Lecture 4 (9/18/2006) 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 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 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 For a particular ion, the surrounding coordination ions define the apices of a polyhedron The number of surrounding ions is the Coordination Number 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

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 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

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

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 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 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 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) Pauling’s Rules of Mineral Structure

Visualizing Crystal Structure Ball and Stick ModelPolyhedra Model Beryl - Be 3 Al 2 (Si 6 O 18 )

Portraying Crystal Structure in Two Dimensions

Isostructural Types AX Compounds – Halite (NaCl) structure AX Compounds – Halite (NaCl) structure Anions – in CCP packing Cations – in octahedral sites Ra/Rx= Examples: Halides: +1 cations (Li, Na, K, Rb) w/ -1 anions (F, Cl, Br, I) Oxides: +2 cations (Mg, Ca, Sr, Ba, Ni) w/ O -2 Sulfides: +2 cations w/ S -2 (See Mineralogy CD: Crystal and Mineral Chemistry – Illustrations of Crystal Structures – Halite)

Isostructural Types AX Compounds – Sphalerite (ZnS) structure AX Compounds – Sphalerite (ZnS) structure R Zn /R S =0.60/1.84=0.32 (tetrahedral)

AX 2 Compounds – Flourite (CaF 2 ) structure AX 2 Compounds – Flourite (CaF 2 ) structure R Ca /R F =1.12/1.31=0.75 (cubic) Examples: Halides (CaF 2, BaCl 2...); Oxides (ZrO 2...) Isostructural Types

ABO 4 Compounds – Spinel (MgAl 2 O 4 )structure ABO 4 Compounds – Spinel (MgAl 2 O 4 )structure - Oxygen anions in CCP array - Two different cations (or same cation with two different valences) in tetrahedral (A) sites (e.g. Mg 2+, Fe 2+, Mn 2+, Zn 2+ ) or octahedral (B) sites (e.g. Al 3+, Cr 3+, Fe 3+ ) Isostructural Types

Nesosilicates Sorosilicates Cyclosilicates Inosilicates (single chain) Inosilicates (double chain) Phyllosilicates Tectosilicates

Next Lecture Crystal Chemistry IV Crystal Chemistry IV Compositional Variation of Minerals Solid Solution Mineral Formula Calculations Graphical Representation of Mineral Compositions Read p Read p