Order-disorder transformations method

Dilatometric methods. This can be a sensitive method and relies on the different phases taking part in the phase transformation having different coefficients of thermal expansion. The expansion/contraction of a sample is then measured by a dilatometer. Cahn et al. (1987) used dilatometry to examine the order-disorder transformation in a number of alloys in the Ni-Al-Fe system. Figure 4.9 shows an expansion vs temperature plot for a (Ni79.9Al2o.i)o.s7Feo.i3 alloy where a transition from an ordered LI2 compound (7 ) to a two-phase mixture of 7 and a Ni-rich f c.c. Al phase (7) occurs. The method was then used to determine the 7 /(7 + 7O phase boundary as a function of Fe content, at a constant Ni/Al ratio, and the results are shown in Fig. 4.10. The technique has been used on numerous other occasions,... 

Phases with order-disorder transformation, like A2IB2 and AI/LI2 can also be described with the sublattice method although this disregards any explicit short range order contributions. A single Gibbs energy function may be used to describe the thermodynamic properties of both the ordered and disordered phases as follows ... 

Earlier work on systems such as Ni-Al-Cr reported in Sanchez et al. (1984b) used FP methods to obtain information on phases for which there was no experimental information. In the case of Ni-base alloys, the results correctly reproduced the main qualitative features of the 7 — 7 equilibrium but cannot be considered accurate enough to be used for quantitative alloy development. A closely related example is the work of (Enomoto and Harada 1991) who made CVM predictions for order/disorder (7 — 7 ) transformation in Ni-based superalloys utilising Lennard-Jones pair potentials. 

In this chapter we have summarized the fundamentals and recent advances in thermodynamic and kinetic approaches to lithium intercalation into, and deintercalation from, transition metals oxides and carbonaceous materials, and have also provided an overview of the major experimental techniques. First, the thermodynamics oflithium intercalation/deintercalation based on the lattice gas model with various approximations was analyzed. Lithium intercalation/deintercalation involving phase transformations, such as order-disorder transition or two-phase coexistence caused by strong interaction oflithium ions in the solid electrode, was clearly explained based on the lattice gas model, with the aid of computational methods. 

Zhang, J., Wang, Y. Q., Tang, M., Valdez, J. A., and Sickafus, K. E. 2010a. Ion irradiation induced order-to-disorder transformations in 5-phase Sc42,Zt3+ (Oi2+ (/2. Nucl. Instrum. Methods B 268(19) 3018-3022. 

In what follows we will discuss systems with internal surfaces, ordered surfaces, topological transformations, and dynamical scaling. In Section II we shall show specific examples of mesoscopic systems with special attention devoted to the surfaces in the system—that is, periodic surfaces in surfactant systems, periodic surfaces in diblock copolymers, bicontinuous disordered interfaces in spinodally decomposing blends, ordered charge density wave patterns in electron liquids, and dissipative structures in reaction-diffusion systems. In Section III we will present the detailed theory of morphological measures the Euler characteristic, the Gaussian and mean curvatures, and so on. In fact, Sections II and III can be read independently because Section II shows specific models while Section III is devoted to the numerical and analytical computations of the surface characteristics. In a sense, Section III is robust that is, the methods presented in Section III apply to a variety of systems, not only the systems shown as examples in Section II. Brief conclusions are presented in Section IV. 

Olvera de la Cruz and Sanchez [76] were first to report theoretical calculations concerning the phase stability of graft and miktoarm AnBn star copolymers with equal numbers of A and B branches. The static structure factor S(q) was calculated for the disordered phase (melt) by expanding the free energy, in terms of the Fourier transform of the order parameter. They applied path integral methods which are equivalent to the random phase approximation method used by Leibler. For the copolymers considered S(q) had the functional form S(q) 1 = (Q(q)/N)-2% where N is the total number of units of the copolymer chain, % the Flory interaction parameter and Q a function that depends specifically on the copolymer type. S(q) has a maximum at q which is determined by the equation dQ/dQ=0. 

With a Fourier transformation of (k) in the distance space, one obtains a separation of the contribution of the various coordination shells. This Fourier transform yields the structural parameters Rj, Nj and ah and thus the near range order of the specimen with respect to the absorbing atoms. The EXAFS analysis for the different absorber atoms within the material yields their specific near range order. Thus, one may get the structure seen form several kinds of absorbing atoms. EXAFS does not require highly crystalline materials. It is a suitable method to study disordered, or even amorphous, structures. The a values provide quantitative information about the thermal and structural disorder. 

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