Determination Of Phase Diagram Research Articles

(Invited) From Solid State Chemistry to Battery Materials Electrochemistry: A Tool for Solid State Chemistry

Researches on battery materials has considerably increased during the last 30 years due to the huge development of lithium-ion batteries for portable devices (laptops, cellular phones, …) and more recently with the need to store energy in order to optimize its consumption. The next goal is the development of batteries for electric vehicles and their use into the grid. Nevertheless, the aqueous batteries (Ni-Cd, Ni-MH and Lead Acid) are always used in numerous applications thanks to their low price. In most of the batteries, the intercalation (deintercalation) of monovalent cations (H+, Li+, Na+) and electrons is the basic electrochemical reaction. The cell voltage is equal to the difference in Fermi level between the two electrodes. If one electrode exhibits a constant voltage it can act as reference and therefore, the cell voltage reflects all structure modifications which occurs on the material upon intercalation. The change is cell voltage depends on: (i) the electronic band filling, (ii) the change in the band structure due to change in composition, (iii) the modification of the Magdelung energy. In some cases the monotonous decreases of the voltage during the intercalation reaction indicates that the reaction occurs through a monophasic domain. In numerous cases, the reaction mechanism is more complicated and involves biphasic domains and/or formation of materials with a specific composition. The voltage vs composition curve is much more complicated and gives directly the phase diagram of the studied system. For the solid state chemist, the studies of the electrochemical reaction using a battery opens new possibilities to determine phase diagram at RT, but also to synthesize new metastable phases from a precursor made by classical solid state chemistry. The in situ or in operando experiments allow to follow directly the structural modifications occurring during the electrochemical reaction. Using synchrotron experiments it is possible to make experiments at high rate and therefore evidence intermediate states and understand the reactions mechanism. In the recent years, XRD diffraction and XAS analysis were intensively used.On the opposite way, very sophisticated Solid State Chemistry techniques like solid state MAS NMR, Mossbauer spectroscopy and high resolution electron microscopy in aberration corrected microscope allowed to characterize battery materials at the atomic level. In this presentation, some typical results obtained in Bordeaux concerning lithium and sodium layered oxides will be presented to emphasize the dual approach: batteries to solid state chemistry and solid state chemistry to batteries.

Liquidus slopes of impurities in ITS-90 fixed points from the mercury point to the copper point in the low concentration limit

A knowledge of the effect of impurities at the level of parts per million on the freezing temperature of very pure metals is essential for realisation of ITS-90 fixed points. New information has become available for use with the thermodynamic modelling software MTDATA, permitting calculation of liquidus slopes, in the low concentration limit, of a wider range of binary alloy systems than was previously possible. In total, calculated values for 536 binary systems are given. In addition, new experimental determinations of phase diagrams, in the low impurity concentration limit, have recently appeared. All available data have been combined to provide a comprehensive set of liquidus slopes for impurities in ITS-90 metal fixed points. In total, liquidus slopes for 838 systems are tabulated for the fixed points Hg, Ga, In, Sn, Zn, Al, Ag, Au, and Cu. It is shown that the value of the liquidus slope as a function of impurity element atomic number can be approximated using a simple formula, and good qualitative agreement with the existing data is observed for the fixed points Al, Ag, Au and Cu, but curiously the formula is not applicable to the fixed points Hg, Ga, In, Sn, and Zn. Some discussion is made concerning the influence of oxygen on the liquidus slopes, and some calculations using MTDATA are discussed. The BIPM’s consultative committee for thermometry has long recognised that the sum of individual estimates method is the ideal approach for assessing uncertainties due to impurities, but the community has been largely powerless to use the model due to lack of data. Here, not only is data provided, but a simple model is given to enable known thermophysical data to be used directly to estimate impurity effects for a large fraction of the ITS-90 fixed points.

Calculation of In[sbnd]As[sbnd]Bi ternary phase diagram

The phase diagrams of the InAsBi system were predicted at different temperatures by using the Calphad method. The calculations were based on the thermodynamic properties of the constituent binary systems. These properties were collected from selected literature. They were then used to calculate the constituent binary phase diagrams (InAs, InBi and AsBi) and the results were compared with the experimentally determined phase diagrams for evaluating the reliability of the binary data before the ternary phase diagrams were calculated. The isothermal sections at different temperatures and liquidus projection of the InAsBi ternary system were calculated. The calculated results predict the domination of solid phases at low temperatures and show also that the fusion temperature depends on crystallographic structure of InAsBi and the chemical Bi and In concentrations. Such results were helpful for successful growth of InAsBi alloys.

Exploration of Vanadate Selenites Solid Phase Space, Crystal Structures, and Polymorphism

Our recent exploration of the Pb–Ni–Se–O “crystallization phase diagram” under hydrothermal conditions has led to the discovery of three new selenites. Here we have applied a similar systematic method to the Pb–V–Se–O system using both hydrothermal and chemical vapor transport crystal growth using either PbO or PbCl2 as the source of lead. In our approach, phases in the presence are meticulously characterized by single crystal X-ray diffraction tests, on the basis of their morphology. Besides the determination of stable predominant phases in the diagram such as Pb2(VO3)-(SeO3)2Cl, it enables the crystallization of three novel vanadate selenites, β-(V5+2O3)(SeO3)2 (I), Pb2(V4+O)(SeO3)3 (II), and β-Pb4(V5+3O8)2(SeO3)3(H2O) (III), depending on the method, pH, and potential of the solution. It is worth noting that in our conditions the solid/liquid crystal growth could be driven by kinetic or thermodynamic control which does not lead to determination of a formal phase diagram, but rather to a “solid-phase spa...

Phase Behavior of Ascorbyl Palmitate Coagels Loaded with Oligonucleotides as a New Carrier for Vaccine Adjuvants

AbstractIn this work, the phase behavior variations of an ascorbyl palmitate (Asc16) system in aqueous solution were analyzed when immunologically active hydrophilic compounds (CpG and OVA) were introduced. This study was carried out through optical polarizing microscopy (OPM) and differential scanning calorimetry (DSC) at different temperatures and over a broad range of concentrations. The combination of both techniques allowed the determination of a complete phase diagram which was compared with those built for Asc16‐water system and it was demonstrated that fixed concentrations of hydrophilic compounds (300 and 24 µg/g for CpG‐ODN and OVA respectively) generate two lamellar liquid crystals, a cubic liquid crystal phase, and also other aggregates. However, no changes were observed in the phase diagram in terms of formation of new mesophases. The aqueous phase behavior was also studied as a function of surfactant and temperature. DSC and Fourier transform infrared spectroscopy (FT‐IR) measurements show differences in the free water and mainly in the secondary hydration layer, which confirm that the studied compounds are situated in the aqueous domain. The construction and analysis of Asc16 phase diagrams with a fixed concentration of CpG‐ODN/OVA allows the comprehension of Asc16 phase behavior and could be easily adapted to other concentrations. Moreover, these findings could be extrapolated to other hydrophilic substances in aqueous solution introduced in liquid crystal phases since they follow a similar behavior as those reported in the literature.

Protein Crystallization in an Actuated Microfluidic Nanowell Device.

Protein crystallization is a major bottleneck of structure determination by X-ray crystallography, hampering the process by years in some cases. Numerous matrix screening trials using significant amounts of protein are often applied, while a systematic approach with phase diagram determination is prohibited for many proteins that can only be expressed in small amounts. Here, we demonstrate a microfluidic nanowell device implementing protein crystallization and phase diagram screening using nanoscale volumes of protein solution per trial. The device is made with cost-effective materials and is completely automated for efficient and economical experimentation. In the developed device, 170 trials can be realized with unique concentrations of protein and precipitant established by gradient generation and isolated by elastomeric valving for crystallization incubation. Moreover, this device can be further downscaled to smaller nanowell volumes and larger scale integration. The device was calibrated using a fluorescent dye and compared to a numerical model where concentrations of each trial can be quantified to establish crystallization phase diagrams. Using this device, we successfully crystallized lysozyme and C-phycocyanin, as visualized by compatible crystal imaging techniques such as bright-field microscopy, UV fluorescence, and second-order nonlinear imaging of chiral crystals. Concentrations yielding observed crystal formation were quantified and used to determine regions of the crystallization phase space for both proteins. Low sample consumption and compatibility with a variety of proteins and imaging techniques make this device a powerful tool for systematic crystallization studies.

The Ternary Lipid Phase Diagram by AFM

Understanding the physical properties and lateral structure of lipid bilayers is the subject of continuing interest, not least due to its emerging role in modifying the function of membrane proteins. A wide variety of experimental techniques have been used to determine phase diagrams of relevant ternary lipid mixtures that exhibit properties of the cell membrane. However, there are still many open questions and ambiguities. We use a variety of modes of atomic force microscopy (AFM) to study domain formation in ternary lipid mixtures. AFM has the unique advantages of having high lateral resolution, of being label free, and of being able to simultaneously measure membrane mechanical properties. A commonly stated disadvantage is that it is necessarily limited to supported bilayers, and that the proximity of the substrate will alter the phase behaviour of membrane. Various strategies have been employed over the years to obviate this effect, such as forming membrane stacks, tethering, and polymer cushioning. In this work we show that a model cell membrane on a mica substrate exhibits the same phase transitions as that observed in GUV's. We use temperature control and Fast-scan AFM across the whole phase diagram to study phase transitions, from binary systems to ternary mixtures exhibiting 2-phase (Ld-Lo, Ld-gel and Lo-gel) and 3-phase regions, and hence construct a complete ternary phase diagram. Dynamics previously undetected on support bilayers have been observed, such as Ostwald ripening and domain coalescence, domain boundary fluctuations and critical fluctuations. Nucleation (including tree-ring growth) and spinodal decomposition mechanisms are characterised. Our work demonstrates that AFM is not only a valid approach to studying phase separation in bilayers but that it is able to complement existing techniques and theories and provide new insights by directly visualizing lateral lipid bilayer structure.

Ab Initio Determined Phase Diagram of Clean and Solvated Muscovite Mica Surfaces.

Focusing on muscovite mica, the most significant phyllosilicate in the mica series, we determine its surface phase diagram employing density functional theory. Surfaces in vacuum and in more realistic environmental conditions, that is, the surface in contact with water or an ionic liquid, are considered. These results naturally explain experimental observations such as the swelling of mica when it comes into contact with water.

Phase diagram determination and thermodynamic modeling of the Cu-Mg-Si system

13 ternary Cu-Mg-Si alloys were prepared by means of the powder metallurgy method. Phase equilibria at 500 and 700 oC of the Cu-Mg-Si system were determined using X-ray diffraction analysis (XRD). The existence of 3 ternary compounds in this system was verified: CuMgSi_Sigma (Cu16Mg6Si7), Tau (Cu3Mg2Si), and Laves ((Cu0.8Si0.2)2(Mg0.88Cu0.12)). A thermodynamic modeling for the Cu-Mg-Si system was then conducted on the basis of the experimental data obtained in this work and those critically reviewed from the literature. The complex phase relationship between Laves phase and other phases has been successfully modeled in this work. Comparisons between the calculated and the measured phase diagrams show that most of the experimental data can be reproduced by the presently obtained thermodynamic parameters.

Spinel-rock salt transformation in LiCoMnO4-δ.

The transformation on heating LiCoMnO4, with a spinel structure, to LiCoMnO3, with a cation-disordered rock salt structure, accompanied by loss of 25% of the oxygen, has been followed using a combination of diffraction, microscopy and spectroscopy techniques. The transformation does not proceed by a topotactic mechanism, even though the spinel and rock salt phases have a similar, cubic close-packed oxygen sublattice. Instead, the transformation passes through two stages involving, first, precipitation of Li2MnO3, leaving behind a Li-deficient, Co-rich non-stoichiometric spinel and, second, rehomogenization of the two-phase assemblage, accompanied by additional oxygen loss, to give the homogeneous rock salt final product; a combination of electron energy loss spectroscopy and X-ray absorption near edge structure analyses showed oxidation states of Co2+ and Mn3+ in LiCoMnO3. Subsolidus phase diagram determination of the Li2O-CoOx-MnOy system has established the compositional extent of spinel solid solutions at approximately 500°C.

Self-energy effects in functional renormalization group flows of the two-dimensionalt−t′Hubbard model away from van Hove filling

We study the impact of the fermionic self-energy on one-loop functional renormalization group flows of the two-dimensional $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model, with emphasis on electronic densities away from van Hove filling. In the presence of antiferromagnetic hot spots, antiferromagnetic fluctuations lead to a flattening of the Fermi surface, shift magnetic phase boundaries, and significantly enhance critical scales. We trace back this effect to the presence of a magnetic first-order transition. For some parameters, the first-order character of the latter is reduced by self-energy effects. For reliably determining phase diagrams, the fermionic self-energy should be taken into account in functional renormalization group studies if scattering between hot spots is important.

Infrared thermography method for fast estimation of phase diagrams

Phase change materials (PCM) are widely used today in thermal energy storage applications. Pure PCMs are rarely used because of non adapted melting points. Instead of them, mixtures are preferred. The search of suitable mixtures, preferably eutectics, is often a tedious and time consuming task which requires the determination of phase diagrams. In order to accelerate this screening step, a new method for estimating phase diagrams in record time (1–3h) has been established and validated. A sample composed by small droplets of mixtures with different compositions (as many as necessary to have a good coverage of the phase diagram) deposited on a flat substrate is first prepared and cooled down to ambient temperature so that all droplets crystallize. The plate is then heated at constant heating rate up to a sufficiently high temperature for melting all the small crystals. The heating process is imaged by using an infrared camera. An appropriate method based on singular values decomposition technique has been developed to analyze the recorded images and to determine the transition lines of the phase diagram. The method has been applied to determine several simple eutectic phase diagrams and the reached results have been validated by comparison with the phase diagrams obtained by Differential Scanning Calorimeter measurements and by thermodynamic modelling.

An apparatus for spatially resolved, temperature dependent reflectance measurements for identifying thermochromism in combinatorial thin film libraries.

A metrology and data analysis protocol is described for high throughput determination of thermochromic metal-insulator phase diagrams for lightly substituted VO2 thin films. The technique exploits the abrupt change in near infrared optical properties, measured in reflection, as an indicator of the temperature- or impurity-driven metal-insulator transition. Transition metal impurities were introduced in a complementary combinatorial synthesis process for producing thin film libraries with the general composition space V(1-x-y)M(x)M'(y)O2, with M and M' being transition metals and x and y varying continuously across the library. The measurement apparatus acquires reflectance spectra in the visible or near infrared at arbitrarily many library locations, each with a unique film composition, at temperatures of 1 °C-85 °C. Data collection is rapid and automated; the measurement protocol is computer controlled to automate the collection of thousands of reflectance spectra, representing hundreds of film compositions at tens of different temperatures. A straightforward analysis algorithm is implemented to extract key information from the thousands of spectra such as near infrared thermochromic transition temperatures and regions of no thermochromic transition; similarly, reflectance to the visible spectrum generates key information for materials selection of smart window materials. The thermochromic transition for 160 unique compositions on a thin film library with the general formula V(1-x-y)M(x)M'(y)O2 can be measured and described in a single 20 h experiment. The resulting impurity composition-temperature phase diagrams will contribute to the understanding of metal-insulator transitions in doped VO2 systems and to the development of thermochromic smart windows.

The NaNO3–KNO3 phase diagram

Many papers have been published in relation to the NaNO3–KNO3 phase diagram determination in the last 160 years. These papers fall in two categories: (1) the solid–liquid equilibrium is assumed to be of the eutectic type, and (2) the solid–liquid equilibrium is considered as a loop with a minimum. The discordance between the two views is related to the slow transition kinetics that complicate the assessment of thermal ‘fluctuations’, and also to the appearance of a metastable form of potassium nitrate. The main result of this paper is the experimental phase diagram constructed with new experimental data so that we can assure that the second option is correct. This phase diagram is defined by a eutectoid invariant, an asymmetric immiscibility gap and a continuous solid solution with a minimum of melting point. Additionally, the ABθ model simulates correctly the experimental piece of evidence.

High-throughput determination of structural phase diagram and constituent phases using GRENDEL

Advances in high-throughput materials fabrication and characterization techniques have resulted in faster rates of data collection and rapidly growing volumes of experimental data. To convert this mass of information into actionable knowledge of material process–structure–property relationships requires high-throughput data analysis techniques. This work explores the use of the Graph-based endmember extraction and labeling (GRENDEL) algorithm as a high-throughput method for analyzing structural data from combinatorial libraries, specifically, to determine phase diagrams and constituent phases from both x-ray diffraction and Raman spectral data. The GRENDEL algorithm utilizes a set of physical constraints to optimize results and provides a framework by which additional physics-based constraints can be easily incorporated. GRENDEL also permits the integration of database data as shown by the use of critically evaluated data from the Inorganic Crystal Structure Database in the x-ray diffraction data analysis. Also the Sunburst radial tree map is demonstrated as a tool to visualize material structure–property relationships found through graph based analysis.

Generalized parametrization dependence in quantum gravity

We critically examine the gauge, and field-parametrization dependence of renormalization group flows in the vicinity of non-Gau\ss{}ian fixed points in quantum gravity. While physical observables are independent of such calculational specifications, the construction of quantum gravity field theories typically relies on off-shell quantities such as $\beta$ functions and generating functionals and thus face potential stability issues with regard to such generalized parametrizations. We analyze a two-parameter class of covariant gauge conditions, the role of momentum-dependent field rescalings and a class of field parametrizations. Using the product of Newton and cosmological constant as an indicator, the principle of minimum sensitivity identifies stationary points in this parametrization space which show a remarkable insensitivity to the parametrization. In the most insensitive cases, the quantized gravity system exhibits a non-Gau\ss{}ian UV stable fixed point, lending further support to asymptotically free quantum gravity. One of the stationary points facilitates an analytical determination of the quantum gravity phase diagram and features ultraviolet and infrared complete RG trajectories with a classical regime.

Calorimetric determination of the magnetic phase diagram of underdoped ortho II YBa2Cu3O6.54 single crystals.

The recent discovery of a charge order in underdoped YBa2Cu3Oy raised the question of the interplay between superconductivity and this competing phase. Understanding the normal state of high-temperature superconductors is now an essential step towards the description of the pairing mechanism in those materials and determining the upper critical field is therefore of fundamental importance. We present here a calorimetric determination of the field–temperature phase diagram in underdoped YBa2Cu3Oy single crystals. We show that the specific heat saturates in high magnetic fields. This saturation is consistent with a normal state without any significant superconducting contribution and a total Sommerfeld coefficient γN∼6.5±1.5 mJ mol−1 K−2 putting strong constraints on the theoretical models for the Fermi surface reconstruction.

Mixed Spins in a Nano-system Built on a Dendrimer Structure: Monte Carlo Study

In this work, we investigate a nano-system built on a hexagonal dendrimer structure, for mixed spins σ = 2 and S = 3/2. First, we study this system in the presence/absence of both an external and crystal magnetic fields. The study of the effect of the coupling exchange interactions and the determination of the ground state phase diagrams are discussed. On the other hand, we focus our interest on the study and determination of these parameters. The elaboration and the discussion of all the stable phases have been outlined. A theoretical study by Monte Carlo simulations (MCS) in the framework of the Ising model is used to find out the understanding of the magnetic properties of this system. The obtained results by means of MCS simulations are the critical temperature and the compensation temperature. For fixed values of the coupling exchange interactions and temperature, the hysteresis loop is established, in order to complete this study.

Use of dynamic light scattering and small-angle X-ray scattering to characterize new surfactants in solution conditions for membrane-protein crystallization.

The structural and interactive properties of two novel hemifluorinated surfactants, F2H9-β-M and F4H5-β-M, the syntheses of which were based on the structure and hydrophobicity of the well known dodecyl-β-maltoside (DD-β-M), are described. The shape of their micellar assemblies was characterized by small-angle X-ray scattering and their intermicellar interactions in crystallizing conditions were measured by dynamic light scattering. Such information is essential for surfactant phase-diagram determination and membrane-protein crystallization.

Individualized Pixel Synthesis and Characterization of Combinatorial Materials Chips

ABSTRACT Conventionally, an experimentally determined phase diagram requires studies of phase formation at a range of temperatures for each composition, which takes years of effort from multiple research groups. Combinatorial materials chip technology, featuring high-throughput synthesis and characterization, is able to determine the phase diagram of an entire composition spread of a binary or ternary system at a single temperature on one materials library, which, though significantly increasing efficiency, still requires many libraries processed at a series of temperatures in order to complete a phase diagram. In this paper, we propose a “one-chip method” to construct a complete phase diagram by individually synthesizing each pixel step by step with a progressive pulse of energy to heat at different temperatures while monitoring the phase evolution on the pixel in situ in real time. Repeating this process pixel by pixel throughout the whole chip allows the entire binary or ternary phase diagram to be mapped on one chip in a single experiment. The feasibility of this methodology is demonstrated in a study of a Ge-Sb-Te ternary alloy system, on which the amorphous-crystalline phase boundary is determined.