Predicting ternary phase diagrams and quaternary excess free-energy using binary data
Ternary phase diagrams and quaternary excess free energy prediction using binary data, applied to Pb-Sn-Zn, Ag-Pd-Cu and Pb-Sn-Cd-Bi systems
Olson, N. J.↗
SEARCH · Engineering Papers
Results for “phase diagram”
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Magnetic Phase Diagram of 2D Magnet Fe 5– x GeTe 2 Revealed by Cryogenic Lorentz 4D-STEM
A two-dimensional van der Waals ferromagnet Fe 5–x GeTe 2 (F5GT) exhibits room-temperature magnetic transition and magnetic anisotropy. Studies have identified diverse magnetic states, including stripe domains, skyrmionic type-I and topologically trivial type-II bubbles, depending on the magnetic and thermal history. Yet, the underlying micromagnetic energetics driving these states remains unclear. Here, we establish the magnetic phase diagram of bulk F5GT using cryogenic Lorentz four-dimensional scanning transmission electron microscopy. We reveal that stripe domains spontaneously form upon zero-field cooling, while metastable magnetic bubbles are stabilized by external fields. Transitions from type-I to type-II bubbles are driven by an oblique external field. Micromagnetic simulations confirm that these transitions arise from the interplay of uniaxial anisotropy, dipolar interactions, and external fields, without requiring significant Dzyaloshinskii–Moriya Interaction (DMI). In conclusion, these findings clarify the micromagnetic origin of spin textures of F5GT and establish it as a tunable platform for nanoscale topological magnetism.
2D Magnets↗
Metrology for femtosecond pulsed x-ray heating in diamond anvil cell experiments at the European XFEL: Revisiting the iron phase diagram up to 150 GPa
The development of pulsed intense x-ray sources, such as free electron laser, offers new avenues for high pressure experiments. Here, we study the feasibility and metrology of x-ray heating in diamond anvil cells at the European x-ray free electron laser. This method enables one to volumetrically heat the sample while inhibiting chemical migration and probing the crystallographic structure of the sample throughout the heating with a high repetition rate. We focus our study on iron, whose phase diagram is well established up to 100 GPa, to explore the possibilities and limitations of this technique. We volumetrically heat iron samples at starting pressures ranging from 10 to 138 GPa, using the x-ray beam pulsed at 4.5 MHz in a serial pump-and-probe experimental design. Experimental challenges arise from temperature gradients within the sample, changes in temperature at the 100 ns timescale, the difficulty of direct temperature estimates, the effect of thermal pressure, and the presence of metastable crystallites due to rapid cycles of heating and cooling. Hence, we develop a multi-crystal-like data processing method that allows us to account for sample heterogeneity in probed conditions. We then calibrate our measurements using known physical properties of iron under pressure. Thermal pressure in our experiments increases from 4% of the isochoric prediction at 10 GPa to 23% at 138 GPa, and we show that our data are in agreement with most previous observations of iron in this pressure range. The method can now be implemented at higher pressures and temperatures and on materials with unknown phase diagrams.
Materials science↗
Superconductivity and phase diagrams of CaK(Fe 1- x Mn x ) 4 As 4 single crystals
In order to study the effects of Mn substitution on the superconducting and magnetic ground state of CaKFe 4 As 4 (T c = 35 K), members of the CaK (Fe 1–x Mn x ) 4 As 4 series have been synthesized by high-temperature solution growth in single-crystalline form and characterized by elemental analysis, thermodynamic, and transport measurements. These measurements show that the superconducting transition temperature decreases monotonically and is finally suppressed below 1.8 K as x is increased from 0 to 0.036. For x values greater than 0.016, signatures of a magnetic transition can be detected in both thermodynamic and transport measurements in which kinklike features allow for the determination of the transition temperature T* that increases as Mn substitution increases. Here, a temperature-composition (T–x) phase diagram is constructed, revealing a half-dome of superconductivity with the magnetic transition temperature T* appearing near 26 K for x ~ 0.017 and rising slowly up to 33 K for x ~ 0.036. In addition to the creation of the T–x phase diagram for CaK(Fe 1–x Mn x ) 4 As 4 , specific-heat data are used to track the jump in specific heat at T c ; the CaK(Fe 1–x Mn x ) 4 As 4 data do not follow the scaling of ΔC p with $T$$^{3}_{c}$ as many of the other Fe-based superconducting systems do. These data suggest that, as magnetic pair breaking is present, the jump in C p for a given T c is reduced. Elastoresistivity coefficients 2m 66 and m 11 – m 12 as a function of temperature are also measured. 2m 66 and m 11 – m 12 are qualitatively similar to CaK(Fe 1–x Ni x ) 4 As 4 . This may indicate that the magnetic order in Mn-substituted system may be still the same as CaK(Fe 1–x Mn x ) 4 As 4 . Superconductivity of CaK(Fe 1–x Mn x ) 4 As 4 is also studied as a function of magnetic field. A clear change in H' c2 (T)/T c , where H' c2 (T) is dH' c2 (T)/dT, at x ~ 0.015 is observed and probably is related to change of the Fermi surface due to magnetic order. Coherence lengths and the London penetration depths are also calculated based on H c1 and H c2 data. Coherence lengths as the function of x also show the changes near x = 0.015, again consistent with Fermi-surface changes associated with the magnetic ordering seen for higher-x values.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Diverse magnetic phase diagram and anomalous Hall effect in antiferromagnetic LuMn 6 Sn 6
The interactions between conduction electrons and magnetism can significantly enhance the Hall signal, a phenomenon known as the anomalous Hall effect (AHE). While the AHE is generally not expected in antiferromagnets, a large AHE is observed in certain antiferromagnets with noncollinear spin textures and nonvanishing Berry curvature. In this work, we present a rich temperature and magnetic phase diagram with eight distinct magnetic phases for the antiferromagnetic kagome compound LuMn 6 Sn 6 . The Hall effect analysis in LuMn 6 Sn 6 reveals both intriguing physical phenomena and methodological challenges. In the coplanar canted antiferromagnetic phase, we observe an AHE, which likely originates from the intrinsic effects. At low temperatures, upon entering the ferromagnetic phase, the AHE sharply increases and exceeds the conventional limits expected from intrinsic mechanisms. We also demonstrate the limitations of standard experimental methods in extracting the topological contribution to the Hall effect data. In particular, we show that accounting for magnetoresistance anisotropy helps reduce spurious contribution that can mimic topological Hall signals, although it does not fully resolve it. Furthermore, these shortcomings in current approaches in partitioning the Hall response necessitate new tools to interpret transport results in complex magnetic materials such as LuMn 6 Sn 6 .
Anomalous Hall effect↗
Out-of-plane magnetic phase diagram of the Kitaev quantum magnet Na 2 Co 2 TeO 6
We have investigated the magnetic properties and mapped out the phase diagram of the honeycomb magnet Na 2 Co 2 TeO 6 with Co 3d 7 in out-of-plane magnetic fields. This material has previously been proposed to show nearest-neighbor Kitaev interactions between Co spins and maybe even Kitaev quantum spin liquid behavior in high fields. At 0.01 T, we observe a thermal phase transition at T N = 27K, transitioning from a paramagnetic state to a canonical ferrimagnetic state. Upon increasing the magnetic field, a spin-floplike phase transition occurred before saturation of J = 1/2 between 10 K and T N . Below 10 K, a peak-dip-peak structure emerges between 10 and 17 T in the magnetic susceptibility (dM/dH) before the magnetic saturation, reminiscent of magnetization plateau behavior. The measurement of the magnetocaloric effect also shows dip-peak-dip behavior in this field range. Our data can be explained by an XXZ model with a single ion anisotropy and possibly small Kitaev and Γ exchange interactions. Finally, we also determined the magnetization saturation field that helps constrain the energy scale of the exchange interactions.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
$A$-type antiferromagnetic order and magnetic phase diagram of the trigonal Eu spin-$\frac{7}{2}$ triangular-lattice compound $\mathrm{EuSn_2As_2}$
The trigonal compound EuSn 2 As 2 was recently discovered to host Dirac surface states within the bulk band gap and orders antiferromagnetically below the N´eel temperature T N = 23.5(2) K from neutron-diffraction measurements. Here the magnetic ground state of single-crystal EuSn 2 As 2 and the evolution of its properties versus temperature T and applied magnetic field H are reported. Included are the zero-field single-crystal neutron diffraction measurements versus T, magnetization M(H, T), magnetic susceptibility χ(H, T) = M(H,T)/H, heat capacity C p (H, T), and electrical resistivity ρ(H, T) measurements. The neutron-diffraction and χ(T) measurements both indicate a collinear A-type antiferromagnetic (AFM) structure below T N , where the Eu 2+ spins S = 7/2 in a triangular ab-plane layer (hexagonal unit cell) are aligned ferromagnetically in the ab plane whereas the spins in adjacent Eu planes along the c axis are aligned antiferromagnetically. The χ(H ab , T) and χ(Hc, T) data together indicate a smooth crossover between the collinear AFM alignment and an unknown magnetic structure at H ≈ 0.12 T. Dynamic spin fluctuations up to 60 K are evident in the χ(T), Cp(T) and ρ(H, T) measurements, a temperature that is more than twice T N . The ρ(H, T) is consistent with a low-carrier-density metal with strong magnetic scattering and does not reflect a contribution of the topological state of the material as reported earlier by ARPES measurements. This observation is consistent with previous ones for other topological insulators where the chemical potential is above the Dirac point so that ARPES readily detects the surface states, whereas resistivity measurements do not. Finally, the magnetic phase diagrams for both H ∥ c and H ∥ ab in the H-T plane are constructed from the T N (H), χ(H, T), Cp(H, T), and ρ(H, T) data.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Thermochemistry of Cesium-oxygen Solutions and Their Gaseous Atmospheres, Estimated from a Phase Diagram
Thermochemistry of cesium-oxygen solutions and their gaseous atmospheres estimated from phase diagram
Tower, L. K.↗
Ubiquity of amplitude-modulated magnetic ordering in the H - T phase diagram of the frustrated non-Fermi-liquid YbAgGe
YbAgGe contains a magnetic geometrically frustrated kagome-like lattice that also features significant local single-ion anisotropy. The electronic state is established by hybridization of 4f and conduction electrons leading to heavy electronic masses. The competition between these various interactions leads to nontrivial behavior under external magnetic field, including a sequence of magnetic phase transitions, non-Fermi-liquid states, and possibly a quantum critical point. We present a series of neutron diffraction experiments performed in the mK temperature range and under magnetic fields up to 8 T in the hexagonal plane, revealing the microscopic nature of the first four subsequent magnetic states of this phase diagram. The magnetic phases are associated with the propagation vectors K 1 =($\frac{1}{3}$ 0 $\frac{1}{3}$) for H < 2 T, K 2 = (0 0 0.32) for 2 T < H < 3 T, K 1 = ($\frac{1}{3}$ 0 $\frac{1}{3}$) for 3 T < H < 4.5 T and k 3 = (0.195 0.195 0.38) for 4.5 T < H < 7 T. Our structural refinements reveal a strong modulation of the magnetic moment amplitude in all phases. We observe that the ordered moments of the three magnetically different Yb sites become increasingly different in field, which complies with the principle local anisotropy directions relative to the field direction. While the ordered moments are aligned predominantly in the hexagonal plane, we also find a significant out-of-plane component and a ferromagnetic contribution above 2 T. Here we discuss possible scenarios that may evolve around the phase boundary at 4.5 T, which is associated with putative quantum criticality as identified by various bulk probes. We propose further steps that are required to better understand the microscopic interactions in this material.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Magnetic field-temperature phase diagram of the spin-$\frac{1}{2}$ triangular lattice antiferromagnet KYbSe 2
A quantum spin liquid (QSL) is a state of matter characterized by fractionalized quasiparticle excitations, quantum entanglement, and a lack of long-range magnetic order. However, QSLs have evaded definitive experimental observation. Several Yb 3+ -based triangular lattice antiferromagnets with effective 𝑆 = $\frac{1}{2}$ have been suggested to stabilize the QSL state as the ground state. Here, in this work, we build a comprehensive magnetic temperature phase diagram of a high-quality single crystalline KYbSe 2 via heat capacity and magnetocaloric effect down to 30 mK with magnetic field applied along the 𝑎 axis. At zero magnetic field, we observe the magnetic long-range order at 𝑇 N =0.29 K entering 120 degrees ordered state in heat capacity, consistent with neutron scattering studies. Analysis of the low-temperature (𝑇) specific heat (𝐶) at zero magnetic field indicates linear 𝑇 dependence of 𝐶/𝑇 and a broad hump of 𝐶/𝑇 in the proximate QSL region above 𝑇 N . By applying magnetic field, we observe the up-up-down phase with 1/3 magnetization plateau and oblique phases, in addition to two new phases. These observations strongly indicate that while KYbSe 2 closely exhibits characteristics resembling an ideal triangular lattice, deviations may exist, such as the effect of the next-nearest-neighbor exchange interaction, calling for careful consideration for spin Hamiltonian modeling. Further investigations into tuning parameters, such as chemical pressure, could potentially induce an intriguing QSL phase in the material.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Characterization of the high-pressure and high-temperature phase diagram and equation of state of chromium
The high-pressure and high-temperature phase diagram of chromium has been investigated both experimentally (in situ), using a laser-heated diamond-anvil cell technique coupled with synchrotron powder X-ray diffraction, and theoretically, using ab initio density-functional theory simulations. In the pressure–temperature range covered experimentally (up to 90 GPa and 4500 K, respectively) only the solid body-centred-cubic and liquid phases of chromium have been observed. Experiments and computer calculations give melting curves in agreement with each other that can both be described by the Simon–Glatzel equation $T_{m}(P) = 2136K (1 + P/25.9)^{0.41}$ In addition, a quasi-hydrostatic equation of state at ambient temperature has been experimentally characterized up to 131 GPa and compared with the present simulations. Both methods give very similar third-order Birch–Murnaghan equations of state with bulk moduli of 182–185 GPa and respective pressure derivatives of 4.74–5.15. According to the present calculations, the obtained melting curve and equation of state are valid up to at least 815 GPa, at which pressure the melting temperature is 9310 K. Finally, from the obtained results, it was possible to determine a thermal equation of state of chromium valid up to 65 GPa and 2100 K.
36 MATERIALS SCIENCE↗
Phase Diagram of a Deep Potential Water Model
Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. Here, the fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII" and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Phase diagram and electrical behavior of silicon-rich iridium silicide compounds
The iridium-silicon phase diagram on the silicon-rich side was investigated by means of X-ray powder diffraction, density, differential thermal analysis, metalography, microprobe analysis, and electrical resistivity. Attempts were made to prepare eight previously reported silicon-rich iridium silicide compounds by arc melting and Bridgman-like growth. However, microprobe analysis identified only four distinct compositions: IrSi, Ir3Si4, Ir3Si5 and IrSi sub about 3. The existence of Ir4Si5 could not be confirmed in this study, even though the crystal structure has been previously reported. Differential thermal analysis (DTA) in conjunction with X-ray powder diffraction confirm polymorphism in IrSi sub about 3, determined to have orthorhombic and monoclinic unit cells in the high and low temperature forms. A eutectic composition alloy of 83 +/- 1 atomic percent silicon was observed between IrSi sub about 3 and silicon. Ir3Si4 exhibits distinct metallic behavior while Ir3Si5 is semiconducting. Both and IrSi and IrSi sub about 3 exhibit nearly temperature independent electrical resistivities on the order of 5-10 x 10 exp -6 ohms-m.
Allevato, C. E.↗
Phase diagram of twisted bilayer graphene at filling factor $v = ±3$
Here, we study the correlated insulating phases of twisted bilayer graphene (TBG) in the absence of lattice strain at integer filling $v = ±3$. Using the self-consistent Hartree-Fock method on a particle-hole symmetric model and allowing translation symmetry breaking terms, we obtain the phase diagram with respect to the ratio of AA interlayer hopping (w 0 ) and AB interlayer hopping (w 1 ). When the interlayer hopping ratio is close to the chiral limit (w 0 /w 1 ≲ 0.5), a quantum anomalous Hall state with Chern number v c = ±1 can be observed consistent with previous studies. Around the realistic value w 0 /w 1 ≈ 0.8, we find a spin and valley polarized, translation symmetry breaking, state with C 2z T symmetry, a charge gap and a doubling of the moiré unit cell, dubbed theC 2z T stripe phase. The real-space total charge distribution of this C 2z T stripe phase in the flat band limit does not have modulation between different moiré unit cells, although the charge density in each layer is modulated, and the translation symmetry is strongly broken. Other symmetries, including C 2z , C 2x , particle-hole symmetry P, and the topology of the C 2z T stripe phase, are also discussed in detail. We observed braiding and annihilation of the Dirac nodes by continuously turning on the order parameter to its fully self-consistent value, and provide a detailed explanation of the mechanism for the charge gap opening despite preserving C 2z T and valley U(1) symmetries. In the transition region between the quantum anomalous Hall phase and the C 2z T stripe phase, we find an additional competing state with comparable energy corresponding to a phase with a tripling of the moiré unit cell.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Surface phase diagrams from nested sampling
From nested sampling, we compute the partition function and, from that, the phase diagram of gas adsorbates, including their anharmonic and configurational degrees of freedom, on flat and stepped surfaces of the Lennard-Jones solid.
Chemistry↗
Determination of the phase diagram for carbon tetrabromide and hexachloroethane
Differential scanning calorimetry is used to determine the binary eutectic phase diagram of the CBr4/C2Cl6 system and measure the enthalpies of fusion of various compositions. The eutectic composition and temperature are found to be 8.4 + or - 0.1 weight percent C2Cl67 and 83 + or - 0.1 C, respectively. A micrograph showing the coarse lamellar structure at the interface is provided.
Kaukler, W. F.↗
Field angle dependent vortex lattice phase diagram in MgB 2
Using small-angle neutron scattering we have studied the superconducting vortex lattice (VL) phase diagram in MgB 2 as the applied magnetic field is rotated away from the c axis and towards the basal plane. The field rotation gradually suppresses the intermediate VL phase which exists between end states aligned with two high-symmetry directions in the hexagonal basal plane for H || c. Above a critical angle, the intermediate state disappears, and the previously continuous transition becomes discontinuous. Finally, the evolution towards the discontinuous transition can be parametrized by a vanishing twelvefold anisotropy term in the VL free energy.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Chemical control of polarization in thin strained films of a multiaxial ferroelectric: Phase diagrams and polarization rotation
The emergent behaviors in thin films of a multiaxial ferroelectric (FE) due to electrochemical coupling between the rotating polarization and surface ions are explored within the framework of the 2–4 Landau-Ginzburg-Devonshire (LGD) thermodynamic potential combined with the Stephenson-Highland (SH) approach. The combined LGD-SH approach allows us to describe the electrochemical switching and rotation of a polarization vector in a multiaxial ferroelectric film covered by surface ions with a charge density defined by the oxygen pressure. In this work, we calculate phase diagrams, analyze the dependence of polarization components on the applied voltage, and discuss the peculiarities of quasistatic ferroelectric, dielectric, and piezoelectric hysteresis loops in thin strained multiaxial ferroelectric films. The nonlinear surface screening by oxygen ions makes the diagrams very different from the known diagrams of, e.g., strained BaTiO 3 films. Quite unexpectedly, we predict the appearance of ferroelectric reentrant phases. The obtained results point to the possibility to control the appearance and features of ferroelectric, dielectric, and piezoelectric hysteresis in multiaxial FE films covered with surface ions by varying their concentration via the partial oxygen pressure. The LGD-SH description of a multiaxial FE film can be further implemented within the Bayesian optimization framework, paving the way toward predictive materials optimization.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗