I.
Lattice Vacancies and Atoms in Interstitial Positions2
1. M. HONIG Purdue University, Lafayette, Indiana
T H E aim of this paper is to present an elementary review of the subject of defects in crystalline solids. Emphasis is placed on those basic concepts or principles which are used to explain a variety of experimental observations in the physics and chemistry of the solid state. The discussion is intended to be suggestive rather than exhaustive, and explanatory rather than rigorous. It will have served the purpose if it stimulates the reader to become better acquainted with the field through further reading. For an over-all survey of the subject, references ( 1 4 ) are recommended. m e r e possible, chemical application of the principles described in this review are briefly presented. The concepts presented below are of importance in discussing some general properties of solids, such as transport phenomena and optical characteristics. Other properties, such as specific heat, are not significantly affected by crystal imperfections. Perhaps the most important application of the ideas to be discussed below occurs in the field of semiconductors which would hardly have advanced to its present state without these concepts.
on the surface of the crystal. Figures 3-6s show a twodimensional array of atoms, (a) free of vacancies, (b) containing 6% vacancies as Schottky defects, (c) containing Schottky defects, attended by a 50% volume relaxation, and (d) showing an internal rearrangement
FRENKEL AND SCHOTTKY DEFECTS IN MONATOMIC CRYSTALS
into crystallites as a result of the initial presence of Schottky defects. Figure 7 illustrates one mechanism of formation of Schottky defects; others will be discussed in the second paper. This figure also shows that lattice atoms may move to fill an adjacent vacancy; in this process, a new empty site is generated at the location from which the atom moved. This process can also he described somewhat loosely as motion of the vacancy from one lattice point to the next; the direction of motion is opposite to that of the moving atom. A certain activation energy is required for these displacements because the atom must overcome m theattractiveforceholda ing it to nearest neigh:.$ , bors before it can move into the adjoining vacancy. Similarly, atoms , , located interstitially can 'b' move to adjacent inter* * * * * stitial positions only if rim=. a. n ~ ~ ~ - they d possess i ~thenecessary ~ ~ ~ Rap-entation or Figuro 1 (after J O . ~ISII activation energy. Oc-
Above 0°K. a certain degree of disorder is always present in otherwise perfect crystals. This disorder occurs because atoms are displaced from their regular lattice positions to some other location in the crystal. Two types of lattice irregularities are encountered: In solids exhibiting Frenkel-type defects (7) the d i e placed atoms enter the crystal interstitially; vacancies are simultaneously created at the locations from which the displacements originate. The interstitial locations are shown in Figures 1 and 2. It is evident that Frenkel defects will occur only in cases where the crystal structure is fairly open and where the atom to be accommodated interstitially is reasonably small. Conversely, in a structure such as shown in Figure 3 ($) it,wonld require a heavy expenditure of energy to squeeze particles into the interstices. Crystals in this latter category exhibit Schottky-type defects (8),in which vacancies are generated but the displaced atoms settle Presented as part of the Symposium on Recent Developments in the Solid State before the Division of Chemical Education at the 129th Meeting.of the American Chemical Society. .. Dallas. April, 1956. The first of two papers on this topic to he published in N A I EDUCATION. consecutive issues of ~ ~ ~ J O UOPRCHEMICAL
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1.
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An Ion i n the Interstitial position of a Faca-c.nt...d Cubic Lattice (after Jost (91)
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The author wishes to express his appreciation to Professor N. Nachtrieb of the Institute for the Study of Metals, University of Chicago, for permis~ionto reproduce these piotures.
JOURNAL OF CHEMICAL EDUCATION
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casionally, a vacancy will wander into the vicinity of an interstitial or a surface atom, in which case the reverse of the defect formation process will occur. Defects are then said to be annihilated. The disordering of crystals requires the expenditure of energy (see for example references (8-15)); one might well ask why defects should exist a t all in solids which would otherwise be perfect. An answer can be provided from two different points of view. Neglecting higher vibrational energy levels, one may think of every lattice atom as being in its ground state, and of every defect as representing an excited state. According to the Boltzmann principle, there is a finite probability that a t any temperature above OmK.,a particle will be found in an excited state, even though it has access to a lower energy level. This law finds its quantitative expression in the familiar relation % / N o - e - c / i > ~ ,where n and No are the number of particles in the excited and ground levels respectively, and r is the energy difference between the two states; k is the Boltzmann constant and T the absolute temperature. I n applying this reasoning to Schottky crystals, let n be the number of defects existing in the crystal of N atoms and let r. be the energy required to create the defect,. Then, NO = N - n and one therefore finds for the number of defects existing a t the temperature, T
Figure 4
Figure 3
Figure 3: 4 twll~hatthe ground state of the crystal is that in which all interstitial positions are unoccupied. If n
