Data on the effect of NbC inoculants on the elastic and microstructural evolution of LBP-DED IN718.

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) was 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.

Data on the occurrence of a Brass texture and elastic anisotropy in laser blown powder processed superalloy IN718.

The additive manufacturing (AM) of components through laser-blown-powder directed-energy-deposition (LBP-DED) is highly applicable to the repair of aerospace components. Fabrication of superalloys with this technique, as with other AM methods, often encounters complications that include the formation of undesired phases, irregular microstructure and texture leading to anisotropic elastic properties. Heat treatments and other post-processing techniques can be used to mitigate these issues. The collected data demonstrates the effects of different heat treatment protocols on the microstructure, elastic properties, and hardness of LBP-DED IN718. In this study eight different heat treatment were used to investigate the effects of treatment time and temperature. The microstructure was investigated through SEM, with XRD and EDX used for phase analysis. The texture was characterised using SEM coupled with EBSD and the elastic properties were determined from resonant ultrasound spectroscopy.

Strain relaxation dynamics of multiferroic orthorhombic manganites.

Resonant ultrasound spectroscopy has been used to characterise strain coupling and relaxation behavior associated with magnetic/magnetoelectric phase transitions in GdMnO3, TbMnO3and TbMn0.98Fe0.02O3through their influence on elastic/anelastic properties. Acoustic attenuation ahead of the paramagnetic to colinear-sinusoidal incommensurate antiferromagnetic transition at ∼41 K correlates with anomalies in dielectric properties and is interpreted in terms of Debye-like freezing processes. A loss peak at ∼150 K is related to a steep increase in electrical conductivity with a polaron mechanism. The activation energy,Ea, of ≳0.04 eV from a loss peak at ∼80 K is consistent with the existence of a well-defined temperature interval in which the paramagnetic structure is stabilised by local, dynamic correlations of electric and magnetic polarisation that couple with strain and have relaxation times in the vicinity of ∼10-6s. Comparison with previously published data for Sm0.6Y0.4MnO3confirms that this pattern may be typical for multiferroic orthorhombicRMnO3perovskites (R= Gd, Tb, Dy). A frequency-dependent loss peak near 10 K observed for TbMnO3and TbMn0.98Fe0.02O3, but not for GdMnO3, yieldedEa⩾ ∼0.002 eV and is interpreted as freezing of some magnetoelastic component of the cycloid structure. Small anomalies in elastic properties associated with the incommensurate and cycloidal magnetic transitions confirm results from thermal expansion data that the magnetic order parameters have weak but significant coupling with strain. Even at strain magnitudes of ∼0.1-1‰, polaron-like strain effects are clearly important in defining the development and evolution of magnetoelectric properties in these materials. Strains associated with the cubic-orthorhombic transition due to the combined Jahn-Teller/octahedral tilting transition in the vicinity of 1500 K are 2-3 orders of magnitude greater. It is inevitable that ferroelastic twin walls due to this transition would have significantly different magnetoelectric properties from homogeneous domains due to magnetoelastic coupling with steep strain gradients.

Order-disorder, ferroelasticity and mobility of domain walls in multiferroic Cu-Cl boracite.

Domain walls in Cu-Cl boracite develop as a consequence of an improper ferroelastic, improper ferroelectric transition, and have attracted close interest because some are conductive and all can be mechanically written and repositioned by application of an electric field. The phase transition and its associated dynamical properties have been analysed here from the perspective of strain and elasticity. Determination of spontaneous strains from published lattice parameter data has allowed the equilibrium long-range order parameter for F [Formula: see text]3c → Pca21 to be modelled simply as being close to the order-disorder limit. High acoustic loss in the cubic phase, revealed by resonant ultrasound spectroscopy, is consistent with the presence of dynamical microdomains of the orthorhombic structure with relaxation times in the vicinity of ∼10-5-10-6 s. Low acoustic loss in the stability field of the orthorhombic structure signifies, on the other hand, that ferroelastic twin walls which develop as a consequence of the order-disorder process are immobile on this time scale. A Debye loss peak accompanied by ∼1% elastic stiffening at ∼40 K is indicative of some freezing of defects which couple with strain or of some more intrinsic freezing process. The activation energy of ⩾∼0.01-0.02 eV implies a mechanism which could involve strain relaxation clouds around local ferroelectric dipoles or freezing of polarons that determine the conductivity of twin walls.

Bio-inspired gas sensing: boosting performance with sensor optimization guided by "machine learning".

The performance of existing gas sensors often degrades in field conditions because of the loss of measurement accuracy in the presence of interferences. Thus, new sensing approaches are required with improved sensor selectivity. We are developing a new generation of gas sensors, known as multivariable sensors, that have several independent responses for multi-gas detection with a single sensor. In this study, we analyze the capabilities of natural and fabricated photonic three-dimensional (3-D) nanostructures as sensors for the detection of different gaseous species, such as vapors and non-condensable gases. We employed bare Morpho butterfly wing scales to control their gas selectivity with different illumination angles. Next, we chemically functionalized Morpho butterfly wing scales with a fluorinated silane to boost the response of these nanostructures to the vapors of interest and to suppress the response to ambient humidity. Further, we followed our previously developed design rules for sensing nanostructures and fabricated bioinspired inorganic 3-D nanostructures to achieve functionality beyond natural Morpho scales. These fabricated nanostructures have embedded catalytically active gold nanoparticles to operate at high temperatures of ≈300 °C for the detection of gases for solid oxide fuel cell (SOFC) applications. Our performance advances in the detection of multiple gaseous species with specific nanostructure designs were achieved by coupling the spectral responses of these nanostructures with machine learning (a.k.a. multivariate analysis, chemometrics) tools. Our newly acquired knowledge from studies of these natural and fabricated inorganic nanostructures coupled with machine learning data analytics allowed us to advance our design rules for sensing nanostructures toward the required gas selectivity for numerous gas monitoring scenarios at room and high temperatures for industrial, environmental, and other applications.

Magnetoelastic properties and behaviour of 4C pyrrhotite, Fe7S8, through the Besnus transition.

Pyrrhotite, Fe7S8, is a commonly occurring carrier of magnetic remanence and has a low temperature transition, the Besnus transition, involving a change in spin state. Variations of the thermodynamic, magnetic and elastic properties through this transition at ∼33 K in a natural sample of 4C pyrrhotite have been tested against a group theoretical model for coupling between order parameters relating to Fe/vacancy ordering (irrep U 1(1/2,0,1/4)) and magnetic ordering (irreps m[Formula: see text] and m[Formula: see text]). Magnetoelastic coupling is weak but the pre-existing microstructure of ferroelastic and magnetic domains, that develop as a consequence of Fe/vacancy and ferrimagnetic ordering during slow cooling in nature (P63/mmc → C2'/c'), causes subtle changes in the low temperature transition (C2'/c' → P [Formula: see text]). The Besnus transition involves a rotation of magnetic moments out of the a-c plane of the monoclinic structure, but it appears that the transition temperature might vary locally according to whether it is taking place within the pre-existing domain walls or in the domains that they separate. Evidence of metamagnetic transitions suggests that the magnetic field-temperature phase diagram will display some interesting diversity. Low temperature magnetic transitions in minerals of importance to the palaeomagnetism community have been used to identify the presence of magnetite and haematite in rocks and the Besnus transition is diagnostic of the existence of pyrrhotite, Fe7S8.

Magnetoelastic coupling associated with vacancy ordering and ferrimagnetism in natural pyrrhotite, Fe7S8.

Magnetoelastic coupling associated with the hexagonal-monoclinic transition in a natural sample of the mineral pyrrhotite, Fe7S8, has been analysed in terms of separate coupling of spontaneous strains with two discrete order parameters, q v for Fe/vacancy ordering and q m for magnetic ordering. Coupling of the two order parameters separately with strain gives rise to two terms for coupling between them, λ [Formula: see text] and λ [Formula: see text], and a pattern of evolution in which q v varies continuously and q m discontinuously through a single transition point. The transition is ferrimagnetic and ferroelastic but the relatively slow relaxation rate for Fe/vacancy ordering, in comparison with magnetic ordering, results in elastic and anelastic properties which are quite different from those observed in other ferroic or multiferroic materials with two instabilities. Instead of classical elastic softening, there is stiffening of the elastic constants which scales with [Formula: see text] and [Formula: see text]. Instead of the normal pattern of acoustic loss associated with the mobility and subsequent freezing for ferroelastic twin walls, the loss is consistently low throughout the temperature range 300 K-875 K.

Ferroelasticity, anelasticity and magnetoelastic relaxation in Co-doped iron pnictide: Ba(Fe0.957Co0.043)2As2.

The hypothesis that strain has a permeating influence on ferroelastic, magnetic and superconducting transitions in 122 iron pnictides has been tested by investigating variations of the elastic and anelastic properties of a single crystal of Ba(Fe0.957Co0.043)2As2 by resonant ultrasound spectroscopy as a function of temperature and externally applied magnetic field. Non-linear softening and stiffening of C 66 in the stability fields of both the tetragonal and orthorhombic structures has been found to conform quantitatively to the Landau expansion for a pseudoproper ferroelastic transition which is second order in character. The only exception is that the transition occurs at a temperature (T S ≈ 69 K) ~10 K above the temperature at which C 66 would extrapolate to zero ([Formula: see text] ≈ 59 K). An absence of anomalies associated with antiferromagnetic ordering below T N ≈ 60 K implies that coupling of the magnetic order parameter with shear strain is weak. It is concluded that linear-quadratic coupling between the structural/electronic and antiferromagnetic order parameters is suppressed due to the effects of local heterogeneous strain fields arising from the substitution of Fe by Co. An acoustic loss peak at ~50-55 K is attributed to the influence of mobile ferroelastic twin walls that become pinned by a thermally activated process involving polaronic defects. Softening of C 66 by up to ~6% below the normal-superconducting transition at T c ≈ 13 K demonstrates an effective coupling of the shear strain with the order parameter for the superconducting transition which arises indirectly as a consequence of unfavourable coupling of the superconducting order parameter with the ferroelastic order parameter. Ba(Fe0.957Co0.043)2As2 is representative of 122 pnictides as forming a class of multiferroic superconductors in which elastic strain relaxations underpin almost all aspects of coupling between the structural, magnetic and superconducting order parameters and of dynamic properties of the transformation microstructures they contain.

Strain relaxation behaviour of vortices in a multiferroic superconductor.

The elastic and anelastic properties of a single crystal of Co-doped pnictide Ba(Fe0.957Co0.043)2As2 have been determined by resonant ultrasound spectroscopy in the frequency range 10-500 kHz, both as a function of temperature through the normal-superconducting transition (T c ≈ 12.5 K) and as a function of applied magnetic field up to 12.5 T. Correlation with thermal expansion, electrical resistivity, heat capacity, DC and AC magnetic data from crystals taken from the same synthetic batch has revealed the permeating influence of strain on coupling between order parameters for the ferroelastic (Q E) and superconducting (Q SC) transitions and on the freezing/relaxation behaviour of vortices. Elastic softening through T c in zero field can be understood in terms of classical coupling of the order parameter with the shear strain e 6, λe 6 [Formula: see text], which means that there must be a common strain mechanism for coupling of the form λ [Formula: see text] Q E. At fields of ~5 T and above, this softening is masked by Debye-like stiffening and acoustic loss processes due to vortex freezing. The first loss peak may be associated with the establishment of superconductivity on ferroelastic twin walls ahead of the matrix and the second is due to the vortex liquid-vortex glass transition. Strain contrast between vortex cores and the superconducting matrix will contribute significantly to interactions of vortices both with each other and with the underlying crystal structure. These interactions imply that iron-pnictides represent a class of multiferroic superconductors in which strain-mediated coupling occurs between the multiferroic properties (ferroelasticity, antiferromagnetism) and superconductivity.

Filtration Markers, Cardiovascular Disease, Mortality, and Kidney Outcomes in Stable Kidney Transplant Recipients: The FAVORIT Trial.

Cystatin C and beta-2-microglobulin (B2M) are filtration markers associated with adverse outcomes in nontransplant populations, sometimes with stronger associations than for creatinine. We evaluated associations of estimated glomerular filtration rate from cystatin C (eGFRcys ), B2M (eGFRB2M ), and creatinine (eGFRcr ) with cardiovascular outcomes, mortality, and kidney failure in stable kidney transplant recipients using a case-cohort study nested within the Folic Acid for Vascular Outcome Reduction in Transplantation (FAVORIT) Trial. A random subcohort was selected (N = 508; mean age 51.6 years, median transplant vintage 4 years, 38% women, 23.6% nonwhite race) with enrichment for cardiovascular events (N = 306; 54 within the subcohort), mortality (N = 208; 68 within the subcohort), and kidney failure (N = 208; 52 within the subcohort). Mean eGFRcr , eGFRcys , and eGFRB2M were 46.0, 43.8, and 48.8 mL/min/1.73m2 , respectively. After multivariable adjustment, hazard ratios for eGFRcys and eGFRB2M <30 versus 60+ were 2.02 (95% confidence interval [CI] 1.09-3.76; p = 0.03) and 2.56 (1.35-4.88; p = 0.004) for cardiovascular events; 3.92 (2.11-7.31) and 4.09 (2.21-7.54; both p < 0.001) for mortality; and 9.49 (4.28-21.00) and 15.53 (6.99-34.51; both p < 0.001) for kidney failure. Associations persisted with additional adjustment for baseline eGFRcr . We conclude that cystatin C and B2M are strongly associated with cardiovascular events, mortality, and kidney failure in stable kidney transplant recipients.

Elastic and anelastic relaxation behaviour of perovskite multiferroics II: PbZr0.53Ti0.47O3 (PZT)-PbFe0.5Ta0.5O3 (PFT).

Elastic and anelastic properties of ceramic samples of multiferroic perovskites with nominal compositions across the binary join PbZr0.53Ti0.47O3-PbFe0.5Ta0.5O3 (PZT-PFT) have been assembled to create a binary phase diagram and to address the role of strain relaxation associated with their phase transitions. Structural relationships are similar to those observed previously for PbZr0.53Ti0.47O3-PbFe0.5Nb0.5O3 (PZT-PFN), but the magnitude of the tetragonal shear strain associated with the ferroelectric order parameter appears to be much smaller. This leads to relaxor character for the development of ferroelectric properties in the end member PbFe0.5Ta0.5O3. As for PZT-PFN, there appear to be two discrete instabilities rather than simply a reorientation of the electric dipole in the transition sequence cubic-tetragonal-monoclinic, and the second transition has characteristics typical of an improper ferroelastic. At intermediate compositions, the ferroelastic microstructure has strain heterogeneities on a mesoscopic length scale and, probably, also on a microscopic scale. This results in a wide anelastic freezing interval for strain-related defects rather than the freezing of discrete twin walls that would occur in a conventional ferroelastic material. In PFT, however, the acoustic loss behaviour more nearly resembles that due to freezing of conventional ferroelastic twin walls. Precursor softening of the shear modulus in both PFT and PFN does not fit with a Vogel-Fulcher description, but in PFT there is a temperature interval where the softening conforms to a power law suggestive of the role of fluctuations of the order parameter with dispersion along one branch of the Brillouin zone. Magnetic ordering appears to be coupled only weakly with a volume strain and not with shear strain but, as with multiferroic PZT-PFN perovskites, takes place within crystals which have significant strain heterogeneities on different length scales.

Strain behavior and lattice dynamics in Ni50Mn35In15.

The lattice dynamics in the polycrystalline shape-memory Heusler alloy Ni50Mn35In15 have been studied by means of resonant ultrasound spectroscopy (RUS). RUS spectra were collected in a frequency range 100-1200 kHz between 10 and 350 K. Ni50Mn35In15 exhibits a ferromagnetic transition at 313 K in the austenite phase and a martensitic transition at 248 K accompanied by a change of the magnetic state. Furthermore it displays a paramagnetic to ferrimagnetic transition within the martensitic phase. We determined the temperature dependence of the shear modulus and the acoustic attenuation of Ni50Mn35In15 and compared it with magnetization data. Following the structural softening, which accompanies the martensitic transition as a pretransitional phenomenon, a strong stiffening of the lattice is observed at the martensitic magneto-structural transition. Only a weak magnetoelastic coupling is evidenced at the Curie temperatures both in austenite and martensite phases. The large acoustic damping in the martensitic phase compared with the austenitic phase reflects the motion of the twin walls, which freezes out in the low temperature region.

Rejuvenation of metallic glasses by non-affine thermal strain.

When a spatially uniform temperature change is imposed on a solid with more than one phase, or on a polycrystal of a single, non-cubic phase (showing anisotropic expansion-contraction), the resulting thermal strain is inhomogeneous (non-affine). Thermal cycling induces internal stresses, leading to structural and property changes that are usually deleterious. Glasses are the solids that form on cooling a liquid if crystallization is avoided--they might be considered the ultimate, uniform solids, without the microstructural features and defects associated with polycrystals. Here we explore the effects of cryogenic thermal cycling on glasses, specifically metallic glasses. We show that, contrary to the null effect expected from uniformity, thermal cycling induces rejuvenation, reaching less relaxed states of higher energy. We interpret these findings in the context that the dynamics in liquids become heterogeneous on cooling towards the glass transition, and that there may be consequent heterogeneities in the resulting glasses. For example, the vibrational dynamics of glassy silica at long wavelengths are those of an elastic continuum, but at wavelengths less than approximately three nanometres the vibrational dynamics are similar to those of a polycrystal with anisotropic grains. Thermal cycling of metallic glasses is easily applied, and gives improvements in compressive plasticity. The fact that such effects can be achieved is attributed to intrinsic non-uniformity of the glass structure, giving a non-uniform coefficient of thermal expansion. While metallic glasses may be particularly suitable for thermal cycling, the non-affine nature of strains in glasses in general deserves further study, whether they are induced by applied stresses or by temperature change.

Elastic and magnetoelastic relaxation behaviour of multiferroic (ferromagnetic + ferroelectric + ferroelastic) Pb(Fe0.5Nb0.5)O3 perovskite.

Resonant Ultrasound Spectroscopy has been used to characterize elastic and anelastic anomalies in a polycrystalline sample of multiferroic Pb(Fe(0.5)Nb(0.5))O(3) (PFN). Elastic softening begins at ~550 K, which is close to the Burns temperature marking the development of dynamical polar nanoregions. A small increase in acoustic loss at ~425 K coincides with the value of T(*) reported for polar nanoregions starting to acquire a static or quasi-static component. Softening of the shear modulus by ~30-35% through ~395-320 K, together with a peak in acoustic loss, is due to classical strain/order parameter coupling through the cubic → tetragonal → monoclinic transition sequence of ferroelectric/ferroelastic transitions. A plateau of high acoustic loss below ~320 K is due to the mobility under stress of a ferroelastic microstructure but, instead of the typical effects of freezing of twin wall motion at some low temperature, there is a steady decrease in loss and increase in elastic stiffness below ~85 K. This is attributed to freezing of a succession of strain-coupled defects with a range of relaxation times and is consistent with a report in the literature that PFN develops a tweed microstructure over a wide temperature interval. No overt anomaly was observed near the expected Néel point, ~145 K, consistent with weak/absent spin/lattice coupling but heat capacity measurements showed that the antiferromagnetic transition is actually smeared out or suppressed. Instead, the sample is weakly ferromagnetic up to ~560 K, though it has not been possible to exclude definitively the possibility that this could be due to some magnetic impurity. Overall, evidence from the RUS data is of a permeating influence of static and dynamic strain relaxation effects which are attributed to local strain heterogeneity on a mesoscopic length scale. These, in turn, must have a role in determining the magnetic properties and multiferroic character of PFN.

Static and dynamic strain coupling behaviour of ferroic and multiferroic perovskites from resonant ultrasound spectroscopy.

Resonant ultrasound spectroscopy (RUS) provides a window on the pervasive influence of strain coupling at phase transitions in perovskites through determination of elastic and anelastic relaxations across wide temperature intervals and with the application of external fields. In particular, large variations of elastic constants occur at structural, ferroelectric and electronic transitions and, because of the relatively long interaction length provided by strain fields in a crystal, Landau theory provides an effective formal framework for characterizing their form and magnitude. At the same time, the Debye equations provide a robust description of dynamic relaxational processes involving the mobility of defects which are coupled with strain. Improper ferroelastic transitions driven by octahedral tilting in KMnF3, LaAlO3, (Ca,Sr)TiO3, Sr(Ti,Zr)O3 and BaCeO3 are accompanied by elastic softening of tens of % and characteristic patterns of acoustic loss due to the mobility of twin walls. RUS data for ferroelectrics and ferroelectric relaxors, including BaTiO3, (K,Na)NbO3,Pb(Mg1/3Nb2/3)O3 (PMN), Pb(Sc1/2Ta1/2)O3 (PST), (Pb(Zn1/3Nb2/3)O3)0.955(PbTiO3)0.045 (PZN-PT) and (Pb(In1/2Nb1/2)O3)0.26(Pb(Mg1/3Nb2/3)O3)0.44(PbTiO3)0.30 (PIN-PMN-PT) show similar patterns of softening and attenuation but also have precursor softening associated with the development of polar nano regions. Defect-induced ferroelectricity occurs in KTaO3, without the development of long range ordering. By way of contrast, spin-lattice coupling is much more variable in strength, as reflected in a greater range of softening behaviour for Pr0.48Ca0.52MnO3 and Sm0.6Y0.4MnO3 as well as for the multiferroic perovskites EuTiO3,BiFeO3, Bi0.9Sm0.1FeO3, Bi0.9Nd0.1FeO3, (BiFeO3)0.64(CaFeO2.5)0.36, (Pb(Fe0.5Ti0.5)O3)0.4(Pb(Zr0.53Ti0.47)O3)0.6. A characteristic feature of transitions in which there is a significant Jahn-Teller component is softening as the transition point is approached from above, as illustrated by PrAlO3, and this is suppressed by application of an external magnetic field in the colossal magnetoresistive manganite Pr0.48Ca0.52MnO3 or by reducing grain size in La0.5Ca0.5MnO3. Spin state transitions for Co(3+) in LaCoO3, NdCoO3 and GdCoO3 produce changes in the shear modulus that scale with a spin state order parameter, which is itself coupled with the order parameter(s) for octahedral tilting in a linear-quadratic manner. A new class of phase transitions in perovskites, due to orientational or conformational ordering of organic molecules on the crystallographic A-site of metal organic frameworks, is illustrated for [(CH3)2NH2]Co(HCOO)3 and [(CH2)3NH2]Mn(HCOO)3 which also display elastic and anelastic anomalies due to the influence of intrinsic and extrinsic strain relaxation behaviour.

Strain relaxation mechanisms of elastic softening and twin wall freezing associated with structural phase transitions in (Ca,Sr)TiO3 perovskites.

Resonant ultrasound spectroscopy has been used to measure the bulk modulus (K), shearmodulus (G) and acoustic dissipation of polycrystalline perovskite samples across theCaTiO(3)­SrTiO(3) solid solution in the temperature range ∼10­1350 K. A remarkable pattern of up to ∼25% softening of G as a function of both temperature and composition is due to coupling of shear strain with order parameters for the Pm3m ↔ I 4/mcm, I 4/mcm↔Pnmaand I 4/mcm↔Pbcm transitions. Anomalies in K associated with the phase transitions are small, consistent with only weak coupling of octahedral tilting order parameter(s) with volume strain. A change from tricritical character for the Pm3m ↔ I 4/mcm transition towards second order character at Sr-rich compositions appears to be due to changing properties of the soft optic mode rather than to changes in magnitude of strain/order parameter coupling coefficients. Precursor softening of G ahead of the Pm3m ↔ I 4/mcm transition, due tof luctuations or clustering, occurs over a temperature interval of up to ∼200 K, and also changes character at the most Sr-rich compositions. The tetragonal structure with Sr-rich compositions is characterized by additional softening with falling temperature which is most likely related to the proximity of a ferroelectric instability. The I 4/mcm↔Pnma transition is accompanied by stiffening, which is attributed to the effects of strong coupling between order parameters for M-point and R-point tilting. The pattern of attenuation at RUS frequencies in the tetragonal phase can be understood in terms of the mobility of twin walls which be come pinned below ∼500 K, and the loss mechanism most likely involves local bowing of the walls by lateral motion of ledges rather than the advance and retraction of needle tips. Twin wall mobility is suppressed in the orthorhombic structure.

Strain heterogeneity and magnetoelastic behaviour of nanocrystalline half-doped La, Ca manganite, La0.5Ca0.5MnO3.

Elastic and anelastic properties of La0.5Ca0.5MnO3 determined by resonant ultrasound spectroscopy in the frequency range ∼100-1200 kHz have been used to evaluate the role of grain size in determining the competition between ferromagnetism and Jahn-Teller/charge order of manganites which show colossal magneto resistance. At crystallite sizes of ∼75 and ∼135 nm the dominant feature is softening of the shear modulus as the charge order transition point, Tco (∼225 K), is approached from above and below, matching the form of softening seen previously in samples with 'bulk' properties. This is consistent with a bilinear dominant strain/order parameter coupling, which occurs between the tetragonal shear strain and the Jahn-Teller (Γ3(+)) order parameter. At crystallite sizes of ∼34 and ∼42 nm the charge ordered phase is suppressed but there is still softening of the shear modulus, with a minimum near Tco. This indicates that some degree of pseudoproper ferroelastic behaviour is retained. The primary cause of the suppresion of the charge ordered structure in nanocrystalline samples is therefore considered to be due to suppression of macroscopic strain, even though MnO6 octahedra must develop some Jahn-Teller distortions on a local length scale. This mechanism for stabilizing ferromagnetism differs from imposition of either an external magnetic field or a homogeneous external strain field (from a substrate), and is likely to lead both to local strain heterogeneity within the nanocrystallites and to different tilting of octahedra within the orthorhombic structure. An additional first order transition occurs near 40 K in all samples and appears to involve some very small strain contrast between two ferromagnetic structures.

CoF2: a model system for magnetoelastic coupling and elastic softening mechanisms associated with paramagnetic ↔ antiferromagnetic phase transitions.

Resonant ultrasound spectroscopy has been used to monitor variations in the elastic and anelastic behaviour of polycrystalline CoF2 through the temperature interval 10-290 K and in the frequency range ∼0.4-2 MHz. Marked softening, particularly of the shear modulus, and a peak in attenuation occur as the Néel point (TN=39 K) is approached from both high and low temperatures. Although the effective thermodynamic behaviour can be represented semiquantitatively with a Bragg-Williams model for a system with spin 1/2, the magnetoelastic coupling follows a pattern which is closely analogous to that of a Landau tricritical transition which is co-elastic in character. Analysis of lattice parameter data from the literature confirms that linear spontaneous strains scale with the square of the magnetic order parameter and combine to give effective shear and volume strains on the order of 1‰. Softening of the shear modulus at T>TN is attributed to coupling of acoustic modes with dynamical local ordering of spins and can be represented by a Vogel-Fulcher expression. At T

Elastic anomalies associated with structural and magnetic phase transitions in single crystal hexagonal YMnO3.

Resonant ultrasound spectroscopy has been used to measure the elastic and anelastic behaviour through known structural and magnetic phase transitions in single crystal hexagonal YMnO3. Anomalous elastic behaviour is observed at the high temperature structural transition at ∼1260 K, with a discontinuity in the elastic constants and nonlinear recovery below Tc, consistent with [Formula: see text] coupling. There is no change in dissipation associated with this high temperature transition, and no evidence in the elastic or anelastic behaviour for any secondary transition at ∼920 K, thus supporting the thesis of a single high temperature transformation. Elastic stiffening is observed on cooling through TN, in accordance with previous studies, and the excess elastic constant appears to scale with the square of the magnetic order parameter. The strains incurred at TN are a factor of ∼20 smaller than those at the structural transition, implying very weak [Formula: see text] coupling and a dominant contribution to the variation in the elastic constants from [Formula: see text]. The increased acoustic dissipation above TN is consistent with an order-disorder process.

Multiferroic (ferroelastic/ferromagnetic/ferrimagnetic) aspects of phase transitions in RCo2 Laves phases.

Magnetic phase transitions in RCo2 Laves phases with R as a rare earth element are accompanied by changes in crystallographic space group. For purely structural transitions they would be described as improper ferroelastic and therefore fulfil the condition for multiferroic phase transitions in combining two out of three properties, ferro/antiferromagnetism, ferroelectricity and ferroelasticity. Here lattice parameter data from the literature and new measurements of elastic and anelastic properties, by resonant ultrasound spectroscopy, for NdCo2 and ErCo2 have been analysed from this perspective. The temperature dependence of symmetry-breaking shear strains is consistent with the cubic ↔ tetragonal transition in NdCo2 being close to tricritical in character and the cubic ↔ rhombohedral transition in ErCo2 being first order. Elastic softening and acoustic loss within the stability ranges of the ferroelastic phases can be understood in terms of a combination of intrinsic softening due to strain/order parameter coupling and ferroelastic twin-wall motion. Softening ahead of the transitions does not fit with standard macroscopic descriptions of dynamic effects from other systems but, rather, in the case of NdCo2, might be attributed to the involvement of a second zone centre order parameter related to a separate instability driven by cooperative Jahn-Teller distortions. In ErCo2, acoustic loss in the temperature interval above the transition point is discussed in terms of a possible tweed microstructure associated with strain coupling to local magnetic ordering. The overall multiferroic behaviour can be understood in terms of a single magnetic order parameter (irrep mΓ+4 of magnetic space group Fd3m1') which couples with a structural order parameter (irrep Γ+3 or Γ+5). The coupling is linear/quadratic which, in the case of two separate instabilities, causes them to combine in a single multiferroic phase transition.