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Analytically differentiable metrics for phase stability

Here, in this work, a long-established but sparsely documented method of obtaining semi-analytic derivatives of thermodynamic properties with respect to equilibrium conditions is briefly reviewed and rigorously derived. This procedure is then leveraged to construct general forms of derivatives of the residual driving force, a metric for measuring phase stability used in CALPHAD model optimization, with respect to overall system and individual phase compositions. Applied examples – calculating heat capacity in the Al-Fe system, thermodynamic factors in the Nb-V-W system, and residual driving force derivatives in the Ni-Ti system – demonstrate the versatility, accuracy, and extensibility of this method. Using the developed method, residual driving force gradients can be applied directly in CALPHAD model optimizers, as well as in materials design frameworks, to identify regions of phase stability with an efficient, gradient-based approach.

36 MATERIALS SCIENCE↗

First-principles insights on phase stability of titanium interstitial alloys

Titanium can dissolve unusually high concentrations of interstitial elements such as carbon and nitrogen to form a rich variety of compounds with beneficial structural and functional properties. Here, a first-principles statistical mechanics study was performed to predict phase stability in the Ti-C and Ti-N binaries. Density functional theory calculations were combined with the cluster-expansion approach to determine ground-state carbon-vacancy and nitrogen-vacancy orderings over the octahedral sites of hcp and fcc Ti. A large number of vacancy-ordered rocksalt phases were found to be stable at low temperature. Monte Carlo simulations showed that the ordered rocksalts transform to a disordered rocksalt that can tolerate high vacancy concentrations at intermediate to high temperatures. Clear trends in phase stability, rooted in electronic structure, are revealed upon a comparison of the calculated Ti-C and Ti-N phase diagrams with the Ti-O phase diagrams from a previous study [N. S. H. Gunda et al., Phys. Rev. Mater. 2, 033604 (2018)].

36 MATERIALS SCIENCE↗

Microstructure-dependent rate theory model of defect segregation and phase stability in irradiated polycrystalline LiAlO 2

We report gamma lithium aluminate (LiAlO 2 ) is a breeder material for tritium and is one of key components in a tritium-producing burnable absorber rod (TPBAR). Dissolution and precipitation of second phases such as LiAl 5 O 8 and voids are observed in irradiated LiAlO 2 . Such microstructure changes cause the degradation of thermomechanical properties of LiAlO 2 and affect tritium retention and release kinetics, and hence, the TPBAR performance. In this work, a microstructure-dependent model of radiation-induced segregation (RIS) has been developed for investigating the accumulation of species and phase stability in polycrystalline LiAlO 2 structures under irradiation. Three sublattices (i.e. [Li, Al, V] I [O, V o ] II [Li i , Al i , O i , V i ] III ), and concentrations of six diffusive species (i.e. Li; vacancy of Li or Al at [Li, Al, V] I sublattice, O vacancy at [O, V o ] II sublattice, and Li, Al and O interstitials at [Li i , Al i , O i , V i ] III interstitial sublattices; are used to describe spatial and temporal distributions of defects and chemistry. Microstructure-dependent thermodynamic and kinetic properties including the generation, reaction, and chemical potentials of defects and defect mobility are taken into account in the model. The parametric studies demonstrated the capability of the developed RIS model to assess the effect of thermodynamic and kinetic properties of defects on the segregation and depletion of species in polycrystalline structures and to explain the phase stability observed in irradiated LiAlO 2 samples. The developed RIS model will be extended to study the precipitation of LiAl 5 O 8 and voids and tritium retention by integrating the phase-field method.

36 MATERIALS SCIENCE↗

Ka-Band Atmospheric Phase Stability Measurements in Goldstone, CA; White Sands, NM; and Guam

As spacecraft communication links are driven to higher frequencies (e.g. Ka-band) both by spectrum congestion and the appeal of higher data rates, the propagation phenomena at these frequencies must be well characterized for effective system design. In particular, the phase stability of a site at a given frequency will govern whether or not the site is a practical location for an antenna array, particularly if uplink capabilities are desired. Propagation studies to characterize such phenomena must be done on a site-by-site basis due to the wide variety of climates and weather conditions at each ground terminal. Accordingly, in order to statistically characterize the atmospheric effects on Ka-Band links, site test interferometers (STIs) have been deployed at three of NASA's operational sites to directly measure each site's tropospheric phase stability. Using three years of results from these experiments, this paper will statistically characterize the simultaneous atmospheric phase noise measurements recorded by the STIs deployed at the following ground station sites: the Goldstone Deep Space Communications Complex near Barstow, CA; the White Sands Ground Terminal near Las Cruces, NM; and the Guam Remote Ground Terminal on the island of Guam.

Interferometry↗

Role of spin-orbit coupling on crystal-field splitting and phase-stability of rare-earth based layered intermetallic

Layered and incommensurate heterostructures have attracted much attention for the occurrence of superconductivity and charge density waves with the possibility of intercalating foreign atoms. However, lanthanide-based heterostructures where (Eu x Sm 1-x )S and TaS 2 are alternatively stacked have been scarcely investigated. In this work, we performed phase stability, bonding behavior and electronic-structure analysis of (Eu x Sm 1-x )TaS 3 using first-principles density-functional theory methods. Our phase stability analysis suggests 50 at.% solubility of Eu in (Eu x Sm 1-x )TaS 3 compared to Eu solubility in all proportions in cubic SmS. The instability of Eu beyond 50 at.% in (Eu x Sm 1-x )TaS 3 was attributed to higher density of Eu-4f states at the Fermi-level. Based on band position calculated from spin-orbit coupling effect, we constructed a qualitative schematic of possible crystal-field analysis. The local change in bond-length and bond-angle around Eu-S in (Eu x Sm 1-x )TaS 3 correlate well with our crystal-field analysis. We believe that quantum mechanical insights provided in this work will be useful to understand other complex heterostructures.

36 MATERIALS SCIENCE↗

Phase stability and tensorial thermal expansion properties of single to high-entropy rare-earth disilicates

Temperature limitations in nickel-base superalloys have resulted in the emergence of SiC-based ceramic matrix composites as a viable replacement for gas turbine components in aviation applications. Higher operating temperatures allow for reduced fuel consumption but present a materials design challenge related to environmental degradation. Rare-earth disilicates (RE 2 Si 2 O 7 ) have been identified as coatings that can function as environmental barriers and minimize hot component degradation. In this work, single- and multiple-component rare-earth disilicate powders were synthesized via a sol-gel method with compositions selected to exist in the monoclinic C 2/m phase (β phase). Phase stability in multiple cation compositions was shown to follow a rule of mixtures and the C 2/m phase could be realized for compositions that contained up to 25% dysprosium, which typically only exists in a triclinic, P $\bar1$, phase. All compositions exhibited phase stability from room temperature to 1200°C as assessed by X-ray diffraction. The thermal expansion tensors for each composition were determined from high-temperature synchrotron X-ray diffraction and accompanying Rietveld refinements. It was observed that ytterbium-containing compositions had larger changes in the α 31 shear component with increasing temperature that led to a rotation of the principal axes. Principal axes rotation of up to 47° were observed for ytterbium disilicate. The results suggest that microstructure design and crystallographic texture may be essential future avenues of investigation to ensure thermo-mechanical robustness of rare-earth disilicate environmental barrier coatings.

36 MATERIALS SCIENCE↗

Exploring phase stability, electronic and mechanical properties of Ce–Pb intermetallic compounds using first-principles calculations

The phase stability, electronic and mechanical properties of Ce–Pb intermetallics have been investigated by using first-principles calculations. Five stable and four metastable phases of Ce–Pb intermetallics were verified. Among them, CePb{sub 2} has been confirmed as HfGa{sub 2}-type structure. For Ce{sub 5}Pb{sub 3}, the high pressure phase transformation from D8{sub m} to D8{sub 8} with trivalent Ce has been predicted to occur at P=1.2 GPa and a high temperature phase transformation has been predicted from D8{sub m} to D8{sub 8} with tetravalent Ce at 531.5 K. The calculated lattice constants of the five stable phases are in good agreement with experimental values. The electronic density of states, charge density and electron localization function of Ce{sub 3}Pb have been calculated, which indicated that the Ce and Pb show ionic behavior. The polycrystalline bulk modulus, shear modulus, Young's modulus, and Poisson's ratio are also estimated from the calculated single crystalline elastic constants. All of the calculated elastic constants satisfy mechanical stability criteria. The microhardness and mechanical anisotropy are predicted. The anisotropic nature of the Ce–Pb intermetallic compounds are demonstrated by the three-dimensional orientation dependent surfaces of Young's moduli and linear compressibility are also demonstrated. The longitudinal, transverse and average sound velocities and the Debye temperatures are also obtained in this work. The Ce{sub 3}Pb has the largest Debye temperature of 192.6 K, which means the Ce{sub 3}Pb has a highest melting point and high thermal conductivity than other compounds. - Graphical abstract: The convex hull plots of the enthalpies of formation for Ce–Pb binary systems calculated at 0 K. - Highlights: • The five stable and four metastable phases in the Ce–Pb binary system were predicted. • The crystal structure of CePb{sub 2} has been confirmed as HfGa{sub 2}-type.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Surface effects and phase stability in metal oxides nanoparticles under visible irradiation

The light induced phase transformation between stable phases of metal oxides nanoparticles is analyzed. The surrounding atmosphere as well as the defect density at the surface play a fundamental role. It has been found that in oxygen poor chamber atmosphere the phase transformation is favored, while the phase transition cannot be achieved if the defects at the surface are properly passivated. The phase transition is activated by intragap irradiation, able to activate the F- center at the surface connected to oxygen vacancies, and promoting the activation of the surface and the nucleation of neighboring crystallites. The phase transition was studied in Titanium oxide (TiO{sub 2}) and in Iron oxide (Fe{sub 2}O{sub 3}): Maghemite is subjected to a phase transformation to α−Fe{sub 2}O{sub 3} (hematite), Anatase nanoparticles converts to Rutile. The general mechanism of the phase transition and, more in general, the possibility to optically control the surface activity of metal oxides is discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Calculation of Defect Concentrations and Phase Stability in Cu$_2$ ZnSnS$_4$ and Cu$_2$ ZnSnSe$_4$ From Stoichiometry

The application of the quarternary compounds Cu$_2$ ZnSnS$_4$(CZTS) and Cu$_2$ ZnSnSe$_4$(CZTSe) as efficient solar cell absorber materials is dependent on the complex behavior of the large variety of intrinsic lattice defects. In this paper, a canonical approach is presented and applied to calculate the defect concentrations and the position of the Fermi level for CZTS and CZTSe at a given temperature as a function of stoichiometry (or a combination of stoichiometry and elemental chemical potentials). With the defect concentrations, the chemical potentials (which are generally not experimentally accessible) can be calculated, allowing the relation of sample composition to the phase stability of CZTS and CZTSe with respect to secondary compounds. Based on the model, it is shown that the stable CZTS with off-stoichiometric composition requires both Cu-poor and Zn-rich conditions, while the compositional space corresponding to stable CZTSe is wider than for CZTS. Additionally, the determination of the Fermi level directly relates the desired p-type conductivity to phase stability in both materials. The method used in this study is applicable to a wide range of complex materials.

14 SOLAR ENERGY↗

An S-band high gain relativistic klystron amplifier with high phase stability

For the purpose of coherent high power microwave combining, an S-band high gain relativistic klystron amplifier with high phase stability is presented and studied. By the aid of 3D particle-in-cell code and circuit simulation software, the mechanism of parasitic oscillation in the device is investigated. And the RF lossy material is adopted in the simulation and experiment to suppress the oscillation. The experimental results show that with an input RF power of 10 kW, a microwave pulse with power of 1.8 GW is generated with a gain of 52.6 dB. And the relative phase difference fluctuation between output microwave and input RF signal is less than ±10° in 90 ns.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

High temperature phase stability in Li{sub 0.12}Na{sub 0.88}NbO{sub 3}: A combined powder X-ray and neutron diffraction study

The phase stabilities of ecofriendly piezoelectric material of lithium doped sodium niobate for composition Li{sub 0.12}Na{sub 0.88}NbO{sub 3} (LNN12) have been investigated by a combination of powder X-ray and neutron diffraction techniques in the temperature range of 300–1100 K. We observed interesting changes with appearance or disappearance of the super-lattice reflections in the powder diffraction patterns. Unambiguous experimental evidence is shown for coexistence of paraelectric and ferroelectric orthorhombic phases in the temperature range of 525 K to 675 K. We identified the correct crystal structure of LNN12 with temperature and correlated it with observed anomaly in the physical properties. Identification of crystal structure also helps in the mode assignments in Raman and infrared spectroscopies. We argued that application of chemical pressure as a result of Li substitution in NaNbO{sub 3} matrix favors the freezing of zone centre phonons in contrast to the freezing of zone boundary phonons in pure NaNbO{sub 3} with the variation of temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Chemical bond and phase stability of Ga-doped Sm2Fe17Cx magnet

Sm2Fe17C3 phase (2:17) is metastable and exhibits excellent intrinsic hard magnetic properties. Doping elements such as Ga facilitate the formation of a single-phase 2:17 structure in arc-melted Sm2Fe17Cx alloys, which opens a promising route for fabricating fully dense bulk Sm2Fe17Cx magnets via high-temperature techniques such as melting and sintering. First-principles electronic structure calculation indicates that Ga prefers to partially replace Fe at the 9d and 18h crystallographic sites in Sm2Fe17C3 and Sm2Fe17, respectively. This difference in site preference is attributed to the distinct chemical environments surrounding the Fe atoms in the two compounds. Ga substitution favors the Sm–Ga bonding formation while avoiding Ga–C interactions. Doped Ga atoms result in more negative formation energy in Sm2(Fe, Ga)17C3, indicating improved structural stability. Crystal Orbital Hamilton Population analysis reveals that carbon insertion weakens the bonding of Sm-Fe (18h) and Sm-Fe (18f) in Sm2Fe17C3. Ga doping facilitates electron redistribution across chemical bonds, thereby reinforcing Fe(18h)–Sm and Fe(18f)–Sm interactions and stabilizing the carbon-centered octahedral local structure. This synergistic effect contributes significantly to the observed enhancement in phase stability of Sm2(Fe, Ga)17Cx. These findings suggest that chemical bond engineering through the selective doping of Ga can enhance phase stability and facilitate the synthesis of Sm2Fe17C3, providing a viable strategy for developing advanced magnets.

Liu, Xubo [Critical Materials Innovation Hub, Divi↗

The effects of carbon on the phase stability and mechanical properties of heat-treated FeNiMnCrAl high entropy alloys

This work systematically investigates the effect of carbon on the phase stability and room- temperature tensile performance of an annealed Fe 40.4 Ni 11.3 Mn 34.8 Al 7.5 Cr 6 (at%) high entropy alloy without (HEA) and with 1.1% carbon (CHEA). Four annealing conditions were investigated: 773 K for 13 d and 42 d, 973 K for 20 d, and 1073 K and 1423 K for 24 h. The resulting microstructures were analyzed using a combination of scanning electron microscopy (SEM), transmission electron microscopy (TEM), energy dispersive spectroscopy (EDS), and atom probe tomography (APT). Vickers hardness testing and room- temperature tensile testing were used to determine the mechanical properties of the annealed HEA and the CHEA. APT composition profiles revealed fine Ni,Mn,Al-enriched matrix precipitates in the CHEA annealed at 773 K for 13 d. After ageing at 773 K for 42 d, colonies of (Ni,Fe) 2 MnAl- enriched Heusler phase lamellae were observed at the grain boundaries (GBs) and in the matrix for the HEA, while GB lamellar colonies of Mn,Cr-enriched M 23 C 6 carbides were observed for the CHEA. Due to the presence of the GB carbides, the resulting room-temperature elongation to fracture for the CHEA annealed at 773 K for 42 d was ~1% compared to ~11% for the HEA given the same anneal. At higher annealing temperatures, the microstructure contains Ni,Al-rich and Mn,Cr,C-rich precipitates that alternate along the GBs and appear to be associated with each other in the matrix. Electron diffraction analysis indicates the aforementioned Ni,Al-precipitates and Mn,Cr-carbides have b.c.c. and f.c.c. crystal structures, respectively. Once again, a low elongation to fracture (2%) was seen for the carbon-containing material compared to its un-doped counterpart (23%) which solely contained Ni,Al-rich b.c.c. precipitates.

36 MATERIALS SCIENCE↗

Martensitic transformation and phase stability of In-doped Ni-Mn-Sn shape memory alloys from first-principles calculations

The effect of the alloying element Indium (In) on the martensitic transition, magnetic properties, and phase stabilities of Ni{sub 8}Mn{sub 6}Sn{sub 2−x}In{sub x} shape memory alloys has been investigated using the first-principles pseudopotential plane-wave method based on density functional theory. The energy difference between the austenitic and martensitic phases was found to increase with increasing In content, which implies an enhancement of the martensitic phase transition temperature (T{sub M}). Moreover, the formation energy results indicate that In-doping increases the relative stability of Ni{sub 8}Mn{sub 6}Sn{sub 2−x}In{sub x} both in austenite and martensite. This results from a reduction in density of states near the Fermi level regions caused by Ni-3d–In-5p hybridization when Sn is replaced by In. The equilibrium equation of state results show that the alloys Ni{sub 8}Mn{sub 6}Sn{sub 2−x}In{sub x} exhibit an energetically degenerated effect for an In content of x = ∼1.5. This implies the coexistence of antiparallel and parallel configurations in the austenite.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

First principles studies on the impact of point defects on the phase stability of (Al{sub x}Cr{sub 1−x}){sub 2}O{sub 3} solid solutions

Density Functional Theory applying the generalised gradient approximation is used to study the phase stability of (Al{sub x}Cr{sub 1−x}){sub 2}O{sub 3} solid solutions in the context of physical vapour deposition (PVD). Our results show that the energy of formation for the hexagonal α phase is lower than for the metastable cubic γ and B1-like phases–independent of the Al content x. Even though this suggests higher stability of the α phase, its synthesis by physical vapour deposition is difficult for temperatures below 800 °C. Aluminium oxide and Al-rich oxides typically exhibit a multi-phased, cubic-dominated structure. Using a model system of (Al{sub 0.69}Cr{sub 0.31}){sub 2}O{sub 3} which experimentally yields larger fractions of the desired hexagonal α phase, we show that point defects strongly influence the energetic relationships. Since defects and in particular point defects, are unavoidably present in PVD coatings, they are important factors and can strongly influence the stability regions. We explicitly show that defects with low formation energies (e.g. metal Frenkel pairs) are strongly preferred in the cubic phases, hence a reasonable factor contributing to the observed thermodynamically anomalous phase composition.

36 MATERIALS SCIENCE↗

Phase stability, ordering tendencies, and magnetism in single-phase fcc Au-Fe nanoalloys

Bulk Au-Fe alloys separate into Au-based fcc and Fe-based bcc phases, but L1 0 and L1 2 orderings were reported in single-phase Au-Fe nanoparticles. Motivated by these observations, we study the structural and ordering energetics in this alloy by combining density functional theory (DFT) calculations with effective Hamiltonian techniques: a cluster expansion with structural filters, and the configuration-dependent lattice deformation model. The phase separation tendency in Au-Fe persists even if the fcc-bcc decomposition is suppressed. The relative stability of disordered bcc and fcc phases observed in nanoparticles is reproduced, but the fully ordered L1 0 AuFe, L1 2 Au 3 Fe, and L1 2 AuFe 3 structures are unstable in DFT. But, a tendency to form concentration waves at the corresponding [001] ordering vector is revealed in nearly-random alloys in a certain range of concentrations. Furthermore, this incipient ordering requires enrichment by Fe relative to the equiatomic composition, which may occur in the core of a nanoparticle due to the segregation of Au to the surface. Effects of magnetism on the chemical ordering are also discussed.

36 MATERIALS SCIENCE↗

Phase stability of injection-locked beam of semiconductor lasers

An experiment on the phase stability of an injection locked beam was done by using AlGaAs semiconductor lasers. The coherence of two beams from master and slave lasers was measured by interference between the beams in the Twymann-Green interferometer. The phase change of the output beam of the slave laser as a function of the driving current was measured in a Mach-Zehnder interferometer consisting of the master and slave lasers, and a value of 2.5 radians/mA was obtained.

Kwon, Jin Hyuk↗