Phonon Dispersion Relations for Chromium and Tantalum

Abstract

Aust. J. Phys., 1975, 28, 57-61 Phonon dispersion curves for the normal modes of vibration in chromium and tantalum are calculated along the symmetry directions [100], [110] and [111] using the five force-constant model of Behari and Tripathi (1970a). The results are compared with experimental values obtained from inelastic neutron spectroscopy and reasonably good agreement is found.

Role of the electron–phonon coupling in tuning the thermal boundary conductance at metal-dielectric interfaces by inserting ultrathin metal interlayers

“…for Ta [24,25]. The dispersions for the substrates follow their orientation: Γ for c-sapphire, and for Si [26,27].…”

“…Interlayer Substrate Al Ni α-Al 2 O 3 θ D = 428 K [51] θ D = 450 K [51] θ D = 1035 K [53] ν L = 9.6 THz [52] ν L = 9.1 THz [29] ν L = 10 THz [31] ν T = 5.7 THz [52] ν T = 4.5 THz [29] ν T = 6.9 THz [31] g = 0.24 × 10 18 W (m −3 •K −1 ) [51] g = 0.36 × 10 18 W (m −3 •K −1 ) [51] ν optical = 26 THz [31] Au Ta Si θ D = 165 K [51] θ D = 225 K [55] θ D = 645 K [57] ν L = 4.6 THz [54] ν L = 5.5 THz [28] ν L = 12 THz [30] ν T = 2.8 THz [54] ν T = 2.6 THz, 3.7 THz [28] ν T = 4 THz [30] g = 0.023 × 10 18 W (m −3 •K −1 ) [51] g = 3.1 × 10 18 W (m −3 •K −1 ) [56] ν optical = 15.5 THz [30] Cr θ D = 630 K [38] ν L = 10 THz [28] ν T = 6 THz, 7.7 THz [28] g = 0.42 × 10 18 W (m −3 •K −1 ) [58]…”

“…The phonon dispersion of each branch ω j (q) is obtained by using a polynomial fit to the experimental dispersion curves along the preferential growth direction reported for our substrates. We choose Γ → X(001) for Al, Γ → L(111) for Ni and Γ → N(011) for Ta [28,29]. The dispersions for the substrates follow their orientation: Γ → Z(0001) for c-sapphire, and Γ → X(001) for Si [30,31].…”

Role of vibrational properties and electron–phonon coupling on thermal transport across metal-dielectric interfaces with ultrathin metallic interlayers

“…Metals were 50 nm thick and interlayers 5 nm thick. [41] ν T = 6 THz, 7.7 THz [42] ν T = 6.9 THz [43] ν A = 3.4 THz ν A = 7.9 THz ν A = 7.9 THz g = 0.023 × 10 18 g = 0.42 [51] ν optical = 16 THz [50] even for materials that are not well characterized in the literature.…”

Elastic Behaviour and Lattice Vibrations in bcc V and Nb

“…These model potentials require further modifications with respect to their non-centrality and dielectric functions for yielding a good comparison between the computed and experimental dispersion data. The later studies [5][6][7][8] of these metals suffer from the deficiency of lattice instability and use extensive fitting procedures. Not only this, the first principle theories [9][10][11] to study the lattice dynamics of transition metals make use of drastic approximations to arrive at useful conclusions and increases computer time many times.…”