Hardness of crystals

Figure 9.6 Hardnesses of crystals in the KCl-KBr alloy system. The four data points are from Armington, Posen, and Lipson (1973). The dashed curve represents the concentration function Ac(c-l) on which the data fall, c = concentration and A is a constant.

The ultra-micro-hardness of inorganic and organic salts has been measured for 15 substances. These are products usually produced in industrial crystallization. The hardness-force-dependency was examined and data are compared to those from literature. In the case of potassium nitrate a strong direction dependency of the hardness was observed. Also effects of impurities in the crystal lattice were analysed. In the end an attempt has been introduced to calculate the hardness of crystals from a physical model. 

All these models for the calculation of the hardness need empirical parameters which cannot be explained by physical properties of the crystals. This problem is solved if the hardness of crystals is described as a volumetric cohensive energy as suggested by Plendl et. al.(20). Then the hardness can be written as the ratio of the cohensive energy U to the molecular volume V, as to be seen in Equation 5. 

There is, to be sure, some correlation between bond type and type of atomic arrangement. Ionic crystals often possess a coordinated structure such that ionic bonds extend throughout the crystal, leading to low volatility. Another structural feature that leads to high melting points and striking hardness of crystals is the hydrogen bond between molecules (Chap. 12). 

Hydrogen-bond formation is of importance also for various other properties of substances, such as the solubility of organic liquids in water and other solvents, melting points of substances under water,1 viscosity of liquids,14 second virial coefficient of gases,18 choice of crystal structure, cleavage and hardness of crystals, infrared absorption spectra, and proton magnetic resonance. Some of these are discussed in the following sections of this chapter. 

Rice R. W., 1979, Internal stress dependence of the hardness of crystallized glasses, J. Mater. Sci., 14, 2768-2772. 

In the case of limited solubility in the solid state, the hardness of crystals as solid solutions depending on the composition of the alloy, should grow in the homogeneity region up to the point of saturation at a given temperature, but should remain invariable on passing into the two-phase region. 

Walker W. W., 1962, Indentation Hardness of Crystals, MS Thesis University of Arizona, Tucson, AZ. 

Julg, A. (1978). Crystals as Giant Molecules. Berlin Springer-Verlag. This is Volume 9 of a series, Lecture Notes in Chemistry. It provides many interesting insights into bonding in solids. Excellent discussion of hardness of crystals. 

With regard to specific properties, we will focus on those that are more relevant to solution crystallization and those that have a direct impact on the quality of the final bulk pharmaceuticals such as purity, form, habit, and size, based upon our own experience. We will leave readers to find other properties, such as miller index for crystal morphology, hardness of crystals, interfacial tension, etc., in other books on crystallization (Mersmann 2001 Mullin 2001), which provide in-depth theoretical discussion on these properties. 

The hardness of crystals is rated based on Mohs hardness values. The higher the Mohs value, the harder the material is to scratch. Which crystal will have the highest Mohs value NaF, NaCl, or KCl ... 

Gilman [124] and Westwood and Hitch [135] have applied the cleavage technique to a variety of crystals. The salts studied (with cleavage plane and best surface tension value in parentheses) were LiF (100, 340), MgO (100, 1200), CaFa (111, 450), BaFj (111, 280), CaCOa (001, 230), Si (111, 1240), Zn (0001, 105), Fe (3% Si) (100, about 1360), and NaCl (100, 110). Both authors note that their values are in much better agreement with a very simple estimate of surface energy by Bom and Stem in 1919, which used only Coulomb terms and a hard-sphere repulsion. In more recent work, however, Becher and Freiman [126] have reported distinctly higher values of y, the critical fracture energy. ... 

Rehbinder and co-workers were pioneers in the study of environmental effects on the strength of solids [144], As discussed by Frumkin and others [143-145], the measured hardness of a metal immersed in an electrolyte solution varies with applied potential in the manner of an electrocapillary curve (see Section V-7). A dramatic demonstration of this so-called Rehbinder effect is the easy deformation of single crystals of tin and of zinc if the surface is coated with an oleic acid monolayer [144]. 

The fonnation of colloidal crystals requires particles tliat are fairly monodisperse—experimentally, hard sphere crystals are only observed to fonn in samples witli a polydispersity below about 0.08 [69]. Using computer... 

There has not been as much progress computing the properties of crystals as for molecular calculations. One property that is often computed is the bulk modulus. It is an indication of the hardness of the material. 

The glass-ceramic phase assemblage, ie, the types of crystals and the proportion of crystals to glass, is responsible for many of the physical and chemical properties, such as thermal and electrical characteristics, chemical durabiUty, elastic modulus, and hardness. In many cases these properties are additive for example, a phase assemblage comprising high and low expansion crystals has a bulk thermal expansion proportional to the amounts of each of these crystals. 

Lead Telluride. Lead teUuride [1314-91 -6] PbTe, forms white cubic crystals, mol wt 334.79, sp gr 8.16, and has a hardness of 3 on the Mohs scale. It is very slightly soluble in water, melts at 917°C, and is prepared by melting lead and tellurium together. Lead teUuride has semiconductive and photoconductive properties. It is used in pyrometry, in heat-sensing instmments such as bolometers and infrared spectroscopes (see Infrared technology AND RAMAN SPECTROSCOPY), and in thermoelectric elements to convert heat directly to electricity (33,34,83). Lead teUuride is also used in catalysts for oxygen reduction in fuel ceUs (qv) (84), as cathodes in primary batteries with lithium anodes (85), in electrical contacts for vacuum switches (86), in lead-ion selective electrodes (87), in tunable lasers (qv) (88), and in thermistors (89). 

Crystallization. Raw natural mbber may freeze or crystallize during transit or prolonged storage, particularly at subzero temperatures. The mbber then becomes hard, inelastic, and usually much paler in color. This phenomenon is reversible and must be differentiated from storage hardening. The rate of crystallization is temperature-dependent and is most rapid at —26° C. Once at this temperature, natural mbber attains its maximum crystallinity within hours, and this maximum is no more than 30% of the total mbber. 

Occurrence. The principal strontium mineral is celestite, naturally occurring strontium sulfate. Celestite and celestine [7759-02-6] both describe this mineral. However, celestite is the form most widely used in Knglish-speaking countries. Celestite has a theoretical strontium oxide content of 56.4 wt %, a hardness of 3—3.5 on Mohs scale, and a specific gravity of 3.96. It is usually white or bluish white and has an orthorhombic crystal form. 

Strontium Carbonate. Strontium carbonate, SrCO, occurs naturally as strontianite in orthorhombic crystals and as isomorphs with aragonite, CaCO, and witherite, BaCO. There are deposits in the United States in Schoharie County, New York in WestphaUa, Germany and smaller deposits in many other areas. None is economically workable. Strontianite has a specific gravity of 3.7, a Mohs hardness of 3.5, and it is colorless, gray, or reddish in color. 

Strontium Sulfate. Strontium sulfate, SrSO, occurs as celestite deposits in beds or veins in sediments or sedimentary rocks. Celestite has a specific gravity of ca 3.97, a Mohs hardness of 3.0—3.5, and is colodess-to-yeUow and often pale blue. Strontium sulfate forms colorless or white rhombic crystals with a specific gravity of 3.96 and an index of refraction of 1.622—1.631. It decomposes at 1580°C and has a solubiUty of 0.0113 g per 100 mL of water at 0°C. 

Even though TiC is much harder than WC at room temperature (3200 kg/mm for TiC, vs 1800 kg/mm for WC), at higher temperatures, TiC oxidi2es and loses its hardness rapidly. Figure 17 is a plot of the variation of hardness of single crystals of various monocarbides with temperature (44). No similar data is available for multicarbides or other refractory hard materials, such as nitrides, borides, oxides, or any combination of them. 

Fig. 17. Variation of hardness of single crystals of various monocarbides with temperature (44).

The greatest use of cubic boron nitride is as an abrasive under the name Bora2on, in the form of small crystals, 1—500 p.m in si2e. Usually these crystals are incorporated in abrasive wheels and used to grind hard ferrous and nickel-based alloys, ranging from high speed steel tools and chilled cast-iron to gas turbine parts. The extreme hardness of the crystals and their resistance to attack by air and hot metal make the wheels very durable, and close tolerances can be maintained on the workpieces. 

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