Relative stability and elastic properties of hcp, bcc, and fcc beryllium under pressure

Ab initio electronic-structure calculations, based on the density-functional theory and the full-potential linear-muffin-tin-orbital method, were used to predict crystal-sructure phase stabilities and elastic constants of beryllium under compression. Specific energies, pressures, elastic constants, and Debye temperatures for three crystal structures, hcp, bcc, and fcc, were calculated over a wide volume range. In agreement with experiments and previous theoretical calculations, the hcp ground state is obtained at ambient conditions and the bcc ground state is found at high pressure and ambient temperature, with the predicted $\mathrm{hcp}\to \mathrm{bcc}$ phase transition at about 2.7 Mbar. A possible phase diagram of beryllium, including hcp, bcc, and fcc phases is constructed in the $(P,T)$ plane.

Figure 1

The calculated axial ratio $c∕a$ as a function of pressure for hcp Be (solid line) compared with experimental data: triangle—Ref. 21, open circle—Ref. 25, filled circle—Ref. 26.

Figure 2

The calculated 300 K isotherm for hcp Be (solid line) compared with experimental data: triangle—Ref. 21, open circle—Ref. 25, filled circle—Ref. 26; the dashed line is the room temperature isotherm derived from experimental shock-wave measurements (see Ref. 37).

Figure 3

Calculated (see Ref. 29) pressure-volume relation for fcc Al (solid line) compared with experimental data (see Ref. 39): open circle—modified ruby pressure scale, filled circle—old ruby pressure scale (see Ref. 40).

Figure 4

Shear modulus of polycrystals and single-crystals of hcp Be as functions of pressure.

Figure 5

Shear modulus of polycrystals and single crystals of bcc Be as functions of pressure.

Figure 6

Shear modulus of polycrystals and single crystals of fcc Be as functions of pressure.

Figure 7

Pressure dependence of $\beta$ and $B∕P$ for bcc Be.

Figure 8

Gibbs potential differences of bcc and fcc Be with respect to hcp Be at $T=300\mathrm{K}$ as functions of pressure.

Figure 9

Gibbs potential differences of bcc and fcc Be with respect to hcp Be at $T=0\mathrm{K}$ as functions of pressure without zero-point contribution to the Gibbs potential.

Figure 10

A possible phase diagram of Be, including hcp, bcc, and fcc phases. The melting curve was calculated from the Lindeman criterion (8).