Melting of aluminum, molybdenum, and the light actinides

Abstract

A semi-empirical model was used to explain why the measured melting curves of molybdenum, and the other bcc transition metals, have an unusually low slope (dT/dP~0). The total binding energy of Mo is written as the sum of the repulsive energy of the ions and sp-electrons (modeled by an inverse 6 th power potential) and the d-band cohesive energy described by the well known Friedel equation. Using literature values for the Mo band width energy, the number of d-electrons and their volume dependence, we find that a small broadening of the liquid d-band width (~1%) leads to an increase in the stability of the liquid relative to the solid. This is sufficient to depress the melting temperature and lower the melting slope to a value in agreement with the diamondanvil cell measurements. Omission of the d-band physics results in an Al-like melting curve with a much steeper melt slope. The model, when applied to the f-electrons of the light actinides (Th-Am), gives agreement with the observed fall and rise in the melting temperature with increasing atomic number.

X-ray diffraction of molybdenum under shock compression to 450 GPa

“…over a broad pressure range 8 . However, it has been argued that such methods may not be accurate for melting of BCC metals if there are substantial changes in the electronic structure upon melting 26 .…”

Melting of transition metals at high pressure and the influence of liquid frustration. I. The late metals Cu, Ni and Fe

“…Melting measurements made for a number of transition metals at high pressure, have reported melting temperatures and melting slopes (dT/dP) that are surprisingly low [2][3][4][5], and defy the predictive capability of current theoretical techniques. In several earlier reports it had been proposed that the low melting slopes were due to the presence of local structures in the melt [6,7]. The idea, that local structures in liquid metals could be based on packing of five-fold symmetric icosahedral units was first suggested by Frank, in order to explain supercooling effects [8].…”

Exploring Thermal and Mechanical Properties of Selected Transition Elements under Extreme Conditions: Experiments at High Pressures and High Temperatures

“…They have shown that there are only minor changes of both atomic and electronic structure in going from the high-temperature bcc solid to the melt and transfer of electrons from s-p states to d states appears to be incompatible with the present DFT calculations. Low melting slope in Ross et al (Ross et al, 2004) calculation could be due to the perfect crystal assumption for the high temperature solid and liquid phases. Cazorla et al ) also showed that bcc crystal structure is the most favored up to 350 GPa (~8650 K).…”

“…Despite a large number of experimental and theoretical efforts (Fateeva and Vereshchagin, 1971;Hixson et al, 1989;Moriarty, 1994;Errandonea, Schwager, et al, 2001b;Errandonea et al, 2003;Ross et al, 2004Ross et al, , 2007Verma, 2004;Errandonea, 2004aErrandonea, , 2005Errandonea, , 2006Cazorla et al, 2007;Cazorla, Gillan, Taioli, and Alfè, 2008;Luo and Swift, 2007;Taioli et al, 2008;Xi and Cai, 2008;Xiu-Lu, 2008;Zhang, Liu, et al, 2008;Santamaria-Perez et al, 2009), agreement on the melting behaviour of Mo, Ta, and W at high pressure has been elusive. The first shock wave experiment on high pressure melting of Mo done by Hixon et al (Hixson et al, 1989) up to 350 GPa, followed by early work of Moriarty (Moriarty, 1994) employed a many-body total energy function to predict the high pressure melting curve of Mo.…”

“…Ross et al (Ross et al, 2004) argue that change of coordination on going from bcc solid to liquid leads to a change of electronic structure, and hence a change in the electron distribution between s-p and d states, and that this redistribution stabilizes the liquid and lowers T m . Errandonea (Errandonea, 2005) (Hixson et al, 1989), and proposed a new phase diagram for Mo.…”