By J. Friedel (auth.), Tormod Riste (eds.)
This NATO complex learn Institute was once the fourth in a sequence dedicated to the topic of part transitions and instabilities with specific recognition to structural section transforma~ions. starting wi th the 1st Geilo institute in 19'(1 we've seen the emphasis evolve from the straightforward quasiharmonic gentle mode description in the Landau conception, throughout the unforeseen spectral constitution re offered through the "central height" (1973), to such topics as melting, turbulence and hydrodynamic instabilities (1975). refined theoretical thoughts reminiscent of scaling legislation and renormalization team thought constructed over an analogous interval have delivered to this wide selection of matters a lovely cohesion. those institutes were instrumental in putting structural variations in actual fact within the mainstream of statistical physics and demanding phenomena. the current Geilo institute keeps many of the counter cul tural flavour of the 1st one by means of insisting each time attainable upon peeking less than the skirts of even the main profitable phenomenology to capture a glimpse of the underlying microscopic methods. in fact the tender mode continues to be 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 yes vital 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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Extra info for Electron-Phonon Interactions and Phase Transitions
C) Narrow d bands in 2 dimensions (planes) This case was first seriously considered for the layered 3 dimensional structures of transition dichalcogenides(12) , where the transition elements build up close packed planes which are separated by rather insulating layers of S, Se or Te. a). b) : Kohn anomalies appear very clearly in compounds with parallel conducting chains separated by more or less insulating material : J. FRIEDEL 18 • • • • • a b • • • • • • • • • • • • • • • c Figure 12 : Three types of two dimensional cases : a parallel planes b parallel chains ; c 3 orthogonal sets of parallel chains.
Ge electron per atomOratio (for fixed q and thus crystal structure). As stressed figure 11, the success~ve Hume Rothery Jones structures met at increasing electron per atom ratio will be actually observed at OK only if their corresponding stabilities are increasing (case a). a) should have a narrow range of stability near the corresponding critical electron per atom ratio. b, which is unstable at OK. A famous example is the BCC 8 phase of Cu Zn alloys. The same condition of Brillouin zone boundary tangent to the Fermi sphere has been used to explain more complex alloy structures where superstructures modulate a fundamental simple crystal structure(lO).
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