Order in solid solutions

In the case of a substitutional solid solution, the atoms of the solute B can occupy a variety of positions in relation to the atoms of the solvent A. 

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Belostotskii VF, Bemkin VM (1988) Ordre dans les solutions solides au cours de la deformation par les ultrasons aux temperatures de l helium liquide Ordering in solid solution during ultrasonic deformation at liquid helium temperatures. Metallokfizika 10(6) 99-101... 

Bragg-Williams treatment of convergent ordering in solid solutions... 

Iverenova, V.I., Katsnel son, A.A. (1977) Short -Range Order in Solid Solutions, Nauka, Moscow, 254 p. 

The kinetics of ordering in solid solutions and even more so rate processes during phase transformations are both expermentally and theoretically very difficult subjects. Furthermore, in light of the previous discussion it is highly questionable whether order-disorder processes as they occur in simple glass forming (i.e., metal alloys) substances also take place in polymers. Nevertheless, attempts are being made to improve... 

Another subject class is concerned with diluted 4f metals. Sarkissian and Coles (1976) have tried to distinguish between spin-glass freezing and helical ordering in solid solutions of Gd, Tb and Dy in Y and Sc by means of resistivity and susceptibility measurements (fig. 12). These materials have attracted recent interest again, because some are candidates for anisotropic spin glasses (Baberschke et al. 1984). It also turned out that spin-glass behavior in yttrium based alloys occurs at much lower concentrations than previously claimed. 

In what follows, we used a phenomenological approach to solve the problem of the most stable ordered structure. As in all studies on the ordering in solid solutions known to us [[19]-[22], we will restrict ourselves to the approximation of effective pair interactions whose form is not specified in deriving the general relations. Within this approximation, we will calculate... 

Of the generic aluminium alloys (see Chapter 1, Table 1.4), the 5000 series derives most of its strength from solution hardening. The Al-Mg phase diagram (Fig. 10.1) shows why at room temperature aluminium can dissolve up to 1.8 wt% magnesium at equilibrium. In practice, Al-Mg alloys can contain as much as 5.5 wt% Mg in solid solution at room temperature - a supersaturation of 5.5 - 1.8 = 3.7 wt%. In order to get this supersaturation the alloy is given the following schedule of heat treatments. 

G. Foumet, Order-disorder phenomena in solid solutions, in. Phase Stability in Metals and Alloys", P S. 

One important use of X-ray probes is in the study of local order and displacements, but this is not within the scope of the present book. The recent availability in intense synchrotron sources with selectable X-ray energies permits high-precision measurements of chemically specific atomic-pair correlations in solid solution alloys. A recent review of the technique is given by G.E. Ice and C.J. Sparks (Modern Resonant X-ray studies of alloys local order and displacement) in Annual Reviews of Materials Science 1999, 29, 25-52. 

The Mossbauer effect, although not a substitute for other analytical methods such as x-ray diffraction, can be used to obtain several kinds of structural information about solids. In favorable cases, it is possible to obtain rather detailed information about the electronic configuration of atoms and the local symmetry of their sites by measuring the isomer shift and quadrupole splitting. If more than one valence state of a given atom is present, a semiquantitative determination of the amount of each kind is possible. In solid solutions, the amount of local or long range order can be estimated, and in certain defect structures the relation between the active atoms and the defects can be studied. 

In this case, trace element and carrier occupy the same structural position both in the solid phase and in the melt and are subject to the same compositional effects in both phases (i.e., extension of the cation matrix in the melt and amount of anorthite component in the solid). Figure 10.9A shows the effect of normalization the conventional partition coefficient of Sr between plagioclase and liquid varies by about one order of magnitude under equal P-T conditions, with increasing anorthite component in solid solution, whereas normalized distribution coefficient D is virtually unaffected. Figure 10.9B shows the same effect for the Ba-Ca couple. 

In order to establish which base metal sulfide minerals host the PGE at the Creighton Mine we calculated a mass balance following the method of Barnes et al. (2008). We used the whole rock PGE content, the concentration of PGE in each sulfide and the mass fraction of each sulfide phase in the ore to determine the proportion (wt. %) of each PGE hosted by the sulfides in solid solution. 

It should be noted, however, that in a multisite substitution where cation ordering occurs, a heat of mixing term could arise even in the absence of a compositional variation of the CFSE. For example, the excess CFSE of mixing would increase to about -8.20 kJ/mole in solid-solution formation of the liebenbergite (Mg0 49Ni0 51)2SiO4, eq. (7.14), if the CFSE of Ni2+ ions in the Ml and M2 sites were to remain constant at -143.1 and -113.2 kJ/mole, respectively. 

The proportionality constant between the applied potential and the charge due to the species ordering in the solution interfacial region is the double layer capacity. The study of the double layer capacity at different applied potentials can be done by various methods. One much used is the impedance technique, which is applicable to any type of electrode, solid or liquid, and is described in Chapter 11. Another method uses electrocapillary measurements. It was developed for the mercury electrode, being only applicable to liquid electrodes, and is based on measurement of surface tension. 

KCl. The calculated value of the change AV in molar volume accompanying the transformation increases slightly with the percentage of KCl suggesting that the transformation remains first order (thermodynamically) even in solid solutions. 

These elements of disorder will not lead to a shift of a sharp peak. Shifts occur only if defects order in such a way as to modify all unit cells of the crystal in the same way (Figure 4). This effect is frequently encountered in solid solutions (Abd Hamid et al., 2003 Langford and Louer, 1996 Valtchev and Bozhilov, 2004), in which atoms of different sizes occupy the same lattice positions. In many cases there are linear... 

Figure 22 Depiction of the arrangements of metal atoms in solid solutions of gold copper alloys (a) disordered stmcture in which the metal atoms are statistically distrihuted and (b) the ordered stmcture with copper atoms (filled circles) are in the face centers and gold atoms (open circles) at the cube comers...

Although experimental distribution ratios are sometimes of the same order of magnitude as the ratio of solubility products, they often disagree widely moreover, D usually varies with the composition of the solid phase, indicating that activities are not directly proportional to concentration in solid solution. Thus with 92 mole % silver chloride the value of D was found to be 2 x 10 , with about 15 mole % silver chloride it was 4 x 10 and with 99.9 + mole % silver chloride it was about 5 X 10 . Nevertheless, in the absence of experimental data an expression similar to (9-12) serves as a useful guide for estimating the possible extent of coprecipitation due to solid-solution formation. 

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