Solid-state Miscibility Gap Research Articles

In Situ Exploration of the Structural Transition during Morphology‐ and Efficiency‐Conserving Halide Exchange on a Single Perovskite Nanocrystal

Controlled fabrication of semiconductor nanostructures with unique physicochemical properties is vital for future technologies. In this study, transformation from red-emitting metal halide perovskite CH3 NH3 PbI3 nanocrystals (NCs) to green-emitting CH3 NH3 PbBr3 NCs was achieved without significant morphological changes and loss of photoluminescence (PL) efficiency via a controlled halide exchange reaction. In situ single-particle PL imaging along with detailed structural and elemental characterizations revealed that sudden cooperative transitions between two light-emitting states via intermediate dark states with >100 s durations during halide exchange originate from two distinct defect-mediated reconstruction processes with different activation energies (0.072 and 0.40 eV), leading to an isokinetic temperature of ca. 314 K, across a solid-state miscibility gap between the I- and Br-rich phases inside a single NC.

Crystal growth of off-stoichiometric [formula omitted] Heusler compounds: Avoiding the solid state miscibility gap

Co2CrAl is predicted as a promising candidate for half-metallic ferromagnetism. Unfortunately, synthesis of the stoichiometric composition is a challenge as the samples prepared so far using various techniques suffer from formation of secondary phases and consequently anomalous physical properties. Off-stoichiometric compounds have been explored as a possible approach to avoid the secondary phase precipitation. The Co2Cr0.8Al1.2, Co2Cr0.6Al1.4 and Co2Cr0.4Al1.6 compositions were synthesized using Floating Zone (FZ) technique as they melt incongruently. The secondary phase fraction was reduced as Cr was partially substituted by Al. FZ-grown Co2Cr0.4Al1.6 was obtained as a single phase, signifying that the composition is out of the two-phase region. Furthermore, combining the data with an earlier work on annealing of spinodally decomposed samples, valuable insight into the extent of immiscibility was obtained.

Non-empirical phase equilibria in the Cr–Mo system: A combination of first-principles calculations, cluster expansion and Monte Carlo simulations

In this work, the low temperature part of the Cr–Mo phase diagram is calculated by a combination of first-principles calculations, cluster expansion, and Monte Carlo simulations without the use of empirical parameters. In brief, the miscibility gap in the bcc phase is computed through lattice Monte Carlo simulations with the energetics of the Cr–Mo system represented by cluster expansion Hamiltonians, wherein the Hamiltonians are firstly constructed using first-principles calculations of formation energies for supercells of various bulk compositions. It is demonstrated that the onset (critical) temperature of the miscibility gap is preliminarily computed to be Tc = 1720 K, and is significantly decreased to 1150 K once excess vibrational contribution to the free energy is considered. The resulting solid-state miscibility gap of the Cr–Mo binary system, largely improved by the contributions of atomic relaxation and positive excess volume of mixing in the Cr–Mo bcc alloys, also favors the approaches that extrapolate the Gibbs energy of the bcc phase retrieved at high temperatures, as in the CALPHAD method.

Contact melting and the structure of binary eutectic near the eutectic point

Computer simulations of contact melting and associated interfacial phenomena in binary eutectic systems were performed on the basis of the standard phase-field model with miscibility gap in solid state. It is shown that the model predicts the existence of equilibrium three-phase (solid–liquid–solid) states above the eutectic temperature, which suggest the explanation of the phenomenon of phase separation in liquid eutectic observed in experiments. The results of simulations provide the interpretation for the phenomena of contact melting and formation of diffusion zone observed in the experiments with binary metal–silicon systems.

Effect of annealing on spinodally decomposed Co2CrAl grown via floating zone technique

Among the large class of Heusler compounds, Co2CrAl is predicted to be 100% spin polarized and is hence, a potential candidate for application in spintronics. So far, the predicted properties have not been experimentally realized which may be attributed to the phase segregated nature of samples. This phase segregation is avoided using floating zone growth. However, the grown sample was found to have undergone phase transformation via spinodal decomposition at low temperatures. In the present work, thermal annealing has been done on the spinodally decomposed samples and its effect on microstructure, crystallographic structure and magnetic properties has been studied. Annealing experiments were done and analyzed in order to understand the extent of the solid state miscibility gap. With regards to the phase diagram, the two-phase regime was found to extend till 1000°C. Even at 1250°C, we are still inside the immiscibility region. The thermodynamic miscibility gap was thus found to exist until high temperatures and alternate routes might be required to obtain a single phase sample with the desired high spin polarization and Curie temperature in the Co–Cr–Al system.

Solid-state wetting transitions at grain boundaries

A previously developed model of the dependence of grain boundary (GB) segregation on GB character has been exercised to investigate solid-state wetting transitions at GBs, and their anisotropy. In the case of binary systems displaying a solid-state miscibility gap, it is shown that the wetting transition temperature for precipitates at a GB is anisotropic, and is inversely related to GB energy. The model also allows calculation of prewetting transitions and associated excursions in adsorption off phase coexistence. These transitions are first order below a prewetting critical point ( T PWC), and higher order at temperatures above T PWC. Investigation of the prewetting behavior provides the means for construction of the two-dimensional phase diagram of a GB.

Phase Diagram for the System RuO2-TiO2 in Air

There are conflicting reports in the literature regarding solid solubility in the system RuO2-TiO2. To resolve this issue a few experiments were conducted in air at 1673, 1723, and 1773 K. The results show limited terminal solid solubility. There is an extended solid-state miscibility gap that intersects the decomposition curve for the RuO2-rich solid solution generating a peritectoid reaction at 1698 K. The measured equilibrium compositions of the solid solutions are used to develop a thermodynamic description of the oxide solid solution with rutile structure. Using the subregular solution model, the enthalpy of mixing can be represented by the expression, \( \Delta H^{\rm M} /{\text{J}} \cdot {\text{mol}}^{{ - 1}} = X_{{{\text{TiO}}_{2} }} X_{{{\text{RuO}}_{2} }} {\left( {34,100X_{{{\text{TiO}}_{2} }} + 30,750X_{{{\text{RuO}}_{2} }} } \right)} \). The binodal and spinodal curves and T-X phase diagram in air are computed using this datum and Gibbs energy of formation of RuO2 available in the literature. The computed results suggest that equilibrium was not attained during solubility measurements at lower temperatures reported in the literature.

Thermodynamic modeling of Al–Ce–Mg phase equilibria coupled with key experiments

The ternary Al–Ce–Mg phase diagram was calculated using the Calphad method and investigated with selected key experiments. Arc melted alloys were annealed at 400 °C for 500 h and the phases were analyzed using quantitative X-ray powder diffraction (XRD). Differential thermal analysis (DTA) was also performed on an alloy with a composition near the ternary phase Al 13CeMg 6 ( τ). Temperatures above 1000 °C could be attained due to a special sealing of the sample under argon by welding in a tantalum crucible to avoid evaporation and oxidation. Only with this procedure could reproducible and reliable DTA signals be obtained. The present experimental investigation and the consistent thermodynamic calculation show that the “ternary phase” Ce(Mg,Al) 2, seemingly isolated in the ternary at 400 °C, can be rationalized as a single solid solution phase between the binary end members if a larger temperature range and a solid state miscibility gap is considered. It is demonstrated that previously reported low values of ternary liquidus temperatures must be related to other phase equilibria. The actually found ternary liquidus temperatures are much higher and widely governed by the high melting compound Ce(Al,Mg) 2 and also by Al 11Ce 3 with primary solidification fields stretching far into the ternary system.

Tie-lines and mixing properties of solid solutions in the system CaO-SrO-PbO-O at 1100 K

Phase relations in the system CaO-SrO-PbO-O2 at 1100 K have been determined by equilibrating samples with different compositions in air, oxygen, or evacuated ampoules for 7 days and characterizing quenched specimens by optical and scanning electron microscopy, energy-dispersive analysis of x-rays (EDX), and x-ray diffraction (XRD). There is a solid-state miscibility gap in the pseudo-binary system CaO-SrO, and continuous solid solubility between Ca2PbO4 and Sr2PbO4 at 1100 K. Substitution of Ca for Sr occurs only to a limited extent (∼2 mol.%) in SrPbO3. The calcium-rich solid solutions (Ca1−y Sr y )2PbO4 characterized by y≤0.255 are in equilibrium with PbO in air; compositions with y≥0.255 coexist with (Ca1−z Sr z )PbO3. There is a three-phase region involving the two monoxide solid solutions (Ca1−x Sr x )O on either side of the miscibility gap with x=0.24 and 0.71 and (Ca1−y Sr y )2PbO4 with y=0.96. Accurately determined are the locations of tie-lines between the solid solutions. Attainment of equilibrium was checked by the conventional tie-line rotation technique. The excess Gibbs energy of mixing of the solid solution with orthorhombic structure is obtained by an analysis of tie-line data; for the mixing of one mole of Ca and Sr represented by (Ca1−y Sr y )Pb0.5O2, ΔG E=y(1−y) [15,840−2950 y] J/mol. The thermodynamic properties suggest the onset of immiscibility in this solid solution below 884 (±5) K. The miscibility gap is asymmetric with a critical composition at y=0.43 (±0.02). Inside the triangle (Ca1−y Sr y )Pb0.5O2−(Ca1−z Sr z )PbO3−PbO, a small liquid-phase region is present close to the PbO corner, surrounded by three two-phase fields. Each corner of the approximately triangular liquid-phase region is associated with a three-phase field.

Activities and immiscibility in the system Cu-Rh

The thermodynamic activity of rhodium in solid Cu-Rh alloys is measured by the electromotive force method in the temperature range from 1050 to 1325 K with a solid-state cell: Rh, Cu 1 Cu2O//(Y2O3)ZrO2//Cu-Rh 1 Cu2O, Rh The activity of copper and the Gibbs energy, enthalpy, and entropy of mixing of the solid solution are derived. Activities exhibit large positive deviation from Raoult’s law. The mixing properties can be represented by a pseudo-subregular solution model in which excess entropy has the same type of functional dependence on composition as the enthalpy of mixing: DH 5 XRh(1 2 XRh)[41,340 1 12,670 XRh] J mol21 DSE 5 XRh(1 2 XRh)[15.46 1 4.72 XRh] J mol21 K21 The results predict a solid-state miscibility gap with Tc 5 1408 (65) K at XRh 5 0.59 (60.02). The computed critical temperature is 15 K lower than that reported in the literature. The coherent spinodal, calculated using Cahn’s model, is characterized by T8c 5 983 (65) K and X8Rh 5 0.43 (60.02). The large difference between the coherent and chemical spinodal is caused by the relatively large difference in lattice parameters of Cu and Rh and high Young’s modulus of the alloy. The positive enthalpy of mixing obtained in this study contrasts with the negative values predicted by Miedema’s model. Thermodynamic properties of liquid alloys are estimated from the data for solid alloys obtained in this study and the approximate location of the liquidus available in the literature.

Thermodynamic mixing properties and solid-state immiscibility in the systems Pd-Rh and Pd-Rh-O

The thermodynamic activity of rhodium in solid Pd-Rh alloys is measured in the temperature range 950 to 1350 K using the solid-state cell: $Pt-Rh, Rh + Rh_2O_3/(Y_2O_3)ZrO_2/Pd_{1-x} Rh _x + Rh_2O_3, Pt-Rh.$ The activity of palladium and the free energy, enthalpy, and entropy of mixing are derived. The activities exhibit strong positive deviation from Raoult's law. The activities obtained by the electro- chemical technique, when extrapolated to 1575 K, are found to be significantly lower than those obtained from vapor pressure measurements. The mixing properties can be represented by a pseudosubregular solution model in which excess entropy has the same type of function dependence on composition as the enthalpy of mixing:$\Delta H = X_{Rh}(1 - X_{Rh})(31 130 + 4 585X_{Rh} J/mol and \DeltaS^{ex} = X_{Rh}(1 - X_{Rh})(10.44+ 1.51X_{Rh}) J/mol·K.$ The positive enthalpy of mixing obtained in this study in qualitative agreement with predictions of semiempirical models. The results predict a solidstate miscibility gap with $T_c = 1210(\pm5)K at X_{Rh} = 0.55(\pm0.02)$. The computed critical temperature is approximately 100 K higher than that reported in the literature. The oxygen chemical potential for the oxidation of Pd-Rh alloys under equilibrium conditions is evaluated as a function of composition and temperature. The Gibbs energy of formation of PdO is measured as a function of temperature. At low temperatures, the alloys are in equilibrium with $Rh_2O_3$, and PdO coexists with Pd and $Rh_2O_3$. At high temperatures, PdO is unstable and Pd-rich alloys are in equilibrium with diatomic oxygen gas.

Thermodynamic properties and phase equilibria for Pt-Rh alloys

The activity of rhodium in solid Pt-Rh alloys is measured in the temperature range from 900 to 1300 K using the solid-state cell $$Pt - Rh,Rh + Rh_2 O_3 /(Y_2 O_3 )ZrO_2 /Pt_{1 - x} Rh_x + Rh_2 O_3 ,Pt - Rh$$ The activity of platinum and the free energy, enthalpy, and entropy of mixing are derived. Activities exhibit moderate negative deviation from Raoult’s law. The mixing properties can be represented by a pseudosubregular solution model in which excess entropy has the same type of functional dependence on composition as the enthalpy of mixing, $$\begin{gathered} \Delta H = X_{Rh} (1 - X_{Rh} )[ - 10,970 + 45X_{Rh} ] {J \mathord{\left/ {\vphantom {J {mol}}} \right. \kern-\nulldelimiterspace} {mol}} \hfill \\ \Delta S^E = X_{Rh} (1 - X_{Rh} )[ - 3.80 + 1.55 \times 10^{ - 2} X_{Rh} ] {J \mathord{\left/ {\vphantom {J {mol}}} \right. \kern-\nulldelimiterspace} {mol}} \cdot K \hfill \\ \end{gathered} $$ The negative enthalpy of mixing obtained in this study is in qualitative agreement with predictions of semiempirical models of Miedema and co-workers and Colinet et al. The results of this study do not support the solid-state miscibility gap suggested in the literature, but are consistent with liquidus data within experimental uncertainty limits.

Solid-state miscibility gap and thermodynamics of the system BaO–SrO

A solid-state miscibility gap in the pseudo-binary system BaO-SrO is delineated by X-ray diffraction studies on samples equilibrated either in vacuum or under flowing inert gas at temperatures between 1073 and 1423 K. For the SrxBa1-xO solid solution an asymmetric phase boundary, characterized by a critical temperature of 1356 (+/-4) K and composition x=0.55 (+/-0.008), is obtained. Thermodynamic mixing properties of the solid solution, derived from the experimental phase boundary compositions and temperatures, can be represented by the expression: Delta G(E)=x(1-x){33 390-7.09T)x+(29 340-6.23T)(1-x)} J mol(-1)It is necessary to include excess entropy terms to obtain a good fit to the experimental data. The chemical spinodal curve is computed from the thermodynamic parameters

Al-Co-Fe(Aluminum-Cobalt-Iron)

[88Ray] reviewed the phase relationships in this system and presented the data as: (1) two partial liquidus surfaces, one for Al-poor Fe-Co alloys and the other for compositions near the Al-corner; (2) an isothermal section at 800{degrees}C for Co-rich alloys; (3) two isothermal sections at 640 and 600{degrees}C for alloys near the Al-corner; and (4) a solid-state miscibility gap at {approx}500{degrees}C in the bcc ({alpha}) region of the ternary Fe-rich alloys, where the order-disorder reactions occur.

High drop tube undercooling experiments on TaZr alloys

Using an ultrahigh vacuum drop tube, undercooling experiments have been performed on the TaZr system, which exhibits a solid state miscibility gap between 12 and 95 wt.% Ta. The two elements were alloyed using a simple in situ technique; experimental problems encountered for Ta-rich samples are reported. The first metallurgical results are presented and discussed.

Molar heat capacities of cdte, hgte and cdte-hgte alloys in the solid state

Using a differential scanning calorimeter, the molar heat capacities of the two components HgTe and CdTe and of ten solid alloys of the CdTeHgTe system were measured at constant pressure between 300 K and 523 K. Irregular variations of the C p = φ( T) curves of CdTeHgTe alloys suggest the existence of a solid state miscibility gap in this system. The limit of the (solid ↔ solid (1) + solid (2)) miscibility gap and coordinates of the critical temperature ( χ CdTe ≠ 0.55, T = 455 K) are proposed. From C P data obtained in a single-phase solid region, the excess molar heat capacities ( ΔC P = C p(exp)− C p(calc)) at 500 K were deduced: the maximum negative excess C P is located at χ CdTe = 0.5.

Structural and thermodynamic data on the pseudobinary phases R(Co 1− xCu x) 5 WITH R ≡ Sm, Y, Ce

For the phases R(Co 1−itxCu itx) 5 with R ≡ Sm, Y, Ce, homogenized at 950 °C, the enthalpies of formation were determined by a calorimetry technique involving dissolution in molten tin and the lattice parameters were measured using X-ray diffraction in a focusing camera. In order to study the effect of substitution of cobalt for copper, the lattice parameters were corrected for the contribution of the departure of R from stoichiometry. For the R(Co 1−itxCu itx) 5 phases with R ≡ Sm, Y, the lattice parameters were also measured after heat treatment at 400 °C. The x dependences of the enthalpies of formation and lattice parameters indicate an ideal behaviour for the mixing of SmCo 5 and SmCu 5 on one hand, and for YCo 5 and YCu 5 on the other hand. This result is consistent with the homogeneous state found for Sm(Co 1−itxCu itx) 5 and Y(Co 1−itxCu itxon the whole x range at 400 °C. For the mixture of CeCo 5 and CeCu 5, the enthalpies of formation exhibit a slightly positive deviation which predicts the solid state miscibility gap previously evidenced in the CeCo 5-CeCu 5 section below 800 °C.

Phase equilibria in the CeCo 5-CeCu 5 system and structural characterization of the Ce(Co 1− xCu x) 5 phases

The phase equilibria of the CeCo 5-CeCu 5 system were determined by DTA and isothermal annealings. Except for the mixtures very rich in Cu, a pseudo-binary behaviour and direct melting of the phases are deduced from the results. A solid state miscibility gap is present below about 800 °C. For the Ce(Co 1− x Cu x ) 5 phases homogenized at 900 °C, the irregular increase of the lattice parameter as a function of x is attributed to a change of the valence state of Ce. The Cu and Co substitution entails a drastic decrease of the Curie temperature of the phases.

Thermodynamic investigations of solid CuNi and FeNi alloys and calculation of the solid state miscibility gap in the CuFeNi system

Activity values for fcc CuNi and FeNi alloys have been determined from solid electrolyte emf measurements. The results are discussed together with values reported by other investigators and evaluated data are presented for the thermochemical properties of CuNi and Fez.sbnd;Ni alloys. The evaluated data have been combined with a published assessment of the CuFe system to calculate the miscibility gap in the fee phase of the CuFeNi system.

Small-angle neutron scattering study of lipid phase diagrams by the contrast variation method.

A small-angle neutron scattering (SANS) study of slightly sonicated liposomes of binary lipid mixtures is presented. It is demonstrated that the neutron scattering of lipid lamellae may be analyzed in terms of the Kratky--Porod model of scattering by two-dimensional systems. The contrast variation technique may thus be applied in order to study the structure and phase diagrams of lipid layers not disturbed by heavy sonication. The thickness of isolated bilayers is measured, and molar volumes of pure lipid phases are determined. Mixtures of deuterated dimyristoylphosphatidylcholine with (1) protonated dipalmitoylphosphatidylcholine and (2) protonated distearoylphosphatidylcholine, respectively, are studied. Excess volumes of lipid mixtures are determined by the contrast variation. For the first mixture positive excess volumes of +86 A3 in the crystalline phase (5 degrees C) and of +49 A3 in the fluid phase (35 degrees C) are obtained. These large positive excess volumes are interpreted in terms of free volume creation at the interface between the monolayers, which indicates that the polar head groups are rather fixed with respect to the lipid--water interface. We show that the phase boundaries at a given temperature may be determined by performing contrast variation experiments for two mixtures with different initial composition. Good agreement with existing experimental data is observed for the first mixture. A miscibility gap is established in the crystalline state of the second mixture. A most interesting result is the finding of an immiscibility in the fluid state. This is interpreted in terms of critical concentration fluctuations caused by the critical demixing point of the solid-state miscibility gap hidden below the liquidus line.