Occupational ratio

The earliest theoretical predictions on the state of interfaces were made by Burton, Cabrera, and Frank [11[, who demonstrated that the interface would, in most cases, be rough at the growth temperature for metal crystals. Jackson [13[ suggested a system in which the solid and liquid phases are separated by an interface with one-layer thickness, and he calculated the energy changes as a function of the ratio of site occupancy of the constituent unit on the interface. When the site occupancy ratio was 50%, the interface was rough, whereas 0 or 100% site occupancy... 

Figure 3.11. Prediction of interface roughness obtained by (a) Jackson [13] and (b) Temkin [14], [15]. (a) The horizontal axis shows the surface site occupancy ratio, and the vertical axis depicts the change in free energy. Numerals are a factors.

It is sometimes not necessary to know the absolute value of zm but rather the order of magnitude of ratio nm/zm, which might be called the occupancy ratio of the degrees of freedom by photons. This may be estimated as follows. Suppose that we knew that the spectrum was like that of a blackbody at temperature T. We could then use the well-known relation for the average number of photons per mode (degree of freedom),... 

High conviction of object Qm, general occupancy ratio njzm High conviction of object Qm, low occupancy ratio njzm... 

High conviction of white object Qm = 1 /M for all m, low occupancy ratio njzm High conviction of white object Qm = 1 /M for all m, high occupancy ratio njzm Maximum ignorance (MacQueen-Mar-schak), general occupancy ratio njzm Impartial conviction, empirical data, general occupancy ratio njzm... 

Raman spectroscopy with high pressure windowed cell (Sum et al., 1997 Thieu et al., 2000) P, T and hydrate phase Yes P, P, hydrate phase vs. time (mins) Typically for sapphire window < 10,000 psi (for capillary tubes <60,000 psi diamond anvil cell GPa s) Guest occupancy ratios, structure, structural transitions... 

Variations of extinction coefficients and spectrum profiles with changes in chemical composition of a mineral provide information on cation ordering in the structure. Examples involving Al3+-Mn3+ ordering in epidotes and andalusites are discussed in 4.4.2 and 4.5, and Mn2+-Fe2+ ordering in olivine is illustrated in fig. 4.8. Compositional variations of intensities of absorption bands in polarized spectra of orthopyroxenes described in 5.5.4. (fig. 5.15) have yielded Fe2+/M2 site populations (Goldman and Rossman, 1979), while similar trends in the crystal field spectra of synthetic Mg-Ni olivines described in 5.4.2.4 (fig. 5.12) have yielded site occupancy ratios of Ni2+ ions in the olivineMl and M2 sites (Hu etal., 1990). 

In a synthetic forsterite doped with 2x Kfr per cent chromium, Cr3 ions were shown by EPR measurements (Rager, 1977) to be slightly enriched in the Ml sites resulting in an occupancy ratio M1 M2 = 60 40, corresponding to 1.2 xl(H per cent Cr3+ in the Ml site. In ferric-bearing forsterites, EPR measurements indicated that Fe3+ ions have a preference for the M2 sites (Weeks et al., 1974). 

The latter holds since the prefactors vAB and vBA are virtually identical. The difference in energy between the A and B configurations AE is determined either from the occupation ratio at equilibrium nB/nA or from the difference between the rotation barriers BA — Eab- The occupation ratio at room temperature remains constant for hours and because many rotation events are observed one can safely assume that the system is in thermodynamic equilibrium. From the observed value nB/nA = 10 at T = 300 K one finds that the B configuration is more stable than the A configuration by AE = 0.06 eV. This corresponds exactly with the observed difference between to the two rotation barriers, i.e. EBA — EAn = 0.70- 0.64 eV. 

The GCMC simulations are performed, in which the systems are in equilibrium with gas phase propane or ethane of several pressure values. The chemical potential is calculated taking account of the second virial coefficient of the spherical molecule. We obtain the mean occupation ratios. 

Figure 13. Mean occupation ratio of the larger cage obtained from GCMC simulations (black circles). Mean occupation ratio evaluated from the direct calculation is also plotted (solid line).

Kashida 1990] and proton disorder could be an alternative decoherence mechanism. Crystal structures determined at various temperatures show that above 150 K protons are distributed over two sites located at 0.3 A off-center of the hydrogen bond (see below Sec. 3). The occupation ratio for the two sites increases from 4 96 at 200 K to 18 82 at 300 K. 

The amount of permeated D2 on counter-permeation, QD m (STP) s ], can be predicted by the following in consideration of occupation ratio of the interstitial sites, at which D atoms can be dissolved on the metal ... 

The most natural index is the cell occupancy ratio, defined as the ratio of the number of occupied cells Nqcc over the total number of cells Ntot... 

Figure 5. REE site-occupancy ratio (REE-Ca2/REE-Cal) of REE-OHAp (Fleet et al. 2000b ) and REE-FAp (Fleet and Pan 1995a, with central dot Fleet and Pan 1997a, ) compared with clmge in unit-cell volume relative to end-member OHAp and (F,OH)Ap solid solution, respectively. Note that plots reveal no site preference for REE at...

The formulas in these equations represent only surface lattice occupancy ratios, not chemically distinct species. 

Collins, M.J. Ratcliffe. C.I. Ripmeester, J.A. NMR studies of guest species in elathrate hydrates Lineshape anisotropies, chemical shifts and the determination of cage occupancy ratios and hydration numbers. J. Phys. Chem. 1990. 94. 157-162. 

Table IV. Equilibrium cage occupancy ratios of type I hydrates at 0 C...

Cady has recently determined [6] accurate compositions of a number of structure I hydrates (equilibrium values of n in M nH2) from which values of the cage occupancy ratio... 

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