ON THE MECHANISM OF DEFECT MIGRATION IN THE LATTICE OF AN IONIC CRYSTAL

A. A. VOROB'EV, S. A. VOROB'EV

Recently, schemes have been developed for possible processes of destruction of color centers with the participation of vacancies. Some modes of the origin and propagation of vacancies in a crystal lattice are considered in the theory of dislocations and in the theory of sintering.

The most widespread is the hypothesis of Ya. I. Frenkel, who considered jumps of a cation or an anion from one lattice site to another, the consequence of which is the appearance of a vacancy and its migration through the lattice in the direction opposite to the motion of the ion.

Below we set forth a hypothesis of vacancy migration based on consideration of the behavior in the lattice of an asymmetric dipole consisting of an ion at a lattice site and the fictitious charge of a vacancy at a neighboring site. The asymmetry of the dipole is due to the difference between the masses of the ion and the vacancy, the effective mass of the vacancy being smaller than the mass of the ion and probably depending on certain conditions, in particular on the crystallographic direction along which its migration occurs.

The ion and its vacancy will rotate about a common center of gravity, while simultaneously oscillating along the line connecting the centers of these particles. The oscillations of such a system are limited by the dimensions of the free volume in the lattice, deformed upon the formation of the vacancy. When the vacancy and the ion are displaced from their initial position by 180°, then the vacancy, in the course of a linear oscillation, can pass into the position of greatest separation from its partner—the ion—and approach another ion of the same name. In this case the vacancy can lose its bond with its former partner ion and again form a dipole with another neighboring ion; that is, the vacancy moves into the place of the ion, and the ion occupies the place of the vacancy in the lattice.

But the crystal lattice exists when the concentration of vacancies is many times smaller than the concentration of ions; therefore we shall observe precisely the migration of vacancies, and not of ions, the exchange of places of which at neighboring sites does not produce an observed transfer of mass. Consequently, in some cases ionic processes must be considered as processes caused by the migration of vacancies in the lattice.

An analogous picture can also be imagined for describing the migration of an electron in the lattice in some cases. An electron vacancy, called a hole, forms with the electron a bound system defined by means of the concept of an exciton. A free electron and a hole

are not inherent in the normal, unexcited lattice of an alkali-halide crystal and are lattice defects. Unlike ionic processes, where the defect was only a vacancy, in electron–hole processes one should speak of the displacement of an electron and a hole, or of an exciton, if the electron and the hole constitute a single state of excitation of the crystal.

The transition of a vacancy from one ion to another gives rise to exchange bonding forces in the lattice between ions. Under the action of the exchange mechanism considered here for the transfer of vacancies along the direction in which ions of the same sign are located, i.e., along face diagonals or cube diagonals, not only does displacement of the vacancy occur, but exchange bonding forces also arise that strengthen the structure. In monoatomic structures the exchange process under consideration can take place along any crystallographic direction.

The presence of a temperature gradient or of an electric field creates the necessary conditions for the process under consideration: the displacement of ions in one direction and of their vacancies in the other direction. The process of exchange by vacancies will be impeded when the lattice is disturbed by impurities, dislocations, block boundaries, and other lattice distortions.