The Biaxial Moduli of Cubic Materials Subjected to an Equi-biaxial Elastic Strain

Formulae for the biaxial moduli along the directions of principal stress for (hkl) interfaces of cubic materials are given for situations in which there is equi-biaxial strain within the plane. These formulae are relevant in the consideration of the deposition of thin films on single crystal substrates such as silicon. Within a particular (hkl), the directions defining these principal biaxial moduli are shown to be those along which there are the extreme values of the shear modulus and Poisson’s ratio. Conditions for stationary values of the biaxial moduli are also derived, from which the conditions for the global extrema of the biaxial moduli are established.This is the final version of the article. It was first available from Springer via http://dx.doi.org/10.1007/s10659-015-9558-

The Directional Dependence of Elastic Stiffness and Compliance Shear Coefficients and Shear Moduli in Cubic Materials

The mathematics associated with the representation surfaces for elastic stiffness and compliance shear coefficients and shear moduli for planes in the standard 001–011–111 stereographic triangle for cubic materials is examined as a function of the degree of anisotropy, A=2c 44/(c 11−c 12), of the material under consideration. Similarities and differences between the surfaces for the elastic stiffness and compliance shear coefficients and the shear moduli are highlighted.PRH would also like to thank the EPSRC/Rolls-Royce plc Strategic Partnership [grant number EP/H500375/1] for financial support during the course of this work.This is the final published version. It first appeared at http://link.springer.com/article/10.1007%2Fs10659-014-9506-1

Growth of devitrite, Na <inf>2</inf> Ca <inf>3</inf> Si <inf>6</inf> O <inf>16</inf>, in soda-lime-silica glass

The morphology and crystal growth of devitrite crystals nucleated heterogeneously on glass surfaces have been studied. The crystals grow as fans of needles, with each needle having a characteristic [100] growth direction with respect to the centrosymmetric triclinic unit cell. An analysis of crystal growth data reported here and a reappraisal of crystal growth data reported in prior studies suggests a best estimate of 260 kJ/mol for the activation enthalpy for the crystal growth of devitrite along [100], higher than the values previously reported.We would like to thank the Nuffield Foundation, London, U.K. for the award of an Undergraduate Bursary to RPT during the course of this workThis article (Knowles, K. M., Thompson, R. P. (2014), Growth of Devitrite, Na2Ca3Si6O16, in Soda–Lime–Silica Glass. Journal of the American Ceramic Society, 97: 1425–1433. doi: 10.1111/jace.12922) is the author accepted manuscript, which can also be found on the publisher's website at: http://onlinelibrary.wiley.com/doi/10.1111/jace.12922/abstract © 2014 The American Ceramic Societ

{1124} Deformation Twinning in Commercial Purity Titanium at Room Temperature

This is the accepted manuscript. It is currently embargoed pending publication.Definitive evidence from both electron back-scattered diffraction and transmission electron microscopy is shown for the existence of 1124 twinning as a rare deformation twinning mode in coarse grained commercial purity titanium after room temperature ballistic impact testing at 103 s−1. Non-Schmid-based twin type selection is demonstrated for 1124 and the conjugate 1122 deformation twinning modes in this material within grains where the c-axis is closely aligned to the loading direction. Limited Schmid-based twin variant selection is shown for 1124 and 1122 deformation twinning modes in this material. The occurrence of high area fractions of 1124 twinning has relevance for high strain rate plasticity modelling of grains of textured titanium compressed parallel to their c-axes.This work was supported by the Rolls-Royce plc / EPSRC strategic partnership under EP/H022309/1

Discontinuous precipitation of Co3V in a complex Co-based alloy

Discontinuous precipitation of chromium-rich Co3V lamellae has been found in a Co-based alloy containing 2 wt% V after prolonged ageing at 800 {\degr}C. This discontinuous precipitation is associated with a noticeable redistribution of alloying elements in the alloy relative to those parts of the aged alloy that preserve the c.c.p.-L12 microstructure found in the as-cast and homogenized condition. The orientation relationship between the c.c.p. Co-rich matrix and these hexagonal phase chromium-rich Co3V precipitates is shown to be || and [1 1 1]Co || , i.e. || and [1 1 1]Co || in the four-index notation. 3 × 3 transformation matrices relating directions and planes in the two phases have been established. The observed orientation relationship between the two phases is consistent with low lattice misfit between the two phases.We would also like to acknowledge the EPSRC/Rolls-Royce plc Strategic Partnership (EP/H500375/1) for funding this work.This is the author accepted manuscript. The final version can be found on the publisher's website at: http://www.tandfonline.com/doi/abs/10.1080/14786435.2013.861946#.U8fYa_ldXH

Very high strain rate deformation twinning behaviour of Ti–6Al–4V

Equiaxed fine-grained and coarse-grained samples of h.c.p. α phase Ti–6Al–4V with trace amounts of retained b.c.c. β phase were ballistically tested at room temperature. The deformed microstructures were characterised by electron back scattered diffraction. The extensive deformation twinning observed in the α phase in both samples was limited to the {1 0 -1 2} and {1 1 -2 1} tensile twinning modes. These two deformation twinning types have very different morphologies: thin {1 1 -2 1} deformation twins span multiple α phase grain boundaries, while the wider {1 0 -1 2} deformation twins are usually limited to individual grains, reorienting almost entire grains to a twinned orientation. Both {1 0 -1 2} and {1 1 -2 1} deformation twins are able to propagate across low angle α lath boundaries, but only the {1 1 -2 1} deformation twinning types can propagate across high angle α grain boundaries.This work was supported by the Rolls-Royce plc/EPSRC strategic partnership under EP/H022309/1

The Plane Strain Young’s Modulus in Cubic Materials

The orientation dependence of the plane strain Young’s modulus, $\tilde E$, of cubic materials has been analysed as a function of the direction along which a uniaxial stress is applied to a single crystal and the perpendicular direction in the single crystal along which the strain is constrained to be zero. The locus of $\tilde E$ in the plane perpendicular to the axis of uniaxial stress is shown to be a circle when this stress is applied along $\langle$111$\rangle$. For materials with anisotropy ratios A > 1, global minima in $\tilde E$ occur when the stress is applied along $\langle$001$\rangle$ and when the strain along one of the two perpendicular $\langle$100$\rangle$ directions is set to zero. Identical global maxima in $\tilde E$ are found when the stress is applied along two different families of $\langle$uuw$\rangle$ directions and the direction of zero strain is along either a perpendicular $\langle$1$\bar 1$0$\rangle$ or $\langle$ww$\bar 2$$\bar u$$\rangle$ direction. For materials with A < 1, the global maxima in $\tilde E$ occur when the stress is applied along $\langle$001$\rangle$ and when the strain along one of the two perpendicular $\langle$100$\rangle$ directions is set to zero, and identical global minima are found when the stress is applied along two different families of $\langle$uuw$\rangle$ directions and the direction of zero strain is along either a perpendicular $\langle$1$\bar 1$0$\rangle$ or $\langle$ww$\bar 2$$\bar u$$\rangle$ direction

Microstructural evolution and characterisation of interfacial phases in Al<inf>2</inf>O<inf>3</inf>/Ag-Cu-Ti/Al<inf>2</inf>O<inf>3</inf> braze joints

Alumina ceramics with different levels of purity have been joined to themselves using an active braze alloy (ABA) Ag–35.3Cu–1.8Ti wt.% and brazing cycles that peak at temperatures between 815 °C and 875 °C for 2 to 300 min. The microstructures of the joints have been studied using scanning electron microscopy, transmission electron microscopy, and energy dispersive X-ray spectroscopy. A limited number of joints prepared with the ABA Ag–26.7Cu–4.5Ti wt.% have also been studied. In terms of characterising the interfacial phases, efforts were made to understand the interfacial reactions, and to determine the influence of various brazing parameters, such as the peak temperature (Tp) and time at Tp (τ), on the microstructure. In addition, the extent to which impurities in the alumina affect the interfacial microstructure has been determined. Ti3Cu3O has been identified as the main product of the reactions at the ABA/alumina interfaces. At the shortest joining time used, this phase was observed in the form of a micron-size continuous layer in contact with the ABA, alongside a nanometre-size layer on the alumina that was mostly composed of γ-TiO grains. Occasionally, single grains of Ti3O2 were observed in the thin layer on alumina. In the joints prepared with Ag–35.3Cu–1.8Ti wt.%, the interfacial structure evolved considerably with joining time, eventually leading to a high degree of inhomogeneity across the length of the joint at the highest Tp. The level of purity of alumina was not found to affect the overall interfacial microstructure, which is attributed to the formation of various solid solutions. It is suggested that Ti3Cu3O forms initially on the alumina. Diffusion of Ti occurs subsequently to form titanium oxide at the Ti3Cu3O/alumina interface.The authors acknowledge the financial support for this study provided by AWE.This is the author accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S1359645415003791

Interfacial reactions between sapphire and Ag-Cu-Ti-based active braze alloys

The interfacial reactions between two commercially available Ag–Cu–Ti-based active braze alloys and sapphire have been studied. In separate experiments, Ag– 35.3Cu–1.8Ti wt.% and Ag–26.7Cu–4.5Ti wt.% alloys have been sandwiched between pieces of R-plane orientated sapphire and heated in argon to temperatures between 750 and 900 °C for 1 min. The phases at the Ag–Cu– Ti/sapphire interfaces have been studied using selected area electron diffraction, energy dispersive X-ray spectroscopy and electron energy loss spectroscopy. Gradual and subtle changes at the Ag–Cu–Ti/sapphire interfaces were observed as a function of temperature, along with the formation of a transient phase that permitted wetting of the sapphire. Unequivocal evidence is shown that when the active braze alloys melt, titanium first migrates to the sapphire and reacts to dissolve up to ~33 at.% oxygen, forming a nanometre-size polycrystalline layer with a chemical composition of Ti₂O₁₋ₓ (x<<1). Ti₃Cu₃O particles subsequently nucleate behind the Ti₂O₁₋ₓ layer and grow to become a continuous micrometre-size layer, replacing the Ti₂O₁₋ₓ layer. Finally at 845 °C, a nanometre-size γ-TiO layer forms on the sapphire to leave a typical interfacial structure of Ag–Cu/Ti₃Cu₃O/γ-TiO/sapphire consistent with that seen in samples of polycrystalline alumina joined to itself with these active braze alloys. These experimental observations have been used to establish a definitive bonding mechanism for the joining of sapphire with Ag–Cu alloys activated by small amounts of titaniumWe are grateful for the financial support for this study provided by AWE.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.actamat.2015.11.01