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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Expression of interfacial Seebeck coefficient through grain boundary engineering with multi-layer graphene nanoplatelets

Energy filtering has been a long-sought strategy to enhance a thermoelectric material's figure of merit zT through improving its power factor. Here we show a composite of multi-layer graphene nanoplatelets (GNP) and n-type Mg 3 Sb 2 leads to the expression of an energy filtering like effect demonstrated by an increase in the material's Seebeck coefficient and maximum power factor, without impact on the material's carrier concentration. We analyse these findings from the perspective of a heterogeneous material consisting of grain and grain boundary phases, instead of a more traditional and common analysis that assumes a homogeneously transporting medium. An important implication of this treatment is that it leads to the development of an interfacial Seebeck coefficient term, which can explain the observed increase in the material's Seebeck coefficient. The contribution of this interfacial Seebeck coefficient to the overall Seebeck coefficient is determined by the relative temperature drop across the grain boundary region compared to that of the bulk material. In Te doped Mg 3 Sb 2 we show the introduction of GNP increases the interfacial thermal resistance of grain boundaries, enhancing the contribution of the interfacial Seebeck coefficient arising from grain boundaries to the overall Seebeck coefficient. Without significant detriment to the electrical conductivity this effect results in a net increase in maximum power factor. This increased interfacial thermal resistance also leads to the synergistic reduction of the total thermal conductivity. As a result, we enhance zT of the Mg 3 Sb 2 to a peak value of 1.7 near 750 K. Considering the two-dimensional nature of the grain boundary interface, this grain boundary engineering strategy could be applied to a few thermoelectric systems utilizing various two-dimensional nanomaterials.

42 ENGINEERING↗
DOE OSTI2021

Phase transition mechanism and bandgap engineering of Sb2S3 at gigapascal pressures

Abstract Earth-abundant antimony trisulfide (Sb 2 S 3 ), or simply antimonite, is a promising material for capturing natural energies like solar power and heat flux. The layered structure, held up by weak van-der Waals forces, induces anisotropic behaviors in carrier transportation and thermal expansion. Here, we used stress as mechanical stimuli to destabilize the layered structure and observed the structural phase transition to a three-dimensional (3D) structure. We combined in situ x-ray diffraction (XRD), Raman spectroscopy, ultraviolet-visible spectroscopy, and first-principles calculations to study the evolution of structure and bandgap width up to 20.1 GPa. The optical band gap energy of Sb 2 S 3 followed a two-step hierarchical sequence at approximately 4 and 11 GPa. We also revealed that the first step of change is mainly caused by the redistribution of band states near the conduction band maximum. The second transition is controlled by an isostructural phase transition, with collapsed layers and the formation of a higher coordinated bulky structure. The band gap reduced from 1.73 eV at ambient to 0.68 eV at 15 GPa, making it a promising thermoelectric material under high pressure.

Cui, Zhongxun (ORCID:0000000275044177)↗
DOE OSTI2023

Occupational disorder as the origin of flattening of the acoustic phonon branches in the clathrate Ba 8 ⁢Ga 16 ⁢Ge 30

In the search for high-performance thermoelectrics, materials such as clathrates have drawn attention due to having both glasslike low phonon thermal conductivity and crystal-like high electrical conductivity. Ba 8 ⁢Ga 16 ⁢Ge 30 (BGG) has a loosely bound guest Ba atom trapped inside rigid Ga-Ge cage structures. Avoided crossings between acoustic phonons and the flat guest atom branches have been proposed to be the source of the low lattice thermal conductivity of BGG. Ga-Ge site disorder with Ga and Ge exchanging places in different unit cells has also been reported. We used time-of-flight neutron scattering to measure the complete phonon spectrum in a large single crystal of BGG and compared these results with predictions of density functional theory to elucidate the effect of the disorder on heat-carrying phonons. Experimental results agreed much better with the calculation assuming the disorder than with the calculation assuming the ordered configuration. Although the atomic masses of Ga and Ge are nearly identical, we found that disorder strongly reduces phonon group velocities, which significantly reduces thermal conductivity. Finally, our work points to a path towards optimizing thermoelectrics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Effective Mass from Seebeck Coefficient

Abstract Engineering semiconductor devices requires an understanding of the effective mass of electrons and holes. Effective masses have historically been determined in metals at cryogenic temperatures estimated using measurements of the electronic specific heat. Instead, by combining measurements of the Seebeck and Hall effects, a density of states effective mass can be determined in doped semiconductors at room temperature and above. Here, a simple method to calculate the electron effective mass using the Seebeck coefficient and an estimate of the free electron or hole concentration, such as that determined from the Hall effect, is introduced here is the Seebeck effective mass, n H is the charge carrier concentration measured by the Hall effect ( n H = 1/ eR H , R H is Hall resistance) in 10 20 cm −3 , T is the absolute temperature in K, S is the Seebeck coefficient, and k B / e = 86.3 μV K −1 . This estimate of the effective mass can aid the understanding and engineering of the electronic structure as it is largely independent of scattering and the effects of microstructure (grain boundary resistance). It is particularly helpful in characterizing thermoelectric materials.

Snyder, Gerald Jeffrey↗
DOE OSTI2025

New layered quaternary Zintl pnictide oxides Ba 2 Zn 2 Pn 2 O ( Pn = Sb, Bi): Discovery, crystal structures, band engineering, and transport properties

Three new heteroanionic oxypnictides, Ba 2 Zn 2 Sb 2 O, Ba 2 Zn 2 Bi 2 O, and the solid solution Ba 2 Zn 2 Sb 2−x Bi x O (x ≈ 1.1–1.6), have been synthesized and structurally characterized. They are isostructural with their Mn-bearing analog, adopting the Ba 2 Mn 2 Sb 2 O-type structure (space group P6 3 /mmc, No. 194), and feature a double-layered 2D $^{2}_{∞}$ [Zn 2 Pn 2 O] 2- substructure (Pn = Sb, Bi, Sb/Bi) composed of corner-sharing, distorted tetrahedral ZnPn 3 O units. Electronic structure calculations reveal a systematic progression from semiconducting Ba 2 Zn 2 Sb 2 O to metallic Ba 2 Zn 2 Bi 2 O as Bi content increases. These trends are corroborated by transport property measurements, with Ba 2 Zn 2 Sb 0.9(1) Bi 1.1 O exhibiting relatively low electrical resistivity, high Hall mobilities of ∼160 cm 2 /V·s, and large Seebeck coefficients from 69 to 132 μV K −1 over the 300–600 K temperature range. Comparison with structurally related Zintl pnictides, such as SrIn 2 As 2 and PrZn 3 As 3 phases, situates Ba 2 Zn 2 Pn 2 O (Pn = Sb, Bi) within a broader family of heteroanionic oxypnictide Zintl compounds, highlighting their structural flexibility and amenability to band engineering. Finally, electronic structure and bonding considerations point to tunable semiconducting behavior and underscore the relevance of these materials for thermoelectric and topological applications.

Band engineering↗
DOE OSTI2022

Disorder driven variations in magnetoresistance and planar Hall effect in Bi 2 Te 3 thin films

The degenerately doped sesquichalcogenide Bi 2 Te 3 , a well-known thermoelectric material, has attracted much attention in recent years as a topological insulator in which conducting surface states lead to exotic electronic transport. Here, in this study, we report the observation of anisotropic magnetoresistance (AMR) and planar Hall effect (PHE) in polycrystalline thin films of Bi 2 Te 3 over a broad range of temperature and magnetic field strength. The values of AMR, PHE and the Hall mobility (μ H ) are compared with results of similar measurements on single crystals and epitaxial films of Bi 2 Te 3 , where these properties are understood in the framework of electronic transport in the topologically protected conducting surface states. Our textured polycrystalline films show a robust metallic character with a carrier density (n s ) and mobility μ H of 9×10 20 cm -3 and 16.7 cm 2 V -1 s -1 respectively. This carrier density is higher and the mobility lower by an order of magnitude compared to the reported values of n s and μ H in epitaxial films and single crystals. However, we see a comparable AMR and PHE in our films for which the concept of conducting surface states is ill-defined due to their polycrystallinity and disordered structure. We suggest that an anisotropic backscattering of charge carriers in the strongly spin – orbit coupled electronic states of this heavy-metal-based non-magnetic compound may lead to the measured resistivity anisotropy. The observation of AMR and PHE in polycrystalline films may be important for scalable production of Bi 2 Te 3 based AMR and PHE sensors of magnetic fields.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Chemistry, Structure, and Function of Lone Pairs in Extended Solids

The lone pair has been a known feature of the electronic structure of molecules for over 100 years. Beginning with the pioneering work of Lewis and others that was later developed into useful guidelines for predicting molecular structure, lone pairs and their steric consequences are now taught at the very earliest stages of a chemistry education. In the crystalline solid state, lone pairs have perhaps had a less visible yet equally consequential role, with a significant impact on a range of properties and functionalities. Important properties associated with s 2 electron-derived lone pairs include their role in creating conditions favorable for ion transport, in the formation and correlation of local dipoles and the resulting polar behavior leading to ferroics and multiferroics, in increasing the refractive index of glass, in reducing the thermal conductivity of thermoelectric materials, and in breaking local symmetry permitting second-harmonic light generation.. In recent years, the role of the lone pair in developing the electronic structure of some topological quantum materials has also been recognized. While structural distortions due to lone pairs have traditionally been characterized through their crystallography, recent advances in scattering and spectroscopy have revealed the presence of local lone pair-driven distortions that do not correlate over long length scales. The role of these crystallographically “hidden” lone pairs, their detection, and their impact on properties have become a growing body of work in the literature. Hidden lone pairs are an effective argument for considering a role for lone pairs that goes beyond their being objects that occupy space in the coordination polyhedra of cations. This Account introduces the chemistry of lone pairs in extended crystalline solids, including a discussion of when they are stereochemically active, how they manifest in the structure, and how their chemistry can be tuned by the chemical environment around them. Eventually, all of these factors work in unison to help develop and tune properties of interest. Certain specific examples of structure–property relationships in materials that are driven by lone pair behavior are described here, including the potential impact of lone pairs on the optical and electronic properties of hybrid halide perovskite compounds that are relevant to their photovoltaic applications. Here, we highlight the role of lone pairs in the dielectric behavior of geometrically frustrated pyrochlores, the temperature-dependent optoelectronic behavior of halide perovskites, the polar phase transitions in lead-free ferroelectric perovskites, and the compositional insulator-to-metal transition in ruthenium pyrochlores. The theme underpinning this Account is that the lone pair can be considered to be a powerful design element for a broad range of material function.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Anisotropic Structural Collapse of Mg 3 Sb 2 and Mg 3 Bi 2 at High Pressure

Alloys between Mg 3 Sb 2 and Mg 3 Bi 2 have recently been shown to be exceptional thermoelectric materials due in part to their anomalously low thermal conductivity. In the present study, in situ high-pressure synchrotron X-ray diffraction was used to investigate the structure and bonding in Mg 3 Sb 2 and Mg 3 Bi 2 at pressures up to 50 GPa. Our results confirm prior predictions of isotropic in-plane and out-of-plane compressibility but reveal large disparities between the bond strength of the two distinct Mg sites. Using single-crystal diffraction, we show that the octahedral Mg–Sb bonds are significantly more compressible than the tetrahedral Mg–Sb bonds in Mg 3 Sb 2 , which lends support to prior arguments that the weaker octahedral Mg bonds are responsible for the anomalous thermal properties of Mg 3 Sb 2 and Mg 3 Bi 2 . Further, we report the discovery of a displacive and reversible phase transition in both Mg 3 Sb 2 and Mg 3 Bi 2 above 7.8 and 4.0 GPa, respectively. Furthermore, the transition to the high-pressure structure involves a highly anisotropic volume collapse, in which the out-of-plane axis compresses significantly more than the in-plane axes. Single-crystal diffraction at high pressure was used to solve the monoclinic high-pressure structure ( C 2/ m ), which is a distorted variant of the ambient-pressure structure containing four unique Mg coordination environments.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Homologous Alkali Metal Copper Rare-Earth Chalcogenides A 2 Cu 2 n Ln 4 Q 7+ n ( n = 1, 2, 3)

Twenty-seven new members of the A 2 Cu 2n Ln 4 Q 7+n (A = Cs, Rb; Ln = La-Nd, Sm, Gd-Yb; Q = S, Se) homologous series were synthesized in one of three structural types (indicated by n = 1, 2, 3). All the compounds contained 3D frameworks with alkali-metal-containing tunnels. For each increment in n, one Cu 2 Q was added, which was incorporated into the framework as an edge-sharing tetrahedron by replacing a square planar chalcogenide site. High-throughput DFT calculations predicted many of the phases to be thermodynamically stable. These predictions were compared with the synthesis results for the phases formed in each composition space. In the syntheses, heavier lanthanides showed a preference to start forming the n = 3 ACu 3 Ln 2 Q 5 , which is consistent with the predictions. RbCuNd 2 Se 4 and RbCuTb 2 Se 4 were found to be thermally stable under vacuum at temperatures up to 1000 °C. Optical measurements revealed band gaps of 1.55(5) and 1.62(5) eV for CsCuCe 2 Se 4 and RbCuTb 2 Se 4 , respectively, and a work function of 4.83(5) eV for CsCuPr 2 Se 4 . Additionally, some n = 3 ACu 3 Ln 2 Qs compounds exhibit a negative phonon mode because of a copper atom coordination, which may distort to a trigonal planar geometry at sufficiently low temperatures. The dynamic instabilities and the predicted distortion in the copper tetrahedra for the n = 3 ACu 3 Ln 2 Q 5 compounds were found to have a linear relationship with the atomic number of the lanthanides and the electronegativity of the lanthanides. In conclusion, the A 2 Cu 2 n Ln 4 Q 7+n compounds can potentially find application as high-temperature thermoelectric materials and other semiconductors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Discovery of Ternary Antimonides A–Al–Sb (A = Rb or Cs) with Desired Structural Motifs Guided by Machine Learning

Specific structural motifs in inorganic solids are often related to their targeted physical properties. For many classes of solids, such as Zintl phases and polar intermetallics, the crystal structures are diverse and not easy to predict. Various antimonides that are potential thermoelectric materials were proposed to be synthesizable on the basis of their estimated formation energies. Their structures were broadly classified as clathrate, channel, layered, or network through a machine learning model trained on existing ternary phases and features based on elemental properties using the sure independence screening and sparsifying operator algorithm. Through experimental validation, three new ternary antimonides were synthesized and confirmed to form layered structures: tetragonal RbAlSb 2 and CsAlSb 2 , which are isopointal but not isotypic to LiBSi 2 ; and monoclinic Rb 2 Al 2 Sb 3 , which adopts the Na 2 Al 2 Sb 3 -type structure. Finally, reinvestigation of the related compound Cs 2 In 2 Sb 3 revealed a low thermal conductivity and p-type semiconducting behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Ambient and High Pressure CuNiSb 2 : Metal-Ordered and Metal-Disordered NiAs-Type Derivative Pnictides

The mineral Zlatogorite, CuNiSb 2 , was synthesized in the laboratory for the first time by annealing elements at ambient pressure (CuNiSb 2 -AP). Rietveld refinement of synchrotron powder X-ray diffraction data indicates that CuNiSb 2 -AP crystallizes in the NiAs-derived structure ( P 3 m 1, #164) with Cu and Ni ordering. The structure consists of alternate NiSb 6 and CuSb 6 octahedral layers via face-sharing. The formation of such structure instead of metal disordered NiAs-type structure ( P 6 3 / mm c, #194) is validated by the lower energy of the ordered phase by first-principle calculations. Interatomic crystal orbital Hamilton population, electron localization function, and charge density analysis reveal strong Ni-Sb, Cu-Sb, and Cu-Ni bonding and long weak Sb-Sb interactions in CuNiSb 2 -AP. The magnetic measurement indicates that CuNiSb 2 -AP is Pauli paramagnetic. First-principle calculations and experimental electrical resistivity measurements reveal that CuNiSb 2 -AP is a metal. The low Seebeck coefficient and large thermal conductivity suggest that CuNiSb 2 is not a potential thermoelectric material. Single crystals were grown by chemical vapor transport. The high pressure sample (CuNiSb 2 -8 GPa) was prepared by pressing CuNiSb 2 -AP at 700 °C and 8 GPa. However, the structures of single crystal and CuNiSb 2 -8 GPa are best fit with a disordered metal structure in the P 3 m 1 space group, corroborated by transmission electron microscopy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Insights into Nucleation and Growth of Colloidal Quaternary Nanocrystals by Multimodal X-ray Analysis

Copper chalcogenide nanocrystals find applications in photovoltaic inks, bio labels, and thermoelectric materials. We reveal insights in the nucleation and growth during synthesis of anisotropic Cu 2 ZnSnS 4 nanocrystals by simultaneously performing in situ X-ray absorption spectroscopy (XAS) and small-angle X-ray scattering (SAXS). Real-time XAFS reveals that upon thiol injection into the reaction flask, a key copper thiolate intermediate species is formed within fractions of seconds, which decomposes further within a narrow temperature and time window to form copper sulfide nanocrystals. These nanocrystals convert into Cu 2 ZnSnS 4 nanorods by sequentially incorporating Sn and Zn. Real-time SAXS and ex situ TEM of aliquots corroborate these findings. Our work demonstrates how combined in situ X-ray absorption and small-angle X-ray scattering enables the understanding of mechanistic pathways in colloidal nanocrystal formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Valence Disproportionation of GeS in the PbS Matrix Forms Pb 5 Ge 5 S 12 Inclusions with Conduction Band Alignment Leading to High n-Type Thermoelectric Performance

Converting waste heat into useful electricity using solid-state thermoelectrics has a potential for enormous global energy savings. Lead chalcogenides are among the most prominent thermoelectric materials, whose performance decreases with an increase in chalcogen amounts (e.g., PbTe>PbSe>PbS). Herein, we demonstrate the simultaneous optimization of the electrical and thermal transport properties of PbS-based compounds by alloying with GeS. The addition of GeS triggers a complex cascade of beneficial events as follows: Ge 2+ substitution in Pb 2+ and discordant off-center behavior; formation of Pb 5 Ge 5 S 12 as stable second phase inclusions through valence disproportionation of Ge 2+ to Ge0 and Ge 4+ . PbS and Pb 5 Ge 5 S 12 exhibit good conduction band energy alignment that preserves the high electron mobility; the formation of Pb 5 Ge 5 S 12 increases the electron carrier concentration by introducing S vacancies. Sb doping as the electron donor produces a large power factor and low lattice thermal conductivity (κ lat ) of ~0.61 Wm -1 K -1 . The highest performance was obtained for the 14% GeS-alloyed samples, which exhibited an increased room temperature electron mobility of ~121 cm 2 V -1 s -1 for 3 × 10 19 cm -3 carrier density, and a ZT, of 1.32 at 923 K. This is ~ 55% greater that the corresponding Sb-doped PbS sample and is one of the highest reported for the n-type PbS system. Moreover, the average ZT (ZT avg ) of ~0.76 from 400 to 923 K is the highest for PbS-based systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Nanoscale imaging of phonon dynamics by electron microscopy

Spatially resolved vibrational mapping of nanostructures is indispensable to the development and understanding of thermal nanodevices, modulation of thermal transport and novel nanostructured thermoelectric materials. Through the engineering of complex structures, such as alloys, nanostructures and superlattice interfaces, one can significantly alter the propagation of phonons and suppress material thermal conductivity while maintaining electrical conductivity. There have been no correlative experiments that spatially track the modulation of phonon properties in and around nanostructures due to spatial resolution limitations of conventional optical phonon detection techniques. Here we demonstrate two-dimensional spatial mapping of phonons in a single silicon–germanium (SiGe) quantum dot (QD) using monochromated electron energy loss spectroscopy in the transmission electron microscope. Tracking the variation of the Si optical mode in and around the QD, we observe the nanoscale modification of the composition-induced red shift. We observe non-equilibrium phonons that only exist near the interface and, furthermore, develop a novel technique to differentially map phonon momenta, providing direct evidence that the interplay between diffuse and specular reflection largely depends on the detailed atomistic structure: a major advancement in the field. Our work unveils the non-equilibrium phonon dynamics at nanoscale interfaces and can be used to study actual nanodevices and aid in the understanding of heat dissipation near nanoscale hotspots, which is crucial for future high-performance nanoelectronics.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Electronic correlations in the semiconducting half-Heusler compound FeVSb

Electronic correlations are crucial to the low-energy physics of metallic systems with localized d and f states; however, their effect on band insulators and semiconductors is typically negligible. Here, we measure the electronic structure of the half-Heusler compound FeVSb, a band insulator with a filled shell configuration of 18 valence electrons per formula unit ( s 2 p 6 d 10 ). Additionally, angle-resolved photoemission spectroscopy reveals a mass renormalization of m * / m bare = 1.4 , where m * is the measured effective mass and m bare is the mass from density functional theory calculations with no added on-site Coulomb repulsion. Our measurements are in quantitative agreement with dynamical mean-field theory calculations, highlighting the many-body origin of the mass renormalization. This mass renormalization lies in dramatic contrast to other filled shell intermetallics, including the thermoelectric materials CoTiSb and NiTiSn, and has a similar origin to that in FeSi, where Hund's coupling induced fluctuations across the gap can explain a dynamical self-energy and correlations. Our work calls for a rethinking of the role of correlations and Hund's coupling in intermetallic band insulators.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Iridium valence variation and carrier sign tuning in ( Ca , Ba ) x La 2 – x CuIrO 6 double perovskites

Here, we report the structure and properties of ( Ca , Ba ) x La 2 – x CuIrO 6 . The rock-salt double perovskite structure goes through a P 1 ¯ to P 2 1 / n phase transition with increasing Ba content but not with Ca content. In both cases, the Ir ion is oxidized from 4 + to 5 + with increasing substitution. Transport and magnetic properties measurements reveal that all compositions are insulating with hysteretic spin-freezing magnetic behavior. Seebeck coefficient measurements reveal a large thermopower change from + 176 μ V /K in La 2 CuIrO 6 to – 223 μ V /K with increasing Ba content in Ba x La 2 – x CuIrO 6 . This behavior is modeled well by the Heikes formula for correlated hopping conduction. ( Ca , Ba ) x La 2 – x CuIrO 6 provides a model system for investigations of other systems with similar carrier sign tuning, with applications toward semiconductors and thermoelectric materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Measurement of Thermal Conductivity in a Supercooled Hydrogel-Salt Complex Near Its Phase Transition

Solid-liquid phase transitions, i.e. solidification processes, have applications in data storage, development of novel thermoelectric materials, cooling of microelectronic substrates and air conditioning condensers. Standard analyses of solidification (Stefan problem) assume constant thermal properties of the solid and liquid sides. It is not known how these properties change across the spatial transition interface, though most studies report a discontinuity in the solid and liquid properties through the transition temperature [1]. When the phase transition releases enthalpy, recent research has shown if the phonon or electron transport time is of the same order of magnitude as the time scale of the atomic transformation, this increases the heat capacity of the solid material at temperatures near the phase transition temperature [2]. A fundamental understanding of the phase transition may help shed light on the molecular origins of supercooling and spontaneous nucleation, which will help with applications involving them. We report studies of supercooling and nucleation of sodium sulfate decahydrate, a salt hydrate which is of recent interest in thermal storage, and of a hydrogel-sodium sulfate complex which shows limited supercooling. We will also report the measurement of their thermal properties during the phase transition process. This will be done with a hot-wire setup which produces small temperature changes of the order of ~1 C.

crystallization, phase transformation, thermal con↗