Diamond normal frequencies

The normal mode refinement method is based on the idea of the normal mode important subspace. That is, there exists a subspace of considerably lower dimension than 3N, within which most of the fluctuation of the molecule undergoing the experiment occurs, and a number of the low frequency normal mode eigenvectors span this same subspace. In its application to X-ray diffraction data, it was developed by Kidera et al. [33] and Kidera and Go [47,48] and independently by Diamond [49]. Brueschweiler and Case [50] applied it to NMR data. 

The Johnsonfigure of merit, based on saturated carrier velocity and dielectric strength (product of power x frequency squared x impedance), predicts the suitability of a material for high power applications. It is normalized with the value of one given to silicon. As shown in Table 13.2 below, diamond is clearly the preferred material on this basis. 

This model assumes that all of the vibrational normal modes act like harmonic oscillators with the same frequency. It is used to represent a crystal of a monatomic substance such as a solidified inert gas, a metal, or a network covalent crystal such as diamond. If a monatomic crystal has N atoms its vibrational energy is given by... 

Although less work has been done on the acoustic reduction of Tj in solids than in liquids, it has been established that, as for liquids, the natural values of Tj in solids can be reduced by the application of ultrasound. By coupling 20 kHz ultrasound to a sample of trisodium phosphate dodecahydrate in an open mesh nylon sack immersed in a liquid, the normal value of the Tj was reduced from 7.1 s (obtained from MAS NMR measurements) to 2.1 s. Subsequently, similar reductions (by a factor of about two) have been observed for the values of for in diamonds to which high frequency piezoelectric transducers were bonded directly. 

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