Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

The non-linear field theories of mechanics

Publisher Summary This chapter reviews the thermal conductivity of nonmetallic crystals at temperatures comparable to or higher than the Debye temperature. It deals with the intrinsic behavior of such pure crystals at high temperatures. In such crystals, the dominant carriers of thermal energy are phonons and the dominant scattering mechanism to be considered is the intrinsic phonon–phonon scattering. This is a small section of the much larger problem of the thermal conductivity of nonmetallic solids and clearly it neglects possible heat transport by photons, charge carriers, polarons, and magnons. It also neglects other possible phonon scattering mechanisms such as isotopes, impurities, vacancies, charge carriers, dislocations, grain boundaries, and crystal boundaries. It presents the absolute value of the thermal conductivity, K, as determined by phonon–phonon scattering, the temperature dependence of K, the volume dependence of K, the change in K upon melting, and the minimum value of K. The chapter discusses a composite curve for the thermal conductivity versus temperature of pure KCl measured at a constant pressure of, say, one atmosphere.

The Thermal Conductivity of Nonmetallic Crystals

Publisher Summary This chapter discusses the elastic constants of crystals. The elastic properties of solid matter hold interest for both technology and basic research. In the first field applied elasticity is an important discipline for those fundamental considerations of engineering design which are usually included under the designation “strength of materials.” The treatment of structural materials requires semiempirical methods, because their compositions are complex and prior treatment has a pronounced effect. On the other hand, basic research into elastic properties is usually concerned with work on specimens in the simplest state which can be obtained reproducibly—for example, annealed single crystals. The complete tabulation of elastic constants for such specimens is valuable, not only for itself, but also because the data can be correlated with other physical measurements and thereby provide possible insight into the nature of the atomic forces in solid matter. The research aspect of elastic studies is of primary interest for this chapter. The case of the isotropic medium is important both for the chronological development of the subject of elasticity and also for its applicability to polycrystals and glasses.

The Elastic Constants of Crystals

Fatigue damage assessment by nonlinear ultrasonic materials characterization

All the important thermal properties of rocks can be estimated from the graphs and tables in this report. Most of the useful published data are summarized herein to provide fairly accurate evaluations of thermal coefficients and parameters of rocks for many engineering and scientific purposes. Graphs of the published data on common rocks and minerals were prepared to show the relationships of thermal conductivity with decimal solidity (one minus decimal porosity), water or air pore content, content of certain highly conducting minerals, and temperature. Tables are given of pressure effect on thermal conductivity of minerals and rocks, anisotropy of conductivity, thermal expansion, heat transfer, density, heat generation in rocks, and activation energies of conduction mechanisms in single crystals of minerals. A series of graphs show the specific heats of rock-forming minerals as a function of temperature; with these graphs the specific heat of a rock can be calculated from its mode as accurately as it can be measured. Calculations of conductivity, diffusivity, and thermal inertia of a rock from its mode are described. Discussions of radiative thermal conductivity, radioactive heat generation, and heat transfer in rocks are provided.

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Thermal properties of rocks

Expressions for the velocities of elastic waves in stressed solids are derived using Murnaghan's theory of finite deformations and third-order terms in the energy. For isotropic materials, in addition to the Lam\'e constants $\ensuremath{\lambda}$ and $\ensuremath{\mu}$, three additional constants, $l$, $m$, and $n$, are required to describe the material.By measuring the transmission time of elastic pulses through the material, the velocities of longitudinal and shear waves are determined as a function of applied stress. By subjecting the material to hydrostatic pressure as well as simple compression, it is found that seven functions of the three constants $l$, $m$, and $n$ can be measured and thus numerical values calculated. Results are given for polystyrene, iron, and Pyrex glass.

Second-Order Elastic Deformation of Solids

The thermal conductivity $K$ of KCL, KBr, fired talc, dunite, and eclogite was measured to pressures as high as 19 kbar and to temperatures as high as 450\ifmmode^\circ\else\textdegree\fi{}C. Fluid pressure was supplied by dry nitrogen. A Manganin resistance gauge and Pt versus Pt-13% Rh thermocouples measured the pressure and temperature, respectively. Data were fitted with the surface $K=\frac{{C}_{1}}{(T+{T}_{0})}\ensuremath{-}\frac{{C}_{2}}{(P+{P}_{0})}$ in the sense of least squares by means of a CDC 1604 computer. Conductivities were found to increase nonlinearly with pressure, the slope of the surface decreasing at higher pressures.

D. S. Hughes

Papers

Second-Order Elastic Deformation of Solids

Thermal Conductivity of Dielectric Solids at High Pressure.