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The use of inoculants added to precursor powder is a method of influencing grain growth during fabrication. Niobium carbide (NbC) particles have been added to IN718 gas atomised powder for additive manufacturing via laser-blown-powder directed-energy-deposition (LBP-DED). The collected data in this study reveals the effects of the NbC particles on the grain structure, texture and elastic properties, and oxidative properties of LBP-DED IN718 in the As-DED and heat-treated conditions. The microstructure was investigated using X-ray diffraction (XRD), scanning electron microscopy (SEM) coupled with electron backscattered diffraction (EBSD), and transmission electron microscopy (TEM) coupled with energy dispersive X-ray spectroscopy (EDS). Resonant ultrasound spectroscopy (RUS) is used to measure the elastic properties and phase transitions during standard heat treatments. Thermogravimetric analysis (TGA) is used to probe the oxidative properties at 650 °C.

Ti-Nb based alloys are of commercial importance due to their damping capabilities via a superelastic transformation. However, the starting microstructure of these alloys is often not consistent between studies, even when produced via a nominally comparable methodology, which has the potential to limit the reversibility of the transformation. As such, samples were produced to investigate whether the thickness of the material influenced the microstructures and behaviours seen. It was shown that a single-phase layer exists close to the surface of a two-phase microstructure, and that in very thin material, this can span across the whole sample, promoting more recoverable transformation behaviour. This is important as it not only rationalises discrepancies in the literature, but may also influence component geometries necessary for industrial application.

Numerous challenges persist with the additive manufacturing of high γ′ containing Ni-based superalloys such as CM247LC. Currently, significant cracking occurs during deposition of CM247LC components using laser powder bed fusion and during post-processing. Whilst post-deposition procedures seek to eliminate or minimise cracks, current procedures do not produce a microstructure suitable for service. This study systematically investigates the microstructural evolution of CM247LC manufactured using laser powder bed fusion following multiple post processing treatments. Phase and textural changes after each processing step were consistent with previous studies, although an additional Hf-rich and Cr-depleted segregation zone was identified along intercellular boundaries in the as-deposited condition, believed to be associated with the cracking propensity. Compositional modification of CM247LC including removal of Hf, reduction of C and addition of Nb eliminated the segregation zone but these changes were associated with an increased susceptibility to solidification and liquation cracking.

The bulk-boundary correspondence relates topologically-protected edge modes to bulk topological invariants, and is well-understood for short-range free-fermion chains. Although case studies have considered long-range Hamiltonians whose couplings decay with a power-law exponent $\alpha$, there has been no systematic study for a free-fermion symmetry class. We introduce a technique for solving gapped, translationally invariant models in the 1D BDI and AIII symmetry classes with $\alpha>1$, linking together the quantized winding invariant, bulk topological string-order parameters and a complete solution of the edge modes. The physics of these chains is elucidated by studying a complex function determined by the couplings of the Hamiltonian: in contrast to the short-range case where edge modes are associated to roots of this function, we find that they are now associated to singularities. A remarkable consequence is that the finite-size splitting of the edge modes depends on the topological winding number, which can be used as a probe of the latter. We furthermore generalise these results by (i) identifying a family of BDI chains with $\alpha, Comment: Simplified treatment of singularities. Additional results and discussion

Ti-Nb-based alloys undergo a martensitic transformation that gives rise to superelastic and shape memory behaviours over a wide range of temperatures. The design of such alloys for industrial applications is commonly based around the reported martensite start temperature for a given composition. However, there are significant variations in these values within the literature that remain unexplained using current thermally driven transformation theories. Recently, a marked difference in the transformation behaviour of Ti-24Nb (at.%) in the cold rolled and solution treated conditions has been reported and a stress based mechanism has been postulated to rationalise these results. Here, the veracity of this stress based theory has been investigated through in situ studies of the transformation behaviour of Ti-24Nb (at.%) in the cold rolled condition using synchrotron X-ray diffraction. Upon heating to 350˚C, all αʺ initially present reverted to the β phase by ~ 300˚C. When cooled from 350˚C, thermally induced martensite was observed below ~ 270˚C and the intensity of the αʺ peaks increased as the temperature decreased. When loaded at temperatures between -150 and 30˚C, further transformation was observed to occur immediately upon the application of a stress. However, critically, αʺ under load was always found to be reversible upon unloading, despite being up to 420˚C below the observed martensite start temperature. This behaviour cannot be accounted for through conventional thermally driven transformation theories for these alloys. Comparison of the stress-strain curves for cold rolled and solution heat treated condition material indicated that their behaviours were similar but offset by a value equivalent to the difference in the critical transformation stress. This offset is readily explained by the total stress-based mechanism proposed and provides further evidence as to its fidelity.

Superelastic alloys, such as those based on Ti2448 (Ti-24Nb-4Zr-8Sn wt%) have potential to be used in vibration damping systems in the aerospace industry. However, the accumulation of strain on superelastic load cycling, which can additionally be shown to depend on the cooling rate from the  phase, is not well characterised or understood and, as such, limits industrial acceptance. This study aims to rationalise the mechanical behaviour of Ti2448 for three sample conditions and suggests a mechanism to explain the evolution of this behaviour with mechanical cycling. By understanding the mechanisms that govern the mechanical response of these materials, alloys can be more specifically designed and processed to achieve the properties desired for industrial applications.

The symmetry-resolved R\'enyi entanglement entropy is the R\'enyi entanglement entropy of each symmetry sector of a density matrix $\rho$. This experimentally relevant quantity is known to have rich theoretical connections to conformal field theory (CFT). For a family of critical free-fermion chains, we present a rigorous lattice-based derivation of its scaling properties using the theory of Toeplitz determinants. We consider a class of critical quantum chains with a microscopic U(1) symmetry; each chain has a low energy description given by $N$ massless Dirac fermions. For the density matrix, $\rho_A$, of subsystems of $L$ neighbouring sites we calculate the leading terms in the large $L$ asymptotic expansion of the symmetry-resolved R\'enyi entanglement entropies. This follows from a large $L$ expansion of the charged moments of $\rho_A$; we derive $tr(e^{i \alpha Q_A} \rho_A^n) = a e^{i \alpha \langle Q_A\rangle} (\sigma L)^{-x}(1+O(L^{-\mu}))$, where $a, x$ and $\mu$ are universal and $\sigma$ depends only on the $N$ Fermi momenta. We show that the exponent $x$ corresponds to the expectation from CFT analysis. The error term $O(L^{-\mu})$ is consistent with but weaker than the field theory prediction $O(L^{-2\mu})$. However, using further results and conjectures for the relevant Toeplitz determinant, we find excellent agreement with the expansion over CFT operators., Comment: 20 pages + appendix

Refractory metal high entropy superalloys (RSA) are being developed for high temperature structural applications. However, recently the microstructures of several RSA have been shown to be unstable, precipitating potentially deleterious intermetallic phases during prolonged exposure at elevated temperatures. For such instability to be acceptable it is necessary for the intermetallic phase formation to be sufficiently sluggish so as to not compromise alloy performance over the time scales likely to be experienced in service. However, the rate of intermetallic phase formation in RSA are not yet known. To address this issue, here, two quaternary Al-Ta-Ti-Zr refractory superalloys that contain all of the key microstructural features of more compositionally complex RSA have been studied following exposures of 1, 10 and 100 hours at temperatures between 700 and 900˚C and compared to those previously obtained following 1000 hour exposures. Critically, needles of an Al-Zr-rich intermetallic phase were observed following only 1 hour exposure at 900˚C, demonstrating rapid formation kinetics. Furthermore, the microstructures continued to coarsen from 100 to 1000 hours, indicating low morphological stability. Higher Al content increased both the prevalence of the Al-Zr-rich intermetallic phase and raised the solvus of the desirable B2 phase. Consequently, this work highlights additional challenges in RSA development for elevated temperature applications.

Quantification of local lattice strain is essential for enhancing our understanding of structure-property relationships, particularly for high entropy alloys; but no common framework currently exists, with a number of possible quantifications in the literature. Here, local static and dynamic displacements are discussed, and different methods of describing their statistical dispersion presented. Similarly, the type of distribution measured, either offsite displacements or bond length, is considered alongside the different experimental and modelling techniques that can yield these distributions. This leads to a suggested numerical quantification for local lattice strain, to enable cross comparison between alloy systems using data obtained from different methodologies.

The equiatomic CrMnFeCoNi alloy exhibits many desirable properties, but its susceptibility to the formation of embrittling intermetallic phases, makes it unsuitable for structural applications at elevated temperatures. As a result, there is an interest in developing alternative alloys from the CrMnFeCoNi system which avoid this limitation. Here we present a detailed study of phase stability in a CrMnFexCoNi series of alloys, where x = 0, 0.5, 1.5 (in atomic ratio), following long-duration heat treatments of 1000 h at 900 and 700˚C, and up to 5000 h at 500˚C. Each alloy was single phase fcc following homogenisation. After exposure at 900˚C, large σ phase precipitates were present in the CrMnCoNi alloy, but alloys containing ≥ 0.5 Fe remained single phase fcc. At 700˚C, the alloys investigated all contained the σ phase, Cr-bcc precipitates were also present in the CrMnCoNi and CrMnFe0.5CoNi alloys and Cr carbide precipitates featured in the CrMnFe1.5CoNi alloy. Heat-treatment of the CrMnCoNi alloy at 500˚C caused a partial bulk decomposition of the fcc matrix, which produced a fine-scale intergrowth of phases: σ, NiMn-L10, Cr-bcc and a secondary solute-depleted fcc phase. In the alloy containing 0.5 Fe, cellular regions consisting of a NiMn-L10, Cr-bcc and solute-depleted matrix phase, developed along the grain boundaries. NiMn-L10 and Cr-rich precipitates also formed on grain boundaries in the 1.5 Fe alloy. From these experimental observations, it was clearly established that Fe stabilises the fcc matrix relative to the σ and bcc phases.

Superelastic Ti alloys have potential across a wide range of industrial sectors, but each application requires specifically tailored transformation behaviour. Composition is well known to influence transformation properties but for a given alloy, the effect of microstructural features, such as grain size, is far less clear. Within the literature, no consistent relationship between grain size and key parameters, such as the transformation stress, SIM, exist. This lack of clarity is a major barrier to engineering uptake of these materials. Therefore, in the present work, the transformation behaviour of Ti-24Nb-4Sn-8Zr (wt%) from two different starting stocks has been studied, with grain sizes varied by changing solution heat treatment time. Irrespective of the material stock, SIM was shown not to vary as a function of grain size. As such, this observation is believed to be a general effect, and as a result, microstructures can be tailored to improve other parameters such as yield stress, without altering the transformation behaviour.

The recently developed refractory metal high entropy superalloys (RSA) have been proposed as novel materials for high temperature service. A key requirement of any material used in such applications is to retain its properties throughout the life of a component. Consequently, it is critical that the microstructures that give rise to these properties are stable across the temperature ranges experienced in service, yet, at present, very little is known about the microstructural stability of RSA. To address this issue, here we report on the microstructural evolution of two alloys from the AlMoNbTaTiZr RSA system following long duration thermal exposures of 1000 h at 1200, 1000 and 800 ˚C. At these temperatures, the initial microstructures were found to be unstable, forming new intragranular precipitates. In AlNbTa0.5TiZr0.5, both Al-Zr hexagonal and Al-Nb rich orthorhombic phases were observed following exposure at 1200 and 1000˚C, whilst additional fine scale phases were found to have formed following exposure at 800˚C. In AlMo0.5NbTa0.5TiZr0.5, the Al-Zr phase was observed to precipitate within the grains following exposure at both 1200 and 1000˚C. A refractory metal-rich secondary bcc phase was observed following exposure at 1000˚C and 800˚C and a Zr-rich phase precipitated at 800˚C. The formation of these additional phases would undoubtedly affect the properties of these alloys, altering their in-service performance. Consequently, these results highlight the need to consider microstructural stability in the future development of RSA and to gain an enhanced understanding of the phase equilibria of these systems.

We construct new families of spin chain Hamiltonians that are local, integrable and translationally invariant. To do so, we make use of the Clifford group that arises in quantum information theory. We consider translation invariant Clifford group transformations that can be described by matrix product operators (MPOs). We classify the translation invariant Clifford group transformations that consist of a shift operator and an MPO of bond dimension two -- this includes transformations that preserve locality of all Hamiltonians; as well as those that lead to non-local images of particular operators but nevertheless preserve locality of certain Hamiltonians. We characterise the translation invariant Clifford group transformations that take single-site Pauli operators to local operators on at most five sites -- examples of Quantum Cellular Automata -- leading to a discrete family of Hamiltonians that are equivalent to the canonical XXZ model under such transformations. For spin chains solvable by algebraic Bethe Ansatz, we explain how conjugating by a matrix product operator affects the underlying integrable structure. This allows us to relate our results to the usual classifications of integrable Hamiltonians. We also treat the case of spin chains solvable by free fermions., Comment: Revised discussion of R-matrix and Yang-Baxter algebra in transformed models. Other minor changes and additional references added. 23 pages + appendix

The effect of Co:Ni ratio on the oxidation performance of γ-γ' alloys based on the (Ni,Co)75Al5Ti5Cr15 system (at.%) was investigated. Seven model superalloys of Co concentration 0, 9, 19, 28, 38, 47 and 56 at.% underwent isothermal oxidation in air at 800°C using both box-furnace exposure (1000 hours) and thermogravimetric analysis (100 hours). Following 1000 hours oxidation at 800°C, alloys containing 28, 38 and 47 at.% Co exhibited a flatter, more compact external scale and Cr2O3 layer as well as reduced oxygen ingress compared with alloys of lower Co content. The alloy containing 47 at.% Co exhibited two distinct morphologies.

Degradation of the mechanical integrity of cobalt-based superalloys can occur as the carbide network is progressively oxidised during high temperature service. In this study, a heat-treatment aimed at redistributing the carbides was tested on two similar commercial Co-based superalloys, one with high C content (Co-101) and one with low C content (Stellite-21), to determine its influence on oxidation resistance. It was found that the carbide phases in the lower C-containing alloy could be solutioned more readily than the higher C-containing alloy, enabling the continuity of the carbide network to be reduced. This resulted in a reduced attack of the carbides down the interdendritic channels during oxidation testing, but increased thickness of the oxide overscale.

The formation of non-equilibrium and transient phases in metastable beta titanium alloys during low temperature thermal treatments is currently of great interest, as they provide a potential method of controlling the size and distribution of the equilibrium alpha phase and, hence, the resulting mechanical properties. Here, for the first time, we report on the formation of a new, B2 structured phase in the Ti-Mo system. The phase was observed in electron transparent material during in situ, and following ex situ, heat treatment at 300 °C. The B2 phase was enriched in Mo compared to the surrounding matrix material and formed in regular arrays of approximately square cross-section particles interspersed by thin beta channels. Electron diffraction indicated that the lattice parameter of this new phase was smaller than that of the parent phase, leading to significant strain in the beta channels. Critically, the B2 phase was only observed in material that had been electro-polished prior to heat treatment, and, therefore, it is hypothesised that this phase forms as a result of the preparation method and thin foil effects.

Refractory metal high entropy superalloys (RMHES) offer potentially superior strength at elevated temperatures and lower densities than Ni-based superalloys. However, concerns exist over their ductility as their microstructures comprise fine distributions of refractory metal solid solution precipitates within a Zr- and Ti-rich ordered matrix. Consequently, identifying methodologies to invert this arrangement is critical. Here, we show that removal of Al from the AlMo0.5NbTa0.5TiZr RMHES, enables a microstructure to be obtained comprising Zr-Ti-rich disordered precipitates within a refractory metal matrix. This observation represents a significant development for the field and may help guide future alloy design.

The development of refractory metal high entropy superalloys has received great interest due to their potential for high temperature structural applications. The formation of a two phase nanoscale microstructure, comprising bcc and ordered B2 phases, is thought to be fundamentally linked to the presence of Al. As such, determining the influence of Al concentration on the microstructural formation and thermal stability of these novel materials is critical for future alloy development. To elucidate this effect, the microstructural evolution of a series of alloys with systematically varying compositions from the Ti-Ta-Zr-Alx system have been studied following homogenisation and long term exposures at 1100, 900 and 700˚C. Nanoscale cuboidal morphologies were observed in all alloys, but ordering was only observed when the bulk Al content was > 5 at.%. These results indicated that a common formation mechanism, thought to be spinodal decomposition, occurred prior to any B2 ordering. The results also showed that the B2 phase was only stable to relatively moderate temperatures, < 900˚C, eliminating order hardening as a high temperature strengthening mechanism. In addition, for the alloy with the greatest Al content, deleterious intragranular Al-Zr-rich intermetallics were observed following the long duration thermal exposures.

Ti-Nb based β-Ti alloys are a promising new class of superelastic, shape-memory, and low-modulus materials for a wide range of applications. A critical phase in β-Ti alloys is the ω phase, which greatly affects the mechanical properties and superelastic/shape-memory behaviour of these materials. Zirconium, an important alloying constituent in many β-Ti alloys, is generally regarded as an ω suppressant, but the body of evidence supporting this view is unconvincing and includes a number of conflicting reports. In this article, the role of Zr on ω phase formation in Ti-Nb alloys is clarified using X-ray diffraction, transmission electron microscopy, and atom-probe tomography. Zirconium additions were found to suppress the formation of athermal ω phase upon quenching from high temperature. However, up to 8 at.% Zr additions to a Ti-24 at.% Nb alloy had little effect on the formation of isothermal ω phase following aging at 300 °C after 100 hours. Furthermore, the isothermal ω precipitates were found to be strongly depleted in Nb but only weakly depleted in Zr. These results challenge the belief that Zr suppresses isothermal ω formation in β-Ti alloys, a result that is likely to be applicable beyond the Ti-Nb system considered here and information that can be used to assist in the design of future β-Ti alloys.

The almost limitless variations in potential compositions of high entropy alloys necessitates the use of computational methods when attempting to optimise for any given application. However, the accuracy of the current thermodynamic approaches commonly being used for this purpose remains under debate, as relatively few validatory studies have been performed. Within the CrMnFeCoNi family of alloys, the formation of the σ phase and how it is influenced by compositional variations is of particular interest for elevated temperature structural applications. Here, the role of Ni on the formation of the σ phase has been studied through a systematic series of CrMnFeCoNix alloys, 0 ≤ x ≤ 1.5, following 1000 hour exposures at temperatures typically found to promote σ formation. Ni was found to have a significant effect on the phase stability of these alloys, suppressing the σ phase such that a single solid solution phase was the only stable phase in the CrMnFeCoNi1.5 alloy, whilst the CrMnFeCo alloy formed the σ phase during solidification. The corresponding thermodynamic predictions varied dramatically from the experimentally observed microstructures, indicating that the underlying databases require further optimisation. Interestingly, it was found that a relatively simple electronic structure based approach, New PhaComp, provided much more accurate predictions of the observed σ phase formation in the CrMnFeCoNix and CrMnxFeCoNi systems and could be manipulated to obtain σ formation temperatures. As such, this method could be extremely useful to those wanting to design CrMnFeCoNi high entropy alloys that are free from the σ phase.

The microstructural stability of nickel-based superalloys is critical for maintaining alloy performance during service in gas turbine engines. In this study, the precipitate evolution in a model polycrystalline Ni-based superalloy during aging to 1000 hours has been studied via transmission electron microscopy, atom probe tomography and neutron diffraction. Variations in phase composition and precipitate morphology, size and volume fraction were observed during aging, whilst the constrained lattice misfit remained constant at approximately zero. The experimental composition of the γ matrix phase was consistent with thermodynamic equilibrium predictions, whilst significant differences were identified between the experimental and predicted results from the γʹ phase. These results have implications for the evolution of mechanical properties in service and their prediction using modeling methods.

Recent research has identified compositions of nickel-based superalloys with microstructures containing appreciable and comparable volume fractions of γ′ and γ″ precipitates. In this work, an alloy capable of forming such a dual-superlattice microstructure was subjected to a range of thermal exposures between 873 and 1173 K (600 and 900 ˚C) for durations of 1 to 1000 hours. The microstructures and nature of the precipitating phases were characterised using synchrotron X-ray diffraction and electron microscopy. These data have enabled the construction of a T-T-T diagram for the precipitating phases. Hardness measurements following each thermal exposure have identified the age-hardening behaviour of this alloy and allowed preliminary mechanical properties to be assessed.

The fcc phase of the equiatomic high entropy alloy, CrMnFeCoNi, has been recently shown to be unstable at temperatures below 800˚C. However, the stability of the constituent CrFeCoNi quaternary alloy, which forms the basis of many other high entropy systems, remains under debate and the existing literature contains very little long duration heat treatment data. Here, the phase equilibria of CrFeCoNi and CrMn0.5FeCoNi are assessed following 1000 hour exposures at 500, 700 and 900˚C. Prior to thermal exposure the cast alloys were homogenised and shown to exist as single phase fcc solid solutions. In line with previous reports, Cr rich particles were observed on the grain boundaries following the prolonged exposures but detailed electron microscopy showed that these features were M23C6 carbides resulting from the unintentional incorporation of C during production. However, no evidence was found for any other phase formation during the heat treatments of either alloy, in direct contrast to the results for CrMnFeCoNi. Consequently, it is concluded that, within the limits of the temperature and times considered, the solid solution phases of both CrFeCoNi and CrMn0.5FeCoNi are stable and that Mn has a destabilising influence when present at sufficient concentrations. This change in behaviour occurs for a Mn content between 11.1 and 20 at.%.

Improving the efficiency of gas turbine engines requires the development of new materials capable of operating at higher temperatures and stresses. Here, we report on a new polycrystalline nickel-base superalloy that has exceptional strength and thermal stability. These properties have been achieved through a four-element composition that can form both gamma prime and gamma double prime precipitates in comparable volume fractions, creating an unusual dual-superlattice microstructure. Alloying studies have shown that further property improvements can be achieved, and that with development such alloys may be suitable for future engine applications.

Alloys with fine-scale eutectic microstructures comprising Ti-based A2 and TiFe B2 phases have been shown to have excellent mechanical properties. In this study, the potential of alloys with further refined A2-B2 microstructures formed through solid-state precipitation has been explored by analyzing a series of six alloys within the Fe-Mo-Ti ternary system. Partial isothermal sections of this system at 1173 K (900 °C) and 1023 K (750 °C) were constructed, from which the ternary solubility limits of the A2 (Ti, Mo), B2 TiFe, D8$_5$ Fe$_7$Mo$_6$ , and C14 Fe$_2$Ti phases were determined. With these data, the change in solubility of Fe in the A2 phase with temperature, which provides the driving force for precipitation of B2 TiFe, was determined and used to predict the maximum potential volume fraction of B2 TiFe precipitates that may be formed in an A2 (Ti, Mo) matrix.

Alloys with fine-scale eutectic microstructures comprising Ti-based A2 and TiFe B2 phases have been shown to have excellent mechanical properties. In this study, the potential of alloys with further refined A2-B2 microstructures formed through solid-state precipitation has been explored by analyzing a series of six alloys within the Fe-Mo-Ti ternary system. Partial isothermal sections of this system at 1173 K (900 °C) and 1023 K (750 °C) were constructed, from which the ternary solubility limits of the A2 (Ti, Mo), B2 TiFe, D85 Fe7Mo6, and C14 Fe2Ti phases were determined. With these data, the change in solubility of Fe in the A2 phase with temperature, which provides the driving force for precipitation of B2 TiFe, was determined and used to predict the maximum potential volume fraction of B2 TiFe precipitates that may be formed in an A2 (Ti, Mo) matrix.

The elastic moduli and acoustic loss behaviour of Ti-6Al-4V (wt.%) in the temperature range 5–298 K have been studied using Resonant Ultrasound Spectroscopy. A peak in the acoustic dissipation was observed at 160 K within the frequency range 250–1000 kHz. Analysis of the data acquired in this study, coupled with complementary data from the literature, showed that this was consistent with a Snoek-like relaxation process with an associated activation energy of 23 3 kJ mol$^{−1}$. However, the loss peak was broader than would be expected for a Snoek-like relaxation, and the underlying process was shown to have a spread of relaxation times. It is suggested that this effect arises as a result of variations in the strain experienced by the β phase due to different local microstructural constraint by the bounding secondary α phase.

In this study, we have used in-situ micro-Laue diffraction combined with micropillar compression of focused ion beam milled Al13Co4 complex metallic alloy to investigate the evolution of deformation in Al13Co4. Streaking of the Laue spots shows that the onset of plastic flow occurs at stresses as low as 0.8 GPa, although macroscopic yield only becomes apparent at 2 GPa. The measured misorientations, obtained from peak splitting, enable the geometrically necessary dislocation density to be estimated as 1.1 × 1013m-2.

The phase evolution of an Al₀.₅CrFeCoNiCu High Entropy Alloy has been characterised following isothermal exposures between 0.1 and 1000 hours at temperatures of 700, 800 and 900˚C. The NiAl based B2 phase formed extremely quickly, within 0.1 hours at the higher exposure temperatures, whilst the Cr-rich σ phase formed more slowly. The solvus temperatures of these two phases were found to be ~ 975 and ~ 875˚C respectively. Compilation of the data presented here with results previously reported in the literature enabled the production of a time-temperature-transformation diagram, which clearly indicates that the diffusion kinetics of this material cannot be considered sluggish.

An isothermal section of the Fe-Mo-Ti ternary system at 1000 °C has been constructed using data acquired from a series of seven alloys. The limit of solubility of Fe in the continuous A2 phase field between Ti and Mo has been determined, as have the extents to which Mo may be accommodated in the B2 TiFe phase, and Ti in the D8$_5$ Fe$_7$Mo$_6$ phase. The B2, D8$_5$ and C14 Fe$_2$ (Ti, Mo) intermetallics were found to have limited tolerance for non-stoichiometric compositions. The positions of the A2 + B2 + C14 and A2 + C14 + D8$_5$ three-phase fields were determined, along with the extents of the A2 + B2, A2 + D8$_5$, A2 + C14, C14 + B2 and C14 + D8$_5$ two-phase fields. No ternary phases were observed in any of the alloys studied.

The effect of cooling rate on the microstructural evolution of Al0.5CrFeCoNiCu has been studied using differential scanning calorimetry and scanning electron microscopy. As-cast Al0.5CrFeCoNiCu contained three phases; Cr-Fe-Co-Ni solid solution dendrites, Cu-rich interdendritic material and L12 precipitates. During cooling at rates between 10 and 50˚C.min-1 , an additional exothermic event, at ~1010˚C, was observed in the heat flow curves. Microstructural examination after cooling revealed the presence of two distinct populations of intragranular precipitates not present in the as-cast material. Energy dispersive X-ray spectroscopy indicated that Cu-rich precipitates formed within the dendrites, whilst a Cr-Fe-Co rich phase formed in the interdendritic constituent. Precipitation during cooling at rates approaching 1˚C.s-1 indicates that the diffusion kinetics of Al0.5CrFeCoNiCu are not, as previously suggested, sluggish.

The high-entropy alloy Al0:5CrFeCoNiCu has been shown to consist of two stable, face-centred cubic solid solutions at temperatures approaching its solidus; one rich in Cr, Fe, Co & Ni (dendritic) and the other rich in Cu (interdendritic). Whilst some studies have suggested that the high-temperature microstructure may be metastably retained to room temperature through rapid cooling, evidence of phase decomposition has also been reported. In this study, fine-scale precipitation has been observed in samples of Al0:5CrFeCoNiCu that have been rapidly cooled after casting, and water quenched following ageing for 1000 h at 1000°C. Contrary to previous reports, in the as-cast state, the two face- centred cubic phases, as well as an L12 phase, were found in both dendritic and interdendritic areas, with the dendritic areas having undergone a spinodal decomposition. After ageing and quenching, L12 precipitates were found in both dendritic and interdendritic areas, and precipitates of the Cr-, Fe-, Co- and Ni-enriched face-centred cubic phase were found in the Cu-rich interdendritic regions. Given the nature of the heat treatments applied, the results suggest that precipitation in the alloy is rapid and cannot be avoided, even when the material is cooled quickly to room temperature.

The extent to which configurational entropy can stabilise a single solid solution in an Al0.5CrFeCoNiCu high entropy alloy has been assessed through characteristion of samples following casting and heat treatment at 1000 C. At temperatures between 1000 C and the onset of melting, the alloy was shown to be within a two phase field and these phases were stable following prolonged exposure at elevated temperature. X-ray and transmission electron diffraction indicated that both constituent phases had an fcc structure. Therefore, these phases share a Gibbs energy curve that must contain two local minima at the solidus temperature, rather than the single minimum required for a continuous solid solution. These observations indicate that there is no temperature at which this material is in a stable, solid state single phase field and that therefore, the configurational complexity is insufficient to stabilise a solid solution phase against enthalpic effects.

The influence of Al:Nb ratio on the microstructure and properties of Ni–Cr–Al–Nb alloys has been investigated following long-term exposure at elevated temperatures. The γ′ volume fraction, size and lattice misfit were seen to increase with a larger Al:Nb ratio, although these changes resulted in reduced hardness. The change in the critical resolved shear stress (CRSS) associated with strong dislocation coupling was determined to be the dominant strengthening mechanism and increased with decreasing Al:Nb ratio. A distribution of tertiary γ′ was observed to be necessary in maximising the mechanical properties of these alloys.

The phase equilibria of an Al0.5CrFeCoNiCu High Entropy Alloy has been studied following 1000 h exposures at 700, 850 and 1000 °C. Above1000 °C, the material comprised of two fcc solid solutions, one a multi-element phase and the other a Cu rich phase. Below 1000 °C, the fcc phases persisted, but were accompanied by the formation of two intermetallic compounds. In contrast to previous reports, the L12 phase was also found to precipitate through a solvus at ~850 °C. The results indicated that a solid state single phase field does not exist in this material at any temperature and all of the observed phases could be rationalised with reference to existing phase diagrams. This suggests that configurational entropy does not overcome the enthalpic contribution to the Gibbs energy, which governs phase equilibria of this alloy.

The assumption that large mammal hunting and scavenging are economically advantageous to hominid foragers is examined in the light of data collected among the Hadza of northern Tanzania. Hadza hunters disregard small prey in favour of larger forms (mean adult mass greater than or equal to 40 kg). Here we report experimental data showing that hunters would reduce their mean rates if they included small animals in the array they target. Still, daily variance in large animal hunting returns is high, and the risk of failure correspondingly great, significantly greater than that associated with small game hunting and trapping. Sharing large kills reduces the risk of meatless days for big game hunters, and obviates the problem of storing large amounts of meat. It may be unavoidable if large carcasses cannot be defended economically against the demands of other consumers. If so, then large prey are common goods. A hunter may gain no consumption advantage from his own big game acquisition efforts. We use Hadza data to model this 'collective action' problem, and find that an exclusive focus on large game with extensive sharing is not the optimal strategy for hunters concerned with maximizing their own chances of eating meat. Other explanations for the emergence and persistence of this practice must be considered.

Superelastic alloys based on Ti-Nb have potential in the aerospace sector for vibration damping applications, due to their wide mechanical hysteresis and tuneable properties. However, their uptake is currently limited by functional fatigue, whereby a degradation in properties is seen on cyclic loading. To understand the mechanisms that underpin this change in behaviour, a combination of ex situ and in situ testing was used to characterise the evolution of the mechanical response in a commercial Ti-Nb based alloy. It was found that the behaviour of these materials changes via a two-step mechanism, driven by the accumulation of transformation related defects and their associated stress fields. This understanding rationalises many discrepancies within the literature and highlights how the overall shape of the load response of these alloys is dominated by changes occurring only in specific regions of the material.

In this study, the effects of NbC inoculants on the elastic properties and microstructure of laser blown powder-directed energy deposition (LBP-DED) IN718 are investigated. The addition of the NbC particles increased the volume fraction of MC-type carbides and decreased that of the Laves phase. It was found that the inoculant containing samples exhibited a marginally increased hardness and an enhanced Brass texture component {110} . The occurrence of this textural enhancement is theorised to be a result of the NbC restricting dendritic growth along specific directions during build. The addition of the inoculant therefore offers a method of achieving a degree of microstructural and textural control during additive manufacturing

Metastable β titanium alloys, such as Ti-24Nb-4Zr-8Sn, have potential for application in vibration damping systems due to their ability to display superelastic behaviour. However, their use is currently limited due to large variations in the temperature range over which this behaviour is stable, which can additionally be shown to depend on the thermal history of the sample. This study demonstrates the sensitivity of the microstructure to thermal history and highlights a possible cause for this variability. Currently held theories of ω formation supressing the martensitic transformation have been called into question and an alternative mechanism based on a total stress approach has been suggested. Understanding this variability enables better design of alloys and processing routes in order to achieve materials with the desired properties required for industrial application.