The order-disorder transformation

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. 

The prediction of a critical temperature is an important feature of the theory of the order-disorder transformation, for it is to be expected that at this temperature many of the physical properties of the alloy will display sharp changes. In particular, anomalies in the specific 

In the above treatment we have assumed implicitly that the alloy is at every temperature in the state of equilibrium appropriate to that temperature and to the value of the parameter V0. This, however, is in practice not necessarily the case, for it may happen that under a given set of conditions the rate of attainment of equilibrium is so slow that an equilibrium state is never in fact achieved. That this is true is, indeed, clear from observations on those systems in which a disordered state can be preserved at low temperatures by quenching, although the superstructure is then intrinsically more stable. Naturally, a discussion of the rate of attainment of equilibrium is of the greatest importance in considering the effect of heat treatment. 

The order-disorder transformations which we have described above are concerned with what may be termed long-range order , i.e. order which extends throughout the crystal and determines whether a given site is occupied by a right or a wrong atom. It is, however, 

Short-range order cannot be as readily detected by X-ray methods as long-range order, and the number of systems in which it has been studied is therefore somewhat limited. It is, however, of particular 

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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. 

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. 

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,... 

As an example of these conditions of higher order stabihty we may mention the order-disorder transformation in the alloy of equimolecular proportions of gold and copper. The affinity of the change is given by the approximate equation (c/. 19.55)... 

To describe these transformations, De Bonder has made systematic use of the concept of the degree of advancement or extent of reaction, denoted by The state of systems studied here can be defined in general by two physical variables such as the volume and temperature and one parameter for each physicochemical change that can occur in the system. The concept of extent of reaction or extent of change can be applied not only to chemical reactions and phase changes which can be represented by stoichiometric equations, but also to changes such as the order-disorder transformation in alloys for which no chemical equation can be written. 

A careful investigation of the order-disorder transformation in NijAl has shown that the order-disorder transition temperature is slightly lower than the solidus temperature for NijAl with less than 23 at.% Al (Cahn et al., 1987). This leads to a more complex ordering process with domain formation which may be beneficial for ductility, whereas in the case of stoichiometric NijAl with an order-disorder transition temperature above the liquidus temperature ordering occurs directly without domain formation. 

There are a number of displacive transitions mentioned in this book. The order-disorder transformation of hydrogen atoms in hydrogen bonds in ferroelectric ceramics (Section 11.3.5) is one example. Displacive transitions that involve a change from an ordered arrangement of atoms to a random arrangement are commonly found in alloys. A subgroup of such order-disorder transitions, martensitic transitions, which can be used to produce shape-memory alloys, are considered in Sections 8.3.2 and 8.3.3. 

Gil] Gillot, B., Study by Infiared Absorption Speelia of die Factors Influencing the Order-disorder Transformation in -y Vacancy Ferrites Obtained from die Oxidation of Ferrous Spinels (in French), Mater. Chem. Phys., 10(4), 375-384 (1984) (Crys. Stracture, Experimental, 17)... 

Another exciting feature is the possibility of observing a continuous decrease in the carrier density when absorbing hydrogen, which gives rise to a metal-insulator (M-I) transition somewhere in the interval between 2 and 3 atoms H per atom R. Moreover, temperature dependent M-I transitions have been observed in the p-phase between 250 and BOOK both in sub-stoichiometric LaHs and CeHs- as well as in super-stoichiometric YH2+J and in RH2+ (R=Gd, Ho, Er) with xf 0.1-0.3, which are driven by the order-disorder transformation in the H sublattice mentioned above. 

So, super lattice is a transformation of one disordered or asymmetric state to one ordered or symmetric state of this alloy and the order-disorder transformation around a temperature establish that the symmetry and asymmetry may be viewed as the two sides of the same coin. 

Chapter 2 looks at the modeling and characterization of solid solutions. Following a quaUtative description of the different types of solid solution of substitution and insertion, the short-distance and long-distance order coefficients are introduced. Simple solution models are briefly described and the thermodynamics of the order/disorder transformations in alloys is presented. The chapter ends with the experimental determination of the activity coefficients of the components of a solid solution. 

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 interplay of the electronic structure and the backbone conformation is observed as chromisms both in the solid state and solution. The reversible appearance and disappearance of the fine structure linked to the peak shift in the electronic spectra obviously demonstrate that the order-disorder transformation in the backbone conformation plays an important role. 

As an example, consider the study by Banerjee et al. (1984) on the effect of electron irradiation on the order-disorder transformation in (DIJ Ni4Mo. Electron micrographs and diffraction patterns were obtained during in situ electron irradiations at 50-1050 K in a HVEM. At temperatures below 200 K, the alloy completely disorders. At 200-450 K, only SRO was observed, and the transition between LRO and SRO, which occurs via the completely disordered state, is consistent with the concentration-wave description of the SRO structure and supports the concept of spinodal ordering. It is believed that an interstitial mechanism is responsible for maintaining the SRO. Above 450 K, LRO persisted for samples initially in this state and SRO was only preserved up to 550 K for samples initially in that state. Between 550 and 720 K, a mixed SRO-LRO state occurred, and at temperatures above 720 K a complete transition to SRO was obtained. It is believed that maintenance of LRO requires a vacancy mechanism. At temperatures below 800 K the SRO-LRO transition occurred in a continuous fashion, while above 800 K a nucleation and growth mechanism was operative. This behavior is characteristic of an ordering transition of the first kind below and above the coherent instability temperature. 

J. B. Cohen, The order-disorder transformation, in Phase Transformations, pp. 561-620, American Society for Metals, Cleveland (1970). 

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