Plasmons in Liquid Metals Studied by Inelastic X-ray Scattering
-
Koji Kimura
,
Toru Hagiya
Abstract
Plasmon is a collective excitation of electrons in materials. Since plasmon can be observed in a wide range of the phase diagram including the solid, liquid, and classical plasma phases, the investigation of the electronic states through the plasmon is of great significance in order to obtain a unified insight into the electronic states in various phases of matter. Inelastic X-ray scattering (IXS) is an ideal tool for such an investigation, because it can be applied to the samples in the liquid state and those in an extreme conditions. In this review, we discuss IXS results on the plasmons in liquid metals, and also describe a formulation to predict the plasmon energy and the lifetime in liquid metals. The formulation takes into account the effect of the ionic structure within the nearly free electron approximation, and reproduces well the experimental results.
Dedicated to: Hirohisa Endo on the occasion of his 90th birthday.
Acknowledgement
We would like to thank late M. Yao, Prof. K. Nagaya, Prof. M. Inui, Prof. Y. Kajihara, and Prof. S. Ohmura for valuable discussions and experimental supports.
References
1. B. Knuth, F. Hensel, W. W. Warren Jr, J. Phys. Condens. Matter 9 (1997) 2693.10.1088/0953-8984/9/13/006Search in Google Scholar
2. A. vom Felde, J. Sprösser-Prou, J. Fink, Phys. Rev. B 40 (1989) 10181.10.1103/PhysRevB.40.10181Search in Google Scholar
3. W. Schölke, Electron Dynamics by Inelastic X-ray Scattering, Oxford University Press, New York (2007).10.1093/oso/9780198510178.001.0001Search in Google Scholar
4. I. Loa, K. Syassen, G. Monaco, G. Vankó, M. Krisch, M. Han, Phys. Rev. Lett. 107 (2011) 086402.10.1103/PhysRevLett.107.086402Search in Google Scholar
5. H.-K. Mao, Y. Ding, Y. Xiao, P. Chow, J. Shu, S. Lebéque, A. Lazicki, R. Ahuja, Proc. Natl. Acad. Sci. U.S.A. 108 (2011) 20434.10.1073/pnas.1116930108Search in Google Scholar
6. J. P. Hill, C. C. Kao, W. A. C. Caliebe, D. Gibbs, B. Hastings, Phys. Rev. Lett. 77 (1996) 3665.10.1103/PhysRevLett.77.3665Search in Google Scholar
7. C. Sternemann, A. Kaprolat, W. Schülke, Phys. Rev. B 57 (1998) 622.10.1103/PhysRevB.57.622Search in Google Scholar
8. C. A. Burns, P. Abbamonte, E. D. Isaacs, P. M. Platzman, Phys. Rev. Lett. 83 (1999) 2390.10.1103/PhysRevLett.83.2390Search in Google Scholar
9. H. Hayashi, Y. Udagawa, C.-C. Kao, J.-P. Rueff, F. Sette, J. Electron Spectrosc. Relat. Phenom. 120 (2001) 113.10.1016/S0368-2048(01)00313-9Search in Google Scholar
10. C. A. Burns, P. Giura, A. Said, A. Shukla, G. Vanká, M. Tuel-Benckendorf, E. D. Isaacs, P. M. Platzman, Phys. Rev. Lett. 89 (2002) 236404.10.1103/PhysRevLett.89.236404Search in Google Scholar PubMed
11. X. Wang, C. A. Burns, A. H. Said, C. N. Kodituwakku, Y. V. Shvydko, D. Casa, T. Gog, P. M. Platzman, Phys. Rev. B 81 (2010) 075104.10.1103/PhysRevB.81.075104Search in Google Scholar
12. S. H. Glenzer, O. L. Landen, P. Neumayer, R. W. Lee, K. Widmann, S. W. Pollaine, R. J. Wallace, Phys. Rev. Lett. 98 (2007) 065002.10.1103/PhysRevLett.98.065002Search in Google Scholar PubMed
13. K. Kimura, K. Matsuda, N. Hiraoka, T. Fukumaru, Y. Kajihara, M. Inui, M. Yao, Phys. Rev. B 89 (2014) 014206.10.1103/PhysRevB.89.014206Search in Google Scholar
14. K. Kimura, K. Matsuda, N. Hiraoka, Y. Kajihara, T. Miyatake1, Y. Ishiguro, T. Hagiya, M. Inui, M. Yao, J. Phys. Soc. Jpn. 84 (2015) 084701.10.7566/JPSJ.84.084701Search in Google Scholar
15. T. Hagiya, K. Matsuda, N. Hiraoka, H. Hayashi, K. Kimura, Y. Kajihara, M. Inui, J. Phys. Soc. Jpn. 87 (2018) 08470310.7566/JPSJ.87.084703Search in Google Scholar
16. K. Tamura, M. Inui, S. Hosokawa, Rev. Sci. Instrum. 70 (1999) 144.10.1063/1.1149556Search in Google Scholar
17. K. Kimura, K. Matsuda, M. Yao, J. Phys. Soc. Jpn. 82 (2013) 115001.10.7566/JPSJ.82.115001Search in Google Scholar
18. N. W. Ashcroft, N. D. Mermin, Solid State Physics, Thomson Learning, Inc., New York (1976).Search in Google Scholar
19. A. L. Fetter, J. D. Walecka, Quantum Theory Of Many-Particle Systems, Dover Publications, Inc. New York (2003).Search in Google Scholar
20. G. F. Giuliani, G. Vignale, Quantum Theory of the Electron Liquid, Cambridge University Press, New York (2005).10.1017/CBO9780511619915Search in Google Scholar
21. D. Pines, Elementary Excitations in Solids, Benjamin, New York (1964).Search in Google Scholar
22. K. S. Singwi, M. P. Tosi, R. H. Land, A. Sjölander, Phys. Rev. 176 (1968) 589.10.1103/PhysRev.176.589Search in Google Scholar
23. P. Vashishta, K. S. Singwi, Phys. Rev. B 6 (1972) 875.10.1103/PhysRevB.6.875Search in Google Scholar
24. Ll. Serra, F. Garcias, M. Barranco, N. Barberán, J. Navarro, Phys. Rev. B 44 (1991) 1492.10.1103/PhysRevB.44.1492Search in Google Scholar
25. G. Kalman, K. Kempa, M. Minella, Phys. Rev. B 43 (1991) 14238.10.1103/PhysRevB.43.14238Search in Google Scholar
26. M. Taut, K. Sturm, Solid Commun. 82 (1992) 295.10.1016/0038-1098(92)90644-OSearch in Google Scholar
27. M. Taut, J. Phys.: Condens. Matter 4 (1992) 9595.10.1088/0953-8984/4/48/014Search in Google Scholar
28. E. Lipparini, S. Stringari, K. Takayanagi, J. Phys. Condens. Matter 6 (1994) 2025.10.1088/0953-8984/6/10/019Search in Google Scholar
29. H. M. Böhm, S. Conti, M. P. Tosi, J. Phys.: Condens. Matter 8 (1996) 781.10.1088/0953-8984/8/7/005Search in Google Scholar
30. M. Hasegawa, M. Watabe, J. Phys. Soc. Jpn. 27 (1969) 1393.10.1143/JPSJ.27.1393Search in Google Scholar
31. M. Hasegawa, J. Phys. Soc. Jpn. 31 (1971) 649.10.1143/JPSJ.31.649Search in Google Scholar
32. K. Sturm, L. E. Oliveira, Phys. Rev. B 24 (1981) 3054.10.1103/PhysRevB.24.3054Search in Google Scholar
33. J. Lindhard, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 28 (1954).Search in Google Scholar
34. N. W. Ashcroft, Phys. Lett. 23 (1966) 48.10.1016/0031-9163(66)90251-4Search in Google Scholar
35. G. Franz, W. Freyland, W. Glaser, F. Hensel, E. Schneider, J. Phys. (Paris), Colloq. 8 (1980) 194.Search in Google Scholar
36. Y. Waseda, The Structure of Non-Crystalline Materials, McGraw-Hill, New York (1980), P. 253.Search in Google Scholar
37. T. E. Faber, Theory of Liquid Metals, Cambridge University Press, Cambridge (1972), P. 326.Search in Google Scholar
38. K. Hoshino, W. H. Young, J. Phys. F: Met. Phys. 16 (1986) 1659.10.1088/0305-4608/16/11/007Search in Google Scholar
39. K. Matsuda, K. Tamura, M. Inui, Phys. Rev. Lett. 98 (2007) 096401.10.1103/PhysRevLett.98.096401Search in Google Scholar PubMed
40. R. W. Ohse, Handbook of Thermodynamic and Transport Properties of Alkali Metals, Blackwell, Oxford, U.K. (1980), P. 316.Search in Google Scholar
41. K Tamura, K Matsuda, M Inui, J. Phys.: Condens. Matter 20 (2008) 114102.10.1088/0953-8984/20/11/114102Search in Google Scholar PubMed
42. F. Aryasetiawan, K. Karlsson, Phys. Rev. Lett. 73 (1994) 1679.10.1103/PhysRevLett.73.1679Search in Google Scholar PubMed
43. K. Matsuda, K. Tamura, Rev. Sci. Inst. 75 (2004) 709.10.1063/1.1646769Search in Google Scholar
44. A. Fleszar, R. Stumpf, A. Eguiluz, Phys. Rev. B 55 (1997) 2068.10.1103/PhysRevB.55.2068Search in Google Scholar
45. W. Jank, J. Hafner, J. Phys.: Condens. Matter 3 (1991) 6947.10.1088/0953-8984/3/35/024Search in Google Scholar
©2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Preface
- Structural studies on fluid Hg and fluid Se at high temperatures and high pressures by means of X-ray diffraction and small angle X-ray scattering
- Structure and Electronic State in a Fluid Alkali Metal: Synchrotron Radiation Studies
- Streak Patterns Observed in Small Angle X-Ray Scattering from Highly Oriented Pyrolytic Graphite (HOPG)
- In situ Raman Spectroscopic Observation of Polymer Chains in Semi-Crystalline Polyethylene Solids
- Plasmons in Liquid Metals Studied by Inelastic X-ray Scattering
- Review Articles
- Transverse acoustic phonon excitations in liquid metals
- Structure study of the chalcogens and chalcogenides by X-ray absorption fine structure
- The Structure of the Amorphous (GeTe)1–x(Sb2Te3)x System and Implications for its Phase-Change Properties
- Dissociation mechanism from highly charged bromophenol: ab initio molecular dynamics simulations
- Photo-induced effects on amorphous and liquid selenium by pulsed laser illumination
- X-ray absorption spectroscopy of small copper-oxide cluster ions for analyses of Cu oxidation state and Ar complexation: CuOAr+ and Cu2O2+
Articles in the same Issue
- Frontmatter
- Preface
- Structural studies on fluid Hg and fluid Se at high temperatures and high pressures by means of X-ray diffraction and small angle X-ray scattering
- Structure and Electronic State in a Fluid Alkali Metal: Synchrotron Radiation Studies
- Streak Patterns Observed in Small Angle X-Ray Scattering from Highly Oriented Pyrolytic Graphite (HOPG)
- In situ Raman Spectroscopic Observation of Polymer Chains in Semi-Crystalline Polyethylene Solids
- Plasmons in Liquid Metals Studied by Inelastic X-ray Scattering
- Review Articles
- Transverse acoustic phonon excitations in liquid metals
- Structure study of the chalcogens and chalcogenides by X-ray absorption fine structure
- The Structure of the Amorphous (GeTe)1–x(Sb2Te3)x System and Implications for its Phase-Change Properties
- Dissociation mechanism from highly charged bromophenol: ab initio molecular dynamics simulations
- Photo-induced effects on amorphous and liquid selenium by pulsed laser illumination
- X-ray absorption spectroscopy of small copper-oxide cluster ions for analyses of Cu oxidation state and Ar complexation: CuOAr+ and Cu2O2+
