Crystal Dynamics of Platinum by Inelastic Neutron Scattering

Abstract

The dispersion relations in platinum have been measured at 90 °K by the inelastic scattering of thermal neutrons. Born–von Kármán models of the force system have been calculated by fitting to the dispersion curves. Fourth-neighbor forces, with weaker interactions probably extending to at least sixth neighbors, are required to fit the data. A frequency distribution has been calculated from the force constants of the most realistic model.Some measurements are also reported of frequencies at a temperature of 473 °K. The mean frequency shift from 90 to 473 °K was found to be −2.0%.In the [0ζζ]T1 branch, anomalous behavior, similar to that observed in palladium, has been studied at temperatures of 90, 296, and 473 °K. As in Pd, the anomaly in Pt is markedly broadened and weakened with increasing temperature. The phonon wave vectors corresponding to possible Kohn transitions in the (001) plane have been determined by machine calculation, using Fermi surfaces given in the literature. These results strongly suggest that the anomaly along the T1 branch arises largely from transitions across the "heavy" hole Fermi sheet formed from the fifth-band electrons. A comparison is made with similar results for palladium and nickel.

Phonon anharmonicity and components of the entropy in palladium and platinum

“…Kohn anomalies were previously reported in the phonon dispersions of both Pd and Pt along the [011] direction [28][29][30] . They are also reproduced by our calculations at q cal ≃ (Fig.…”

“…More specifically, we prepared ensembles of ten supercells with atoms displaced with a Monte Carlo algorithm 46 for phonons calculated with experimental force constants 29,47,48 . For each configuration of displaced atoms, the electronic DOS (N MC ) was calculated, and an ∆S ad el,ep was calculated as…”

Vibrational properties of phonons in random binary alloys: An augmented space recursive technique in thekrepresentation

“…The concentrations are chosen so that we may compare our results with existing work. [27] and that for Cr is taken from [14] III. RESULTS AND DISCUSSION…”

Strain-Induced and 'Electrochemical' Interactions of Solute Atoms in Solid Solutions of the F.C.C.-(Fe,Ni)–C System and Isomorphous Ones

“…Ці форми фононного спек-тру враховують експериментальні дані (наприклад, [47][48][49][50]) стосо-вно дисперсійних кривих тільки для деяких симетрійних напрям-ків у оберненому просторі. Енергії деформаційної s-s-та i-s-взаємодії у α-Ni і γ-Fe були оцінені тільки в декількох роботах, на-506 В. А. ТАТАРЕНКО, В. М. НАДУТОВ самперед, у [3,25,34,35].…”

“…(Для γ-Fe при 1428 К застосовувані параметри Бор-на-Кармана можуть також бути прийнятими згідно [47], а для α-Ni при кімнатній температурі -згідно [49] або [50].) У інших напівфеноменологічних моделях динаміки ґратки, що задовольняють умовам інваріантності потенціальної енергії ГЦК-кристалу щодо трансляцій і поворотів кристалу як жорсткого тіла, динамічна матриця, у відношенні до фононних властивостей, може бути вираженою достатньо короткосяжними (у реальному просторі) силовими параметрами.…”