Phase transformations order-disorder

Keywords interstitial solid solutions, crystal structure, phase transformation, order-disorder, isotopic effect, antiphase domains, neutron diffraction, TiN026Hoi5, TiN026Doi5, TiN0.MH0.075D0.075 ... 

Khidirov, I., Karimov, I., Em, V.T. et al. (1981) Neutron diffraction study of phase transformations of disordered-ordered in nitridohydride titanium, Izv Akad Nauk SSSR, Neorg Mater, 17 (8), 1416-1420. 

Physical metallurgy is a rather wide field of applications of Mossbauer spectroscopy and it is possible to enumerate only the main topics phase analysis, order-disorder alloys, surfaces, alloying, interstitial alloys, steel, ferromagnetic alloys, precipitation, diffusion, oxidation, lattice defects etc. Alloys are well represented by the iron-carbon system, the mechanism of martensite transformation, high-manganese and iron-aluminium alloys, iron-silicon and Fe-Ni-X alloys. 

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 ... 

The SME process can be illustrated by the Cu—Zn system, one of the first SMAs to be studied. A single orientation of the bcc P-phase on cooling goes through an ordering process to a B2 phase. In a disordered alloy, the lattice sites are randomly occupied by both types of atoms, but on ordering the species locate at particular atomic sites, yielding what is called a supedattice. When the B2 phase is cooled below the Mp it transforms to... 

In the examples given below, the physical effects are described of an order-disorder transformation which does not change the overall composition, the separation of an inter-metallic compound from a solid solution the range of which decreases as the temperature decreases, and die separation of an alloy into two phases by spinodal decomposition. 

Even when complete miscibility is possible in the solid state, ordered structures will be favored at suitable compositions if the atoms have different sizes. For example copper atoms are smaller than gold atoms (radii 127.8 and 144.2 pm) copper and gold form mixed crystals of any composition, but ordered alloys are formed with the compositions AuCu and AuCu3 (Fig. 15.1). The degree of order is temperature dependent with increasing temperatures the order decreases continuously. Therefore, there is no phase transition with a well-defined transition temperature. This can be seen in the temperature dependence of the specific heat (Fig. 15.2). Because of the form of the curve, this kind of order-disorder transformation is also called a A type transformation it is observed in many solid-state transformations. 

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,... 

A sublattice phase can be envisaged as being composed of interlocking sublattices (Fig. 5.3) on which the various components can mix. It is usually crystalline in nature but the model can also be extended to consider ionic liquids where mixing on particular ionic sublattices is considered. The model is phenomenological in nature and does not define any crystal structure within its general mathematical formulation. It is possible to define internal parameter relationships which reflect structure with respect to different crystal types, but such conditions must be externally formulated and imposed on the model. Equally special relationships apply if the model is to be used to simulate order-disorder transformations. 

S.4.3.4 Order-disorder transformations. The previous examples considered strict site preference for the components in sublattice phases. For example, in the (Cr, Fe)2B compound, B is not considered to mix on the metal sublattice, nor are Cr and Fe considered to mix on the B sublattice. This strict limitation on occupancy does not always occur. Some phases, which have preferential site occupation of elements on different sublattices at low temperatures, can disorder at higher temperatures with all elements mixing randomly on all sublattices. 

It was demonstrated by Sundman (1985) and later by Ansara et al. (1988) that an order-disorder transformation could be modelled by setting specific restrictions on the parameters of a two>sublattice phase. One of the first phases to be considered was an A B-ordered compoimd. In such circumstances the sublattice formula A, B)j(A, B) can be applied and the possible relationships between site fiactions and mole fiactions are given in Figure 5.6. The dashed lines denoted xb = 0.25, 0.5 and 0.75 show variations in order of the phase while the composition is maintained constant. When these lines cross the diagonal joining AjA and B3B the phase has disordered completely as Vb Vb As the lines go toward the boundary edge the phase orders and, at the side and comers of the composition square, there is complete ordering of A and B on the sublattices. 

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 some thermodynamic models there are also potential minima associated with different site occupations, even though the composition may not vary, e.g., a phase with an order/disorder transformation. This must be handled in a somewhat different fashion and the variation in Gibbs energy as a function of site fraction occupation must be examined. Although this is not, perhaps, traditionally recognised as a miscibility gap, there are a number of similarities in dealing with the problem. In this case, however, it is the occupation of sites which govern the local minima and not the overall composition, per se. 

Nucleation and Growth (Round 1). Phase transformations, such as the solidification of a solid from a liquid phase, or the transformation of one solid crystal form to another (remember allotropy ), are important for many industrial processes. We have investigated the thermodynamics that lead to phase stability and the establishment of equilibrium between phases in Chapter 2, but we now turn our attention toward determining what factors influence the rate at which transformations occur. In this section, we will simply look at the phase transformation kinetics from an overall rate standpoint. In Section 3.2.1, we will look at the fundamental principles involved in creating ordered, solid particles from a disordered, solid phase, termed crystallization or devitrification. 

Magnetically soft Fe-Ni alloys can have their properties altered by heat treatment. The compound NisFe undergoes an order-disorder transformation at about 500°C. Since the susceptibility of the ordered phase is only about half that of the disordered phase, a higher susceptibility is realized when the alloy is quenched from 600°C, a process that retains the high-temperature, disordered structure. Heat treatment of Fe-Ni alloys in a magnetic field further enhances their magnetic characteristics (see Figure 6.61), and the square hysteresis loop of 65 Permalloy so processed is desirable in many applications. A related alloy called Supermalloy (see Table 6.19) can have an initial susceptibility of approximately one million. 

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