Part 1: Crystal Chem Part A

Front 1

Paulings Rule: Coordination polyhedron of anions surrounding the cation

Back 1

a) There is a coordination polyhedronof anions about each cation
b) The cation-anion distance is the sum of their radii
c) Thecoordination number(CN) is determined by the radius ratio
-triangle (trigonal coordination) CN = 3
-tetrahedron (tetrahedral coordination) CN = 4
-octahedron (octahedral coordination) CN = 6
-cube (cubic coordination) CN=8

Front 2

Paulings Rule: Local charge balance” (or, Electrostatic valence rule)

Back 2

-The total strength of valence which reaches the anion from all neighboring cations is equal to the charge on the anion
-Total valence reaching F: (+1/4) +(+1/4) + (+1/4) + (+1/4) = +1
charge on the anion: -1

Front 3

Paulings Rule: Shared polyhedral elements

Back 3

-Shared edges and especially faces decreases stability of the crystal.
-this effect is large for cations
of high valence and low CN (e.g., Si)
-(corners, edges, faces)
-cation-cation repulsion due to much shorter cation-cation distances withshared edges and faces

Front 4

Paulings Rule: Dispersion of high-valence cations

Back 4

- In a crystal containing differe
nt cations, those with high valence
and small CN tend not to share polyhedral elements.
-Si tetrahedra tend to not share polyhedral elements, unless the Si-content of the mineral is high

Front 5

Paulings Rule: Rule of parsimony

Back 5

The number of essentially different kinds of constituents in a crystal tends to be small.
•In essence, most minerals contain relatively few "sites" for cations.
•However, we will see that ions of similar size can
substitute for one another in a crystal, so that
minerals tend to be very complex chemically.
-amphiboles

Front 6

X-ray diffraction
X-rays
Diffraction

Back 6

- The main method for determining how atoms are arranged in a crystal (mineral)Also used to identify minerals.
- electromagnetic radiation (light with high energy, short wavelength) have wavelength of about 1-10 Å, similar to the distance between atoms.
-reflection” of the X-ray beam only in certain directions (coherent scattering) Beam of X-rays when aimed at a crystal “diffracts” – reflects only in certain directions, giving a pattern of spots on the film (or detector) placed behind the crystal

Front 7

Ionic Substitution

Back 7

-minerals have complex chemistry because many different elements can substitute for each other in the crystal structure
-Size-ions of similar size (and CN) can substitute
-Charge-all charges in a mineral must balance
-Temperature-minerals can tolerate greater “size mismatch” at higher temperature

Front 8

exsolution

Back 8

- a homogeneous solid solution becomes 2 different crystal minerals w/o adding or subtracting any minerals
ex: perthite

Front 9

Simple substitution

Back 9

-involves the same sites in the crystal structure
complete solid solution: ions have same charge and nearly same size, substitute freely for each other
Mn2+and Fe2

Front 10

coupled substitution

Back 10

- ions have nearly same size, but different charge; balance charge by simultaneous substitution on a second site.
Si4+and Al3+(CN=4); balance by also substituting Ca2+
for Na+on a different site.write as a charge-balanced reaction: Si4+ + Na+= Al3+ + Ca2+

Front 11

Interstitial substitution

Back 11

-coupled substitution where the charge balancing substitution is accommodated on a site normally vacant
in the mineral.
Si4+(CN=4) = Al3+(CN=4) + Na+(“A”-site)

Front 12

Vacancy substitution

Back 12

charge is balanced by leaving sites vacant.
example: pyrrhotite: Fe
(1-x)S contains both Fe2+ and Fe3+ for charge balance 3(Fe2+) = 2(Fe3+) + where ” represents and Fe-site that is vacant