16 - Lecture notes for GEOL3010

Klein 91-103
Nesse 172--174; 69-73

Solid solutions and oxide percentages

Many minerals have oxygen as the dominant anion. For this reasons and by convention we choose to report the abundance of cations as oxides. In this way the valence state of the cation is balanced by the number of oxygen atoms (assuming a 2- valence state of oxygen). For example, ferric iron (Fe3+) is balanced by 1 1/2 oxygens or Fe2O3. Likewise ferrous iron (Fe2+) is balanced by 1 oxygen or FeO.

In the example of olivine recalculation below we assume that Fe, Mn, aned Mg occupy the same structural site and they  are randomly mixed in solid solution. Recall that the structural model chosen is determined from information obtained by elemental analysis, X-ray diffraction and use of Pauling's Rules.



 A

B

C

D

E

 F

G

H

1

 Olivine

Wt. %

Molecular

weights

Molecular

proportions

Atomic Prop.

cations

 Atomic Prop.

oxygen

cations

per 4

oxygen

# of

cations

per site

2

 SiO2 34.96 60.09 0.5818 0.5818  1.1636 0.9888

(tetrahedral)

0.9888

3

 FeO 36.77 71.85 0.5118 0.5118  0.5118 0.8698

(octahedral)

0.8698 0.0125 +1.1401

2.0224

4

 MnO 0.52 70.94 0.0073 0.0073  0.0073 0.0125

5

 MgO 27.04 40.31 0.6708 0.6708  0.6708 1.1401

6

 Total 99.29

T=

  2.3535

7
Fo= 57

Fa = 43  

Please reference class room demonstration of spread sheet to do these calculations. Examples given below refer to cell numbers in a spread sheet calculation.

Column A = oxide constitutents

Column B = Measured weight percent of oxides

Column C = Molecular weight of the oxides

Column D = Molecular proportions of the oxides obtained by division. (B÷C or D2 = B2/C2)

Column E = Atomic proportions of cations obtained by multiplying the molecular proportions by the number of cations in the oxide. (E2 = D2 * # cations in oxide: for example # of silicons in SiO2 = 1).

Column F = Atomic proportions of oxygen obtained by multiplying the molecular proportions by the number of oxygen atoms in the oxide. (E2 = D2 * # oxygens in oxide: for example # of oxygens in SiO2 = 2).

Total number (T) proportional to the number of oxygen atoms associated with each element. (F6 =SUM(F2:F5)

The olivine formula is based upon 4 oxygen atoms (1 /4 the unit cell contents). The oxygen atomic proportions must be recast to total 4. This is accomplished by multiplying the total proportions by (4÷T), where T is the sum value calculated in cell F6.

Column G = Normalized cation numbers (G2 = E2*(4/$F$6))

Formula can be written as Mg1.14 Fe0.87 Mn0.01 SiO4

End-member series

Mg2 SiO4 = forsterite

Fe2 SiO4 = fayalite

A shorthand notation for the relative forsterite or fayalite component is written as Fo56 or Fa44. This is a normalization of the Fe and Mg content, put on a scale of 0-100.

Fo content is defined as mole fraction of 100 x Mole fraction of Mg ÷ (Mole fraction of Fe + Mole fraction of Mg).

Likewise,

Fa content is defined as mole fraction of 100 x Mole fraction of Fe ÷ (Mole fraction of Fe + Mole fraction of Mg).

Graphical Representations

 

Compositional variations in minerals - Purity of composition in a mineral is more the exception than the rule.

Most minerals display variability in composition. Compositional variation is a result of the substitution of one ion or ionic compound for another ion or ionic compound into similar structural sites. The reasons for chemical variation in minerals is best understood by the study of mineral thermodynamics.

This is termed solid-solution is defined as: a mineral structure with specific atomic sites occupied by two or more ions or ionic groups in variable proportions.

Conditions for solid-solution

1. Similarity of ion size.

The relative size of two different ions in the same valence state can be evaluated by the ratio of the one ionic radius to the other . For example ionic radius of Fe3+ is 0.65Å when in octahedral coordination. The ionic radius of Al3+ is 0.54 Å when in octahedral coordination. 0.65/0.54 = 1.20. It could also be said that the Fe3+ ion is 20% larger than the Al3+ ion. This is determine by taking the difference between the ionic radii and dividing by the radius of smaller ion. (0.65 - 0.54)/0.54 = 20%

Some common examples;

ion A

ion B

Ratio A/B

 Relative size difference
Fe2+ = 0.74 Å Mg2+ = 0.66 Å

1.12

 9%
Al3+ = 0.51 Å Si4+ = 0.42 Å

1.21

 21%
OH- = 1.36 Å (O2-) F- = 1.33 Å

1.02

 2%
Mn2+ = 0.80 Å Fe2+ = 0.74 Å

1.08

 8%

A rule of thumb for determining the likelihood for ionic substitution :

Ranges: <15% common, 15-30% limited, >30% unlikely

2. The charges of ions involved must be the same. If not, then there must be a compensating substitution in another site so as to maintain electric neutrality.

3. In general, the higher the temperature during crystallization, the greater the chance for substitution.

Three types of solid-solution mechanisms

1. Substitutional - Most common type of solid solution.

The solid-solution example of the fosterite - fayalite olivine series. (i.e., Mg for Fe).

If minerals are formed at high temperature, thermal disorder is prevalent. In this case, a greater range in differences are allowed. A common example is the feldspar Sanidine KAlSi3O8 which incorporates Na.

K+ = 1.33 Å and Na+ = 0.97 Å results in a size difference = 37%

Recall a mineral must always be electrically neutral. If a divalent substitutes for a monovalent cation, then a compensating charge change must be made somewhere in the structure. In this case, the type of substitution is known as a coupled-cationic substitution.

2A2+ <---> B+ + C3+

Plagioclase series

NaAlSi3O8+ Ca2+ + Al3+ <----> CaAl2Si2O8 + Na1+ + Si4+

2. Interstitial solid-solutions

Certain structures have large interstices or voids (e.g., ring-silicates such as beryl; sheet silicates such as clay minerals and tectosilicates such as the zeolites).

See for example the beryl structure.

Water and carbon dioxide are a common examples of neutral compounds occupying an interstitial site with varying amounts.

2. Omission solid-solutions

In some cases, sites within a mineral structure will be unoccupied or unfilled. This phenomenon can be caused by several conditions. Structural defects including 1) point, 2) line and 3) planer defects.

Schottky (ion missing from structure) and Frenkel (ion displaced from its normal site) defects (see figure 4.52 a and b K page 153 or  see figure 5.11 a and b Nesse page 84).

Best known example of omission solid-solution is pyrrhotite. Pyrrhotite is an Fe and S structure with Fe2+octahedrally coordinated by S.

R = Fe2+/S2- = 0.74/1.84= 0.40 ---> C.N. = 6

If all sites are full, then the structural formula is FeS. In some cases, the Fe site is left vacant. Vacancies can occur with nearly 20% Fe missing from the structure. Because this is variable the formula of pyrrhotite is typically given as Fe(1-x)S.

Recall that the structure must be electrically neutral. The compensation is made through a redox state of the iron.

3 Fe2+ ---> 2 Fe3+

The formula is then written as:

Fe2+(1-3x) Fe3+(2x)__(x) S

__ denotes a cation vacancy.

Example for a 20% vacancy,

let x = 0.125,

Then

Fe2+(0.625) Fe3+(0.250) __(0.125) S

or

Fe2+5 Fe3+2 __1 S8

or

Fe7S8

Pyrrhotite, Fe7S8 - iron sulphide.

The sulphur atoms are arranged in an approximately hexagonal close-packed array, with iron atoms occupying octahedral interstices between the layers. One in 8 of the octahedral interstices is vacant. Consequently this can be regarded as a "defect structure", with many options for disordering of the vacancies. Click here to see an image

The mixed iron valence states is what imparts the ferrimagnetic property of pyrrhotite.