Displacive Phase Transition Research Articles

The first-order flexibility of a crystallographic framework

Four sets of necessary and sufficient conditions are obtained for the first-order rigidity of a periodic bond-node framework C in Rd which is of crystallographic type. In particular, an extremal rank characterisation is obtained which incorporates a multi-variable matrix-valued transfer function ΨC(z) defined on the product space C⁎d=(C﹨{0})d. In general the first-order flex space is the closed linear span of polynomially weighted geometric velocity fields whose geometric multi-factors in C⁎d lie in a finite set. It is also shown that, paradoxically, a first-order rigid crystal framework may possess a nontrivial continuous motion. Examples of this phenomenon are given which are associated with aperiodic displacive phase transitions between periodic states.

Atomic-scale Evidence for Open-system Thermodynamics in the Early Solar Nebula

Abstract We report a new integrated framework that combines atomic-length-scale characterization via aberration-corrected scanning transmission electron microscopy with first-principles-driven thermodynamic modeling and dust-transport models to probe the origins of some of the first-formed solids in the solar system. We find that within one of the first solids that formed in our solar system, spinel, nominally MgAl2O4, occurs as a twinned inclusion within perovskite, CaTiO3, and contains vanadium segregated to its twin boundary as atomic columns. Our results support a scenario in which spinel condensed at 1435 K in the midplane of the solar protoplanetary disk and was later transported inward to a hotter region where perovskite condensed around it at 1681 K. The spinel became twinned as a result of a displacive phase transition in the perovskite after which it was later transported to cooler regions of the disk and incorporated into its parent asteroid. The condensation, transport, and phase transformation can all be explained within the developed self-consistent framework that reproduces the observed phase assemblage and atomic-scale structure. This framework suggests that planetary materials evolved within a thermodynamically open system and, moving forward, motivates such an approach in order to understand the thermodynamic landscape on which planetary materials formed.

Nanometer structure as a key to various phenomena in ferroelectrics

The results of studying ferroelectric materials obtained at the Institute of Automation and Electrometry of the Siberian Branch of the Russian Academy of Sciences in 1973-2020 are reported. Mechanisms of the photovoltaic effect and photorefraction, emergence and role of polar regions in ferroelectric crystals, methods of detection of polar regions, and mechanisms of manifestation of the displacive and order-disorder phase transitions in various ferroelectrics are discussed. The results of experimental and theoretical investigations allow one to conclude that imperfections of a crystal structure play a key role in phenomena observed in ferroelectrics.

Polymorphism and Fast Potassium-Ion Conduction in the T5 Supertetrahedral Phosphidosilicate KSi2 P3.

The all‐solid‐state battery (ASSB) is a promising candidate for electrochemical energy storage. In view of the limited availability of lithium, however, alternative systems based on earth‐abundant and inexpensive elements are urgently sought. Besides well‐studied sodium compounds, potassium‐based systems offer the advantage of low cost and a large electrochemical window, but are hardly explored. Here we report the synthesis and crystal structure of K‐ion conducting T5 KSi2P3 inspired by recent discoveries of fast ion conductors in alkaline phosphidosilicates. KSi2P3 is composed of SiP4 tetrahedra forming interpenetrating networks of large T5 supertetrahedra. The compound passes through a reconstructive phase transition from the known T3 to the new tetragonal T5 polymorph at 1020 °C with enantiotropic displacive phase transitions upon cooling at about 155 °C and 80 °C. The potassium ions are located in large channels between the T5 supertetrahedral networks and show facile movement through the structure. The bulk ionic conductivity is up to 2.6×10−4 S cm−1 at 25 °C with an average activation energy of 0.20 eV. This is remarkably high for a potassium ion conductor at room temperature, and marks KSi2P3 as the first non‐oxide solid potassium ion conductor.

Phase transitions in 2D materials

The discovery and control of new phases of matter is a central endeavour in materials research. The emergence of atomically thin 2D materials, such as transition-metal dichalcogenides and monochalcogenides, has allowed the study of diffusive, displacive and quantum phase transitions in 2D. In this Review, we discuss the thermodynamic and kinetic features of 2D phase transitions arising from dimensionality confinement, elasticity, electrostatics, defects and chemistry unique to 2D materials. We highlight polymorphic, ferroic and high-temperature diffusive phase changes, and examine the technological potential of controlled 2D phase transitions. Finally, we give an outlook to future opportunities in the study and applications of 2D phase transitions, and identify key challenges that remain to be addressed. Phase transformations in 2D materials have distinct kinetic and thermodynamic features, resulting from their reduced dimensionality and unique interactions. This Review discusses the properties of phase transitions and defects in 2D materials, and examines technological applications and challenges in the study of 2D phase transitions.

Soft mode theory of ferroelectric phase transitions in the low-temperature phase

Historically, the soft mode theory of ferroelectric phase transitions has been developed for the high-temperature (paraelectric) phase, where the phonon mode softens upon decreasing the temperature. In the low-temperature ferroelectric phase, a similar phonon softening occurs, also leading to a bosonic condensation of the frozen-in mode at the transition, but in this case the phonon softening occurs upon increasing the temperature. Here we present a soft mode theory of ferroelectric and displacive phase transitions by describing what happens in the low-temperature phase in terms of phonon softening and instability. A new derivation of the generalized Lyddane–Sachs–Teller (LST) relation for materials with strong anharmonic phonon damping is also presented which leads to the expression ɛ 0/ɛ ∞ = |ω LO|2/|ω TO|2. The theory provides a microscopic expression for T c as a function of physical parameters, including the mode specific Grüneisen parameter. The theory also shows that , and again specifies the prefactors in terms of Grüneisen parameter and fundamental physical constants. Using the generalized LST relation, the softening of the TO mode leads to the divergence of ϵ 0 and to a polarization catastrophe at T c. A quantitative microscopic form of the Curie–Weiss law is derived with prefactors that depend on microscopic physical parameters.

Composition, Thermal Expansion and Phase Transitions in Framework Silicates: Revisitation and Review of Natural and Synthetic Analogues of Nepheline-, Feldspar- and Leucite-Mineral Groups

Framework silicates form about 70% of the Earth’s crust, mainly feldspars ~50–60% and quartz ~10–15%. Less-abundant feldspathoids include nepheline-, leucite-, and sodalite-group minerals, rich in structurally challenging properties. This review paper deals with anhydrous feldspar-, nepheline-, and leucite/pollucite groups, emphasising the importance of parallel studies on natural and synthetic samples. Four topics are covered. For decades, petrologists have analysed nephelines and recalculated their compositions as endmember molecules but, by not following rules of stuffed-tridymite crystal chemistry, have not estimated reliably the excess SiO2 present in solid solution. Some materials scientists make similar mistakes, and a new approach is described here. Synthesis studies of analogue feldspars, nephelines, and leucite/pollucites led to collaborative studies, mainly using laboratory and synchrotron X-ray powder diffraction methods at room and elevated temperatures, to study thermal expansion and displacive phase transitions. Such work was recently expanded to address the spontaneous strain relations. Topics covered here include work on nepheline/kalsilite analogues in the system SrAl2O4—BaAl2O4; thermal expansion of (K,Na)Al-, RbAl-, RbGa-, and SrAl-feldspars; and thermal expansion and phase transitions in analogue leucites KGaSi2O6 (tetragonal to cubic) and K2MgSi5O12 (monoclinic to orthorhombic). Results are reviewed in the context of research published in mineralogical and more-widely in physical sciences journals.

Four-dimensional imaging of lattice dynamics using ab-initio simulation

Time-resolved mapping of lattice dynamics in real- and momentum-space is essential to better understand several ubiquitous phenomena such as heat transport, displacive phase transition, thermal conductivity, and many more. In this regard, time-resolved diffraction and microscopy methods are employed to image the induced lattice dynamics within a pump–probe configuration. In this work, we demonstrate that inelastic scattering methods, with the aid of theoretical simulation, are competent to provide similar information as one could obtain from the time-resolved diffraction and imaging measurements. To illustrate the robustness of the proposed method, our simulated result of lattice dynamics in germanium is in excellent agreement with the time-resolved x-ray diffuse scattering measurement performed using x-ray free-electron laser. For a given inelastic scattering data in energy and momentum space, the proposed method is useful to image in-situ lattice dynamics under different environmental conditions of temperature, pressure, and magnetic field. Moreover, the technique will profoundly impact where time-resolved diffraction within the pump–probe setup is not feasible, for instance, in inelastic neutron scattering.

A linear scaling law for predicting phase transition temperature via averaged effective electronegativity derived from A2M3O12-based compounds.

The chemical flexibility of A2M3O12-based compounds enables the design of materials with versatile functionalities such as ferroelastic switching, ion conduction and negative thermal expansion (NTE) above the ferroelastic transition temperature (Tt), which is promising for a variety of applications. Quantitative prediction of Tt is essential but lacking. Herein we propose a concept of averaged effective electronegativity (AEE) and establish a linear relationship between the Tt and AEE for A2M3O12-based compounds. The linear scaling law is validated using first principles calculations of the effective charge on oxygen and its effectiveness is verified experimentally by designing high entropy compounds Scx1Zrx2Hfx3Fex4Moy1Vy2O12 and a NTE compound Zr2MoVPO12 with expected Tt. Generalization of the linear scaling law to other NTE oxides with displacive phase transition is also demonstrated. The findings can be used as a simple and effective approach to guide the design of novel compounds with desired properties and Tt.

Phase transitions in CaCO3 under hydrous and anhydrous conditions: Implications for the structural transformations of CaCO3 during subduction processes

AbstractThe transport of calcium carbonate (CaCO3) into the Earth’s interior through subduction is one of the key processes in the global cycling of carbon. To develop a better understanding of the CaCO3 structural stability during subduction processes, the phase transitions among CaCO3-I (calcite), CaCO3-II, -III/IIIb, and aragonite under pressure-temperature (P-T) conditions up to 2.5 GPa and 600 °C, in hydrous and anhydrous environments, were investigated using a hydrothermal diamond-anvil cell. One displacive and two reconstructive processes during the phase transitions among CaCO3 polymorphs were confirmed from the results obtained from in situ observations and Raman spectroscopic measurements. Meanwhile, the effect of Ca-substitutional metal cations (e.g., Mg2+) in CaCO3 and the presence of an aqueous fluid on the phase transition processes have been determined. Specifically, the CaCO3-I ↔ -II phase transition is a displacive process, occurring instantly at pressures varying from 1.6 GPa at room temperature to 1.5 GPa at 500 °C with the phase equilibrium boundary having a minimum P-T point at ~1.4 GPa at 300 °C, and is completely reversible upon cooling and decompression. The CaCO3-II → -III phase transition is a reconstructive process, observed at P-T conditions from 2.0 GPa at room temperature to 2.5 GPa at 150 °C, and is accomplished by solid recrystallization starting from CaCO3-II, transitioning through an intermediate CaCO3-IIIb, and ending at the CaCO3-III structure. The phase transition between CaCO3-I or -II and aragonite, which is also a reconstructive process, was found to occur by progressive solid recrystallization under high P-T hydrous and anhydrous conditions, or alternatively, via dissolution-precipitation under low-P-T hydrous conditions, depending on the presence of aqueous fluids and the heating rate of the system. The substitution for Ca2+ by other metal cations (e.g., Mg2+, Mn2+, Fe2+) in CaCO3 results in a significant increase in the pressures for the displacive and solid recrystallization reconstructive phase transitions, but has no detectable influence on the CaCO3-I/II ↔ aragonite transformation via a dissolution-precipitation process under hydrous conditions. Our results show that the presence of Ca-substitutional metal cations in CaCO3 is a key factor controlling the phase stability of CaCO3 under high P-T conditions, and suggest that aragonite should be the predominant phase in the upper mantle in subduction zones where the heating rate is very low and slab dehydration is prevalent.

Motion of phase boundary during antiferroelectric–ferroelectric transition in a PbZrO3 -based ceramic

The in situ biasing transmission electron microscopy technique is employed to investigate the nucleation and growth of the ferroelectric phase during the electric field-induced phase transition in ${\mathrm{Pb}}_{0.99}{{\mathrm{Nb}}_{0.02}{[{({\mathrm{Zr}}_{0.57}{\mathrm{Sn}}_{0.43})}_{0.94}{\mathrm{Ti}}_{0.06}]}_{0.98}}{\mathrm{O}}_{3}$, a ${\mathrm{PbZrO}}_{3}$-based antiferroelectric ceramic. The first-order displacive phase transition is found to be highly reversible with the initial antiferroelectric domain configuration almost completely recovered upon removal of the applied field. In the forward transition from the antiferroelectric to ferroelectric phase, ${{100}}_{\mathrm{c}}$ facets are dominant on the phase boundary; while in the reverse transition from the ferroelectric to antiferroelectric phase during bias unloading, the phase boundary is segmented into ${{101}}_{\mathrm{c}}$ and ${{121}}_{\mathrm{c}}$ facets. The motion of the phase boundary is nonuniform, taking the form of sequential sweeping of facet segments. The elastic distortion energy and the depolarization energy at the antiferroelectric/ferroelectric phase boundary is suggested to dictate the facet motion.

Making EuO multiferroic by epitaxial strain engineering

Multiferroics are materials exhibiting the coexistence of ferroelectricity and ideally ferromagnetism. Unfortunately, most known magnetoelectric multiferroics combine ferroelectricity with antiferromagnetism or with weak ferromagnetism. Here, following previous theoretical predictions, we provide clear experimental indications that ferroelectricity can be induced by epitaxial tensile strain in the ferromagnetic simple binary oxide EuO. We investigate the ferroelectric phase transition using infrared reflectance spectroscopy, finding that the frequency of the soft optical phonon reduces with increasing tensile strain and decreasing temperature. We observe such a soft mode anomaly at 100 K in (EuO)2/(BaO)2 superlattices grown epitaxially on (LaAlO3)0.29-(SrAl1/2Ta1/2O3)0.71 substrates, which is a typical signature for a displacive ferroelectric phase transition. The EuO in this superlattice is nominally subjected to 6.4% biaxial tensile strain, i.e., 50% more than believed needed from previously published calculations. We interpret our results with new first-principles density functional calculations using a hybrid functional, which provides a better quantitative agreement with experiment than the previously used local-density approximation and generalized gradient approximation functionals.

Inversion of quartz solid solutions at cryogenic temperatures

AbstractQuartz solid solution crystals of six different compositions were obtained from crystallization of glass powders belonging to the Li2O–Al2O3‐SiO2 (LAS) system. They were analyzed in situ by laboratory‐based X‐ray diffraction down to cryogenic temperatures (−190°C). Temperature‐resolved analysis of their lattice parameters allowed determination of the critical inversion temperature Tc in these materials, marking the displacive phase transition from a high‐quartz‐ to a low‐quartz‐like lattice. Integrating available data from other literature sources, an updated phase diagram for the occurrence of high and low quartz solid solution phases is provided for the LAS system; these data are expected to support future development of functional materials relying on these crystalline phases.

Hydrogen-Bonded Crystalline Molecular Machines with Ultrafast Rotation and Displacive Phase Transitions.

Two new crystalline rotors 1 and 2 assembled through N-H⋅⋅⋅N hydrogen bonds by using halogenated carbazole as stators and 1,4-diaza[2.2.2]bicyclooctane (DABCO) as the rotator, are described. The dynamic characterization through 1 H T1 relaxometry experiments indicate very low rotational activation barriers (Ea ) of 0.67 kcal mol-1 for 1 and 0.26 kcal mol-1 for 2, indicating that DABCO can reach a THz frequency at room temperature in the latter. These Ea values are supported by solid-state density functional theory computations. Interestingly, both supramolecular rotors show a phase transition between 298 and 250 K, revealed by differential scanning calorimetry and single-crystal X-ray diffraction. The subtle changes in the crystalline environment of these rotors that can alter the motion of an almost barrierless DABCO are discussed here.

High permittivity BaTiO3 and BaTiO3-polymer nanocomposites enabled by cold sintering with a new transient chemistry: Ba(OH)2∙8H2O

Cold sintering process (CSP) offers a promising strategy for the fabrication of innovative and advanced high permittivity dielectric nanocomposite materials. Here, we introduce Ba(OH)2∙8H2O hydrated flux as a new transient chemistry that enables the densification of BaTiO3 in a single step at a temperature as low as 150 °C. This remarkably low temperature is near its Curie transition of 125 °C, associated with a displacive phase transition. The cold sintered BaTiO3 shows a relative density of 95 % and a room temperature relative permittivity over 1000. This new hydrated flux permits the fabrication of a unique dense BaTiO3-polymer nanocomposite with a high volume fraction of ceramics ((1-x) BaTiO3 – x PTFE, with x = 0.05). The composite exhibits a relative permittivity of approximately 800, at least an order of magnitude higher than previous reports on polymer composites with BaTiO3 nanoparticle fillers that are typically well below 100. Unique high permittivity dielectric nanocomposites with enhanced resistivities can now be designed using polymers to engineer grain boundaries and CSP as a processing method opening up new possibilities in dielectric materials design.

Sub-picosecond photo-induced displacive phase transition in two-dimensional MoTe2

Photo-induced phase transitions (PIPTs) provide an ultrafast, energy-efficient way for precisely manipulating the topological properties of transition-metal ditellurides and can be used to stabilize a topological phase in an otherwise semiconducting material. Using first-principles calculations, we demonstrate that the PIPT in monolayer MoTe2 from the semiconducting 2H phase to the topological 1T′ phase can be triggered purely by electronic excitations that soften multiple lattice vibrational modes. These softenings, driven by a Peierls-like mechanism within the conduction bands, lead to structural symmetry breaking within sub-picosecond timescales, which is shorter than the timescale of a thermally driven phase transition. The transition is predicted to be triggered by photons with energies over 1.96 eV, with an associated excited carrier density of 3.4 × 1014 cm−2, which enables a controllable phase transformation by varying the laser wavelength. Our results provide insight into the underlying physics of the phase transition in 2D transition-metal ditellurides and show an ultrafast phase-transition mechanism for manipulation of the topological properties of 2D systems.

Reply to Kroll and Schmid-Beurmann's comment on “Water decreases displacive phase transition temperature in alkali feldspar” by Liu et al. (2018)

Abstract. It has long been known that hydrogen impurities can be incorporated in the structure of nominally anhydrous minerals (NAMs) and substantially influence their physical properties. One of the geologically most prominent NAMs is feldspar. The hydrogen concentration in NAMs is usually expressed in parts per million of water by weight (ppm H2O wt.) In this paper, we use the term “hydrogen” for uniformity, except when we use “water” for describing its amount expressed as parts per million of H2O by weight. In our article (Liu et al., 2018), we carried out in situ high-temperature X-ray powder diffraction and Raman spectroscopic studies on three natural anorthoclase samples with similar Or (K-feldspar) contents (Ab67Or31An2, Ab66Or31An2, and Ab65Or33An3) and Al–Si disordering but contrasting water contents. The spectroscopic results suggested that the displacive phase transition temperature is higher for the nearly anhydrous anorthoclase sample than the anorthoclase samples with about 200 ppm water, and we thus concluded that hydrogen is another factor impacting the displacive phase transition temperature. We thank Kroll and Schmid-Beurmann for pointing out the weakness in our interpretation that hydrogen is a possible important factor (Kroll and Schmid-Beurmann, 2020). To clarify this issue, we conducted transmission electron microscopy (TEM) experiments on the three samples to check texture effects. The TEM studies indicated that the nearly anhydrous anorthoclase sample consists of two feldspar phases, a K-poor and a K-rich one, and that the K-poor area may be responsible for the higher displacive phase transition temperature. According to the observation that the temperature of redistribution of hydrogen is accordant with the displacive phase transition temperature, the effect of hydrogen could not be ruled out. Based on these results, it can be concluded that hydrogen may not be the sole possible factor, and it was a proposition more than a definitive proof for the moment. Natural feldspars are complex, and factors affecting displacive phase transitions are multiple (e.g., Salje et al., 1991; Harrison and Salje, 1994; Hayward and Salje, 1996; Dobrovolsky et al., 2017). Therefore, to further investigate hydrogen effects on displacive phase transition in feldspar, synthetic samples with pure chemical compositions and hydrogen species are necessary. In the following, we address each issue in the same order as in the comment by Kroll and Schmidt-Beurmann (2020).

Advances in High-Throughput in-Situ X-Ray Diffraction Analysis of Lithium Ion Batteries

X-ray diffraction using hard radiation (>17 keV) is able to measure lattice parameter and phase changes of cathode and anode materials simultaneously during battery cycling. Advances in hard radiation optics and detectors, combined with data logging software to correlate diffractometer and potentiostat data, are being used to improve in-situ battery analysis using laboratory diffractometers. Research previously done at synchrotrons can now be conducted with the laboratory diffractometer, improving opportunities for long-term experimental design. In this study, a reversible displacive phase transition in NMC cathodes, marked by significant contraction of the unit cell, is observed during cycling at a modest 4.2V potential. The magnitude of lattice contraction is dependent on the Ni content. This phase transition appears distinct from the H1 to H2 phase transition. Quantitative Rietveld anlaysis is used to precisely track lattice parameter changes in the cathode material. Because transmission diffraction measures cathode and anode simultaneously, anode phase content is quantified between C, LiC12, and LiC6 and these quantities are correlated to behavior of the cathode.

Composition design of PMN-PH-PT piezoelectric ceramics for high-temperature actuator applications

High-Curie temperature (Tm) piezoelectric ceramics 0.15Pb(Mg1/3Nb2/3)O3-xPbHfO3-(0.85-x)PbTiO3 (0.15PMN-xPH-(0.85-x)PT, x = 0.36, 0.38, 0.39, 0.40, 0.42, 0.15PMN-PH-PT) were synthesized by the solid-state reaction method via the columbite precursor route. The synthesized 0.15PMN-PH-PT ceramics exhibit pure perovskite structure with compositions locate near the morphotropic phase boundary (MPB), where the rhombohedral phase and the tetragonal phase coexist. The sintered samples present high densification, in which the 0.15Pb(Mg1/3Nb2/3)O3-0.38PbHfO3-0.47PbTiO3 (0.15PMN-0.38PH-0.47PT) ceramics present the highest relative density, being 97.76%. The dielectric performance-temperature curves measured at different frequencies, the Curie-Weiss law fitting and the quadratic law fitting indicate that the ferroelectric phase transition from ferroelectric phase to paraelectric phase occurred at T0 in the 0.15PMN-PH-PT ceramics is driven by the displacive phase transition, and the 0.15PMN-PH-PT ceramics belong to normal ferroelectrics with diffused phase transition characteristic. Due to the MPB effect and high relative density, the 0.15PMN-0.38PH-0.47PT ceramics exhibit the best integral electrical properties, excellent thermal stability and large electric field induced strain, which present prospect promising for actuator applications under elevated environmental temperatures.

Displacive phase-field crystal model

A phase-field crystal model that spontaneously undergoes displacive phase transitions is introduced by explicitly studying a two-component two-dimensional square crystal reminiscent of a perovskite. When the intercomponent free energy is a simple polynomial, the crystal undergoes displacive transitions in the $\ensuremath{\langle}10\ensuremath{\rangle}$ and $\ensuremath{\langle}11\ensuremath{\rangle}$ directions. When the interaction is a correlation function, displacements in any direction can occur. This displacive phase-field crystal (DPFC) model maps to Landau-Ginzburg-Devonshire (LGD) theories for ferroelectrics, and the DPFC and LGD models are compared in terms of phase transitions and domain walls. Dynamical simulations of quadrijunctions were also performed and found stable spiraling quadrijunctions and unstable nonspiraling quadrijunctions. Last, domain coarsening across a small-angle grain boundary demonstrates multiple forms of non-mean-curvature-driven growth.