Extended solid solution

Compounds isotypic with the k phases arc found among intcrmetallics, borides, carbides and oxides and also with silicides, germanides, arsenides, sulfides and sclcnides no nitrides, however, are found. The mode of filling the various voids in the metal host lattice of the k phases follows the schemein Ref. 4 and is presented in Table 1 for all those compounds for which the atom distribution is well known from x-ray or neutron diffraction. Accordingly, B atoms in tc-borides, Zr, Mo, W, Re)4B and Hfy(Mo, W, Re, Os)4B , occupy the trigonal prismatic interstices within the parent metal framework of a Mn, Aln,-type structure (see Table 1 see also ref. 48). Extended solid solutions are found for (Hf, Al)[Pg.140]

First rule Effect of the size factor. If the atomic sizes of the two components differ more than 15%, extended solid solution formation is not expected. 

A few general remarks about a group of metal-hydrogen phases have been included in 3.8.4.1 where interstitial hydrogen solutions in metallic structures have been described. However, as previously observed, a number of intermediate phases are also formed in several systems. A short summary of these is shown in Table 5.2 where their formulae very often have only an indicative character and several structure types correspond to more or less extended solid solution ranges. 

Remarks on the alloy crystal chemistry of the 4th group metals. Selected groups of isostructural phases, pertaining to simple common structural types have been collected in Table 5.25. A number of them (for instance CsCl, AuCu types, Laves phases, AuCu3 type) correspond to more or less extended solid solution... 

Both L coefficients and / factors can, in principle, be calculated from microscopic models. For the evaluation of L,j, the random-alloy model [J. R. Manning (1968) A. R. Allnatt, A. B. Lidiard (1987)] is sometimes used. For the evaluation of thermodynamic factors, one takes advantage of the empirical rule that in extended solid solutions AO-BO, the cation vacancy concentration and the oxygen potential are related to each other as... 

In /l-Si3N4 the Si and N ions can be replaced by Al and O ions to form an extended solid solution according to the formula... 

Solid Solutions of NaCl Type. On the other side of the L2S3-MS diagrams, we observed the formation of extended solid solutions of the NaCl type. 

The results of our experiments are given in Table VII. Extended solid solutions are observed only with the last rare earth sulfides—Dy2S3, Y2S3, Er2S3, and Yb2S3—when added to MgS, MnS, or CaS. Extremely limited solid solutions are observed when one of these rare earth sulfides is added to SrS. We never observed solid solutions of the NaCl type with other rare earth sulfides, nor with BaS. 

While at least 15 different nitride phases with compositions ranging between W2N and WN2 have been reported, none of them appear to be very well characterized. As for the Mo-N system, an fee nitride WNi x appears to exist since nitridation experiments under pressure in the Mo-W-N system have shown that the fee MoNi x phase is able to form extended solid solutions with the isotypic phase WNi x. The pressure... 

On the other hand, berylium is within the favourable range for copper, and magnesium is similarly situated with regard to the possibility of extended solid solution in silver once again... 

Other Factors. It must now be emphasised that extended solid solubility is not always found when size-factors are favourable, since other factors may enter into the problem, and a discussion of these will follow. It has, howTever, been confirmed that a favourable size-factor is the first essential in deciding whether one metal may be expected to form extended solid solutions in another. Again, when size-factor restricts solid solubility it is usually found that solid solubility increases with rise of temperature, so that considerations of such combinations may result in the development of new precipitation hardening alloys, in wdiich low solid solubility at ordinary temperatures is, of course, essential. 

Valency Factor. We have already seen that wdien attempting to determine whether any tw o metals will, on alloying, form extended solid solutions, the first things to consider are the size-factors of the atoms concerned. It has been sliowm that when the 14 per cent, size-factor is unfavourable solid... 

Effect of Increasing Valency of Solute. It has been found that when size-factors are favourable extended solid solutions are most lilcely to be formed when the metals concerned have atoms with the same number of outer-layer electrons, i.e. when they have the sa ne valency. When size-factors arc favourable and valencies unequal tin4 extent of solid solubility will decrease as the difference between the respective valencies increases. To examine the effect of the valency-factor we may consider the extent of the solid solubility in copper ((1u).of the favourable size-factor but increasing valency metals, zinc (Zn), gallium (Ga), germanium (Ge) and arsenic (As), and in silver (Ag) of the corresponding favourable size-factor metals, cadmium (Cd), indium (In), tin (Sn) and antimony (8b). The necessary atomic diameters and valency data (vide p. bl), and the results of experimental work on these1 alloys, as far as the primary solid solutions are concerned, an1 summarised in Fables IX (a) and (h). 

Solid Solubility when Size-Factors are favourable and Valencies the same. Having dealt with the effects on solid solubility of both higher valency and lower valency solutes, we may now pass on to deal with the structures of those alloys in which the metals have favourable size-factors and the same valency. We may assume that under such conditions the introduction of atoms of the one metal into the lattice of the other will bring about the minimum distortion in both the ion lattice and the electron cloud, so that everything favours extended solid solution. Data for such alloys are given in Table X. 

The discussion in literature on the existence of the compound 8164 is referred to in Sect. 4.1. Due to the documented isotypy of B4C and 8164 (i.e.-the solid solution SiB2.89-3.65) complete solid solution at B = const. = 80 at.% was assumed [219]. However, due to the experimental work of Gugel et al. and Kieffer et al. [223] and Telle [4] it is generally accepted today that no extended solid solution exists. Telle [4] additionally rules out a complete solid solution between SiB3 and B4C because of significant differences in the electron configurations. 

Based on the results of X-ray phase and stmctural analysis of the Lai xCaxCri yTiy03 samples synthesized by a ceramic technique in air at 1620 K, the isothermal sections of the CaTi03-LaCr 03-CaCr 03 quasi-temary system has been constmcted [3]. Extended solid solution with perovskite-like GdFe03-type of stmcture (space group Pbnm) is formed in this system in a wide homogeneity range. The existence area of the solid solution at used experiment conditions reaches up to 0.6- -0.7 molar fractions of CaCr 03. 

The formation of an extended solid solution (Cej j,.Prj,.)3Si2 crystallizing with the U3Si2-type of structure and with a Ce substitution up to 58 a/o Pr was reported by Mokra (1979). For details of sample preparation, see Ce-Y-Si. 

The La-Ge-Si system has been investigated by various authors no ternary compounds are formed and phase equilibria as presented in an isothermal section at 600 °C in fig. 31 are mainly characterized by extended solid solutions. 

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