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