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Ab initio melting curve of molybdenum by the phase coexistence method
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Image of FIG. 1.
FIG. 1.

Comparison of LDA and GGA pressure as function of volume for bcc Mo from the PAW method with different exchange-correlation functionals and valence sets. Long-dashed and solid lines (practically coincident) show GGA results with and without states in the valence set. Short-dashed and dotted lines show LDA results with and without states in the valence set. Dots show experimental results (Ref. 5).

Image of FIG. 2.
FIG. 2.

Comparison between PAW and FP-LAPW results for the GGA(PBE) and LDA(CA) approximations for . Solid and dashed curves show GGA(PBE) and LDA(CA) FP-LAPW results, respectively; short-dashed and dotted curves show GGA(PBE) and LDA(CA) PAW calculations, respectively. Solid dots show experimental data (Ref. 5).

Image of FIG. 3.
FIG. 3.

Density of electronic states obtained with the PAW (dashed line) and FP-LAPW (solid line) at zero temperature and 0, 150, and 300 GPa. Fermi energies are shifted to zero (dotted line).

Image of FIG. 4.
FIG. 4.

FP-LAPW calculation of the energy bands of Mo at 0 and 300 GPa (left and right panels, respectively). The valence band (energy between and at the point) rises in energy more quickly than valence bands with increasing pressure.

Image of FIG. 5.
FIG. 5.

Comparison of calculated (curves) and experimental (solid squares) phonon dispersion relations of Mo at zero pressure. Experimental data are from Ref. 51.

Image of FIG. 6.
FIG. 6.

Density profile in simulation of coexisting solid and liquid Mo at , after 60 ps. The simulation is performed with the embedded-atom reference model on a system of 6750 atoms.

Image of FIG. 7.
FIG. 7.

Calculated ab initio melting curve (filled circles and solid line) of this work compared with previous results: generalized pseudopotential calculations of Moriarty (Ref. 6, dotted line), dislocation-mediated models of Belonoshko et al. (Ref. 9, long-dashed line), and Verma et al. (Ref. 59, dashed-dotted line); experimental shock-wave (Ref. 4) and DAC (Ref. 1) measurements are shown with empty squares and triangles, respectively. Filled and inverted-empty triangles show solid and liquid ab initio molecular dynamics calculations of Belonoshko et al. (Ref. 9), respectively. Empty circles show results of this work obtained with the EAM model without free-energy corrections.

Image of FIG. 8.
FIG. 8.

Ab initio fractional volume change on melting of Mo as a function of pressure. Solid and dashed curves: present work, with and without free-energy correction, respectively.

Image of FIG. 9.
FIG. 9.

Calculated radial distribution function of Mo for: solid at and (solid line), solid at and (dotted line), solid at and (long-dashed line) and liquid at and (short-dashed line).

Image of FIG. 10.
FIG. 10.

Density of valence electronic states of Mo at finite temperature and on melting. Left: solid at and (dotted line), solid at and (short-dashed line), solid at and (solid line) and liquid at and (long-dashed line). Right: solid at and (solid line) and liquid at and (dashed line). Fermi energy levels are shifted to zero.


Generic image for table
Table I.

Convergence of mean phonon frequency [see Eq. (6)] with supercell size, grid, and Fermi broadening .

Generic image for table
Table II.

Parameters of the EAM potential deduced for Mo and used for the coexistence simulations. Values are obtained by fitting to ab initio simulations on solid and liquid.

Generic image for table
Table III.

Difference between the liquid and solid thermal averages of the difference of ab initio and reference energies, and thermal averages in solid and liquid of the squared fluctuations of , with averages evaluated in the reference system and normalized by dividing by the number of atoms . Melting temperatures for the reference and ab initio systems are also reported.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Ab initio melting curve of molybdenum by the phase coexistence method