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Pressure Dependence of Phonon Anomalies in Molybdenum


A collaborative group of researchers from Lawrence Livermore National Laboratory and the ESRF have been able to pin down the high-pressure lattice dynamics of the transition metal molybdenum by mapping its phonon energies under extremely high pressure. Using the inelastic X-ray scattering beamline ID28 at the European Synchrotron Radiation Facility (ESRF) and theoretical calculations, the team tracked the pressure evolution of a dynamical anomaly within molybdenum that has challenged scientists for over 40 years.

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Much of the interest in the H-point phonon is derived from its anomalous increase in energy with increasing temperature. This observation stimulated numerous theoretical attempts to explain this strange behaviour. Changing the temperature or pressure is helpful in that it allows one to probe systems in different thermodynamic configurations. Indeed, the study of materials at high pressure is very useful for gaining insight into the nature of the chemical bonds in materials. Notably, the study of lattice dynamics at high pressures in general cannot be performed with neutrons due to the requirement of relatively large samples.

The group developed a new technique for preparing extremely small single Mo crystals of high crystalline quality [1]. These samples (40 micrometres in diameter by 20 micrometres thick) were placed into diamond anvil cells and taken to pressures as high as 40 GPa (400,000 atmospheres) to observe the evolution of the anomaly.


A small molybednum single crystal loaded in the helium pressure medium.

Fig. 1: A small molybednum single crystal loaded in the helium pressure medium. The photomicrograph was taken of the sample in situ at high pressure in the diamond anvil cell.

The researchers observed strong changes in the phonon dispersions at high pressure [2]. The most significant was a large difference in the Gruneisen parameter of modes at the H-point and those around q=0.65 along [001]. These differences lead to a dramatic decrease in the magnitude of the H-point anomaly with increasing pressure. Using theoretical codes developed to model molybdenum, the group showed that there is strong sensitivity of the H-point phonon on the electronic band structure. In fact, the decrease in the H-point anomaly required significant pressure induced broadening to match the experimental data. This implied a strong coupling between electronic states and phonons. With compression, the combination of an increase in the Fermi energy together with a broadening of the electronic states, leads to a significant decrease in this electron-phonon coupling. Thus, molybdenum becomes a much more 'normal' bcc metal at high pressures possibly explaining it's extraordinary stability in the bcc structure to pressures in excess of 400 GPa.

Phonon dispersions in molybdenum at high pressure.

Fig. 2: Phonon dispersions in molybdenum at high pressure. The filled symbols show IXS data taken at 17 GPa at ID28, the open symbols are inelastic neutron scattering results at one atmosphere. Circles are longitudinal acoustic modes; squares transverse acoustic modes. Along [0] the triangles and squares show the two non-degenerate transverse acoustic modes TA[110]<-110> and TA[110]<001> respectively. The dashed lines show the calculations performed at one atmosphere, and the solid lines the calculations at 17 GPa.



[1] D.L. Farber, D. Antonangeli, C. Aracne, J. Benterou, High Pressure Research 26, 1 (2006).
[2] D.L. Farber, M. Krisch, D. Antonangeli et al., Physical Review Letters 96, 115502 (2005).

Principal Publication and Authors

D.L. Farber (a), M. Krisch (b), D. Antonangeli (a,b), A. Beraud (b), J. Badro (a,c), F. Occelli (a), D. Orlikowski (d), Physical Review Letters 96, 115502 (2005).
(a) Earth Science Division, Lawrence Livermore National Laboratory and Department of Earth Sciences, University of California (USA)
(b) ESRF
(c) Département de Minéralogie, Institut de Minéralogie et de Physique des Milieux Condensés, Institut de Physique du Globe de Paris, Université Paris (France)
(d) Physics and Advanced Technology Directorate, Lawrence Livermore National Laboratory, California (USA)