Electron-atom Ratio Research Articles

Effect of Phase Stability on Some Physical and Mechanical Properties in β-Ti Single Crystal for Biomedical Applications

The electron-atom ratio (e/a) dependence of the appearance of the lattice modulation and physical properties in β-phase Ti-xNb alloys (x = 28, 30, 34 and 40) were investigated by using some physical properties measurements, compressive test and transmission electron microscope observations (TEM observations), focusing on the β-phase stability. The microstructure, physical properties, deformation mode depend on the e/a ratio which is closely related to the β-phase stability in Ti-Nb alloys. The e/a ratio is defined by the average electrons per atom in free atom configuration. Athermal ω-phase is suppressed in Ti-30Nb alloy single crystal with low e/a ratio. The Ti-30Nb alloy single crystal also exhibits a lattice modulation and low Debye temperature. These results imply that the β-phase stability in β-phase Ti alloys decreases with decreasing the e/a ratio and are related to the softening of elastic stiffness, c′. Consequently, a decrease in the e/a ratio leads to the softening of c′ and a significant reduction in modulus along the [100] direction in β-phase Ti alloys single crystal. In fact, the Young’s modulus along [100] of the Ti-15Mo-5Zr-3Al alloy (wt.%) single crystal with low e/a ratio exhibits as low as 45 GPa, which is comparable to that the human cortical bone. That is, controlling the e/a ratio is an ultimate strategy to develop the future superior biocompatible implant materials with extremely low Young’s modulus and good deformability.

Prediction of formation enthalpies for Al 2X-type intermetallics using back-propagation neural network

A back-propagation artificial neural network (ANN) was established to predict the formation enthalpies of Al 2X-type intermetallics as a function of some physical parameters. These physical parameters include the electronegativity difference, the electron density difference, the atomic size difference, and the electron–atom ratio ( e/ a). The values calculated by the ANN method agree with experiments well to typically within 10%, indicating that the well-trained back-propagation (BP) neural network is feasible, and can precisely predict the formation enthalpies of Al 2X-type intermetallics. The method comparison based on the predicted formation enthalpies suggests that our ANN method is superior to Miedema's model. Some trends of formation enthalpies for Al 2X-type intermetallics were also observed from the ANN.

Phase Constitution and Mechanical Properties of Ti-(Cr, Mn)-Sn Biomedical Alloys

In order to produce new β (bcc) Ti alloys for medical applications, effects of Mn substitution for Cr on phase constitution and mechanical properties of Ti-Cr-Sn alloys were investigated. All the Ti-7mol%(Cr, Mn)-3mol%Sn alloys investigated by XRD analysis were identified as β (bcc) alloys, and athermal ω phase was also detected in Ti-7mol%Mn-3mol%Sn . The lattice parameter of β was slightly decreased by Mn substitution. Besides, the Mn substitution for Cr raised the hardness and the strength while reduced the ductility of the Ti-Cr-Sn alloys. The hardening by Mn substitution must be due to ω precipitation. The hardening is discussed from the viewpoint of electron atom ratio (e/a) in comparison with Ti-Cr binary alloys in the literature.

Phase Equilibrium of the AuMn-Cu<sub>2</sub>MnGa System

Phase equilibrium and phase constitution of the Au-Cu-Ga-Mn quaternary system at 873 K was studied along the AuMn-Cu2MnGa (=CuMn0.5Ga0.5) both of which are ferromagnetic shape memory alloys. Three alloys were investigated: AuMn, Cu2MnGa and Au0.5Cu0.5Mn0.75Ga0.25 (AuMn:CuMn0.5Ga0.5=1:1). It was found that 1 ordered bct phase with the axis ratio c/a=0.948 was formed in the AuMn alloy due to the Mn reduction by evaporation during melting. The CuMn0.5Mn0.5 alloy was composed of MgZn2-type Laves phase and Cu9Al4-type  phase. Besides, the following three phases existed in the Au0.5Cu0.5M0.75Ga0.25 alloy: Laves,  and 2 ordered bct with c/a=1.041. The c/a value of the ordered bct phase is decreased by Cu and/or Ga substitution in AuMn. The values of electron atom ratio (e/a) calculated based on chemical compositions for the  phases were 1.61 and 1.68, which were close to the ideal value of 1.62 (=21/13). Based on the results, ordered bcc  (transforming into bct at lower temperature), and Laves are judged to be equilibrium phases at 873 K along the AuMn-Cu2MnGa.

The estimation of concentration fluctuations in liquid Ag–Si and Au–Si alloys

The specific electrical resistivity was measured for liquid states of Ag–Si and Au–Si with deep eutectic points for which the ‘electron atom ratio’ at the eutectic composition is 1.33 and 1.56, respectively. On lowering the temperature, the specific electrical resistivity deviates from the straight line, which was obtained by extrapolating its behavior from high to low temperatures. The concentration dependence of this deviation at the liquidus shows the largest value at the eutectic composition. The analysis based on the effective medium theory tells us that the volume fraction of concentration fluctuation in the homogeneous liquid phase is largest at the eutectic composition. The degree of concentration fluctuation was summarized on one systematic trend among metal–semiconductor eutectic systems. It is concluded that the large concentration fluctuation develops in the homogeneous liquid phase of eutectic systems. The possibility of the poor supercooling tendency of homogeneous liquids at the eutectic composition was revealed with relation to this concentration fluctuation.

Effects of ternary additions on martensitic transformation of TiAu

The effects of ternary element additions on martensitic transformation start temperature ( M s) and factors for controlling M s were investigated for the Ti–Au alloy systems. The ternary elements X selected were Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Ir and Pt, which substitute for the Au sites. The concentration of ternary elements was chosen to be 1 and 3 mol%. The alloys of Ti 50(Au, X) 50 were fabricated by Ar arc-melting followed by a homogenization at 1173 K for 3.6 ks. M s was measured by differential scanning calorimetry. It was found that the apparent phases at room temperature identified by θ − 2 θ X-ray diffraction were B19 regardless of ternary additions. The correlations between M s or the change in M s by adding 1 mol% of X (Δ M s) are discussed in terms of electron atom ratio ( e/a), valence electron number ( N e), Mendeleev number ( N M) and lattice parameter ratio between c- and b-axes ( c/b) of B19 martensite phase. It was found that M s decreases linearly with increasing amount of ternary additions and that Δ M s is −40 K/mol% for Ru and −5 K/mol% for Cu, for example. Besides, the dependence of M s on the above factors is presented and linear correlations are obtained.

ALCHEMI study of an Al72Ni20Co8 decagonal quasicrystal

Electron channeling patterns, which record the intensity variation of characteristic X-ray emission as a function of the incident direction of an electron beam, have been taken from an Al72Ni20Co8 decagonal quasicrystal for the first time. The channeling patterns show that Al atoms and transition metals occupy respectively different lattice sites, but that both of Ni and Co atoms occupy in disorder the same lattice sites. This supports that the alloy is an electron compound, where the composition of Ni and Co adjusts the value of the electron atom ratio of the alloy.

Annealing treatment of AB2-type hydrogen storage alloys: I. crystal structures

Abstract As part of a study on annealing effects on AB 2 -type hydrogen storage alloys, the crystal structures of two multi-component alloys have been studied. There exist three, the C15 and C14 Laves phases and the Zr 7 Ni 10 phase in the as-cast alloys. Annealing treatment leads to a transition from a multiphase structure to a single stable Laves phase structure. The stable Laves phase type (C15 or C14) is dependent on the electron-atom ratio. It was also found that annealing treatment results in the increase of the lattice parameters of the C15 phase and the decrease of that of the C14 phase.

Cyclic deformation behavior of Cu–30 wt% Zn single crystals oriented for single slip—I. Cyclic deformation response and slip band behavior

Cyclic deformation behavior of Cu–30% Zn single crystals oriented for single slip was studied at constant plastic shear strain amplitudes ( γ pl) in the range of 3.8×10 −5–6.4×10 −3 in order to understand systematically the fundamental fatigue behavior of low stacking fault energy materials. Results indicate that the cyclic hardening behavior strongly depends on the strain amplitude applied. For low strain amplitudes ( γ pl<3×10 −4), cyclic saturation occurred after an initial cyclic hardening stage, but for high strain amplitudes ( γ pl≥6.0×10 −4) saturation could not be reached until fatigue failure. The initial cyclic hardening rate ( θ 0.2) was found to decrease with increase in the applied strain amplitude. Slip bands were found to behave very similarly to Lüders band appearance at the beginning as well as in the middle stage of cyclic deformation. Particularly, the similarity of the cyclic hardening behavior at low and high strain amplitudes to the work hardening response in stages I and II of tensile deformation of the same alloy has been pointed out. Cyclic stress was further decomposed into two terms, the effective stress and the internal stress, and both were found to increase continuously with cyclic deformation. It has been demonstrated that the activities of secondary slips played an important role in the continuous cyclic hardening at high γ pl. A comparison of the present result with previous relevant work on both wavy and planar slip materials has been attempted. The transition of wavy slip mode to planar slip mode of Cu–Al and Cu–Zn alloys has been discussed in terms of the electron–atom ratio and the critical value of the ratio for such a transition is found to be 1.18–1.19 for both alloys.

Effect of ternary addition on the formation of Cu3Pt and CuPt order phases in the Cu-Pt system

The effect of addition of ternary elements, mainly In and Pd, on the phase fields of CuPt3 with the L12 type of ordered structure and CuPt with an L11 type of ordered structure in the Cu-Pt system has been investigated and the results compared with the substitution behaviour of the added elements and the electron-atom (e/a) ratio of the alloys. Electrical resistivity measurements and structural analysis by X-ray diffraction reveal that the addition of In leads to a shift of the phase field of the Cu3Pt towards the higher temperature regime and the Pt-rich side, and to a shift of the phase field of the CuPt towards the lower temperature regime and the Pt-rich side in the phase diagram of the Cu-Pt system. In contrast, the addition of Pd leads to a shift of the phase fields of both Cu3Pt and CuPt towards the lower temperature regime and the Cu-rich side. However, by plotting these phase fields on a temperature-e/a diagram, it is seen that the range of e/a ratio for each phase field is about 0.71-0.97 for the Cu3Pt phase and about 0.25-0.71 for the CuPt phase irrespective of the kind and amount of the added element.

Some regularities of melting points of AB-type intermetallic compounds

Abstract A modified cellular model is proposed for the investigation of melting point regularities of AB-type intermetallic compounds. By this model, five parameters of constituent elements: electronegativity difference, ΔX; valence electron density difference, Δ( Z R 3 ) ; electron-atom ratio, e a ; metallic radius ratio, R A R B ; and the average melting point of constituent elements, Tavg, are used to find a mathematical model for the melting point prediction, with the artificial neural network as the method of computation. The error of prediction is usually about 5% of the absolute temperature of melting point.

Alloys Design of PdTi-Based Shape Memory Alloys Based on Defect Structures and Site Preference of Ternary Elements

Defect structures and site preference of ternary elements in B2-type PdTi alloys are evaluated in order to design PdTi-based smart materials using the pseudo-ground state analysis (or analysis performed at near zero Kelvin). It has been found that this analysis can predict types of defect structures in these alloys which are of antistructure (substitution) type regardless of alloy compositions. Substitution behavior predicted is as follows: (1) most elements belonging to groups 1A through 5A occupy Ti sites only; (2) most elements belonging to groups 6A through 8A occupy Pd sites only; and (3) the others studied occupy either sites when these sites are unfilled with the corresponding constituent elements (Pd or Ti). Moreover, effects of both offstoichiometry and 3dtransition elemental additions on martensitic transformation start temperature (MS) in PdTi alloys are evaluated as a function of electron-atom ratio (e/a). It has been found that M, is strongly related to the e/a value when 3d electrons of ternary additions are taken into account, although the effect of e/a on M, differs if their substitution behavior is different. Changes in M, per e/a are estimated to be 900 K when Pd-site substitution elements, such as Cr, Mn, Fe, Co, and Ni are added, while changes in M, per e/a are 790 K when Ti-site substitution elements such as V are added. This suggests that M, is influenced not only by the e/a value but also by atomic configurations.

Magnetic and structural studies of Fe and Ni substituted CoAl alloys

Previous work has shown that the substitution of a 3d element (Ti, V, Cr or Mn) for Al in the equiatomic intermetallic compound CoAl results in the onset of ferromagnetic order beyond a critical concentration. The systems appear magnetically and structurally similar to the equivalent CoGa substituted compounds for which the critical concentration appears to be correlated with an average electron-atom ratio rather than woth any obvious change in the crystallographic order. The present paper completes the investigation of the CoAl series by presenting results for the systems CoAl 1− x Fe x and CoAl 1− x Ni x . X-ray and pulsed neutron diffraction techniques showed that the ordered B2 (CsCl) structure is retained for both these series but for the Ni series a second phase fcc structure was also observed. The neutron diffraction data was consistent with Fe atoms occupying Al sites alone and Ni atoms occupying Co sites with a consequent displacement of Co atoms to Al sites. A striking feature is that although CoAl is paramagnetic only a small amount of Fe ( x≥0.03) produces ferromagnetic order with a subsequent rapid increase in Curie temperature (to ≈ 900 K for x=0.2). The disparity between the moments obtained from the high temperature paramagnetic and low temperature ferromagnetic regimes is suggestive of an itinerant magnetism and an analysis is attempted using spin fluctuation models of magnetism. Results for the entire series of CoAl substituted alloys are reviewed and compared with those for the related compounds of CoGa.

Composition Dependence of Bainite Morphology in Cu&amp;ndash;Zn&amp;ndash;Al Alloys

The morphology of bainite structure is examined by optical and electron microscopy for Cu–Zn–Al alloys with various compositions. It depends not only on the heat treatment for the bainite formation but also strongly on the electron atom ratio, e⁄a, and the Ms temperature of the alloy. In alloys with e⁄a smaller than 1.46, the 9R bainite plates are formed with a pair of the variants having (551) and (55\bar1) habit planes in a form of long hinge. As e⁄a increases, the numbers of bainite plates decrease with increasing the size. The trace of habit plane keeps linear until the second structural change, 9R to fcc, takes place in the plates. As the Ms temperature decreases or the aging temperature increases, this change becomes easier to take place. If e⁄a is larger than 1.46, the bainite plate is transformed with γ2 particles or a complex eutectic structure consisting of α and γ2 phases is constructed. In a specimen with e⁄a=1.47, incommensurate γ phase is observed in electron microscopy and the bainite plates are considerably smaller than those in the specimen with e⁄a=1.44. The observed morphological change due to the alloy composition is discussed by using a pseudo-binary phase diagram constructed with the form of Cu–(Znkx–Alx), where the ratio k of the atomic concentrations of Zn and Al is assumed to be unchanged.

Methods for Calculation of α-β Equilibria in Multicomponent Titanium Alloys

In order to design superplastic titanium alloys having an improved strength-density ratio, it is necessary to control the compositional and microstructural parameters such as volume fraction and degree of solid-solution strengthening for the primary a phase and electron-atom ratio for the prior β phase in titanium alloys. For that purpose, a method for calculation of α-β phase equilibria in multi-component titanium alloys, based on the analyses of a and β phase compositions, was developed by using multicomponent 20 titanium alloys. The reliability of the method was confirmed to be satisfactory by excellent agreements between the observed value and the value calculated by the method for the volume fraction of a phase and the partition ratio of each element between a and β phases in not only 20 alloys which were used to construct the method but also other 8 alloys. Furthermore, thermodynamic calculation was performed on multi-component 20 titanium alloys. The good agreements between the calculated value and the observed value for the volume fraction of α phase and the partition ratio of each element between α and β phases demonstrate that an adequately selected set of parameters can describe the thermodynamics of the α and β phases in multi-component titanium alloys.

Electronic, lattice and superconducting properties of B2 alloys V54-xRu46Osxand V54Ru46-xOsx

Electronic, lattice and superconducting properties have been studied through low-temperature specific heat on both B2 systems V54-xRu46Osx and V54Ru46-xOsx, where a cubic-to-tetragonal transformation occurs upon cooling and shows a decisive correlation with superconductivity. An increase of the parameter x in V54-xRu46Osx, where the electron-atom ratio e/a increases linearly with x causing a rise of the transformation temperature TL, lowers the electronic specific heat coefficient gamma and the superconducting transition temperature Tc, while it gives no effect on the Debye temperature theta D. In contrast, an increase of x in V54Ru46-xOsx with e/a=6.38, where no transformation occurs, causes no variation of the values of gamma , Tc and theta D. The enhancement of superconductivity, which is accompanied by a decrease in TL as e/a is lowered, is mainly attributed to an increase of the electronic density of states rather than a softening of phonon modes.

Effect of structural transformation on electronic properties of near-equiatomic V-Ru alloys

The change in electronic structure caused by the transformation from cubic to tetragonal phase has been investigated in near-equiatomic V-Ru and V-M-Ru (M=Ti, Ta) alloys through measurements of electrical resistivity, Hall coefficient and Knight shift of 51V. The absolute values of these properties in a specimen increase with the transformation, which means a decrease in the electronic density of states. The values in all the specimens are universally dependent on the electron-atom ratio Z in both cubic and tetragonal phases. This universal dependence on Z implies the validity of the rigid-band approximation. The increase in Z lowers the values in the cubic phase, while raising them in the tetragonal phase. These results suggest that the transformation is caused by the band Jahn-Teller effect.

Correlation between structural transformation and superconductivity in B2 alloys V-Ru-Os

The inter-relationship between structural transformation and superconductivity has been studied on B2 systems V54-xRu46Osx, V54Ru46-xOsx and V52Ru48-xOsx with 0<or=x<or=4. An increase of the parameter x in V54-xRu46Osx, where the electron-atom ratio e/a increases linearly with x, raises the transformation temperature TL sharply while lowering the superconducting transition temperature Tc rapidly. This is in contrast with the results for both systems V54Ru46-xOsx and V52Ru48-xOsx, where e/a is a constant independent of x. All samples in V54Ru46-xOsx with e/a=6.38 undergo no structural transformation, while showing superconductivity at nearly the same temperatures around 5 K. All samples in V52Ru48-xOsx with e/a=6.44, however, show no superconductivity, while undergoing transformation at nearly the same temperature around 200 K. Taken together, these facts confirm that both TL and Tc are completely dominated by the value of e/a; the lowering of TL, which is accompanied by a decrease of e/a, causes sharp enhancement of Tc. This provides decisive evidence for the electronic transition and its strong correlation with superconductivity.

Theory of Interplanar Interaction in Metals of Close-Packed Structures on Free Electron Model

Interplanar interactions between the hexagonal net planes in close-packed metals are discussed as a function of the electron-atom ratio on the same model that Blandin et al. used. Now the expansions are done to second order, whereas those by Blandin et al. are only to first. The second order asymptotic expansions show that the anomaly in the interplanar interactions at ≈1.140, found by Blandin et al. , disappears. These expansions are applied to evaluate approximate values of the stacking fault energy, γ SF , and the difference Δ U HF in the binding energies between HCP and FCC lattices. Comparisons of these values with those accurately calculated show that the second order expansion is a good approximation. The approximate relation γ SF ≈2 N p Δ U HF holds in =1.0∼1.2, where N p is the density of lattice points on the net plane.

Phase transformation and age-hardening of Au-Cu-Pd ternary alloys

Phase transformations in Au-Cu-Pd single-phase alloys Were studied. Age-hardening of the alloys examined vvas attributed to the formation of fine domainu of long-range ordered (LRO) AuCuI type lattice in the interior of the grain. Prolonged ageing caused formation of large LRO domains of single variant at the grain boundary or microtwinning of LRo in the interior of the grain, depending on the ordering rate of the alloy. The electron-atom ratio (e/a) of the alloy and the axial ratio (c/a) of the ordered lattice seemed to playa part in the phase transformation behaviour in this alloy system. The effectiveness of rhodium addition on the grain refining was proved experimentally. These resuRs will be helpful in developing low nobility and high corrosion resistant dental alloys.