Bulk Modulus. Compressibility

The compressibility x of Tm Se varies strongly with x and reaches a maximum at the stoichiometric composition, as shown by pressure-volume relationships of TmxSe single crystals at 300 K  

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Intermetallic compounds, various alloys, and additional semimetallic compounds of berkelium should be prepared and characterized to extend the knowledge of the physicochemical behavior of berkelium in these kinds of solids. Studies of such materials under pressure would be of interest in determining the effects of the non-berkelium component on physical properties such as bulk modulus (compressibility), pressure for the onset of 5f-electron delocalization, and possible volume collapse associated with a change in the metallic valence of Bk from 3 to 4. 

Mechanical Properties. Measuremeat of the mechanical properties of diamoad is compHcated, and references should be consulted for the vahous qualifications (7,34). Table 1 compares the theoretical and experimental bulk modulus of diamond to that for cubic BN and for SiC (29) and compares the compressive strength of diamond to that for cemented WC, and the values for the modulus of elasticity E to those for cemented WC and cubic BN. 

Cauchy number number Nc o5 II 1 hO K- = bulk modulus (Inertial/compressible) forces Compressible flow... 

Other authors have studied other correlations. Two are Povarennykh (1964), and Goble and Scott (1985). The latter emphasized compressibility (inverse bulk modulus) as did Beckmann (1971). The bulk modulus is not a reliable measure for the same reason as the cohesive energy. It is volume dependent rather than shear dependent. Still another attempt to correlate hardness and compressibility was that of Yang et al. (1987). This was followed by a proposal by Liu and Cohen (1990) that hardness and bulk moduli are related. This proposal was refuted by Teter (1998) who showed that hardness values correlate better with shear moduli than with bulk moduli. 

R. J. Goble and S. D. Scott, The Relationship between Mineral Hadness and Compressibility (Or Bulk Modulus), Canadian Mineralogist, 23,273 (1985). 

Equations of state for solids are often cast in terms of the bulk modulus, Kp, which is the inverse of the isothermal compressibility, Kp, and thus defined as... 

Once the density and compressibilities of mixed electrolyte solutions are known at 1 atm, values at high pressures can be made by using the secant bulk modulus equation of state. The major difficulty, at present, with using additivity methods to estimate the PVT properties of mixed electrolytes is the lack of experimental data for binary solutions over a wide range of concentrations and temperatures. Hopefully, in the near future we will be able to provide some of these data by measurements in our laboratory in Miami. 

A brief review is made of the methods that are currently being used to determine the density (p) and compressibility (6) of electrolyte solutions as a function of pressure. The high pressure equations of state used to represent these properties are also discussed. The linear secant bulk modulus [K = Ppp/(pP - p )] equation of state... 

One of the consequences of close packing in solids and liquids is much higher densities in comparison with gases for instance, ice and water have densities that are a thousand times higher than water vapor at room pressure. Another consequence is that solids and liquids have much lower compressibility, so that the density is not sensitive to the pressure. The bulk modulus B is defined as B = —AP/ AV/V), which has the units of pressure. This parameter measures the fractional volumetric response of a material, when pressure is applied to all faces of the material at the same time. 

Knowledge of the sample pressure is essential in all high-pressure experiments. It is vital for determinations of equations of state, for comparisons with other experimental studies and for comparisons with theoretical calculations. Unfortunately, one cannot determine the sample pressure directly from the applied force on the anvils and their cross-sectional area, as losses due to friction and elastic deformation cannot be accurately accounted for. While an absolute pressure scale can be obtained from the volume and compressibility, by integration of the bulk modulus [109], the most commonly-employed methods to determine pressures in crystallographic experiments are to use a luminescent pressure sensor, or the known equation of state of a calibrant placed into the sample chamber with the sample. W.B. Holzapfel has recently reviewed both fluorescence and calibrant data with the aim of realising a practical pressure scale to 300 GPa [138]. 

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