On the design and feasibility of refractory metal-base Superalloys

Over the last 60 years, the evolution of nickel-base superalloys has enabled successive generations of gas turbine engines to operate at progressively higher temperatures. However, despite continued research activity, capability enhancement has become incremental and it seems unlikely that nickel-base superalloys will be able to support the requirements of future engine designs. Therefore, to enable a step change in operating temperatures, it is necessary to identify and develop new alloy systems, which, in addition to higher temperature capability, also have the correct balance of mechanical and environmental properties. Here, we outline an alloy design philosophy and report on the initial characterisation of one of the potential alloy systems. High temperature properties are dominated by the melting temperature and crystal structure of the principal element. Thus, only 11 elements offer capability above that of nickel-base alloys. However, if terrestrial abundance and cost are also considered, then only the bcc refractory metals remain as viable options. Intrinsic environmental resistance above 1000˚C can be afforded only by the formation of protective silica or alumina scales, requiring the incorporation of at least one of these elements in reasonable concentrations. In addition the required balance of mechanical properties is only likely to be achieved by the production of a microstructure containing a fine dispersion of small intermetallic precipitates, which have a coherent superlattice structure of solid solution matrix. The simplest materials identified by this approach are ternary refractory metal-base alloys, e.g. Ta‑Al‑Co. However, the phase equilibria of these systems, particularly in the refractory rich corners, are poorly defined. To address this issue and explore the potential of these materials, a series of alloys in the Ta-rich corner of the Ta‑Al‑Co system have been created and characterised following 500 hour heat treatments at temperatures between 1000 and 1300 ̊C. As part of this work the first conclusive evidence of a large-unit-celled Ta2AlCo phase was obtained, which may give potential for refractory metal-base superalloys

Design, characterisation and properties of Mo-Ti-Fe alloys reinforced by ordered intermetallic precipitates

Reinforcement of solid solution matrices with ordered intermetallic precipitates is known to be an effective strategy for obtaining high strength, damage tolerant alloys and has been central to the success of nickel based superalloys. This strategy has also been exploited in a number of bcc-based systems, for example in maraging steels where ferrite is strengthened by L21 (Heusler) and/or B2 structured intermetallic precipitates. However, only limited studies have explored the possibility of extending this approach to bcc alloys based on refractory metals and titanium. Recent research has shown that titanium-iron alloys comprising eutectic A2 Ti and B2 TiFe phases may be produced with strengths of over 2.5 GPa, alongside elongations to failures of ~15%. These impressive properties are thought to be a result of a fine microstructural length scale and a high lattice misfit between the phases. Here, we report on the phase equilibria in the Mo-Ti-Fe ternary system. In this system, an extensive two-phase field was identified between B2 TiFe intermetallic phase and the A2 (Ti, Mo) solid solution, that extended to Mo rich compositions. Knowledge of how this phase equilibrium varies with temperature enabled the design of alloys that could be homogenised in the single-phase solid solution and subsequently reinforced by solid state precipitates following a lower temperature heat treatment. The microstructure obtained was finer than has been produced through an invariant reaction and an initial assessment of their mechanical properties revealed substantial strength. The prospects for modifying these alloys to enable their use at higher temperatures will be discussed. This work was supported through the Rolls-Royce/EPSRC Strategic Partnership under EP/H022309/1 and EP/H500375/1, as well as the DARE project under EP/L025213/1

An assessment of the lattice strain in the CrMnFeCoNi high-entropy alloy

The formation of single phase solid solutions from combinations of multiple principal elements, with differing atomic radii, has led to the suggestion that the lattices of high-entropy alloys (HEAs) must be severely distorted. To assess this hypothesis, total scattering measurements using neutron radiation have been performed on the CrMnFeCoNi alloy and compared with similar data from five compositionally simpler materials within the same system. The Bragg diffraction patterns from all of the studied materials were similar, consistent with a face-centered cubic structure, and none showed the pronounced dampening that would be expected from a highly distorted lattice. A more detailed evaluation of the local lattice strain was made by considering the first six coordination shells in the pair distribution functions (PDF), obtained from the total scattering data. Across this range, the HEA exhibited the broadest PDF peaks but these widths were not disproportionately larger than those of the simpler alloys. In addition, of all the materials considered, the HEA was at the highest homologous temperature, and hence the thermal vibrations of the atoms would be greatest. Consequently, the level of local lattice strain required to rationalise a given PDF peak width would be reduced. As a result, the data presented in this study do not indicate that the local lattice strain in the equiatomic CrMnFeCoNi HEA is anomalously large.The authors would like to thank the EPSRC/Rolls-Royce Strategic Partnership for funding (EP/M005607/1 and EP/H022309).This is the final version of the article. It first appeared from Elsevier via https://doi.org/10.1016/j.actamat.2016.09.03

The Physical Principles of Quantum Mechanics. A critical review

The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more physically motivated formulation is discussed. The existence of non commuting observables, which characterizes quantum mechanics with respect to classical mechanics, is related to operationally testable complementarity relations, rather than to uncertainty relations. The drawbacks of Dirac argument for canonical quantization are avoided by a more geometrical approach.Comment: Bibliography and section 2.1 slightly improve

Superfluid Flow Past an Array of Scatterers

We consider a model of nonlinear superfluid flow past a periodic array of point-like scatterers in one dimension. An application of this model is the determination of the critical current of a Josephson array in a regime appropriate to a Ginzburg-Landau formulation. Here, the array consists of short normal-metal regions, in the presence of a Hartree electron-electron interaction, and embedded within a one-dimensional superconducting wire near its critical temperature, $Tc$. We predict the critical current to depend linearly as $A (Tc-T)$, while the coefficient $A$ depends sensitively on the sizes of the superconducting and normal-metal regions and the strength and sign of the Hartree interaction. In the case of an attractive interaction, we find a further feature: the critical current vanishes linearly at some temperature $T*$ less than $Tc$, as well as at $Tc$ itself. We rule out a simple explanation for the zero value of the critical current, at this temperature $T*$, in terms of order parameter fluctuations at low frequencies.Comment: 23 pages, REVTEX, six eps-figures included; submitted to PR

Quantitative analysis of bone reactions to relative motions at implant-bone interfaces

Connective soft tissues at the interface between implants and bone, such as in human joint replacements, can endanger the stability of the implant fixation. The potential of an implant to generate interface bone resorption and form soft tissue depends on many variables, including mechanical ones. These mechanical factors can be expressed in terms of relative motions between bone and implant at the interface or deformation of the interfacial material.\ud \ud The purpose of this investigation was to determine if interface debonding and subsequent relative interface motions can be responsible for interface degradation and soft tissue interposition as seen in experiments and clinical results. A finite element computer program was augmented with a mathematical description of interface debonding, dependent on interface stress criteria, and soft tissue interface interposition, dependent on relative interface motions. Three simplified models of orthopaedic implants were constructed: a cortical bone screw for fracture fixation plates, a femoral resurfacing prosthesis and a straight stem model, cemented in a bone. The predicted computer configurations were compared with clinical observations. The computer results showed how interface disruption and fibrous tissue interposition interrelate and possibly enhance each other, whereby a progressive development of the soft tissue layer can occur.\ud \ud Around the cortical bone screw, the predicted resorption patterns were relatively large directly under the screw head and showed a pivot point in the opposite cortex. The resurfacing cup model predicted some fibrous tissue formation under the medial and lateral cup rim, whereby the medial layer developed first because of higher initial interface stresses. The straight stem model predicted initial interface failure at the proximal parts. After proximal resorption and fibrous tissue interposition, the medial interface was completely disrupted and developed an interface layer. The distal and mid lateral side maintained within the strength criterion.\ud \ud Although the applied models were relatively simple, the results showed reasonable qualitative agreement with resorption patterns found in clinical studies concerning bone screws and the resurfacing cup. The hypothesis that interface debonding and subsequent relative (micro)motions could be responsible for bone resorption and fibrous tissue propagation is thereby sustained by the results

Diffeomorphisms as Symplectomorphisms in History Phase Space: Bosonic String Model

The structure of the history phase space $\cal G$ of a covariant field system and its history group (in the sense of Isham and Linden) is analyzed on an example of a bosonic string. The history space $\cal G$ includes the time map $\sf T$ from the spacetime manifold (the two-sheet) $\cal Y$ to a one-dimensional time manifold $\cal T$ as one of its configuration variables. A canonical history action is posited on $\cal G$ such that its restriction to the configuration history space yields the familiar Polyakov action. The standard Dirac-ADM action is shown to be identical with the canonical history action, the only difference being that the underlying action is expressed in two different coordinate charts on $\cal G$. The canonical history action encompasses all individual Dirac-ADM actions corresponding to different choices $\sf T$ of foliating $\cal Y$. The history Poisson brackets of spacetime fields on $\cal G$ induce the ordinary Poisson brackets of spatial fields in the instantaneous phase space ${\cal G}_{0}$ of the Dirac-ADM formalism. The canonical history action is manifestly invariant both under spacetime diffeomorphisms Diff$\cal Y$ and temporal diffeomorphisms Diff$\cal T$. Both of these diffeomorphisms are explicitly represented by symplectomorphisms on the history phase space $\cal G$. The resulting classical history phase space formalism is offered as a starting point for projection operator quantization and consistent histories interpretation of the bosonic string model.Comment: 45 pages, no figure

Phase stability of the AlxCrFeCoNi alloy system

The addition of Al to the A1 CrFeCoNi alloy has been shown to promote the formation of intermetallic phases, offering possibilities for the development of alloys with advantageous mechanical properties. However, despite numerous experimental investigations, there remain significant uncertainties as to the phase equilibria in this system particularly at temperatures below 1000°C. The present study makes a systematic assessment of the literature data pertaining to the equilibrium phases in alloys of the AlxCrFeCoNi system. Two alloys, with atomic ratios, x = 0.5 and 1.0, are then selected for further experimental investigation, following homogenisation (1200°C/72 h) and subsequent long-duration (1000 h) heat-treatments at 1000, 850 and 700°C. The Al0.5 alloy was found to be dual-phase A1 + B2 in the homogenised condition and following exposure at 1000°C but D8b phase precipitates developed following heat-treatment at the lower temperatures. In the Al1.0 alloy, B2, A2 and A1 phases were identified in the homogenised condition and at 1000°C. At 850 and 750°C, the A2 phase was replaced by the D8b phase. These experimental observations were used alongside literature data to assess the veracity of CALPHAD predictions made using the TCHEA4 thermodynamic database

Haldane's Fractional Exclusion Statistics for Multicomponent Systems

The idea of fractional exclusion statistics proposed by Haldane is applied to systems with internal degrees of freedom, and its thermodynamics is examined. In case of one dimension, various bulk quantities calculated show that the critical behavior of such systems can be described by $c=1$ conformal field theories and conformal weights are completely characterized by statistical interactions. It is also found that statistical interactions have intimate relationship with a topological order matrix in Chern-Simons theory for the fractional quantum Hall effect.Comment: 12 pages, Revtex, preprint YITP/K-107