Electrical Conductivity in Polycrystalline Materials

Polycrystalline or multicrystalline materials, or polycrystals are solids that are composed of many crystallites of varying size and orientation. Most inorganic solids are polycrystalline, including all common metals, many ceramics, rocks and ice. The extent to which a solid is crystalline (crystallinity) has important effects on its physical properties. Sulfur, while usually polycrystalline, may also occur in other allotropic forms with completely different properties. Although crystallites are referred to as grains, powder grains are different, as they can be composed of smaller polycrystalline grains themselves. While the structure of a (monocrystalline) crystal is highly ordered and its lattice is continuous and unbroken. amorphous materials, such as glass and many polymers, are non-crystalline and do not display any structures as their constituents are not arranged in an ordered manner. Polycrystalline structures and paracrystalline phases are in between these two extremes. Electrical Conductivity in Polycrystalline Materials examines the influence of composition, structure, and size factor on the dielectric permittivity and electrical conductivity of polycrystalline materials. The problem of the determination of the macroscopic conductivity of statistically homogeneous and isotropic polycrystalline materials in terms of the principal values of the conductivity tensor of the constituent crystals is considered. A perturbation expansion, in terms of correlation functions with an optimal value of the zeroth-order estimate of the effective conductivity, is derived in which a separation is established into texture dependent and independent quantities. Consistence with the analogous expansion for the effective resistivity is demonstrated. This Book is intended for students, post-graduate students, and scientists in the field of polycrystalline materials. Polycrystalline or multicrystalline materials, or polycrystals are solids that are composed of many crystallites of varying size and orientation. Most inorganic solids are polycrystalline, including all common metals, many ceramics, rocks and ice. The extent to which a solid is crystalline (crystallinity) has important effects on its physical properties. Sulfur, while usually polycrystalline, may also occur in other allotropic forms with completely different properties. Although crystallites are referred to as grains, powder grains are different, as they can be composed of smaller polycrystalline grains themselves. While the structure of a (monocrystalline) crystal is highly ordered and its lattice is continuous and unbroken. amorphous materials, such as glass and many polymers, are non-crystalline and do not display any structures as their constituents are not arranged in an ordered manner. Polycrystalline structures and paracrystalline phases are in between these two extremes. Electrical Conductivity in Polycrystalline Materials examines the influence of composition, structure, and size factor on the dielectric permittivity and electrical conductivity of polycrystalline materials. The problem of the determination of the macroscopic conductivity of statistically homogeneous and isotropic polycrystalline materials in terms of the principal values of the conductivity tensor of the constituent crystals is considered. A perturbation expansion, in terms of correlation functions with an optimal value of the zeroth-order estimate of the effective conductivity, is derived in which a separation is established into texture dependent and independent quantities. Consistence with the analogous expansion for the effective resistivity is demonstrated. This Book is intended for students, post-graduate students, and scientists in the field of polycrystalline materials. Polycrystalline or multicrystalline materials, or polycrystals are solids that are composed of many crystallites of varying size and orientation. Most inorganic solids are polycrystalline, including all common metals, many ceramics, rocks and ice. The extent to which a solid is crystalline (crystallinity) has important effects on its physical properties. Sulfur, while usually polycrystalline, may also occur in other allotropic forms with completely different properties. Although crystallites are referred to as grains, powder grains are different, as they can be composed of smaller polycrystalline grains themselves. While the structure of a (monocrystalline) crystal is highly ordered and its lattice is continuous and unbroken. amorphous materials, such as glass and many polymers, are non-crystalline and do not display any structures as their constituents are not arranged in an ordered manner. Polycrystalline structures and paracrystalline phases are in between these two extremes. Electrical Conductivity in Polycrystalline Materials examines the influence of composition, structure, and size factor on the dielectric permittivity and electrical conductivity of polycrystalline materials. The problem of the determination of the macroscopic conductivity of statistically homogeneous and isotropic polycrystalline materials in terms of the principal values of the conductivity tensor of the constituent crystals is considered. A perturbation expansion, in terms of correlation functions with an optimal value of the zeroth-order estimate of the effective conductivity, is derived in which a separation is established into texture dependent and independent quantities. Consistence with the analogous expansion for the effective resistivity is demonstrated. This Book is intended for students, post-graduate students, and scientists in the field of polycrystalline materials.