Raman Frequency Shifts for Ammonia Solid I Near the Melting Point

Abstract

We have performed in this study the calculation of the Raman frequencies for two translational modes and one librational mode in the ammonia solid I near the melting point. We have obtained the Raman frequencies as a function of temperature for some fixed pressure by means of the Grüneisen relation using the volume data from the literature. Our calculated Raman frequencies can be compared with experimental data available in the literature.

Pressure Dependence of the Raman Frequencies of Ammonia Solid I near the Melting Point

“…W e cal cul ate the Ram an frequenci es of two tra nsl ati ona l mo des ( ¤ 1 0 0 cm À 1 and ¤ 1 3 0 cm À 1 ) and of one l i bra ti ona l mode ( ¤ 2 8 0 cm À 1 ) i n am monia sol i d I, whi ch ha ve b een measured exp eri menta l l y [3]. The R ama n frequenci es a re cal cul ated as a functi on of pressure at some Ùxed tem pera tures using our vol ume val ues cal cul ated i n our recent study [6], whi ch were ba sed on the work of Pruza n et al . [4].…”

“…It ha s been stated tha t the am monia underg oes a second -order pha se tra nsi ti on pri or to m elti ng, b ecause of the p ower-l aw b ehavi our of the i sotherm al com pressibi l i ty and therm al expansivi ty [4,5]. V ery recentl y, we ha ve studi ed the cri ti cal b ehavi our for amm onia sol id I and sol id I I [6]. W e ha ve then appl i ed the Pi ppa rd rel ati ons to am monia sol i d I and sol id I I [7].…”

Modified Pippard relationship describing the Raman frequency shifts of the rotatory lattice mode of ammonia solid II in the vicinity of its melting point

“…This allows us to determine the temperature dependence of the thermal expansivity α p . By determining the frequency shift, (1/ν)(∂ν/∂P) T , and the thermal expansivity, α p , at various temperatures, we are able to examine the second Pippard relation in our modified version (10).…”

“…3 Using the measured frequencies of the translational modes of ~ 100 and ~ 130 cm -1 , and the librational mode of ~280 cm -1 , 3 we have calculated the Raman frequencies of these modes at various temperatures for pressures between 0 and 3⋅07 kbars in ammonia solid I. 10 In this crystalline system, we have also calculated the Raman frequencies of these modes at various pressures, for fixed temperatures between 196 and 217 K. 11 For ammonia solid II, the Raman spectra have been obtained, and in particular, the frequencies of the translational mode of ~ 54 cm -1 , and the librational mode of ~ 280 cm -1 , have been measured as functions of temperature for constant pressures of 3⋅65, 5⋅02 and 6⋅57 kbars respectively. 12,13 Using the measured Raman frequencies of the librational mode of ~ 280 cm -1 , we have calculated the Raman frequencies of this mode at various temperatures for those fixed pressures cited above, 14 and as a function of pressure for the fixed temperatures of 230⋅4, 263⋅4 and 297⋅5 K 15 respectively, in ammonia solid II.…”

A linear variation of the thermal expansivity with the isothermal compressibility for ammonia solid III near the melting point

“…The Raman frequencies of the lattice modes of solid I, in particular, have been measured as a function of pressure at 214 K [3]. We have investigated the volume dependence of the Raman frequencies in ammonia solid I by calculating the Raman frequencies of the two translational and one librational mode for this crystalline system as a function of temperature near the melting point [10]. For ammonia solid II near the melting point, we have also calculated the Raman frequencies of a rotatory lattice mode as a function of pressure [11].…”