Raman scattering in hcp rare gas solids under pressure

We present Raman measurements of hcp rare gas solids (RGSs) at megabar pressures together with lattice dynamics calculations. The $E_{2g}$ phonon was measured in Xe up to metallization near 135 GPa and in Ar up to 58 GPa. A comparative analysis of first-principles and semiempirical calculations shows that three-body forces contribute to the energetics at low pressures and that at volume compressions greater than $\sim 2.6$ higher-order many-body forces become important. The distinct behavior of He under pressure relative to that of the rest of the RGS family is discussed.

Figure 1

Raman spectra of hcp Xe at selected pressures.

Figure 2

(Color online) Experimental and calculated Raman frequencies as a function of pressure for hcp Ar and Xe. Experiment: present work (empty squares); full circles (Ref. 12). Semiempirical calculations: many-body potentials (solid lines); pair potentials (dashed lines); and effective pair potentials (dotted lines). DFT calculations (empty triangles); the dot-dash line through the empty triangles for Ar serves as a guide for the eyes.

Figure 3

(Color online) Raman frequencies of hcp RGS as a function of volume. Semiempirical many-body calculations: Ar (solid line), Kr (dotted line), and Xe (dot-dash line). Experiment: present work—Ar (empty squares); Xe (full diamonds), full circles—Ref. 12. He: semiempirical many-body calculations (solid black curve); DFT calculations (asterisks); experiment: Raman data [full black circles;[11] neutron data [full black squares[10]]; open triangles (calculated using $C_{44}$ data from Ref. 28). Inset: Grüneisen parameter as a function of volume.

Figure 4

(Color online) Calculated $C_{44}$ as a function of pressure for all hcp RGS. Lines correspond to theoretical Raman frequencies. Symbols: He—empty triangles are experimental $C_{44}$ data from Ref. 28; Ar—four-pointed stars are data of ab initio calculations, other symbols are $C_{44}$ values corresponding to experimental Raman frequencies: He—black full circles,[11] Ar—empty squares (this work), Xe—full circles[12], and empty diamonds (this work).