Brillouin scattering in single crystals of fcc and hcp argon alloys

Abstract

The fcc arid hcp adiabatic elastic constants of the alloys of Ar containing 0₂ and N₂ as impurity have been determined to an accuracy of better than 2% by the high resolution Brillouin scattering technique. Large single crystals of Ar-0₂ and Ar-N₂ were grown in a cylindrical quartz tube of 3 mm internal diameter situated in a liquid helium cryostat. The quality of the crystal, whether It was hcp or fcc, and its orientation with respect to the lab co-ordinates were determined by analyzing X-ray Laue transmission photographs. The light of 5145 Å from an Ar⁺ laser was incident along the cylindrical axis of the sample cell, and scattered light at 90⁰ was analyzed by a piezoelectrically scanned triple-passed Fabry-Perot Interferometer. The spectrum was recorded by a photon counting apparatus consisting of a photomultiplier tube, an amplifier/discriminator and a commercial data acquisition and stabilization system (Burleigh, DAS-1). -- It was found that the fcc phase of Ar accepts up to about 4% of 0₂ and remains stable, contrary to the published phase diagrams. Hcp single crystals could only be grown with about 6½% 0₂ in the solid; above 7½% dendritic growth was observed. To within the experimental error, the fcc elastic constants do not vary with a change in the concentration of 0₂ up to about 4%. The fcc elastic constants of Ar-2% 0₂ were determined at 83.0 ± 0.3 K to be (units: 10⁹ Nm⁻2): c₁₁ = 2.40 ± 0.03 , c₁₂ = 1.59 ± 0.02 , c₄₄ = 1.11 ± 0.02 . For fcc Ar-4% 0₂, the elastic constants at 82.2 ± 0.3 K were: c₁₁ = 2.39 ± 0.03 , c₁₂ = 1.59 ± 0.02 , c₄₄ = 1.09 ± 0.02 . The fcc elastic constants of Ar-5% N₂ at 77.8 ± 0.3 K were: c₁₁ = 2.43 ± 0.05 , c₁₂ = 1.61 ± 0.04 , c₄₄ = 1.07 ± 0.03 . The decreasing tendency in c₄₄ may well reflect mode softening. -- The hcp elastic constants of Ar-6½% 0₂ crystals at 81.3 ± 0.3 K were determined to be: c₁₁ = 2.90 ± 0.04 , c₁₂ = 1.50 ± 0.03 , c₁₃ = 1.18 ± 0.02, c₃₃ = 3.24 ± 0.05 , c₄₄ = 0.65(6) ± 0.011 . -- A comparison of the pure Ar fcc elastic constants (transformed to trigonal orientation and converted to hcp values by taking internal strains into account) and hcp Ar-6½% 0₂ elastic constants revealed that the two sets of values are equal within the experimental error except for c₁₃ which is greater in the latter case by about 8%. An attempt has been made to explain this significant change. It is, however, still not well understood as to whether this change in c₁₃ is a structure or an impurity effect. Nevertheless, it is clear that future theoretical calculations should concentrate on c₁₃ and should include anisotropies in the potentials.