OreOre MineralogyMineralogy (EMR(EMR 331)331)
CrystalCrystal chemistrychemistry CrystalCrystal ChemistryChemistry
PartPart 1:1:
Atoms,Atoms, ElementsElements andand IonsIons WhatWhat isis CrystalCrystal Chemistry?Chemistry?
studystudy ofof thethe atomicatomic structure,structure, physicalphysical properties,properties, andand chemicalchemical compositioncomposition ofof crystallinecrystalline materialmaterial basicallybasically inorganicinorganic chemistrychemistry ofof solidssolids thethe structurestructure andand chemicalchemical propertiesproperties ofof thethe atomatom andand elementselements areare atat thethe corecore ofof crystalcrystal chemistrychemistry therethere areare onlyonly aa handfulhandful ofof elementselements thatthat makemake upup mostmost ofof thethe rockrock --formingforming mineralsminerals ofof thethe earthearth ChemicalChemical LayersLayers ofof thethe EarthEarth
SiO2 – 45% MgO – 37% FeO – 8% Al2O3 – 4% CaO – 3% others – 3%
Fe – 86% S – 10% Ni – 4% CompositionComposition ofof thethe EarthEarth ’’ss CrustCrust AverageAverage compositioncomposition ofof thethe EarthEarth ’’ss CrustCrust (by(by weight,weight, elements,elements, andand volume)volume) TheThe AtomAtom
The Bohr Model The Schrodinger Model Nucleus - contains most of the weight (mass) of the atom - composed of positively charge particles (protons) and neutrally charged particles (neutrons) Electron Shell - insignificant mass - occupies space around the nucleus defining atomic radius - controls chemical bonding behavior of atoms ElementsElements andand IsotopesIsotopes
Elements are defined by the number of protons in the nucleus (atomic number). In a stable element (non -ionized), the number of electrons is equal to the number of protons Isotopes of a particular element are defined by the total number of neutrons in addition to the number of protons in the nucleus (isotopic number). Various elements can have multiple (2-38) stable isotopes, some of which are unstable (radioactive) Isotopes of a particular element have the same chemical properties, but different masses. Isotopes of Titanium (Z=22) Isotope Half-life Spin Parity Decay Mode(s) or Abundance 38Ti 0+ 39Ti 26 ms (3/2+) EC=100, ECP+EC2P ~ 14 40Ti 50 ms 0+ EC+B+=100 41Ti 80 ms 3/2+ EC+B+=100, ECP ~ 100 42Ti 199 ms 0+ EC+B+=100 43Ti 509 ms 7/2- EC+B+=100 44Ti 63 y 0+ EC=100 45Ti 184.8 m 7/2- EC+B+=100 46Ti stable 0+ Abundance=8.0 1 47Ti stable 5/2- Abundance=7.3 1 48Ti stable 0+ Abundance=73.8 1 49Ti stable 7/2- Abundance=5.5 1 50Ti stable 0+ Abundance=5.4 1 51Ti 5.76 m 3/2- B-=100 52Ti 1.7 m 0+ B-=100 53Ti 32.7 s (3/2)- B-=100 54Ti 0+ 55Ti 320 ms (3/2-) B-=100 56Ti 160 ms 0+ B-=100, B-N=0.06 sys 57Ti 180 ms (5/2-) B-=100, B-N=0.04 sys 58Ti 0+ 59Ti (5/2-) B-=? 60Ti 0+ B-=? 61Ti (1/2-) B-=?, B-N=? Source: R.B. Firestone UC-Berkeley StructureStructure ofof thethe PeriodicPeriodic TableTable
# of Electrons in Outermost Shell Noble Gases
Anions
------Transition Metals------
Primary Shell being filled Ions,Ions, IonizationIonization Potential,Potential, andand ValenceValence StatesStates
Cations – elements prone to give up one or more electrons from their outer shells; typically a metal element
Anions – elements prone to accept one or more electrons to their outer shells; always a non -metal element
Ionization Potential – measure of the energy necessary to strip an element of its outermost electron
Electronegativity – measure strength with which a nucleus attracts electrons to its outer shell
Valence State (or oxidation state) – the common ionic configuration(s ) of a particular element determined by how many electrons are typically stripped or added to an ion 1st Ionization Potential
Anions
Cations
Elements with a single outer s orbital electron
Electronegativity ValenceValence StatesStates ofof IonsIons commoncommon toto RockRock --formingforming MineralsMinerals Cations – generally +1 +2 relates to column +3 +4 +5 +6 +7 in the periodic table; most -2 -1 transition metals have a +2 ------Transition Metals------valence state for transition metals, relates to having two electrons in outer Anions – relates electrons needed to completely fill outer shell Anionic Groups – tightly bound ionic complexes with net negative charge CrystalCrystal ChemistryChemistry
PartPart 2:2:
BondingBonding andand IonicIonic RadiiRadii ChemicalChemical BondingBonding inin MineralsMinerals
BondingBonding forcesforces areare electricalelectrical inin naturenature (related(related toto chargedcharged particles)particles) BondBond strengthstrength controlscontrols mostmost physicalphysical andand chemicalchemical propertiesproperties ofof mineralsminerals (in(in general,general, thethe strongerstronger thethe bond,bond, thethe harderharder thethe crystal,crystal, higherhigher thethe meltingmelting point,point, andand thethe lowerlower thethe coefficientcoefficient ofof thermalthermal expansion)expansion) FiveFive generalgeneral typestypes bondingbonding types:types: IonicIonic CovalentCovalent MetallicMetallic vanvan derder WaalsWaals HydrogenHydrogen CommonlyCommonly differentdifferent bondbond typestypes occuroccur inin thethe samesame mineralmineral IonicIonic BondingBonding
CommonCommon betweenbetween elementselements thatthat will...will... 1) easilyeasily exchangeexchange electronselectrons soso asas toto stabilizestabilize theirtheir outerouter shellsshells (i.e.(i.e. becomebecome moremore inertinert gasgas --like)like) 2) createcreate anan electronicallyelectronically neutralneutral bondbond betweenbetween cationscations andand anionsanions Example:Example: NaClNaCl Na (1s22s22p63s1) –> Na +(1s22s22p6) + e - Cl (1s22s22p63s23p5) + e - –> Cl - (1s22s22p63s23p6) PropertiesProperties ofof IonicIonic BondsBonds
ResultsResults inin mineralsminerals displayingdisplaying moderatemoderate degreesdegrees ofof hardnesshardness andand specificspecific gravity,gravity, moderatelymoderately highhigh meltingmelting points,points, highhigh degreesdegrees ofof symmetry,symmetry, andand areare poorpoor conductorsconductors ofof heatheat (due(due toto ionicionic stability)stability) StrengthStrength ofof ionicionic bondsbonds areare related:related: 1)1) thethe spacingspacing betweenbetween ionsions 2)2) thethe chargecharge ofof thethe ionsions CovalentCovalent BondingBonding
formed by sharing of outer shell electrons strongest of all chemical bonds produces minerals that are insoluble, high melting points, hard, nonconductive (due to localization of electrons), have low symmetry (due to directional bonding). common among elements with high numbers of vacancies in the outer shell (e.g. C, Si , Al, S) Diamond TendenciesTendencies forfor IonicIonic vs.vs. CovalentCovalent PairingPairing
Ionic Pairs Covalent Pairs MetallicMetallic BondingBonding
atomicatomic nucleinuclei andand innerinner filledfilled electronelectron shellsshells inin aa ““seasea ”” ofof electronselectrons mademade upup ofof unboundunbound valencevalence electronselectrons YieldsYields mineralsminerals withwith mineralsminerals thatthat areare soft,soft, ductile/malleable,ductile/malleable, highlyhighly conductiveconductive (due(due toto easilyeasily mobilemobile electrons).electrons). NonNon --directionaldirectional bondingbonding producesproduces highhigh symmetrysymmetry vanvan derder WaalsWaals (Residual)(Residual) BondingBonding
createdcreated byby weakweak bondingbonding ofof oppositelyoppositely dipolarizeddipolarized electronelectron cloudsclouds commonlycommonly occursoccurs aroundaround covalentlycovalently bondedbonded elementselements producesproduces solidssolids thatthat areare soft,soft, veryvery poorpoor conductors,conductors, havehave lowlow meltingmelting points,points, lowlow symmetrysymmetry crystalscrystals HydrogenHydrogen BondingBonding
ElectrostaticElectrostatic H+ bondingbonding betweenbetween anan H+H+ ionion withwith anan anionanion Close packing of Anions oror anionicanionic complexcomplex polarized molecules oror withwith aa polarizedpolarized moleculesmolecules WeakerWeaker thanthan ionicionic oror covalent;covalent; stronger than van polarized H 2O stronger than van Ice derder WaalsWaals molecule SummarySummary ofof BondingBonding CharacteristicsCharacteristics MultipleMultiple BondingBonding inin MineralsMinerals
Graphite – covalently bonded sheets of C loosely bound by van der Waals bonds.
Mica – strongly bonded silica tetrahedra sheets (mixed covalent and ionic) bound by weak ionic and hydrogen bonds
Cleavage planes commonly correlate to planes of weak ionic bonding in an otherwise tightly bound atomic structure AtomicAtomic RadiiRadii
Absolute radius of an atom based on location of the maximum density of outermost electron shell Effective radius dependent on the charge, type, size, and number of neighboring atoms/ions - in bonds between identical atoms, this is half the interatomic distance - in bonds between different ions, the distance between the ions is controlled by the attractive and repulsive force between the two ions and their charges
F = k [(q +)(q -)/d 2] Coulomb ’s law Control of CN (# of nearest neighbors) on ionic radius
Reflects expansion of cations into larger “pore spaces” between anion neighbors CrystalCrystal ChemistryChemistry
PartPart 3:3: CoordinationCoordination ofof IonsIons PaulingPauling ’’ss RulesRules CrystalCrystal StructuresStructures CoordinationCoordination ofof IonsIons
ForFor mineralsminerals formedformed largelylargely byby ionicionic bonding,bonding, thethe ionion geometrygeometry cancan bebe simplysimply consideredconsidered toto bebe sphericalspherical SphericalSpherical ionsions willwill geometricallygeometrically packpack ((coordinatecoordinate)) oppositelyoppositely chargedcharged ionsions aroundaround themthem asas tightlytightly asas possiblepossible whilewhile maintainingmaintaining chargecharge neutralityneutrality ForFor aa particularparticular ion,ion, thethe surroundingsurrounding coordinationcoordination ionsions definedefine thethe apicesapices ofof aa polyhedronpolyhedron TheThe numbernumber ofof surroundingsurrounding ionsions isis thethe CoordinationCoordination NumberNumber CoordinationCoordination NumberNumber andand RadiusRadius RatioRatio
See Mineralogy CD: Crystal and Mineral Chemistry - Coordination of Ions CoordinationCoordination withwith OO --22 AnionsAnions WhenWhen RaRa (cation) /Rx/Rx (anion ) ~1~1 ClosestClosest PackedPacked ArrayArray
See Mineralogy CD: Crystal and Mineral Chemistry – Closest Packing PaulingPauling ’’ss RulesRules ofof MineralMineral StructureStructure
RuleRule 11:: AA coordinationcoordination polyhedronpolyhedron ofof anionsanions isis formedformed aroundaround eacheach cationcation ,, wherein:wherein: -- thethe cationcation --anionanion distancedistance isis determineddetermined byby thethe sumsum ofof thethe ionicionic radii,radii, andand Linus Pauling -- thethe coordinationcoordination numbernumber ofof thethe polyhedronpolyhedron isis determineddetermined byby thethe cationcation /anion/anion radiusradius ratioratio (( Ra:RxRa:Rx )) PaulingPauling ’’ss RulesRules ofof MineralMineral StructureStructure
RuleRule 2:2: TheThe electrostaticelectrostatic valencyvalency principleprinciple TheThe strengthstrength ofof anan ionicionic (electrostatic)(electrostatic) bondbond (( e.ve.v .).) betweenbetween aa cationcation andand anan anionanion isis equalequal toto thethe chargecharge ofof thethe anionanion (z)(z) divideddivided byby itsits coordinationcoordination numbernumber (n):(n): e.ve.v .. == z/nz/n InIn aa stablestable (neutral)(neutral) structure,structure, aa chargecharge balancebalance resultsresults betweenbetween thethe cationcation andand itsits polyhedralpolyhedral anionsanions withwith whichwhich itit isis bonded.bonded. PaulingPauling ’’ss RulesRules ofof MineralMineral StructureStructure
RuleRule 3:3: AnionAnion polyhedrapolyhedra thatthat shareshare edgesedges oror facesfaces decreasedecrease theirtheir stabilitystability duedue toto bringingbringing cationscations closercloser together;together; especiallyespecially significantsignificant forfor highhigh valencyvalency cationscations
RuleRule 4:4: InIn structuresstructures withwith differentdifferent typestypes ofof cationscations ,, thosethose cationscations withwith highhigh valencyvalency andand smallsmall CNCN tendtend notnot toto shareshare polyhedrapolyhedra withwith eacheach other;other; whenwhen theythey do,do, polyhedrapolyhedra areare deformeddeformed toto accommodateaccommodate cationcation repulsionrepulsion PaulingPauling ’’ss RulesRules ofof MineralMineral StructureStructure
Rule 5: The principle of parsimony
Because the number and types of different structural sites tends to be limited, even in complex minerals, different ionic elements are forced to occupy the same structural positions – leads to solid solution.
See amphibole structure for example (See Mineralogy CD: Crystal and Mineral Chemistry – Pauling’s Rules - #5) ChargeCharge BalanceBalance ofof IonicIonic BondsBonds FormationFormation ofof AnionicAnionic GroupsGroups
ResultsResults fromfrom highhigh valencevalence cationscations withwith electrostaticelectrostatic valenciesvalencies greatergreater thanthan halfhalf thethe valencyvalency ofof thethe polyhedralpolyhedral anions;anions; otherother bondsbonds withwith thosethose anionsanions wwillill bebe relativelyrelatively weaker.weaker.
Carbonate Sulfate CrystalCrystal ChemistryChemistry
PartPart 4:4: CompositionalCompositional VariationVariation ofof MineralsMinerals SolidSolid SolutionSolution MineralMineral FormulaFormula CalculationsCalculations GraphicalGraphical RepresentationRepresentation ofof MineralMineral CompositionsCompositions SolidSolid SolutionSolution inin MineralsMinerals
WhereWhere atomicatomic sitessites areare occupiedoccupied byby variablevariable proportionsproportions ofof twotwo oror moremore differentdifferent ionsions DependentDependent on:on: similarsimilar ionicionic sizesize (differ(differ byby lessless thanthan 1515 -- 30%)30%) resultsresults inin electrostaticelectrostatic neutralityneutrality temperaturetemperature ofof substitutionsubstitution (more(more accommodatingaccommodating atat higherhigher temperatures)temperatures) TypesTypes ofof SolidSolid SolutionSolution 1) Substitutional Solid Solution Simple cationic or anionic substitution
e.g. olivine (Mg,Fe) 2SiO 2; sphalerite (Fe,Zn)S Coupled substitution
e.g. plagioclase (Ca,Na)Al (1-2)Si (3-2)O8 (Ca 2+ + Al 3+ = Na + + Si 4+) 2) Interstitial Solid Solution Occurrence of ions and molecules within large voids within certain minerals (e.g., beryl, zeolite ) 3) Omission Solid Solution Exchange of single higher charge cation for two or more lower charged cations which creates a vacancy (e.g.
pyrrhotite – Fe (1-x) S) RecalculationRecalculation ofof MineralMineral AnalysesAnalyses
ChemicalChemical analysesanalyses areare usuallyusually reportedreported inin weightweight percentpercent ofof elementselements oror elementalelemental oxidesoxides ToTo calculatecalculate mineralmineral formulaformula requiresrequires transformingtransforming weightweight percentpercent intointo atomicatomic percentpercent oror molecularmolecular percentpercent ItIt isis alsoalso usefuluseful toto calculatecalculate (and(and plot)plot) thethe proportionsproportions ofof endend --membermember componentscomponents ofof mineralsminerals withwith solidsolid solutionsolution SpreadsheetsSpreadsheets areare usefuluseful waysways toto calculatecalculate mineralmineral formulasformulas andand endend --membermember componentscomponents