Erratum: Anharmonic elastic and phonon properties of Si

Abstract

Errata 15 DECEMBER 1990-I Erratum: Low-order anharmonic contributions to the internal energy of the one-component plasma [Phys. Rev. B 33, 5180 (1986)] A factor-of-3 error was recently found in the computer code used to generate the cubic and quartic contributions to the internal energies in the high-temperature limit. This error causes the values we reported for u3 and u4 in the hightemperature limit to be exactly -, ' of their true values. Thus, instead of 7.198 and 3.551, u3 and u4 should be 21.594 and 10.653, respectively This error also invalidates the estimate for the Ill term in Eq. (6b). In addition, a typographical error caused the sign of the Ill to be erroneously negative. Equation (6b) should therefore read NkT

Analysis of Distortions in ?110? Tilt Silicon Bicrystals

“…Knowing the energies E B , E C 11 , E TA (X), E LAO (X), E TO (X) and E LTO (G) and all the coefficients d ab , it is possible to obtain the rigidities k ab by solving the linear system E Mk in which E is the column formed by the six energies, k is the column formed by the six rigidities and M is the 6±6 matrix formed by the coefficients d ab . It is given in Table 1 in agreement with the results of Vanderbilt et al [12].…”

“…The method is based on a Taylor expansion of the potential energy E p with respect to the distortions involved in the system [12]. The expansion limited to second-order terms is first recalled and then applied to find the elastic and phonon components of any distortion in the elastic domain.…”

“…In generalizing the Keating potential, Vanderbilt et al [12] gave an expression containing third-and fourth-order terms aside second-order ones, with coupling between two-, three-and four-body interactions. In particular, they introduced a four-body second-order term between third neighbours and such long-range terms have been shown to be necessary to correctly describe the TA(X) phonons [19,20].…”

“…It may be noted that other forms are less used [9 to 11]. More recently, Vanderbilt et al [12] proposed a generalization of the Keating potential. All those potentials differ from each other by their analytic form, by the choice of the physical properties used in fitting their parameters, and by the number of neighbours they involve around one atom.…”

“…The difference between elastic distortions and phonon ones leads to a quantitative comparison of the different potentials with respect to each kind of distortions. Then, in Section 4, the method of Vanderbilt et al [12] is used in its harmonic form to define a set containing both kinds of distortions and to represent the energy of any possible distortion. A method is deduced to analyse the energy into an elastic component and a phonon one.…”