotopes Average bulk earth abundance:Average bulk earth abundance:

1616O – 99.757%O – 99.757% 1717O – 0.038%O – 0.038% 1818O – 0.205%O – 0.205%

Materials (minerals, water, air, shells, etc) Materials (minerals, water, air, shells, etc) have variable ratios of these isotopeshave variable ratios of these isotopes

1818O = ratio of O = ratio of 1818O/O/1616OOsamplesample to to 1818O/O/1616OOstandardstandard

Radioactive isotopeRadioactive isotope Potassium (z=19)Potassium (z=19)

4040K has 21 neutronsK has 21 neutrons Natural abundance = 0.0117%Natural abundance = 0.0117% RadioactiveRadioactive Decays to Decays to 4040Ar, basis of one type of age datingAr, basis of one type of age dating Half life = 1.248 x 10Half life = 1.248 x 1099 a a

3939K has 20 neutronsK has 20 neutrons Natural abundance = 93.3%Natural abundance = 93.3% Stable (not radioactive)Stable (not radioactive)

4141K has 22 neutronsK has 22 neutrons Natural abundance = 6.7%Natural abundance = 6.7%

Chemical ReactionsChemical Reactions

Based on electron transfers, charge Based on electron transfers, charge balancebalance

If number of electrons = number of If number of electrons = number of protons, no electrical chargeprotons, no electrical charge

Orbit nucleus in systematic wayOrbit nucleus in systematic way Organized according to energy levelsOrganized according to energy levels Shells filled according to energyShells filled according to energy

Electron Quantum numberElectron Quantum number

Quantum number - reflects energy of Quantum number - reflects energy of electronelectron

Unique for each electronUnique for each electron No two electrons in atom can have same No two electrons in atom can have same

quantum numberquantum number Controls how electrons fill shellsControls how electrons fill shells Controls their chemical reactivityControls their chemical reactivity

Formation of ionsFormation of ions

Ions – excess or deficit of electrons Ions – excess or deficit of electrons relative to protonsrelative to protons Anions – net negative chargeAnions – net negative charge Cations – net positive chargeCations – net positive charge

Valence or Oxidation state is the Valence or Oxidation state is the value of the charge on the ionvalue of the charge on the ion

Configuration of valence electrons Configuration of valence electrons controls whether gain or lose controls whether gain or lose electronelectron Metals – typically lose one or two Metals – typically lose one or two

valence electron: form valence electron: form cationscations Non-metals – typically require a few Non-metals – typically require a few

electrons to fill valence shells: form electrons to fill valence shells: form anionsanions

Valence shells fill systematically – see Valence shells fill systematically – see table 3-3 for how shells filledtable 3-3 for how shells filled Atomic number 1-20 and 31-38 – fill s & p Atomic number 1-20 and 31-38 – fill s & p

subshellssubshells Between atomic number 20 and 31 – Between atomic number 20 and 31 –

shells fill from internal subshells – fill 3d shells fill from internal subshells – fill 3d shell (4s shell filled)shell (4s shell filled)

Transition metalsTransition metals Elements may have differing numbers of Elements may have differing numbers of

shells filledshells filled E.g. Ferrous and Ferric ironE.g. Ferrous and Ferric iron

Fig. 3-Fig. 3-33

Noble Gases, He, Ne, Ar, KrNoble Gases, He, Ne, Ar, Kr

Lose electrons (cations) Lose electrons (cations) to become noble gas coreto become noble gas core

Note the various Note the various oxidation states for the oxidation states for the transition metalstransition metals

Ferric Fe (+3)

Ferrous Fe (+2)

Metallic FeGain

electrons (anions)

Clearly – gain or loss of electrons Clearly – gain or loss of electrons importantimportant

““Quantified” as property called Quantified” as property called ElectronegativityElectronegativity

ElectronegativityElectronegativity Defined by Linus PaulingDefined by Linus Pauling Propensity of element to gain or lose Propensity of element to gain or lose

electronelectron Based on arbitrary scale: Li = 1, C = 2.5, Based on arbitrary scale: Li = 1, C = 2.5,

F = 4F = 4 Low electronegativity - the more likely Low electronegativity - the more likely

to lose electron form cationsto lose electron form cations High electronegativity – likely to gain High electronegativity – likely to gain

electron to form anionselectron to form anions See Table 3-4 for valuesSee Table 3-4 for values

Coming upComing up

1)1) Abundance of elements on earthAbundance of elements on earth

2)2) Types of electron sharing bonds – Types of electron sharing bonds – ionic, covalent, metallicionic, covalent, metallic

3)3) How to estimate bond types from How to estimate bond types from electronegativityelectronegativity

Earth abundances of Earth abundances of elementselements

What elements are most abundant?What elements are most abundant? These elements will make up common These elements will make up common

mineralsminerals What part of earth do they occur?What part of earth do they occur?

Crust?Crust? Bulk earth?Bulk earth?

Crust - 8 common elementsCrust - 8 common elements OO2-2-, Si, Si4+4+, Al, Al3+3+, Fe, Fe2+,3+2+,3+, Ca, Ca2+2+, Na, Na++, K, K++ and Mg and Mg2+2+

Most minerals are made of these elementsMost minerals are made of these elements Determination of crustal abundance – simply collect Determination of crustal abundance – simply collect

large number of samples and measurelarge number of samples and measure Bulk earth compositionBulk earth composition The same 8 elements are common in bulk, but different ratiosThe same 8 elements are common in bulk, but different ratios

Table 3.6Table 3.690% of atoms are Si, Al, & O

Crust

Core/Mantle

Mantle

Bulk Earth composition:Bulk Earth composition: Difficult to assess – impossible to directly Difficult to assess – impossible to directly

sample mantle or coresample mantle or core Estimated byEstimated by

Mass and density based on geophysical Mass and density based on geophysical measurementsmeasurements

Composition of mantle magmas and Composition of mantle magmas and xenolithsxenoliths

Composition of meteoritesComposition of meteorites

Chemical bondingChemical bonding Eight common elements (plus all others) Eight common elements (plus all others) bondbond to to

form mineralsform minerals Bonding controls spatial arrangement of atomsBonding controls spatial arrangement of atoms

Two categoriesTwo categories Sharing of valence electrons: Sharing of valence electrons: ionic, covalent and ionic, covalent and

metallicmetallic No sharing: No sharing: van der Waals and hydrogenvan der Waals and hydrogen

These 5 types of bonds are “end members”These 5 types of bonds are “end members” Rarely just one type or the otherRarely just one type or the other

However: We’ll consider most minerals to be However: We’ll consider most minerals to be ionically bondedionically bonded

Ionic BondingIonic Bonding Transfer of electron(s) from one Transfer of electron(s) from one

element to anotherelement to another Results in filled valence shells of bothResults in filled valence shells of both The electrostatic attraction keep atoms The electrostatic attraction keep atoms

togethertogether The distance between ions depends The distance between ions depends

on attractive forces (Coulomb law) on attractive forces (Coulomb law) and repulsive forces (Born repulsion)and repulsive forces (Born repulsion)

Fig. 3-4Fig. 3-4

Attractive forces

Repulsive forces

Face centered Face centered cubic lattice cubic lattice arrangement of arrangement of halitehalite

Bonding in HaliteBonding in Halite

Equilibrium distance = 2.8 Å

Fig. 2-10Fig. 2-10

Ionic bondingIonic bonding Ions bond so that positive = negative Ions bond so that positive = negative

chargescharges Minerals Minerals mustmust be electrically neutral be electrically neutral NaCl (Halite), Na(Mg,Fe,Li,Al)NaCl (Halite), Na(Mg,Fe,Li,Al)33AlAl66[Si[Si66OO1818]]

(BO(BO33))33(O,OH,F)(O,OH,F)44 (tourmaline – not all ionic (tourmaline – not all ionic bonds here) bonds here)

Characteristics:Characteristics: Ions act like spheresIons act like spheres Alternating cations and anionsAlternating cations and anions One of the strongest bondsOne of the strongest bonds Brittle because like ions repelBrittle because like ions repel Cleavage is commonCleavage is common

Covalent BondsCovalent Bonds Electrons shared when orbitals of two Electrons shared when orbitals of two

different elements overlapdifferent elements overlap Shared by only two atomsShared by only two atoms Differs from metallic (later – all atoms Differs from metallic (later – all atoms

share electrons)share electrons) Electrons move around nucleus of both Electrons move around nucleus of both

atomsatoms

Examples – Diamond and GraphiteExamples – Diamond and Graphite Diamond Diamond

Stable Ne configuration by either gain or loss Stable Ne configuration by either gain or loss of 4 electronsof 4 electrons

Ionic bonding not possible because all Ionic bonding not possible because all electrons exactly the same electronegativityelectrons exactly the same electronegativity

One carbon won’t “steal” electron from One carbon won’t “steal” electron from anotheranother

Instead share electrons – very strong bondingInstead share electrons – very strong bonding

Fig. 3-5Fig. 3-5

Covalent Covalent bonding in bonding in diamonddiamond

• 4 orbitals shown 4 orbitals shown as bonds, call as bonds, call bondsbonds• bonds distortedbonds distorted

Each bold line Each bold line represents represents another similar another similar bondbond

GraphiteGraphite

Fig. 3-6

Similar Similar bonds, but bonds, but only in layersonly in layers

Additional Additional Sharing Sharing electrons, electrons, bonds. bonds.

Metallic bondsMetallic bonds

A type of covalent bondA type of covalent bond Electrons shared without systematic Electrons shared without systematic

change in orbitalschange in orbitals Free to move throughout crystal Free to move throughout crystal

structurestructure Formed with low electronegativity – Formed with low electronegativity –

weakly held valence electronsweakly held valence electrons

Relation between valence-Relation between valence-dependent bondsdependent bonds

Most bonds not purely ionic, covalent Most bonds not purely ionic, covalent or metallicor metallic

Amount of bond type depends on Amount of bond type depends on electronegativity (tendency to give electronegativity (tendency to give up electrons)up electrons)

Greater difference in Greater difference in electronegativity between ions electronegativity between ions means more ionic characteristicmeans more ionic characteristic

Only 1 anion (of 8 common Only 1 anion (of 8 common elements)elements) OxygenOxygen Electronegativity of O = 3.5Electronegativity of O = 3.5 Electronegativity of other common Electronegativity of other common

elements range from 0.8 (K) to 1.8 (Si)elements range from 0.8 (K) to 1.8 (Si)

Qualitative difference in electronegativity:Qualitative difference in electronegativity: O-K = 3.5 – 0.8 = 2.7, more ionic O-K = 3.5 – 0.8 = 2.7, more ionic

characteristicscharacteristics O-Si = 3.5 – 1.8 = 1.7, less ionic O-Si = 3.5 – 1.8 = 1.7, less ionic

characteristicscharacteristics Possible to quantify % ionic bonding:Possible to quantify % ionic bonding:

O-element bonding of 8 common elements O-element bonding of 8 common elements ranges from 50% ionic (Si-O) to 80% ionic (K-ranges from 50% ionic (Si-O) to 80% ionic (K-O)O)

Eq. 3.4Eq. 3.4Fig. 3-10Fig. 3-10

% ionic character = 1 – e-0.25(Xa – Xc)2

Note negative sign, typo in 1st edition

O-Si ~50 % ionic

O-K ~80 % ionic

X = electronegativity of a, anion and c, cation

Native elementsNative elements

Examples: S, Fe, Au…Examples: S, Fe, Au… No differences in electronegativityNo differences in electronegativity Bonding intermediate between Bonding intermediate between

covalent and metalliccovalent and metallic Low electronegativity values (Cu, Ag, Low electronegativity values (Cu, Ag,

Au) favor metallic bondingAu) favor metallic bonding High electronegativity values (non-High electronegativity values (non-

metals, C, S) favor covalent bondingmetals, C, S) favor covalent bonding

Fig. 3-9Fig. 3-9

Con

tinuo

us v

aria

tions

Continuous variations

Limited variations

100% covalent, metallic or ionic

50 % covalent & 50% metallic

Part covalent, part metallic, and part ionic

Range of possible mixtures of electron-Range of possible mixtures of electron-sharing valence bond typessharing valence bond types

PercentagesNot

Allowed

Physical Properties caused by Physical Properties caused by Valence bondsValence bonds

Electrical conductanceElectrical conductance Ionic and covalentIonic and covalent have little have little

conductanceconductance MetallicMetallic highly conductive highly conductive

SolubilitySolubility IonicIonic highly soluble (think halite) highly soluble (think halite)

BrittlenessBrittleness IonicIonic highly brittle – cleavage common highly brittle – cleavage common

Halite – perfect {001} cubic cleavageHalite – perfect {001} cubic cleavage

HardnessHardness Covalent Covalent – strongest bonding, so – strongest bonding, so

hardest. Think diamondhardest. Think diamond MalleableMalleable

MetallicMetallic easily worked easily worked

Non-valence bondsNon-valence bonds

Result of asymmetric charge Result of asymmetric charge distributiondistribution Create electrostatic forcesCreate electrostatic forces Two typesTwo types

Van der Waals and HydrogenVan der Waals and Hydrogen

Hydrogen BondingHydrogen Bonding Ice exampleIce example

HH22O is polar moleculeO is polar molecule 2 H atoms at angle to O atom (not straight 2 H atoms at angle to O atom (not straight

line)line) O is more electronegative than HO is more electronegative than H O = 3.5, H = 2.1O = 3.5, H = 2.1 O “claims” more of the electronO “claims” more of the electron Net negative charge on O side of moleculeNet negative charge on O side of molecule

The asymmetric charges allow solidifying The asymmetric charges allow solidifying liquid when T < 0º C @ 1 atm Pliquid when T < 0º C @ 1 atm P

Fig. 3-11 & 18-2Fig. 3-11 & 18-2

Asymmetrical charge - polar

Hydrogen bond

Hexagonal symmetry

Ice – viewed down c axis

Van der WallsVan der Walls Carbon exampleCarbon example

Graphite – carbon bonded in sheetsGraphite – carbon bonded in sheets Bonding within sheets is covalent – Bonding within sheets is covalent – bonds bonds Over time electrons evenly distributedOver time electrons evenly distributed At given time, excess electrons on one side At given time, excess electrons on one side

of sheetof sheet Creates weak electrostatic attractionCreates weak electrostatic attraction

Physical propertiesPhysical properties Typically softTypically soft Graphite good lubricantGraphite good lubricant

Fig. 3-12Fig. 3-12

Covalent bonds within the sheets

Van der Waal forces between the sheets,Caused by bonds on top of sheets

Other examples:talcserpentine/smectite

Atoms and ion sizeAtoms and ion size

Assume that atoms are spheresAssume that atoms are spheres Clear simplification – electron Clear simplification – electron

distributions are not sphericaldistributions are not spherical Assumption works well for arrangement Assumption works well for arrangement

in solidsin solids Atoms pack together in regular Atoms pack together in regular

arrangementarrangement

If we assume the ions are spheresIf we assume the ions are spheres Can assume an Can assume an effective radiuseffective radius Measure distance between adjacent atoms in the Measure distance between adjacent atoms in the

solidsolid Measured with X-ray diffraction, d spacingMeasured with X-ray diffraction, d spacing

Effective radius a measure of size of the atomsEffective radius a measure of size of the atoms

Very important – one control of how atoms Very important – one control of how atoms pack togetherpack together

Bond length – sum of effective radius of Bond length – sum of effective radius of two adjacent atomstwo adjacent atoms Metallic bonds: all same effective radiusMetallic bonds: all same effective radius

½ distance between nuclei½ distance between nuclei Ionic bonds: effective radius different between Ionic bonds: effective radius different between

two atomstwo atoms Not ½ distance between nucleiNot ½ distance between nuclei

Fig. 3-13Fig. 3-13

Metallic bondingBond length = d spacingIonic radius = ½*d spacing

Covalent and ionic bondingBond length = d spacingd spacing = Ra + Rc

Clearly – what types of ions present Clearly – what types of ions present control ionic radiuscontrol ionic radius

Primary variables controlling ionic Primary variables controlling ionic radius:radius: Oxidation state Oxidation state – i.e. charge on ion– i.e. charge on ion Coordination number Coordination number – i.e. number of – i.e. number of

ions surrounding central ionsions surrounding central ions

Oxidation stateOxidation state

Inversely relatedInversely related More oxidized (less negative, more More oxidized (less negative, more

positive) means smaller effective radiuspositive) means smaller effective radius e.g., Fee.g., Fe3+3+ or Fe or Fe2+2+

Cations smaller than anions, OCations smaller than anions, O2-2- very very largelarge

Positive charge holds electron closer to Positive charge holds electron closer to nucleusnucleus

Fig. 3-15Fig. 3-15ChargeCharge

(higher oxidation state)(higher oxidation state)

Ion

ic r

ad

ius

(Å)

Coordination numbers

CoordinationCoordination

Positive correlation – high Positive correlation – high coordination number, smaller ionscoordination number, smaller ions Think of solids as large anions Think of solids as large anions

surrounding small spaces filled by cationssurrounding small spaces filled by cations Size of space determined by effective Size of space determined by effective

radius of anionsradius of anions Cation effective radius changes to fill Cation effective radius changes to fill

spacespace

Fig. 3-16Fig. 3-16Coordination numberCoordination number

Ion

ic r

ad

ius

Note – increase in Note – increase in ionic radius ionic radius independent of independent of charge on ioncharge on ion