D. K. C. MacDonald

Bio: D. K. C. MacDonald is an academic researcher from National Research Council. The author has contributed to research in topics: Anharmonicity & Morse potential. The author has an hindex of 3, co-authored 3 publications receiving 553 citations.

The Thermal Expansion of Solids

Abstract: Under appropriate conditions, the thermal expansion of a solid is closely related to the Gr\"uneisen parameter $\ensuremath{\gamma}$. This in turn may be derived from the variation of the characteristic frequency of the lattice with volume. If, however, this variation is calculated from the usual expressions for the velocity of sound in solids at zero pressure, the $\ensuremath{\gamma}$ does not agree with that predicted from lattice theory, and an anomalous thermal expansion is predicted for a solid with a purely harmonic atomic potential.General expressions for the dependence on volume of the velocity of plane waves in one-, two-, and three-dimensional lattices are obtained, and hence the corresponding Gr\"uneisen $\ensuremath{\gamma}'\mathrm{s}$. The three-dimensional $\ensuremath{\gamma}$ differs by a numerical constant from that used by Slater. All three expressions are now consistent when applied to a body with a purely harmonic atomic potential and predict no thermal expansion.

Lattice Thermal Conductivity

Abstract: Consideration of the anharmonic properties of a linear chain suggests that the dimensionless quantity $\ensuremath{\alpha}\ensuremath{\gamma}T$ is in general a measure of the anharmonicity of a lattice ($\ensuremath{\alpha}$ is the thermal expansion coefficient and $\ensuremath{\gamma}$ the Gr\"uneisen parameter). It is therefore proposed that the mean free path for lattice vibrations in an insulator should, in the classical temperature region, be approximately $\frac{{A}_{0}}{\ensuremath{\alpha}\ensuremath{\gamma}T}$, where ${A}_{0}$ is the lattice spacing. Reasonably good agreement with experiment is found.

Vibrational Anharmonicity and Lattice Thermal Properties

Abstract: It has been believed for some time that anharmonicity of lattice vibrations is responsible for the continued rise of the specific heats of certain solids in the classical temperature region. A general analysis is here carried out of the linear chain model interacting through a Morse potential. All the major thermal properties, such as specific heats, thermal expansion, and compressibility are derived, and a tentative comparison is made with observed properties of the alkali metals.It is found that the linear chain then exists in two widely different states with properties characteristic of condensed and gas-like phases; these two states are separated by a relatively narrow transition region in temperature where the specific heat passes through a rather sharp maximum (except at high pressures when the maximum ultimately disappears).

Materials for thermoelectric energy conversion

Abstract: The field of thermoelectric energy conversion is reviewed from both a theoretical and an experimental standpoint. The basic theory is introduced and the thermodynamic and solid state views are compared. An overview of the development of thermoelectric materials is presented with particular emphasis being placed on the most recent developments in high-temperature semiconductors. A number of possible device applications are discussed and the successful use and suitability of these devices for space power is manifest.

Materials selection guidelines for low thermal conductivity thermal barrier coatings

Abstract: Materials selection guidelines are desirable in identifying and developing alternative materials for higher-temperature capability thermal barrier coatings. Some relate to identifying candidate materials that exhibit particularly low values of thermal conductivity at high temperatures and others relate to thermodynamic stability in contact with the thermally grown oxides formed on bond-coat alloys and superalloys. By using existing theories of the minimum thermal conductivity, a materials parameter is developed that can be used to identify candidate alternatives to yttria-stabilized zirconia for high-temperature applications.

The Thermal Conductivity of Nonmetallic Crystals

Abstract: 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.

Phonon engineering through crystal chemistry

Abstract: Mitigation of the global energy crisis requires tailoring the thermal conductivity of materials. Low thermal conductivity is critical in a broad range of energy conversion technologies, including thermoelectrics and thermal barrier coatings. Here, we review the chemical trends and explore the origins of low thermal conductivity in crystalline materials. A unifying feature in the latest materials is the incorporation of structural complexity to decrease the phonon velocity and increase scattering. With this understanding, strategies for combining these mechanisms can be formulated for designing new materials with exceptionally low thermal conductivity.