Validité de la Méthode de Kramers-Kronig et Application à la Dispersion Infrarouge de la Magnésie

Abstract

Resume. Le spectre de rflexion de la magn6sie 293°K est analyse par la th6orie classique, avec deux oscillateurs.Pour la determination du terme d'amortissement une variante de cette m6thode est propose, dans le cas o le facteur de rflexion avoisine l'unit6. Cette variante, applique la magn6sie 293°K et 77°K, utilise les mesures d'absorption aux fr6quences 16gerement inf6rieures la rsonance.La m6thode de Kramers-Kronig est soumise une analyse critique. Le manque de precision dans le calcul des faibles dphasages limite la validit de cette m6thode un intervalle de fr6quence, souvent inf6rieur celui o R(a) est connu exp6rimentalement. L'influence des donn6es des divers domaines de fr6quence, sur les parametres de dispersion est discut6e. L'attention particuliere port6e sur la rgion du minimum de rflexion, dont les valeurs exp6rimentales sont trop lev6es, explique les dphasages ngatifs rencontr6s aux basses fr6quences ainsi que les absorptions anormalement 6lev6es, que l'on calcule aux fr6quences sup6rieures celle du mode optique longitudinal.

Magnesium Oxide (MgO)

“…Among several possible choices for this task we have chosen the work of Piriou and Cabannes [77], who fitted reflectance data with a classical oscillator model. When only transmission or absorptance measurements are given, it is necessary to apply a correction for surface reflection.…”

Theory and Practice – Lattice Vibrations and Spectroscopy of Mantle Phases

“…However, the bonding within these ionic crystals is now highly 'polar', so that long-range Coulombic interactions also contribute substantially to the lattice dynamics. IR reflectance studies at ambient P indicate that a corresponding LO mode exists at higher frequency ($720 cm À1 ; Piriou and Cabannes, 1968). In fact, a single peak is observed in IR absorption studies, at $380 cm À1 (Gillet et al, 1998).…”

“…Information on intrinsic vibrational mode anharmonicities are also obtained directly from analysis of IR reflectance data via damped oscillator models, in which a related anharmonicity parameter (À i ) for each IR active mode is empirically adjusted to fit the observed reflectivity line shape (Piriou and Cabannes, 1968;Gervais et al, 1973aGervais et al, , 1973bGervais and Piriou, 1975;Gervais, 1983;McMillan, 1985;Hofmeister, 1987Hofmeister, , 1997McMillan and Hofmeister, 1988). Information on intrinsic vibrational mode anharmonicities are also obtained directly from analysis of IR reflectance data via damped oscillator models, in which a related anharmonicity parameter (À i ) for each IR active mode is empirically adjusted to fit the observed reflectivity line shape (Piriou and Cabannes, 1968;Gervais et al, 1973aGervais et al, , 1973bGervais and Piriou, 1975;Gervais, 1983;McMillan, 1985;Hofmeister, 1987Hofmeister, , 1997McMillan and Hofmeister, 1988).…”

“…In fact, a single peak is observed in IR absorption studies, at $380 cm À1 (Gillet et al, 1998). The LO mode frequencies appear as poles in the IR reflectance spectra, however, and they also cause band broadening in powder transmission experiments (Piriou and Cabannes, 1968;McMillan, 1985;McMillan and Hofmeister, 1988;Hofmeister et al, 1990;Hofmeister, 1997 For complex minerals with n atoms in the primitive cell, the generalized LST relation becomes: IR reflectance studies at ambient P indicate that a corresponding LO mode exists at higher frequency ($720 cm À1 ; Piriou and Cabannes, 1968).…”

“…The TO and LO mode anharmonic parameters of pure MgO have been measured experimentally to T $ 1000 C, using IR reflectance techniques at ambient P (Piriou and Cabannes, 1968). Ambient T pressure shifts have been determined directly by IR transmission studies up to 22 GPa (Gillet et al, 1998) (Figure 7).…”