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Averaging disorder

In hydroxylapatite the hydroxyls are located -0.35 A above or below each mirror plane. To achieve the average disordered P63//W structure, half the hydroxyls in any... [Pg.8]

Yes - Possibility that a space-average disorder (detected by NMR) is accompanied by a time-average increase in viscosity (detected by EPR). The relaxation times in NMR are several orders of magnitude slower than in EPR. [Pg.170]

In general, it is diflfieult to quantify stnietural properties of disordered matter via experimental probes as with x-ray or neutron seattering. Sueh probes measure statistieally averaged properties like the pair-correlation function, also ealled the radial distribution function. The pair-eorrelation fiinetion measures the average distribution of atoms from a partieular site. [Pg.131]

Unlike the solid state, the liquid state cannot be characterized by a static description. In a liquid, bonds break and refomi continuously as a fiinction of time. The quantum states in the liquid are similar to those in amorphous solids in the sense that the system is also disordered. The liquid state can be quantified only by considering some ensemble averaging and using statistical measures. For example, consider an elemental liquid. Just as for amorphous solids, one can ask what is the distribution of atoms at a given distance from a reference atom on average, i.e. the radial distribution function or the pair correlation function can also be defined for a liquid. In scattering experiments on liquids, a structure factor is measured. The radial distribution fiinction, g r), is related to the stnicture factor, S q), by... [Pg.132]

The ACGIH recommended maximum time-weighted average concentration in the workplace atmosphere for eight-hour daily exposure is 10 ppm. OSHA has set the permissible exposure level at 2 ppm. It maybe desirable to exclude alcohoHcs, persons with chronic disorders of the Hver, kidneys, and central nervous system, and those with nutritional deficiencies from working with chloroform. [Pg.527]

Figure 14 Measures of disorder m the acyl chains from an MD simulation of a fluid phase DPPC bilayer, (a) Order parameter profile of the C—H bonds (b) root-mean-square fluctuation of the H atoms averaged over 100 ps. Figure 14 Measures of disorder m the acyl chains from an MD simulation of a fluid phase DPPC bilayer, (a) Order parameter profile of the C—H bonds (b) root-mean-square fluctuation of the H atoms averaged over 100 ps.
To define the correlation functions of partly quenched systems requires one to consider fluctuations. There are two types of fluctuations thermal fluctuations for a given configuration of matrix species, and fluctuations induced by disorder. We characterize the average over disorder of thermal fluctuations by the variance... [Pg.300]

Then, performing a disorder average in Eq. (19), and using Eq. (18) we can obtain the following two relations for the connected and blocking correlation functions... [Pg.301]

In the microemulsion the role of A is played by the period of damped oscillations of the correlation functions (Eq. (7)). The surface-averaged Gaussian curvature Ky, = 2t x/ S is the topological invariant per unit surface area. Therefore the comparison between Ryyi = Kyy / in the disordered microemulsion and in the ordered periodic phases is justified. We calculate here R= Since K differs for diffused films from cor-... [Pg.736]

Draw ratio Degree of crystallinity Lattice disorder coefficient (k) Average crystallite size perpendicular to the crystallographic plane (hkl) Dhki (nm) ... [Pg.844]

In the early days of alloy theory, Lifshitz argued on intuitive grounds that one can calculate the properties of a disordered alloy from one sufficiently large sample," and referred to this property of a large sample as self-averaging. It can be seen most easily in exact... [Pg.3]

In this paper, the electronic structure of disordered Cu-Zn alloys are studied by calculations on models with Cu and Zn atoms distributed randomly on the sites of fee and bcc lattices. Concentrations of 10%, 25%, 50%, 75%, and 90% are used. The lattice spacings are the same for all the bcc models, 5.5 Bohr radii, and for all the fee models, 6.9 Bohr radii. With these lattice constants, the atomic volumes of the atoms are essentially the same in the two different crystal structures. Most of the bcc models contain 432 atoms and the fee models contain 500 atoms. These clusters are periodically reproduced to fill all space. Some of these calculations have been described previously. The test that is used to demonstrate that these clusters are large enough to be self-averaging is to repeat selected calculations with models that have the same concentration but a completely different arrangement of Cu and Zn atoms. We found differences that are quite small, and will be specified below in the discussions of specific properties. [Pg.4]

Figure 2. The average number of electron charges transferred from Zn atoms to Cu atoms in fee disordered alloys. The solid dots are calculated with the LSMS. The open circles are obtained using the CPA-LSMS. The squares are obtained using the SCF-KKR-CPA. Figure 2. The average number of electron charges transferred from Zn atoms to Cu atoms in fee disordered alloys. The solid dots are calculated with the LSMS. The open circles are obtained using the CPA-LSMS. The squares are obtained using the SCF-KKR-CPA.
Figure 3. The probabililities for finding a charge between q and q+dq on a Cu atom for the five fee disordered alloys. The average charge on the Cu sites is indicated by the heavy line. Figure 3. The probabililities for finding a charge between q and q+dq on a Cu atom for the five fee disordered alloys. The average charge on the Cu sites is indicated by the heavy line.

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See also in sourсe #XX -- [ Pg.10 ]




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