Coherent Nucleation Research Articles

On the theory of nucleation of coherent inclusions in irradiated crystals

Based on a critical analysis of the existing model for the effect of excess vacancies and interstitials on the nucleation of coherent particles under irradiation, a new nucleation model is developed that uses the Brailsford-Bullough model for the steady state occupation probabilities of vacancies and interstitials at the particle interface, recently refined by the author. It is shown that, depending on the surface tension γ of a coherent particle, the nucleation mechanism can be qualitatively different. In the case of a relatively small γ, an instability can arise in the irradiated solid solution leading to the barrier-free nucleation of coherent precipitates. In the opposite case of a relatively large γ, the classical one-dimensional theory of homogeneous nucleation is applicable. In order to eliminate the uncertainty in the magnitude of surface tension (from the literature) and to better understand the underlying mechanisms of coherent particle nucleation in irradiation tests, additional atomistic studies are recommended.

Coherent Phase Change in Interstitial Solutions: A Hierarchy of Instabilities.

Metal hydrides or lithium ion battery electrodes can take the form of interstitial solid solutions with a miscibility gap. This work discusses theory approaches for locating, in temperature-composition space, coherent phase transformations during the charging/discharging of such systems and for identifying the associated transformation mechanisms. The focus is on the simplest scenario, where instabilities derive from the thermodynamics of the bulk phase alone, considering strain energy as the foremost consequence of coherency and admitting for stress relaxation at free surfaces. The extension of the approach to include capillarity is demonstrated by an example. The analysis rests on constrained equilibrium phase diagrams that are informed by geometry- and dimensionality-specific mechanical boundary conditions and on elastic instabilities-again geometry-specific-as implied by the theory of open-system elasticity. It is demonstrated that some scenarios afford the analysis of chemical stability to be based entirely on a linear stability analysis of the mechanical equilibrium, which provides closed-form solutions in a straightforward manner. Attention is on the impact of the system geometry (infinitely extended or of finite size) and on the chemical (closed or open system) and mechanical (incoherent or coherent) boundary conditions. Transformation mechanism maps are suggested for documenting the findings. The maps reveal a hierarchy of instabilities, which depend strongly on each of the above characteristics. Specifically, realistic, finite-sized systems differ qualitatively from idealized systems of infinite extension. Among the transformation mechanisms exposed by the analysis are a uniform switchover to the other phase when the open system reaches its chemical spinodal, practical coherent nucleation, as well as chemo-elastically coupled spontaneous buckling modes, which may take the form of either, single-phase or dual-phasestates.

The Mechanism of Dendrite Formation in a Solid-State Transformation of High Aluminum Fe-Al Alloys.

The mechanism of solid-state dendrite formation in high-aluminum Fe-Al alloys is not clear. Applying an in-situ observation technique, the real-time formation and growth of FeAl solid-state dendrites during the eutectoid decomposition of the high-temperature phase Fe5Al8 is visualized. In-situ experiments by HT-CSLM reveal that proeutectoid FeAl usually does not preferentially nucleate at grain boundaries regardless of rapid or slow cooling conditions. The critical radii for generating morphological instability are 1.2 μm and 0.9 μm for slow and rapid cooling, respectively. The morphology after both slow and rapid cooling exhibits dendrites, while there are differences in the size and critical instability radius Rc, which are attributed to the different supersaturation S and the number of protrusions l. The combination of crystallographic and thermodynamic analysis indicates that solid-state dendrites only exist on the hypoeutectoid side in high-aluminum Fe-Al alloys. A large number of lattice defects in the parent phase provides an additional driving force for nucleation, leading to coherent nucleation from the interior of the parent phase grains based on the orientation relationship {3¯30}Fe5Al8//{1¯10}FeAl, <111¯>Fe5Al8//<111¯>FeAl. The maximum release of misfit strain energy leads to the preferential growth of the primary arm of the nucleus along <111¯> {1¯10}. During the rapid cooling process, a large supersaturation is induced in the matrix, driving the Al atoms to undergo unstable uphill diffusion and causing variations in the concentration gradient as well as generating constitutional undercooling, ultimately leading to morphological instability and the growth of secondary arms.

The coupling of lattice-strain and phonon induced order-disorder phase transition in layered LiGaO2

Recently, order-disorder phase transition has been considered as an emerging method to engineer bandgap in semiconductors. In this work, we uncovered that the coupling of lattice strain and phonon dominates the pressure-induced order-disorder phase transition in α-LiGaO2 via in situ high-pressure angle dispersive X-ray diffraction (ADXRD) and Raman scattering experiments, with the aids of first-principles calculations. Upon compression, ADXRD experiments show that the anisotropic compression of the layered structure leads to the order-disorder phase transition. Combining with lattice dynamics, we observed that the transition begins at about 16 GPa based on coherent nucleation induced by the oxygen atoms opposite motion that is the result of the coupling of lattice strain and phonon mode A1g. This result further shows that the disorder in crystal can be a correlated behavior and controlling the disorder in crystal can be used to create materials with new or improved functionality.

The mechanism of thermal transformation hysteresis in ZrO2-CeO2 shape-memory ceramics

Hysteresis is an important phase transformation property to understand and control in shape-memory materials. While a detailed understanding of hysteresis has been developed in shape-memory alloys (SMAs), it is far less understood in emerging shape-memory ceramics (SMCs). Here, we systematically study thermal hysteresis of the tetragonal-monoclinic martensitic transformation in ZrO2-CeO2 SMCs. We present calorimetry measurements of thermal hysteresis, which reveal a non-monotonic trend with CeO2 content as well as significant rate dependence, and correlate these findings with the transformation crystallography measured by in situ X-ray diffraction. We quantitatively analyze these results in the framework of martensite nucleation theory and conclude that the initial decrease in hysteresis with CeO2 content can be attributed to improving interface compatibility (λ2) for coherent nucleation whereas the sharp increase in hysteresis at higher CeO2 contents (below temperatures of ~773 K) is a result of interface friction consistent with thermally-activated interactions with the Peierls barrier of the crystal. Our analysis gives an activation energy of ~136 kJ/mol, which is consistent with previously reported activation energies of isothermal transformation in these materials. These findings clarify contradicting reports in the ZrO2 literature and confirm that the same controlling factors of hysteresis in SMAs, namely λ2 and thermal friction, are also operative in SMCs.

The Mechanism of Thermal Transformation Hysteresis in Zro 2-Ceo 2 Shape-Memory Ceramics

Hysteresis is an important phase transformation property to understand and control in shape-memory materials. While a detailed understanding of hysteresis has been developed in shape-memory alloys (SMAs), it is far less understood in emerging shape-memory ceramics (SMCs). Here, we systematically study thermal hysteresis of the tetragonal-monoclinic martensitic transformation in ZrO2-CeO2 SMCs. We present calorimetry measurements of thermal hysteresis, which reveal a non-monotonic trend with CeO2 content as well as significant rate dependence, and correlate these findings with the transformation crystallography measured by in situ X-ray diffraction. We quantitatively analyze these results in the framework of martensite nucleation theory and conclude that the initial decrease in hysteresis with CeO2 content can be attributed to improving interface compatibility (λ2) for coherent nucleation whereas the sharp increase in hysteresis at higher CeO2 contents (below temperatures of ~773 K) is a result of interface friction consistent with thermally-activated interactions with the Peierls barrier of the crystal. Our analysis gives an activation energy of ~136 kJ/mol, which is consistent with previously reported activation energies of isothermal transformation in these materials. These findings clarify contradicting reports in the ZrO2 literature and confirm that the same controlling factors of hysteresis in SMAs, namely λ2 and thermal friction, are also operative in SMCs.

Phase Separation in Liquid Metal Nanoparticles

Nanoparticles produced from gallium-based liquid metal alloys have been explored for developing applications in the fields of electronics, catalysis, and biomedicine. Nonetheless, physical properties, such as phase behavior at micro-/nanosize scale, are still significantly underexplored for such nanoparticles. Here, we conduct an in situ investigation of phase behavior for gallium-based liquid metal nanoparticles and discover the unprecedented coexistence of solid particles in spherical liquid metal shells without the support of a crystalline substrate. The particles can also transform into solid Janus nanoparticles after temperature cycling. In addition, we investigate the optical properties of the nanoparticles before and after phase separation using in situ electron energy-loss spectroscopy. Most importantly, we discover that increasing the content of indium within the nanoparticle can stabilize the solid-core/liquid-shell structure at room temperature. This study provides a foundation to engineer liquid metal nanoparticles for developing new applications in nanoscale optical platforms and shape-configurable transformers.Although various electronic, chemical, and biomedical applications have been demonstrated for nanoparticles made from gallium-based liquid metal alloys, fundamental physical properties such as phase behavior of such nanoparticles are still significantly underexplored. Here, Tang and coworkers present the in situ investigation of phase separation in binary and ternary spherical liquid metal nanoparticles upon cooling, and demonstrate the coexistence of solid core/liquid shell without the support of a crystalline substrate. This study provides insight into engineering such nanoparticles for the development of new applications.Despite gallium-based liquid metal alloys attracting extensive attention for various applications, their phase behavior at the nanoscale is still underexplored. Understanding the impact of phase separation in nanoparticles can be extremely useful for developing new structures and exploring suitable applications. Here, we report on the investigation of phase behavior for spherical nanoparticles made from gallium-based liquid metal alloys upon cooling. We discover the thermally stable coexistence of solid cores in spherical liquid metal shells without the support of a crystalline substrate at room temperature. Given the unique properties of liquid metal, together with the facile process for producing core-shell and Janus nanoparticles, this work will encourage further investigation of the properties of such nanoparticles for developing applications in the fields of electronics, catalysis, nanomedicine, and beyond.

Electrochemical Oscillation in Li-Ion Batteries

Summary Two-phase reactions are prevalent in Li-ion batteries, whereas the underlying dynamics of phase separation in a real electrode still remain elusive, since numerous electrode particles constitute a formidably complex system for existing experimental techniques. Here we present an intriguing oscillatory phenomenon in the typical phase-separating electrode material Li 4 Ti 5 O 12 . During galvanostatic processes, the voltage oscillates due to the discrete nature of multi-particle phase-separating reactions, and the subtle oscillatory signals allow us to evaluate the fraction of actively phase-separating particles in real time. Through the analysis of oscillatory phenomena, we unveil the dependence of the active fraction on the depth of charge/discharge, cycling current, and working temperature, considerably deepening our understanding of the multi-particle phase-separation reaction. Moreover, it is the first time that electrochemical oscillations have been identified in rechargeable battery systems, opening up a new frontier for both theoretical and experimental researchers.

Pressure induced solid-solid reconstructive phase transition in LiGaO2 dominated by elastic strain

Pressure induced solid-solid reconstructive phase transitions for graphite-diamond, and wurtzite-rocksalt in GaN and AlN occur at significantly higher pressure than expected from equilibrium coexistence and their transition paths are always inconsistent with each other. These indicate that the underlying nucleation and growth mechanism in the solid-solid reconstructive phase transitions are poorly understood. Here, we propose an elastic-strain dominated mechanism in a reconstructive phase transition, $\ensuremath{\beta}\ensuremath{-}\mathrm{LiGa}{\mathrm{O}}_{2}$ to $\ensuremath{\gamma}\ensuremath{-}\mathrm{LiGa}{\mathrm{O}}_{2}$, based on in situ high-pressure angle dispersive x-ray diffraction and single-crystal Raman scattering. This mechanism suggests that the pressure induced solid-solid reconstructive phase transition is neither purely diffusionless nor purely diffusive, as conventionally assumed, but a combination. The large elastic strains are accumulated, with the coherent nucleation, in the early stage of the transition. The elastic strains along the $\ensuremath{\langle}100\ensuremath{\rangle}$ and $\ensuremath{\langle}001\ensuremath{\rangle}$ directions are too large to be relaxed by the shear stress, so an intermediate structure emerges reducing the elastic strains and making the transition energetically favorable. At higher pressures, when the elastic strains become small enough to be relaxed, the phase transition to $\ensuremath{\gamma}\ensuremath{-}\mathrm{LiGa}{\mathrm{O}}_{2}$ begins and the coherent nucleation is substituted with a semicoherent one with Li and Ga atoms disordered.

From olivine to ringwoodite: a TEM study of a complex process

AbstractThe study of shock metamorphism of olivine might help to constrain impact events in the history of meteorites. Although shock features in olivine are well known, so far, there are processes that are not yet completely understood. In shock veins, olivine clasts with a complex structure, with a ringwoodite rim and a dense network of lamellae of unidentified nature in the core, have been reported in the literature. A highly shocked (S5‐6), L6 meteorite, Asuka 09584, which was recently collected in Antarctica by a Belgian–Japanese joint expedition, contains this type of shocked olivine clasts and has been, therefore, selected for detailed investigations of these features by transmission electron microscopy (TEM). Petrographic, geochemical, and crystallographic studies showed that the rim of these shocked clasts consists of an aggregate of nanocrystals of ringwoodite, with lower Mg/Fe ratio than the unshocked olivine. The clast's core consists of an aggregate of iso‐oriented grains of olivine and wadsleyite, with higher Mg/Fe ratio than the unshocked olivine. This aggregate is crosscut by veinlets of nanocrystals of olivine, with extremely low Mg/Fe ratio. The formation of the ringwoodite rim is likely due to solid‐state, diffusion‐controlled, transformation from olivine under high‐temperature conditions. The aggregate of iso‐oriented olivine and wadsleyite crystals is interpreted to have formed also by a solid‐state process, likely by coherent intracrystalline nucleation. Following the compression, shock release is believed to have caused opening of cracks and fractures in olivine and formation of olivine melt, which has lately crystallized under postshock equilibrium pressure conditions as olivine.

Eight-phase alkali feldspars: low-temperature cryptoperthite, peristerite and multiple replacement reactions in the Klokken intrusion

Eight feldspar phases have been distinguished within individual alkali feldspar primocrysts in laminated syenite members of the layered syenite series of the Klokken intrusion. The processes leading to the formation of the first four phases have been described previously. The feldspars crystallized as homogeneous sodian sanidine and exsolved by spinodal decomposition, between 750 and 600 °C, depending on bulk composition, to give fully coherent, strain-controlled braid cryptoperthites with sub-μm periodicities. Below ~500 °C, in the microcline field, these underwent a process of partial mutual replacement in a deuteric fluid, producing coarse (up to mm scale), turbid, incoherent patch perthites. We here describe exsolution and replacement processes that occurred after patch perthite formation. Both Or- and Ab-rich patches underwent a new phase of coherent exsolution by volume diffusion. Or-rich patches began to exsolve albite lamellae by coherent nucleation in the range 460–340 °C, depending on patch composition, leading to film perthite with ≤1 μm periodicities. Below ~300 °C, misfit dislocation loops formed, which were subsequently enlarged to nanotunnels. Ab-rich patches (bulk composition ~Ab91Or1An8), in one sample, exsolved giving peristerite, with one strong modulation with a periodicity of ~17 nm and a pervasive tweed microtexture. The Ab-rich patches formed with metastable disorder below the peristerite solvus and intersected the peristerite conditional spinodal at ~450 °C. This is the first time peristerite has been imaged using TEM within any perthite, and the first time peristerite has been found in a relatively rapidly cooled geological environment. The lamellar periodicities of film perthite and peristerite are consistent with experimentally determined diffusion coefficients and a calculated cooling history of the intrusion. All the preceding textures were in places affected by a phase of replacement correlating with regions of extreme optical turbidity. We term this material ultra porous late feldspar (UPLF). It is composed predominantly of regions of microporous very Or-rich feldspar (mean Ab2.5Or97.4An0.1) associated with very pure porous albite (Ab97.0Or1.6An1.4) implying replacement below 170–90 °C, depending on degree of order. In TEM, UPLF has complex, irregular diffraction contrast similar to that previously associated with low-temperature albitization and diagenetic overgrowths. Replacement by UPLF seems to have been piecemeal in character. Ghost-like textural pseudomorphs of both braid and film parents occur. Formation of patch perthite, film perthite and peristerite occurred 104–105 year after emplacement, but there are no microtextural constraints on the age of UPLF formation.

Symmetric magnetization reversal in polycrystalline exchange coupled systems via simultaneous processes of coherent rotation and domain nucleation

Training in exchange bias systems plays an essential role in understanding the very origin of the biasing effect. The nonequilibrium arrangement of antiferromagnetic (AF) spins at the antiferromagnetic-ferromagnetic interface, related to the AF uniaxial anisotropy, plays a crucial role during the initial training. Our system of choice, IrMn/CoFe, possesses softer uniaxial anisotropy compared to other AF systems (e.g., CoO), thereby reducing the energy penalty due to nonequilibrium spins. Different methods have been applied to initialize or modify the unidirectional anisotropy. We apply an in-plane field (a) during field growth, (b) during field cooling below its blocking temperature, and (c) in an in-plane magnetic field during ion irradiation, along and opposite the field applied during field growth. Magnetization reversal mechanisms were investigated during the first two field cycles to identify the role of each method on the training. A detailed analysis of polarized neutron scattering using the distorted wave Born approximation reveals a simultaneous process of domain nucleation and coherent rotation for magnetization reversal.

Olivine–wadsleyite–pyroxene topotaxy: Evidence for coherent nucleation and diffusion-controlled growth at the 410-km discontinuity

We have synthesized a hydrous peridotite-composition sample at 13GPa and 1400°C with co-existing coarse grains (∼100μm) of olivine, wadsleyite, clinoenstatite, plus melt in a multi-anvil press. Some of the olivine grains contain fine-scale (0.5–2μm-wide) lamellae of wadsleyite and clinoenstatite that likely resulted from transformation caused by small temperature fluctuations during the four-hour experiment. Phase compositions were determined by electron probe microanalysis (EPMA) and secondary ion mass spectroscopy (SIMS). The olivine ranges from Fo94 to Fo90 in composition and contains about 4000ppm wt. H2O. The wadsleyite is Fo87±1 in composition and contains about 10,000ppm wt. H2O. The clinoenstatite is En93±1 in composition and about 1400ppm wt. H2O. Transmission electron microscopy of the wadsleyite lamellae and host olivine shows that the two phases share their close-packed oxygen planes so that the wadsleyite lamellae are nearly planar and perpendicular to the [100] of olivine. The wadsleyite lamellae thus have their {101} and {021} planes parallel to the (100) plane of olivine. Additionally, larger incoherent grains of wadsleyite in olivine are found. Dislocation microtexures in the olivine and iron concentration profiles across the lamella interface suggest heterogeneous nucleation and diffusion-controlled growth of coherent wadsleyite lamellae on defects in the olivine followed by the nucleation of faster-growing incoherent grains on the lamellae. The results show that, under hydrous conditions, the olivine–wadsleyite transformation occurs close to equilibrium at conditions of the 410-km discontinuity. Furthermore, inheritance of crystallographic preferred orientations (and therefore seismic anisotropy) across the 410-km discontinuity is unlikely to be significant. In addition, hydrogen distributions among the various phases indicate that dehydration by melt extraction at 410km will be inefficient and that H contents greater than about 4000ppm wt. H2O are needed to initiate melting at 410km.

Coarsening kinetics of coexisting peristerite and film microperthite over 104 to 105 years

Alkali feldspar crystals from the Klokken syenite pluton (South Greenland) have a coarse patch perthite exsolution texture, on the scale of hundreds of micrometers, produced by dissolution-reprecipitation reactions at ~500 °C. We have discovered that Ab-rich patches (Ab92An7Or1) subsequently exsolved by spinodal decomposition to give peristerite, with a periodicity of 17 nm. This is the first time a peristerite has been characterized by TEM within a perthite, and the first peristerite to be found outside regional metamorphic rocks and pegmatites. The coexisting Or-rich patches, Ab16Or84(An0.3), unmixed over the same temperature interval to yield coherent film microperthite with periodicities ≤1 μm. Because the peristerite and film perthite from a single hand specimen from the Klokken intrusion have shared exactly the same cooling history, they provide a novel opportunity to test the utility of diffusion coefficients obtained in the laboratory for prediction of coarsening rates over 105 yr time scales, in the light of a calculated cooling trajectory for the pluton. We find good agreement between observed and predicted periodicities for the film perthite, which began to exsolve by coherent nucleation at the coherent solvus for ordered feldspars at ~420 °C, ~32 000 yr after crystal growth, and took a further 13 000-39 000 yr to coarsen to a periodicity of 1 μm. Peristerite exsolution began at the conditional spinodal at ~450 °C, but on the basis of the best existing experimental data would have taken ~520 000-4 600 000 yr to coarsen, incompatible with the cooling history. We speculate on changes to these “best” parameter values to describe NaSi-CaAl interdiffusion that would lead to peristerite coarsening rates compatible with the cooling history of the Klokken intrusion. We find that an interdiffusion expression:

Monitoring magnetization reversal and perpendicular anisotropy by the extraordinary Hall effect and anisotropic magnetoresistance.

Simultaneous magnetotransport measurements of the extraordinary Hall effect and anisotropic magnetoresistance were used to monitor the normal and in-plane projections of magnetization in thin Co/Pd multilayers with perpendicular anisotropy. By reconstructing the magnitude and orientation of the magnetization vector we were able to track the reversal of magnetization and distinguish among the processes of coherent rotation and domain nucleation. The Stoner–Wohlfarth model was used to extract anisotropy constants from data collected during the coherent rotation. We show that magnetization reversal occurs coherently over a major part of the cycle under a canted magnetic field when the field's inclination exceeds a certain sample-dependent angle. The applicability range of the Stoner–Wohlfarth model and thus reliability of the calculated anisotropy constants is significantly improved when measurements are performed under canted fields.

ANALYTICAL DETERMINATION OF NUCLEATION FIELD AND MAGNETIC REVERSAL MODES IN EXCHANGE-COUPLED NANOLAYERS

General formulae for coherent/incoherent nucleation fields have been obtained as functions of the thickness of the hard and soft layers within a self-contained micromagnetic model for a hard/soft trilayer. The nucleation modes are determined reliably by direct comparison of the nucleation fields for different modes. It is shown that coherent nucleation cannot take place no matter how small the layer thickness. For small soft layer thickness, the magnetic reversal mode is an incoherent nucleation. As the soft layer thickness increases, the dominant magnetic reversal process is domain-wall motion/pinning. Analyses demonstrate that negative nucleation field and very small coercivity occur when the easy axes of neighboring layers are perpendicular. The results could shade light on Brown's coercivity paradox (where the measured coercivity is much smaller than the one given by the previous theories).

Cathode-Spot Dynamics in a High-Current Pulsed Arc: A Noise Study

Cathode spots are the locus for plasma production in cathodic vacuum arcs, and measurements of the discharge voltage provide information about the physics. The voltage noise and cathode-erosion patterns of a high-current pulsed titanium arc were studied as a function of time, current, and pulse shape. Enhanced noise and a 1/f <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> trend in the spectral power density were observed when cathode spots are close together at the initiation of an arc for fast rising currents (>1.3 kA in 30 mus) or when the total current exceeds a threshold value of 1.6 kA. We propose a model in which the individual currents associated with the spot substructure can act as noise generators coupled via magnetic fields or coherent spot nucleation.

Coherent Rotation and Effective Anisotropy

It is shown in this paper that the concept of effective anisotropy is of sound physical sense only when the nucleation mode is coherent rotation. Comparison of coherent and incoherent nucleation fields demonstrates that the coherent rotation can take place at very small defect size. The critical size below which the coherent rotation is favorable is roughly the domain wall-width with 3-D soft defects and is smaller for oriented exchange-coupled permanent magnets with planar soft defects. The effect of misaligned grains has also been considered and it is illustrated that the effective anisotropy has to be used very carefully: it can only be used in limited cases and its expression varies as the microstructures change

Analytical Modeling of the Interaction of Vacancies and Oxygen for Oxide Precipitation in RTA Treated Silicon Wafers

We have investigated the impact of rapid thermal annealing (RTA) induced vacancy supersaturation on oxide precipitation based as much as possible on experimental and theoretical values. Oxygen precipitation after RTA processing was found to be controlled by the initial concentration of interstitial oxygen in a sixth power dependency and frozen vacancies just in a cubic dependency. The formation of tensile strained clusters seems to be the favored process for coherent nucleation of oxide precipitates. The reduction of interstitial oxygen can be accurately modeled for the temperature range from 1150 to using Ham’s theory for precipitate growth and an empirical relation based on nucleation of oxide precipitates by agglomeration of complexes. During RTA treatments at temperatures vacancies seem to be consumed by other processes. Below RTA temperatures of , oxide precipitation is dominated by shrunken as-grown precipitate nuclei because as-grown nuclei can be dissolved only at RTA temperatures .

Orientation relationships and lattice matching for the S phase in Al–Cu–Mg alloys

The form and crystallography of precipitate S phase have been examined in overaged Al–Cu–Mg alloys of low Cu:Mg atomic ratio using high-resolution electron microscopy and diffraction. Orthorhombic S takes the form of laths elongated parallel to [1 0 0] S//[1 0 0] α in face-centred cubic (fcc) matrix α solid solution and, in any given sample, may adopt a continuous or near-continuous range of orientation relationships, distinguished by rotation of up to 7° about these common axes between two discrete limits defined by the relationships: ( 0 0 1 ) S / / ( 0 2 1 ) α , [ 1 0 0 ] S / / [ 1 0 0 ] α and ( 0 2 ¯ 1 ) S / / ( 0 1 4 ) α , [ 1 0 0 ] S / / [ 1 0 0 ] α Such variation in orientation is accompanied by accommodating changes in interface orientation and structure, and by a systematic variation in the lattice parameters of the S phase. It is demonstrated that these changes are, in turn, associated with, at least local, changes in matrix α lattice parameter, likely to be attributable to heterogeneous coherent nucleation in association with pre-existing defects and/or solute or solute/defect clusters.