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1

Mineral/Crystal Chemistry

and

Classification of Minerals Revisited

Coordination, Solid Solution, Polymorphs
and Isomorphs, Mineral Classes

2

Mineral and Crystal Chemistry

Minerals have:


Characteristic geometric arrangement or structure of
constituent atoms that is regular and repeating in a 3
-
D
arrangement (CRYSTALLINE SOLID)


Arrangement of atoms depends on their ionic radius and
valence


Many minerals can be conceptualized as anions (or anion
complexes) tightly packed together with cations filling in the
intervening spaces (COORDINATION POLYHEDRA)


Fixed or fixed range of chemical composition
(FORMULA)


Substitution of one element for another (SOLID SOLUTION)


Depends on their ionic radius and valence


Substitution may be complete or limited, simple or coupled, and
varies with P
-
T conditions

3

Atomic Theory


Ionic radius (IR) and Valence


Cations (+)

> generally smaller IR


Anions (
-
)

> generally larger IR


Variable dependant on atomic number and interaction with
other ions

4

The Coordination Principle:

Geometry of Atomic Building Blocks



In an ionically bonded substance (all minerals
for our purposes) cations are surrounded by
anions (or anionic complexes)


In stable mineral crystals


The
number

and
arrangement

of anions surrounding
a cation forms a

Coordination polyhedron

5

The Coordination Principle

Coordination polyhedron


If all atoms are the same size, they can be packed
together so that each atom touches 12 others
(Hexagonal or Cubic closest packing)

6

The Coordination Principle

Coordination polyhedron


BUT atoms vary in size


So the size and shape of the coordination
polyhedron is determined by the ionic radii of the
cation and anion (anion complex) involved


Radius ratio (cation radius/anion radius)


This shape is
described by
the number of
anions
surrounding a
cation:


Coordination
number
(C.N.)


7

Coordination Polyhedron

A. Triangular (CN
= 3)

B. Tetrahedral
(CN 4)

C. Octahedral
(CN 6)

D. Cubic (CN 8)

E. Dodecahedral
(CN 12)

8

The Coordination Principle


Oxygen (O
-
2
) is the
most common
anion in
coordination
polyhedron


Cations coordinate
with oxygen in
predicable ways
(see Ch. 4, p. 10)


Minerals have
specific physical
locations (sites)
that can hold only a
few types of ions


Each site has
specific
coordination
polyhedron type

9

The Coordination Principle


Coordination
explains anion
groups


O is more tightly
bonded to central,
highly charged cation
than to other cations


Examples:


C
+4

in triangular
coordination (CN = 3)
produces (CO
3
)
-
2


S
+6

in tetrahedral
coordination (CN = 4)
produces (SO
4
)
-
2



Si
+4

in tetrahedral
coordination (CN = 4)
produces (SiO
4
)
-
4


10

Mineral Formulas


Formula reflects the proportions of elements
(cations and anions) present in the mineral


Common conventions:


Subscripts indicate atomic proportions; superscripts
indicate charge


Commas for either
-
or; ex: olivine [(Mg,Fe)
2
SiO
4
]


Anion complexes typically in parentheses; ex: dolomite
[CaMg(CO
3
)
2
]


Historically determined by wet chemical techniques


Modern techniques typically use focused energy
beam (electron or ion microprobe)


Reported at wt% of elements or oxides


Must be converted to atomic proportions

11

Mineral Formulas: Recalculation


Formula = CuFeS
2

Wt%

Atomic wt
(gm/mole)

Atomic
proportions*

Atomic
ratio**

Cu

34.30

63.54

0.5398

~1

Fe

30.59

55.85

0.5477

~1

S

34.82

32.07

1.0857

~2

SUM

99.71


Converts wt% of elements or oxides into a mineral
formula (pure substance or solid solution)

*Calculated by wt%/atomic wt

Ex for Cu: 34.30/63.54 = 0.5398

**Normalized to make the smallest

number equivalent to 1

12

Mineral Formulas: Graphical
Representation


Can show relative proportions of elements in a mineral


In wt%, oxide wt%, or atomic proportions


Especially useful in showing multi
-
component systems and solid
solution systems

100% C

100% A

100% B

100% A

100% B

0% B

0% A

Two components

Three
components

13

Mineral Formulas: Graphical
Representation


Example:


CaO


MgO


SiO
2

system

14

Atomic Substitution/Solid Solution


Homogeneous
crystalline solids of
variable chemical
composition


Many minerals vary
in their composition


Elements are
readily substituted
(atomic substitution)
for one another in
many crystal
structures,
when
certain conditions
are met

15

Atomic Substitution/Solid Solution

Requires:


Valences of
substituting
ions are no
more different
than 1


Na
+1

for Ca
+2


Al
+3

for Si
+4


Difference in
the size of
substituting
ions must be
<15%
(at room
temperature)

16

Atomic Substitution/Solid Solution


Some substitutions involve
complete solid solution



Involves ions of (nearly) equal charge and size


Any composition (mixture) may occur between end member
compositions


Examples:


Olivine series: Forsterite
(Mg
2
SiO
4

) to Fayalite
(Fe
2
SiO
4
)



Plagioclase feldspar
series: Albite
(NaAlSi
3
O
8
) to Anorthite
(CaAl
2
Si
2
O
8
)

17

Atomic Substitution/Solid Solution


Some substitutions involve
partial or limited solid solution



Involve ions of different sizes or charges


Limited compositions (mixtures) may occur between end
members


Examples:


Carbonates: Limited
solid solution between
Calcite (CaCO
3
) to
Dolomite [CaMg(CO
3
)
2
]
and Magnesite
(MgCO
3
) to Dolomite



Pyroxene group: Limited
solution between
Hypersthene (MgSiO
3
)
and Diopside
(CaMgSi
2
O
6
)

18

Atomic Substitution/Solid Solution


Some substitutions are
simple



1 for 1 substitution of ions of equal charge


Some substitutions are
coupled



Substitution involves 2 or more ions


Necessary to balance different charges


Examples:


Carbonates: Simple
solid solution between
Magnesite (MgCO
3
) and
Siderite (FeCO
3
)



Plagioclase feldspar:
Coupled solution
between Albite
(NaAlSi
3
O
8
) to Anorthite
(CaAl
2
Si
2
O
8
)

19

Solid Solution & T
-
P Controls


Atomic substitution is greater at higher temperature

(crystal lattices are more open) and can accommodate
greater ionic radius deviation (than 15%)


Na
+1

IR = 0.97


K
+1

IR = 1.33


Ca
+2

IR = 0.99



Atomic substitution is
greater at higher
pressure

because it can
change the size of
crystallographic sites and
ions, thus accommodate
greater ionic radius
deviation

20

Polymorphism


The same chemical formula applies to two (or more) distinct
mineral species


Chemical composition may not be sufficient to designate a specific
mineral species (physically homogeneous and separable portion of a
material system)


Polymorphs have different crystal forms (atomic arrangements) and
different physical properties


Different polymorphs occur as a result of differing environmental
conditions, principally temperature and pressure

Pyrite, FeS
2
(Fe
+2
S
2
)
,
Cubic

Marcasite, FeS
2
(Fe
+2
S
2
)
,
Orthorhombic

21

Polymorphs


Examples:


Diamond and Graphite (C);

Geobarometer:

(determines pressure of formation)

Graphite

Diamond

22

Polymorphs


Examples:


Quartz,
Tridymite, and
Cristobolite
(SiO
2
);

Quartz

Tridymite

Cristobalite

23

Polymorphs


Example:


Calcite
and
Aragonite
(CaCO
3
);

Calcite

Aragonite

24

Isomorphism (Isostructuralism)


Minerals with analogous formulas where the
relative sizes of cations and anions are similar
and crystal structure is identical or closely
related


Typically (but not always) the basis for grouping and
classification, e.g.


Garnet group, Amphibole group, Mica group, Pyroxene group

Galena, PbS

Halite, NaCl

25

Isomorphism


Anions and cations of
isomorphic minerals
have


The same relative size


The same coordination


Crystallize in the same
crystal structure


Share similarity of
crystal structure but not
(necessarily) chemical
behavior


Ex: Halite and galena

Galena, PbS

Halite, NaCl

26

Isomorphism


Some
isomorphic
minerals share
closely related
formulas and
identical crystal
structures



Ex: Aragonite
(orthorhombic)
and Calcite
(trigonal)
Groups

27

Isomorphism and Solid Solution


Some isomorphic minerals have such similar compositions
and structures that they form solid solution


Complete solid solution between Albite (NaAlSi
3
O
8
) and Anorthite
(CaAl
2
Si
2
O
8
)


Limited solid solution between Calcite (CaCO
3
) and Magnesite
(MgCO
3
)


Isomorphism and solid solution are distinct though
related concepts


Some isomorphic minerals do
not have solid solution; Ex:
Halite (NaCl) and Galena
(PbS)



Some solid solutions do not
have isomorphic end
members; Ex: Sphalerite (Zn,
Fe)S (cubic) and Pyrrhotite
Fe
1
-
x
S (hexagonal)


Sphalerite

Pyrrhotite

28

Hierarchy of Mineral Classification


Class
(chemical
-

anion complex)


Subclass
(atomic structure)


Group
(chemical and structural)


Species
(individual mineral


name)

»
Variety
(specific variation)


Class: Silicate
(SiO
4
4
-
)


Subclass: Tektosilicate
(framework)


Group: Plagioclase Series

(An
-
Ab)


Species: Oligoclase
(70
-
90% Ab)

»
Variety: Sunstone
(red
-
orange gemstone)

29

Mineral Classes


Based on the
anion or
anionic
complexes

in
the crystal
structure


Types of
bonding and
structures are
the same (or
similar)


Physical
properties can
be very similar
within classes

Hierarchy of Mineral Classification:

30

Hierarchy of Mineral Classification

Mineral Subclasses



Classified on basis of
structure


Example: silicates


Nesosilicates
: SiO
4
,
independent silica
tetrahedra


Sorosilicates
: Si
2
O
7
, double
silica tetrahedra


Cyclosilicates
: SiO
3
, ring of
silica tetrahedra


Inosilicates
: Si
4
O
11
, chains of
silica tetrahedra


Phyllosilicates
: Si
2
O
5
,
sheets of silica
tetrahedra


Tektosilicates
: Si0
2
,
frameworks of silica
tetrahedra

31

Hierarchy of Mineral Classification


Mineral Groups
; mineral species with close
chemical and structural relationship e.g.
(typically due to atomic substitution/solid
solution)


Example: Amphibole, Feldspar, Mica, Pyroxene,
Garnet, Olivine, Spinel

32

Hierarchy of Mineral Classification


Example: Plagioclase
Group (Series)


Albite: NaAlSi
3
0
8


Oligoclase


Andesine


Labradorite


Bytownite


Anorthite: CaAl
2
Si
2
O
8

Mineral Species



naturally occurring homogeneous crystalline substance of inorganic
origin, possessing characteristic physical properties, with either definite
chemical composition
or range in composition between certain
limits”

33

Hierarchy of Mineral Classification

Mineral Variety


Slight variation in trace (non
-
structural) element content
and resultant distinctive physical properties (typically
color)


Corundum

> Ruby (red), Sapphire (blue) [AL
2
O
3
]


Classification tending to move away from species and variety
names to names using a modifier of main species, e.g.


Fe in magnesite (MgCO
3
)

> ferroan magnesite

Ruby

Sapphire

34

Collaborative Activity

In groups, answer the following. Show all calculations.

1.
Predict the coordination number (CN) and name the
coordination polyhedron for each of the following cation
-
anion pairs:


A. Zn (0.6
Å
)


S (1.84
Å
)


B. Rb (1.61
Å
)


Cl (1.81
Å
)

2.
The handout has two analyses of the mineral ilmenite.



A. For analysis #1, convert the given weight proportions into atomic
proportions and calculate the mineral formula


B. Analysis #2 shows that a bit of solid solution is possible in the
ilmenite structure, with Mg and/or Mn substituting for Fe. Calculate
the formula for this analysis

3.
Plot the following compositions on the TiO
2
-
FeO
-
Fe
2
O
3

diagram:

Ilmenite (from analysis #1), Rutile (TiO
2
), Hematite (Fe
2
O
3
),
Magnetite (Fe
3
O
4
), and Ulv
ö
spinel (Fe
2
TiO
4
)

4.
Plot the following compositions on the same diagram:


A. 10% TiO
2
, 10% FeO, 80% Fe
2
O
3


B. 40% TiO
2
, 25% FeO, 35% Fe
2
O
3