Short range ordered state

We use the formulas from the preceding sections to study the short-range ordered states in some typical disordered alloys. Our Monte Carlo calculations start from a code written for the simple cubic lattice by Loren P. Meissner to illustrate the use of array intrinsic functions in fortran 90 and 95. It treats the 2 interpenetrating cubic lattices in bcc or the 4 interpenetrating lattices in fee as blocks. We use the Ising Hamiltonian,... 

All of these calculations indicate that the short-range ordered state shown by the a(k) and the SROP for temperatures above the order-disorder transformation are closely related to the ground state structures. Remnants of the correlations that exist in the ground states will persist into the short-range ordered states as described, for example, by Hata. The SROP for concentrations in the neighborhood of 62.5%, which corresponds to the chemical potential v =2.0, are shown in Fig, 8. The order parameter -Cg for the... 

The calculations in the preceding section indicate that the correlations in the low temperature ordered state are carried over into the short-range ordered state at higher temperature. This is similar to the conclusion reached from high-resolution electron diffraction studies. It should be noted, however, that our Monte Carlo calculations generate thermodynamic equilibrium states. The electron difibaction experiments as well as the dynamic Monte Carlo method used to explain them focus on ncm-equilibrium states. ... 

W Garlipp, M Migschitz and W Pfeiler, Short-range ordering in AgZn alloys for various states of defect... 

M. Migschitz, W GarUpp and W. Pfeiler, Short-range order Kinetics in a-AgZn for various states of post-... 

FIG. 1. Schematic density of states distribution. Bands of (mobile) extended states exist due to short-range order. Long-range disorder causes tails of localized states, whereas dangling bonds show up around midgap. The dashed curves represent the equivalent states in a crystal. 

In contrast to crystalline solids characterized by translational symmetry, the vibrational properties of liquid or amorphous materials are not easily described. There is no firm theoretical interpretation of the heat capacity of liquids and glasses since these non-crystalline states lack a periodic lattice. While this lack of long-range order distinguishes liquids from solids, short-range order, on the other hand, distinguishes a liquid from a gas. Overall, the vibrational density of state of a liquid or a glass is more diffuse, but is still expected to show the main characteristics of the vibrational density of states of a crystalline compound. 

Packing efficiency can also be described by the extent of short-range order in the amorphous state. Mitchell has shown through X-ray scattering studies that, while the local molecular organization of noncrystalline polymers is random, in many cases, there are additional correlations that do not perturb the chain trajectory but will impact polymer properties.15 These correlations have a limited spatial range (<50A) but will have a particular impact on bulk properties... 

A consequence of the intermolecular forces is that any molecule in the liquid state has a large coordination number so that the structure has a low energy configuration. In other words there is short-range order in the liquid state. A significant amount of work must be done to remove a molecule from this structure - the latent heat of vaporisation. 

A clear indication of the various intermediate phase stability may be obtained from the values of their Afi (AfG). The enthalpies of formation, in the liquid and in the solid state, of divalent metal alloys with Pb, as a typical element in the p-block, have been measured, and their trend discussed, by Sommer et al. (2006). The most exothermic values observed, for instance, in the Ca-Pb and Ba-Pb systems, correspond (for the solid compounds, in kJ/mol of atoms, at 300 K) to — 62 2 (for Ca2Pb) and —13 2 (for BaPb). A relevant compound forming tendency was observed also for the liquid alloys, for which the association model (see 3.2) was successfully applied confirming the existence of strong chemical short-range order. 

In this contribution we focus on the region that is sandwiched between the FE and glass phase states, i.e. the range of x-values 0.20 < x < 0.35. In [10] we have shown that the low temperature glass state (0.35 < x < 0.65) consists predominantly of short range ordered AFE clusters with a mean correlation length of about 1 nm. The fact that no FE clusters were found was explained by the unfavourable ratio of electric surface to volume energy, which makes... 

Fig. 4 Stacked Fourier transforms of the NMR spin echoes in D-RADP-25 versus echo delay time at T = 65 K. In contrast to D-RADP-20 (Fig. 2) there are still two rims present at this low temperature indicating the coexistence of two different phase states. The rim at the Larmor frequency vl originates from Rb spins localized in short range ordered glass clusters, whereas the rim at vl + 8 kHz is produced by spins sitting in FE clusters [17]...

---