Dreikörperkräfte und die Stabilität einfacher Kristallgitter

Observed stability of crystal structures for rare-gas atoms, alkali halides and for those II–VI and III–V compounds whose ions are isoelectronic with rare-gas atoms is correlated with atomic and ionic interactions in dense media. On the basis of central forces essential discrepancies between theory and experiment occur. Further analysis indicates that strong, simultaneous interactions of exchange type between three atoms or three ions play an important role in determining the stable crystal structure. An evaluation of such three-body interactions is carried out in first and second orders of perturbation theory, using effective-electron wave functions of Gaussian form. It is shown that the theory accounts for all observed stability relations on a quantitative basis. The stability of the face-centered cubic configuration for solids of heavy rare gases is explained. Also, the occurrence of the cesium chloride structure for some of the heavy alkali halides and the magnitude of observed transition pressures are reproduced by the theory. In addition, it is shown that three-ion interactions are responsable for the occurrence of the sphalerite (zincblende) and wurtzite configurations with II–VI and III–V compounds, without covalent bonding between the ions being involved. General laws are given which govern the relative stability of the sodium chloride, cesium chloride, sphalerite and wurtzite configurations for these types of compounds.