Electronic fluctuation, the nature of interactions and the structure of liquid metals

In the case of relatively low-Z A elements with few electrons per nucleus it is now possible to apply many-body quantum Monte carlo simulation techniques to (1). See.G. Sugiyama, G. Serah andB. J. Alder:Physica A,156, 144 (1989), for the case of lithium.

For a more detailed discussion of the quantum-statistical issues, seeN. W. Ashcroft:The Liquid State of Matter: Fluids Simple and Complex, edited byE. W. Montroll andJ. L. Lebowitz (North Holland, Amsterdam, 1982).

J. Cheung andN. W. Ashcroft:Phys. Rev. B,23, 2484 (1981), see also ref. [2] For a more detailed discussion of the quantum-statistical issues, seeN. W. Ashcroft:The Liquid State of Matter: Fluids Simple and Complex, edited byE. W. Montroll andJ. L. Lebowitz (North Holland, Amsterdam, 1982).

H. Hellman:Acta Physicochem. USSR,1, 913 (1935);E. Antoncik:J. Phys. Chem. Solids,10, 314 (1959);J. C. Phillips andL. Kleinman:Phys. Rev.,116, 287 (1959).

For a comprehensive review, seeJ. Hafner:From Hamiltonians to Phase Diagrams (Springer, Berlin, 1987).

N. W. Ashcroft andD. C. Langreth:Phys. Rev.,155, 682 (1967).

M. H. Cohen:Metalic Solid Solutions, edited byJ. Friedel andA. Guinier (Benjamin, New York, N. Y., 1962), p. IX-1.

V. Heine:Solid State Phys.,24, 1 (1971).

E. G. Brovman andYu. Kagan:Sov. Phys. JETP,30, 721 (1970);J. Hammerberg andN. W. Ashcroft:Phys. Rev. B,2, 409 (1974).

For analysis of the consequences of both short-range and long-range behaviour in pair potentials possessing Friedel oscillations of the form (18) seeJ. Hafner andV. Heine:J. Phys. F,13, 2479 (1983);16, 1429 (1986).

W. A. Harrison:Pseudopotentials in the Theory of Metals, see alsoPhys. Rev. B,7, 2403 (1973). See alsoP. L. Taylor:Phys. Rev.,131, 1995 (1963).

The point is that, if Δ/ℏ>ωp,dynamic valence electron screening must be largely suppressed; seeJ. J. Rehr, E. Zaremba andW. Kohn:Phys. Rev. B,12, 2062 (1975), andJ. Mahanty andR. Taylor:Phys. Rev. B,17, 554 (1978).

For further detaile seeK. K. Mon, N. W. Ashcroft andG. V. Chester:Phys. Rev. B,19, 5103 (1979).

See, for exampleA. C. Maggs andN. W. Ashcroft:Phys. Rev. Lett.,59, 113 (1987).

D. C. Langreth andS. H. Vosko:Phys. Rev. Letts.,59, 497 (1987).

The termpseudoatom or pseudoparticle has also been introduced in the dynamic context byC. S. Jayanthi, H. Bilz, W. Kress andG. Benedek:Phys. Rev. Lett.,59, 795 (1987). See alsoR. Goldstein, A. Parola andA. Smith:J. Chem. Phys.,91, 1843 (1989).

SeeY. Morino, T. Ukaij andT. Ito:Bull. Chem. Soc. Jpn.,39, 64 (1966);K. Raghavachari, R. C. Haddon andJ. S. Binkley:Chem. Phys. Lett.,122, 219 (1985) and references therein.

P. Salmon:J. Phys. F.,18, 2345 (1988). These more recent neutron scattering data seem to differ significantly from the data used byG. Kahl andJ. Hafner:Phys. Rev. A,9, 3310 (1984).

R. L. Henderson:Phys. Lett. A,49, 197 (1974). Strictly speaking,uniqueness is guaranteed providingexistence is first established.

The picture is one in which vibrational motion carries on for a significanr number of periods about quasi-equilibrium sitesb ij o before any fast exchange may literally tranfer an atom to another dynamic unit. This is accord with the suggestion ofOrton (J. Phys. (Paris),41, Suppl. #8, Coll. C8, C8–280 (1980)) that directional order can be weakened in some fluids, but not lost.

See, for exampleN. W. Ashcroft andN. D. Mermin:Solid State Phys. (Holt Saunders, 1976), appendix N.

N. W. Ashcroft andJ. Lekner:Phys. Rev.,145, 83 (1966).

A. Bererhi A. Bizid, L. Bosio, R. Cortes, A. Defrain andC. Seqaud:J. Phys. (Paris),41, Suppl. #8, Coll. C8, C8–218 (1980);M. C. Bellisent-Funel, R. Belisent andG. Tourand:J. Phys. (Paris),41, Suppl. #8, Coll. C8, C8-262 (1980).

T. E. Faber:The theory of Liquid Metals (Cambridge University Press, 1972;J. P. Hansen andI. R. McDonald:Theory of Simple Liquids, 2nd edition (Academic, New York, N. Y., 1986).

The structure factor of the fluid has recently been measured byR. Bellisent, C. Bergmann, R. Ceolin andJ. P. Gaspard:Phys. Rev. Lett.,59, 661 (1987), and it clearly exhibits complex behavior suggestive of polyatomic dynamic units. The structure is similar to but more extreme than that found for phosphorus (J. S. Granada andJ. C. Dore:Mol. Phys.,46, 757 (1982). Again P4 is a relatively stable entity in the vapor phase.

An interpretation of the data of ref. [31] The structure factor of the fluid has recently been measurded byR. Bellisent, C. Bergmann, R. Ceolin andJ. P. Gaspard:Phys. Rev. Lett.,59, 661 (1987), and it clearly exhibits complex behavior suggestive of polyatomic dynamic units. The structure is similar to but more extreme than that found for phosphorus (J. S. Granada andJ. C. Dore:Mol. Phys.,46, 757 (1982)) Again P4 is a relatively stable entity in the vapor phase. has recently been given byJ. Hafner:Phys. Rev. Lett.,62, 784 (1988), on the basis of ametallic state with 5 valence eletrons/atom, and single ions as the characteristic dynamic units (the first of the viewpoints discussed above). A difficulty here is that the experiment shows the fluid to be nonmetallic; further, thes-states are asserted to lie far belowp, and the assigment of 5 free electrons in a common band would also seem to be inappropriate even if the system were metallic.

M. S. Daw andM. I. Baskes:Phys. Rev. Lett.,50, 1285 (1983).

R. Car andM. Parrinello:Phys. Rev. Lett.,55, 2471 (1985).

D. Weaire:J. Phys. C,1, 201 (1968).

J. Hefner andG. Kahl:J. Phys. F,14, 2259 (1984).