12 - Lecture notes for GEOL3010


Crystal Chemistry


Average chemistry of the crust (in other words... elements we are most likely to encounter, thus the most likely to end up as mineral constituents).

element
weight %
atom %
ionic radius
volume %
O
46
63
1.40
94
Si
28
21
0.42
<1
Al
8
7
0.51
<1
Fe
5
2
0.74
<1
Ca
4
2
0.99
1
Na
3
3
0.97
1
K
3
1
1.33
2
Mg
2
2
0.66
<1
Total
99
100

100

Atomic Structure

Atom structure and mineral properties are intimately related. Mineral properties are function of (1) the atom types present, (2) the geometrical arrangement of the atoms and, (3) the bonding forces that exist between the atom pairs.


Chemistry Review

(This review is only to highlight concepts that you should already be familiar with and should have been covered in 100-level chemistry)

Quantum chemistry - theory that views the atoms are composed of particles, with each part containing discrete amounts of energy. The electrons, represent the outer "reactive" portion of an atom and are viewed probabilistically, existing with specific "orbitals".

Probability vs. distance

Electrons can be viewed as clouds with a probability of occupying a region within the cloud. Major energy gaps occur between them.

 electron orbitals.
electron shapes

Each electron orbital in an atom is assigned a set of principle quantum numbers. (n)

1. This number describes the volume of the orbital (recall the numbers must be integer values).

2. Orbital shape. s (spherical or sharp), p (dumbbell shaped or principal), d (diffuse or 4-fold symmetry) and f (fundamental), respectively.

Non-spherically shaped orbital have strong directionalities, which is important for bonding.

Arranged in increasing atomic weight. All weights are given relative to 12C which is taken to be exactly 12.000

Characteristics are dependent upon the electronic structure of the atoms. Therefore, atoms are further arranged (into Groups) by chemical properties.

Group number relates the number of electrons in the outermost orbital.

Think of the periodic table as an ordering of elements based upon their chemical properties, that in part, depend upon the outermost (valence) electrons. These electrons become available for chemical bonding.

Because certain atoms have similar electron configurations, they will occupy similar crystallographic sites.


Ionic Radii - related to the number of valance electrons as well as the density of electrons. Also related to the number and type of nearing neighbors. In a metals (e.g., Cu) it is half the distance between atoms.

Ionic interactions

Between any pair of oppositely charged ions there is an attractive force proportional to the products of their charges and inversely proportional to the square of the distance between their centers. (i.e., Coulomb's Law)


Where:

Example of determining Cl- ionic radius in LiCl

Using LiCl, Assume anion-to-anion (Cl-Cl) contact. This is reasonable because Li+ is small (Z=3) and Cl- is large (Z= 17).

Given LiCl unit cell edge as a = 5.14


Therefore, the distance between Cl- centers is 3.63 and the radius = 1.81.

Example for the case of structures containing bigger cations (Halite)

Given unit cell dimension of halite (a = 5.627) the distance between Na+ and Cl- can be estimated by simply subtracting the Cl- radius from the interatomic distance along the unit cell edge (i.e., a/2 = 2.813)

2.813 - 1.81 = 1.00

Actual radius of Na+ is 0.95. The sodium atom "rattles" around in the lattice.

Using the same logic for Sylvite (KCl) where a = 6.28

For K+ : r K+ + r Cl- = 1/2 (6.28) , r K+ = 1.33 (fits just right).

Atomic radii are not necessarily constant from one crystal structure to another. The radius will vary with 1) type of bond, 2) nearing neighbors and the shape of the atoms (recall that atoms and ions are not rigid shapes).

The tendency for an ion to reshape (or redistribution of charge) due to external electric fields is termed polarization.

The more the electron density is localized between two ions the more "covalent" the bonding.


Bonding Forces in Crystals

The forces that bind together atoms in a crystalline solid are electrical in nature.

Grouping of types of electrical forces or chemical bond in five principle types

Bonding type is determined by crystal structure (packing) and atom types and ionization state.

Physical properties are intimately related to these factors as can be seen from the table below.

Melting temperatures and hardness of various compounds

 Compound
Interionic distance
Melting point C
 Hardenss (Mohs)
LiF
2.01
842
 ?
 NaF
 2.31
 988
 3.2
NaCl
2.81
801
 2.5
 KCl
3.14 
776
 2.5
 MgO
2.10
2800
 6.5
CaO
2.40
2580
 4.5
 BaO
2.76
1923
 3.3

Specific bonds can share the character of more than one bond type.

More than one bond type ususally occurs within a crystal structure.