Phase Transitions In Solid Solutions Research Articles

Percolation phase transition, self-organization processes and thermal conductivity in PbSe1-xTex semiconductor solid solutions at small Te concentration

ABSTRACT The isotherms of the lattice thermal conductivity λ L for the PbSe1-xTex semiconductor solid solutions (х = 0–0.045) were obtained in the temperature range T = (200–600) K. The λ L(x) dependences exhibit a general trend to a decrease in λ L with increasing x, but the peaks are observed near x = 0.007, 0.015 and 0.0025 indicating the presence of phase transformations. We associated the first peak with a percolation-type phase transition to the impurity continuum and estimated the critical index for λ L within the framework of dynamic scaling theory. The second and third peaks were attributed to the self-organization processes in the PbSe1-xTex after the percolation threshold reaching. The effective cross-sections σ s for phonon scattering by impurity (Te) atoms were determined experimentally and calculated theoretically using the Klemens theory. The data obtained are another confirmation of our assumption about the presence of such percolation-type phase transition in any solid solution.

Predominant P3-Type Solid-Solution Phase Transition Enables High-Stability O3-Type Na-Ion Cathodes.

Layered O3-type oxides are one of the most promising cathode materials for Na-ion batteries owing to their high capacity and straightforward synthesis. However, these materials often experience irreversible structure transitions at elevated cutoff voltages, resulting in compromised cycling stability and rate performance. To address such issues, understanding the interplay of the composition, structure, and properties is crucial. Here, we successfully introduced a P-type characteristic into the O3-type layered structure, achieving a P3-dominated solid-solution phase transition upon cycling. This modification facilitated a reversible transformation of the O3-P3-P3' structure with minimal and gradual volume changes. Consequently, the Na0.75Ni0.25Cu0.10Fe0.05Mn0.15Ti0.45O2 cathode exhibited a specific capacity of approximately 113 mAh/g, coupled with exceptional cycling performance (maintaining over 70% capacity retention after 900 cycles). These findings shed light on the composition-structure-property relationships of Na-ion layered oxides, offering valuable insights for the advancement of Na-ion batteries.

Thermodynamics of multi-sublattice battery active materials: from an extended regular solution theory to a phase-field model of LiMnyFe1-yPO4

Phase separation during the lithiation of redox-active materials is a critical factor affecting battery performance, including energy density, charging rates, and cycle life. Accurate physical descriptions of these materials are necessary for understanding underlying lithiation mechanisms, performance limitations, and optimizing energy storage devices. This work presents an extended regular solution model that captures mutual interactions between sublattices of multi-sublattice battery materials, typically synthesized by metal substitution. We apply the model to phospho-olivine materials and demonstrate its quantitative accuracy in predicting the composition-dependent redox shift of the plateaus of LiMnyFe1-yPO4 (LFMP), LiCoyFe1-yPO4 (LFCP), LiCoxMnyFe1-x-yPO4 (LFMCP), as well as their phase separation behavior. Furthermore, we develop a phase-field model of LFMP that consistently matches experimental data and identifies LiMn0.4Fe0.6PO4 as a superior composition that favors a solid solution phase transition, making it ideal for high-power applications.

Physicochemical property and chromium leaching behavior in different environments of glass ceramics prepared from AOD stainless steel slag

Herein, we prepare Cr-containing glass ceramics from argon-oxygen-decarburization stainless steel slag and characterize their physicochemical properties (e.g., Cr stability), revealing the occurrence of a diopside solid solution → akermanite-gehlenite solid solution phase transition with increasing slag content. The properties of all ceramics (slag content = 40–80 wt%) met the requirements of the construction industry for building materials, with the highest flexural strength (137.83 MPa) as well as good acid and alkali resistance achieved at a slag content of 50 wt%. Moreover, the prepared ceramics were subjected to Cr leaching tests, which revealed that (i) Cr leached into aqueous solution was mainly present in the form of Cr3+ and largely precipitated as Cr(OH)3 and (ii) the layered structure of akermanite-gehlenite glass ceramics can partially bind Cr and thus facilitate its effective immobilization.

Magnetic phase transitions in solid solutions of Fe-containing perovskite multiferroics

Concentration dependences of magnetic phase transitions temperatures TM for several solid solutions of perovskite multiferroics BiFeO3, PbFe1/2Nb1/2O3 (PFN), and PbFe0.5Sb0.5O3 (PFS) have been studied using Mössbauer spectroscopy. In all the solid solutions studied, the values of TM were found to depend not only on the concentration of the Fe3+ ions in the lattice, but also on the short-range and/or long-range ordering of Fe3+ and B5+ ions, as well as on the mean lattice parameter values and on the nontrivial magnetic superexchange involving the empty p-orbitals of Pb2+ and Bi3+ cations.

Diffraction spectra of order–order transition structural states in titanium monoxide

A new class of M(n−i)X(n−i) superstructures (n is an integer constant and i is a rational variable) that are formed after incomplete equilibrium second-order order–order phase transitions in solid solutions and in compounds with atom–vacancy ordering is proposed. New superstructures are superpositions of partially disordered M n −X n superstructures of various symmetries in the matrix of the basic crystal structure. The model parameters affecting the positions and intensities of superstructure reflections on diffraction patterns have been studied by example of the high-temperature ordered phase β-TiO of titanium monoxide. It has been shown that the diffraction spectra of the low-symmetric M(5-i)X(5-i) superstructure (space group P1m1) and the high-symmetric M5X5 superstructure (space group Pm3m) at certain parameters are identical in the positions of superstructure reflections.

The Phase Transition of Corundum-Eskolaite Mineral Series Probed by X-Ray Absorption Spectroscopy

The red color of ruby is caused by Cr3+ impurities substituting Al3+ in Al2O3 structure. The complete substitution of Al3+ by Cr3+ produces Cr2O3 that has the green color. In this study, we focused on the phase transition of solid solution between corundum (Al2O3) and eskolaite (Cr2O3) mineral series. A series of Al2O3-Cr2O3 samples were prepared by mixing fine powder of Al2O3 and Cr2O3 in various ratios. They were ground together and then recrystallized. The obtained crystals were ground again in powder form for X-ray absorption near edge structure (XANES) measurements to avoid polarization dependence. The measurements were carried out at the Cr K-edge absorption energy using a 13-channel array Ge detector in the fluorescence mode. The XANES spectra showed line-shape transitions for 0.125 to 100% variation of Cr2O3. Significant variations in transitions were found when the Cr2O3 content was between 20% and 80%. With Cr2O3 concentration increasing, the sample colors apparently turned from pink to dark green. CIELAB color index measurements were performed. The variations of line-shape spectra of the Al2O3-Cr2O3 samples were found to be consistent with the CIELAB color index results. This Cr K-edge XANES study could be useful for the research in mineral sciences.

Determining the boundaries of second-type phase transitions in Ag–Mg–Cd alloys by means of diffusion couples

The interaction between elements in the transition zones of diffusion couples Mg + AgCd–alloy are studied. Isothermal sections of the Ag–Mg–Cd ternary system at 573 K are constructed. The existence of a Heusler phase based on H–Ag2MgCd compound is found in the field of the solid β′-solution. It is shown that the interdiffusion of components prevents the formation of ordered phases in the transition zones of bimetals, allowing us to determine the boundaries of second-type phase transitions in solid solutions.

On the mathematical modelling of cellular (discontinuous) precipitation

Cellular precipitation is a dynamic phase transition in solid solutions (such as alloys) where a metastable phase decomposes into two stable phases : an approximately planar (but corrugated) boundary advances into the metastable phase, leaving behind it interleaved plates (lamellas) of the two stable phases.The forces acting on each interface (thermodynamic, elastic and surface tension) are modelled here using a first-order ODE, and the diffusion of solute along the interface by a second-order ODE, with boundary conditions at the triple junctions where three interfaces meet. Careful attention is paid to the approximations and physical assumptions used in formulating the model.These equations, previously studied by approximate (mostly numerical) methods, have the peculiarity that $v,$ the velocity of advance of the interface, is not uniquely determined by the given physical data such as $c_0$, the solute concentration in the metastable phase. It is hoped that our analytical treament will help to improve the understanding of this.We show how to solve the equations exactly in the limiting case where $v=0$. For larger $v$, a successive approximation scheme is formulated. One result of the analysis is that there is just one value for $c_0$ at which $v$ can be vanishingly small.

Vibrational contributions to the phase stability of PbS-PbTe alloys

The thermoelectric figure of merit $(ZT)$ of semiconductors such as PbTe can be improved by forming nanostructures within the bulk of these materials. Alloying PbTe with PbS causes PbS-rich nanostructures to precipitate from the solid solution, scattering phonons and increasing $ZT$. Understanding the thermodynamics of this process is crucial to optimizing the efficiency gains of this technique. Previous calculations of the thermodynamics of PbS-PbTe alloys [(J. W. Doak and C. Wolverton, Phys. Rev. B 86, 144202 (2012)] found that mixing energetics alone were not sufficient to quantitatively explain the thermodynamic driving force for phase separation in these materials: first-principles calculations of the thermodynamics of phase separation overestimate the thermodynamic driving force for precipitation of PbS-rich nanostructures from PbS-PbTe alloys. In this work, we re-examine the thermodynamics of PbS-PbTe, including the effects of vibrational entropy in the free energy through frozen-phonon calculations of special quasirandom structures (SQS) to explain this discrepancy between first-principles and experimental phase stability. We find that vibrational entropy of mixing reduces the calculated maximum miscibility gap temperature ${T}_{G}$ of PbS-PbTe by 470 K, bringing the error between calculated and experimental ${T}_{G}$ down from 700 to 230 K. Our calculated vibrational spectra of PbS-PbTe SQS exhibit dynamic instabilities of S ions that corroborate reports of low-$T$ ferroelectriclike phase transitions in solid solutions of PbS and PbTe, which are not present in either of the constituent compounds. We use our calculated vibrational spectra to obtain phase transition temperatures, which are in qualitative agreement with experimental results for PbTe-rich alloys, as well as to predict the existence of a low-$T$ displacive phase transition in PbS-rich PbS-PbTe, which has not yet been experimentally investigated.

Synthesis and characterization of oriented linked LiFePO4 nanoparticles with fast electron and ion transport for high-power lithium-ion batteries

LiFePO4 nanoparticles with different morphologies and sizes were synthesized via a solvothermal method using environmentally benign and low-cost glycerol as the surfactant. The morphology, size, and structure of the particles were found to relate closely to the concentration of glycerol. Oriented linked LiFePO4 nanorods along mostly non-[010] were obtained with the proper concentration of glycerol. The nanorods showed good electronic and ionic conductivities, resulting in superior rate capability and cycling performance. This performance was attributed to the oriented linkages along mostly non–[010], the small particle size along [010], and the occupation of Li at Fe sites. Initial discharge capacities of 162.4 mA·h·g–1 at 0.1 C and 102.1 mA·h·g–1 at 30 C were achieved, with capacity retentions after 500 cycles at 5 and 20 C of 99.5% and 93.2%, respectively. At the rate of 40 C, the solid-solution phase transition dominated during lithiation and delithiation of all samples.

High electrochemical performance of high-voltage LiNi0.5Mn1.5O4 by decoupling the Ni/Mn disordering from the presence of Mn3+ ions

Electrochemical activity in high-voltage spinel LiNi0.5Mn1.5O4 (LNMO) is strongly affected by the disordering of Ni/Mn and the presence of Mn3+ ions. However, understanding the effect of the Ni/Mn disordering or the presence of Mn3+ ions on electrochemical properties is not trivial because disordering is typically coupled with the presence of Mn3+ ions. Here, we demonstrate for the first time that the doping of Li instead of Ni increases Ni/Mn disordering, which is decoupled from the presence of Mn3+ ions. The resultant material has a particle size of ~1–2 μm and can achieve 120 mAh g−1 at 10 C for 50 cycles and further deliver about 60 mAh g−1 even at a rate of ~60 C (1 min discharge). Superior electrochemical performance is achieved by increased solid-solution phase transition behavior, which is caused by increased Ni/Mn disordering during delithiation. By decoupling, we find that the electrochemical properties in LNMO strongly depend on the phase transformation behavior and that the Ni/Mn disordering, rather than Mn3+ ions, affects the phase transformation by increasing the solid-solution reaction. The fundamental understanding gained from this work could be applied to the development of other phase-separating compounds to improve their electrochemical performance. Doping LiNi0.5Mn1.5O4 (LNMO) with Li instead of Ni significantly improves its electrochemical performance, find scientists in Korea. Cathode materials with high redox potentials are needed to realize lithium-ion batteries with high energy densities. The high-voltage spinel LNMO is a promising cathode material, but its electrochemical performance is strongly affected by the disordering of Ni/Mn in the presence of Mn3+ ions. Now, Junghwa Lee, Chaeah Kim and Byoungwoo Kang at Pohang University of Science and Technology in Korea have found that doping LNMO with Li decouples Ni/Mn disordering from the presence of Mn3+ ions. This significantly improves its electrochemical performance through enhanced solid-solution phase transition. The researchers anticipate that the results of the current study can be used to improve the electrochemical performance of other phase-separating compounds. We at the first time demonstrate that the Ni/Mn disordering in LNMO spinel is decoupled from the presence of Mn3+ ions by doping Li and strongly affects phase transformation resulting in the increase of solid-solution phase transformation. The resulting material with 1–2 μm achieves superior rate capability, 120 mAh g−1 at ~38 C and 60 mAh g−1 at 60 C.

Concentration phase transitions in Li x Na1 − x Ta y Nb1 − y O3 solid solutions

The ferroelectric-antiferroelectric concentration phase transitions in solid solutions of LixNa1 − xTayNb1 − yO3, which are promising environmentally friendly (lead-free) ferropiezoelectric materials, are studied by means of Raman spectroscopy.

The role of lone pairs in the ferroelastic phase transition in the palmierite-type lead phosphate-arsenate solid solution

Abstract The structural changes associated with the R-3m to C2/c ferroelastic phase transition in the solid solution Pb3(P1–x As x O4)2 have been followed by Raman spectroscopy on samples with x = 0.00, 0.08, 0.37, 0.57, 0.65, 0.80, 1.00 over the temperature range 80–850 K. The high-temperature structural state of four intermediate samples with x = 0.37, 0.57, 0.65 and 0.80 was also studied by synchrotron single-crystal X-ray diffraction. The new results, in combination with previous data, reveal that Pb3(P1–x As x O4)2 undergoes a complex sequence of transformation processes with several characteristic temperatures that can be clearly identified in addition to that of the ferroelastic phase transition at T c. These structural changes are mainly driven by two phonon modes: vibrations of the Pb2 atoms (stereochemically active in the C2/c phase perpendicular to the layers characteristic of the palmierite-type structure), and rotational modes of the PO4 and AsO4 units within the plane of the layers. The former ensures coupling of the atomic displacements both within and between the layers, while the latter favours the coupling of the monoclinic species within the layers. With decreasing temperature, at T 4 ≫ T c the Pb2 atoms are displaced from their special positions on the triad axis of the R-3m structure. At T 3 the size of the nanoclusters composed of coupled displacements of Pb2 atoms on the monoclinic pattern is sufficient to produce both macroscopic effects in all compositions (diffuse super-lattice intensities in the diffraction patterns, non-symmetry-breaking strain in the unit-cell parameters, a step in the C p curve) and microscopic effects in the broadening of the vibrational modes of the Pb2 atoms. The temperature interval between T 3 and T 4 is considerably smaller for the intermediate compositions than for the end-members indicating that the chemical disorder on the tetrahedral site facilitates the condensation of monoclinic species, probably by smearing the potential barrier between different monoclinic orientational states. At T 2 < T 3, but still above T c, the AsO4 tetrahedra undergo monoclinic deformation in order to better coordinate the adjacent displaced Pb2 atoms, while the geometry of the PO4 tetrahedra remains unchanged down to T c (and for As-rich compositions, slightly below T c). At T c the ordered Pb2 displacements and rotated tetrahedra drive a displacement of the Pb1 atoms from their trigonal (paraelastic) positions and long-range-ordered ferroelastic domains are formed. However, for all compounds, residual disorder of the Pb2 displacements persists below T c to a further characteristic temperature T 1 at which the displacements of all types of atoms become completely ordered on all length scales.

Study of ferroelectric phase transitions in solid solutions based on bismuth vanadate

The structural, thermal, nonlinear optical, and conducting properties of Bi4(V1 − xMex)2O11 − y solid solutions (Me = Zr, Ga, Fe) have been investigated. The effect of domain wall pinning, accompanying the α ↔ β ferroelectric phase transition, is revealed. It is found that the conductivity in all studied series of solid solutions increases with an increase in x.

Lattice dynamics and ferroelectric phase transitions in solid solutions PbSc1/2Nb1/2O3 and PbSc1/2Ta1/2O3

The calculation of the lattice dynamics and ferroelectric phase transitions for disordered and ordered solid solution PbSc1/2Nb1/2O3 and PbSc1/2Ta1/2O3 in the framework of the Gordon-Kim model are performed. The unstable ferroelectric modes were found in all cases. The model Hamiltonian for the study finite temperature behavior during for the ferroelectric phase transition is used. The transition temperatures, phase sequences and spontaneous polarizations are calculated by Monte-Carlo method.

In-situ XRD investigations on structure changes of ZrO 2-coated LiMn 0.5Ni 0.5O 2 cathode materials during charge

The structural changes of pristine and ZrO 2-coated LiMn 0.5Ni 0.5O 2 cathode materials were investigated by using in situ X-ray diffraction (XRD) during charging process. An obviously solid solution phase transition from a hexagonal structure (H1) to another hexagonal structure (H2) was observed during the charging process at a constant current of 0.3 mA in the potential range of 2.5–5.7 V. The second hexagonal structure has a shorter a-axis and a longer c-axis before the crystal collapse. Before the structure collapses the c-axis length increases to maximum and then significantly decreases to 14.1 Å. The c-axis length of the pristine and ZrO 2-coated LiMn 0.5Ni 0.5O 2 increases to the maximum at the charge capacity of 119.2 and 180.9 mAh g −1, respectively. It can be concluded that the ZrO 2 coating can strongly stabilize the crystal structure of the LiMn 0.5Ni 0.5O 2 compound from the comparison of the lattice parameter variations between the pristine and the ZrO 2-coated LiMn 0.5Ni 0.5O 2 compounds upon charge. The potential fluctuation resulting from the decomposition of electrolytes starts at the charge capacity of around 200 and 260 mAh g −1 for the pristine and ZrO 2-coated LiMn 0.5Ni 0.5O 2, respectively. It suggests that the ZrO 2 coating layer can impede the reaction between the cathode material and electrolyte.

Kinetics of the phase transition in solid solutions of He4 in He3 at different degrees of supersaturation

Precision measurements of the pressure during phase separation in samples of solid solutions of He4 in He3 have been used to obtain data on the characteristic times of the phase transition. A processing of the results gives additional evidence supporting the view that homogeneous nucleation is realized in He3–He4 solid solutions at significant supercoolings and heterogeneous nucleation at the smallest supercoolings. Two different ways are proposed for comparing the results with a theoretical calculation taking into account the processes at the boundary of a nucleus of the new phase. Both give roughly similar values of the coefficient of surface tension at the nucleus–matrix boundary, and those values agree with those obtained in other studies. It is conjectured that the bcc–hcp transition has a substantial influence on the kinetics of separation at the lowest supersaturations.

Study of the Ferroelectric Domain Structure and Phase Transitions by Confocal Scanning Optical Microscopy

Confocal scanning optical microscopy (CSOM) has been shown to be a promising method to investigate different properties of ferroelectric domain structures. It combines diffraction-limited spatial resolution with non-invasiveness and sensitivity of optical techniques. We have obtained optical and electrooptic images in ac modulation mode using model ferroelectrics systems, including both single crystals and thin films. The origin of CSOM contrast, its dependence on mutual orientation of the electric field, ferroelectric polarization, and light polarization vector have been established. The direction of ferroelectric polarization in a given point can be determined accurately, within a few degrees. The phase transition in solid solution (Ba,Sr)TiO 3 thin films with different compositions has been studied. It has been shown that paraelectric and ferroelectric areas coexist on both sides of dielectric permittivity maximum. The phase transition was observed to be locally sharp, contrary to wide diffused peak in macroscopic characteristic. Local ferroelectricity was also observed in pure SrTiO 3 thin films, a quantum paraelectric in bulk form.

Description of ferroelectric phase transitions in solid solutions of relaxors in the framework of the random-field theory

A model based on the random-field theory is proposed for calculating the properties of solid solutions of ferroelectric relaxors. The electric dipoles randomly distributed in the system are treated as sources of random fields. The random field distribution function is calculated taking into account the contribution of nonlinear and correlation effects and the differences in the dipole orientations for different solid solution components. The dependence of the phase transition temperature Tc on the concentration of solid solution components is analyzed. Numerical calculations are performed for the lead scandoniobate and lead scandotantalate solid solutions (PbSc1/2Nb1/2O3)1−x(PbSc1/2Ta1/2O3)x with different degrees of ordering and the lead magnoniobate and lead titanate solid solution (PbMg1/3Nb2/3O3)1−x(PbTiO3)x. It is shown that the higher transition temperature for more disordered solid solutions of the composition (PbSc1/2Nb1/2O3)1−x(PbSc1/2Ta1/2O3)x in the range 0≤x<0.5 is associated with the larger nonlinearity coefficient for PbSc1/2Nb1/2O3 as compared to that for PbSc1/2Ta1/2O3. The theory provides a means for calculating the region of the coexistence of the phases with different symmetry groups in the temperature-composition phase diagram of the (PbMg1/3Nb2/3O3)1−x(PbTiO3) solid solution. Numerical calculations with the use of the fitting parameters obtained from the known transition temperatures Tc for the solid solution components adequately describe the experimental phase diagrams for the aforementioned solid solutions of ferroelectric relaxors.