The ground state electronic properties of bulk (W) were studied within the density functional theory (DFT). We have also analyzed the momentum- (q-) dependent loss function, dielectric constant, and optical conductivity (OC) within TD-DFT random-phase approximation (RPA). The loss function is plotted in the energy range 0–55？eV. The energy loss function spectrum shows four prominent peaks, two lower peaks below along with two sharp peaks above 30？eV. The different nature of peaks depends on the momentum transfer q. The peak caused by interband transition showed a less pronounced dispersion. From the dielectric function curve we have predicted the plasmon excitation at around 1.75？eV and calculated the corresponding plasma frequency ？s？1. 1. Introduction Tungsten (derived from the Swedish phrase “tung sten,” meaning heavy stone) is a hard, brittle, steel-grey metal that is difficult to work with in the very pure state, unless it is malleable and ductile [1]. Tungsten is an interesting element whose unique physical properties make it an essential component in many industrial applications. Critical properties include very high melting point, very high density, hardness close to diamond, thermally stable, and excellent conductor [2]. The electronic structure and Fermi surface of tungsten have been studied extensively, experimentally and theoretically [3–7]. Some of the metallic crystals exhibit optical properties due to the interplay between electronic plasma screening and geometrical scattering effects [8]. Under suitable circumstances, this might be used to enhance thermal emission of photons in the visible region relative to lower frequencies and serve as a lighting technology [9]. Optical measurements provide several important microcharacteristics of the conduction electrons, their plasma frequency, and the relaxation frequency, as well as the energy gaps between the bands in the region of allowed electronic transitions. The optical properties of bulk polycrystalline tungsten have been investigated by Roberts [10] in the 0.5–0.8？μ region and also by Lenham and Treherne [11] in the 0.35–20？μ region. Juenker et al. measured the reflectivity of tungsten from 0.577 to 0.05？μ [12]. Sudarshan et al. studied the angular distribution of backward reemitted positrons from a W(100) single crystal which showed that the mean energy of the emitted positrons increased with angular deviation from normal, with incident positron energies of 250 and 600？eV. The increase in the energy is explained in terms of energy-dependent refraction of positrons traversing the
References
[1]
S. Albert, A Guide to the Elements, Oxford University Press, New York, NY, USA, 2nd edition, 2002.
[2]
E. Paul DeGarmo, Materials and Processes in Manufacturing, MacMillan, New York, NY, USA, 5th edition, 1979.
[3]
B. L. Ahuja, A. Rathor, V. Sharma, Y. Sharma, A. R. Jani, and B. Sharma, “Electronic structure and compton profiles of tungsten,” Zeitschrift fur Naturforschung—Section A, vol. 63, no. 10-11, pp. 703–711, 2008.
[4]
D. M. Bylander and L. Kleinman, “Self-consistent semirelativistic pseudopotential calculation of the energy bands, cohesive energy, and bulk modulus of W,” Physical Review B, vol. 27, no. 6, pp. 3152–3159, 1983.
[5]
H. J. F. Jansen and A. J. Freeman, “Total-energy full-potential linearized augmented-plane-wave method for bulk solids: electronic and structural properties of tungsten,” Physical Review B, vol. 30, no. 2, pp. 561–569, 1984.
[6]
S.-H. Wei, H. Krakauer, and M. Weinert, “Linearized augmented-plane-wave calculation of the electronic structure and total energy of tungsten,” Physical Review B, vol. 32, no. 12, pp. 7792–7797, 1985.
[7]
A. Debernardi, M. Alouani, and H. Dreyssé, “Ab initio thermodynamics of metals: Al and W,” Physical Review B—Condensed Matter and Materials Physics, vol. 63, no. 6, Article ID 064305, 2001.
[8]
A. Moroz, “Three-dimensional complete photonic-band-gap structures in the visible,” Physical Review Letters, vol. 83, no. 25, pp. 5274–5277, 1999.
[9]
Z.-Y. Li, “Modified thermal radiation in three-dimensional photonic crystals,” Physical Review B, vol. 66, Article ID 241103R, 2002.
[10]
S. Roberts, “Optical properties of nickel and tungsten and their interpretation according to drude's formula,” Physical Review, vol. 114, no. 1, pp. 104–115, 1959.
[11]
A. P. Lenham and D. M. Treherne, Optical Properties and Electronic Structure of Metals and Alloys, North Holland, Amsterdam, The Netherlands, 1966.
[12]
D. Juenker W, J. L. LeBlanc, and R. C. Martin, “Optical properties of some transition metals,” Journal of the Optical Society of America, vol. 58, no. 2, pp. 164–171, 1968.
[13]
K. Sudarshan, S. N. Samarin, P. Guagliardo, V. N. Petrov, A. H. Weiss, and J. F. Williams, “Angle-resolved energy distribution of re-emitted positrons from a W(100) single crystal,” Physical Review B: Condensed Matter and Materials Physics, vol. 87, no. 8, Article ID 085418, 2013.
[14]
V. N. Korobenko and A. D. Rakhel, “Direct measurements of thermodynamic functions and electrical resistivity of fluid tungsten over a wide range of densities,” Physical Review B—Condensed Matter and Materials Physics, vol. 88, no. 13, Article ID 134203, 2013.
[15]
B. Liu, M. Gu, L. X. Liu, et al., “First-principles study of lattice dynamics and thermodynamics ofosmium under pressure,” Chinese Physics B, vol. 19, no. 2, Article ID 26301, 2010.
[16]
G. Wortmann, U. Ponkratz, B. Bielemeier, and K. Rupprecht, “Phonon density-of-states in bcc and hcp Eu metal under high pressure measured by 151Eu nuclear inelastic scattering of synchrotron radiation,” High Pressure Research, vol. 28, no. 4, pp. 545–551, 2008.
[17]
T. Kuzumaki, S. Kitakata, K. Enomoto, T. Yasuhara, N. Ohtake, and Y. Mitsuda, “Dynamic observation of the bending behavior of carbon nanotubes by nanoprobe manipulation in TEM,” Carbon, vol. 42, no. 11, pp. 2343–2345, 2004.
[18]
Y. Zhu, C. Ke, and H. D. Espinosa, “Experimental techniques for the mechanical characterization of one-dimensional nanostructures,” Experimental Mechanics, vol. 47, no. 1, pp. 7–24, 2007.
[19]
M. S. Bobji, J. B. Pethica, and B. J. Inkson, “Indentation mechanics of Cu-Be quantified by an in situ transmission electron microscopy mechanical probe,” Journal of Materials Research, vol. 20, no. 10, pp. 2726–2732, 2005.
[20]
K. W. Urban, “Is science prepared for atomic-resolution electron microscopy?” Nature Materials, vol. 8, no. 4, pp. 260–262, 2009.
[21]
M. Benaissa, W. Sigle, M. Korytov, J. Brault, P. Vennéguès, and P. A. van Aken, “Plasmon energy from strained GaN quantum wells,” Applied Physics Letters, vol. 103, no. 2, Article ID 021901, 2013.
[22]
R. F. Egerton, “Electron energy-loss spectroscopy in the TEM,” Reports on Progress in Physics, vol. 72, no. 1, Article ID 016502, 2009.
[23]
M. Wibbelt, H. Kohl, and P. Kohler-Redlich, “Multiple-scattering calculations of electron-energy-loss near-edge structures of existing and predicted phases in the ternary system B-C-N,” Physical Review B—Condensed Matter and Materials Physics, vol. 59, no. 18, pp. 11739–11745, 1999.
[24]
A. Alkauskas, S. D. Schneider, S. Sagmeister, C. Ambrosch-Draxl, and C. Hébert, “Theoretical analysis of the momentum-dependent loss function of bulk Ag,” Ultramicroscopy, vol. 110, no. 8, pp. 1081–1086, 2010.
[25]
F. H. Featherston and J. R. Neighbours, “Elastic constants of tantalum, tungsten, and molybdenum,” Physical Review, vol. 130, no. 4, pp. 1324–1333, 1963.
[26]
E. Williams M, Ab-initio elastic and thermodynamic properties of high-temperature cubic intermetallics at finite temperatures [M.S. thesis], Brigham Young University, 2008.
[27]
A. Zunger and M. L. Cohen, “Self-consistent pseudopotential calculation of the bulk properties of Mo and W,” Physical Review B, vol. 19, no. 2, pp. 568–582, 1979.
[28]
A. Debernardi, M. Alouani, and H. Dreyssé, “Ab initio thermodynamics of metals: Al and W,” Physical Review B: Condensed Matter and Materials Physics, vol. 63, no. 6, Article ID 064305, 2001.
[29]
P. W. Bridgman, “High Pressure Polymorphism,” Daedalus-Journal of the American Academy of Arts and Sciences, vol. 77, no. 1, p. 187, 1949.
[30]
S. H. Chen and B. N. Brockhouse, “Lattice vibrations of tungsten,” Solid State Communications, vol. 2, no. 3, pp. 73–77, 1964.
[31]
J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Physical Review Letters, vol. 77, no. 18, pp. 3865–3868, 1996.
[32]
W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Physical Review A, vol. 140, pp. A1133–A1138, 1965.
[33]
P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and J. Luitz, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties. Wien2K User's Guide, Technische Universit？t Wien, Vienna, Austria, 2008.
[34]
J. K. Dewhurst, S. Sharma, and C. Ambrosch-Draxl, “Code development under the RT network EXCITING funded by the EU,” contract HPRN-CT-2002-00317, 2005.
[35]
M. Petersilka, U. J. Gossmann, and E. K. U. Gross, “Excitation energies from time-dependent density-functional theory,” Physical Review Letters, vol. 76, no. 8, pp. 1212–1215, 1996.
[36]
L. S. Dubrovinsky and S. K. Saxena, “Thermal expansion of periclase (MgO) and tungsten (W) to melting temperatures,” Physics and Chemistry of Minerals, vol. 24, no. 8, pp. 547–550, 1997.
[37]
F. D. Murnaghan, “The compressibility of media under extreme pressures,” Proceedings of the National Academy of Sciences of the United States of America, vol. 30, pp. 244–247, 1944.
[38]
J. H. Weaver, C. G. Olson, and D. W. Lynch, “Optical properties of crystalline tungsten,” Physical Review B, vol. 12, no. 4, pp. 1293–1297, 1975.
[39]
L. V. Nomerovannya, M. M. Kirillova, and M. M. Noskov, “Optical properties of tungsten monocrystals,” Soviet physics, JETP, vol. 33, p. 405, 1971.
[40]
J. X. Zhang and L. C. Chen, “Pressure dependence of phonon dispersion in bcc tungsten,” Chinese Journal of Physics, vol. 51, no. 2, pp. 359–367, 2013.
[41]
A. D. B. Woods and S. H. Chen, “Lattice dynamics of molybdenum,” Solid State Communications, vol. 2, no. 8, pp. 233–237, 1964.
[42]
T. H. Geballe, “Superconductivity in the transition metals,” Reviews of Modern Physics, vol. 36, no. 1, pp. 134–138, 1964.
[43]
M. M. Kirillova and B. A. Charikov, “Study of the optical properties of transition metals,” Optics and Spectroscopy, vol. 17, pp. 134–135, 1964.
[44]
D. W. Lynch, C. G. Olson, and J. H. Weaver, “Optical properties of Ti, Zr, and Hf from 0.15 to 30 eV,” Physical Review B, vol. 11, no. 10, pp. 3617–3624, 1975.
[45]
R. de Hoff, Thermodynamics in Materials Science, Taylor & Francis, Boca Raton, Fla, USA, 2nd edition, 2006.
[46]
A. A. Quong and A. Y. Liu, “First-principles calculations of the thermal expansion of metals,” Physical Review B, vol. 56, no. 13, pp. 7767–7770, 1997.
[47]
G. J. Ackland, X. Huang, and K. M. Rabe, “First-principles thermodynamics of transition metals: W, NiAl, and PdTi,” Physical Review B: Condensed Matter and Materials Physics, vol. 68, no. 21, Article ID 214104, 2003.
[48]
P. Giannozzi, S. de Gironcoli, P. Pavone, and S. Baroni, “Ab initio calculation of phonon dispersions in semiconductors,” Physical Review B, vol. 43, no. 9, pp. 7231–7242, 1991.
[49]
W. Windl, P. Pavone, K. Karch et al., “Second-order Raman spectra of diamond from ab initio phonon calculations,” Physical Review B, vol. 48, no. 5, pp. 3164–3170, 1993.
[50]
G. Onida, L. Reining, and A. Rubio, “Electronic excitations: density-functional versus many-body Green's-function approaches,” Reviews of Modern Physics, vol. 74, no. 2, pp. 601–659, 2002.
