Nuclear Specific Heat of Gold-Silver Alloys

Abstract

PHYSICAL REVIEW LETTERS 15 MAY 1967 in Ref. 5, it was necessary, to make the computation of A (2) tt(0) tractable, to employ a static limit for the full dynamic potential. 9 Also a spherical average over the directions of p was introduced. It should be stressed, however, that it was not possible to show that the analytic expressions .themselves ensure positive definiteness. In fact, they almost certainly do not. Nevertheless, the remaining descrepancy for a = 0.25 is small as compared to the RPA result, which in absolute value comes out to be more than twice the average electron density.We have shown that the same difficulties arise, at short distances, in the RPA calculation of the displaced charge about a light test charge as is encountered in the calculation of the spinup-spin-down pair distribution function in an imperfect electron gas. Further, we have managed to show how these difficulties can be removed to a large extent by simply summing ladders. We conclude that when, calculating properties of an electron gas, such as g\\(r), which depend mainly on the short-range correlations, it is essential to metallic densities to treat particle-particle ladders. A detailed calculation of the Coulomb hole at finite dis-Pure gold 1 ' 2 (nuclear spin /= f) and silver 3 (7=1) do not show a nuclear specific heat because there is no electronic magnetic moment to interact with the nuclear magnetic moment and the degeneracy associated with the nuclear electric quadrupole moment of gold is not removed in the symmetrical cubic environment. However, although gold-silver alloys are facecentered cubic (fee) for all compositions, they show no long-range order and, therefore, the cubic symmetry is disturbed. This may be the explanation of a term proportional to 7"~2 observed in the specific heat of these alloys and presumed to be a nuclear specific heat.The solid points in Fig. 1 show the results tances will be presented elsewhere. It is a pleasure to thank my colleague Ed Woll, Jr., for discussion. . 4 B. Bergersen, thesis, Brandeis University, 1964 (unpublished). 5 J. P. Carbotte, Phys. Rev. 155, 197 (1967). 6 It is the electronic density at the positron position that determines the lifetime of a positron in an electron gas. Such measurements, in metals, represent a direct check of our theory in this case. 7 J. S. Langer and S. H. Vosko, J. Phys. Chem. Solids 12, 196 (1959). 8 It is perhaps worth mentioning, in passing, that reversing the sign of the results found by these authors so as to get the case of a repulsive impurity again leads to a net negative electron density at the impurity for r s values in the metallic range. 9 For a discussion of the physics underlying the use of the zero-frequency limit J7(q*,0) as an approximation to U(q;v), see also J. P. Carbotte and S. Kahana, Phys. Rev. 139, A213 (1965); 129, 1622 (1963.up to 1°K of two sets of measurements on a chill-cast, homogenized, and quenched goldsilver alloy containing 50 at.% gold. The measurements extended up to 3°K. The open points and line show the fit...

Specific heat below 3 °K of a gold–zinc and a gold–indium alloy

“…given by Martin (1968c), for purezinc Martin,2 where I i s the nuclear spin, Q is the electric quadand for pure indium by O'Neal and Phillips ,upole moment (=0.58 10-z4 Cm2 for gold), (1965). Linear interpolation between these results , is the charge on an electron, eq the electric field would give, for the goldlo atomic % zinc alloy, gradient, R the gas constant, and k is BOltzmann's estimated (Stern 1966) to be about 0.2 electrons The variation on alloying of the per atom.…”

“…uated, sealed, internally carbon-coated quartz A small nuclear specific-heat term was noticed (Martin 1967a(Martin , 1968a in nonmagnetic facecentered-cubic gold-silver alloys. It was suggested that, although the lattice was cubic, electric field gradients would exist in these disordered alloys and remove the degeneracy associated with the nuclear electric quadrupole moment of gold.…”