Thermal expansion solid elements

EXP6 supports a wide range of elements and condensed detonation products. We have applied a Mumaghan[24] equation of state (EOS) form to a variety of metals, metal oxides and other solids. We have also matched phase transition data for many of these solids. For example, this form has recently been applied to the EOS of carbon[31]. Thermal effects in the EOS are included through the dependence of the coefficient of thermal expansion on temperature, which can be directly compared to experiment. We find that we can replicate shock Hugoniot and isothermal compression data for a wide variety of solids with this simple form. 

The transition between the viscous state and the solid state is characterized by a temperature Tg called glass transition temperature. This temperature corresponds to a discontinuity of physical parameters and in particular of the thermal expansion coefficient. The discontinuity observed when T decreases seems to result from the freezing, for T < Tt, of rotation and of large motions of chain elements. 

X10. The next three rows present the viscosity rj, the surface tension, and its tenqterature dependence, in the liquid state. The next properties are the coefficient of linear thermal expansion a and the sound velocity, both in the solid and in the liquid state. A number of quantities are tabulated for the presentation of the elastic properties. For isotropic materials, we list the volume compressihility k = —(l/V)(dV/dP), and in some cases also its reciprocal value, the bulk modulus (or compression modulus) the elastic modulus (or Young s modulus) E the shear modulus G and the Poisson number (or Poisson s ratio) fj,. Hooke s law, which expresses the linear relation between the strain s and the stress a in terms of Young s modulus, reads a = Ee. For monocrystalline materials, the components of the elastic compliance tensor s and the components of the elastic stiffness tensor c are given. The elastic compliance tensor s and the elastic stiffness tensor c are both defined by the generalized forms of Hooke s law, a = ce and e = sa. At the end of the list, the tensile strength, the Vickers hardness, and the Mohs hardness are given for some elements. 

FIGURE 27 (A) d electron number versus linear expansion coefficient transition metals (White, 1979). (B) Linear thermal expansion coefficient a (closed circles) and bulk modulus (solid line) Bo of the rare earth elements (Benedict and Holzapfel, 1993 Spedding et al., 1961). 

Until recently the main factor in the breakdown of solids was considered to be the mechanical load. However, the dilaton theory of strength which has appeared in the past decade has altered these concepts radically. From this point of view, the mechanical load plays only the role of supplier of the energy pumped into the dilaton and causing thermal expansion of the bonds up to their breakdown. Thus, the difference between mechanical and other forms of breakdown of solids is removed. The heat ageing of a vulcanisate is one of the most common causes of failure of structural elements manufactured from it. In the general case the heat ageing of a material can be described by a first-order reaction. 8 refs. 

TABLE V Specific Heat, Thermal Conductivity, and Coefficient of Thermal Expansion of the Solid Elements at 25°C... 

A variety of physical properties of several liquids and polymers can be quantitatively described by considering a crystalline arrangement of molecules or other volume elements bound by non-directional forces. In some cases we propose that the intermolec-ular forces in the liquid or solid under question are simply due to van der Waals interactions. In those cases we demonstrate that physical properties such as surface energy cohesive strength compressibility thermal expansion and work of vaporization can be calculated from atomic constants and related to one another by the proposed model. In the case of other liquids and polymers intermolecular forces cannot be described in terms of van der Waals binding alone and other (directional) forces such as dipole-dipole binding must be included. It will be shown that a variety of the calculated properties favorably compare with experimental results. 

An expansion of the solution TMP approach involves a cothermolytic strategy, whereby two or more molecular species that thermally convert to materials under mild heating are converted simultaneously in the same solution [83,128-130]. This cothermolysis method allows the composition of the final material to be tuned to variable stoichiometries, and has proven useful in the generation of catalytic materials where even small variations in elemental content can lead to dramatic performance changes. The remainder of this section serves to provide examples of the materials that can be formed via simple solid phase or solution TMP routes. 

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