Transformation order-disorder

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. 

There are other intermediate kinds of transformations, such as the bainitic and massive transformations, but going into details would take us too far here. However, a word should be said about order-disorder transformations, which have played a major role in modern physical metallurgy (Barrett and Massalski 1966). Figure 3.17 shows the most-studied example of this, in the Cu-Au system the nature of the... 

Tanner, L.E, and Leamy, H.J. (1974) The microstructure of order-disorder transitions, in Order-Disorder Transformations in Alloys, ed. Warlimont, H. (Springer, Berlin) p. 180. 

The order-disorder transformation is not unique to two-layer fluids, which is readily concluded from the second maximum of n in the vicinity of s 3.55 where the fluid consists of three strata. However, it turns out that only the innermost, middle stratum undergoes the same kind of structural reorganization just explained for the two-layer fluid the two contact strata (i.e., the strata closest to the substrate) do not participate in the transformation. The intensity of the second maximum in n is therefore reduced by roughly 2/3 compared with the first one, as one would expect. 

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. 

The Type N thermocouple (Table 11.60) is similar to Type K but it has been designed to minimize some of the instabilities in the conventional Chromel-Alumel combination. Changes in the alloy content have improved the order/disorder transformations occurring at 500°C and a higher silicon content of the positive element improves the oxidation resistance at elevated temperatures. 

The simplest example of an order-disorder transformation in which only one element is involved is the ferro- to diamagnetic transformation of b.c.c. a-iron, when the magnetic properties change over a range of temperature, the completion of the transformation being at the Curie temperature. Since this transformation only requires a randomization of electron spins without atomic diffusion, the process is very rapid, and the degree of spin disorder closely follows the thermodynamic model as the temperature of the solid is brought up to the Curie temperature. 

A schematic representation of cubic lattice complexes is given in Figs 3.14 and 3.15 this could also be useful as an indication of possible combinations and splitting . Such relations may be useful while comparing different structures and studying their interrelations and possible transformations (order-disorder transformations, etc.)... 

Carpenter M. A. (1985). Order-disorder transformations in mineral solid solutions. In Reviews in Mineralogy, P. H. Ribbe (series ed.), Mineralogical Society of America, 14 187-223. 

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. 

A structure can be defined as possessing long-range order if at least two sets of positions can be distinguished by a different average occupation. These classes are usually called sub-lattices. The simplest example of an order/disorder transformation occurring in a b.c.c. lattice may be described in terms of two interpenetrating simple cubic arrays. If the occupation probability of each species is the same on both sublattices, then this is equivalent to a fully disordered b.c.c. stmcture, A2 (Fig. 7.1). 

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