Ore Mineralogy (EMR 331)Ore Mineralogy (EMR 331)

Crystal chemistryCrystal chemistry

Crystal ChemistryCrystal Chemistry

Part 1: Part 1:

Atoms, Elements and IonsAtoms, Elements and Ions

What is Crystal Chemistry?What is Crystal Chemistry?

�� study of the atomic structure, physical properties, study of the atomic structure, physical properties,

and chemical composition of crystalline material and chemical composition of crystalline material

�� basically inorganic chemistry of solidsbasically inorganic chemistry of solids

�� the structure and chemical properties of the atom the structure and chemical properties of the atom

and elements are at the core of crystal chemistry and elements are at the core of crystal chemistry

�� there are only a handful of elements that make there are only a handful of elements that make

up most of the rockup most of the rock--forming minerals of the earthforming minerals of the earth

Fe Fe –– 86%86%

S S –– 10%10%

Ni Ni –– 4%4%

Chemical Layers of the EarthChemical Layers of the Earth

SiO2 SiO2 –– 45%45%

MgOMgO –– 37%37%

FeOFeO –– 8%8%

Al2O3 Al2O3 –– 4%4%

CaOCaO –– 3% 3%

others others –– 3%3%

Composition of the EarthComposition of the Earth’’s Crusts Crust

Average composition of the EarthAverage composition of the Earth’’s Crusts Crust

(by weight, elements, and volume)(by weight, elements, and volume)

The AtomThe Atom

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

Elements and IsotopesElements and Isotopes

�� Elements are defined by the number of protons in the Elements are defined by the number of protons in the nucleus (atomic number). nucleus (atomic number).

�� In a stable element (nonIn a stable element (non--ionized), the number of electrons ionized), the number of electrons is equal to the number of protonsis equal to the number of protons

�� Isotopes of a particular element are defined by the total Isotopes of a particular element are defined by the total number of neutrons in addition to the number of protons number of neutrons in addition to the number of protons in the nucleus (isotopic number). in the nucleus (isotopic number).

�� Various elements can have multiple (2Various elements can have multiple (2--38) stable isotopes, 38) stable isotopes, some of which are unstable (radioactive)some of which are unstable (radioactive)

�� Isotopes of a particular element have the same chemical Isotopes of a particular element have the same chemical properties, but different masses. properties, but different masses.

Isotopes of Titanium (Z=22)Isotope Half-life Spin Parity Decay Mode(s) or Abundance38Ti 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

Structure of the Periodic TableStructure of the Periodic Table

# of Electrons in Outermost Shell Noble Gases

Anions

--------------------Transition Metals------------------

Primary Shell being filled

Ions, Ionization Potential, and Valence StatesIons, Ionization Potential, and Valence States

CationsCations –– elements prone to give up one or more electrons elements prone to give up one or more electrons from their outer shells; typically a metal elementfrom their outer shells; typically a metal element

AnionsAnions –– elements prone to accept one or more electrons elements prone to accept one or more electrons to their outer shells; always a nonto their outer shells; always a non--metal elementmetal element

Ionization PotentialIonization Potential –– measure of the energy necessary to measure of the energy necessary to strip an element of its outermost electron strip an element of its outermost electron

ElectronegativityElectronegativity –– measure strength with which a nucleus measure strength with which a nucleus attracts electrons to its outer shellattracts electrons to its outer shell

Valence StateValence State (or oxidation state) (or oxidation state) –– the common ionic the common ionic configuration(sconfiguration(s) of a particular element determined by ) of a particular element determined by how many electrons are typically stripped or added to an how many electrons are typically stripped or added to an ionion

1st Ionization Potential

Electronegativity

Elements with a single outer s orbital electron

Anions

Cations

Valence States of Ions common to Valence States of Ions common to

RockRock--forming Mineralsforming MineralsCationsCations –– generally generally

relates to column relates to column in the periodic in the periodic table; most table; most transition metalstransition metalshave a +2 have a +2 valence state for valence state for transition metals, transition metals, relates to having relates to having two electrons in two electrons in outer outer

AnionsAnions –– relates relates electrons needed electrons needed to completely fill to completely fill outer shellouter shell

Anionic Groups Anionic Groups ––tightly bound tightly bound ionic complexes ionic complexes with net negative with net negative chargecharge

+1 +2+3 +4 +5 +6 +7

-2 -1

-----------------Transition Metals---------------

Crystal ChemistryCrystal Chemistry

Part 2: Part 2:

Bonding and Ionic RadiiBonding and Ionic Radii

Chemical Bonding in MineralsChemical Bonding in Minerals

�� Bonding forces are electrical in nature (related to Bonding forces are electrical in nature (related to charged particles)charged particles)

�� Bond strength controls most physical and Bond strength controls most physical and chemical properties of mineralschemical properties of minerals

(in general, the stronger the bond, the harder (in general, the stronger the bond, the harder the crystal, higher the melting point, and the the crystal, higher the melting point, and the lower the coefficient of thermal expansion)lower the coefficient of thermal expansion)

�� Five general types bonding types: Five general types bonding types:

IonicIonic CovalentCovalent MetallicMetallicvan van derder WaalsWaals HydrogenHydrogen

Commonly different bond types occur in the Commonly different bond types occur in the same mineralsame mineral

Ionic BondingIonic Bonding

Common between elements that will... Common between elements that will...

1)1) easily easily exchangeexchange electrons so as to stabilize their electrons so as to stabilize their

outer shells (i.e. become more inert gasouter shells (i.e. become more inert gas--like)like)

2)2) create an electronically neutral bond between create an electronically neutral bond between

cationscations and anionsand anions

Example: Example: NaClNaCl Na (1sNa (1s222s2s222p2p663s3s11) ) ––> Na> Na++(1s(1s222s2s222p2p66) + e) + e--

ClCl (1s(1s222s2s222p2p663s3s223p3p55) + e) + e-- ––> > ClCl-- (1s(1s222s2s222p2p663s3s223p3p66) )

Properties of Ionic BondsProperties of Ionic Bonds

�� Results in minerals displaying moderate Results in minerals displaying moderate degrees of hardness and specific gravity, degrees of hardness and specific gravity, moderately high melting points, high moderately high melting points, high degrees of symmetry, and are poor degrees of symmetry, and are poor conductors of heat (due to ionic stability)conductors of heat (due to ionic stability)

�� Strength of ionic bonds are related: Strength of ionic bonds are related:

1) the spacing between ions1) the spacing between ions

2) the charge of the ions 2) the charge of the ions

Covalent BondingCovalent Bonding�� formed by sharing of outer shell formed by sharing of outer shell

electronselectrons

�� strongest of all chemical bonds strongest of all chemical bonds

�� produces minerals that are produces minerals that are

insoluble, high melting points, insoluble, high melting points,

hard, nonconductive (due to hard, nonconductive (due to

localization of electrons), have localization of electrons), have

low symmetry (due to low symmetry (due to

directional bonding). directional bonding).

�� common among elements with common among elements with

high numbers of vacancies in high numbers of vacancies in

the outer shell (e.g. C, the outer shell (e.g. C, SiSi, Al, S), Al, S)Diamond

Tendencies for Ionic vs. Covalent PairingTendencies for Ionic vs. Covalent Pairing

Ionic Pairs

CovalentPairs

Metallic BondingMetallic Bonding

�� atomic nuclei and inner filled electron atomic nuclei and inner filled electron shells in a shells in a ““seasea”” of electrons made up of of electrons made up of unbound valence electronsunbound valence electrons

�� Yields minerals with minerals that are soft, Yields minerals with minerals that are soft, ductile/malleable, highly conductive (due ductile/malleable, highly conductive (due to easily mobile electrons). to easily mobile electrons).

�� NonNon--directional bonding produces high directional bonding produces high symmetrysymmetry

van van derder WaalsWaals (Residual) Bonding(Residual) Bonding

�� created by weak bonding of oppositely created by weak bonding of oppositely

dipolarizeddipolarized electron cloudselectron clouds

�� commonly occurs around covalently bonded commonly occurs around covalently bonded

elementselements

�� produces solids that are soft, very poor produces solids that are soft, very poor

conductors, have low melting points, low conductors, have low melting points, low

symmetry crystalssymmetry crystals

Hydrogen BondingHydrogen Bonding

��Electrostatic Electrostatic

bonding between an bonding between an

H+ ion with an anion H+ ion with an anion

or anionic complex or anionic complex

or with a polarized or with a polarized

moleculesmolecules

��Weaker than ionic Weaker than ionic

or covalent; or covalent;

stronger than van stronger than van

derder WaalsWaals

polarized H2O molecule Ice

Close packing of polarized molecules

Anions

H+

Summary of Bonding CharacteristicsSummary of Bonding Characteristics

Multiple Bonding in MineralsMultiple Bonding in Minerals

�� Graphite Graphite –– covalently bonded covalently bonded sheets of C loosely bound by sheets of C loosely bound by van van derder WaalsWaals bonds.bonds.

�� Mica Mica –– strongly bonded silica strongly bonded silica tetrahedratetrahedra sheets (mixed sheets (mixed covalent and ionic) bound by covalent and ionic) bound by weak ionic and hydrogen weak ionic and hydrogen bondsbonds

�� Cleavage planes commonly Cleavage planes commonly correlate to planes of weak correlate to planes of weak ionic bonding in an otherwise ionic bonding in an otherwise tightly bound atomic structuretightly bound atomic structure

Atomic RadiiAtomic Radii

�� Absolute radiusAbsolute radius of an atom based on of an atom based on location of the maximum density of location of the maximum density of outermost electron shelloutermost electron shell

�� Effective radiusEffective radius dependent on the dependent on the charge, type, size, and number of charge, type, size, and number of neighboring atoms/ionsneighboring atoms/ions

-- in bonds between identical atoms, this in bonds between identical atoms, this is half the is half the interatomicinteratomic distancedistance

-- in bonds between different ions, the in bonds between different ions, the distance between the ions is controlled distance between the ions is controlled by the attractive and repulsive force by the attractive and repulsive force between the two ions and their chargesbetween the two ions and their charges

F = k [(qF = k [(q++)(q)(q--)/d)/d22] Coulomb] Coulomb’’s laws law

Control of CN(# of nearest neighbors) on ionic radius

Reflects expansion of cations into larger “pore spaces”between anion neighbors

Crystal ChemistryCrystal Chemistry

Part 3: Part 3:

Coordination of IonsCoordination of Ions

PaulingPauling’’ss RulesRules

Crystal StructuresCrystal Structures

Coordination of IonsCoordination of Ions

�� For minerals formed largely by ionic bonding, For minerals formed largely by ionic bonding, the ion geometry can be simply considered to be the ion geometry can be simply considered to be sphericalspherical

�� Spherical ions will geometrically pack Spherical ions will geometrically pack ((coordinatecoordinate) oppositely charged ions around ) oppositely charged ions around them as tightly as possible while maintaining them as tightly as possible while maintaining charge neutralitycharge neutrality

�� For a particular ion, the surrounding For a particular ion, the surrounding coordination ions define the apices of a coordination ions define the apices of a polyhedronpolyhedron

�� The number of surrounding ions is the The number of surrounding ions is the Coordination NumberCoordination Number

Coordination Coordination

Number and Number and

Radius RatioRadius Ratio

See Mineralogy CD: Crystal See Mineralogy CD: Crystal and Mineral Chemistry and Mineral Chemistry --Coordination of IonsCoordination of Ions

Coordination Coordination

with Owith O--22

AnionsAnions

When When

RaRa(cation)(cation)/Rx/Rx(anion(anion))

~1~1

Closest Closest

Packed Packed

ArrayArray

See Mineralogy See Mineralogy CD: Crystal and CD: Crystal and Mineral Chemistry Mineral Chemistry –– Closest PackingClosest Packing

PaulingPauling’’ss Rules of Mineral StructureRules of Mineral Structure

Rule 1Rule 1: A coordination polyhedron : A coordination polyhedron

of anions is formed around each of anions is formed around each

cationcation, wherein: , wherein:

-- the the cationcation--anion distance is anion distance is

determined by the sum of the determined by the sum of the

ionic radii, and ionic radii, and

-- the coordination number of the the coordination number of the

polyhedron is determined by the polyhedron is determined by the

cationcation/anion radius ratio (/anion radius ratio (Ra:RxRa:Rx))

Linus Pauling

Rule 2:Rule 2: The electrostatic The electrostatic valencyvalency principleprinciple

The strength of an ionic (electrostatic) The strength of an ionic (electrostatic) bond (bond (e.ve.v.) between a .) between a cationcation and an anion and an anion is equal to the charge of the anion (z) is equal to the charge of the anion (z) divided by its coordination number (n):divided by its coordination number (n):

e.ve.v. = . = z/nz/n

In a stable (neutral) structure, a charge In a stable (neutral) structure, a charge balance results between the balance results between the cationcation and its and its polyhedral anions with which it is bonded.polyhedral anions with which it is bonded.

PaulingPauling’’ss Rules of Mineral StructureRules of Mineral Structure

�� Rule 3:Rule 3: Anion Anion polyhedrapolyhedra that share edges or that share edges or faces decrease their stability due to bringing faces decrease their stability due to bringing cationscations closer together; especially significant for closer together; especially significant for high high valencyvalency cationscations

�� Rule 4:Rule 4: In structures with different types of In structures with different types of cationscations, those , those cationscations with high with high valencyvalency and and small CN tend not to share small CN tend not to share polyhedrapolyhedra with each with each other; when they do, other; when they do, polyhedrapolyhedra are deformed to are deformed to accommodate accommodate cationcation repulsionrepulsion

PaulingPauling’’ss Rules of Mineral StructureRules of Mineral Structure

�� Rule 5:Rule 5: The principle of parsimonyThe principle of parsimony

Because the number and types of different structural Because the number and types of different structural sites tends to be limited, even in complex minerals, sites tends to be limited, even in complex minerals, different ionic elements are forced to occupy the same different ionic elements are forced to occupy the same structural positions structural positions –– leads to solid solution.leads to solid solution.

See amphibole structure for example See amphibole structure for example (See Mineralogy CD: (See Mineralogy CD: Crystal and Mineral Chemistry Crystal and Mineral Chemistry –– PaulingPauling’’ss Rules Rules -- #5)#5)

PaulingPauling’’ss Rules of Mineral StructureRules of Mineral Structure

Charge Balance Charge Balance

of Ionic Bondsof Ionic Bonds

Formation of Anionic GroupsFormation of Anionic Groups

Results from high valence Results from high valence cationscations with electrostatic with electrostatic

valenciesvalencies greater than half the greater than half the valencyvalency of the of the

polyhedral anions; other bonds with those anions will polyhedral anions; other bonds with those anions will

be relatively weaker.be relatively weaker.

Carbonate Sulfate

Crystal ChemistryCrystal Chemistry

Part 4: Part 4:

Compositional Variation of Compositional Variation of

Minerals Solid SolutionMinerals Solid Solution

Mineral Formula CalculationsMineral Formula Calculations

Graphical Representation of Graphical Representation of

Mineral CompositionsMineral Compositions

Solid Solution in MineralsSolid Solution in Minerals

Where atomic sites are occupied by variable Where atomic sites are occupied by variable

proportions of two or more different ionsproportions of two or more different ions

Dependent on: Dependent on:

�� similar ionic size (differ by less than 15similar ionic size (differ by less than 15--

30%)30%)

�� results in electrostatic neutralityresults in electrostatic neutrality

�� temperature of substitution (more temperature of substitution (more

accommodating at higher temperatures)accommodating at higher temperatures)

Types of Solid SolutionTypes of Solid Solution

1) 1) SubstitutionalSubstitutional Solid SolutionSolid Solution

Simple cationic or anionic substitutionSimple cationic or anionic substitution

e.g. olivine (Mg,Fe)e.g. olivine (Mg,Fe)22SiOSiO22; ; sphaleritesphalerite ((Fe,Zn)SFe,Zn)S

Coupled substitutionCoupled substitution

e.g. plagioclase (Ca,Na)Ale.g. plagioclase (Ca,Na)Al(1(1--2)2)SiSi(3(3--2)2)OO88

(Ca(Ca2+2+ + Al+ Al3+3+ = Na= Na++ + Si+ Si4+4+))

2) Interstitial Solid Solution2) Interstitial Solid Solution

Occurrence of ions and molecules within large voids Occurrence of ions and molecules within large voids

within certain minerals (e.g., beryl, within certain minerals (e.g., beryl, zeolitezeolite))

3) Omission Solid Solution3) Omission Solid Solution

Exchange of single higher charge Exchange of single higher charge cationcation for two or more for two or more

lower charged lower charged cationscations which creates a vacancy (e.g. which creates a vacancy (e.g.

pyrrhotitepyrrhotite –– FeFe(1(1--x)x)S)S)

Recalculation of Mineral AnalysesRecalculation of Mineral Analyses

�� Chemical analyses are usually reported in weight Chemical analyses are usually reported in weight

percent of elements or elemental oxidespercent of elements or elemental oxides

�� To calculate mineral formula requires To calculate mineral formula requires

transforming weight percent into atomic percent transforming weight percent into atomic percent

or molecular percentor molecular percent

�� It is also useful to calculate (and plot) the It is also useful to calculate (and plot) the

proportions of endproportions of end--member components of member components of

minerals with solid solution minerals with solid solution

�� Spreadsheets are useful ways to calculate Spreadsheets are useful ways to calculate

mineral formulas and endmineral formulas and end--member componentsmember components