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Theoretical investigation of the high pressure structure, lattice dynamics, phase transition, and thermal equation of state of titanium metal
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10.1063/1.3407560
/content/aip/journal/jap/107/9/10.1063/1.3407560
http://aip.metastore.ingenta.com/content/aip/journal/jap/107/9/10.1063/1.3407560

Figures

Image of FIG. 1.
FIG. 1.

Zero temperature isotherms of Ti. The solid lines are the present work. The solid and open symbols are experimental data from Vohra and Spencer (Ref. 11) and Errandonea et al. (Ref. 17), respectively.

Image of FIG. 2.
FIG. 2.

Lattice parameters , , and axial ratio as a function of pressure for (a) and (b) . The solid and open circles are the experimental data from Zhang et al. (Ref. 16) and Errandonea et al. (Ref. 17), respectively.

Image of FIG. 3.
FIG. 3.

The aggregate sound velocities (, , and ) of - and vs pressure at 0 K.

Image of FIG. 4.
FIG. 4.

Phonon dispersion curves of (a) -, (b) -, and (c) at 0 GPa and 0 K. The solid circles in (a) and (c) are the experimental data measured by Stassis et al. (Ref. 42) and Petry et al. (Ref. 43), respectively. The experimental data for were measured at 1293 K.

Image of FIG. 5.
FIG. 5.

Phonon dispersion curves of (a) and (b) at different pressures.

Image of FIG. 6.
FIG. 6.

Mode Grüneisen parameter of and at zero pressure.

Image of FIG. 7.
FIG. 7.

Phase diagram of Ti. The thin solid and thick grey lines are the present results. The dashed line and dashed-dotted line are the theoretical results from Mei et al. (Ref. 8) and Henning et al. (Ref. 6), respectively. The dashed-dotted-dotted and dotted lines are the experimental data from Zhang et al. (Ref. 14) and Young (Ref. 12), respectively.

Image of FIG. 8.
FIG. 8.

Thermal EOS of (a) -, (b) -, and , together with the experimental data (solid symbols) at the same condition (Ref. 16). The solid circles in the right plane of (b) are the experimental data at 8.1 GPa (Ref. 16), the grey line in the right plane of (b) locate at .

Image of FIG. 9.
FIG. 9.

The thermal pressure as a function of volume and temperature. The solid triangles, circles, and squares in the left panel of the figure are the calculated data at 900, 673, and 300 K for (Ref. 16). The grey line in the right panel of the figure is the linear fitted results for the calculated data (open circles) (Ref. 16).

Image of FIG. 10.
FIG. 10.

The isothermal bulk modulus and adiabatic bulk modulus vs (a) temperature at 0 GPa and (b) pressure. The solid and open stars are the experimental data from Ogi et al. (Ref. 46) and Fisher et al. (Ref. 49), respectively. The two grey vertical lines in (a), including Figs. 11(a) and 12(a), located at 146 K and 1143 K, respectively.

Image of FIG. 11.
FIG. 11.

The first and second order pressure derivative of ( and ) vs (a) temperature at 0 GPa and (b) pressure.

Image of FIG. 12.
FIG. 12.

Entropy of -, -, and as functions of (a) temperature at 0 GPa, compared with the experimental data from NIST-JANAF (open diamonds) (Ref. 50) and (b) pressure.

Tables

Generic image for table
Table I.

The equilibrium axial ratio , volume , zero pressure bulk modulus (GPa), pressure derivative , (1/GPa), and static energy (eV/atom).

Generic image for table
Table II.

The calculated elastic modulus (GPa), Poisson’s Ratio of Ti under pressure (GPa) at 0 K. The experimental data (Refs. 28 and 39) for were measured at room pressure (RP) and 293 K, and for were at 1273 K.

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/content/aip/journal/jap/107/9/10.1063/1.3407560
2010-05-04
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Theoretical investigation of the high pressure structure, lattice dynamics, phase transition, and thermal equation of state of titanium metal
http://aip.metastore.ingenta.com/content/aip/journal/jap/107/9/10.1063/1.3407560
10.1063/1.3407560
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