Short-range order parameter

Short-range order parameter a Standard enthalpy of activa- m... 

Figure 2 Time sequence of th< spin configuration on a (100) plane at 50% when the system at T=2.5 (snapshot a) is quenched down to T—1.7 and is subject to an isothermal aging. Snapshots demonstrated in figs, b, c and d correspond to time t=20,000, 43,000 and 50,000. The long range and short range order parameters input from the PPM calculations and resultant ones in the simulated lattice are also demonstrated [22, 24, 28]. ...

TABLE I.a Comparison of Observed Activity Coefficients of Cu and Au with Values Calculated from Observed Short-Range Order Parameters by the First-Order Quasi-Chemical Theory... 

This equation effectively imposes the condition that py — Pji = xaXb, with the important result that sro is totally excluded, because, when the pair probability is equal to x xb, the short-range-order parameter a becomes zero (see Section 7.1.2). 

As assumed, the relaxation time corresponds to the time required for the z -type channel migration of hydrogen to change the short-range order parameter value in e times. The temperature dependence of Vh has its usual definition given by a Boltzmann distribution ... 

The long-range order parameter t and the short-range order parameter [Pg.302]

If positions a and do not correlate, the short-range order parameter a becomes 0. Above Tc, a can be considered the equilibrium constant for the occurrence of pair AB. For the Aq.s o.s alloy, x equals If the alloy is completely ordered, — 1... 

Figure 5.8. Bulk ff) and surface long-range order parameters i o and the bulk (

The plot of U versus 1/T (at constant volume) shows the characteristic sigmoid shape (fig. 2.6.1). The curves for the ordered and disordered phases meet at the apparent second order transition point T, which is also the temperature at which the short-range order parameter ( P icos 6 )y in the isotropic phase = l/(z — 1). The first order transition point is the temperature at which the shaded areas are equal, i.e., when the Helmholtz free energies of the ordered and disordered phases are the same. The calculation gives (2J,— T )/2J, = 0.062 for z = 8,0.04 for z = 4 and 0.03 for z = 3. This is an improvement over the Maier-Saupe value of 0.092, though still much higher than the experimental value of 0.003. 

Fig. 2.6.2. Short-range order parameter and the long-range order parameters s and (,P cos6)y versus T/T, calculated in the Krieger-James approximation. The long-range order disappears at the transition but the short-range order persists even in the isotropic phase.

Fig. 2.6.4. Short-range order parameters , and the long-range order parameter s versus T/T. The negative value of signifies antiparallel ordering. The curves are calculated for A B = 0.5. ...

Site populations in Al2Si205 kyanite and short range order parameters in CaAl2Si20g anorthite have been determined by using Al MQMAS NMR with quadrupolar Carr-Purcell-Meiboom-Gill echo train and FAM-II triple quantum to single quantum conversion pulses (MQ-QCPMG-MAS NMR). " ... 

In liquid crystals intermolecular interactions are short-range and Cp is dominantly related to short-range order fluctuations. Since fluctuations in local order occur above and below the transition, one expects, in contrast to the mean-field situation, anomalous Cp behavior above as well as below T. Unfortunately models taking short-range order parameter fluctuations into account are much more difficult to handle and analytic solutions are only available for some special cases. However, sophisticated renormalization group (RG) analyses have been carried out for several types of n vector order parameter models of which the three-dimensional cases are of particular relevance for liquid crystals [7, 10, 11]. 

Table 2. Warren-Cowley short-range order parameters for impurities in the (Gao.9325MnJ 04O625M o-oo9375- o.oi75)As alloy at T = 1400 K.

SHORT-RANGE ORDER PARAMETERS IN FCC BINARY ALLOYS... 

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