Gibbs Triangle Research Articles

Introducing concepts of estimating tracer and intrinsic diffusion coefficients in a ternary system: a case study in the FCC Fe-Mn-Cr solid solution

ABSTRACT Estimating tracer and intrinsic diffusion coefficients following the diffusion couple method with systematic composition variation can be challenging because of the diffusion paths’ serpentine or double serpentine nature on the Gibbs triangle. Moreover, the possibility of estimating these diffusion coefficients from a single diffusion profile can have immense benefits. We have demonstrated four ways of estimating tracer and impurity diffusion coefficients in the FCC Fe-Mn-Cr solid solution: (i) We have shown that these can be estimated directly at the Kirkendall marker plane from a single conventional ternary diffusion profile. (ii) We have, for the first time, demonstrated that the estimation at the intersection of a conventional ternary and constrained pseudo-binary diffusion path is helpful for systematically generating composition-dependent tracer diffusion coefficients. (iii) We have followed the Kirkaldy-Lane method for estimating these diffusion coefficients at the intersection of two conventional ternary diffusion couples (for comparison of the data measured by new methods), although for data generation at random compositions. This was proposed a long time ago but practised occasionally. It helps to compare with the estimated data following other methods. (iv) Additionally, we have estimated the impurity diffusion coefficients of Cr and Mn in Fe following the Hall method, which helps in understanding the variation of the diffusion coefficients in Fe-Mn-Cr alloys compared to pure Fe. The sensitivity of data estimation following different methods, i.e. different equation schemes, is discussed, explaining the strategic design of diffusion couple for a small error range.

Phase Behavior of Ternary Polymer Mixtures in a Common Solvent.

The Edmond-Ogston model for phase separation is extended to ternary polymer mixtures in a common solvent (de facto a quaternary mixture). The model assumes a truncated virial expansion of the Helmholtz free energy up to the second-order terms in the concentration of the polymers, and the second virial coefficients (B11, B22, B33, B12, B13, B23) are the six parameters of the model. New results from this model are presented in relation to earlier work on binary mixtures: a necessary condition for the virial coefficients for the occurrence of phase separation in two or three phases, an analysis of the different regions of (local) thermodynamic instability using the Descartes sign rule, an expression for the critical curves, a relation between the tangents in points along the critical curve, a relation between the concentration of components in the different phases according to the so-called Lambert-W function, and a consistency check for the composition of coexisting phases in ternary mixtures. The obtained results are evaluated in the maximally symmetric version of the model, where (B11, B22, B33) are equal and (B12, B13, B23) are equal, which leads to two remarkable observations: the concentration range over which two phases are formed is relatively narrow; not all phase separation occurs within a Gibbs triangle, but also, "out-of-Gibbs-triangle" binodals are observed. These results lead to a deeper insight into the phase behavior of ternary mixtures and show promise as a stepping stone toward modeling phase separation in mixtures with many components.

Durability of Mortars with Fly Ash Subject to Freezing and Thawing Cycles and Sulfate Attack

Destruction of cement composites occurs due to the alternate or simultaneous effects of aggressive media, resulting in the destruction of concrete under the influence of chemical and physical factors. This article presents the results of changes in the measurement of linear strains of samples and changes in the microstructure of cement after 30 freezing and thawing cycles and immersed in 5% sodium sulfate solution. The compressive strengths ratios were carried out at the moment when the samples were moved to the sulfate solution after 30 cycles and at the end of the study when the samples showed visual signs of damage caused by the effect of 5% Na2SO4. The composition of the mixtures was selected based on the Gibbs triangle covering the area up to 40% replacement of Portland cement with low and high-calcium fly ashes or their mixture. Air-entrained and non-air entrained mortars were made of OPC, in which 20%, 26.6%, and 40% of Portland cement were replaced with low and/or high-calcium fly ash. Initial, freezing and thawing cycles accelerated the destruction of non- air-entrained cement mortars immersed in 5% sodium sulfate solution. The sulfate resistance, after the preceding frost damage, decreased along with the increase in the amount of replaced fly ash in the binder. Air-entrained mortars in which 20% of cement was replaced with high-calcium fly ash showed the best resistance to the action of sodium sulfate after 30 freezing and thawing cycles.

High Throughput Screening of Na-Fe-Mn-O Sodium-Ion Cathode Materials

With the rapid development of sodium-ion batteries in recent years, the prospect of replacing lithium-ion batteries for some applications like personal electronics is more and more promising. The abundant reserve of sodium element and the cheap transition metals for layered oxides are the decisive advantages to solve the cost of electricity storage and environmental pollution, which may make massive energy storage accessible. During the past ten years, layered oxides of the form NaxFeyMnzO2 have received a lot of attention with high specific capacities and eco-friendly transition metal selection. Since the radius of sodium ion is significantly larger than that of lithium ion, the configurations of the sodium layered oxides are more complex, which allows sodium ions to be located in either octahedral (O-type) or prismatic (P-type) sites. Meanwhile, the electrochemical properties of sodium layered oxides vary dramatically with the composition. Despite this, a relatively small number of compositions have been studied to date in the Na-Fe-Mn-O system. Herein, we apply high-throughput methods to systematically analyze both structures and battery performance across the entire NaxFeyMnzO2 system.The high-throughput methods established elsewhereare used here to make and characterize 64 different materials simultaneously. In total, materials at 304 different compositions were made for this study, all of which were examined by X-ray diffraction (XRD) and 184 compositions were also studied by high-throughput electrochemistry as they are particularly interesting as potential battery materials. Qualitative phase identification based on the XRD is performed as well as quantitative fitting of the data to extract phase compositions and lattice parameters. Each of P2-, P3- and O3-type sodium layered oxides are identified in the phase diagram and their solid solution regions were determined and will be discussed in detail. High-throughput cyclic voltammetry (CV) is used to obtain the charge/discharge voltages and specific capacities for 15 cycles thereby allowing some discrimination of the quality of extended cycling. These methods enable a rapid and highly precise screening across very wide compositions. Figure 1 shows both the experimental setup used for key steps in the synthesis and also a map of specific capacity across the phase diagram. Such maps will be correlated to the structural phase diagram obtained by XRD in order to extract meaningful structure-property relationships. Moreover, high-throughput XPS is used to study the surface stability after over 6 months of storage in air. Interestingly, some compositions show a greater tendency to form carbonates and have consequences on the electrochemical performance. Figure 1. Steps in the high-throughput electrochemical methods used to study 64 samples at once: a) a well plate containing sol-gel precursors in various ratios to map out a region of the phase diagram, (b) the samples after sintering at 850 °C, (c) combinatorial cell used to collect the CVs shown in (d), and (e) specific capacities extracted from the CVs plotted on the Na-Fe-Mn-O pseudo-ternary Gibbs triangle. Compositions P2-Na2/3Fe1/2Mn1/2O2 and O3-Na2/3Fe1/2Mn1/2O2 are labeled on the ternary plot.References Liu, Q.; Hu, Z.; Chen, M.; Zou, C.; Jin, H.; Wang, S.; Chou, S. L.; Dou, S. X., Recent progress of layered transition metal oxide cathodes for sodium‐ion batteries. Small 2019, 15 (32), 1805381.Yabuuchi, N.; Kajiyama, M.; Iwatate, J.; Nishikawa, H.; Hitomi, S.; Okuyama, R.; Usui, R.; Yamada, Y.; Komaba, S., P2-type Na x [Fe 1/2 Mn 1/2] O 2 made from earth-abundant elements for rechargeable Na batteries. Nature materials 2012, 11 (6), 512.Adhikari, T.; Hebert, A.; Adamic, M.; Yao, J.; Potts, K.; McCalla, E., Development of High-Throughput Methods for Sodium-Ion Battery Cathodes. ACS combinatorial science 2020, 22 (6), 311. Figure 1

The Soret coefficients of the ternary system water/ethanol/triethylene glycol and its corresponding binary mixtures

Thermodiffusion in ternary mixtures is considered prototypic for the Soret effect of truly multicomponent systems. We discuss ground-based measurements of the Soret coefficient along the binary borders of the Gibbs triangle of the highly polar and hydrogen bonding ternary DCMIX3-system water/ethanol/triethylene glycol. All three Soret coefficients decay with increasing concentration, irrespective of the choice of the independent component, and show a characteristic sign change as a function of temperature and/or composition. With the exception of triethylene glycol/ethanol at high temperatures, the minority component always migrates toward the cold side. All three binaries exhibit temperature-independent fixed points of the Soret coefficient. The decay of the Soret coefficient with concentration can be related to negative excess volumes of mixing. The sign changes of the Soret coefficients of the binaries allow to draw far-reaching conclusions about the signs of the Soret coefficients of the corresponding ternary mixtures. In particular, we show that at least one ternary composition must exist, where all three Soret coefficients vanish simultaneously and no steady-state separation is observable.Graphic abstract

First-principles Calculations of Bulk and Interfacial Thermodynamic Properties of the T1 phase in Al-Cu-Li alloys

We recently proposed a new, low-energy atomic structure of the Al2CuLi (T1) phase using first-principles calculations based on density functional theory [Acta Mater. 145 (2018) 337-346]. Here, we refine the Li positions in the proposed T1 structure and find that the T1 phase has a tie-line with Al at finite-temperature by vibrational entropic stabilization on the Gibbs triangle of the ternary Al-Cu-Li system. We also derive a low-energy T1/Al coherent interfacial structure and find that Ag and Mg solutes are predicted to segregate to the coherent interface, which is in agreement with recent experimental observations by atom probe tomography.

Reexamination of the phase diagram of the BaO-ZrO2-Y2O3 system: investigation of the presence of separate region in Y-doped BaZrO3 solid solution and the dissolution of Zr in Ba3Y4O9

Y-doped BaZrO3 (BZY) is a promising candidate for electrolytes in protonic ceramic fuel cells. To achieve the high proton conductivities of sintered electrolyte membranes, the poor sintering nature is one of the problems because of the high resistance at grain boundaries. To obtain single-phase BZY with sufficient grain growth (> 1 μm), the information of phase stable conditions of BZY is important. However, in previous studies, there are discrepancies in the single-phase composition range of BZY, and the phase relationships between BZY and other phases at a sintering temperature (1600 °C). In this work, we clarified the phase stable conditions of BZY by reexamining the critical part of the phase diagram of the BaO-ZrO2-Y2O3 system. Based on X-ray diffraction, at certain temperatures below 1600 °C, the single-phase composition range of BZY is not continuous at ~ 10% in the molar ratio of Y/(Zr + Y). Even when sintering at 1600 °C, this separate region probably retards the formation of single-phase and grain growth. Besides, we revealed the other ternary phases, i.e., γ phase and Zr-substituted Ba3Y4O9 are stable in XBaO < 50 mol% and can coexist with BZY at 1600 °C. This information is discussed on the Gibbs triangles and should be useful for all researchers working on BZY.

Strategic policy of companies in the area of social responsibility: Covid-19 challenges

COVID 19 is a litmus test for TNCs in the field of social responsibility. A scientific and methodological approach to determining the level and activation of corporate social responsibility (CSR) of business in the national economy in the form of a three-dimensional matrix model of positioning the level of development of CSR of business units in the coordinate system: social, environmental and economic components of CSR has been developed. The methods used in the study, the construction of the Gibbs Triangle and the method of taxonomy to determine the most influential aspects of GRI reporting (G4), allowed to propose a CSR monitoring system for key business performance indicators. The results of the analysis of this study allow distinguishing five areas of responsibility: the necessary level of responsibility - for statutory obligations, the developed level - active charitable and sponsorship, high level - responsibility to internal and external stakeholders, strategic - focus on the social investment state level, as well as synergetic - a comprehensive combination of all components of the CSR. In conclusion, the level and activation of corporate social responsibility of industrial enterprises in the form of a three-dimensional matrix model of positioning the level of development of business units in the coordinate system: social, environmental, and economic components, has been determined to develop alternative scenarios to justify management decisions.

Statistical model used to assessment the sulphate resistance of mortars with fly ashes

Abstract The use of low (LCFA) and high (HCFA) calcium fly ashes in the cement industry allows the implementation of European Union proposals on waste management and energy saving. However, the possibility of using HCFA is limited, because the properties of such waste from coal-fired power plants must comply with national regulations. The paper shows the effect of partial replacement of Portland cement (OPC) by these fly ashes on the resistance of the sulphate attack of the mortars immersed in a 5% solution of sodium sulphate. In order to determine the optimal amount of ash additive, a research plan was designed using statistical methods using the Gibbs triangle for mixtures. Samples of control mortars of OPC, binary mixtures of HCFA or LCFA and ternary mixtures of HCFA/LCFA were made. The composition of the blends was designed in accordance with the statistical plan of the experiment for mixtures. The testing program included linear strains, compressive strength and microstructure tests using SEM with EDXA and XRD analysis. The results of laboratory tests and statistical analyzes have shown that fly ash has a positive effect on the sulphate resistance of cementitious composites.

Simulation of atomic mobilities, interdiffusivities and diffusional evolution in fcc Ni-Cu-Ti alloys

As a contribution to establish a general Ni-based mobility database, the atomic mobilities in fcc Ni-Cu-Ti alloys were explored in this work. Diffusion couples were annealed at 1273 K for 150 h, and the interdiffusion coefficients were evaluated at common composition points of diffusion profiles. By combining such interdiffusion coefficients and the available thermodynamic information, the atomic mobilities of Ni, Cu and Ti in fcc Ni-Cu-Ti alloys were assessed as functions of temperature and compositions within the CALPHAD framework. Further verification of the obtained atomic mobilities was conducted by comparing the calculated and measured interdiffusvities, diffusion profiles in diffusion couples and diffusion paths in the Gibbs triangle.

Thermodynamic properties of Ag–Au–Pd alloys measured by a solid-state EMF method

Although the Ag–Au–Pd system is crucial for several industrial applications and for the research on fundamental physics, no thermodynamic data on this ternary system at low temperatures have been reported in the literature. In the present study, activities of silver are directly measured by employing a solid-state EMF method, by using AgI as the solid electrolyte. The EMF was determined using a galvanic cell $$ \left( - \right){\text{Pt}}\left| {\text{C}} \right.\left| {\text{Ag}} \right|{\text{AgI}}\left| {{\text{Ag-Au-Pd alloy}}} \right|{\text{C}}\left| {{\text{Pt}}\left( + \right)} \right. $$ , which produced novel experimental data on the thermodynamic properties of Ag–Au–Pd alloys. Darken method was used to calculate integral excess thermodynamic properties from the data. New thermodynamic characteristics, such as integral excess mixing Gibbs energy, entropy and enthalpy of the Ag–Au–Pd alloys, have been generated in a temperature range of 475 and 675 K. Isoactivity lines of silver in the system have been drawn throughout the Gibbs triangle. Thermodynamic properties of the binary Au–Pd alloys have been compared with the previous investigations.

Phase Relations in Ternary Systems in the Subsolidus Region: Methods To Formulate Solid Solution Equations and To Find Particular Compositions

A good understanding of ternary phase diagrams is required to advance and/or to reproduce experimental research in solid-state and materials chemistry. The aim of this paper is to describe the solutions to problems that appear when studying or determining ternary phase diagrams. A brief description of the principal features shown in phase diagrams of ternary systems in the subsolidus region is included. We present a systematic procedure to obtain specific compositions of particular interest as well as to calculate binary and ternary ratios of compounds inside the Gibbs triangle and a step-by-step methodology to formulate solid solution equations in binary, ternary, or higher-composition compounds. Specific problems and their solutions are presented as a practical guide, linking the learned concepts with their applications in ceramics and solid-state chemistry research. In addition, ready-to-go exercises with worked-out solutions are included for practice. The procedures described herein may be helpful to those interested in phase diagram interpretation, preparation, and analysis.

Phase diagram of the Fe-Sn-Zr system at 800 °C

New experimental results on the Fe-Sn-Zr phase diagram at 800 °C are presented, particularly in the central, Fe rich and Sn rich regions of the Gibbs triangle. Seven ternary alloys were designed, produced and examined by different techniques: optical and scanning electron microscopy, semi-quantitative microanalysis, quantitative microanalysis and X-ray diffraction. The results of this work and previous experimental data were used to determine the phase diagram section at 800 °C which contains at least five ternary compounds: Fe6Sn6Zr, Y, X′, θ and C36.

Investigation of the phase relations in the U-Al-Ge ternary system: Influence of the Al/Ge substitution on the properties of the intermediate phases

The phase relations within the U-Al-Ge ternary system were studied for two isothermal sections, at 673K for the whole Gibbs triangle and at 1173K for the concentration range 25–100at% U. The identification of the phases, their composition ranges and stability were determined by x-ray powder diffraction, scanning electron microscopy coupled to energy dispersive spectroscopy and differential thermal analysis. The tie-lines and the solubility domains were determined for the U-Ge and U-Al binaries, the UAl3-UGe3 solid-solution and for the unique ternary intermediate phase U3Al2−xGe3+x. The experimental isopleth section of the pseudo-binary UAl3-UGe3 reveals an isomorphous solid solution based on the Cu3Au-type below the solidus. The U3Al2−xGe3+x solid solution extends for −0.1≤x≤1.35 and −0.2≤x≤1.5 at 673K and 1173K respectively. It crystallizes in the I-centered tetragonal symmetry. The reciprocal lattice of several compositions of the U3Al2−xGe3+x solid solution was examined by electron diffraction at room temperature, revealing the presence of a c-glide plane. Their crystal structure was refined by single crystal x-ray diffraction suggesting an isomorphous solid solution best described with the non-centrosymmetric space group I4cm in the paramagnetic domain. The magnetic measurements confirm the ferromagnetic ordering of the solid solution U3Al2−xGe3+x with an increase of Tc with the Al content. The thermal variation of the specific heat bear out the magnetic transitions with some delocalized character of the uranium 5f electrons.

Atomic Mobilities and Interdiffusivities for fcc Ni-Cr-Nb Alloys

The atomic mobilities and diffusion characteristics for fcc Ni-Cr-Nb alloys are explored by diffusion couples annealed at 1273 K (1000 °C) for 200 hours. The interdiffusion coefficients are extracted from intersection points of two diffusion paths, after which the atomic mobilities of Ni, Cr, and Nb in fcc Ni-Cr-Nb alloys are inversely obtained within the CALPHAD framework with the aid of related thermodynamic descriptions. In order to verify the quality of obtained kinetic parameters so that an accurate Ni-based atomic mobility database can be established, the composition profiles in diffusion couples and the diffusion paths superimposed upon Gibbs triangle are explored, where the experimentally measured and calculated values show good agreement.

Правила и опыт применения литологического треугольника для построения фациальных карт

Lithological triangles are used in order to construct a geological lithofacies map under the conditions of significant bore-hole mud weight. The placement of these triangles’ points and their triangular coordinates do not always coincide. Gibbs triangle and Gibbs-Rosebom triangle are used in physical chemistry. The second is better developed. The planimetry theorems are the basis for the rules of constructing and using the triangle. When applying nomographic methods it is suggested to use a standard triangle to construct lithofacies maps (maps with a lithological cut).

Numerical Prediction of the Thermodynamic Properties of Ternary Al-Ni-Pd Alloys

AbstractThermodynamic properties of ternary Al-Ni-Pd system, such as exGAlNPd, µAl(AlNiPd),µNi(AlNiPd) and µPd(AlNiPd) at 1,373 K, were predicted on the basis of thermodynamic properties of binary systems included in the investigated ternary system. The idea of predicting exGAlNiPd values was regarded as calculation of values of the exG function inside a certain area (a Gibbs triangle) unless all boundary conditions, that is values of exG on all legs of the triangle are known (exGAlNi, exGAlPd, exGNiPd). This approach is contrary to finding a function value outside a certain area, if the function value inside this area is known. exG and LAl,Ni,Pd ternary interaction parameters in the Muggianu extension of the Redlich–Kister formalism were calculated numerically using the Excel program and Solver. The accepted values of the third component xx differed from 0.01 to 0.1 mole fraction. Values of LAlNiPd parameters in the Redlich–Kister formula are different for different xx values, but values of thermodynamic functions: exGAlNiPd, µAl(AlNiPd), µNi(AlNiPd) and µPd(AlNiPd) do not differ significantly for different xx values. The choice of xx value does not influence the accuracy of calculations.

Diffusion behavior and atomic mobilities for fcc Cu–Cr–Ni alloys

In this work, diffusion couples of fcc Cu–Cr–Ni alloys annealed at 1373 K for 80 h are investigated. The interdiffusion coefficients are retrieved from common compositions of two diffusion couples, which are then combined with thermodynamic descriptions to explore atomic mobilities of Cu, Cr and Ni in fcc Cu–Cr–Ni alloys within the CALPHAD framework. In order to confirm the quality of such kinetic characteristics, a comparison between calculated and experimentally measured concentration profiles of diffusion couples and diffusion paths in Gibbs triangle is made, where the agreement is excellent. The results of this study contribute to the establishment of a general Ni-based mobility database for alloy design.

Numerical Approach to Predicting Thermodynamic Properties of Ternary Al-Ni-Pt Alloys

Thermodynamic properties of ternary Al Ni Pt system, such as GAlNiPt, μAl(AlNiPt), μNi(AlNiPt), and μPt(AlNiPt) at 1373 K were predicted on the basis of thermodynamic properties of binary systems included in the investigated ternary system. The idea of predicting GAlNiPt values was regarded as calculation of values of G function inside a certain area (a Gibbs triangle) unless all boundary conditions, that is values of G on all legs of the triangle are known (GAlNi, GAlPt, GNiPt). This approach is contrary to nding the function value outside a certain area, if the function value inside this area is known. G and Lijk ternary interaction parameters in the Muggianu extension of the Redlich Kister formalism are calculated numerically using the Mathematica program. The accepted values of the third component concentration xx di ered from 0.01 to 0.1 mol fraction. Values of L parameters in the Redlich Kister formula vary for di erent xx values, the LAlNiPt value in particular. Values of thermodynamic functions: GAlNiPt, μAl(AlNiPt), μNi(AlNiPt) and μPt(AlNiPt) do not di er signi cantly for di erent xx values. The choice of xx value does not in uence the accuracy of calculations.

Calorimetric investigation of mixing enthalpy of liquid (Co + Cu + Zr) alloys at T = 1873 K

The enthalpies of mixing of liquid (Co+Cu+Zr) alloys have been determined using the high-temperature isoperibolic calorimeter. The measurements have been performed along three sections (xCo/xCu=3/1, 1/1, 1/3) with xZr=0 to 0.55 at T=1873K. Over the investigated composition range, the partial mixing enthalpies of zirconium are negative. The limiting partial enthalpies of mixing of undercooled liquid zirconium in liquid (Co+Cu) alloys are (−138±18)kJ·mol−1 (the section xCo/xCu=3/1), (−155±10)kJ·mol−1 (the section xCo/xCu=1/1), and (−130±22)kJ·mol−1 (the section xCo/xCu=1/3). The integral mixing enthalpies are sign-changing. The isenthalpic curves have been plotted on the Gibbs triangle. The main features of the composition dependence of the integral mixing enthalpy of liquid ternary alloys are defined by the pair (Co+Zr) and (Cu+Zr) interactions.