How One Crystal Face Can Have Two Different Hardnesses (Kyanite & Diamond)—And How Specific-Gravity "Heft" Exposes Imitation Gems
Direct Crystallographic Hardness Anisotropy & Hydrostatic Specific Gravity Summary: In 1801, René Just Haüy christened blue Kyanite (Al2SiO5) with the name "Disthène"—Greek for "Two Strengths". Why? Because Kyanite is built from tightly bonded chains of edge-sharing `[AlO6]` octahedra running parallel to its long c-axis (`[001]`). When you drag a steel knife blade (`Mohs 5.5`) lengthwise up-and-down the crystal (`0°`), the point slips between the chains and parts the weaker lateral bonds—recording a soft Mohs 4.5 (Knoop microhardness `~450 kg/mm²`). Turn the blade 90° sideways across the exact same `{100}` face, and the tip must shear straight through the covalent `Al–O–Si` rebar chains—jumping to Mohs 7.0 (`~1,150 kg/mm²`) so hardened steel skids right off! This exact same principle solves the famous Diamond Cutter's Paradox: how do you polish a Mohs-10 Diamond using diamond dust? Because a diamond's Octahedral `{111}` face is the hardest surface in the universe (`~115 GPa`, impossible to polish flat), whereas its Cube `{100}` face along the `<100>` 4-point direction is up to 10 times softer to abrasion—allowing the random `{111}` corners of diamond grit on the spinning scaife wheel to plane down the gem's `{100}` and `{110}` faces! This lab also tests Genuine Turquoise (`Mohs 6.0`) vs. Dyed White Howlite (`Mohs 3.5`) and lets you heft transparent crystals heavier than solid iron (Scheelite `SG 6.10`, Cassiterite `SG 7.05`, Cinnabar `SG 8.18`, and 2026 IMA discoveries Zlatogorite `SG 8.42` & Plumbogottlobite `SG 5.36`).
🔬 Directional Knoop Hardness Tensor, Diamond Grain & Archimedes SG Equations
- Kyanite `{100}` Face Directional Mohs & Knoop Microhardness (HK) as a Function of Scratch Angle (θ):
Mohs(θ) = 4.50 + 2.50 · sin²(θ)|HK(θ) = 450 + 690 · sin²(θ) kg/mm²(0° = 4.5→90° = 7.0!) - Diamond Abrasion Resistance Ratio Between Octahedral `{111}` & Cube `{100}` `<100>` Polishing Directions:
R_wear = Rate_{100}<100> / Rate_{111}<112̄> > 10 : 1(Why `{111}` diamond grit cuts `{100}` diamond tables!) - Archimedes Hydrostatic Specific Gravity (SG) From Weight in Air (Wair) vs. Submerged in Water (Wwater):
SG = W_air / ( W_air − W_water ) = ρ_mineral / ρ_H₂O(ScheeliteSG = 6.10feels2.3×heavier than Quartz!)
Complete Reference Chart: 8 Dual-Hardness, Polish-Anisotropic & Heavy Minerals
| Mineral / Gem & Formula | Soft Direction (0°) | Hard Direction (90°) | Specific Gravity (SG) & ID Test |
|---|---|---|---|
Blue Kyanite ("Disthene")Al₂SiO₅ (Triclinic P1̄) |
Mohs 4.5 – 5.0 (Parallel to c-Axis `[001]`) |
Mohs 7.0! (Across Blade Width `[100]`) |
SG = 3.65; steel knife cuts lengthwise (0°) but skids off crosswise (90°)! |
Natural DiamondC (Cubic Fd3̄m) |
Polishable `<100>` Cube 4-Point (~60 GPa) |
Unpolishable `{111}` Octahedron (~115 GPa!) |
SG = 3.52; cutters must tilt table 2°–4° off `{111}` cleavage to polish it |
Turquoise vs. Dyed HowliteCuAl₆(PO₄)₄(OH)₈·4H₂O vs. Borate |
Fake Howlite: Mohs 3.5! (Scratches White w/ Coin) |
Real Turquoise: Mohs 6.0! (Scratches Window Glass) |
Turquoise SG = 2.76–2.85; dyed Howlite (SG 2.55) shows white core in drill holes |
Scheelite & CassiteriteCaWO₄ (I4₁/a) & SnO₂ (P4₂/mnm) |
Scheelite: Mohs 4.5–5.0 | Cassiterite: Mohs 6.5–7.0 | SG = 6.10 to 7.05! Looks like clear/amber quartz, yet feels heavy as cast iron! |
Cinnabar ("Dragon's Blood")HgS (Trigonal P3₁21) |
Mohs 2.0 – 2.5 (Very Soft Sectile) |
Mohs 2.5 (RI = 2.90–3.25!) |
SG = 8.18! Heavier than solid steel (7.8); 3× heavier than red jasper or quartz |
Calcite ("One-Way Scratch")CaCO₃ (Trigonal R3̄c · {101̄1}) |
Toward c-Apex: Mohs 2.7 (Scratchable by Copper!) |
Away From Apex: Mohs 3.3 (Resists Copper Coin!) |
SG = 2.71; scratching uphill vs. downhill along `{10-11}` cleavage changes hardness! |
Zlatogorite (2026 IMA)CuNiSb₂ (Trigonal P3̄m1) |
Basal `{0001}` Cleavage Slip Direction |
Prismatic Antimonide Octahedral Chains |
SG = 8.42! Approved Feb 2026 in Mineralogical Magazine Vol. 90 (IMA 2025-070) |
Plumbogottlobite & AlmagreraitePbMg(VO₄)(OH) / CuZnMn₃O₈ |
Mohs 4.0 – 5.0 (Oct 2026 Am. Min.) |
Mohs 5.0 – 5.5 (Hyperkagome Sheets) |
SG = 5.36 & 5.174! Published Oct 1, 2026 in American Mineralogist Vol. 111(10) |
Frequently Asked Questions
Why does Kyanite have two hardnesses while its twin sisters Andalusite and Sillimanite have uniform hardness?
Kyanite, Andalusite, and Sillimanite are trimorphs—all three share the exact same formula (Al2SiO5)! However, Kyanite forms deep in subduction zones under high pressure (>4 to 8 kilobars), squeezing all of its aluminum ions into dense 6-coordinated `[AlO6]` octahedral chains running down the c-axis (`SG = 3.65`), whereas Andalusite (`SG = 3.15`) and Sillimanite (`SG = 3.24`) have half their aluminum in cross-linking 4- or 5-coordinated sites. That extreme 1D chain packing in Kyanite creates the gap between Mohs 4.5 parallel to the chains and Mohs 7.0 across the chains!
What is the "One-Way Scratch Trick" on a Calcite cleavage rhomb?
On a cleavage face (`{10-11}`) of Iceland Spar Calcite, if you drag a copper penny (`Mohs 3.0`) upward toward the blunt 3-fold c-axis corner, the penny pushes against the imbricated atomic cleavage steps and easily scratches the calcite (`Mohs ~2.7`). Drag the exact same penny backward down the exact same line (away from the apex), and the penny glides smoothly over the sloping atomic steps without leaving a mark (`Mohs ~3.3`)!
Why do old miners call Scheelite and Cassiterite "Heavy Spar / Tin Stone"?
Most transparent silicate rocks (Quartz `SG 2.65`, Feldspar `SG 2.60`) feel light in your hand and wash out of a gold pan. Scheelite (`CaWO4`, SG = 6.10), Cerussite (`PbCO3`, SG = 6.55), and Cassiterite (`SnO2`, SG = 7.05) are packed with heavy Tungsten, Lead, and Tin atoms—making a palm-sized crystal feel nearly three times heavier than quartz and sink straight to the bottom of a miner's pan alongside gold!