Ore Mineralogy (EMR 331) Crystal chemistry

Crystal Chemistry Part 1: Atoms, Elements and Ions

What is Crystal Chemistry?









study of the atomic structure, physical properties, and chemical composition of crystalline material basically inorganic chemistry of solids the structure and chemical properties of the atom and elements are at the core of crystal chemistry there are only a handful of elements that make up most of the rock-forming minerals of the earth

Chemical Layers of the Earth

SiO2 – 45% MgO – 37% FeO – 8% Al2O3 – 4% CaO – 3% others – 3%

Fe – 86% S – 10% Ni – 4%

Composition of the Earth’s Crust

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

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

Elements and Isotopes








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 38Ti 39Ti 40Ti 41Ti 42Ti 43Ti 44Ti 45Ti 46Ti 47Ti 48Ti 49Ti 50Ti 51Ti 52Ti 53Ti 54Ti 55Ti 56Ti 57Ti 58Ti 59Ti 60Ti 61Ti

Half-life 0+ 26 ms 50 ms 80 ms 199 ms 509 ms 63 y 184.8 m stable stable stable stable stable 5.76 m 1.7 m 32.7 s 320 ms 160 ms 180 ms

Spin Parity

Decay Mode(s) or Abundance

(3/2+) 0+ 3/2+ 0+ 7/20+ 7/20+ 5/20+ 7/20+ 3/20+ (3/2)0+ (3/2-) 0+ (5/2-) 0+ (5/2-) 0+ (1/2-)

EC=100, ECP+EC2P ~ 14 EC+B+=100 EC+B+=100, ECP ~ 100 EC+B+=100 EC+B+=100 EC=100 EC+B+=100 Abundance=8.0 1 Abundance=7.3 1 Abundance=73.8 1 Abundance=5.5 1 Abundance=5.4 1 B-=100 B-=100 B-=100 B-=100 B-=100, B-N=0.06 sys B-=100, B-N=0.04 sys B-=? B-=? B-=?, B-N=?

Source: R.B. Firestone UC-Berkeley

Structure of the Periodic Table # of Electrons in Outermost Shell

Noble Gases

Anions

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

Primary Shell being filled

Ions, Ionization Potential, and Valence States 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

Valence States of Ions common to Rock-forming Minerals +1 +2

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

Cations – generally relates to column in the periodic table; most transition metals have a +2 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

Crystal Chemistry Part 2: Bonding and Ionic Radii

Chemical Bonding in Minerals Bonding forces are electrical in nature (related to charged particles)
Bond strength controls most physical and chemical properties of minerals (in general, the stronger the bond, the harder the crystal, higher the melting point, and the lower the coefficient of thermal expansion)
Five general types bonding types:


Ionic Covalent van der Waals

Metallic Hydrogen

Commonly different bond types occur in the same mineral

Ionic Bonding Common between elements that will... 1) easily exchange electrons so as to stabilize their outer shells (i.e. become more inert gas-like) 2) create an electronically neutral bond between cations and anions Example: NaCl Na (1s22s22p63s1) –> Na+(1s22s22p6) + eCl (1s22s22p63s23p5) + e- –> Cl- (1s22s22p63s23p6)

Properties of Ionic Bonds





Results in minerals displaying moderate degrees of hardness and specific gravity, moderately high melting points, high degrees of symmetry, and are poor conductors of heat (due to ionic stability) Strength of ionic bonds are related: 1) the spacing between ions 2) the charge of the ions

Covalent Bonding









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

Tendencies for Ionic vs. Covalent Pairing Ionic Pairs Covalent Pairs

Metallic Bonding








atomic nuclei and inner filled electron shells in a “sea” of electrons made up of unbound valence electrons Yields minerals with minerals that are soft, ductile/malleable, highly conductive (due to easily mobile electrons). Non-directional bonding produces high symmetry

van der Waals (Residual) Bonding










created by weak bonding of oppositely dipolarized electron clouds commonly occurs around covalently bonded elements produces solids that are soft, very poor conductors, have low melting points, low symmetry crystals

Hydrogen Bonding Electrostatic bonding between an H+ ion with an anion or anionic complex or with a polarized molecules Weaker than ionic or covalent; stronger than van der Waals

H+

Close packing of polarized molecules

polarized H2O molecule

Anions

Ice

Summary of Bonding Characteristics

Multiple Bonding in Minerals


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

Atomic Radii





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-)/d2] Coulomb’s law

Control of CN (# of nearest neighbors) on ionic radius Reflects expansion of cations into larger “pore spaces” between anion neighbors

Crystal Chemistry Part 3: Coordination of Ions Pauling’s Rules Crystal Structures

Coordination of Ions











For minerals formed largely by ionic bonding, the ion geometry can be simply considered to be spherical Spherical ions will geometrically pack (coordinate) oppositely charged ions around them as tightly as possible while maintaining charge neutrality For a particular ion, the surrounding coordination ions define the apices of a polyhedron The number of surrounding ions is the

Coordination Number

Coordination Number and Radius Ratio

See Mineralogy CD: Crystal and Mineral Chemistry Coordination of Ions

Coordination with O-2 Anions

When Ra(cation)/Rx(anion) ~1

Closest Packed Array

See Mineralogy CD: Crystal and Mineral Chemistry – Closest Packing

Pauling’s Rules of Mineral Structure Rule 1: A coordination polyhedron of anions is formed around each cation, wherein: - the cation-anion distance is determined by the sum of the ionic radii, and - the coordination number of the polyhedron is determined by the cation/anion radius ratio (Ra:Rx)

Linus Pauling

Pauling’s Rules of Mineral Structure Rule 2: The electrostatic valency principle The strength of an ionic (electrostatic) bond (e.v.) between a cation and an anion is equal to the charge of the anion (z) divided by its coordination number (n): e.v. = z/n In a stable (neutral) structure, a charge balance results between the cation and its polyhedral anions with which it is bonded.

Pauling’s Rules of Mineral Structure


Rule 3: Anion polyhedra that share edges or faces decrease their stability due to bringing cations closer together; especially significant for high valency cations




Rule 4: In structures with different types of cations, those cations with high valency and small CN tend not to share polyhedra with each other; when they do, polyhedra are deformed to accommodate cation repulsion

Pauling’s Rules of Mineral Structure


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)

Charge Balance of Ionic Bonds

Formation of Anionic Groups Results from high valence cations with electrostatic valencies greater than half the valency of the polyhedral anions; other bonds with those anions will be relatively weaker. Carbonate

Sulfate

Crystal Chemistry Part 4: Compositional Variation of Minerals Solid Solution Mineral Formula Calculations Graphical Representation of Mineral Compositions

Solid Solution in Minerals Where atomic sites are occupied by variable proportions of two or more different ions Dependent on:
similar ionic size (differ by less than 1530%)
results in electrostatic neutrality
temperature of substitution (more accommodating at higher temperatures)

Types of Solid Solution 1) Substitutional Solid Solution Simple cationic or anionic substitution e.g. olivine (Mg,Fe)2SiO2; sphalerite (Fe,Zn)S Coupled substitution e.g. plagioclase (Ca,Na)Al(1-2)Si(3-2)O8 (Ca2+ + Al3+ = Na+ + Si4+) 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)

Recalculation of Mineral Analyses











Chemical analyses are usually reported in weight percent of elements or elemental oxides To calculate mineral formula requires transforming weight percent into atomic percent or molecular percent It is also useful to calculate (and plot) the proportions of end-member components of minerals with solid solution Spreadsheets are useful ways to calculate mineral formulas and end-member components