Infrared activity in elemental crystals

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Date

1994-03

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American Physical Society

Abstract

In a previous paper, Zallen [Phys. Rev. 173, 824 (1968)] reported a group-theoretical analysis of the competition between unit-cell complexity and crystal symmetry in determining the presence or absence of infrared-active phonons in an elemental crystal. Here we correct an error in that paper's treatment of certain hexagonal space groups. Our results modify the minimum-complexity condition for infrared activity: For 228 of the 230 space groups, a necessary and sufficient condition for the existence of symmetry-allowed infrared-active modes in an elemental crystal is the presence of three or more atoms in the primitive unit cell. The two exceptional space groups are P6/mmm (D6h1) and P6(3)/mmm (D6h4); for each of these symmetries, there exists one structure with four atoms per cell and no infrared modes. The P6(3)/mmc structure includes, as special cases, Lonsdaleite (or ''wurtzite silicon'') as well as a c-axis-aligned hcp arrangement of diatomic molecules which is relevant to models of solid molecular hydrogen at high pressure.

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Keywords

megabar pressures, solid hydrogen, physics, condensed matter

Citation

Zallen, R.; Martin, R. M.; Natoli, V., "Infrared activity in elemental crystals," Phys. Rev. B 49, 7032 DOI: http://dx.doi.org/10.1103/PhysRevB.49.7032