9/15/2014
Enstatite Pbcn
• Cell a=9.306; b=8.892 c= 5.349 Å
Stoichiometry
Chemical Analyses and
Formulas
• Mg1
• Mg2
• Si
(0, 0.1006, 0.25)
(0, 0.2625, 0.25)
(0.2928, 0.0897,0.0739)
• O1
• O2
• O3
(0.1200, 0.0942, 0.0770)
(0.3773, 0.2463, 0.0677)
(0.3481, 0.9836, 0.3079)
Enstatite Pbcn
Stoichiometry
• Chemical elements occur in
specific integer ratios in minerals
because of the crystal structure.
• Oxygen is the dominant anion in
minerals of the crust and mantle.
• Elements (cations) of similar radius
and charge can substitute at
specific sites.
Stoichiometry
• Chemical analyses of oxygen
bearing minerals are given as
weight percents of oxides.
• We need to be able to
recalculate oxide analyses to
cations per given number of
oxygens to derive a chemical
formula.
Geochemical Classification
of the Elements
• How do the elements partition
between coexisting fluid (melt)
phases?
–
–
–
–
Gas Phase : Atmophile : Van der Waals
Oxide phase: Lithophile : Ionic
Sulfide Phase: Chalcophile: Covalent
Metal Phase: Siderophile: Metallic
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Oxides of Lithophile Cations
•
•
•
•
•
SiO2
Al2O3
MgO
CaO
Na2O
TiO2
Cr2O3
MnO
Fe2O3
FeO
K2O
H2O
(4+)
(3+)
(2+)
(2+)
(1+)
Electron Microprobe
Electron Microprobe
• Quantitative Chemical analysis
• Major and minor element
• Uses electrons to excite secondary X-
rays from sample.
• Electrons can be focussed onto a
10μm spot
• Sample is polished thin section
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9/15/2014
Electron Microprobe
Example 1
Weight percents to formula
• Oxide
•
Wt% MolWt
Oxide
• SiO2
• MgO
•
59.85 60.086
40.15 40.312
100.0
Moles Moles Moles
Oxide Cation Oxygen
Example 1
Weight percents to formula
Example 1
Weight percents to formula
• Oxide
•
Wt% MolWt
Oxide
• SiO2
• MgO
•
59.85
40.15
100.0
Moles Moles Moles
Oxide Cation Oxygen
Example 1
Weight percents to formula
• Oxide
•
Wt% MolWt
Oxide
Moles Moles Moles
Oxide Cation Oxygen
• SiO2
• MgO
•
59.85 60.086
40.15 40.312
100.0
.9960
.9960
Example 1
Weight percents to formula
• Oxide
•
Wt% MolWt
Oxide
Moles Moles Moles
Oxide Cation Oxygen
• Oxide
•
Wt% MolWt
Oxide
Moles Moles Moles
Oxide Cation Oxygen
• SiO2
• MgO
•
59.85 60.086
40.15 40.312
100.0
.9960 .9960 1.9920
.9960 .9960 .9960
2.9980
• SiO2
• MgO
•
59.85 60.086
40.15 40.312
100.0
.9960 .9960 1.9920
.9960 .9960 .9960
2.9980
• Mole ratios Mg : Si : O = 1 : 1 : 3
• MgSiO3
3
9/15/2014
Example 2
Formula to weight percents
• Kyanite is Al2SiO5
• Calculate the weight percents
of the oxides:
– SiO2
– Al2O3
Example 2
Formula to weight percents:
Kyanite: Al2SiO5
•
•
•
•
•
Example 2
Formula to weight percents:
Kyanite: Al2SiO5
•
•
•
•
•
Oxide
Moles
PFU
1
MolWt
Oxide
Grams
Oxide
Wt%
Percent
SiO2
Al2O3
Formula weight
Oxide
Moles
PFU
SiO2
1
Al2O3
1
Formula weight
MolWt
Oxide
60.086
101.963
Grams
Oxide
60.086
101.963
Wt%
Percent
Moles
PFU
MolWt
Oxide
Grams
Oxide
Wt%
Percent
SiO2
Al2O3
Formula weight
Example 2
Formula to weight percents:
Kyanite: Al2SiO5
•
•
•
•
•
Example 2
Formula to weight percents:
Kyanite: Al2SiO5
•
•
•
•
•
Oxide
Oxide
Moles
PFU
SiO2
1
Al2O3
1
Formula weight
MolWt
Oxide
Grams
Oxide
Wt%
Percent
Example 2
Formula to weight percents:
Kyanite: Al2SiO5
•
•
•
•
•
Oxide
Moles
PFU
SiO2
1
Al2O3
1
Formula weight
MolWt
Oxide
60.086
101.963
Grams
Oxide
60.086
101.963
162.049
Wt%
Percent
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9/15/2014
Example 2
Formula to weight percents:
Kyanite: Al2SiO5
•
•
•
•
•
Oxide
Moles
PFU
SiO2
1
Al2O3
1
Formula weight
MolWt
Oxide
60.086
101.963
Grams
Oxide
60.086
101.963
162.049
Wt%
Percent
37.08
62.92
Example 3: Solid Solutions
Weight percents to formula
• Alkali Feldspars may exist with any
composition between NaAlSi3O8 and
KAlSi3O8.
• Formula has 8 oxygens:
(Na,K)AlSi3O8
• The alkalis may substitute in any
ratio, but total alkalis to Al is 1 to 1.
Example 3: Solid Solutions Weight
percents to formula (8 oxygens).
Example 3: Solid Solutions Weight
percents to formula (8 oxygens).
• Oxide
•
Wt% MolWt
Oxide
• Oxide
•
Wt% MolWt
Oxide
Moles Moles Moles
Oxide Cation Oxygen
•
•
•
•
68.20
19.29
10.20
2.32
•
•
•
•
•
•
•
68.20
19.29
10.20
2.32
1.1350
0.1892
0.1646
0.0246
SiO2
Al2O3
Na2O
K2O
–
Moles Moles Moles
Oxide Cation Oxygen
60.086
101.963
61.9796
94.204
100.00
•
SiO2
Al2O3
Na2O
K2O
60.086
101.963
61.9796
94.204
100.00
8.000
Example 3: Solid Solutions Weight
Example 3: Solid Solutions Weight
percents to formula (8 oxygens).
• Oxide
•
Wt% MolWt
Oxide
Moles Moles Moles
Oxide Cation Oxygen
• Oxide
•
Wt% MolWt
Oxide
Moles Moles Moles
Oxide Cation Oxygen
•
•
•
•
•
•
•
68.20 60.086
19.29 101.963
10.20 61.9796
2.32 94.204
100.00
1.1350 1.1350
0.1892 0.3784
0.1646 0.3291
0.0246 0.0493
•
•
•
•
•
•
68.20 60.086
19.29 101.963
10.20 61.9796
2.32 94.204
100.00
1.1350 1.1350
0.1892 0.3784
0.1646 0.3291
0.0246 0.0493
percents to formula (8 oxygens).
SiO2
Al2O3
Na2O
K2O
8.000
SiO2
Al2O3
Na2O
K2O
2.2701
0.5676
0.1646
0.0246
3.0269 x 2.6430=
8.000
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9/15/2014
Example 3: Solid Solutions Weight
percents to formula (8 oxygens).
• Oxide
•
Wt% MolWt
Oxide
Moles Moles Moles
Oxide Cation Oxygen
•
•
•
•
•
•
•
•
68.20 60.086
19.29 101.963
10.20 61.9796
2.32 94.204
100.00
1.1350 1.1350
0.1892 0.3784
0.1646 0.3291
0.0246 0.0493
SiO2
Al2O3
Na2O
K2O
2.2701
3.0
0.5676
1.0
0.1646
0.87
0.0246
0.13
3.0269 x 2.6430=
8.000
Mole ratios Na 0.87 K 0.13 Al 1.00 Si 3.00 O8
calculated as cations per 8 oxygens
Simple Solid Solutions
• NaAlSi3O8 - KAlSi3O8 Alkali Feldspars
• MgSiO3- FeSiO3 Enstatite-Ferrosilite
(pyroxene)
• MgCaSi2O6-FeCaSi2O6 DiopsideHedenbergite
• Mg2SiO4- Fe2SiO4 Forsterite-Fayalite
• Mg3Al2Si3O12- Fe3Al2Si3O12 Pyrope Almandine
Example 4
Weight Percent Oxides from
Formula
• Given the formula En70Fs30 for an
orthopyroxene, calculate the weight
percent oxides.
• En = enstatite = Mg2Si2O6
• Fs = ferrosilite = Fe2Si2O6
• Formula is (Mg0.7Fe0.3)2Si2O6 =
(Mg1.4Fe0.6)Si2O6
Example 4 (Mg1.4Fe0.6)Si2O6
Weight Percent Oxides from
Formula
•
•
•
•
•
Oxide
SiO2
MgO
FeO
Moles
PFU
2
1.4
0.6
• Formula weight
MolWt
Oxide
60.086
40.312
71.846
Grams
Oxide
Wt%
Percent
SiO2
MgO
FeO
Moles
PFU
2
1.4
0.6
MolWt
Oxide
60.086
40.312
71.846
Grams
Oxide
Wt%
Percent
• Formula weight
Example 4 (Mg1.4Fe0.6)Si2O6
Weight Percent Oxides from
Formula
•
•
•
•
•
Oxide
Example 4 (Mg1.4Fe0.6)Si2O6
Weight Percent Oxides from
Formula
•
•
•
•
•
Oxide
SiO2
MgO
FeO
Moles
PFU
2
1.4
0.6
• Formula weight
MolWt
Oxide
60.086
40.312
71.846
Grams
Oxide
120.172
56.437
43.108
Wt%
Percent
219.717
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9/15/2014
Example 4 (Mg1.4Fe0.6)Si2O6
Weight Percent Oxides from
Formula
•
•
•
•
•
Oxide
SiO2
MgO
FeO
Moles
PFU
2
1.4
0.6
MolWt
Oxide
60.086
40.312
71.846
• Formula weight
Grams
Oxide
120.172
56.437
43.108
Wt%
Percent
54.69
25.69
19.62
219.717
100.00
Example 5
Weight Percent Oxides from
Formula
• A pyroxene is a solid solution of 40%
jadeite (NaAlSi2O6) and 60% acmite
(NaFeSi2O6).
• Calculate the weight percent oxides
• Formula is Na(Al0.4Fe0.6)Si2O6
Formula is Na(Al0.4Fe0.6)Si2O6
Calculate Weight Percent
Oxides
•
•
•
•
•
•
•
Oxide
Moles
PFU
SiO2
2.0
Al2O3
0.2
Fe2O3
0.3
Na2O
0.5
Formula weight
MolWt
Oxide
60.086
101.963
159.692
61.980
Grams
Oxide
120.172
20.393
47.908
30.990
219.463
Coupled Substitutions
• Plagioclase feldspar NaAlSi3O8 -
Wt%
Percent
54.76
9.29
21.83
14.12
100.00
CaAl2Si2O8
• Jadeite-diopside NaAlSi2O6 -
CaMgSi2O6
An40 Ab60 is
Coupled Substitution
40% Anorthite; 60% Albite
Calculate Weight percent
Oxides
• First write the formula
• Anorthite is CaAl2Si2O8
• Albite is NaAlSi3O8
• An40 Ab60 is Ca.4Na.6Al1.4Si2.6O8
Ca.4Na.6Al1.4Si2.6O8
•
•
•
•
•
•
•
Oxide
SiO2
Al2O3
CaO
Na2O
Moles
PFU
2.6
0.7
0.4
0.3
MolWt
Oxide
Grams
Oxide
Wt%
Percent
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9/15/2014
An40 Ab60 is
An40 Ab60 is
Ca.4Na.6Al1.4Si2.6O8
•
•
•
•
•
•
•
Oxide
SiO2
Al2O3
CaO
Na2O
Moles
PFU
2.6
0.7
0.4
0.3
MolWt
Oxide
60.086
101.963
55.96
61.980
Grams
Oxide
Wt%
Percent
Ca.4Na.6Al1.4Si2.6O8
•
•
•
•
•
•
•
An40 Ab60 is
Oxide
Moles
PFU
SiO2
2.6
Al2O3
0.7
CaO
0.4
Na2O
0.3
Formula weight
MolWt
Oxide
60.086
101.963
55.96
61.980
Grams
Oxide
156.22
71.37
22.38
18.59
268.58
Moles
PFU
SiO2
2.6
Al2O3
0.7
CaO
0.4
Na2O
0.3
Formula weight
Wt%
Percent
58.17
26.57
8.33
6.92
100.00
•
•
•
•
•
•
•
SiO2
Al2O3
MgO
CaO
Na2O
Wt% MolWt
Oxide
56.64 60.086
7.21 101.963
13.30 40.312
18.46 55.96
4.38 94.204
99.99
Normalize to 8 oxygens
Moles Moles Moles
Oxide Cation Oxygen
Grams
Oxide
156.22
71.37
22.38
18.59
268.58
Wt%
Percent
• Jadeite is NaAlSi2O6
• Diopside is CaMgSi2O6
Jadeite - Diopside
• Oxide
•
MolWt
Oxide
60.086
101.963
55.96
61.980
Example Given Analysis
Compute Mole percents of
Jadeite and Diopside
Ca.4Na.6Al1.4Si2.6O8
•
•
•
•
•
•
•
Oxide
Jadeite - Diopside
• Oxide
•
•
•
•
•
•
•
•
SiO2
Al2O3
MgO
CaO
Na2O
Wt% MolWt
Oxide
56.64 60.086
7.21 101.963
13.30 40.312
18.46 55.96
4.38 94.204
99.99
Normalize to 6 oxygens
Moles Moles Moles
Oxide Cation Oxygen
.9426
.0707
.3299
.3299
.0246
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Jadeite - Diopside
• Oxide
•
•
•
•
•
•
•
•
Wt% MolWt
Oxide
SiO2
Al2O3
MgO
CaO
Na2O
56.64 60.086
7.21 101.963
13.30 40.312
18.46 55.96
4.38 94.204
99.99
Normalize to 6 oxygens
Jadeite - Diopside
Moles Moles Moles
Oxide Cation Oxygen
• Oxide
•
.9426
.0707
.3299
.3299
.0246
•
•
•
•
•
•
•
.9426
.1414
.3299
.3299
.0493
1.8852
.2121
.3299
.3299
.0246
Wt% MolWt
Oxide
SiO2
Al2O3
MgO
CaO
Na2O
56.64 60.086
7.21 101.963
13.30 40.312
18.46 55.96
4.38 94.204
99.99
Normalize to 6 oxygens
Moles Moles Moles
Oxide Cation Oxygen
.9426
.0707
.3299
.3299
.0246
.9426
.1414
.3299
.3299
.0493
1.8852
.2121
.3299
.3299
.0246
2.8278 x 2.1218=
6.000
• Na.3Ca.7Al.3Mg.7 Si2O6 =
• 30% Jadeite 70% Diopside
Jadeite - Diopside
• Oxide
•
Wt% MolWt
Oxide
Moles Moles Moles
Oxide Cation Oxygen
•
•
•
•
•
•
56.64
7.21
13.30
18.46
4.38
99.99
.9426
.0707
.3299
.3299
.0246
SiO2
Al2O3
MgO
CaO
Na2O
60.086
101.963
40.312
55.96
94.204
• Normalize to 6 oxygens
.9426
.1414
.3299
.3299
.0493
1.8852
2.0
.2121
0.3
.3299
0.7
.3299
0.7
.0246
0.3
2.8278 x 2.1218=
6.000
• Na.3Ca.7Al.3Mg.7 Si2O6 =
• 30% Jadeite 70% Diopside
Cell Volume (1Å3=10-24 cm3)
•
•
•
•
•
•
Cubic
Tetragonal
Hex/Trigonal
Orthorhombic
Monoclinic
Triclinic
V
V
V
V
V
=
=
=
=
=
a3
a2c
a2c sin 120º
abc
abc sin β
• V = abc (1 + 2cos α cos β cos γ - cos2α -
Unit Cells and Mineral Density
• Unit cell is basic repeat unit of
•
•
•
•
structure.
Parallel-piped box: a, b, c (Å), α, β, γ (º)
Å = 10-8cm
Avogadro’s number (# atoms / mole) =
6.02 x1023
If you know the contents of the box
and the size of the box you can
calculate the density.
Avogadro’s Number
• The number of atoms in a mole.
• A mole of any compound is the
molecular weight in grams.
• 6.022 x 1023
cos2β - cos2γ)1/2
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9/15/2014
Density
Example Density Calculation
• Calculate the density of ferberite
• Volume of Avogadro’s number of unit cells = AV
• The number of formula units per unit cell = Z
(FeWO4), which is monoclinic with
• a = 4.73; b = 5.70; c = 4.95; β =
90.01; Z = 2.
• Calculate the gram formula weight:
– Z is a small integer 1 to about 16.
• Weight of Avogadro’s number of unit cells
= Z* FW
–
–
–
–
Example Density
Calculation:
Ferberite FeWO4
• V = abc sin β = (4.73)(5.70)(4.95)(sin
•
•
•
•
90.01º)
V = 133.46 Å3
V = 1.335 x 10-22 cm3
ρ = ZFw/AV = 2 (303.70) / 6.02 1023
*1.335 10-22
ρ = 7.56 g/cm3
1 Fe (55.847) =
55.847
1 W (183.85) = 183.85
4 O (15.9995) 63.998
FW =
303.695 g
Example Density
Calculation:
Witherite BaCO3
•
•
•
•
•
Witherite is orthorhombic Pmcn
a = 5.316; b = 8.892; c = 6.428
V = 303.85
Z=4
FW = 197.34g
Example Density
Calculation:
Witherite BaCO3
V = 303.85 Å3
• V = 3.0385 x 10-22 cm3
• ρ = ZFw/AV = 4 (197.34) / 6.02 1023
*3.038 10-22
• ρ = 4.31 g/cm3
10