Quasi-harmonic finite strain equations of state of solids

Vol. 12, No. 6 8.

ABSTRACTS OF ARTICLES TO APPEAR IN J. PHYS. CHEM. SOLIDS

PSEUDOPOTENTIAL CALCULATIONS OF RELAXATION AND FORMATION ENERGY OF A (+~M) INTERSTITIAL DEFECT IN ALUMINUM Roger Chang, Science Center, North American Rockwell Corporation, Thousand Oaks, Califor. nia 91360 U.S.A., and L.M. Falicov, Department of Physics, University of California, Berkeley, California 94720 U.S.A.

The pseudopotei~tiaIform factors used previously by the authors to study the vacancy formation in aluminum are employed to calculate the atom displacements around and formation energy of an interstitial aluminum atom placed at the center (f, ~)of the face.centered cubic unit cell with encouraging results. ~,

Received 27 November 1972

9.

AN ANALYSIS OF CLUSTERING AND ORDER. ING IN MULTICOMPONENT SOUD SOLUTIONS II. FLUCTUATIONS AND KINETICS —

D. de Fontaine, School of Engineering and Applied Science, University of California, Los Angeles, California. The free energy of a multicomponent substitutional solid solution is rederived on the basis of a more rigorous averaging procedure than the one used in I. The resulting expression is a quadratic form in the Fourier transforms of the concentration variables, Application of the Landau theory of fluctuations then leads to a set of formulas for the expectation values of concentration fluctuation intensities, which are the extension to multicomponents of the Clapp and Moss formulas for binary systems. Coupled discrete.space diffusion equations are derived and solved by diagonalization of the diffusion matrix.Principal directions in composition space and static and kinetic eigenvectors are defined. The effect of the positive definite mobility matrix is to rotate the directions of fastest and slowest initial concentration changes (kinetic directions) away from the principal free energy directions but in such a way that asymptotic directions are never crossed. Examples of ternary systems are given and asymptotic directions in quatemary systems are discussed qualita. tively.

10.

QUASI-HARMONIC FINITE STRAIN EQUATIONS OF STATE OF SOLIDS Geoffrey F. Davies, Seismological Laboratory, California Institute of Technology, Pasadena, California 91109.

Thomsen’s ‘fourth-order anharmonic’ theory, which explicitly evaluates thermal effects in finite strain equations of elasticity according to the fourthorder approximation in lattice dynamics, is reconsidered for the special case of isotropic stresses and strains. It is shown that the approximations made in the finite strain theory are independent of those made in the lattice dynamics theory, with the result that strain dependence may be described in terms of any frame. indifferent strain tensor, not just the ‘Lagrangian’ strain tensor,1I, and that the finite strain expansions may be taken to any order, not just the fourth. This result is valid for general stresses and strains. Illustrative pressure-volume equations are derived in terms of three strain measures, including q and the frame-indifferent analogue, E, of the ‘Eulerian’ strain tensor, t. The reference state is here left arbitrary, rather than identifying it with the ‘rest’ state. This results in greater convenience in applying the equations. Not being restricted to fourth order, the present equations do not depend for their application on knowing the second pressure derivatives of the bulk modulus. Expressions are obtained for isentropes and Hugoniots in terms of the same parameters as enter the original equations, which have the form of isotherms. Ultrasonic, thermal expansion and calorimetric data for MgO are used to evaluate the parameters of third-order equations of state of MgO, The equations of state are tested and refmed with Hugoniot data. The third.order ‘E’ Hugo. niot is much closer to the data than the third-order ‘n’ Hugoniot. Inclusion of fourth-order terms allows both ‘E’ and ‘ii’ Hugoniots to fit the data within their scatter. The separation of Hugoniots corresponding to different initial densities is predicted within the accuracy of the data by the thermal part of this theory. Received 24 January 1972 Revised 15 December 1972

11.

ULTRASONIC DETECTION OF THE PINNING OF DISLOCATIONS BY POINT DEFECTS IN LEAD II. MODEL FOR DISLOCATION DEFECT INTERACTION —

Received 4 October 1972

vii

ABSTRACTS OF ARTICLES TO APPEAR IN J. PHYS. CHEM. SOUDS N.B. Meisner, D.S. Woo, H.B. Huntington and G.L. Salinger, Physics Department, Rensselaer Polytechnic Institute, Troy, New York 12181, and LV. Meisel, Benet Laboratory, Watervliet Arsenal, Watervliet, New York 12189. Experiments are presented to establish that irradiation produced defects in lead not only pin disloca. tions but also can be trapped at the ends of dislocation lines in agreement with the model proposed by Thompson, Buck, Huntington and Barnes. This model indicates that there is a temperature T* at which there is a maximum pinning of dislocations. T* is found to be near 140K. The data of Part I are analyzed according to this model using reasonable values of the dislocation density and the binding energy of the defect in the trap. The resulting activation energy for the region A process in the reaction kinetics model is found to be 0.15 eV which is consistent with the value found from an eigenvalue expansion model. Received 1 September 1972

12.

ACOUSTIC NMR IN SPIN-i SYSTEMS S.K. Sinha and S.K. Ghatak, Saha Institute of Nuclear Physics, Calcutta-9, India.

Acoustic magnetic resonance, both pulsed and Continuous has been discussed in terms the Bloch— Wangsness—Redfield formulation of theofmagnetic resonance phenomenon. The quadrupolar mechanism has been taken for the spin—phonon coupling and the mutual interaction has been treated in the ‘effective field approximation’. The expressions for the power absorbed both for ~A~m = ± I and ~ m = ± 2 have been obtained. It is found that from the measurements of the relaxation parameters for ~.m = ± 1 and ~m = ±2 it is possible to estimate the non-secular contributions to the line-width. The power absorbed in pulse excitation comes out to be small for short pulse (short cornpared to the relaxation parameter) and it reduces to the value obtained in continuous excitation for a long pulse. It is seen that for a given pulse-width the signal decreases with theasincrease of the isrelaxation and this happens temperature lowered. parameter The sawration of electromagnetic signal in presence of the acoustic excitation has also been studied. The analysis indicates that the relaxation parameter obtained from the plot of the relative signal ( I

~)vs. the acoustic frequency w, is always 1’~ssthan its true value

Vol. 12, No. 6

which can be determined by observing the frequency -dependence of the relative fractional signal defined as <~>0 ~

13.

—

<~‘ >(~

1

I

<~>0

<~>2~o

—

<~>

2~~,0

HEAT CAPACITY BEHAVIOR OF Pu—Fe EUTECTIC ALLOY (10 a/o Fe) BETWEEN 15 AND 373 K. EVIDENCE FOR ORDER— DISORDER AND AN ANTIPHASE STRUCTURE BELOW ROOM TEMPERATURE Thomas A. Sandenaw and Delbert R. Harbur, Los Alamos Scientific Laboratory of the Univer. sity of California, Los Alamos, New Mexico, 87544 U.S.A.

Low temperature heat capacity studies of Pu—Fe eutectic alloy(10 a/o Fe) have suggested the possibility of order—disorder of atoms and an antiphase structure below room temperature. Slow cooling and temperature cycling below 76K was required for appearance of the postulated antiphase structure. Fermi surface—Brillouin zone boundary interactions are suggested as an explanation for the low temperature behavior of the eutectic alloy as well as for the resistivity maximum in both Pu6Fe and cr-Pu. The best values for S 0(29 8) and {U°(298) H°(0)} were ± judged be 14.20 ±0.10 1 K1 and 1660 3Ocalto mo1’. cal mol’ Received 14 September 1970 —

14.

DIFFUSION OF 22Na IN Cd DOPED SILVER BROMIDE AND SILVER CHLORIDE —

R.J. Robertson and J.R. Wynnyckyj, Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada. The diffusion coefficients of 22Na tracer in zonerefined, CdBr 2-doped, polycrystalline AgBr were measured. An approach is developed to calculate the intrinsic concentration of Frenkel defects AgBr 22Na diffusion data.inThe theory and AgCl based on the is based on the usual assumptions of random walk and electroneutrality. Received 12 October 1972