THE INFRARED SPECTRUM OF GYPSUM, $CaSO_{4}.2H_{2}O^{*}$
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Date
1955
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Ohio State University
Abstract
The infrared reflection and transmission spectrum of gypsum, $CaSO_{4}.2H_{2}O$, has been investigated in the frequency range $450-4000 cm^{-1}$ using polarized radiation for various orientations of the crystal. The reflection spectra were transformed into absorption spectra using the method of Robinson and $Price.^{1}$ The calculations are lengthy and have been carried out on MIDAC (Michigan Digital Automatic Electronic Computer). Since most of the fundamentals are quite intense, measurement of the reflection spectra avoided the necessity of procuring very thin samples for the usual transmission method. According to x-ray $studies,^{2}$ the space group of gypsum is $C^{6}_{2{h}}$ and the crystallographic unit cell contains four molecules of $CaSO_{4}.2H_{2}O$. The Bravais unit cell contains only two molecules of $CaSO_{4}.2H_{2}O$. The sulfate ions are located on sites of $C_{2}$ symmetry and the water molecules are located on sites of $C_{1}$ symmetry. The infrared active fundamentals can be divided into those having transition moments along the crystal $C_{2}$ axis (species $A_{u}$) and those having transition moments perpendicular to the $C_{2}$ axis(species $B_u$). The four internal fundamentals (one nondegenerate, one doubly-degenerate, two triply-degenerate) of an isolated sulfate ion give rise to nine infrared active fundamentals and nine Raman active fundamentals. Seven infrared active fundamentals have been found disrtibuted among the species $A_{u}$ and $B_{u}$ in accordance with the factor group selection rules. The direction of the transition moments of the $B_{u}$ fundamentals is not uniquely determined by symmetry since they may lie anywhere in a plane. The direction in this plane can be correlated with certain features of the crystal structure. Each fundamental of an isolated water molecule gives rise to two infrared active fundamentals, one belonging to species $A_{u}$ and the other to species $B_{u}$. Assuming an ``oriented gas” model with the positions of the hydrogens as derived from x-ray and nuclear magnetic resonance $investigations,^{3}$ the ratio of the intensity of the $A_{u}$ to $B_{u}$ bands can be predicted. Good agreement between the predicted and observed ratios is obtained for the $\mu_{2}$ (deformation) fundamental but large discrepancies are found for the $\mu_{1}$ and $\mu_{3}$ (stretching) fundamentals. Possible explanations will be discussed.
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Author Institution: The Harrison M. Randall Laboratory of Physics, University of Michigan