Atoms in Motion 6.1.Lattice Defects and Diffusion So far,when discussing the properties of materials we tacitly as- sumed that the atoms of solids remain essentially stationary.From time to time we implied,however,that the behavior of solids is af- fected by the thermally induced vibrations of atoms.The changes in properties increase even more when atoms migrate through the lattice and take new positions.In order to gain a deeper insight into many mechanical properties,we therefore need to study the "dy- namic case."It will become obvious during our endeavor that the motion of atoms through solids involves less effort (energy)when open spaces are present in a lattice,as encountered,for example, by empty lattice sites.Thus,we commence with this phenomenon. 6.1.1 Lattice We have repeatedly pointed out in previous chapters that an ideal Defects lattice is rarely found under actual conditions,that is,a lattice in which all atoms are regularly and periodically arranged over large distances.This is particularly true at high temperatures, where a substantial amount of atoms frequently and randomly change their positions leaving behind empty lattice sites,called vacancies.Even at room temperature,at which thermal motion of atoms is small,a fair number of lattice defects may still be found.The number of vacancies per unit volume,ny,increases exponentially with the absolute temperature,T,according to an equation whose generic type is commonly attributed to Arrhenius: ny=ns exp (6.1) ISvante August Arrhenius(1859-1927),Swedish chemist and founder of modern physical chemistry,received in 1903,as the first Swede,the Nobel prize in chemistry.The Arrhenius equation was originally formulated by J.J. Hood based on experiments,but Arrhenius showed that it is applicable to almost all kinds of reactions and provided a theoretical foundation for it.6 So far, when discussing the properties of materials we tacitly as￾sumed that the atoms of solids remain essentially stationary. From time to time we implied, however, that the behavior of solids is af￾fected by the thermally induced vibrations of atoms. The changes in properties increase even more when atoms migrate through the lattice and take new positions. In order to gain a deeper insight into many mechanical properties, we therefore need to study the “dy￾namic case.” It will become obvious during our endeavor that the motion of atoms through solids involves less effort (energy) when open spaces are present in a lattice, as encountered, for example, by empty lattice sites. Thus, we commence with this phenomenon. We have repeatedly pointed out in previous chapters that an ideal lattice is rarely found under actual conditions, that is, a lattice in which all atoms are regularly and periodically arranged over large distances. This is particularly true at high temperatures, where a substantial amount of atoms frequently and randomly change their positions leaving behind empty lattice sites, called vacancies. Even at room temperature, at which thermal motion of atoms is small, a fair number of lattice defects may still be found. The number of vacancies per unit volume, nv, increases exponentially with the absolute temperature, T, according to an equation whose generic type is commonly attributed to Arrhenius: 1 nv
ns exp  k E BT f  , (6.1) 6.1.1 Lattice Defects Atoms in Motion 6.1 • Lattice Defects and Diffusion 1Svante August Arrhenius (1859–1927), Swedish chemist and founder of modern physical chemistry, received in 1903, as the first Swede, the Nobel prize in chemistry. The Arrhenius equation was originally formulated by J.J. Hood based on experiments, but Arrhenius showed that it is applicable to almost all kinds of reactions and provided a theoretical foundation for it.