Volume 89, Issue 12

The effect of alloying with Al on phase stability and crystal structure of the Laves phases NbCo 2 and TaFe 2 was studied as part of extended work on Laves phases of transition metals. The ternary phases can be described as Nb(Co 1– x Al x ) 2 and Ta(Fe 1– x Al x ) 2 in view of the respective ternary phase diagrams. Melting temperatures and lattice constants have been measured. The phase equilibria between Ta(Fe 1– x Al x ) 2 and bcc Fe–Al, Fe 3 Al with D0 3 structure and FeAl with B2 structure have been studied. The cubic C15 structure of NbCo 2 transforms to the hexagonal C14 structure in the temperature range 1050 to 1350 °C and is unstable for Al contents above 5 at.% Al. The stability of Laves phases with C15 structure is favoured by a high valence electron concentration.

Experimental information on the heat capacity of DyFe 2 is analyzed in terms of a vibrational contribution represented by the Einstein model, a magnetic contribution represented by the Inden-Hillert-Jarl model as well as a second order contribution aT + bT 2 , a and b being adjustable parameters. As a comparison the heat capacity was obtained by the Neumann-Kopp rule with a magnetic contribution added.

Instability criteria for tricritical systems of binary alloys with ordering and phase separation are derived from linearized coupled kinetic equations for local composition and local degree of order. The analysis clearly shows that deviation from stoichiometry leads to instability against heterogeneous ordering associated with compositional fluctuations, when the degree of order is around 1/ 3 $ 1/\sqrt 3 $ of the equilibrium value. Heterogeneous ordering or spinodal decomposition is expected to occur even in the single phase field of the order phase as well as within the miscibility gap between ordered and disordered phases. Transmission electron microscopy on an Fe-14.6 at.% Si alloy revealed that D0 3 -type ordering is accompanied by heterogeneous fluctuations of the degree of order as predicted by the derived instability criteria.

A new model describing the structural and bonding properties of the omega phase in Zr–Nb alloys has recently been presented [ G. B. Grad et al.: Z. Metallkd. 87, (1996) 726]. This model, which was aimed at explaining the composition dependence of the bonding distances, predicts that the omega phase in Zr–Nb alloys is ordered, i.e., that some of the crystallographic sites are preferently occupied for Zr atoms. This feature of the omega phase is not contradicted by the most recent studies of the lattice parameters, but it has not yet been tested against direct measurements of the atomic ordering. In this paper we identify, theoretically, the Bragg reflections that appear only if the alloy is ordered, and show that among the three prototypical isoelectronic systems Ti–V, Zr–Nb and Hf–Ta, the former is the most suitable one for an experimental test of the model. The use of neutron scattering and transmission experiments is critically discussed, and the optimum composition for experiments with Ti–V alloys is presented.

Phase equilibria at 1073 K, 1173 K, and 1273 K in the Fe–Cu portion of the Fe–Cu–Al system were determined by a diffusion couple technique, metallography, and transmission electron microscopy (TEM). It is shown that there is a miscibility gap of the bcc phase which is divided into A2 + A2, A2 + B2 and B2 + B2 two-phase regions. Based on the experimental data of phase equilibria of the present as well as of previous studies, a thermodynamic assessment of phase equilibria was made, in which the order–disorder transition of the bcc phase is taken into account. The thermodynamic parameters of fcc, bcc, and liquid phases were evaluated to describe the Gibbs energy of each phase leading to a better fit between calculations and experimental findings above 1073 K.

The aim of this work has been to develop a model for short range order within the compound energy formalism. The short range order contribution to the Gibbs energy is described as a number of internal variables, here called ϵ -variables. This work is restricted to ordered and disordered phases with fcc structures.

The Fe–Mn system has been used to demonstrate the key role of anti-ferromagnetic contributions to the martensitic transformation behaviour and the stacking fault energy of fee Fe–Mn alloys. An analysis of previous work leads to the conclusion that the optimum magnetic characterisation in the low temperature region may differ substantially from the behaviour deduced from a high temperature analysis. An alternative model has been developed, which leads to the satisfactory quantitative prediction of the relevant M s, A s and T 0 temperatures as well as stacking fault energies and the model is capable of being extended to ternary systems. The results also have a bearing on current expressions for the phase stability of the γ–ε transformation in pure iron.

The effect of interaction between the magnetic and chemical ordering reactions on the phase equilibria between the bcc phases, A2, B2 and DO 3 has been studied by using the four-sublattice Compound Energy Model (CEM) taking account of the magnetic contribution to the Gibbs energy. An interaction between the magnetic and chemical ordering arises when the Curie temperature is formulated as a function of the site fraction of elements on each sublattice. A positive interaction arises from the higher deviation of the Curie temperature of the ordered state from that of the disordered one and leads to a two-phase separation between the ferro- and paramagnetic B2 phases. A lower deviation causes a negative interaction which introduces a convexity in the Gibbs energy curve around the composition of the intersection point between the Curie temperature and the order-disorder transition temperature. As a result, two-phase separations between either para- or ferro-magnetic A2 phase and paramagnetic B2 phase are introduced.

The system Ti–Sn was investigated with regard to the phases forming in the Sn-rich region and the reaction between titanium and liquid tin. Phase equilibria were studied by isothermal annealing of powder and melted alloy samples in the range of 29 to 88 at.% Sn and 350 °C to 1100 °C. Phase compositions were determined using XRD, SEM and EDX methods. The reaction kinetics between solid Ti and liquid Sn were investigated using both thin film and bulk diffusion couples. Surface contamination, presumably oxide layers, initially inhibits any reaction between bulk Ti and Sn. Reaction layers after isothermal annealing of the diffusion couples were analyzed with optical microscopy, SEM/EDX, and XRD. The experiments show that in this system a new intermetallic phase TiSn x with a composition of about 60 at.% Sn exists, which is stable up to about 750 °C. This phase is evidently the fastest forming intermetallic if liquid Sn is reacting with Ti or Ti-rich phases. Thus it is dominating in annelaed powder and alloy samples as well as in bulk and thin film diffusion couples. However, during solidification from Sn-rich melts another phase, Ti 6 Sn 5 is dominating. A revised phase diagram of the Ti–Sn system is presented, incorporating the TiSn x phase. Since the formation of TiSn x is slow and the thermal stability of TiSn x is not as high as expected for the more Ti-rich phases the system Ti–Sn is not suitable for Transient Liquid Phase (TLP)-bonding.

The total energies of formation of Cu–Ni, Ag–Ni and Au–Ni superstructures based on a fcc lattice have been calculated using the linear-muffin-tin-orbital (LMTO) method in the full potential approach. Both unrelaxed and relaxed structures have been included in the calculations. The energy of formation is decomposed into three terms, a volume deformation contribution, a chemical contribution and a relaxation contribution. The enthalpies of mixing of the disordered solid solutions have been calculated using an Ising-like cluster expansion for both the chemical and relaxation effects. In the Gibbs energy of mixing, a configurational entropy of mixing calculated with the cluster variation method (CVM) has been introduced and the thermal excitations due to the electronic and vibrational effects have been taken into account. The miscibility gaps displayed in the three considered binary systems have been calculated.

Energies of unrelaxed antiphase boundaries (APBs) right after they are formed are formulated and calculated for the B2 and D0 3 structures, using the numerical results of the (irregular) tetrahedron approximation of CVM, which takes into account the first and second neighbour_interactions. Three cases, a 0 ⟨100⟩ (001), a 0 ⟨100⟩ (01 1¯ $ \overline 1 $ ) and a 0 /2 ⟨1 11¯ $ \overline {11} $ ⟩(01 1¯ $ \overline 1 $ ) are treated. The numerical results obtained for the bcc Fe–Al system at 1000 K and 623 K show that the APB energies for the first two cases are negligibly small except for the stability region of the D0 3; phase at 623 K. Use of the tetrahedron approximation makes it possible to clearly reveal the effect of the short-range order.