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| 1 | +title: Crystal Systems |
| 2 | +description: The seven crystal systems and their characteristic symmetry elements. |
| 3 | +order: 1 |
| 4 | +category: fundamentals |
| 5 | +difficulty: beginner |
| 6 | +icon: cube |
| 7 | +related: |
| 8 | + - physical-properties |
| 9 | + - optical-properties |
| 10 | +tags: |
| 11 | + - crystallography |
| 12 | + - symmetry |
| 13 | + - identification |
| 14 | + |
| 15 | +sections: |
| 16 | + - title: Overview |
| 17 | + content: | |
| 18 | + All crystals belong to one of seven crystal systems, classified by their unit cell |
| 19 | + geometry and symmetry elements. Understanding these systems is fundamental to |
| 20 | + crystallography and gem identification. |
| 21 | +
|
| 22 | + Crystal systems are defined by the relationship between crystallographic axes |
| 23 | + (a, b, c) and the angles between them (α, β, γ). Each system has characteristic |
| 24 | + symmetry elements that determine possible crystal forms. |
| 25 | +
|
| 26 | + - title: Symmetry Elements |
| 27 | + items: |
| 28 | + - name: Rotation Axes |
| 29 | + description: 2-fold, 3-fold, 4-fold, 6-fold rotational symmetry |
| 30 | + - name: Mirror Planes |
| 31 | + description: Reflection symmetry planes |
| 32 | + - name: Center of Symmetry |
| 33 | + description: Inversion through a point |
| 34 | + |
| 35 | + - title: The Seven Systems |
| 36 | + subsections: |
| 37 | + - title: Cubic (Isometric) |
| 38 | + content: The highest symmetry system with four threefold axes. |
| 39 | + items: |
| 40 | + - name: Axes |
| 41 | + value: "a = b = c" |
| 42 | + - name: Angles |
| 43 | + value: "α = β = γ = 90°" |
| 44 | + - name: Minimum Symmetry |
| 45 | + value: "4 threefold axes" |
| 46 | + - name: Point Groups |
| 47 | + value: "m3m, 432, -43m, m3, 23" |
| 48 | + - name: Example Gems |
| 49 | + description: Diamond, Spinel, Garnet |
| 50 | + examples: |
| 51 | + - Diamond |
| 52 | + - Spinel |
| 53 | + - Garnet |
| 54 | + - Fluorite |
| 55 | + |
| 56 | + - title: Hexagonal |
| 57 | + content: Characterized by one sixfold axis. |
| 58 | + items: |
| 59 | + - name: Axes |
| 60 | + value: "a₁ = a₂ = a₃ ≠ c" |
| 61 | + - name: Angles |
| 62 | + value: "α = β = 90°, γ = 120°" |
| 63 | + - name: Minimum Symmetry |
| 64 | + value: "1 sixfold axis" |
| 65 | + - name: Point Groups |
| 66 | + value: "6/mmm, 622, 6mm, -62m, 6/m, 6, -6" |
| 67 | + - name: Example Gems |
| 68 | + description: Beryl, Apatite |
| 69 | + examples: |
| 70 | + - Emerald |
| 71 | + - Aquamarine |
| 72 | + - Morganite |
| 73 | + - Apatite |
| 74 | + |
| 75 | + - title: Trigonal (Rhombohedral) |
| 76 | + content: Characterized by one threefold axis. |
| 77 | + items: |
| 78 | + - name: Axes |
| 79 | + value: "a₁ = a₂ = a₃ ≠ c" |
| 80 | + - name: Angles |
| 81 | + value: "α = β = 90°, γ = 120°" |
| 82 | + - name: Minimum Symmetry |
| 83 | + value: "1 threefold axis" |
| 84 | + - name: Point Groups |
| 85 | + value: "-3m, 32, 3m, -3, 3" |
| 86 | + - name: Example Gems |
| 87 | + description: Quartz, Corundum, Tourmaline |
| 88 | + examples: |
| 89 | + - Quartz |
| 90 | + - Ruby |
| 91 | + - Sapphire |
| 92 | + - Tourmaline |
| 93 | + |
| 94 | + - title: Tetragonal |
| 95 | + content: Characterized by one fourfold axis. |
| 96 | + items: |
| 97 | + - name: Axes |
| 98 | + value: "a = b ≠ c" |
| 99 | + - name: Angles |
| 100 | + value: "α = β = γ = 90°" |
| 101 | + - name: Minimum Symmetry |
| 102 | + value: "1 fourfold axis" |
| 103 | + - name: Point Groups |
| 104 | + value: "4/mmm, 422, 4mm, -42m, 4/m, 4, -4" |
| 105 | + - name: Example Gems |
| 106 | + description: Zircon, Rutile |
| 107 | + examples: |
| 108 | + - Zircon |
| 109 | + - Rutile |
| 110 | + |
| 111 | + - title: Orthorhombic |
| 112 | + content: Three twofold axes or two mirror planes. |
| 113 | + items: |
| 114 | + - name: Axes |
| 115 | + value: "a ≠ b ≠ c" |
| 116 | + - name: Angles |
| 117 | + value: "α = β = γ = 90°" |
| 118 | + - name: Minimum Symmetry |
| 119 | + value: "3 twofold axes or 2 planes" |
| 120 | + - name: Point Groups |
| 121 | + value: "mmm, 222, mm2" |
| 122 | + - name: Example Gems |
| 123 | + description: Topaz, Peridot, Chrysoberyl |
| 124 | + examples: |
| 125 | + - Topaz |
| 126 | + - Peridot |
| 127 | + - Chrysoberyl |
| 128 | + - Tanzanite |
| 129 | + |
| 130 | + - title: Monoclinic |
| 131 | + content: One twofold axis or one mirror plane. |
| 132 | + items: |
| 133 | + - name: Axes |
| 134 | + value: "a ≠ b ≠ c" |
| 135 | + - name: Angles |
| 136 | + value: "α = γ = 90°, β ≠ 90°" |
| 137 | + - name: Minimum Symmetry |
| 138 | + value: "1 twofold axis or 1 plane" |
| 139 | + - name: Point Groups |
| 140 | + value: "2/m, 2, m" |
| 141 | + - name: Example Gems |
| 142 | + description: Orthoclase, Jadeite, Spodumene |
| 143 | + examples: |
| 144 | + - Kunzite |
| 145 | + - Orthoclase |
| 146 | + - Jadeite |
| 147 | + |
| 148 | + - title: Triclinic |
| 149 | + content: Lowest symmetry - no rotational symmetry. |
| 150 | + items: |
| 151 | + - name: Axes |
| 152 | + value: "a ≠ b ≠ c" |
| 153 | + - name: Angles |
| 154 | + value: "α ≠ β ≠ γ ≠ 90°" |
| 155 | + - name: Minimum Symmetry |
| 156 | + value: "No rotational symmetry" |
| 157 | + - name: Point Groups |
| 158 | + value: "-1, 1" |
| 159 | + - name: Example Gems |
| 160 | + description: Plagioclase, Rhodonite |
| 161 | + examples: |
| 162 | + - Turquoise |
| 163 | + - Labradorite |
| 164 | + - Rhodonite |
| 165 | + |
| 166 | + - title: Identifying Crystal Systems |
| 167 | + content: | |
| 168 | + When examining a crystal or gemstone, you can often determine its crystal system |
| 169 | + by observing: |
| 170 | +
|
| 171 | + - **Crystal habit** - The external shape and face arrangement |
| 172 | + - **Optic character** - Isotropic (cubic) vs. uniaxial vs. biaxial |
| 173 | + - **Interference figure** - Under polarized light microscopy |
| 174 | + - **Cleavage directions** - Related to internal symmetry |
| 175 | +
|
| 176 | + - title: Quick Reference |
| 177 | + table: |
| 178 | + caption: Crystal Systems and Optic Character |
| 179 | + headers: |
| 180 | + - System |
| 181 | + - Optic Character |
| 182 | + - RI Values |
| 183 | + rows: |
| 184 | + - ["Cubic", "Isotropic", "Single RI (n)"] |
| 185 | + - ["Hexagonal, Trigonal, Tetragonal", "Uniaxial", "Two RI values (ω, ε)"] |
| 186 | + - ["Orthorhombic, Monoclinic, Triclinic", "Biaxial", "Three RI values (α, β, γ)"] |
| 187 | + |
| 188 | + - title: Common Gemstones by System |
| 189 | + comparison: |
| 190 | + items: |
| 191 | + - title: Cubic |
| 192 | + points: |
| 193 | + - Diamond |
| 194 | + - Spinel |
| 195 | + - "Garnet (almandine, pyrope, grossular)" |
| 196 | + - Fluorite |
| 197 | + - title: Trigonal |
| 198 | + points: |
| 199 | + - "Quartz (amethyst, citrine)" |
| 200 | + - Ruby |
| 201 | + - Sapphire |
| 202 | + - Tourmaline |
| 203 | + - title: Hexagonal |
| 204 | + points: |
| 205 | + - Emerald |
| 206 | + - Aquamarine |
| 207 | + - Morganite |
| 208 | + - Apatite |
| 209 | + - title: Orthorhombic |
| 210 | + points: |
| 211 | + - Topaz |
| 212 | + - Peridot |
| 213 | + - Chrysoberyl |
| 214 | + - Tanzanite |
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