Temperature-composition Phase Diagram Research Articles

From electrons to phase diagrams with machine learning potentials using pyiron based automated workflows

AbstractWe present a comprehensive and user-friendly framework built upon the integrated development environment (IDE), enabling researchers to perform the entire Machine Learning Potential (MLP) development cycle consisting of (i) creating systematic DFT databases, (ii) fitting the Density Functional Theory (DFT) data to empirical potentials or MLPs, and (iii) validating the potentials in a largely automatic approach. The power and performance of this framework are demonstrated for three conceptually very different classes of interatomic potentials: an empirical potential (embedded atom method - EAM), neural networks (high-dimensional neural network potentials - HDNNP) and expansions in basis sets (atomic cluster expansion - ACE). As an advanced example for validation and application, we show the computation of a binary composition-temperature phase diagram for Al-Li, a technologically important lightweight alloy system with applications in the aerospace industry.

A new set of gas-structure-dependent parameters to improve gas hydrate equilibrium calculations and structure descriptions by van der Waals-Platteeuw model

The traditional Kihara potential parameters employed in the van der Waals-Platteeuw (vdW-P) model were only related to the species of hydrate-forming gases. Although our previous study (Chemical Engineering Science 248, 117213) proposed a framework for optimizing the gas-dependent Kihara potential parameters in vdW-P model to improve the hydrate equilibrium calculations, the predictions for hydrate structures are barely satisfactory. Thus, this study provides a new set of Kihara potential parameters which are dependent on not only the gas species but also the hydrate structures. With the constraints on hydrate structure changes, a novel procedure for fitting the gas-structure-dependent parameters is developed. The calculation results show that the newly obtained parameters improve the performances of vdW-P model in predicting the hydrate equilibria for the pure-gas and gas-mixture systems. Besides, the vdW-P model coupled with gas-structure-dependent parameters can provide reliable temperature-composition phase diagrams and properly identify the crystalline structures for various gas hydrates.

Multiphase Behavior of the Water + 1-Butanol + Deep Eutectic Solvent Systems at 101.3 kPa

The growing demand for more sustainable routes and processes in the mixture separation and purification industry has generated a need to search for innovations, with new solvent alternatives being a possible solution. In this context, a new class of green solvents, known as deep eutectic solvents (DESs), has been gaining prominence in recent years in both academic and industrial spheres. These solvents, when compared to ionic liquids (ILs), are more environmentally friendly, less toxic, low-cost, and easier to synthesize. In addition, they have significantly lower melting points than their precursors, offering a promising option for various applications in this industrial sector. Understanding and studying the thermodynamic behavior of systems composed of these substances in purification and separation processes, such as liquid–liquid extraction and azeotropic distillation, is extremely important. This work aimed to study the phase behavior of liquid–liquid equilibrium (LLE) and vapor–liquid equilibrium (VLE) of water + 1-butanol + DES (choline chloride + glycerol) systems with a molar ratio of 1:2. Experimental LLE data, obtained at 298.15 K and 101.3 kPa, and VLE data, obtained at 101.3 kPa and in the temperature range of 364.05 K–373.85 K, were submitted to the thermodynamic quality/consistency test, proposed by Marcilla et al. and Wisniak, and subsequently modeled using the gamma–gamma approach for the LLE and gamma–phi for the VLE. The non-random two-liquid (NRTL) model was used to calculate the activity coefficient. The results are presented for the VLE in a temperature–composition phase diagram (triangular prism) and triangular phase diagrams showing the binodal curve and tie lines (LLE). The separation and distribution coefficients of LLE were determined to evaluate the extractive potential of the DES. For the VLE, the values of the relative volatility of the system were calculated, considering the entrainer free-basis, to evaluate the presence or absence of azeotropes in the range of collected points. From these data, it was possible to compare DES with ILs as extracting agents, using data from previous studies carried out by the research group. Therefore, the results indicate that the NRTL model is efficient at correlating the fluid behavior of both equilibria. Thus, this study serves as a basis for future studies related to the understanding and design of separation processes.

Design of shape memory alloys with low hysteresis via multiple phase coexistence

Shape memory alloys (SMAs) are the key components of actuators and sensors due to their shape memory effect and superelasticity. However, the thermal hysteresis associated with martensitic phase transformation limits their use in the long-duration precise control. We report a strategy that obtains SMAs with low hysteresis by constructing a composition-temperature pseudo phase diagram. This strategy is inspired by the physically parallel ferroelectric system where the hysteresis is minimized at the multiple phase coexistence point, due to the absence of energy barrier across different phases. Following this, an alloy in the phase diagram with a low hysteresis of about 5 K is synthesized. In contrast, those alloys compositionally different from the optimal one have large hysteresis. Microstructures characterization and diffraction analysis are employed to identify the multiple phase coexistence. The proposed strategy should be general and can shed light on the rational design of SMAs with low hysteresis.

Optimization of energy storage and electrocaloric performance in Pb(Zr,Ti)O3 via A-Site La and Bi Co-doping

Lead-based ferroelectrics are one of the most fascinating candidates in the field of state-of-the-art electronic technology. Their intriguing properties are further enriched via the realization of morphotropic phase boundaries. Moreover, the A-site chemical substitution provides insight into the emergence of various exotic phases. Here, we employ co-doping of La3+ and Bi3+ at the A-site of Pb(Zr,Ti)O3 (PZT) ferroelectric to broaden the practical perspective of relaxor systems. Here, we emphasize that the A-site co-doping approach introduces technologically appealing amendments in the well-established temperature composition phase diagram of the PZT system. La3+ and Bi3+ doping favors the evolution of a novel response to thermal and field fluctuations. The maximum values of −ΔS are found to be ∼0.157, 0.118 and 0.176 J (kg·K)−1 for x=0.01, 0.02 and 0.03 , respectively. We employ the electrocaloric characteristics and Arrott plot as probing tools. The observation of a negative electrocaloric effect and the systematic reversal of Arrott lines, followed by a poling effect on the dielectric constant, reveals the emergence of ergodic phase as a novel phase. This further reveals that the Bi doping approach leads to the emergence of exotic characteristics in the chemically modified PZT system. The maximum observed recoverable energy for the composition for x = 0.01 is 0.0479 J cm−3 at a temperature of 388 K.

Solid Solutions of Plastic/Ferroelectric Crystals: Toward Tailor-Made Functional Materials.

Plastic crystals that show ferroelectricity are highly promising materials for a wide range of applications. Their inherent remarkable malleability and highly symmetric cubic structures in the plastic crystal phase ensure that their ferroelectricity and related properties are retained in their bulk polycrystals. To develop functional materials based on such plastic/ferroelectric crystals, methods to tune their properties for specific applications are required. Here, we report the preparation of solid solutions of plastic/ferroelectric ionic crystals by mixing crystals with a common anion but different cations, or crystals with a common cation but different anions, which allows a continuous modification of the Curie temperature of the ferroelectric system over a range of 100 K. This adjustment of the Curie temperature allows the flexible tuning of the pyroelectric properties of the solid solutions, including a significant enhancement of room-temperature performance. The solid solutions also exhibit morphotropic phase boundaries in the composition-temperature phase diagrams, which shows an abrupt change in crystal structures with a variation of composition. This study showcases a simple and versatile property-tuning method that can be expected to pave the way for major progress in the development of materials based on plastic/ferroelectric crystals, which will eventually advance to the stage of pursuing tailor-made functional materials with desired properties.

Design, synthesis and Characterization of a novel antiferroelectric solid solution (1-x)PbHfO3-xBiAlO3

Antiferroelectric (AFE) materials are potentially useful for energy storage applications. Lead hafnate (PbHfO3) is one of the prototypical AFE materials. However, its critical field (Ecr) which is needed to induce the AFE to ferroelectric phase transition is close to the dielectric breakdown strength. To reduce Ecr, we prepare the solid solutions of (1-x)PbHfO3–xBiAlO3 (x = 0.00–0.04) via solid state synthesis. The crystal structures, dielectric behaviour, ferroelectric properties, and energy storage properties are investigated. A temperature-composition phase diagram is established. At room temperature, the crystal symmetry of all compositions is orthorhombic with the Pbam space group. Upon heating, the transition to the AFE orthorhombic Imma phase is observed at the temperature TC1, which slightly decreases with increasing x, followed by the transition to the cubic phase at the temperature TC2, which does not depend on x. Distinct dielectric anomalies are observed at TC1 and TC2. It is found that BiAlO3 substitution reduces Ecr and the polarization–electric field relations display characteristic double hysteresis loops. For x = 0.04, at a comparatively small applied field of 130 kV/cm, the values of recoverable energy density (Wrec) and efficiency of 0.24 J/cm3 and 84 %, respectively, are obtained. At 190 °C, a Wrec = 0.75 J/cm3 and a very high efficiency of 92 % are obtained at the field of 50 kV/cm. Thus, the prepared material can potentially be used in high-temperature pulsed power capacitors for energy storage applications within the temperature range from room temperature up to 190 °C.

Thermodynamic stability and ionic conductivity in lithium–germanium binary system

Lithium–germanium binary compounds are promising anode materials for secondary lithium-ion batteries due to their high capacity, low operating voltage, and high electronic conductivity of lithiated Ge. For their successful application in batteries, it is essential to know the temperature stability of different Li–Ge phases and the variation of their ionic conductivity depending on the operating temperatures of the batteries. This work aims to comprehensively study the thermodynamic stability and ionic conductivity in Li–Ge binary compounds using a combination of first-principle computations and machine-learning interatomic potentials. We calculated convex hulls of the Li–Ge system at various temperatures and a temperature–composition phase diagram was obtained, delineating stability fields of each phase. Our calculations show that at temperatures higher than 590 K, LiGe undergoes a I41/a–P4/mmm transition, which leads to a change in the ionic conductivity. We show that all stable and metastable Li–Ge compounds have high ionic conductivity, but LiGe and Li7Ge12 have the lowest lithium diffusion. Trajectories of diffusion and Ge arrangements depend on lithium concentration. Based on advanced theoretical approaches, this study provides insights for the development of Li–Ge materials in lithium-ion and lithium-metal battery applications.

Phase diagram and density of SiO2–H2O fluid across critical conditions

The SiO2–H2O binary system serves as a basis for understanding complex silicate-water systems. In this study, based on limited existing experimental data of solubility, we propose a new thermodynamic model for SiO2–H2O fluid by modifying the traditional non-random two-liquid model with a simplified polymerization reaction. This model is applicable from 773 K to the anhydrous quartz melting temperature and from 0.5 GPa to at least 2 GPa across the critical conditions. It can predict solid–liquid equilibrium and vapor–liquid equilibrium in good agreement with available experiments. The upper critical endpoint of the SiO2–H2O system is predicted to be at ~ 1.14 ± 0.18 GPa and 1344 ± 87 K. With the new model, we obtain a quantitative three-dimensional pressure–temperature–composition phase diagram of the SiO2–H2O fluid, which greatly facilitates the understanding of the complex phase behavior of this binary around the upper critical endpoint. In addition, since the model is based on the Gibbs free energy foundation, we further discuss the derived density variations of SiO2–H2O fluid along with its complex phase changes in typical geochemical processes.

Magnetic properties, phase diagram and low-temperature specific heat of Ni50Mn50-xSbx alloys

This study examines the magnetic properties and temperature-composition phase diagram of the Ni50Mn50-xSbx alloys. The addition of Sb into the antiferromagnetic Ni50Mn50 alloy introduces ferromagnetic interaction, resulting in a sudden decrease in the Néel temperature. The characteristic regions of ferromagnetic (FM) and antiferromagnetic (AFM) interactions were determined on temperature-composition phase diagram, as well as compositional dependence of Néel temperature was computed. Increase of Sb content gives rise to an interplay between AFM and FM interactions, leading to the emergence of a spin glass-like state. We identified six distinct magnetic phases in the Ni50Mn50-xSbx system, encompassing AFM, paramagnetic, and FM martensite, as well as spin glass, and paramagnetic and FM austenite. Importantly, this behavior may extend to other Ni50Mn50-xZx (Z = In, Sn) alloys, where addition of Z elements leads to the introduction of FM interaction. Moreover, a significant impact of magnetic ordering on low-temperature specific heat is demonstrated. Neglecting the magnetic contribution in ferromagnetic phase leads to the overestimation of electronic specific heat coefficient by factor of 2.

Ab initio computation of low-temperature miscibility gap of V(Se,Te)2

Monolayers of quasi-binary transition metal dichalcogenides are a focus of attention as they are expected to exhibit many exciting physical properties, but not much is known about their thermodynamic stability. In this study, we use a combination of global energy landscape exploration, local minimization using density functional theory, and thermodynamic analysis, to compute the composition-temperature phase diagram of the quasi-binary V(Se,Te)2 system, both for a 2H monolayer and for the analogous bulk material. We find that the phase diagram exhibits a miscibility gap, with a critical temperature T c = 500 K and T c = 650 K for monolayer and bulk, respectively, indicating that the system prefers to form solid solution phases. In particular, at room temperature, the thermodynamically stable phase of the monolayer would correspond to a decomposition into two solid solution monolayers, with ca. 90% Se and Te content, respectively.

First principles phase diagram and electronic structure estimation of ZnO1-xSex photoanodes

Terminal solid solutions in the ZnO1−xSex system (0≤x≤0.15,0.95≤x≤1) exhibit extreme bandgap reduction attributable to band anti-crossing (BAC). In this work, we perform a theoretical investigation of alloying in this system (0≤x≤1). The temperature-composition phase diagram of ZnO1−xSex is obtained via first principles and cluster expansion-based Monte–Carlo simulations. For 0≤x≤0.05, a solid solution in the wurtzite structure and for 0.5≤x≤1, a solid solution in the sphalerite structure is obtained. The alloy system exhibits a miscibility gap in the range of 0.05≤x≤0.5. Only the solid solutions are seen to obey bandgap reduction predicted by BAC. The bandgap of the alloys, calculated using the Δ-sol method, shows a bowing behavior as predicted by the BAC model. Difference in the electronegativities of O and Se atoms in the lattice leads to hybridization of O-2p and Se-4p electronic states. Interaction between these electronic states also leads to a split in the valence band edge at the O-rich end and a split in the conduction band edge at the Se-rich end. The effective mass, estimated from the density of states, of holes at the O-rich end and that of electrons at the Se-rich end, increases with alloying. These fundamental insights should help in choosing suitable alloy compositions for optimal photocurrent density when these materials are used as photoanodes.

Critical Influence of Water on the Polymorphism of 1,3-Dimethylurea and Other Heterogeneous Equilibria.

It is shown that the presence of hundreds of ppm of water in 1,3-dimethylurea (DMU) powder led to the large depression of the transition temperature between the two enantiotropically related polymorphic forms of DMU (Form II → Form I) from 58 °C to 25 °C, thus explaining the reported discrepancies on this temperature of transition. Importantly, this case study shows that thermodynamics (through the construction of the DMU-water temperature-composition phase diagram) rather than kinetics is responsible for this significant temperature drop. Furthermore, this work also highlights the existence of a monohydrate of DMU that has never been reported before with a non-congruent fusion at 8 °C. Interestingly, its crystal structure, determined from X-ray powder diffraction data at sub-ambient temperature, consists of a DMU-water hydrogen bonded network totally excluding homo-molecular hydrogen bonds (whereas present in forms I and II of DMU).

Thermodynamics and Ferroelectric Properties of Pb1-xSrxTiO3 Solid Solutions

Pb1-xSrxTiO3 solid solutions have been utilized to compositionally tune the phase transitions and ferroelectric properties and thus are attractive for potential applications in tunable microwave devices and pyroelectric energy harvesters. However, a reliable thermodynamic description of the Pb1-xSrxTiO3 system is currently lacking. Here, we establish a thermodynamic free energy density function for the Pb1-xSrxTiO3 solid solution system taking into account both the polarization and octahedral tilt, and validated it by reproducing the experimentally measured polarization, lattice parameters, and dielectric constant values. Based on the thermodynamic model, we successfully explain the experimentally observed dielectric anomalies by analyzing the interactions between ferroelectric and octahedral tilt order parameters and constructed a comprehensive temperature-composition Pb1-xSrxTiO3 phase diagram which can be used to guide future experimental synthesis and thin film growth. The thermodynamic model developed in this work can be employed not only to predict the ferroelectric and structural states and their properties for compositions that have not yet been synthesized but also used as input to model the formation of mesoscale domain structures using the phase-field method.

Temperature-gradient investigation of phase transitions in ferroelectrics using cooling and heating stage

A cooling and heating stage has been developed to investigate the properties of materials under temperature gradients. We utilized the ferroelectric material BaTiO3 to show the coexistence of cubic and tetragonal crystal structures within a single crystal at the high-temperature and low-temperature sides, respectively, under the temperature gradient around 403 K. Through the Raman mapping and synchrotron X-ray diffraction mapping, we successfully visualized the coexisting crystal structures along with the boundary. Additionally, using Raman mapping, we also visualized the coexistence state of the higher-temperature-tetragonal and lower-temperature-orthorhombic phases. Our developed stage demonstrated its capability as a means to continuously vary the temperature direction in the composition-temperature phase diagram, providing valuable insights into the phase transitions.

First-Principles Investigation of Doping Engineering Towards Mitigating Phase Transformation in LiNiO2

Cobalt-Free Layered LiNiO2 Has Resurfaced to Attract Intensive Research Due to the Scarcity and High Cost of Cobalt. Despite Its High Theoretical Capacity, LiNiO2 Suffers from Poor Cycling Stability, Which Is Mainly Due to Oxygen Loss and Phase Transformation Induced Structural Instability, Especially When Operated at High Voltages. Herein, We Present a Doping Strategy to Mitigate Phase Transformation in Li1−XNiO2 during Cycling from First-Principles Calculations. Temperature-Composition Phase Diagrams of Pristine and Doped Li1−XNiO2 Are Obtained Using a Cluster-Based Monte Carlo Simulation Approach. We Investigate the Effects of Dopant Oxidation States, Sizes and Concentrations on the Dopant Distribution in As-Synthesized LiNi1−YMyO2 As Well As the Phase Transitions during Delithiation. By Comparing Phase Transformations across Different Cathode Chemistries As Well As Li-Dopant and Dopant-Dopant Interactions, We Propose to Introduce High-Valence Dopants with Ionic Radii Similar to That of Ni3+ into LiNiO2 to Stabilize the Cathode Bulk Structure. the Derived Materials Design Principles Not Only Provide the Guidance on Doping Engineering Ultrahigh-Ni, Zero-Co Cathodes, but Also Shed Light on Stabilizing the Bulk Structure of All High Energy-Density Cathodes.

Ionic Conductivity of Lithium Phosphides

We comprehensively study the ionic conductivity in lithium phosphides, promising materials for energy storage applications, by using a combination of first-principles computations and machine learning interatomic potentials. Using the quasiharminic approximation, we calculated convex hulls of the Li-P system at various temperatures and the temperature-composition phase diagram was obtained, delineating the stability regions of each phase. The ionic conductivity of stable (Li3P, LiP, Li3P7, Li3P11, LiP7) and metastable (Li4P3, Li5P4, LiP5) compounds was studied as a function of temperature. In some compounds we found have high ionic conductivity at room temperatures (10−3–10−2 S cm−1). Structures with the lowest ionic conductivity are LiP, Li3P11, and LiP7, in which diffusion is negligible in the whole temperature range 300–500 K. In Li3P, Li3P7, and Li4P3, LiP, there is the 3D diffusion of Li atoms, while in Li5P4 the 2D mechanism prevails, and in LiP5 and LiP7 the 1D mechanism was observed. This study may provide insights for the development of Li-P materials in lithium ion and lithium metal battery applications.

Mitigating the High-Charge Detrimental Phase Transformation in LiNiO2 Using Doping Engineering

Cobalt-free layered LiNiO2 has gained increased interest due to the scarcity and high cost of cobalt. However, LiNiO2 suffers from poor cycling stability, which is mainly due to oxygen loss and structural instability, especially when operating at high voltages. Herein, we present a doping strategy to mitigate the detrimental O3-to-O1 phase transformation in LiNiO2 from first-principles calculations. Temperature–composition phase diagrams of pristine and doped Li1–xNiO2 are obtained using a cluster-expansion and Monte Carlo simulation approach. We investigate the effects of dopant oxidation states, sizes, and concentrations on the dopant distribution in LiNi1–yMyO2 (M = Sb, Ti, Si, Al, and Mg) as well as the phase transitions during delithiation. We find that introducing high-valence dopants with ionic radii similar to that of Ni3+ into LiNiO2 stabilizes the O3-phase cathode bulk structure at high charge. Our results provide a general guidance on using doping engineering to realize Ni-rich, Co-free cathodes for lithium-ion batteries.

Mn(Pt1−xPdx)5P : Isovalent tuning of Mn-sublattice magnetic order

We report the growth and characterization of ${\mathrm{MnPd}}_{5}\mathrm{P}$, a rare-earth-free ferromagnet, with ${T}_{C}\ensuremath{\approx}295\phantom{\rule{4pt}{0ex}}\mathrm{K}$ and planar anisotropy, and conduct a substitutional study with its antiferromagnetic analog ${\mathrm{MnPt}}_{5}\mathrm{P}$. All compounds in the family adopt the layered anti-${\mathrm{CeCoIn}}_{5}$-type structure with the space group $P4/mmm$, and EDS and x-ray diffraction results indicate that ${\mathrm{MnPt}}_{5}\mathrm{P}$ and ${\mathrm{MnPd}}_{5}\mathrm{P}$ form a complete solid solution. Based on measurements of the temperature- and field-dependent magnetization and resistance, we construct a temperature-composition ($T\text{\ensuremath{-}}x$) phase diagram for $\mathrm{Mn}{({\mathrm{Pt}}_{1\ensuremath{-}x}{\mathrm{Pd}}_{x})}_{5}\mathrm{P}$ and demonstrate that the essentially antiferromagnetic order found in ${\mathrm{MnPt}}_{5}\mathrm{P}$ is extraordinarily sensitive to Pd substitution. At low Pd fractions ($x<0.010$), the single antiferromagnetic-like transition in pure ${\mathrm{MnPt}}_{5}\mathrm{P}$ splits into a higher-temperature ferromagnetic transition followed first, upon cooling, by a lower temperature ferromagnetic to antiferromagnetic transition and then by a re-entrant antiferromagnetic to ferromagnetic transition at even lower temperatures. The antiferromagnetic region makes up a bubble phase that persists up to $x\ensuremath{\approx}0.008$--0.009 for $T\ensuremath{\approx}150\phantom{\rule{4pt}{0ex}}\mathrm{K}$, with all samples $0\ensuremath{\le}x<0.008$ recovering their initial ferromagnetic state upon further cooling to base temperature. Once $x>0.010$, $\mathrm{Mn}{({\mathrm{Pt}}_{1\ensuremath{-}x}{\mathrm{Pd}}_{x})}_{5}\mathrm{P}$ undergoes a only single transition into the ferromagnetic phase. The Curie temperature initially increases rapidly with $x$, rising from ${T}_{C}\ensuremath{\approx}197\phantom{\rule{4pt}{0ex}}\mathrm{K}$ at $x$ = 0.013 to a maximum of ${T}_{C}\ensuremath{\approx}312\phantom{\rule{4pt}{0ex}}\mathrm{K}$ for $x\ensuremath{\approx}0.62$, and then falling back to ${T}_{C}\ensuremath{\approx}295\phantom{\rule{4pt}{0ex}}\mathrm{K}$ for pure ${\mathrm{MnPd}}_{5}\mathrm{P}$ $(x=1.00)$. Given that Pt and Pd are isoelectronic, this work raises questions as to the origin of the extreme sensitivity of the magnetic ground state and the nature of the re-entrant ferromagnetism at dilute Pd levels.

Substitution driven ground states of Fe1-xCrxSi: A resistivity study

We report the electrical resistivity of Fe1-xCrxSi with nominal compositions of × = 0.0, 0.005, 0.025, 0.075, 0.1, 0.125, 0.15, 0.2, 0.5, 0.75 and 1. Composition-temperature (x-T) phase diagram is constructed based on the variation of electrical properties with substitution and temperature. The compositions below the critical concentration of metal-to-insulator transition (i.e., xc ∼ 0.02) are noticed to exhibit Kondo behaviour at low temperatures and semiconducting behaviour (due to activated charge carriers) at high temperature. Above xc, a gradual reduction of low temperature insulating phase is compensated by the enhancement of metallic phase. Additionally, the high temperature semiconducting phase is noticed to reduce with increasing x. For the compositions xc ≤ x < 0.5, the low temperature rise of electrical resistivity with the reduction of temperature is attributed to the magnetic correlations aided by localization effects. The two-band (metallic and semiconducting parallel conductive channels) analysis reveals the formation of impurity states and reduction of energy gap. Nevertheless, the compositions × ≥ 0.5 exhibit pseudo-gap behavior. The energy band gap of CrSi is found to be 0.320 ± 0.019 meV with a residual resistivity of 4.773 μΩ-cm.