Ore Mineralogy (EMR 331)

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

Crystal chemistry

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Crystal Chemistry Crystal Chemistry

Part 1:

Atoms, Elements and Ions

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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 rock

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

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Fe –Fe – 86%86%

S –S – 10%10%

Ni –Ni – 4%4%

Chemical Layers of the Earth Chemical 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%

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Composition of the Earth

Composition of the Earth ’ ’ s Crust s Crust

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Average composition of the Earth

Average composition of the Earth ’ ’ s Crust s Crust (by weight, elements, and volume)

(by weight, elements, and volume)

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The Atom The 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

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Elements and Isotopes Elements 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 protons

is 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).

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.

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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

49Ti stable 7/2- Abundance=5.5 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

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Structure of the Periodic Table Structure of the Periodic Table

# of Electrons in Outermost Shell Noble

Gases

Anions

---Transition Metals---

Primary Shell being filled

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

Cations

Cations –– 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 element

from their outer shells; typically a metal element

Anions

Anions –– elements prone to accept one or more electrons elements prone to accept one or more electrons to their outer shells; always a non

to their outer shells; always a non--metal elementmetal element

Ionization Potential

Ionization 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

Electronegativity

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

attracts electrons to its outer shell

Valence State

Valence State (or oxidation state) (or oxidation state) –– the common ionic the common ionic configuration(s

configuration(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

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1^st Ionization Potential

Electronegativity

Elements with a single outer s orbital electron

Anions Cations

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

Rock Rock - - forming Minerals forming Minerals

Cations

Cations –– generally generally relates to column relates to column in the periodic in the periodic table; most table; most

transition metals transition metals have 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 Anions

Anions –– relates relates

electrons needed electrons needed to completely fill to completely fill outer shell

outer shell Anionic Groups Anionic Groups ––

tightly bound tightly bound ionic complexes ionic complexes with net negative with net negative charge

charge

+1 +2

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

---Transition Metals---

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Crystal Chemistry Crystal Chemistry

Part 2:

Bonding and Ionic Radii

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Chemical Bonding in Minerals Chemical 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 minerals

chemical 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:

Ionic

Ionic Covalent Covalent Metallic Metallic van van der der Waals Waals Hydrogen Hydrogen

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

same mineral

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Ionic Bonding Ionic Bonding

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 gas

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

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

cations and anionsand anions Example:

Example: NaClNaCl ^{Na (1s}^{Na (1s}²²^2s^2s²²^2p^2p⁶⁶^3s^3s¹¹^{) –}⁾^{–> Na}^{> Na}⁺⁺^(1s^(1s²²^2s^2s²²^2p^2p⁶⁶^{) + e}^{) + e}^-^-

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

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Properties of Ionic Bonds Properties 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 ions 1) the spacing between ions

2) the charge of the ions

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Covalent Bonding Covalent Bonding

formed by sharing of outer shell formed by sharing of outer shell electrons

electrons

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).

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, Si, Al, S)Si, Al, S)

Diamond

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

Ionic Pairs

Covalent Pairs

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Metallic Bonding Metallic Bonding

atomic nuclei and inner filled electron atomic nuclei and inner filled electron shells in a

shells in a “ “ sea sea ” ” of electrons made up of of electrons made up of unbound valence electrons

unbound 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).

Non Non - - directional bonding produces high directional bonding produces high symmetry

symmetry

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van van der der Waals Waals (Residual) Bonding (Residual) Bonding

created by weak bonding of oppositely created by weak bonding of oppositely dipolarized

dipolarized electron cloudselectron clouds

commonly occurs around covalently bonded commonly occurs around covalently bonded elements

elements

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 crystals symmetry crystals

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Hydrogen Bonding Hydrogen 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 molecules

molecules

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⁺

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Summary of Bonding Characteristics

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Multiple Bonding in Minerals Multiple 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 tetrahedra

tetrahedra sheets (mixed sheets (mixed

covalent and ionic) bound by covalent and ionic) bound by

weak ionic and hydrogen weak ionic and hydrogen

bonds bonds

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 structure tightly bound atomic structure

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Atomic Radii Atomic 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 shell outermost 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/ions neighboring 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 charges between the two ions and their charges

F = k [(q

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

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

Reflects

expansion of cations into larger “pore spaces”

between anion neighbors

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Crystal Chemistry Crystal Chemistry

Part 3:

Coordination of Ions Coordination of Ions

Pauling

Pauling ’ ’ s s Rules Rules

Crystal Structures

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Coordination of Ions Coordination 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

spherical spherical

Spherical ions will geometrically pack Spherical ions will geometrically pack

((

coordinate coordinate

) oppositely charged ions around ) oppositely charged ions around them as tightly as possible while maintaining them as tightly as possible while maintaining

charge neutrality charge 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

polyhedron polyhedron

The number of surrounding ions is the The number of surrounding ions is the

Coordination Number

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Coordination Coordination Number and Number and Radius Ratio Radius Ratio

See Mineralogy CD: Crystal See Mineralogy CD: Crystal and Mineral Chemistry

and Mineral Chemistry -- Coordination of Ions Coordination of Ions

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Coordination Coordination

with O with O

^-^-²²

Anions

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When When

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

~1~1

Closest Closest

Packed Packed

Array Array

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

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Pauling

Pauling ’ ’ s s Rules of Mineral Structure Rules of Mineral Structure

Rule 1

Rule 1: A coordination polyhedron : A coordination polyhedron of anions is formed around each of anions is formed around each

cation

cation, 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

cation

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

Linus Pauling

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Rule 2:

Rule 2: The electrostatic The electrostatic valency valency principle principle The strength of an ionic (electrostatic) The strength of an ionic (electrostatic)

bond (

bond ( e.v e.v .) between a .) between a cation cation 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.v e.v . = . = z/n z/n

In a stable (neutral) structure, a charge In a stable (neutral) structure, a charge

balance results between the

balance results between the cation cation and its and its polyhedral anions with which it is bonded.

polyhedral anions with which it is bonded.

Pauling

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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

cations

cations 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 cations

cations, 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

Pauling

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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)

Pauling

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Charge Balance Charge Balance

of Ionic Bonds

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Formation of Anionic Groups Formation of Anionic Groups

Results from high valence

Results from high valence cationscations with electrostatic with electrostatic valencies

valencies 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.

Carbonate Sulfate

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Crystal Chemistry Crystal Chemistry

Part 4:

Compositional Variation of Compositional Variation of Minerals Solid Solution

Minerals Solid Solution

Mineral Formula Calculations Mineral Formula Calculations

Graphical Representation of Graphical Representation of

Mineral Compositions

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Solid Solution in Minerals Solid Solution in Minerals

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

proportions of two or more different ions proportions of two or more different ions Dependent on:

Dependent on:

similar ionic size (differ by less than 15 similar ionic size (differ by less than 15 - - 30%) 30%)

results in electrostatic neutrality results in electrostatic neutrality

temperature of substitution (more temperature of substitution (more

accommodating at higher temperatures)

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Types of Solid Solution Types of Solid Solution

1) Substitutional1) Substitutional Solid SolutionSolid Solution

Simple cationic or anionic substitution Simple cationic or anionic substitution

e.g. olivine (Mg,Fe)

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

Coupled substitution

e.g. plagioclase (Ca,Na)Al

e.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 Solution

2) 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 Solution

3) 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.

pyrrhotite

pyrrhotite –– FeFe_(1-₍₁_-x)_x)S)S)

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Recalculation of Mineral Analyses Recalculation of Mineral Analyses

Chemical analyses are usually reported in weight Chemical analyses are usually reported in weight percent of elements or elemental oxides

percent 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 percent or molecular percent

It is also useful to calculate (and plot) the It is also useful to calculate (and plot) the proportions of end

proportions 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 end

mineral formulas and end--member componentsmember components