Vibrational Frequencies and Structural Properties of Transition Metals via Total-Energy Calculations

Abstract

Fu, Chong-Long, "Vibrational frequencies and structural properties of transition metals via total-energy calculations " (1983 INFORMATION TO USERSThis reproduction was made from a copy of a document sent to us for microfilming. While the most advanced technology has been used to photograph and reproduce this document, the quality of the reproduction is heavily dependent upon the quality of the material submitted.The following explanation of techniques is provided to help clarify markings or notations which may appear on this reproduction. 1.The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure complete continuity. When an image on the film is obliterated with a round black mark, it is anindication of either blurred copy because of movement during exposure, duplicate copy, or copyrighted materials that should not have been filmed. For blurred pages, a good image of the page can be found in the adjacent frame. If copyrighted materials were deleted, a target note will appear listing the pages in the adjacent frame.3. When a map, drawing or chart, etc., is part of the material being photographed, a definite method of "sectioning" the material has been followed. It is customary to begin filming at the upper left hand comer of a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again-beginning below the first row and continuing on until complete.

Effects of temperature and ferromagnetism on the γ-Ni/γ′-Ni3Al interfacial free energy from first principles calculations

“…Using this methodology we calculate a series of total energy differences between atomic configurations with and without a single displaced atom. This information is utilized to populate the dynamical matrix, and hence, to evaluate the phonon frequencies [21][22][23]. We employed the harmonic approximation for all vibrational calculations.…”

Thermal Stability of α Phase of Titanium by Using X-Ray Diffraction

“…AT ambient conditions, Ti crystallizes in the hexagonal-close-packed (hcp) structure, called the a phase, having 2 atoms per unit cell and c/a ratio of~1.58 with space group P6 3 /mmc, [1,2] and the unit cell parameters are a = 2.957 Å and c = 4.685 Å . [3][4][5] At ambient pressure and high temperature (1155 K (882°C)), before reaching the melting temperature, it transforms to the body-centered-cubic (bcc) structure or the b phase having 1 atom per unit cell with space group Im " 3m; [2] and the unit cell parameter is a = 3.33 Å .…”

Pressure-induced transition in titanium metal: a systematic study of the effects of uniaxial stress

“…In particular, the pressureinduced martensitic α (hcp) → ω (hexagonal) transformation in pure titanium (Ti) [7] has significant implications in the aerospace industry because the ω phase formation affects the toughness and ductility of Ti. The α phase (space group number: 194, P6 3 /mmc) [8] has two atoms per unit cell at (1/3,2/3,1/2) and (2/3,1/3, 3/2) and a c/a ratio of ~ 1.58. On the other hand, the ω phase (space group number: 191, P6/mmm) has an interesting crystal structure with three atoms per unit cell at (0,0,0), (1/3,2/3,1/2), and (2/3,1/3,1/2) and a c/a ratio of ~ 0.61.…”