Broz,M.E., Cook,R.F. and Whitney,D.L.(2006): Microhardness, toughness, and modulus of Mohs scale minerals. American Mineralogist, 91, 135-142.

『モース硬度計鉱物の微小硬度・靭性・弾性率』

『Abstract
　we report new results of microhardness and depth-sensing indentation (DSI) experiments for the first nine minerals in the Mohs scale: talc, gypsum, calcite, fluorite, apatite, orthoclase, quartz, topaz, and corundum. The Mohs scale is based on a relative measure of scratch resistance, but because scratching involves both loading and shearing, scratch resistance is not equivalent to hardness as measured by modern loading (indentation) methods; scratch resistance is also related to other material properties (fracture toughness, elastic modulus). To better understand the relationship of hardness to scratch resistance, we systematically determined hardness, fracture toughness, and elastic modulus for Mohs minerals. We measured hardness and toughness using microindentation, and modulus and hardness with DSI (“nanoindentation”) experiments. None of the measured properties increases consistently or linearly with Mohs number for the entire scale.

Keywords: Mechanical properties; hardness; fracture toughness; elastic modulus; Mohs minerals; new technique; nanoindentation』

Introduction
Overview of hardness and related properties
　A brief history of hardness testing
　Determination of material properties using Mohs, microindentation, and depth-sensing indentation methods
Microindentation and DSI of the Mohs minerals
　Materials and methods
　Results
Discussion
　Mineral properties and geological applications　
　Mineral properties and the Mohs scale
　The Mohs scale as a teaching tool
Acknowledgments
References cited

Table 1. Mohs minerals compositions and crystal structures
Mohs number Mineral Chemical formula Crystal system Cleavage
1 talc Mg3Si4O10(OH)2 monoclinic perfect {001}
2 gypsum CaSO4・2H2O monoclinic perfect {010}, good {100}
3 calcite CaCO3 trigonal perfect {1010}
4 fluorite CaF2 isometric perfect {111}
5 apatite Ca5(PO4)3F hexagonal poor {001}
6 orthoclase KAlSi3O8 monoclinic perfect {001}, good {010}
7 quartz SiO2 trigonal none
8 topaz Al2SiO4(OH,F)2 orthorhombic perfect {0001}
9 corundum Al2O3 trigonal none
10 diamond C isometric perfect {111}

Table 2. The names, descriptions, and indentation planes of samples used for this study
Mineral Description Indentation plane
talc White, massive Mg end-member with randomly oriented crystals. We were not able to separate an indivisual crystal, so indented the poly-cryatalline mass. 　
gypsum Clea crystal with obvious cleavage planes. {010}
calcite Translucent cleavage rhomb. {1010}
fluorite Translucent purple crystals. {111}
apatite Fluorapatite variety (＜0.45 wt％ Cl), yellow hexagonal prism from Durango, Mexico. {0001}
orthoclase Pink-orange, minor perthite texture, one obvious cleavage. {101}
quartz Clear prismatic with crystal faces. {0001}
topaz Clear prismatic with crystal faces. {001}
corundum Clea synthetic crystal. {0001}

Table 3. Physical properties of the Mohs minerals
Mohs number Mineral Microhardness
(GPa)		 DSI hardness
(GPa)		 DSI modulus
(GPa)		 Toughness
(MPa・m1/2)
1 talc 0.14±0.03 0.30±0.18 16.2±6.6 -
2 gypsum 0.61±0.15 1.03±0.13 25.3±1.9 -
3 calcite 1.49±0.11 2.21±0.16 78.1±5.2 0.39±0.12
4 fluorite 2.00±0.10 2.37±0.02 139.7±3.8 0.89±0.13
5 apatite 5.43±0.33 6.73±0.38 150.8±6.4 0.76±0.13
6 orthoclase 6.87±0.66 9.11±0.58 89.2±7.1 0.88±0.13
7 quartz 12.2±0.6 14.54±0.42 117.6±2.7 1.60±0.16
8 topaz 17.6±1.0 21.38±1.32 268.8±5.6 1.04±0.10
9 corundum 19.6±0.5 29.29±0.45 376.1±9.8 2.38±0.22
10 diamond (115*) - (1050†) (5*)
Note: Uncertainties listed are one standard deviation.
*Values from Novikov and Dub (1991).
†Value from Kong and Ashby (1992).

FIGURE 3. (a) Microhardness and DSI hardness vs. Mohs number, (b) Toughness vs. Mohs number, (c) Experimental and literature modulus vs. Mohs number. References for literature values listed next to each point: a = Alexandrov and Ryzhova (1961); b = Hearmon (1946); c = Hearmon (1956); d = Yoon and Newnham (1969); e = Alexandrov and Ryzhova (1962); f = Huntington (1958). Dashed lines are guides to the eye and do not imply trends.

〔Broz,M.E., Cook,R.F. and Whitney,D.L.(2006): Microhardness, toughness, and modulus of Mohs scale minerals. American Mineralogist, 91, 135-142.から〕

戻る