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The use of the concepts of favourable and unfavourable size factor in predicting solid solubilities in metallic systems is discussed. The original concept of Hume-Rothery, Mabbott and Channel-Evans involved the use of atomic diameters which were defined as the closest distances of approach of atoms in the crystals of the elements. Atomic diameters defined in this way give a much better correlation with solid solubilities than do the Goldschmidt atomic diameters and a slightly better correlation than the Pauling single bond metallic radii. Recent suggestions that atomic diameters should be replaced by atomic volumes are reviewed and it is shown that the atomic volumes do not correlate well with the solid solubilities in alloy systems. In spite of the different crystal structures involved, the atomic volumes in the sequences Cu→ Zn → Ga→ Ge, Ag → Cd → In and Au → Hg → Tl show an almost exactly linear increase with atomic number.

The equilibrium diagram of the system gold-gallium has been determined by a combination of thermal analysis, and microscopical and X-ray metallography. The work has led to the discovery of a close-packed α-phase, with ABAC… stacking sequence, lying outside the Au-rich α-solid solution. The small β-phase region claimed by Weibke and Hesse has been shown not to exist, whilst three new phases have been discovered in the intermediate region.

The equilibrium diagram of the system molybdenum-cobalt has been investigated by a combination of thermal analysis, microscopy, and X-ray techniques, and the crystal structures and lattice spacings of the different phases have been determined. Molybdenum can dissolve about 11.5 at. % cobalt at 1620°C, the temperature of the peritectic reaction αMo + Liq /agσ. Cobalt dissolves about 18 at. % molybdenum at 1335°C, the temperature of the (βCo + e) eutectic. The σ-phase extends over a slight range of composition in the region 37–38 at. % cobalt, and decomposes eutectoidally at 1250°C to form (αMo + e). The e-phase lies in the region (50–55) at. % cobalt. The crystal structure is of the D85 type, and the lattice constants were determined as a = 4.666 ± 0.005 kX, c = 25.6 ± 0.02 kX. At high temperatures, the e-phase is in equilibrium with β-Co, but at1200°C a new phase, denoted θ, is formed peritectoidally, and decomposes at 1025°C; the θ-phase gives a diffraction pattern whose lines can be fitted to a hexagonal cell with a = 2.5921 ± 0.0005 kX, and ca = 1.6218. The kappa, or Co3Mo phase is formed peritectoidally at 1025°C, and crystallises in the Do19 type of structure with a = 5.12 kX, ca = 0.803; this may be regarded as a superlattice of the close-packed hexagonal structure, with a doubled a spacing and a halved axial ratio. The results are discussed, and confirm the tendency of the σ-phases to occur at an electron concentration of 7.0–7.3.

The equilibrium diagram of the system niobium-nickel has been determined by a combination of thermal analysis, microscopical metallography, and X-ray techniques. Nickel is able to dissolve up to 12.5 at. % Nb at high temperatures, whilst niobium dissolves only 4.5 at. % of Ni. The system contains an intermediate phase (β) Ni3Nb with the Cu3Ti type of structure, which gives rise to a maximum on the liquidus curve at 1402°C. There is also a γ-phase of composition limits 50–54 atomic % Nb, formed by a peritectic reaction at 1295°C.

The Engel-Brewer theory of metal and alloy crystal structures is examined critically. The conclusion reached is that, for pure metals, the correlation between electron configuration and crystal structures exist only for the elements of Groups IIIA–VIA. The application of the theory to alloy structures is shown to involve many inconsistencies.

The equilibrium diagram of the system bismuth-palladium has been studied in the region 0–65 at.-% Pd by thermal analysis and microscopical methods. The freezing point of bismuth is depressed by the addition of palladium and sinks to a eutectic at 5.83 at.-% Pd and 256°C. The liquidus then rises to 485.4°C, at which temperature the compound “Bi 2 Pd” melts without change of composition. The compound BiPd gives rise to a pronounced maximum in the liquidus curve at 618°C, and there is a palladium-rich eutectic at 577°C. At low temperatures the composition of the “Bi 2 Pd” phase is about 34 at.-% Pd. It undergoes a transformation at 380°C, in contrast to the earlier work of Zhuravlev And Zhdanov , according to whom the transformation took place at 200°C. There is a remarkable resemblance between the equilibrium diagrams of the systems Pd-Sb and Pd-Bi. Both give rise to compounds of the type PdX 2 , the melting points of the Sb-compounds being systematically higher.

The equilibrium diagram of the system molybdenum-nickel has been determined by a combination of thermal, microscopical, and X-ray methods. The system contains an intermediate γ-phase whose composition limits include the value corresponding to MoNi3; this phase has an orthorhombic structure. In contradiction to previous work, the composition of the intermediate δ-phase does not include the equiatomic ratio, and has a slight composition range centred at about 47 at.% Ni. The intermediate β-phase has a composition in the region of 80.5–81 at.% Ni, and does not include the exact ratio MoNi4; the structure is tetragonal and may be regarded as derived from a MoNi4 superlattice of the f.c.c. Ni solid solution. The lattice spacings of the terminal solid solutions have been determined. The equilibrium diagram of the systems Mo-Co and Mo-Ni show many similarities, and these are discussed.

Previous work suggested that the compound Bi4Rh existed in three modifications with transformation temperatures α/β 310°C and β/γ 390°C. Diffraction films taken in a high temperature X-ray camera show that only one structure exists between room temperature and 460°C, the temperature of the Bi4Rh ± Bi2Rh + Liq. peritectic horizontal. The crystal structure of this one modification is body-centred cubic, space group No. 230, lattice parameter 14.9274 ± 0.0002 A at 20°C, and is identical with the α-Bi4Rh modification of previous investigators. The liquidus curve of Bi-rich BiRh alloys has been redetermined and the most probable equilibrium diagram is reproduced.

The equilibrium diagram of the system Au-Cd has been investigated by thermal, microscopical, and X-ray diffraction methods. At high temperatures the phases present are 1. (1) the α solid solution of cadmium in gold, 2. (2) the α 2 phase which is of variable composition with close-packed hexagonal structure, and 3. (3) the β′ body-centred cubic phase which remains highly ordered at a few degrees below the melting point. No evidence was found for the existence of the α 3 phase claimed by Owen et al . or of the α″ phase postulated by Bystrom and Almin. On the cadmium-rich side, the α 2 phase has a normal close-packed hexagonal structure but, in the range 27–34 at. % Cd, highly faulted structures are observed, and a possible cause of this is suggested in terms of the curves of densities of electronic states. In the region of 25 at. % Cd, at low temperatures, a face-centred tetragonal phase is formed, and also a new face-centred cubic phase which has not been described before.

The equilibrium relations in the system bismuth-rhodium are examined. In agreement with the authors' previous work, no evidence is found for the existence of more than one modification of the compound Bi 4 Rh. Attempts to prepare further modifications by cooling from above the liquidus (as was done by Russian investigators) were unsuccessful. No evidence was found for the existence of the compound Bi 3 Rh claimed by Zhdanov et al . The compound Bi 2 Rh is shown to exist in two modifications, with a transition temperature of 425°C. The structure of the compound BiRh was confirmed as being of the NiAs type. The lattice spacings were measured up to 970°C, and kinks in the curves of c and c / a against temperature were found to exist at 800°C, and a less pronounced kink occurred in the curve for the a spacings, whilst the curve for temperature versus mean volume per atom was smooth.

The equilibrium diagram of the system molybdenum-ruthenium has been determined for temperatures above 1450°C. Molybdenum dissolves about 30.5 at.% Ru at high temperatures and the solubility diminishes quickly as the temperature falls. Ruthenium dissolves 51 at.% Mo at high temperatures and the solubility diminishes slowly with falling temperature. The sigma phase exists in the region of 37.0 ± 1 at.% Ru and is formed by a peritectoid reaction slightly below the 1945°C eutectic horizontal between the solid solutions in molybdenum and ruthenium. The lattice spacings of the different phases have been measured, and the V.P. hardness numbers were determined for alloys in the “as-sintered” state prepared by powder methods.

The equilibrium diagram of the system niobium-cobalt has been determined by a combination of thermal analysis, microscopical metallography, and X-ray diffraction techniques. The freezing point of cobalt is lowered markedly on addition of niobium, and the liquidus curves sink to a eutectic point at 13.9 at.% Nb and 1237°C. The constituents of the eutectic are a solid solution of Nb in Co (5.5 at.% Nb), and an NbCo 3 -phase whose structure is based on that of the Laves C36 type. This decomposes peritectically at 1247°C to form liquid plus a “Co 2 Nb” phase whose composition extends from 27 to 33.3 at.% Nb and whose structure is of the Laves C 15 type. This gives rise to a maximum on the liquidus curve, and forms a eutectic with a phase denoted μ which exists over the range 50.5–52.7 at.% Nb, and whose structure is that of the W 6 Fe 7 type. The μ-phase gives rise to a flat maximum on the liquidus curve, surrounded by (NbCo 3 + μ) and (μ + Nb solid solution) eutectics. The maximum solubility of cobalt in solid niobium is 3.1 at.% at the 1374°C eutectic temperature. The significance of these results is discussed.

The complete constitutional diagram of the system Au-Hg has been determined by thermal analysis and X-ray diffraction methods, supplemented by microscopical work on gold-rich alloys. Much of the work was carried out in sealed tubes, and the pressure was an undetermined variable. The gold-rich alloys contain two intermediate phases denoted α' and ζ. The α'-phase is formed by a peritectic reaction at 419°C; it has a hexagonal crystal structure with lattice parameters a = 8.736 A and c = 9.577 A , and the unit cell contains 36 atoms. The ζ-phase is formed peritectically at 388°C. A phase Au2Hg was observed at temperatures below 122°C, and this appears to be of fixed composition; it is hexagonal with lattice parameters a = 13.98 A and c = 17.20 A . In contrast to the conclusions of some earlier workers, no evidence was found for the existence of any intermediate phase richer in mercury than Au2Hg.

Two X-ray cameras are described which can be used to very high temperatures. One of these is a Debye-Scherrer camera after the model of Westgren 1 in which electric current for heating passes through the specimen itself and this camera has been used up to 3100°C. In the application of this camera to Cr, Rh, Ru and W, only the room temperature modifications were detected, while for Hf photographs were obtained of the high temperature b.c.c. modification. The other camera is of the symmetrical parafocusing type with a refractory metal heater surrounding the specimen. The specimen, which is in the form of a block of the material under study, has a small hole drilled in it which forms effectively a black body cavity for temperature measurement. This camera has been used to determine accurately the temperature variation of the lattice parameter of Mo up to 1733°C.

The equilibrium diagrams of the later transition metals of the Second and Third Long Periods are examined systematically. It is shown that the body-centred cubic, close-packed hexagonal, and face-centred cubic phases have composition ranges whose boundaries appear to be controlled mainly by the Average Group Numbers of the alloys. Group Numbers of 6, 7, 8, 9, and 10 are allotted to the elements of Groups VIA, VIIA, VIIIA, B, and C respectively, so that an equiatomic alloy of Mo and Ru has an AGN value of 7.0. Relations with the elements of the first transition series are discussed.

ABS>The fact that Yb and Th exhibit very limited mutual solid and liquid miscibilities was interpreted in terms of a rule involving an electronegativity vs radius (for coordination number 12) graph. In this rule, an ellipse is drawn around one element on the graph, and the elements within the ellipse are predicted to form extensive solid solutions with this element, while the other elements lying outside the ellipse have limited solubilities. Numerous exceptions to the rule are given with Au, Ag, Cu, and Mg as solvent, and the justification of the rule is doubtful. Some of the reasons for the exceptions are discussed. It is concluded that an extreme difference in electronegativity (e.g., Au-Mg, AuIn, Ag-Li) does not preclude the formation of extensive solid solutions. (D.L.C.)