Disordered solid solution

Figure 1 Intrinsic stacking fault energy for chemically disordered solid solution Al-X (where X=Cu or Mg) as a function of composition.

Taking into account thatiVAA = /VBB and Nm =zN - /VAA - NBB the energy of the disordered solid solution becomes... 

The possibility of simulating the actual BWG ordering energy, rather than Cp, using a polynomial approximation was also examined by Inden (1976) using the disordered solid solution as a reference state. The following expression was suggested for a continuous second-order transformation such as A2/B2 ... 

Consider the A-B binary system. If A and B form a random solid solution with, say, 10 atom percent B, the probability of finding a B atom on any specific lattice site is just 0.1. Under certain conditions, however, B atoms may favour certain specific sites than die test. B atoms will then preferentially position themselves on these specific sites. The probability of finding B atoms in these sites will greatly increase. This type of arrangement is referred to as an ordered structure. The process in which a random disordered solid solution is rearranged into an ordered solid solution is called an order-disorder transition. 

Khidirov, I., Kurbonov, I.I., Padurets, L.N. (1993) Neutron diffraction study of disordered Solid Solution TiN0.26H0.15, Metallofizika, 15 (18), 87-90. 

The accomplishment of an absolute asymmetric synthesis with a quantitative enantiomeric yield required at this point a better understanding of the nature of the disordered solid solution of racemic (2) in order to be able to overcome the unfavourable interactions which are responsible for the metastability of this phase this we tried to achieve by different chemical and crystallographic approaches which are described below. 

It is clear from these data that in the temperature range 320-392 °C an intermediate degree of order prevails and that as T is raised there is a progressive transition from the tetragonal superstructure towards the cubic arrangement of the disordered solid solution. 

Solid-fluid phase diagrams of binary hard sphere mixtures have been studied quite extensively using MC simulations. Kranendonk and Frenkel [202-205] and Kofke [206] have studied the solid-fluid equilibrium for binary hard sphere mixtures for the case of substitutionally disordered solid solutions. Several interesting features emerge from these studies. Azeotropy and solid-solid immiscibility appear very quickly in the phase diagram as the size ratio is changed from unity. This is primarily a consequence of the nonideality in the solid phase. Another aspect of these results concerns the empirical Hume-Rothery rule, developed in the context of metal alloy phase equilibrium, that mixtures of spherical molecules with diameter ratios below about 0.85 should exhibit only limited solubility in the solid phase [207]. The simulation results for hard sphere tend to be consistent with this rule. However, it should be noted that the Hume-Rothery rule was formulated in terms of the ratio of nearest neighbor distances in the pure metals rather than hard sphere diameters. Thus, this observation should be interpreted as an indication that molecular size effects are important in metal alloy equilibria rather than as a quantitative confirmation of the Hume-Rothery rule. 

DFT studies of binary hard-sphere mixtures predate the simulation studies by several years. The earliest work was that of Haymet and his coworkers [221,222] using the DFT based on the second-order functional Taylor expansion of the Agx[p]- Although this work has to some extent been superceded, it was a significant stimulus to much of the work that followed both with theory and computer simulations. For example, it was Smithline and Haymet [221] who first analyzed the Hume-Rothery rule in the context of hard sphere mixture behavior and who first investigated the stability of substitutionally ordered solid solutions. The most accurate DFT results for hard-sphere mixtures have come from the WDA-based theories. In particular the results of Denton and Ashcroft [223] and those of Zeng and Oxtoby [224] give qualitatively correct behavior for hard spheres forming substitutionally disordered solid solutions. 

In somewhat earlier work, Vlot et al. [229,230] made calculations of Lennard-Jones binary mixtures in which the pure components are identical but in which the unlike interactions have departures from the Lorentz-Berthelot combining rules. They use this as a model of mixtures of enantiomers. A variety of solid-fluid phase behavior can be obtained from the model. Both substitutionally ordered and substitutionally disordered solid solutions were found to occur. 

FcjAl is formed on cooling by ordering reactions in the solid state that transform the b.c.c. disordered solid solution, which... 

Chen, D.Q., Lei, L., Xu, J., Yang, A.P., Wang, Y.S., 2013. Abnormal size-dependent upconversion emissions and multi-color tuning in Er -doped Cap2—YbFs disordered solid-solution nanocrystals. Nanotechnology 24, 085708. 

Fig. 1.12 Phase diagrams of disordered solid solutions EuxSri xS (a) and Fe Mg -xCh (b) [26]...

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