Density functional theory investigation of the phonon instability, thermal equation of state and melting curve of Mo

Abstract

The phonon instability and thermal equation of state of Mo are extensively investigated using density functional theory. The calculated phonon dispersion curves agree well with experiments. Under compression, we captured a large softening in the transverse acoustic (TA) branches of body-centred cubic Mo. When the pressure is raised to 716 GPa, the frequencies along Γ-N in the TA branches soften to imaginary frequencies, indicating structural instability. For face-centred cubic Mo, the phonon calculations predicted the stability by promoting the frequencies from imaginary to real. Within quasi-harmonic approximation, we predicted the thermal equation of state and some other properties including the thermal expansion coefficient α, product αK(T), heat capacity C(V), entropy S, Grüneisen parameter γ and Debye temperature Θ(D). The melting curves of Mo were also obtained successfully.

Pressure Dependency Grüneisen Parameter r for bcc Mo

“…Fitting Equation (3) to the MGD relation yields q = 0.24, which is different from the values 1.2 and 1.0 discussed by Zeng et al (Zeng, 2011) .While q=1.2 and q=1.0, Equation (3) agrees with the results calculated by Zeng et al (Zeng, 2011) at low and high pressure, respectively.…”

“…They found that the Burakovsky−Preston approach diverges the DAC experimental melting data while the Errandonea parameters reproduce it. But γ becomes much smaller than 1 for the Errandonea approach which doesn't agree with the density functional theory performed by Zeng et al (Zeng, 2011).They then concluded that the Lindemann law doesn't work satisfactorily for the transition metals.…”

“…It's found that (Litasov, 2013)the values of γ derived from the model Mo-1 seem too high, whereas the model Mo-2 yielded consistent results with shock-wave (SW) data (Asimow, 2009) and theoretical calculations (Zeng, 2011).…”

“…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).…”

Thermoelectric transport properties of molybdenum fromabinitiosimulations

“…It is therefore important to know the location of the melt boundary. Explicit calculations of the melt boundary are not performed here, however, because of the extensive previous experimental [24][25][26][27][28] and theoretical [29][30][31][32][33][34][35] work regarding the phase diagram of molybdenum. All thermodynamic conditions of interest here (1000 K to 20 000 K and up to 2 Mbar) are either in the fluid or in the bcc solid, and we thus calculate the transport properties for these two phases.…”