By J. Friedel (auth.), Tormod Riste (eds.)

This NATO complex research Institute used to be the fourth in a sequence dedicated to the topic of section transitions and instabilities with specific recognition to structural part transforma~ions. starting wi th the 1st Geilo institute in 19'(1 we've seen the emphasis evolve from the straightforward quasiharmonic tender mode description in the Landau idea, in the course of the unforeseen spectral constitution re awarded by means of the "central height" (1973), to such matters as melting, turbulence and hydrodynamic instabilities (1975). refined theoretical thoughts comparable to scaling legislation and renormalization crew thought constructed over a similar interval have dropped at this wide selection of matters a delightful team spirit. those institutes were instrumental in putting structural variations in actual fact within the mainstream of statistical physics and significant phenomena. the current Geilo institute keeps the various counter cul tural flavour of the 1st one by way of insisting every time attainable upon peeking lower than the skirts of even the main winning phenomenology to seize a glimpse of the underlying microscopic tactics. in fact the smooth mode is still an invaluable idea, however the significant em phasis of this institute is the microscopic reason for the mode softening. The discussions given the following illustrate that for convinced very important periods of solids the reason lies within the electron phonon interplay. 3 significant sorts of structural transitions are thought of. in relation to metals and semimetals, the electron phonon interplay relie6 seriously at the topology of the Fermi surface.

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The development of the long range Coulomb interaction between A and B gives rise to a pair interaction between electric dipoles on A and B. If A and B have no permanent dipoles, only dipoles induced by mutual polarization interact. Thus if C is the Coulomb correlation term in the hamiltonian describing the pair, its only matrix elements different from zero are

B) 58 587 (1973) ; Renker B. et al. Phys. Rev. Lett. 30, 1144 (1973). Comes R. , Phys. Rev. B8, 571 (1973) ; Phys. Rev. Lett. 35, 1518 (1975). -Labbe J. , J. Physique 27, 153, 303, 708 (1966). , J. Phys. Chem. Solids 31,1621 (1970). Gor'kov L. , J. E. T. P. --17, 379 (1973) ; Soviet Phys. J. E. T. P. 38,830 (1974). -Stoner E. :Proc. Roy. Soc. A 154, 656 (1936). Slater J. C. Phys. Rev. 82, 5350951) ; Lidiard A. B. Proc. Roy. Soc. A 224, 161 (1954). , Pr~ Phys. Soc. 80, 489 (1962). Ziman J. , Principles of the Theory of Solids, Cambridge University Press, 2d edition (1972).

10 --- - --............. 1 : Contribution to cohesion in a transitional series (schematic) :a - EO;b,c: EI ; d - E2 ; e - Total. J. 1). The second order contribution E2 is the first correction for electron-electron correlations. As U » J, only the term in V2 need be considered. As U induces virtual transitions between occupied and unoccupied valence states, with number ~ and 1- ~ 10 10 per atomic orbital, an estimate neglecting conservation of momentum in electron-electron collisions gives w/2 w/2 Un(El)n(E2)n(E3)n(E4)dEldE2dE3dE4 f wf w f f E +E -E -E E I 2 3 4 -"2 -"2 EM M This is approximately (for rectangular d bands)(5) E2 ""'.