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Gemology -Crystallography-
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( Crystallography )
Chemistry of Crystal
(crystalline gems)
Quartz Diamond Corundum Tourmaline Topaz
(amorphous gems)
(SiO2) (SiO2)
Crystalline SiO2 (Quartz)
Amorphous SiO2 (Glass)
Crystalline matter Amorphous matter
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1. Chemical bonding
(chemical bonding) 2
(Ionic bond) (covalent bond)
(cation) IA IIA IIIA (Mg)
2 Mg2+ (anion)
VA VIA VIIA (O) 2
O2-
(Na : Z=11) (Cl : Z=17) I
(valence electron) 1
VII 7 1
NaCl Na+ Cl- 1
NaCl
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2
()
IV Periodic 4
4
4 3
(SiO2)
3
(Van der waals force)
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3
( )
4 Beryllium Be2+ 0.35 5 Boron B3+ 0.23 6 Carbon C4+ 0.15 8
Oxygen O2- 1.40 9 Fluorine F- 1.36
12 Magnesium Mg2+ 0.66 13 Aluminium Al3+ 0.51 14 Silicon Si4+
0.40 19 Potassium K+ 1.33 20 Calcium Ca2+ 0.99 22 Titanium Ti4+
0.68 23 Vanadium V2+ 0.74 24 Chromium Cr3+ 0.63 25 Manganese Mn2+ ,
Mn3+ 0.80 , 0.66 26 Iron Fe2+ , Fe3+ 0.74 , 0.64 28 Nickel Ni2+
0.69 29 Copper Cu+ 0.96 40 Zirconium Zr4+ 0.79
2. Closet packing
(closet packing) 2
1. Hexagonal closet packing : hcp
1 6 A
2 B 3 1
AB AB AB
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2. Cubic closet packing : ccp
1 4 ABC
ABC
2 12
6 3 3
(coordination number)
12
3. Phenomena
( )
1. Isomorphism
(NaCl) (MgO)
Periclase NaCl
MgO
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X2Y3(SiO4)3 X2
Y3
2. Polymorphism
(CaCO3) 2 Calcite
Aragonite Calcite
Hexagonal Trigonal Aragonite Orthorhombic
Diamond Graphite
NaCl MgO
Calcite Aragonite
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3. Ionic substitution and solid solution
(coloring agents)
Chromium Corundum, Vanadium Emerald, Iron Aquamarine
( Cr3+ , V2+ , Fe2+ , Fe3+ )
Corundum (Al2O3) Al3+ Cr3+
Cr2O3 1% Corundum Pyrope
(Mg3Al2Si3O12) Almandine (Fe3Al2Si3O12)
Pyrope
Pyrope
(solid solution)
4. Exsolution
(solute atom)
(Exsolution)
Corundum Titanium Oxide (Ti2O3)
Ti3+ Al3+
(TiO2 : rutile needle) Corundum
(host crystal) Corundum
Hexagonal 60/120
Corundum
Corundum
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Crystallography
(Crystallography)
Gemology
1. Type of crystal 2
1. Single crystal
Quartz Diamond Corundum
2. Aggregate Polycrystalline
2
1) Microcrystalline material
Nephrite
2) Cryptocrystalline material
microcrystalline Quartz
Chalcedony
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2. Bravais lattice
(space lattices)
space lattices Unit cell
a, b c X, Y Z ,
b c, a c a b a , b , c , (lattice constants)
.. 1849 Auguste Bravais
14 14 unit cell Bravais lattice
Bravais lattice 14 unit cell 4
1) Simple Primitive
unit cell unit cell
2) Body-centered
unit cell unit cell 1 unit cell
3) Face-centered
unit cell unit cell unit cell
4) End-centered
unit cell unit cell 2
unit cell
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3. Crystal face
unit cell unit cell
unit cell ()
unit cell
n2 unit cell ( n = 5 n3 = 125 )
unit cell
unit cell
(tabular) () () 3 6
unit cell
(octahedron) () (dodecahedron) ()
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Peridot unit cell Olivine unit
cell () unit cell ()
h unit cell () k
Peridot
Peridot
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(Striations) Tourmaline, Quartz
unit cell lattice
Nicolas Steno
Stenos law
Goniometer
4. Crystal symmetry
(crystal symmetry)
3
1) Planar symmetry
2
2) Axial symmetry
2 2
(2 fold axis) cc 4 (4 fold
axis) AA3 A2A4 2
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3) Central point symmetry
C
5. Form & Habit (Form) (outward appearance)
(Habit) (external shape)
2 (closed form)
2 (dipyramid) (open form)
(prism) (pinacoid)
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1) Pinacoid form
1 () ()
2) Prism form
3
3, 4, 6, 8 12
3) Pyramid form
3, 4, 6, 8 12
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4) Bipyramid form
2 6, 8, 12, 16
24
(shape)
(cube) (octahedron) (prism)
Ruby
Aggregate
(acicular) (bladed) (tabular) (stubby)
(columnar) Aggregate Cryptocrytalline
(granular massive) (fibrous)
6. Crystal system (crystal system) 6 a, b c a
- b - c -
a1, a2 a3 , ,
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1) Isometric or Cubic System : 3
: a1 = a2 = a3
: = = = 90
Diamond, Garnet, Spinel, Synthetic Spinel, YAG, Synthetic
Cubic
Zirconia CZ, Strontium Titanate
a. Cube 6 Diamond, Fluorite, Pyrite, Cuprite
b. Octahedron 2 8 Diamond, Spinel, Fluorite, Cuprite,
Lazurite
c. Dodecahedron 12 Diamond, Garnet, Cuprite, Sodalite,
Polluzite, Lazurite,
Pyrite
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d. Trapesohedron 24 Diamond, Garnet
2) Tetragonal System : 3
: 2 1 a = b c
: = = = 90
Zircon, Synthetic Rutile
a. Square prism Diamond, Zircon, Synthetic Rutile,
Cassiterite
b. Acicular Rutile
3) Hexagonal System : 4
: 3 a1 = a2 = a3
1 a = b c
: 3 60
4 = = 90 , = 120
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Beryl, Apatite, Beniotite
a. Hexagonal prism Beryl, Apatite, Quartz
Beryl Apatite Quartz
b. Tabular Beryl, Apatite, Beniotite
4) Trigonal or Rhombohedral Subsystem
Trigonal Hexagonal system
Hexagonal 6 Trigonal
3
Corundum, Quartz, Tourmaline, Calcite, Rhodochrosite,
Dioptase
a. Prism Corundum, Quartz, Tourmaline
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b. Dipyramid Quartz, Corundum
c. Rhombohedron Calcite, Rhodochrosite, Dioptase
d. Tabular Corundum, Calcite
e. Barrel-Shaped Corundum
f. Acicular Tourmaline, Penakyte
g. Botryoidal- Smithsonite
h. Granular massive Quartz, Calcite
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5) Orthorhombic System : 3
: 3 a b c
: 90 , = = = 90
Peridot, Topaz, Iolite, Chrysoberyl, Zoisite, Andalusite
a. Prism Topaz, Andalusite, Zoisite
b. Blocky- Peridot, Topaz, Chrysoberyl, Barite
c. Granular massive Topaz Prehnite, Aragonite, Zoisite
d. Pseudo-hexagonal twin Chrysoberyl
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6) Monoclicnic System : 3
: 3 a b c
: 2 90 1 2
= = 90 , 90
Spodumene, Nephrite, Jadite, Orthoclase, Actinolite,
Malachite,
Diopside
a. Prism Spodumene, Orthoclase, Actinolite
b. Blocky- Orthoclase, Datolite
c. Botryoidal- Malachite, Azurite
d. Granular massive Jadite, Nephrite, Actinolite
e. Fibrous Actinolite, Nephrite
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7) Triclinic System : 3
: 3 a b c
: , 90
Turquoise, Labradorite, Rhodonite, Microcline, Amazonite,
Kyanite
a. Prism Turquoise, Amazonite, Albite
b. Tabular or Blocky Rhodonite, Axinite
Axinite Rhodonite c. Bladed Kyanite
d. Granular massive Turquoise
