Griineisen thermodynamic

The expansion coefficient of a solid can be estimated with the aid of an approximate thermodynamic equation of state for solids which equates the thermal expansion coefficient with the quantity where yis the Griineisen dimensionless ratio, C, is the specific heat of the solid, p is the density of the material, and B is the bulk modulus. For fee metals the average value of the Griineisen constant is near 2.3. However, there is a tendency for this constant to increase with atomic number. 

Hugoniot data have been fitted by the equation = Cq + su + qu, where Uj is the shock velocity and the associated particle velocity. Griineisen parameters have been obtained from best estimates of zero pressure thermodynamic parameters, which are sometimes of dubious value. The pressures and velocities describing the valid range of the fits do not necessarily indicate the onset or completion of a transition. 

An alternative definition of the Griineisen parameter is in terms of thermodynamic properties [87]... 

This isothermal bulk modulus (Kj) measured by static compression differs slightly from the aforementioned adiabatic bulk modulus (X5) defining seismic velocities in that the former (Kj) describes resistance to compression at constant temperature, such as is the case in a laboratory device in which a sample is slowly compressed in contact with a large thermal reservoir such as the atmosphere. The latter (X5), alternatively describes resistance to compression under adiabatic conditions, such as those pertaining when passage of a seismic wave causes compression (and relaxation) on a time-scale that is short compared to that of thermal conduction. Thus, the adiabatic bulk modulus generally exceeds the isothermal value (usually by a few percent), because it is more difihcult to compress a material whose temperature rises upon compression than one which is allowed to conduct away any such excess heat, as described by a simple multiplicative factor Kg = Kp(l + Tay), where a is the volumetric coefficient of thermal expansion and y is the thermodynamic Griineisen parameter. 

If this parameter is assumed to be the same for all vibrations, one can obtain a bulk thermodynamic definition for y. The bulk Griineisen parameter is found to be about 4 for polymers from the effect of pressure on the velocity of sound. The data suggest that for the heat capacity only the interchain contribution should be taken into account. With this assumption, an order of magnitude calculation shows that the bulk Griineisen parameter for proteins is of the same order of magnitude as that of polymers. This suggests that the thermal expansion and the compressibility of proteins reflect primarily the movement between the secondary structures. These movements are reflected in the low frequency part of the... 

The thermodynamics of crystalline substances (including polymers) have been considered either based on the Griineisen parameter, yo, or deriving the statistical thermodynamic lattice theory of solid polymers. The Griineisen dimensionless parameter was originally defined as a density gradient of the crystalline lattice frequency, v [Warfield et al., 1983] ... 

Hofmeister, A. M., and Mao, H.-K., Redefinition of the mode Griineisen parameter for polyatomic substances and thermodynamic implications, PNAS Geophys., 99, 559-564 (2002). 

One can explain these phenomena again with a Griineisen parameter mechanism. Defining an appropriate thermodynamic potential... 

Scaling behavior and Griineisen relations 3.1. Thermodynamics of scaling... 

Let us consider among the thermodynamic characteristics the lattice Griineisen parameter y, which accounts for anharmonicity of intermolecular bonds [1, 80] and is applied widely for the description of states of polymers [81]. The value of y can be determined according to the equation [1] ... 

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