Mineral group Anion or anion gp

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Mineral Structures


From definition of a mineral:


“…an ordered atomic arrangement…”


How do Pauling’s rules control “ordered
atomic arrangement?”


How can crystal structure make one
mineral different from another?


Can mineral structures be used to group
minerals (e.g. classify them)?

Illustrations of mineral structures


2
-
D representation of 3
-
D materials


Ions represented as spheres


drawn to
scale


Stick and ball method


Polyhedron method


Hybrid: Stick and Ball, plus polyhedron


Map view


unit cell dimensions

Fig. 4
-
10


Olivine


view
down a
crystallographic
axis

Structures


Isostructural

minerals


Same structure, different composition


Polymorphism


polymorphic minerals


Same composition, different structures

Isostructural

Minerals


Many minerals have identical structures,
different compositions


Example: halite (
NaCl
) and Galena (
PbS
)


Differ in many physical properties
-

composition


Identical symmetry, cleavage, and habit


elemental arrangement

Isostructural group


Several
isostructural

minerals


Have common anion group


Much substitution between cations


Example: calcite group


Polymorphism


The ability for compounds with identical
compositions to crystallize with more than
one structure


Polymorphs


Polymorphic groups


Caused by balance of conflicting
requirements and environmental factors:


Attraction and repulsion of cations and anions
(charge)


Fit of cations in coordination site (size)


Geometry of covalent bonds


P & T


Polymorphs controlled by P and T
conditions:


High P favors tightly packed lattice, high
density


High T favors open lattice, low density, wide
substitution


Composition of environment unimportant


All same elements in polymorphs


Presence or absence of polymorphs
provide information on P and T conditions


Four types of mechanisms to create
polymorphs:

1.
Reconstructive


break bonds

2.
Order
-
disorder


cation placement

3.
Displacive



kink bonds

4.
Polytypism



stacking arrangement

1. Reconstructive polymorphism


Requires breaking bonds


major
reorganization


Symmetry and/or structural elements may
differ between polymorphs


Symmetry and/or structural elements may be
similar because identical composition


Example: C

C = Diamond and Graphite


Diamond


all 100% covalent bonds


Graphite


covalent bonds within sheets,
van der Waal bonds between sheets



What conditions cause one mineral or the
other to form?


Graphite


stable at earth surface T and P



Diamond stable only at high P and T


but
found on earth surface


Won’t spontaneously convert to graphite


Minerals that exists outside of their stability
fields are
metastable

Fig. 4
-
11


Found on a
Phase Diagram


e.g. for single component

~200 km depth

~100 km depth

Where on (in) the earth would diamond form/be stable?

Single component = C

Increasing

Depth

What are temperatures at these depths?

Red line is
geothermal
gradient

Kimberlite

Diamond stability versus geothermal gradient

Diamond window

Phase diagram

Conceptual model of earth

Stability
Boundary of
Diamond
and
Graphite

Asthenosphere

Lithosphere


Metastable

minerals occur because of
energy required for conversion


Bonds must be broken to switch between
polymorphs


Cooling removes energy required to break
bonds


Rate of cooling often important for lack of
conversion


e.g. fast cooling removes energy
before reactions occur


Quenching


“frozen”: e.g.
K
-
feldspars


Example of
Order
-
disorder polymorphism

2. Order
-
disorder polymorphism


The mineral structure remains same
between polymorphs


Difference is in the location of cations in
structure


Good examples are the K
-
feldspars


K
-
feldspar has 4 tetrahedral sites called T1 and
T2 (two each)


Idealized feldspar structure

Fig. 12
-
6

Si or Al

K (or Na, Ca)

Si or Al

“K
-
spars”


KAlSi
3
O
8



one Al
3+

substitutes for one Si
4+


High Sanidine (high T)


Al can substitute for
any Si


completely disordered


Low Microcline (low T)


Al restricted to one
site


completely ordered


Orthoclase (Intermediate T)


Intermediate
number of sites with Al

Fig. 4
-
13


Order
-
disorder in the K
-
feldspars

High Sanidine


Al
3+
equally
likely to be in any one of
the four T sites

Microcline


Al
3+

is restricted
to one T1 site. Si
4+

fills other
three sites


Degree of order depends on T


High T favors disorder


Low T favors order


Sanidine formed in magmas found in
volcanic rocks


quenched at disordered
state:
metastable


Microcline found in plutonic rocks


slow
cooling allows for ordering to take place


Over time, sanidine will convert to
microcline


3.
Displacive

Polymorphism


No bonds broken


a

and
b

quartz are good examples


b

quartz
(AKA
high quartz
)


1
atm

P and > 573º C, SiO
2

has 6
-
fold
rotation axis.


a

quartz
(AKA
low quartz
)


1
atm

P and < 573º C, SiO
2

distorted to 3
-
fold
axis

Fig. 4
-
12


b

quartz

a

quartz

View down c
-
axis



Conversion can not be quenched, always
happens



Never find metastable
b

quartz

6
-
fold rotation
axis

3
-
fold rotation
axis


External crystal shape may be retained
from conversion to low form


Causes strain on internal lattice


Strain may cause
twinning

or
undulatory

extinction


Must have sufficient space for mineral to form

Undulatory extinction

(4)
Polytypism


Stacking diffrences


Common examples are micas and clays

Fig. 4
-
14


Orthorhombic,
single stacking
vector, 90º

Orthorhombic,
two stacking
vectors, not
90º

Monoclinic,
single stacking
vector, not 90º


Eventually will get to controls on
compositional variations


First some “housekeeping”


necessary
skills:


Scheme for mineral classification


Rules for chemical formulas


A graphing technique


ternary diagrams

Mineral Classification


Based on major anion or anionic group


Consistent with chemical organization of
inorganic compounds


Families of minerals with common anions
have similar structure and properties


Cation

contents commonly quite variable


Follows from Pauling’s rules


1, 3, and 4 (coordination polyhedron &
sharing of polyhedral elements)
-

anions
define basic structure


2: (electrostatic valency principle) anionic
group separate minerals


Mineral group

Anion or anion gp

Native elements

N/A

Oxides

O
2
-

Hydroxides

OH
-

Halides

Cl
-
, Br
-
, F
-

Sulfides

S
2
-

Sulfates

SO
4
2
-

Carbonates

CO
3
2
-

Phosphates

PO
4
3
-

Silicates

SiO
4
4
-

Mineral Formulas


Rules


Cations first, then anions or anionic group


Charges must balance


Cations of same sites grouped


Cations listed in decreasing coordination
number


Thus also decreasing ionic radius


Also increasing valence state

Examples


Diopside



a pyroxene: CaMgSi
2
O
6


Charges balance


Ca

-

8 fold coordination: +2 valence


Mg
-

6 fold coordination: +2 valence


Si


4 fold coordination: +4 valence


Anionic group is
Si
2
O
6


Substitution within sites indicated by
parentheses:


Ca(
Fe,Mg
)Si
2
O
6


Intermediate of two end
-
members:
Diopside

(CaMgSi
2
O
6
)


Hedenbergite

(CaFeSi
2
O
6
)
complete solid solution series

(more on “solid solution” in a moment)



Can explicitly describe substitution


E.g. Olivine: (Mg
2
-
x
,Fe
x
)SiO
4


0 ≤ x ≤ 2


Alternatively: Can describe composition by
relative amounts of end members:


Forsterite = Fo


Fayalite = Fa


All of the following are the same:


(Mg
0.78
Fe
0.22
)
2
SiO
4


Mg
1.56
Fe
0.44
SiO
4


Fo
78
Fa
22

(here numbers are percentages of
amount of each mineral)


Fo
78
(here implied that the remainder is Fa
22
)


Fa
22


How to calculate chemical
formulas for solid solutions


Eg
. Plagioclase feldspars:


Albite,
Ab



NaAlSi
3
O
8


Anorthite
, An


CaAl
2
Si
2
O
8


What is chemical composition of say
Ab
25
An
75
?

Graphic representation


Common to have three “end members”


Ca
2+
, Mg
2+

and Fe
2+
common substitutions
between silicate minerals


Ternary diagrams


Used to describe distribution of each end
member


Total amount is 100%


See page 84

Fig. 4
-
17


Pyroxenes:

(Mg,Fe,Ca)
2
Si
2
O
6

8% Fs

50% Wo

42% En

Composition is:


En
42
Fs
8
Wo
50


(Mg
0.42
Fe
0.08
Ca
0.5
)
2
Si
2
O
6

Ca
2
Si
2
O
6

Fe
2
Si
2
O
6

Mg
2
Si
2
O
6

Compositional Variation


Think of minerals as framework of anions


Form various sites where cations reside


Principle of parsimony


Not all sites need to be filled


Some sites can accommodate more than one
type of ion (e.g. polymorphism in feldspar,
solid solution in olivine)



Solid solution


Occurs when different cations can occur in a
particular site


Three types: Substitution, omission, and
interstitial


Anions can substitute for each other, but
this is rare


Tourmaline

Na(
Mg,Fe,Li,Al
)
3
Al
6
[Si
6
O
18
] (BO
3
)
3
(O,OH,F)
4




W = usually Na, sometimes Ca or K

X = usually Mg and Fe, sometimes
Mn
, Li,
and Al

Y = usually Al, Less commonly Fe
3+

or Mg

B = Borate ions, B is small,
trigonal

Fig. 15.9

Terms


Substitution series
or
solid solution series
:
the complete range of composition of a
mineral


End members
: the extremes in the range
of compositions


E.g. olivine:
Forsterite

and
Fayelite

Terms


Continuous

or
complete solid solution
series
: all intermediate compositions are
possible


E.g. Olivine


Incomplete

or
discontinuous solid solution
series:
a restricted range of compositions


E.g

Calcite
-

magnesite

Substitutional Solid Solution


Two requirements for substitution


Size


substituting ions must be close in size


Charge


electrical neutrality must be
maintained

Size


Comes from Pauling rule 1: coordination


In general size of ions must be < 15%
different for substitution


Tetrahedral sites: Si
4+

and Al
3+


Octahedral sites: Mg
2+
, Fe
2+
, Fe
3+
, Al
3+


Larger sites: Na
+

and Ca
2+


Temperature is important


Example is K and Na substitution in alkali
feldspar (Sanidine and Albite)


Size difference is about 25%


Complete solid solution at high T


Limited solid solution at low T


Results in
exsolution

Types of substitution


Substitutional solid solution


Simple substitution


Coupled substitution


Omission substitution


Interstitial substitution


Different types have to do with where the
substitution occurs in the crystal lattice

Simple Substitution


Occurs with cations of about same size
and same charge


Example: Olivine

Fig. 4
-
15


View down a axis

Olivine
-

(Fe
.22
Mg
.78
)
2
SiO
4

22% Fe

78% Mg

Coupled Substitution


Coupling two substitutions


One that raises charge


Linked one that decreases charge


Example: Albite (NaAlSi
3
O
8
) and
Anorthite

(CaAl
2
Si
2
O
8
)


Ca and Na occupy distorted 8
-
fold site


Al and Si occupy tetrahedral sites


Fig. 4
-
15


Coupled substitution:

Na
+

+ Si
4+

= Ca
2+

+ Al
3+

Coupled substitution


The substitution doesn’t always have to be
different sites


Corundum (Al
2
0
3
)


Fe
2+

and Ti
4+

substitute for 2Al
3+

(makes
sapphire). Cr
3+

makes Ruby


Both elements are in octahedral sites


Can couple cations and anions


Hornblende: Fe
2+

and OH
-

substitutes for Fe
3+

and O
2
-

Omission substitution


Charge balance maintained by leaving site
vacant


Pyrrhotite
: variable amounts of Fe
2+

and
Fe
3+


Formula: Fe
(1
-
x)
S where 0<X<0.13


General substitution:


(n+1)M
n+

=
nM
(n+1)+

+



where


is vacant, n is the number of sites

Fig. 4
-
15


14Fe
2+

= 8 Fe
2+

+ 4 Fe
3+

+ 2


28+ = 28+

14 sites = 14 sites

Interstitial substitution


Type of omission substitution


Difference is that regular lattice
framework site is not location of
substitution


Example: Beryl, a ring silicate


Large openings can have K
+
,
Rb
+

and Cs
+

Fig. 15
-
6


Substitution important: Cr
substition makes emerald,
other substitutions make
Aquamarine


blue green
variety of emerald

Structure of Beryl

Be
3
Al
2
Si
6
O
8

Rings

Al 6
-
fold coordination

Be 4
-
fold coordination

Fig. 4
-
15


Al, Be substition for Si

Charge balance
maintained by interstitial
substitution