From ergodicity to extended phase diagrams

Structure prediction of stable and metastable phases is put on equal footing for the first time, with a solid thermodynamical background. How to estimate the lifetime of metastable phases is demonstrated by recent groundbreaking work of Jansen, Pentin, and Sch?n. At the heart lies the exploration of the Gibbs free-energy landscapes and the extended phase diagrams for complex systems.     

Hydrothermal synthesis of two perovskite rare-earth manganites, HoMnO3 and DyMnO3

Two perovskite rare-earth manganites RMnO₃ (R=Ho, Dy) were synthesized from the hydrothermal redox reactions of KMnO₄ and MnCl₂ at 250 °C and characterized by means of X-ray diffraction, scanning electron microscopy and SQUID. They are orthorhombic, whereas the hexagonal phases, which were competitive strongly with the orthorhombic phases in solid-state reactions, are avoided in the hydrothermal systems. The pure metastable manganites may serve as a model for understanding the magnetisms of Jahn-Teller distortion and charge ordering. This new synthetic approach leaves many rooms for new doped or undoped RMnO₃ compounds.     

Diffusion of Noble Metals,Zn and Ge in GaSb Single Crystals

Diffusion of Cu, Ag, Au, Ge and Zn in single crystal gallium antimonide has been carried out by measuring Hall effect according to van der Pauw, conductivity, energy dispersive X-ray (EDX) and surface electron microscopy. The best results have been obtained in excess of antimony. The resulting diffusion data in GaSb are diffusivity D_o, activation enthalpy Q, carrier density p and mobility μ at 300 K: Ag: D_o=1.8·10⁻⁴ cm² s⁻¹, Q=1.2 eV, p=6·10¹⁸ cm⁻³, μ=550 cm² (Vs)⁻¹ Au: D_o=6.6·10⁺³ cm² s⁻¹, Q=2.7 eV, p=5·10¹⁸ cm⁻³, μ=500 cm² (Vs)⁻¹ Cu: D_o=3.2·10⁺⁸ cm² s⁻¹, Q=2.7 eV, p=2·10¹⁸ cm⁻³, μ=150 cm² (Vs)⁻¹ Zn: D_o=9.2·10⁻² cm² s⁻¹, Q=1.8 eV, p=2·10²⁰ cm⁻³, μ=80 cm² (Vs)⁻¹ Ge: D_o=1.0·10⁻¹ cm² s⁻¹, Q=1.7 eV, p=1·10¹⁹ cm⁻³, μ=320 cm² (Vs)⁻¹. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermal Analysis of Solid-Solid Interactions in Binary Mixtures of Alkylcyclohexanes Using DSC

Differential scanning calorimetry (DSC) was used to construct phase diagrams of binary mixtures of alkylcyclohexanes and to characterize metastable phases formed in the binary mixtures. The experimentally measured liquidus curves were compared to the liquidus curves calculated using ideal solution theory. The measured phase diagrams of pentadecylcyclohexane/nonadecylcyclohexane and octadecylcyclohexane/nonadecylcyclohexane binary mixtures are consistent with theoretical phase diagrams constructed based on the assumption that these mixtures form eutectic systems. It was also observed that a metastable phase formed in some binary mixtures of pentadecylcyclohexane/nonadecylcyclohexane under fast cooling conditions. It is hypothesized that this metastable phase recrystallizes into the eutectic phase upon heating. This revised version was published online in July 2006 with corrections to the Cover Date.     

Ab initio computation of the low-temperature phase diagrams of the alkali metal iodide-bromides: MBr(x)I1-x (0 </= x </= 1), Where M = Li, Na, K, Rb, or Cs

We have studied the low-temperature phase diagrams of the systems MBr-MI (M = Li, Na, K, Rb, or Cs) via global exploration of the enthalpy landscapes for many different compositions, leading to candidates for solid solution-like and ordered crystalline phases. For all of these candidates the free enthalpies are computed at the ab initio level, and the low-temperature phase diagrams of the five chemical systems are derived. We find not only the expected stable solid solution in the rocksalt structure type but also metastable solid solutions based on the CsCl type for the RbBr-RbI and CsCl-CsI systems. Furthermore, additional metastable structure candidates exhibiting ordered crystalline structures exist for several compositions. In the case of the LiBr-LiI system, the metastable solid solution based on the wurtzite type was generated, and the location of the miscibility gap was predicted.     

Liquid–Solid Phase Diagrams of PrOH–Water and BuOH–Water Systems from Differential Scanning Calorimetry

The freezing process in i-PrOH- and tert-BuOH-water systems were investigatedto obtain reliable liquid=nsolid phase diagrams by differential scanning calorimetry(DSC), especially focusing on formation of metastable solid phases. In addition,n-BuOH, sec-BuOH, and i-BuOH were studied within their solubility limits. Inmost systems studied, there exist metastable solid phases and, with increasingbranching of alkyl groups, the number of metstable solid phases increases. Themost complicated is i-PrOH-water where curious phenomena were found,probably because of the abnormally high viscosity of the solution at low temperatures.The relation between hydration in the liquid and formation of solid phases isdiscussed. It is suggested that the positional relation between methyl groups andalcoholic OH groups plays an important role; the increase in number ofalphamethyl group seems to strengthen hydration and stabilizes solid hydrates.     

Extension rules

The statement that the solubility is higher for metastable phases than for stable phases can be proved by a relatively simple imaginary experiment. Hence, it follows that the metastable extensions of the solubility limit curves, surfaces, and hypersurfaces in the phase diagrams of binary, ternary, and multicomponent systems cannot run in the single-phase solvent region. A special case for binary systems is the Hollmann’s rule.     

Equilibrium and non-equilibrium phase transitions studied by adiabatic calorimetry

An adiabatic calorimetry was used for some investigations of equilibrium and non-equilibrium phase transitions. For one of the substances studied (4,4′-di-n-heptyloxyazoxybenzene) it was possible to determine temperature dependence of an order parameter and number of clusters of high temperature phase in a region of a phase transition. For another substance (liquid 3,4 dimethylpiridine) an anomaly on the specific heat curves was interpreted as being responsible for a decay of molecules’ clusters. Non-equilibrium phase transitions were investigated for some liquid crystal substances. The process of transformation between metastable and stable phases was described quantitatively. The conclusions obtained concern the stability of metastable phases.     

Ab initio prediction of the low-temperature phase diagrams in the systems KBr-NaBr, KX-RbX, and LiX-RbX (X=Cl,Br)

The authors have calculated the low-temperature phase diagrams for the ternary alkali halides KBr-NaBr, KX-RbX, and LiX-RbX (X=Cl,Br) systems on the ab initio level without any recourse to experimental information. Via global exploration of the enthalpy landscapes for many different compositions in these systems, candidates for both ordered stoichiometric modifications and crystalline solid solution phases have been identified. Next, their free enthalpies were computed on ab initio level, and the respective low-temperature phase diagram has been derived. They find miscibility gaps in the systems KBr-NaBr and KX-RbX (X=Cl,Br), while in LiX-RbX (X=Cl,Br) only crystalline ordered phases should be present, in agreement with available experimental data. Furthermore, they predict several new thermodynamically stable and metastable phases in these systems.     

Ab initio prediction of the low-temperature phase diagrams in the systems CsX–LiX (X = F, Cl, Br, I)

We have calculated the low-temperature phase diagrams for the ternary alkali halides CsX–LiX (X = F, Cl, Br, I) at an ab initio level without any recourse to experimental information. The starting point of our general approach is the global exploration of the enthalpy landscapes for many different compositions in these systems. Candidates for both ordered stoichiometric modifications and crystalline solid-solution phases are identified, and their free enthalpies are computed at an ab initio level. From this the low-temperature phase diagrams are derived. We find that in all systems under investigation only crystalline ordered phases should be present, in agreement with available experimental data. Furthermore, we predict several new thermodynamically stable and metastable phases in these systems.     

Structural Features of Phosphate and Sulfate Modified Zirconia Prepared by Sol–Gel Route

This paper describes the effect of sulfate, phosphate and nitrate complexing ligands on the structural features of amorphous xerogels and on the crystallization of metastable zirconia phases during the xerogel-ceramic conversion. Powdered samples were prepared by a sol–gel route using zirconyl chloride precursors chemically modified by complexing ligands. The structural evolution of ZrO₂ phases as function of firing temperature was analyzed by XRPD, EXAFS and ³¹P NMR/MAS. The experimental results show the formation of metastable t-ZrO₂ during the low firing temperature of xerogels modified by sulfate or phosphate groups. The martensitic tetragonal-monoclinic transformation occurs during desorption of sulfate groups. The largest temperature interval of stability of metastable tetragonal zirconia was observed for phosphate-modified xerogels.     

Role of the oriented attachment mechanism in the phase transformation of oxide nanocrystals

"Bottom-up" methods to obtain nanocrystals usually result in metastable phases, even in processes carried out at room temperature or under soft annealing conditions. However, stable phases, often associated with anisotropic shapes, are obtained in only a few special cases. In this paper we report on the synthesis of two well-studied oxides-titanium and zirconium oxide-in the nanometric range, by a novel route based on the decomposition of peroxide complexes of the two metals under hydrothermal soft conditions, obtaining metastable and stable phases in both cases through transformation. High-resolution transmission electron microscopy analysis reveals the existence of typical defects relating to growth by the oriented attachment mechanism in the stable crystals. The results suggest that the mechanism is associated to the phase transformation of these structures.     

Retarded solid state reactions III [1]

Solid state reactions and reconstructive phase transitions exhibit more or less a large hysteresis between reaction temperatures taken from DTA-heating and -cooling curves. For ternary lanthanide chlorides the equilibrium temperatures could be obtained bye.m.f.-measurements in galvanic chlorine cells for solid electrolytes usingA ⁺-ion (A=alkaline metal) conducting diaphragms. By quenching, high-temperature phases can often be transformed to metastable room-temperature phases. In this case the equilibrium state must be established by annealing at sufficiently high temperature, or it must be tried to synthesize the compound in its stability range from suitable precursor systems.I want to thank the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie for supporting our research work for more than thirty years.     

Chiral dopant induced twist grain boundary phases

A diarylethane alpha-chloro ester was mixed with a chiral dopant of high helical twisting power at variable concentration to study its capability for induction of twist grain boundary phases. With increasing concentration of the chiral dopant, TGBA* and TGBC* phases were observed with a rather broad region of existence. In contrast to homeotropic alignment, planar boundary conditions seem to enhance the phase stability of the TGB phases, resulting in metastable TGB states and phase coexistence with the respective smectic phases. The phase growth of SmA*/SmC* out of the TGBA*/TGBC* state was studied under isothermal conditions as a function of temperature and concentration of the chiral dopant.     

Stable Prenucleation Calcium Carbonate Clusters Define Liquid–Liquid Phase Separation

Liquid–liquid phase separation (LLPS) is an intermediate step during the precipitation of calcium carbonate, and is assumed to play a key role in biomineralization processes. Here, we have developed a model where ion association thermodynamics in homogeneous phases determine the liquid–liquid miscibility gap of the aqueous calcium carbonate system, verified experimentally using potentiometric titrations, and kinetic studies based on stopped‐flow ATR‐FTIR spectroscopy. The proposed mechanism explains the variable solubilities of solid amorphous calcium carbonates, reconciling previously inconsistent literature values. Accounting for liquid–liquid amorphous polymorphism, the model also provides clues to the mechanism of polymorph selection. It is general and should be tested for systems other than calcium carbonate to provide a new perspective on the physical chemistry of LLPS mechanisms based on stable prenucleation clusters rather than un‐/metastable fluctuations in biomineralization, and beyond.     

Coprecipitation from aqueous solutions to prepare binary fluorides

The synthesis of binary fluoride phases, specifically nanofluorides, by coprecipitation from aqueous solutions is considered in terms of phase equilibria. Phases have been precipitated in NaF-RF₃ systems (where R stands for a rare-earth element), MF₂-YF₃ systems (where M = Ca, Sr, Ba), BaF₂-ScF₃, and CaF₂-BaF₂ systems. In the MF₂-YF₃ systems, unordered metastable congruently soluble phases are precipitated instead of ordered fluorite-like phases. In the BaF₂-ScF₃ system, the congruently soluble compound Ba₃Sc₂F₁₂ is precipitated. In the NaF-RF₃ systems, incongruently soluble metastable phases with a fluorite-like structure (for R = Er, Lu, Y) and the gagarinite structure (NaGdF₄) are formed. In the CaF₂-BaF₂ system, intermediate phases have not been formed.     

When is H2O not water?

We have combined a computational search strategy with first-principles density-functional-theory calculations to identify metastable phases of H(2)O under pressure. The most stable structures consist of water molecules, while the most energetic metastable phases consist of oxygen and hydrogen molecules. In between lie many other metastable phases, consisting of various combinations of a few small molecules. It may be possible to synthesize some of these metastable phases, and we use our results to understand the nature of the crystalline metastable phase of H(2)O recently synthesized by Mao et al. [Science 314, 636 (2006)].     

Phase equilibrium and p s-T-x diagrams of the Ln2S3-LnS2 (Ln = La, Pr, Nd, Sm-Er) systems

A new methodology is proposed and the phase equilibrium is investigated in the Ln₂S₃-LnS₂ systems, in which the low-temperature behavior of nonstoichiometric phases is controlled by the kinetics of the ordering of defects. It is shown that, under equilibrium conditions, the phase equilibrium in the systems is represented not only by a polysulfide with a wide homogeneity region, but also by several (or one) phases of constant irrational compositions combined in the homologous series Ln_nS_2n?1 (n = 3, 4, 7, 8, and 10). The formation of sulfur vacancies and isolated [S₂]^2? ions (which compensate the charge) in the anionic S^2? layer is the basic mechanism of changing the composition of the members of the series. On the basis of structural data, the possible mechanisms of the ordering of defective LnS_2?x polysulfides are examined and it is shown that the formation of stable or metastable phases is a kinetics-controlled process. The role of p _s-T-x diagrams in the interpretations of complex structures of metastable phases from the point of view of attainment of the equilibrium state is discussed.     

Laser induced metastable phases in microcrystalline silicon

It has been found using Raman spectroscopy that metastable Si phases reversibly appear in silicon microparticles (µ-Si) due to local heating on increasing the power of a He–Ne excitation laser from 0.03 to 3 mW. Prolonged annealing of these phases by laser radiation makes it possible to estimate that local heating occurs to a temperature of ∼250 °C rather than 1000 °C as it was believed previously.     

Size-dependent phase stability of a molecular nanocrystal: a proxy for investigating the early stages of crystallization

We make the link between the size-dependent phase stability of a nanocrystal and the phase-transition behavior of emerging crystallites during the earliest stages of crystallization, by using the former as a proxy for the latter. We outline an extension of the classical nucleation theory to describe crystal nucleation and subsequent transformations of competing polymorphic phases that characterize Ostwald's rule of stages. The theoretical framework reveals that the relative stability of the competing phases is a function of cluster size, which in turn varies with time, and therefore explains the complex transformation behavior observed for some systems. We investigated the stability of a nanocrystal of dl-norleucine by means of molecular simulation as a proxy for post-nucleation phase-transformation behavior in emerging crystallites. The simulations reveal that, for nanocrystals, the surface energy of the transition state of a transformation can dominate the barrier to phase change, thus causing metastable phases to be stabilized, not because they are thermodynamically stable, but rather due to kinetic hindering. Therefore, in the context of the earliest stages of crystal growth, not only does phase stability vary as a function of cluster size, and hence time, but thermodynamically feasible transformations are also prone to kinetic hindering.