International Union of Pure and Applied Chemistry Inorganic Chemistry Division Commission on High Temperature Materials and Solid State Chemistry Definitions of Terms for Diffusion in the Solid State

This document provides definitions of terms and processes which are used in describing the migration of host and foreign species through solid materials. Both the phenomenological theory of diffusion and the detailed atomistic mechanisms by which atom transport occurs are treated. Also included are the various types of gradients such as electrical, chemical, thermal and mechanical, which provide the driving forces for diffusion. INTRODUCTION The definitions in this document relate specifically to the solid state and are intended for the professional scientist. But they will not necessarily meet all the needs of the specialist chemist, physicist or materials scientist. An attempt has been made to produce a set of concise definitions. In certain instances, definitions have been quoted directly from the literature, while in others, definitions have been modified or abridged to suit the document. Certain definitions have been expanded where clarification was considered necessary. A system of cross-referencing has been used in which italicised terms refer to other entries where relevant information is available and where terms are known by more than one name. The references cited in the bibliography are not unique but provide additional reading on specific definitions. INDEX OF SYMBOLS a0 lattice constant [m] b mobility [m/N/s] c amount (of substance) concentration [mol/m] D diffusion coefficient [m/s] Di self diffusion coefficient of species i [m /s] D̃ chemical diffusion coefficient or interdiffusion coefficient [m/s] Di * tracer diffusion coefficient of species i [m /s] D̄i intrinsic diffusion coefficient of species i [m /s] DR random walk diffusion coefficient [m /s] e elementary charge [C] E electrical field (vector) [V/m] f correlation factor F force [N] G Gibbs energy [J] h Planck constant [J s] HR Haven ratio J flux [m/s] k Boltzmann constant [J/K] Ni mole fraction of species i NA Avogadro constant [mol ] 1308 COMMISSION ON HIGH TEMPERATURE MATERIALS AND SOLID STATE CHEMISTRY q 1999 IUPAC, Pure Appl. Chem. 71, 1307–1325 p probability P pressure [Pa] q electrical charge (q 1⁄4 ze) [C] Q activation energy [J/mol] R gas constant (R 1⁄4 NAk) [J/K/mol] T thermodynamic temperature [K] t time [s] u electrical mobility [m/V/s] v drift velocity [m/s] V̄j partial molar volume of species j [m ] x cartesian coordinate [m] Xi thermodynamic force on species i (generalised force in Onsager’s relation) z charge number ∂ partial derivative operator D finite difference = gradient operator F thermodynamic factor gi thermodynamic activity coefficient of species i Gi jump frequency of species i [s ] h electrochemical potential [J/mol] m chemical potential [J/mol] s electrical conductivity [S/m] S summation sign v0 atom or vacancy jump frequency [s ] z nearest-neighbour co-ordination number DEFINITION OF TERMS Activation energy The parameter Q, which characterises the exponential temperature dependence of the diffusion coefficient D in the empirical equation D 1⁄4 D0 exp(1Q/RT). D0 is a temperature independent constant, R is the gas constant and T the thermodynamic temperature. Q is called the activation energy for diffusion. D0 is often referred to as the pre-exponential factor. Activation volume The pressure dependence of a diffusion coefficient, D, is often represented by ð∂ ln D=∂PÞT 1⁄4 1ðDV =RTÞ þ ð∂ ln q0 =∂PÞT where DV is called the activation volume, R is the gas constant, T the thermodynamic temperature and v0 is the atom jump frequency. The second term on the right is a small correction, only a few per cent of the first term, so in good approximation: DV < 1RTð∂ ln D=∂PÞT Ambipolar diffusion Diffusion in systems with two (or more) diffusing species with opposite electrical charge. See: effective diffusion coefficient. Definitions of terms for diffusion in the solid state 1309 q1999 IUPAC, Pure Appl. Chem. 71, 1307–1325 Ascending diffusion A specific type of diffusion that can take place in alloys of metals under the influence of stress gradients. When the constituents are of different sizes the larger elements tend to move in the directions of the dilated regions. Thus ascending diffusion disturbs the uniform distribution of the constituents and sets up a concentration gradient which opposes the stress gradient. Attempt frequency See: jump frequency Barycentric frame of reference See: mean-mass frame of reference Boltzmann–Matano analysis A procedure to determine the chemical diffusion coefficient in binary or multiphase systems from experimentally measured concentration profiles. Bulk diffusion See: lattice diffusion. Chemical diffusion Diffusion under the influence of a gradient in chemical composition. In concentrated solid solutions, e.g. A11xBx, or in diffusion couples, the motion of one constituent causes a counterflow of the other constituent(s) or vacancies. In this case one can define a diffusion coefficient for the intermixing, which is called the chemical diffusion coefficient or interdiffusion coefficient D̃. One can also define diffusion coefficients for each of the constituents i, called intrinsic diffusion coefficient D̄i. See: Darken equation. Chemical diffusion coefficient In N-component diffusion the chemical diffusion coefficient or interdiffusion coefficient D̃ij is obtained from the flux J̃i of species i, with concentration ci, measured with respect to the laboratory frame of reference by applying Fick’s First law (expressed here in one dimension):