Metastable Phase Boundaries Research Articles

Absolute measurements of anomalous small-angle X-ray scattering intensity using glassy carbon at the Mg K absorption edge

Absolute measurements of small-angle X-ray scattering (SAXS) intensities at the K absorption edge of Mg have been performed using glassy carbon as an intensity standard. Glassy carbon samples polished down to give appropriate transmission have been prepared as a secondary standard to be used at 1.3 keV. Al–Mg binary alloys were used to assess the metastable phase boundary for the Al3Mg metastable precipitation from the absolute scattering intensity. The assessed phase boundary agreed with the previous reports. Glassy carbon was concluded to be an appropriate candidate for an intensity standard sample for transmission measurements of SAXS in the tender X-ray regions.

Stability of phase boundary between L12-Ni3Al phases: A phase field study

The evolution and stability of phase boundaries (PBs) between L12-Ni3Al phases in Ni75Al11V14 alloy aged at 1050k was studied using the microscopic equation phase-field method (MPFM). Four types of L12 PBs were found through atomic configuration, migration and occupation probability (OP). The evolution of metastable PBs and formation of stable PBs were tracked and explored, the effect of coherent elastic strain energy on the evolution and stability of PBs is also investigated by coupling the micro elastic theory with MPFM. In addition, the formation enthalpy, interface energy and electron distribution function of PBs are calculated by FP method, and the stability of PBs is further quantitatively predicted from the perspective of thermodynamic energy and gaining or losing electrons. FP calculation results are consistent with MPFM prediction, and the essence of the transition and stability of PBs is revealed based on the atomic migration dynamics, interface evolution morphology and thermodynamic energy. This is an effective method to further explore the formation and structure of PBs and design high stability PBs.

Phase decomposition and precipitation of metastable A2 phase in B2 ordered Co–Al–Fe alloys

Abstract Phase decomposition in rapidly solidified Co–Al – Fe B2 alloys during isothermal ageing at 923 K has been investigated by means of X-ray diffraction and transmission electron microscopy. At the early stage of ageing, A2 disordered particles precipitate inside B2 matrix grains, being aligned along the <100> direction of the matrix, and equilibrium A1 phase (α-Co) is also formed mostly on grain boundaries. With further ageing, the plate-like A2 particles increase in size. On the other hand, the A1 phase on grain boundaries increases in size and also spreads into the B2 grain like tree branches as so-called Widmanstätten precipitate. Finally, the A2 phase disappears. The A1 phase remains on grain boundaries and also inside the B2 grains as spherical particles. Using the composition gradient method, the metastable precipitation limit of the A2 phase, that is the metastable phase boundary B2/(A2 + B2), was experimentally determined at 923 K. It extends smoothly into the stable A2 + B2 two-phase field on the Co–Fe side of the ternary Co–Al –Fe system.

Optical Identification of Materials Transformations in Oxide Thin Films.

Recent advances in high-throughput experimentation for combinatorial studies have accelerated the discovery and analysis of materials across a wide range of compositions and synthesis conditions. However, many of the more powerful characterization methods are limited by speed, cost, availability, and/or resolution. To make efficient use of these methods, there is value in developing approaches for identifying critical compositions and conditions to be used as a priori knowledge for follow-up characterization with high-precision techniques, such as micrometer-scale synchrotron-based X-ray diffraction (XRD). Here, we demonstrate the use of optical microscopy and reflectance spectroscopy to identify likely phase-change boundaries in thin film libraries. These methods are used to delineate possible metastable phase boundaries following lateral-gradient laser spike annealing (lg-LSA) of oxide materials. The set of boundaries are then compared with definitive determinations of structural transformations obtained using high-resolution XRD. We demonstrate that the optical methods detect more than 95% of the structural transformations in a composition-gradient La-Mn-O library and a Ga2O3 sample, both subject to an extensive set of lg-LSA anneals. Our results provide quantitative support for the value of optically detected transformations as a priori data to guide subsequent structural characterization, ultimately accelerating and enhancing the efficient implementation of micrometer-resolution XRD experiments.

Application of a simple subregular solution model to the computation of phase boundaries and free dendritic growth in the Ag-Cu system

Adopting of a simple, but dependable analytic thermodynamic solution model in the simulation of phase transformation kinetics reduces the complexity of computation and the need for extensive thermodynamic data and hence is desired in the practical application of kinetic theories in materials processing. A simple subregular solution model with linear temperature dependency, which can calculate G curves with limited information extracted from an equilibrium phase diagram, is presented and applied to the calculation of (1) the binary Ag-Cu phase diagram with metastable phase boundaries and (2) the kinetics of free dendritic growth in supercooled Ag-Cu melts. The simple T-dependent subregular solution model can duplicate the published Ag-Cu phase diagram with the predicted metastable extensions to the same accuracy as that of calculations with highly structured models that require more computation and wider range of thermodynamic data. Its integration with a free dendritic growth model permits the calculation of correct values of the driving force at non-Henrian interfacial solute concentrations that occur in rapid solidification. The use of the simple T-dependent subregular solution model to calculate the interfacial driving force greatly improves the mathematical stability in the transition stage from mass transfer-limited growth to heat transfer-limited crystal growth.

Nature of phase transitions in crystalline and amorphous GeTe-Sb2Te3 phase change materials

The thermodynamic nature of phase stabilities and transformations are investigated in crystalline and amorphous Ge(1)Sb(2)Te(4) (GST124) phase change materials as a function of pressure and temperature using high-resolution synchrotron x-ray diffraction in a diamond anvil cell. The phase transformation sequences upon compression, for cubic and hexagonal GST124 phases are found to be: cubic → amorphous → orthorhombic → bcc and hexagonal → orthorhombic → bcc. The Clapeyron slopes for melting of the hexagonal and bcc phases are negative and positive, respectively, resulting in a pressure dependent minimum in the liquidus. When taken together, the phase equilibria relations are consistent with the presence of polyamorphism in this system with the as-deposited amorphous GST phase being the low entropy low-density amorphous phase and the laser melt-quenched and high-pressure amorphized GST being the high entropy high-density amorphous phase. The metastable phase boundary between these two polyamorphic phases is expected to have a negative Clapeyron slope.

Material decomposition mechanisms in femtosecond laser interactions with metals

A numerical hydrodynamic study of femtosecond laser ablation is presented. A detailed analysis of material decomposition is performed using a thermodynamically complete equation of state with separate stable and metastable phase states and phase boundaries. The lifetime of the metastable liquid state is estimated based on the classical theory of homogeneous nucleation. In addition, mechanical fragmentation of the target material is controlled based on available criteria. As a result, several ablation mechanisms are observed. A major fraction of the ablated material, however, is found to originate from the metastable liquid region, which is decomposed either thermally in the vicinity of the critical point into a liquid-gas-mixture or mechanically at high strain rate and negative pressure into liquid droplets and chunks. The calculation results explain available experimental findings.

Formation and chemical evolution of magnesium chloride brines by evaporite dissolution processes—Implications for evaporite geochemistry

The evolution of magnesium chloride brines with high bromide contents via a multistage reaction and dissolution process has been studied in brine seeps of a German potash mine. The observed chemical trends and phase equilibria can be modeled and interpreted in terms of a NaCl solution (cap rock brine) infiltrating into a potash zone characterized by the metamorphic mineral assemblage kieserite + sylvite + halite + anhydrite. Establishment of a persistent, stable equilibrium assemblage and constant fluid composition in the invariant point IP1 of the six component (Na-K-Mg-Ca-Cl-SO 4-H 2O) system of oceanic salts is prevented by the perpetually renewed input of NaCl-brine and by the intermittent exposure of incompatible kieserite. Instead, the solutions develop towards the metastable invariant point IP1(gy), with the mineral assemblage carnallite + polyhalite + sylvite + halite + gypsum, where gypsum takes the place of anhydrite (stage I). The temporary exposure of kieserite and the ensuing formation of polyhalite effectively buffer the solutions along the metastable polyhalite phase boundary during stages II and III. Eventually, in stage IV, polyhalite becomes depleted and admixture of more NaCl brine leads to low sulfate solution compositions, which are now only constrained by carnallite + sylvite + halite, and the once hexary system degenerates to a quaternary one (Na-K-Mg-Cl-H 2O) in point E. Bromide in brines shows equilibrium partitioning with respect to the wall rock minerals. The pattern of evolving brine compositions may serve as a model for similar brine occurrences, which in some cases may have been misinterpreted as remains of fossil, highly concentrated and chemically modified seawater. Similar magnesium chloride brines of salt lakes (e.g., Dead Sea, Dabusun Lake) show subtle differences and are constrained by fewer mineral equilibria (more degrees of freedom), and their low sulfate contents are due to gypsum precipitation, driven by calcium chloride input from dolomitization reactions. Finally, the observed reaction sequence is generalized, and a model for the formation of magnesium sulfate depleted, chloride-type potash salts and bischofite deposits by leaching of sulfate-type evaporites is proposed.

Texture development and deformation mechanisms during uniaxial straining of U–Nb shape-memory alloys

The shape–memory effect is well documented in uranium–niobium alloys near the α″–γo metastable phase boundary. In situ neutron diffraction measurements during uniaxial loading indicate that U–14 at.% Nb (in the α″ monoclinic phase field) deforms by stress–induced twin reorientation. Alternatively, U–16 at.% Nb (initially γo tetragonal) undergoes a stress–induced phase transformation to the α″ monoclinic phase. The crystallographic texture of the monoclinic phase of both compositions has been measured and qualitatively interpreted by considering the orientation relationship between the most favoured α′′ variant and the parent phase. In addition, previously published observations of deformation structures within the shape–memory regime of a U–13 at.% Nb alloy are discussed within the context of the same model.

05/00534 Preparation of solar grade silicon from optical fibers wastes with thermal plasmas: Ma, W. et al. Solar Energy Materials and Solar Cells, 2004, 81, (4), 477–483

The evolution of magnesium chloride brines with high bromide contents via a multistage reaction and dissolution process has been studied in brine seeps of a German potash mine. The observed chemical trends and phase equilibria can be modeled and interpreted in terms of a NaCl solution (cap rock brine) infiltrating into a potash zone characterized by the metamorphic mineral assemblage kieserite + sylvite + halite + anhydrite. Establishment of a persistent, stable equilibrium assemblage and constant fluid composition in the invariant point IP1 of the six component (Na-K-Mg-Ca-Cl-SO4-H2O) system of oceanic salts is prevented by the perpetually renewed input of NaCl-brine and by the intermittent exposure of incompatible kieserite. Instead, the solutions develop towards the metastable invariant point IP1(gy), with the mineral assemblage carnallite + polyhalite + sylvite + halite + gypsum, where gypsum takes the place of anhydrite (stage I). The temporary exposure of kieserite and the ensuing formation of polyhalite effectively buffer the solutions along the metastable polyhalite phase boundary during stages II and III. Eventually, in stage IV, polyhalite becomes depleted and admixture of more NaCl brine leads to low sulfate solution compositions, which are now only constrained by carnallite + sylvite + halite, and the once hexary system degenerates to a quaternary one (Na-K-Mg-Cl-H2O) in point E. Bromide in brines shows equilibrium partitioning with respect to the wall rock minerals. The pattern of evolving brine compositions may serve as a model for similar brine occurrences, which in some cases may have been misinterpreted as remains of fossil, highly concentrated and chemically modified seawater. Similar magnesium chloride brines of salt lakes (e.g., Dead Sea, Dabusun Lake) show subtle differences and are constrained by fewer mineral equilibria (more degrees of freedom), and their low sulfate contents are due to gypsum precipitation, driven by calcium chloride input from dolomitization reactions. Finally, the observed reaction sequence is generalized, and a model for the formation of magnesium sulfate depleted, chloride-type potash salts and bischofite deposits by leaching of sulfate-type evaporites is proposed.

Doping and grain size effects in nanocrystalline ZrO2–Sc2O3system with complex phase transitions: XRD and Raman studies

Weakly-agglomerated nanocrystalline (ZrO2)1−x(Sc2O3)x (x = 0.02–0.16) powders with high surface area (106–186 m2 g−1) and uniform particle size (5.7–9.5 nm) were synthesized by a two-step hydrothermal process in the presence of urea, and their complex phase evolution upon calcinations over 400–1400 °C were studied by a combined utilization of X-ray diffraction, in situ high temperature X-ray diffraction, near infrared Fourier transform Raman and ultraviolet Raman spectroscopies. It was discovered that the growth of the grains comprised two stages, and the apparent activation energies, Ea1 (<800 °C) and Ea2 (>800 °C), are in the range of 5.5–12 kJ mol−1 and 80–140 kJ mol−1, respectively. The crystallite size, microstrain, surface area and growth activation energy of the samples showed a strong dependence on the Sc3+ doping concentration. The nanocrystalline (ZrO2)1−x(Sc2O3)x samples underwent complex phase transitions upon calcination from 800 to 1000 °C. Tetragonal and cubic phases have been preserved when the samples calcined below 800 °C as a result of crystallite size and doping effects. At elevated calcination temperature of 1000 °C, the compositions at x = 0.04, 0.10 and 0.14 seemed to be in the metastable phase boundaries of m + t, t + β (Sc2Zr7O17) and β + γ (Sc2Zr5O13), respectively. As calcined at 1400 °C, the grain size was in the micrometre regime, and t → m, c → t″, c → β and c → γ phase transitions occurred on the cooling stage for x ≤ 0.04, x = 0.08, 0.10 ≤ x ≤ 0.12 and x ≥ 0.14, respectively, resulting in the existence of m, t, t″, β and γ phases in turn at room temperature. Moreover, it was found that the tetragonal phase has been enriched at the surface region for the as-calcined (ZrO2)0.94(Sc2O3)0.06 and (ZrO2)0.92(Sc2O3)0.08 samples.

Secondary ageing in Al-Cu-Mg

Secondary ageing, that is microstructural evolution occurring at room temperature after short heating at temperatures above the metastable phase boundary of Guinier-Preston zones, has been studied for an Al-Cu-Mg alloy with a high Cu-to-Mg ratio. Combined data from positron annihilation spectroscopy, Vickers microhardness measurements and differential scanning calorimetry show that, on secondary ageing after 5 or 7min at 190°C, firstly, hardening takes place at a rate nine to 16 times slower than natural age hardening; secondly, vacancies slowly released by Cu-rich aggregates formed during the heat treatment at 190°C promote further formation of solute aggregates, with a time-dependent chemical composition; thirdly, the thermal stability of the structures formed during secondary ageing increases with increasing dwell time at room temperature; and, fourthly, solute aggregates formed at 190°C undergo a structural reorganization and possibly a change in the composition, leading to species with a different thermal stability. The slow release of vacancies from Cu-rich aggregates is proposed as one of the limiting factors of the hardening rate.

Computation of metastable phases in tungsten-carbon system

Metastable phase equilibria in the W-C system are presented in the vicinity of the metastable reactions involving W2C, WC1−x , and WC. Metastable phase boundaries were obtained by reproducing the stable boundaries using optimized Gibbs energy formulations and extrapolating them into regions of metastability. Four metastable reactions were obtained: a metastable congruent melting reaction of WC at 3106 K, a metastable eutectic reaction between WC1−x and graphite at 2995 K, a metastable eutectic reaction between W2C and WC at 2976 K, and a metastable eutectic reaction between W2C and graphite at 2925 K. The reaction enthalpies and entropies associated with these transitions are also computed using the available Gibbs energy data. Furthermore, possible kinetic paths that could lead to metastability are discussed.

Control of protein crystal nucleation around the metastable liquid-liquid phase boundary.

The capability to enhance or suppress the nucleation of protein crystals opens opportunities in various fundamental and applied areas, including protein crystallography, production of protein crystalline pharmaceuticals, protein separation, and treatment of protein condensation diseases. Herein, we show that the rate of homogeneous nucleation of lysozyme crystals passes through a maximum in the vicinity of the liquid-liquid phase boundary hidden below the liquidus (solubility) line in the phase diagram of the protein solution. We found that glycerol and polyethylene glycol (which do not specifically bind to proteins) shift this phase boundary and significantly suppress or enhance the crystal nucleation rates, although no simple correlation exists between the action of polyethylene glycol on the phase diagram and the nucleation kinetics. The control mechanism does not require changes in the protein concentration, acidity, and ionicity of the solution. The effects of the two additives on the phase diagram strongly depend on their concentration, which provides opportunities for further tuning of nucleation rates.

Strategies for the development of nanocrystalline materials through devitrification

The crystallization of metallic glass through devitrification reactions can yield ultrafine nanocrystalline product structures. The recent discovery of Al-rich glasses containing85 at.% Al and a combination of transition and rare earth element additions has yielded microstructures of Al nanocrystals in an amorphous matrix with nanocrystal volume fractions approaching 20% and excellent mechanical properties. Similar behavior is reported for Fe-based alloy glass systems such as Fe-Nb-B, and Fe-Si-B. This characteristic microstructure is synthesized by a primary crystallization reaction that yields a density of > 10 20 m −3 nanocrystals and limited growth. The systematic control of the nanocrystal development can be addressed by strategies based on thermodynamic and kinetic factors. The first issue is the initial glass formation which may be approached on the basis of the Egami size factor criteria. However, this must be applied to the amorphous phase that coexists with the nanocrystals following primary crystallization based on metastable phase boundaries. The growth control limitation has been identified to arise from diffusion field impingement. This control is enhanced for compositions that yield the highest initial particle densities for a given nanocrystal volume fraction. For example, the addition of transition elements to the Al-based glasses initially enhances the range of glass-forming conditions as the solute level increases, but excess levels diminish the driving force for fcc nanocrystal formation while increasing the driving force for intermetallic formation. The kinetic strategies also indicate processing directions to promote and retain a high density of nanocrystal dispersions including the possible utilization of sequential intermetallic crystallization reactions to modify the nanocrystal-amorphous matrix stability. The alloying strategies to promote and retain a high density of nanocrystal dispersions are quite general and may be applied to any system exhibiting primary nanocrystal formation through devitrification, including the Fe-based FINEMET alloys.

DIRECT MEASUREMENTS OF SURFACE STRESS USING TRANSMISSION ELECTRON MICROSCOPY

Surface stress and energy are concepts which are often misunderstood. In this work, we will clarify the difference between the two. We describe the use of transmission electron microscopy to measure surface stress by quantitative analysis of strain contrast images. We find that images of surface-stress-induced strain fields can be used to measure quantitative differences in surface stress provided the imaging parameters are accurately determined. We have applied this method to measure the stress difference between the 7×7 and high temperature "1×1" phases of the Si(111) surface at the phase coexistence temperature and between metastable phase boundaries on the Si(111) and amorphous-Ge interface. We discuss the significance of these measurements and pitfalls to be avoided in image simulations.

Order-disorder changes in Fe3Al based alloys and the development of an iron-base α-α″ superalloy

FeAl alloys containing slightly less than 25% Al are a two phase mixture of disordered plus DO3-ordered phases at temperatures somewhat below 550°C. The morphology and stability of microstructure has been examined in one such binary FeAl alloy when in the two-phase state, and compared with a ternary FeAlSi alloy showing similar phase mixtures at similar temperatures. Phase changes in these alloys can be understood on the basis of the equilibrium phase diagram, including metastable phase boundary extensions and conditional spinodal decompositions to account for order changes occurring faster than chemical diffusional changes. Such two-phase microstructures are relatively stable against coarsening at these intermediate temperatures, particualrly for the FeAlSi alloy which is believed to be due to its lower diffusivity and smaller interface energy. Such two-phase alloys, particularly when the composition is carefully chosen for the required stability and ordered volume fraction at a given temperature, should represent an Fe-base b.c.c. equivalent to the Ni-base superalloys.

Low‐Temperature Phase Equilibria by the Flux Method and the Metastable–Stable Phase Diagram in the ZrO2–CeO2 System

Low‐temperature phase equilibria ranging from 1000° to 1200°C in the ZrO2–CeO2 system were investigated by annealing compositionally homogeneous ZrO2–CeO2 solid solutions in a Na2B2O7.1 NaF flux. The 5 mol% CeO2 samples decomposed into monoclinic (m) and tetragonal (t) phases during annealing at 1100°2 and 1120°C, and the t‐phase transformed diffusionlessly into monoclinic (m′) symmetry during quenching. A eutectoid reaction, t→ (m + c), was confirmed to occur at 1055°± 10°C, where the equilibrium compositions of the t‐, m‐, and c‐phases were 11.2 ± 2.8, 0.9 ± 0.9, and 84 ± 1 mol% CeO2, respectively. The equilibrium phase boundaries were almost independent of the annealing time and/or the flux:sample ratio, which indicates that the flux accelerates the reaction rate withouts affecting the equilibration. The previous data are discussed using metastable–stable phase diagrams. The discrepancies of the low‐temperature phase diagram in the literature are attributable to either regarding the metastable phase boundaries as stable ones or ignoring the sluggish kinetics.

Simple computer program used for the calculation of stable and metastable phase boundary lines for the pseudobinary edges in the BaO-CuO x-YO 1.5 system

A simple computer program is tested to calculate pseudobinary edges of BaO-CuO x -YO 1.5 and the results are compared with other experimentally measured and theoretically calculated data with good success. Some discrepancies were noticed between tabulated and actually used thermochemical data for the compounds in question.

Metastable phase equilibria in the lead-tin alloy system: Part I. Experimental

Several metastable phase boundaries in the Pb-Sn alloy system have been determined in undercooled droplets containing different phase mixtures by means of X-ray diffraction lattice parameter and thermal analysis measurements. With droplets equilibrated as (α-Pb+L) mixtures, the metastable α-Pb solidus has been determined to reach 46 at. pct Sn with a corresponding liquidus at 87 at. pct Sn for a temperature 73°C below that for the stable eutectic. An extension of the metastable liquidus and solidus boundaries implies a melting of fcc Sn at about 5°C which agrees well with thermodynamic model calculations. With some solidification treatments a metastable, intermediate, body-centered tetragonal α1 phase can form in alloys with compositions between 35 and 73 at. pct Sn. Upon heating, the α1-phase decomposes to a supersaturated α-Pb phase and liquid by a peritectic reaction at 127°C. Calorimetric measurements yield an enthalpy of ΔHα1 = 3.16 ± 0.3 kJ/g atom for the α1/(α-Pb + L) peritectic reaction. The combination of the measured stable equilibria, the partial metastable equilibria determination, and phase equilibria modeling has allowed for a more complete description of metastable equilibrium behavior and for the analysis of some of the solidification pathways that are available for the synthesis of metastable product structures.