The Hume-Rothery rules and phase stabilities in noble metal alloys

Results from martensitic transformations are used to evaluate stabilities of the equilibrium phases in the Hume-Rothery electron compounds based on Cu, Ag and Au, and to give arguments why the electron concentration plays such an important role in the selection of the crystal structures. It is shown that the vibrational entropy difference observed for the martensitic transformation from ordered bcc to the close packed martensite and its e/a dependence can also account for the entropy difference ΔS ^α/β between the equilibrium α and β at high temperatures, and can be made largely responsible for the composition dependence of the (α+β) two phase field. The enthalpy of mixing can be decomposed into a small term which depends on the average periodic lattice, which is different in α and β but which is nearly the same in all alloys studied, and a contribution which is due to the difference in the properties of the atoms and which can be expressed by pair interchange energies. This contribution depends strongly on the specific alloy system, but is independent of structure, which is compatible with a pair interchange energy depending only on pair distance but not on structure, as suggested by simple pseudopotential theory. The same pair interchange energies account also for long range order and the critical ordering temperature. The evaluation for several alloy systems shows a surprisingly good agreement within this picture, and permits to understand better why the electron concentration plays such an important role also for other structures, although the energy contribution of the conduction electrons is only a small part of the total enthalpy of formation of any of the equilibrium structures.     

The influence of microstructure on the martensitic transformation in Cu–Zn–Al melt-spun ribbons

The martensitic transformation was investigated in a set of twin roller melt-spun Cu–Zn–Al shape memory alloys, solidified at tangential wheel speeds between 20 and 40 m/s. The resulting microstructures were analyzed using X-ray diffraction, optical and transmission electron microscopy techniques. The characteristic martensitic transformation temperature, M _S, was determined for each condition by conventional resistometric methods. The ribbons are homogeneous in shape and for each quenching rate they exhibit a quite uniform M _S temperature. By proper thermal treatments, the different factors affecting M _S could be separately examined and from temperature measurements, the contribution of L2₁ antiphase boundaries evaluated. A calculation of this contribution using pair interchange energies is in good agreement with the experimental results.     

Room temperature precipitation in quenched Al–Cu–Mg alloys: a model for the reaction kinetics and yield strength development

The microstructural evolution during low temperature ageing of two commercial purity alloys (Al–1.2Cu–1.2Mg–0.2Mn and Al–1.9Cu–1.6Mg–0.2Mn?at.%) was investigated. The initial stage of hardening in these alloys is very rapid, with the alloys nearly doubling in hardness during 20?h ageing at room temperature. The microstructural evolution during this stage of hardening was investigated using differential scanning calorimetry (DSC), isothermal calorimetry and three–dimensional atom probe analysis (3DAP). It is found that, during the hardening, a substantial exothermic heat evolution occurs and that the only microstructural change involves the formation of Cu–Mg co–clusters. The kinetics of cluster formation is analysed and the magnitude of the hardening is discussed on the basis of a model incorporating solid solution hardening and modulus hardening originating from the difference in modulus between Al and clusters.     

The Hume-Rothery rules and phase stabilities in noble metal alloys

Results from martensitic transformations are used to evaluate stabilities of the equilibrium phases in the Hume-Rothery electron compounds based on Cu, Ag and Au, and to give arguments why the electron concentration plays such an important role in the selection of the crystal structures. It is shown that the vibrational entropy difference observed for the martensitic transformation from ordered bcc to the close packed martensite and its e/a dependence can also account for the entropy difference ΔS ^α/β between the equilibrium α and β at high temperatures, and can be made largely responsible for the composition dependence of the (α+β) two phase field. The enthalpy of mixing can be decomposed into a small term which depends on the average periodic lattice, which is different in α and β but which is nearly the same in all alloys studied, and a contribution which is due to the difference in the properties of the atoms and which can be expressed by pair interchange energies. This contribution depends strongly on the specific alloy system, but is independent of structure, which is compatible with a pair interchange energy depending only on pair distance but not on structure, as suggested by simple pseudopotential theory. The same pair interchange energies account also for long range order and the critical ordering temperature. The evaluation for several alloy systems shows a surprisingly good agreement within this picture, and permits to understand better why the electron concentration plays such an important role also for other structures, although the energy contribution of the conduction electrons is only a small part of the total enthalpy of formation of any of the equilibrium structures.     

Atomistic details of precipitates in lean Al–Mg–Si alloys with trace additions of Ag and Ge studied by HAADF-STEM and DFT

Abstract

Bonding energies and volume misfits for alloying elements and vacancies in multicomponent Al–Mg–Si alloys have been calculated using density functional theory (DFT). A detailed atomic scale analysis has been done for characteristic precipitate structures, using high-angle annular dark-field scanning transmission electron microscopy. Two new stacking configurations of the important strengthening phase β′′ were discovered in the Ge-added alloy. All three stacking variations were found to be energetically favourable to form from DFT calculations. The second stacking configuration, β₂′′, contains vacated columns in its unit cell, consequently requiring less solute to create the same volume fraction of precipitate needles. DFT suggests a lower formation enthalpy per atom for β₂′′ when Si is exchanged with Ge. In the alloy containing Ag additions, a new Q’/C-like local configuration containing Ag instead of Cu was discovered, also this phase was deemed energetically favourable from DFT.     

Early stage ageing effects and shallow positron traps in Al–Mg–Si alloys

Room temperature ageing, so-called natural ageing, of Al–Mg–Si alloys has a subtle but striking influence on the mechanical properties achievable by subsequent ageing at more elevated temperatures. Though strongly debated, different clustering processes are generally accepted to give rise to this effect. Using temperature-dependent positron lifetime measurements of naturally aged Al–Mg–Si alloys, it is shown that in the early stages of ageing, small clusters of alloying atoms without embedded vacancies take part in the decomposition process. These clusters serve as shallow positron traps with a binding energy of about 55(10) meV, grow in the course of natural ageing and transform to deep positron traps with binding energies well above thermal energies. Thus, results of positron annihilation spectroscopy techniques need to be interpreted carefully with respect to the microstructure of age-hardenable Al alloys. Moreover, it is shown that a simple approach to bind positron states using a three-dimensional potential well and (bulk) positron affinities cannot explain the present findings.     

Thermal and structural characterization of Cu–Al–Mn–X (Ti,Ni) shape memory alloys

In this study, the Cu–Al–Mn–X (X = Ni, Ti) shape memory alloys at the range of 10–12 at.% of aluminum and 4–5 at.% manganese were produced by arc melting. We have investigated the effects of the alloying elements on the transformation temperatures, and the structural and the magnetic properties of the quaternary Cu–Al–Mn–X (X = Ni, Ti) shape memory alloys. The evolution of the transformation temperatures was studied by differential scanning calorimetry with different heating and cooling rates. The characteristic transformation temperatures and the thermodynamic parameters were highly sensitive to variations in the aluminum and manganese content, and it was observed that the nickel addition into the Cu–Al–Mn system decreased the transformation temperature although Ti addition caused an increase in the transformation temperatures. The effect of the nickel and the titanium on the thermodynamic parameters such as enthalpy and entropy values was investigated. The structural changes of the samples were studied by X-ray diffraction measurements and by optical microscope observations at room temperature. It is evaluated that the element Ni has been completely soluble in the matrix, and the main phase of the Cu–Al–Mn–Ni sample is martensite, and due to the low solubility of the Ti, the Cu–Al–Mn–Ti sample has precipitates, and a martensite phase at room temperature. The magnetic properties of the Cu–Al–Mn, Cu–Al–Mn–Ni and Cu–Al–Mn–Ti samples were investigated, and the effect of the nickel and the titanium on the magnetic properties was studied.     

Mechanism of the shape memory effect in martensitic alloys: an assessment

The (one-way) shape memory effect is a phenomenon that when a martensitic alloy is deformed in a martensitic state it recovers its original shape upon heating to the parent phase. This is a universal effect for certain martensitic alloys. We will assess the mechanism of the effect critically and select the essential factors which govern the effect. We try to understand it from a unified view, invoking the group–subgroup symmetry relation between the parent and martensite phase, along with analysis of reversible twinning modes in martensite. By such an assessment, we will show why typical shape memory alloys, such as Ti–Ni, Cu–Al–Ni etc., exhibit good shape memory characteristics, while others, such as ferrous alloys, do not. Thus, we will show that most of the shape memory characteristics of various martensitic alloys can be understood consistently from such an approach.     

Microstructure and texture development of 7075 alloy during homogenisation

The microstructure evolution of Al–Zn–Mg–Cu alloy during homogenisation was studied by optical microscope, field emission scanning electron microscope, energy dispersive X-ray Spectroscopy, differential scanning calorimetry and X-ray diffraction in detailed. It has been found that primary cast structure consisted of primary α (Al), lamellar eutectic structure η Mg(Zn, Cu, Al)₂ and a small amount of θ (Al₂Cu) phase. A transformation of primary eutectic phase from η Mg(Zn, Cu, Al)₂ to S (Al₂CuMg) was observed after 6 h of homogenisation treatment. The volume fraction of dendrite network structure and intermetallic phase was decreased with increase in holding time and finally disappeared after 96 h of homogenisation, which is consistent with the results of homogenisation kinetic analysis. Crystallographic texture of this alloy after casting and 96 h of homogenisation was also studied. It was found that casting process led the development of strong Goss, Brass, P and CuT components, while after homogenisation Cube, S and Copper components became predominant. Mechanical tests revealed higher hardness, yield strength and tensile strength for cast materials compared to homogenised alloys due to the presence of coarse micro-segregation of MgZn₂ phase. The significant improvement of ductility was observed after 96-h homogenisation, which was attributed to dissolution of second phase particles and grain coarsening. Fracture surfaces of the cast samples indicated the presence of shrinkage porosity and consequently failure occurred in the interdendritic regions or grain boundaries with brittle mode, while homogenised alloys failed under ductile mode as evident by the presence of fine dimple surfaces.     

Origin of tweed in Au–Cu–Al alloys

The premartensitic tweed in Au–Cu–Al alloys, contrary to previous thought that resort to defects, is confirmed to be associated with the coherent embryos of an intermediate phase (I phase) embedded in parent phase. The parent?→?I phase transformation temperature was measured by differential scanning calorimeter and dynamic mechanical analysers, which shifts from 82.3 to 557.6?°C depending on the alloy composition. X-ray diffraction and transmission electron microscopes (TEM) results show that the parent?→?I phase transformation is a charge density wave transition that cannot be suppressed even by melt-spun method, which shows obvious compositional inhomogeneity between I phase and parent. The results imply that the parent?→?I phase transition is a fast displacive transformation coupled with diffusion. Moreover, accompanying the parent?→?I phase transformation, alloys demonstrate diversified microstructure revealed by TEM observation, from tweed to chessboard nanowires or twins. These findings provide the experimental evidence for that parent?→?I phase transformation in Au–Cu–Al alloys is originated from pseudospinodal decomposition as theoretically predicted.     

Viscosity and diffusivity in melts: from unary to multicomponent systems

Viscosity and diffusivity, two important transport coefficients, are systematically investigated from unary melt to binary to multicomponent melts in the present work. By coupling with Kaptay’s viscosity equation of pure liquid metals and effective radii of diffusion species, the Sutherland equation is modified by taking the size effect into account, and further derived into an Arrhenius formula for the convenient usage. Its reliability for predicting self-diffusivity and impurity diffusivity in unary liquids is then validated by comparing the calculated self-diffusivities and impurity diffusivities in liquid Al- and Fe-based alloys with the experimental and the assessed data. Moreover, the Kozlov model was chosen among various viscosity models as the most reliable one to reproduce the experimental viscosities in binary and multicomponent melts. Based on the reliable viscosities calculated from the Kozlov model, the modified Sutherland equation is utilized to predict the tracer diffusivities in binary and multicomponent melts, and validated in Al–Cu, Al–Ni and Al–Ce–Ni melts. Comprehensive comparisons between the calculated results and the literature data indicate that the experimental tracer diffusivities and the theoretical ones can be well reproduced by the present calculations. In addition, the vacancy-wind factor in binary liquid Al–Ni alloys with the increasing temperature is also discussed. What’s more, the calculated inter-diffusivities in liquid Al–Cu, Al–Ni and Al–Ag–Cu alloys are also in excellent agreement with the measured and theoretical data. Comparisons between the simulated concentration profiles and the measured ones in Al–Cu, Al–Ce–Ni and Al–Ag–Cu melts are further used to validate the present calculation method.     

Amorphous and metastable crystalline structures in rapidly solidified Sn–Al system using melt-spinning technique

Three alloys of compositions Sn–5Al, Sn–5Al–2.5Ag and Sn–5Al–2.5Ag–0.5Cu (in weight percent) were produced by rapid solidification using the melt-spinning technique. X-ray diffraction analysis revealed a broad main peak at low Bragg angle that characterizes the amorphous phase. Also, the formation of a new metastable intermediate phase AlSn, was observed. The crystal structure of AlSn was found to be cubic (S.G. F4¯3m) with lattice parameter a?=?15.623?Å, and the unit cell contains 112 atoms. AlSn was found to be stable at room temperature.     

Partial pair correlation functions and viscosity of liquid Al–Si hypoeutectic alloys via high-energy X-ray diffraction experiments

The liquid structure of Al–Si hypoeutectic binary alloys was characterized by diffraction experiments using a high-energy X-ray (synchrotron) beam source. The diffraction experiments were carried out for liquid pure Al, Al–3?wt% Si, Al–7?wt% Si, Al–10?wt% Si and Al–12.5?wt% Si alloys at several temperatures. The salient structure information such as structure factor (SF), pair distribution function (PDF), radial distribution function (RDF), coordination number (CN) and atomic packing densities (PD) were quantified as a function of Si concentration and melt temperatures. Reverse Monte Carlo (RMC) analysis was carried out using the diffraction experimental data to quantify the partial pair correlation functions, such as partial structure factor, partial pair distribution function (PPDF) and partial radial distribution function. Furthermore, the partial pair distribution function and the liquid atomic structure information were used in a semi-empirical model to evaluate the viscosity of these liquid alloys at various melt temperatures. The results show that the viscosity determined by semi-empirical methods using the atomic structure information is in good agreement with the experimentally determined viscosity values.     

63Cu NMR analysis of microstructure evolution in Al–Cu–Mg alloys

⁶³Cu NMR spectroscopy has been used to detect metastable Guinier–Preston–Bagaryatsky (GPB) zones and nanoscale precipitates of equilibrium S-phase (Al₂CuMg) in dilute alloys of aluminium containing copper and magnesium with compositions which lie in the α?+?S phase field. The GPB zones are observed to form rapidly at room temperature with a time development closely related to the Vickers hardness. The final development of S-phase in the alloy has been confirmed by the observation of a line shape in the alloy identical to that observed in a specimen prepared from stoichiometric Al₂CuMg. Analysis of the hyperfine structure of the ⁶³Cu line shape observed for S-phase shows clearly that two Cu sites are present with approximately equal population. This result suggests that possibly two crystallographically distinct Al₂CuMg phases are present. The addition of small amounts of silver to Al–Cu–Mg alloys in the α?+?θ phase field is known to induce the formation of Ω-phase: a slight distortion of tetragonal θ-phase Al₂Cu. A hyperfine-structured ⁶³Cu line shape assigned to Ω-phase, indicating one distinct Cu site, has been observed in two separate Al–1.7?at.%?Cu–0.33?at.%?Mg alloys containing 0.1 and 0.18?at.%?Ag, but not in the same Al–Cu–Mg alloy without Ag.     

Electronic structures and magnetisms of the Co_2TiSb_(1-x)Sn_x(x= 0, 0.25, 0.5) Heusler alloys: A theoretical study of the shape-memory behavior

The total energy, electronic structures, and magnetisms of the Al Cu2Mn-type Co2TiSb1-xSnx(x = 0, 0.25, 0.5) with the different lattice parameter ratios of c/a are studied by using the first-principles calculations. It is found that the phase transformation from the cubic to the tetragonal structure lowers the total energy, indicating that the martensitic phase is more stable and that a phase transition from austenite to martensite may happen at a lower temperature. Thus, a ferromagnetic shape memory effect can be expected to occur in these alloys. The Al Cu2Mn-type Co2TiSb1-xSnx(x = 0, 0.25, 0.5) alloys are weak ferrimagnets in the austenitic phase and martensitic phase.     

基于β-FeSi2的(Fe, M)Si2三元合金相形成规律

二元β-FeSi₂相是一种重要的窄带半导体型金属硅化物,研究了基于该二元相的三元合金的形成规律,以丰富其材料范围.首先,利用团簇线判据作为理论依据,选取一个团簇和一个连接原子构成的模型,添加不同的第三组元作为连接原子,设计了Fe₃Si₈M(M=B, Cr, Ni, Cu, Co, Al）系列合金成分,即用添加组元替代二元相中的Fe连接原子.然后,用真空吸铸和真空甩带方法制备合金棒以及薄带,以获得无成分偏析的均匀合 关键词： 2')" href="#">β-FeSi₂ 三元合金 团簇线     

Influence of Al3Ni crystallisation origin particles on hot deformation behaviour of aluminium based alloys

Abstract

Binary Al–Ni, Al–Mg and ternary Al–Mg–Ni alloys containing various dispersions and volume fraction of second-phase particles of crystallisation origin were compressed in a temperature range of 200–500 °C and at strain rates of 0.1, 1, 10, 30 s^?1 using the Gleeble 3800 thermomechanical simulator. Verification of axisymmetric compression tests was made by finite-element modelling. Constitutive models of hot deformation were constructed and effective activation energy of hot deformation was determined. It was found that the flow stress is lowered by decreasing the Al₃Ni particle size in case of a low 0.03 volume fraction of particles in binary Al–Ni alloys. Intensive softening at large strains was achieved in the alloy with a 0.1 volume fraction of fine Al₃Ni particles. Microstructure investigations confirmed that softening is a result of the dynamic restoration processes which were accelerated by fine particles. In contrast, the size of the particles had no influence on the flow stress of ternary Al–Mg–Ni alloy due to significant work hardening of the aluminium solid solution. Atoms of Mg in the aluminium solid solution significantly affect the deformation process and lead to the growth of the effective activation energy from 130–150 kJ/mol in the binary Al–Ni alloys to 170–190 kJ/mol in the ternary Al–Mg–Ni alloy.     

On array models theoretical predictions versus measurements for the growth of cells and dendrites in the transient solidification of binary alloys

Most of the theoretical studies of the growth of cells/dendrites in the literature are based on the assumption that it is a steady-state phenomenon. The analysis of cells/dendritic structures in the unsteady-state regime is very important, since it encompasses the majority of industrial solidification processes. The aim of the present investigation was to validate the predictions furnished by the cellular and primary dendritic growth models in the literature for unsteady-state conditions against a large spectrum of experimental data, which includes those for a variety of Al alloys (Al–Cu, Al–Si, Al–Fe, Al–Bi, Al–Ni, Al–Sn) and low thermal diffusivity alloys, such as Sn–Pb and Pb–Sb. The predictions furnished by the Hunt–Lu model do not match the cellular experimental scatter for any examined alloy system. However, this model matches well with the primary dendritic growth of Al alloys, with the exception of Al–Sn alloys, for which the Hunt–Thomas approach has to be applied. The primary dendritic predictions of Bouchard–Kirkaldy's model, performed with the originally suggested a ₁ calibration factors are, in most cases, located above the experimental points. Experimental growth laws relating cellular and dendritic spacings with the tip growth rate and the cooling rate, respectively, are established.     

Temperature dependence of twinning stress – Analogy between Cu–Ni–Al and Ni–Mn–Ga shape memory single crystals

Abstract

To obtain a direct non-magnetic analogy to Ni–Mn–Ga 10M martensite with highly mobile twin boundaries, we present the recalculation of twinning systems in Cu–Ni–Al martensite. In this approach, the twinning planes denoted as Type I, Type II and compound have similar orientations for both alloys (Ni–Mn–Ga and Cu–Ni–Al). In Cu–Ni–Al, compound twinning exhibits the twinning stress of 1 to 2 MPa comparable to twining stress of Ni–Mn–Ga. In contrast Type II twinning stress of Cu–Ni–Al is approximately 20 MPa, i.e. much higher than twinning stress for Type II in Ni–Mn–Ga (0.1 to 0.3 MPa). Similarly to Ni–Mn–Ga, the twinning stress of Type II in Cu–Ni–Al is temperature independent. Moreover, no temperature dependence was found also for compound twinning in Cu–Ni–Al.