Improving the understanding of the melting behaviour of Mo, Ta, and W at extreme pressures

Abstract

We discus existent conflicts between experimentally measured and theoretically calculated melting curves of Mo, Ta, and W. By assuming that vacancy formation plays a fundamental role in the melting process, an explanation for the measured melting curves is provided.Furthermore, we show that the Lindemann law fits well all the measured melting curves of bcc transition metals if the Grüneisen parameter is written as a power series of the interatomic distance. For completeness, we examine possible reasons for current disagreements between shockwave and DAC experiments. To solve them, we propose the existence of an extra high P-T phase for Mo, Ta, and W.In materials science and geophysics, it is essential to understand how elements undergo the transition between solid and liquid phases at high pressures. For example, an accurate picture of materials performance under extreme conditions and detailed models of planetary interiors both depend on this knowledge. In recent years, the generation and measurement of simultaneous high pressures and high temperatures has undergone rapid development with the diamond-anvil cell (DAC) technique [1 -3]. As a consequence of this, the amount of available data on melting behaviour at high pressure is increasing [4,5]. The bcc transition metals (i.e. molybdenum (Mo), tantalum (Ta), and tungsten (W)) are especially interesting in this regard because they have very high melting points at ambient pressure and, in addition, at room temperature (RT) they remain in a stable body-centered cubic (bcc) structure up to extremely high pressures [6,7]. Mo, Ta, and W therefore are valuable test cases for studying how materials melt.Despite a large number of experimental and theoretical efforts, however, agreement on the melting behaviour of Mo, Ta, and W at high pressure has been elusive. A number of experimental studies have been carried out with the use of shock-wave measurements [8 -10] and laser-heated diamond-anvil cells [11,12]. Likewise, theoretical studies have attempted to predict the melting curve of Mo, Ta,. Unfortunately, substantial variation exists in the results of these earlier efforts owing to the use of different experimental and theoretical techniques.The above-mentioned discrepancies are illustrated in Fig. 1 for the case of Ta.This figure presents the melting curves reported by different authors [11,12,13,15,18] including a new data point (3850 ± 150 K at 98 GPa) obtained by us using the technique described in Ref. [12]. It shows that at 30 GPa a melting temperature of 3600 ± 100 K was measured using the in situ speckle method [11] and synchrotron x-ray diffraction [12] whereas theoretical calculations [13] and Lindemann estimates [15] give a melting

Experimental research on high pressure phase transitions of Mo and Ta

“…However, in the pressure range close to 100 GPa, there still exists large discrepancy in T m data measured between DAC [2-4, 16, 17] and SW [6] experiments. Furthermore, the dT m /dP behavior does not significantly change when P-T m locus evolves across the triple point of bcc-hcp-liquid, at about 210 GPa, conjectured by Errandonea [16] from Hixson's Hügoniot C measurements [7]. The melting curve in this work is against the twosegment melting curve model proposed by Errandonea [16].…”

Microscopic evidence of a flat melting curve of tantalum

“…Using this technique, melting of Ta was detected in the pressure range from 250 to 300 GPa, with a calculated melting temperature of 7000-10000 K (Dai et al, 2009;Shaner et al, 1984). After applying a superheating correction, M T may be as low as 5000-8000 K (Errandonea, 2005;Errandonea, 2006;Luo et al, 2003). A linear extrapolation of the DAC data to 300 GPa, puts an upper limit of 4800 M TK  .…”

“…Triangles: (Fatteva, et al, 1971). Calculated melting curves are included [FP (Taioli, et al, 2007) and QB (Moriarty et al, 2002)] together with the Lindemann (L) estimates (Errandonea, D., 2005).…”

Pressure Dependency Grüneisen Parameter r for bcc Mo

“…At low temperatures, Mo is stable in the body-centered-cubic (bcc) phase up to a pressure (P) of about 700GPa, where it transforms to fcc phase (Belonoshko, 2008). Considerable experimental and theoretical methods had been developed for Mo to study its thermodynamic properties such as melting temperature T m , thermal equation of state (EOS), Grüneisen parameter γ and Debye temperature Θ D , et al (Hixson, 1992;Zhang, 2008;Errandonea, 2005;Burakovsky, 2004;Kushwah, 2013;Zeng, 2011;Litasov, 2013;Al'tshuler, 1987;Asimow, 2009;Cazorla, 2007;Vinet, 1989). It's found that there exist great discrepancies in the melting curves between laser-heated diamond anvil cell (DAC) (Santamaría-Pérez, 2009) and shock-wave (SW) measurements (Hixson, 1992;Zhang, 2008).…”

“…It's found that there exist great discrepancies in the melting curves between laser-heated diamond anvil cell (DAC) (Santamaría-Pérez, 2009) and shock-wave (SW) measurements (Hixson, 1992;Zhang, 2008). Errandonea (Errandonea, 2005) considered the following expression for the volume dependence of γ similar to that proposed by Burakovsky and Preston (Burakovsky, 2004 ):…”