Thermal Properties of Solids

Now that we know something about how the molecules in a solid vibrate, we are in a position to connect these vibrations to the thermal properties such as heat capacity, thermal conduction, and thermal expansion. 

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The theory of Debye is certainly the most complete and successful attempt to represent the thermal properties of solids which has yet been made by the aid of the theory of ergon ic distribution. 

The concept of quantization enabled physicists to solve problems that nineteenth-century physics could not. One of these involved the thermal properties of solids when they are heated to incandescence. The other involved the induction of electrical current in metals when they are exposed to only specific frequencies of electromagnetic radiation. 

A parameter that has been widely used in the study of the structure and thermal properties of solid organic materials (13-16) and particularly coals (14-16) is the NMR second moment. To compute such a parameter from our solid echo data requires its Fourier transformation from the time domain to obtain a complex frequency domain NMR spectrum, i.e. g (v) u (v) + iv (v). The quadrature components of this spectrum represent linear combinations of the pure absorptive (u(v)) and dispersive (v(v)) modes of the true spectrum, i.e,... 

The analysis that leads to Eq. (4.39) can be repeated for three-dimensional systems and for solids with more than one atom per unit cell, however analytical results can be obtained only for simple models. Here we discuss two such models and their implications with regard to thermal properties of solids. We will focus on the heat capacity, Eq. (4.35), keeping in mind that the integral in this expression is actually bound by the maximum frequency. Additional infonnation on this maximum frequency is available via the obvious sum rule... 

The Thermal Properties of Solids, H. J. Goldsmid. 1.35 Microwave Spectroscopy, Walter Gordy, William V. Smith, and Ralph F. Trambarulo. 3.00... 

For the thermal properties of solids, Einstein developed an equation that could predict the heat capacity of solids in 1907. This model was then refined by Debye in 1912. Both models predict a temperature dependence of the heat capacity. At... 

Electronic io- -io-5 Emission and absorption spectra photoelectric effect electric, magnetic, thermal properties of solids The Schrodinger equation pseudopotentials density functional theory tight-binding approximation embedded atom method... 

TRANSIENT METHODS OF MEASURING THERMAL PROPERTIES OF SOLIDS. 

SOME THERMAL PROPERTIES OF SOLIDS AT LOW TEMPERATURES. PH.D. THESIS. 

Electronic, Magnetic, and Thermal Properties of Solid Materials, Klaus Schr der... 

At a finite temperature the atoms that form a crystalline lattice vibrate about their equilibrium positions, with an amplitude that depends on the temperature. Because a crystalline solid has symmetries, these thermal vibrations can be analyzed in terms of collective modes of motion of the ions. These modes correspond to collective excitations, which can be excited and populated just like electronic states. These excitations are called phonons. Unlike electrons, phonons are bosons their total number is not fixed, nor is there a Pauli exclusion principle governing the occupation of any particular phonon state. This is easily rationalized, if we consider the real nature of phonons, that is, collective vibrations of the atoms in a crystalline solid which can be excited arbitrarily by heating (or hitting) the solid. In this chapter we discuss phonons and how they can be used to describe thermal properties of solids. 

The vibrations of the atoms in the crystalline lattice are important in understanding the thermal properties of both metallic and nonmetallic solids. The energy involved in these vibrations represents thermal energy hence lattice vibrations are primarily resporrsible for the heat capacity of solids. Also, these vibrations are able to transport heat and are the dominant source of thermal conductivity in nonmetals. Therefore, in order to understand thermal properties of solids, it is necessary to start with a general understanding of the nature of lattice d5mamics. 

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