Raman scattering and lattice-dynamical calculations of alkali-metal sulfates.

Raman-scattering measurements on single crystals of K2SO4, Rb2SO4, and Cs2SO4 have been made at both room and liquid-nitrogen temperatures. Lattice-dynamical calculations, based on a rigid-ion model using the Gordon-Kim method to calculate the short-range potentials, were performed. The influence of the alkali-metal ions on the lattice-dynamical properties of the crystals is discussed. ©1991 The American Physical Society. Used by permission. URL: http://link.aps.org/doi/10.1103/PhysRevB.44.7387 DOI: 10.1103/PhysRevB.44.7387 7388 D. LIU, H. M. LU, J. R. HARDY, AND F. G. ULLMAN 44 11. EXPERIMENTAL PROCEDURES Buehler microcloth and 0.05 p m A1,O1 slurry were used Raman-scattering measurements were made with a Spectra Physics 2016 argon-ion laser. The 514.5-nm line was used throughout this experiment. The laser power incident on the sample was about 80 mW. The sample was mounted in an exchange-gas-coupled liquid-nitrogen cryostat with computer-controlled temperature to within 0.1 K, which enabled Raman measurements to be made from 78 K to room temperature. A Spex 1401 75-cmfocal-length, f /6.8, double monochromator, combined with a thermoelectrically cooled photomultiplier, was used to collect and detect the scattered light. The slit widths of the monochromator used give a resolution of about 2.0 cm-'. The photon-counting time was about 10 s at each frequency, and the scanning was in steps of 0.5 cm'. The crystals used were all grown from aqueous solution by evaporation at constant temperature or with slow cooling. Rb2S0, and Cs2S04 powders used for crystal growing were obtained from Aldrich Chemicals Company with purities of 99.9%. K2S04 powders were obtained from Fisher Scientific Company with a purity of 99%. The crystals were polished into rectangular prisms with the surfaces perpendicular to the crystal axes. for polishing. The directions of the crystal axes were identified with two polarizers. The orientations of the crystals were determined by comparing their Raman spectra with known results. The samples usually had dimensions of several millimeters in each direction. 111. EXPERIMENTAL AND CALCULATION RESULTS The measured Raman frequencies of the three alkalimetal sulfates are listed in Tables 1-111, together with the calculated values. The Raman spectra of the three crystals at liquid-nitrogen temperature in the external mode region are plotted in Figs. 2-4. According to the factor group analysis,5 the number of external modes should be 7Ag, 7B,,, 5B2,, and 5B3,. All the A, external modes were identified for all three crystals, as were the B,, and B3, external modes. There should be the same number of B1, external modes as A, external modes; however, not all could be identified. All of the internal modes of the three crystals were identified. The details of the calculation method to treat molecular ionic crystals were given in Refs. 7 and 8. The basic concept is to give separate consideration to intramolecuTABLE I. Experimental and calculated Raman frequencies of K2S0, (in cm-'1. --P--A, B1, 298 K 78 K Calc. 298 K 78 K Calc. B2, B3, 298 K 78 K Calc. 298 K 78 K Calc.