P. G. Klemens

Ceramic materials for thermal barrier coatings

A method for identifying ceramics suitable for use as thermal barrier coatings is presented, based on parameters associated with thermal conductivity, oxygen diffusivity, thermal expansion coefficient, maximum temperature capability, hardness, elastic modulus, density, and chemical reactivity. A ceramic thermal barrier coating and method of manufacture is further presented, the ceramic comprising yttrium aluminum garnet (Y3 Al5 O12, or YAG)-based ceramics. Such ceramics are based on yttrium aluminum garnet or other ceramics with the garnet structure and alloys thereof. The ceramics in accordance with the present invention have low thermal conductivity, and are more potentially durable than prior art zirconia based ceramics.

The Scattering of Low-Frequency Lattice Waves by Static Imperfections

The scattering of lattice waves by static imperfections is treated by second-order perturbation theory. The transition matrix is composed of contributions due to the mass difference of lattice points, changes in the elastic constants of linkages between lattice points, and elastic strain. Point imperfections are shown to scatter as the fourth power of frequency, dislocations as the first power, and grain boundaries independently of frequency. The magnitude of the scattering cross section is estimated for a variety of lattice defects in alkali halides, for screw and edge dislocations and for grain boundaries. These results are discussed in relation to thermal conduction by the lattice at low temperatures.

Thermal Conductivity and Lattice Vibrational Modes

Publisher Summary This chapter discusses thermal conductivity and lattice vibrational modes. The heat transport by lattice waves in solids is governed by the anharmonicities of the lattice forces (which are also responsible for thermal expansion), by the various imperfections of the crystal lattice, and by the external boundaries. In the case of metallic and semi-metallic solids, the lattice component of thermal conduction is also governed by the free electrons. Not only may many different factors influence the thermal conductivity, but the processes that provide the principal sources of thermal resistance may vary from one material to another. In fact, they may vary in different temperature regions in any one material. Thus, the phenomenon of thermal conduction by lattice waves offers great diversity and provides an interesting field of study, both from a fundamental point of view, in which one desires to attain agreement between observation and the theoretical concepts, and from the more applied viewpoint in which one desires to use thermal conductivity as a tool in the study of lattice imperfections. Thermal conduction by lattice waves also occurs in metallic solids, but here the lattice conductivity is small, as a consequence of the scattering of lattice waves by conduction electrons, so that it is often overshadowed by the electronic thermal conductivity.

Thermal conductivity of dense and porous yttria-stabilized zirconia

The thermal conductivity of dense and porous yttria-stabilized zirconia (YSZ) ceramics has been measured as a function of temperature in the range 25 to 1000 °C. The dense specimens were either single crystal (8 mol% YSZ) or sintered polycrystalline (3 mol% and 8 mol% YSZ). The porous specimens (3 mol% YSZ) were prepared using the “fugitive” polymer method, where different amounts of polymer spheres (of two different average sizes) were included in the starting powders before sintering. This method yielded materials with uniformly distributed porosities with a tight pore-size distributions. A theory has been developed to describe the thermal conductivity of dense YSZ as a function of temperature. This theory considers the reduction in the intrinsic thermal conductivity due scattering of phonons by point defects (oxygen vacancies and solute) and by the “hopping” of oxygen vacancies. It also considers an increase in the effective thermal conductivity at high temperatures due to radiation. This theory captures the essential features of the observed thermal conductivity. The Maxwell theory has been used to analyze the thermal conductivity of the porous materials. An adequate agreement was found between the theory and experiment.

Thermal Conductivity of Solids

Problem: Thermal conductivity is an intensive physical property of a material that relates the heat flow through the material per unit area to temperature gradient across the material. The thermal conductivity of a material is basically a measure of its ability to conduct heat. In a wide variety of applications ranging from building insulation to electronics, it is important to determine a material’s thermal conductivity. Typical methods of thermal conductivity measurement can be categorized as either steady-state or non-steadystate. In steady-state techniques, equilibrium heat flux and temperature gradient are measured. In nonsteady-state techniques, a variable heat flux is produced and the time-variant temperature gradient is measured. The method you are asked to investigate involves the transient heating of spherical shaped samples.

Thermal conductivity of thermal barrier coatings

Abstract In thermal barrier coatings and other ceramic oxides, heat is conducted by lattice waves, and also by a radiative component which becomes significant at high temperatures. The theory of heat conduction by lattice waves is reviewed in the equipartition limit (above room temperature). The conductivity is composed of contributions from a spectrum of waves, determined by the frequency dependent attenuation length. Interaction between lattice waves (intrinsic processes), scattering by atomic scale point defects and scattering by extended imperfections such as grain boundaries, each limit the attenuation length in different parts of the spectrum. Intrinsic processes yield a spectral conductivity which is independent of frequency. Point defects reduce the contribution of the high frequency spectrum, grain boundaries and other extended defects that of the low frequencies. These reductions are usually independent of each other. Estimates will be given for zirconia containing 7wt% Y 2 O 3 , and for yttrium aluminum garnet. They will be compared to measurements. The effects of grain size, cracks and porosity will be discussed both for the lattice and the radiative components. While the lattice component of the thermal conductivity is reduced substantially by decreasing the grain size to nanometers, the radiative component requires pores or other inclusions of micrometer scale.

Theory of thermal conduction in thin ceramic films

The theory of heat conduction in ceramics by phonons, and at high temperatures also by infrared radiation, is reviewed. The phonon mean free path is limited by three-phonon interactions and by scattering of various imperfections. Point defects scatter high-frequency phonons; extended imperfections, such as inclusions, pores, and grain boundaries, affect mainly low-frequency phonons. Thermal radiation is also scattered by imperfections, but of a larger size, such as splat boundaries and large pores. Porosity also reduces the effective index of refraction. For films there are also external boundaries, cracks, and splat boundaries, depending on the method of deposition. Examples discussed are cubic zirconia, titanium oxide, and uranium oxide. Graphite and graphene sheets, with two-dimensional phonon gas, are discussed briefly.

Heat balance and flow conditions for electron beam and laser welding

The conditions of energy and material flow during beam welding are investigated theoretically to determine the factors which govern the shape of the vapor cavity and of the molten zone. Flow conditions in the horizontal plane determine the dimensions of the weld. Material is moved around the advancing vapor cavity mainly by liquid flow, but there is some vapor flow across the cavity, providing the pressure which drives the liquid. The pressure inside the vapor cavity and its variation with depth is governed by surface tension, by the hydrostatic pressure in the liquid, and by the viscous forces acting on the vapor stream. These factors govern the radius of the cavity as a function of depth. The penetration is limited by the beam power or by the absorption of the beam. For the laser beam, absorption is decreased in the hot center, and beam penetration increases with power, but is insensitive to collimation. For electrons, absorption occurs mainly near the walls of the cavity, and the beam penetration depen...

Thermal conductivity of ceramics in the ZrO 2 -GdO 1.5 system

Low thermal conductivity ceramics in the ZrO 2 -GdO 1 . 5 system have potential in structural (refractories, thermal barrier coatings, thermal protection) and nuclear applications. To that end, the thermal conductivities of hot-pressed x GdO 1 . 5 . (1 - x)ZrO 2 (where x = 0.05, 0.15, 0.31, 0.50, 0.62, 0.75, 0.89, and 1.00) solid solutions were measured, for the first time, as a function of temperature in the range 25 to 700 °C. On the ZrO 2 -rich side, the thermal conductivity first decreased rapidly with increasing concentration of GdO 1 . 5 and then reached a plateau. On the GdO 1 . 5 -rich side, the decrease in the thermal conductivity with increasing concentration of ZrO 2 was less pronounced. The thermal conductivity was less sensitive to the composition with increasing temperature. The thermal conductivity of pyrochlore Gd 2 Zr 2 O 7 (x = 0.5) was higher than that of surrounding compositions at all temperatures. A semiempirical phonon-scattering theory was used to analyze the experimental thermal conductivity data. In the case of pure ZrO 2 and GdO 1 . 5 , the dependence of the thermal conductivity to the absolute temperature (T) was less than 1/T. Therefore, the minimum thermal conductivity theory was applied, which better described the temperature dependence of the thermal conductivity of pure ZrO 2 and GdO 1 . 5 . In the case of solid solutions, phonon scattering by cation mass fluctuations and additional scattering by oxygen vacancies on the ZrO 2 -rich side and by gadolinium vacancies on the GdO 1 . 5 -rich side seemed to account for the composition and temperature dependence of the thermal conductivity.

Phonon scattering by oxygen vacancies in ceramics

Abstract The theory of phonon scattering by vacancies is applied to oxygen vacancies in zirconia and rutile. These vacancies are the major source of point defect scattering in stabilized zirconia. It is shown that the theory agrees well with thermal diffusivity reductions in reduced rutile. This lends confidence to the effect of oxygen vacancies on the thermal conductivity of stabilized zirconia, particularly in thermal barrier coatings.