Using general properties of the crystal site representation normal mode matrix, we provide some simple bounds on localized modes in crystals with point defects. I. DERIVATION OF THE TRACE CONDITION The substitutional insertion of a point defect impurity into an otherwise perfect crystal will typically (see e.g. [1]) modify the spectrum of the 3N normal modes of the crystal, leading in certain c...

Introduction: In terrestrial studies of rocks and soils, Mössbauer spectroscopy has not found routine application for mineral identification because other methods such as x-ray diffraction are usually more definitive. On the Mars Exploration Rovers (MERs), however, Mössbauer spectrometers [1] have been called upon to assist in defining the mineralalogy, despite the overlapping Mössbauer paramet...