Pre-transition softening and anomalous pressure dependence of shear constants in alkali and alkaline-earth metals due to band-structure effects

Abstract

Band-structure andshear-constant (C,,) calculations have been performed for the Li, Na and Ba BCC phase and the Cr, Ca and Sr BCC and FCC phases within a broad range of mmpressions(~fromOto40-55~.Todescribethe'baiidwntributionstoC,.,useismade of calculations based on the linear muffin-tin orbital/atomic sphere approximation (LMTO-ASA) method; the other contributions to C,. are described by using the semiempirical 'electrostatic' model. At U = 0 the calculated C,. values are usually close to the observed ones. We have revealed pronounced effects of softening for the shear constants, up to the loss of stability (C,, < 0). when the Fermi level approaches the maximum points of the density of states n(~), as well as under certain changes of shape of " ( P ) . The compression values, at which this softening takes place, are in good agreement with the position of structural phase transitions under pressure. observed in the metals considered. A number of anomalies in the C'(W and C, ( U) dependences are predicted. in particular a sharp drop of C'(LJ'J near the phase transition points U = U, in BCC Li and Ba and FCCCS. Ca and Sr. as well as a significant decrease of C d U ) with rising U in FCC Cs and BCC Sr at U a 0.5.

The most incompressible metal osmium at static pressures above 750 gigapascals

“…However, this contribution is dominant only at a very low temperatures (typically of the order of 10 K or below), and phonon contribution should be considered. For acoustic phonons with small wave vectors, the Grüneisen parameter and thus the thermal expansion coefficient are proportional to hC ii /hu (typically there is only one shear modulus that is especially sensitive to the ETT, and it is the modulus that should be considered 51 ). Because 51 hC ii / dN(E F ), the low-temperature phonon thermal expansion coefficient is as singular as the electronic one.…”

Lattice instabilities in metallic elements

“…Ca and Sr transform from fcc to bcc, and Ba from bcc to hcp, under pressure (Chen, Ho, and Harmon, 1988;Jona and Marcus, 2006;Qiu and Marcus, 2009). C 0 and C 44 in Ca, Sr, and Ba show sudden elastic variations and instabilities as a function of pressure (Vaks et al, 1991). Pollack et al (1997) found that the T ¼ 0 K low transverse [110] phonon branch becomes stabilized in bcc Be, Mg, Ca, Sr, and Ba under pressure.…”

Electronic structure of materials under pressure

“…Initiated by the pioneering works of Hume-Rothery and Jones [97], this problem can be formulated in modern terms as how the proximity of a VHS to the Fermi level (E F ) and the ETT associated with it [98] affects the lattice structure, elastic moduli, phonon spectra, and other lattice properties. Numerous theoretical works devoted to this problem using both model [92,93] and ab initio [94,95] approaches have found (i) a considerable softening of shear moduli, even resulting in the total destabilization of a crystal structure [94,95], (ii) less prominent but still noticeable anomalies in short-wavelength phonon frequencies [92,93], and (iii), in thermodynamical properties of metals, heat capacity (see, e.g., [99] for Cd 1−x Mg x alloys) and thermal expansion. One result of the theory is the prediction of anisotropic thermal expansion for noncubic metals near an ETT at temperatures much lower than the Debye temperature.…”