Strong Temperature Dependence Research Articles

Protein dynamics underlies strong temperature dependence of heat receptors

Ion channels are generally allosteric proteins, involving specialized stimulus sensor domains conformationally linked to the gate to drive channel opening. Temperature receptors are a group of ion channels from the transient receptor potential family. They exhibit an unprecedentedly strong temperature dependence and are responsible for temperature sensing in mammals. Despite intensive studies, however, the nature of the temperature sensor domain in these channels remains elusive. By direct calorimetry of TRPV1 proteins, we have recently provided a proof of principle that temperature sensing by ion channels may diverge from the conventional allosterity theory; rather it is intimately linked to inherent thermal instability of channel proteins. Here, we tackle the generality of the hypothesis and provide key molecular pieces of evidence on the coupling of thermal transitions in the channels. We show that while wild-type channels possess a single concerted thermal transition peak, the chimera, in which strong temperature dependence becomes disrupted, results in multitransition peaks, and the activation enthalpies are accordingly reduced. The data show that the coupling with protein unfolding drives up the energy barrier of activation, leading to a strong temperature dependence of opening. Furthermore, we pinpoint the proximal N-terminus of the channels as a linchpin in coalescing different parts of the channels into concerted activation. Thus, we suggest that coupled interaction networks in proteins underlie the strong temperature dependence of temperature receptors.

Kinetic, thermodynamic, and ab initio insights of AsnGly isomerisation as a ticking time bomb for protein integrity

Under physiological conditions in peptides or proteins, the -AsnGly- motif autonomously rearranges within hours/days to β-Asp and α-Asp containing sequence, via succinimide intermedier. The formation of the succinimide is the rate-limiting step, with a strong pH and temperature dependence. We found that Arg(+) at the (n + 2) position (relative to Asn in the nth position) favors isomerisation by forming a transition-state like structure, whereas Glu(-) disfavors isomerisation by adopting a β-turn like conformer. Four to six key intermediate structures (proton transfer, transition-state formation, ring-closure and ammonia-release steps) have been identified along the intrinsic reaction coordinate pathways. We explain how, under the right conditions, the N-atom of a backbone amide, hardly a potent nucleophile, can nevertheless initiate isomerisation. The new data are useful for the design of self-structuring motifs, more resistant protein backbones, antibodies, etc.

The hare and the hedgehog – Similar thermal expansion of argento- and aurophilic contacts for different reasons

Abstract This study investigates the thermal expansion properties of argentophilic and aurophilic contacts in coordination complexes of the form [( iPrNHC)2Ag]ClO4 and [( iPrNHC)2Au]ClO4. Using X-ray crystallography distinct structural changes and phase transitions at varying temperatures are revealed. Both complexes exhibit a similar strong temperature dependence of the metallophilic distances. Analysis shows that the shallower, more anharmonic aurophilic interaction is counterbalanced by the smaller vibrational amplitude of the heavier gold atoms, resulting in comparable thermal elongation despite differing atomic dynamics.

Abnormally enhanced Hall Lorenz number in the magnetic Weyl semimetal NdAlSi

In Landau’s celebrated Fermi liquid theory, electrons in a metal obey the Wiedemann–Franz law at the lowest temperatures. This law states that electron heat and charge transport are linked by a constant L0, i.e., the Sommerfeld value of the Lorenz number (L). Such relation can be violated at elevated temperatures where the abundant inelastic scattering leads to a reduction of the Lorenz number (L < L0). Here, we report a rare case of remarkably enhanced Lorenz number (L > L0) discovered in the magnetic topological semimetal NdAlSi. Measurements of the transverse electrical and thermal transport coefficients reveal that the Hall Lorenz number Lxy in NdAlSi starts to deviate from the canonical value far above its magnetic ordering temperature. Moreover, Lxy displays strong nonmonotonic temperature and field dependence, reaching its maximum value close to 2L0 in an intermediate parameter range. Further analysis excludes charge-neutral excitations as the origin of enhanced Lxy. Alternatively, we attribute it to the Kondo-type elastic scattering off localized 4f electrons, which creates a peculiar energy distribution of the quasiparticle relaxation time. Our results provide insights into the perplexing transport phenomena caused by the interplay between charge and spin degrees of freedom.

Effect of temperature on the growth of Cupric and Cuprous Nanoparticles in a wet chemical synthesis

Cuprous oxide (Cu2O) and cupric oxide (CuO) particles were synthesized using a wet chemical surfactant free method at different synthesis temperatures from 25 °C to 60 °C. Morphology, size, and chemical composition of the prepared Cu2O particles were analyzed by FESEM, PXRD, and UV-vis. We discovered that the chemical composition of the Cu2O particles remained unaffected by the synthesis temperature. However, morphology and size of the particles showed a strong temperature dependency. This could be attributed to the temperature induced formation of CuO species from the copper hydroxide (Cu(OH)2) precursor which also functions as copper precursor for the Cu2O particle growth. The cupric oxide species was determined to be the main cause for the formation of micrometer sized particles, whereas with the Cu(OH)2 precursor species for the Cu2O particles nanocubes with smaller edge lengths as well as octahedrons were obtained.

Influence of Temperature and Pressure on the Wetting Progress in 21700 Lithium‐Ion Battery Cells: Experiment, Model, and Lattice Boltzmann Simulation

AbstractThe electrolyte filling and subsequent wetting of the active material is a time‐critical process in the manufacturing of lithium‐ion batteries. Due to the metallic cell housing, the process phenomena are insufficiently accessible, preventing the replication of the wetting processes by mathematical or simulative methods and hindering efforts to accelerate the wetting process. Therefore, this publication employs a glass cell housing for electrolyte filling of a 21700 cylindrical cell to investigate the wetting at different temperatures and process pressures. In parallel, a mathematical replication of the wetting, as well as a lattice Boltzmann pore‐scale simulation, is used to evaluate the influence of these varying process boundary conditions. The results show a strong temperature dependence on electrolyte wetting and the positive effect of pressure changes in the wetting process. These findings are particularly relevant to the process design of large‐scale cylindrical cell manufacturing.

Volatile Organic Compound Emissions in the Changing Arctic

Arctic ecosystems have long been thought to be minimal sources of volatile organic compounds (VOCs) to the atmosphere because of their low plant biomass and cold temperatures. However, these ecosystems experience rapid climatic warming that alters vegetation composition. Tundra vegetation VOC emissions have stronger temperature dependency than current emission models estimate. Thus, warming, both directly and indirectly (via vegetation changes) likely increases the release and alters the blend of emitted plant volatiles, such as isoprene, monoterpenes, and sesquiterpenes, from Arctic ecosystems. Climate change also increases the pressure of both background herbivory and insect outbreaks. The resulting leaf damage induces the production of volatile defense compounds, and warming amplifies this response. Soils function as both sources and sinks of VOCs, and thawing permafrost is a hotspot for soil VOC emissions, contributing to ecosystem emissions if the VOCs bypass microbial uptake. Overall, Arctic VOC emissions are likely to increase in the future, with implications for ecological interactions and atmospheric composition.

Higher temperatures exacerbate effects of antibiotics on methanogenesis in freshwater sediment

Methane (CH4) emissions from natural systems are rising in a concerning manner with an incomplete understanding of its drivers. Recently, chemical stressors such as antibiotics have been suggested as a thus far overlooked factor increasing methanogenesis in freshwaters. Since usage and toxicological impact of antibiotics could increase in a warming climate, we assessed the temperature-dependence of antibiotic effects on methanogenesis. In this light, we conducted anaerobic incubations with freshwater sediment at 10, 15, and 20 °C in presence of a mixture of five antibiotics at field-relevant concentrations. Weekly measurements of CH4 showed a strong temperature dependence of antibiotic effects by changing effect sizes, directions and dynamics. While antibiotics reduced CH4 production at 10 °C, methanogenesis was elevated at 15 °C with the most pronounced increase occurring at 20 °C. Furthermore, antibiotics changed the prokaryotic assemblage at all temperatures and effect patterns of CH4 producing Methanomicrobia strongly followed the patterns observed for methanogenesis. While analyses of compound-specific stable isotopes and the metatranscriptome suggest the acetoclastic pathway as most relevant, linking prokaryotic structure to function remains one of the most significant research challenges. Nevertheless, the evidence provided by this study suggests a positive relationship between temperature and the stimulating effects of antibiotics on CH4 production.

A synchronous improvement of strength and elongation caused by solid solution in low-silver SAC solder with superior necking resistance properties

The current SAC(Sn–Ag–Cu) solder often experiences rapid degradation of mechanical properties at high temperatures and is prone to fracture under dynamic loads, thus failing to meet the interconnection requirements of industrial electronic products that operate under high power and vibration loads. In light of this, this paper aims to enhance the overall performance of the alloy by reducing the fraction of the second phase in SAC305 alloy, altering the type of second-phase particles, and strengthening the matrix β-Sn phase. Additionally, based on thermodynamic calculations of phase diagrams, the internal phases and elemental solid solubility of the alloy under different temperature conditions are accurately designed, thereby improving the alloy's strength while maintaining its elongation almost unchanged. The experimental results indicate that the designed Sn1.0Ag0.7Cu–3Bi4In1.5Sb alloy exhibits a higher rate sensitivity factor m (0.0559), which is more than double that of the Sn1.0Ag0.7Cu–5Bi4In3Sb alloy (0.0239). This improvement is primarily attributed to the enhanced interaction between the matrix β-Sn and the solid solution effect. Larger compound phases, such as Cu6Sn5 and Ag3Sn, only play a role in the low-rate loading region. Additionally, the alloy demonstrates strong temperature dependence, which is also related to the dissolution of the In element in the matrix β-Sn. The solid solution of the In element significantly enhances the high-temperature elongation rate of the alloy, increasing from 11.9% at low temperatures to 21.3% at high temperatures. The successful development and implementation of this research provides a new solution for interconnection of electronic devices under high-speed dynamic loading and high-temperature service.

Unveiling Mechanism of Temperature‐Dependent Self‐Trapped Exciton Emission in 1D Hybrid Organic–Inorganic Tin Halide for Advanced Thermography

AbstractLead‐free hybrid metal halide phosphors/crystals showing self‐trapped exciton (STE) emission have been recently explored for thermography due to the strong temperature dependence of their photoluminescence (PL) lifetime (τ). However, realizing high‐spatial‐resolution thermography using polycrystalline powders or crystals presents a challenge. Moreover, the underlying mechanism of temperature‐dependent STE remains elusive. Herein, a homogeneous 1D ODASn2I6 (ODA, 1,8‐octanediamine) nm‐scale thin film exhibiting efficient STE emission is investigated. The PL decay shows a strong temperature dependence from 275 K (τ ≈ 1.31 µs) to 350 K (τ ≈ 0.65 µs) yielding a thermal sensitivity of 0.014 K−1. By employing temperature‐dependent transient absorption spectroscopy, detailed information is obtained about the relaxation processes prior to the STE formation. Simultaneous analyses of steady‐state and time‐resolved spectroscopies lead to a self‐consistent model where the thermally activated phonon‐assisted nonradiative pathway explains the temperature dependence of the PL lifetime via a conical intersection between the ground state and STE potential energy surfaces. Finally, a discernible 50 ns variation in PL lifetimes across different heated regimes over a distance of 1.15 mm is successfully demonstrated with fluorescence lifetime imaging microscopy, underscoring the substantial potential of ODASn2I6 thin film for high‐spatial‐resolution thermography.

Rb2InCl5·H2O doped with Te4+ for fluorescence thermometry and coordinated water-related structural phase transformation.

Here, we synthesized Rb2InCl5·H2O with x Te4+ doping by the coprecipitation method, which converts the original nonluminance for pure Rb2InCl5·H2O into orange luminescence ascribed to Te4+ incorporation with an emission peak at 648 nm and a full width at half maximum of 142 nm (420.3 meV) at room temperature. The photoluminescence (PL) lifetime of Te4+-doped Rb2InCl5·H2O exhibits a strong temperature dependence, with a maximum absolute sensitivity (SA) of 12 × 10-3 K-1 at 260 K and a relative sensitivity (SR) of 3.5%K-1 at 300 K, demonstrating its capability for non-contact remote temperature measurement. Additionally, we capture the dynamic changes of coordinated water with temperature in Rb2InCl5·H2O through temperature-dependent Raman spectroscopy, analyze the resulting structural phase transformation associated with coordinated water, and investigate the reversibility of this phase transformation.

A novel strategy for obtaining lead-based piezoelectric ceramics with giant piezoelectricity and high-temperature stability through the construction of “slush-like” polar states

Maintaining high piezoelectric response and piezoelectric temperature stability of lead-based piezoceramics is critical for applications under high-temperature environments. Unfortunately, the piezoelectric response of lead-based piezoceramics shows strong temperature dependence. Herein, an innovative strategy was proposed to solve this problem. The method consisted of constructing “slush-like” polar states by introducing localized heterostructures in the tetragonal phase structure to lower the energy barriers. The presence of the tetragonal phase stabilized the domain structure, providing excellent temperature stability, while the localized heterostructures also flattened the free energy landscape and enhanced the piezoelectric response. The strategy was implemented by using 0.11Pb(In0.5Nb0.5)O3-0.89Pb(Hf0.47Ti0.53)O3(PIN-PHT) piezoceramics doped with heterovalent ion Nb5+ to form a “slush-like” polar state with strong interactions inside the ceramics. The piezoelectric response and relaxor behavior of the ceramics were then investigated using piezoelectric force microscopy to reveal the mapping relationship between the complex ferroelectric domain structure and both the piezoelectric response and temperature stability. At Nb5+ doping amount of 0.8 mol%, the ceramics showed excellent comprehensive performances with d33 = 764 pC/N, Tc = 319.1 °C, εr = 3253.59, kp = 0.67, and tanδ = 0.0122. At an external ambient temperature of 300°C, the d33 of PIN-PHT-0.8Nb5+ remained high at 734 pC/N, with piezoelectric performance retention of 96.1%, showing excellent temperature stability. Overall, a new path was proposed for developing Pb-based piezoceramics with both good piezoelectric response and high-temperature stability, promising to broaden the temperature range of high-temperature piezoceramics for various applications.

Liquid state properties and amorphous solidification kinetics of multicomponent Fe_{50-x}Co_{x}Cr_{14}Mo_{14}C_{9}B_{8}Tm_{5} alloys investigated under containerless processing conditions.

The liquid state thermophysical properties and amorphous solidification kinetics of Fe_{50-x}Co_{x}Cr_{14}Mo_{14}C_{9}B_{8}Tm_{5} (x=10, 15, 20, and 25) alloys were explored by electromagnetic and electrostatic levitation techniques. It was found that the surface tension of liquid alloys with Fe contents below 30 at.% had a strong temperature dependence. The high surface tension led to a sharp increase in the interfacial free-energy penalty. A high nucleation barrier was formed inside the melt, which greatly inhibited the nucleation rate. The liquid viscosity revealed the strong liquid feature of this alloy series, which became the dominant kinetic factor determining their solidification mechanisms. The high viscosity hindered atomic diffusion and delayed nucleation. The long crystallizing incubation time of Fe_{30}Co_{20}Cr_{14}Mo_{14}C_{9}B_{8}Tm_{5} ensured a strong glass-forming ability and a low critical cooling rate of 2.11×10^{3}Ks^{-1}. As a result, a bulk metallic glass rod with an 8-mm diameter was successfully prepared by a convenient casting procedure. This rod could remain in a glassy state at a higher temperature and over a wider temperature range due to its high glass-transition temperature and large undercooled liquid region. The apparent activation energy for nucleation was derived as 463.8 kJmol^{-1} according to the nonisothermal crystallization kinetics, indicating that the bulk metallic glass had to absorb a large amount of energy to overcome the potential barriers before nucleation and thus exhibited excellent thermal stability.

Landau Quantization and Lifshitz Transition‐Modulated High Magneto‐Thermoelectric Performance

AbstractOne of the necessary conditions for achieving high thermoelectric (TE) performance is the large longitudinal (Sxx) and transverse thermopower (Syx), which are closely related to the Fermi level position and the energy‐dependent density of states (DOS) at the Fermi level. Herein, it is demonstrated that HfTe5 has both high‐mobility induced significant quantum oscillations with an ultra‐low quantum limit of 2.7 T, and a significant Lifshitz transition where the Fermi level shows strong temperature dependence. The Landau levels yielded by the magnetic field distort the DOS with many equally‐spaced delta functions and significantly enhance the Sxx and Syx. The drastically enhanced magneto‐longitudinal and transverse TE performance in HfTe5 is achieved under an ultra‐low magnetic field of 1.4 T, which can be easily realized by a permanent magnet. Moreover, the Lifshitz transition further modulates its TE and magneto‐TE performance. Ultimately, the peak values of magneto‐longitudinal and transverse power factors (PF) reach 64 µW cm−1 K−2 at 150 K and 0.9 T and 19 µW cm−1 K−2 at 80 K and 1.4 T, respectively, which are comparable to the best TE materials such as Bi2Te3. This work provides novel methods and significant guidance for the development of TE and magneto‐TE materials.

Effects of high temperature and strain rate on the impact-induced inter-laminar shear behavior of plain woven CF/PEEK thermoplastic composites

This paper aims to investigate the interlaminar shear properties and failure mechanisms of plain woven carbon fabric/polyetheretherketone (CF/PEEK) thermoplastic composites under high strain rate impact loads at different temperatures (25°C, 120°C, 295°C). A reliable hot air flow heating method with SHPB is creatively employed for short beam shear experiments. A multi-scale model was developed to predict the impact behavior of plain CF/PEEK composites. Both results show that the thermoplastic composites have strong strain rate and temperature dependence, and which are more sensitive to temperature effect. As the temperature increases, the thermoplastic composites are mainly affected by the softening effect of the matrix due to the glass transition temperature. The shear modulus and peak stress appear to decline at high temperatures, while the failure strain tends to increase. The damage mode changes from interlayer delamination cracking at the glassy state to shear fracture and fiber pullout at a highly elastic state. As the strain rate increases, the failure strain decreases, while the shear modulus and peak stress show the opposite trend. Fiber bundle breakage, debonding, matrix cracking, and significant interlayer delamination occur at high strain rates.

Giant Photocaloric Effects across a Vast Temperature Range in Ferroelectric Perovskites.

Solid-state cooling presents an energy-efficient and environmentally friendly alternative to traditional refrigeration technologies that rely on thermodynamic cycles involving greenhouse gases. However, conventional caloric effects face several challenges that impede their practical application in refrigeration devices. First, operational temperature conditions must align closely with zero-field phase-transition points; otherwise, the required driving fields become excessively large. However, phase transitions occur infrequently near room temperature. Additionally, caloric effects typically exhibit strong temperature dependence and are sizable only within relatively narrow temperature ranges. In this Letter, we employ first-principles simulation methods to demonstrate that light-driven phase transitions in polar oxide perovskites have the potential to overcome such limitations. Specifically, for the prototypical ferroelectric KNbO_{3} we illustrate the existence of giant "photocaloric" effects induced by light absorption (ΔS_{PC}∼100 J K^{-1} kg^{-1} and ΔT_{PC}∼10 K) across a vast temperature range of several hundred Kelvin, encompassing room temperature. These findings are expected to be generalizable to other materials exhibiting similar polar behavior.

Heterogeneous Photo-Fenton Degradation of Azo Dyes over a Magnetite-Based Catalyst: Kinetic and Thermodynamic Studies

Textile wastewater containing dyes poses significant environmental hazards. Advanced oxidative processes, especially the heterogeneous photo-Fenton process, are effective in degrading a wide range of contaminants due to high conversion rates and ease of catalyst recovery. This study evaluates the heterogeneous photodegradation of the azo dyes Acid Red 18 (AR18), Acid Red 66 (AR66), and Orange 2 (OR2) using magnetite as a catalyst. The magnetic catalyst was synthesized via a hydrothermal process at 150 °C. Experiments were conducted at room temperature, investigating the effect of catalyst dosage, pH, and initial concentrations of H2O2 and AR18 dye. Kinetic and thermodynamic studies were performed at 25, 40, and 60 °C for the three azo dyes (AR18, AR66, and OR2) and the effect of the dye structures on the degradation efficiency was investigated. At 25 °C for 0.33 mmolL−1 of dye at pH 3.0, using 1.4 gL−1 of the catalyst and 60 mgL−1 of H2O2 under UV radiation of 16.7 mWcm−2, the catalyst showed 62.3% degradation for AR18, 79.6% for AR66, and 83.8% for OR2 in 180 min of reaction. The oxidation of azo dyes under these conditions is spontaneous and endothermic. The pseudo-first-order kinetic constants indicated a strong temperature dependence with an order of reactivity of the type OR2 &gt; AR66 &gt; AR18, which is associated with the molecular size, steric hindrance, aromatic conjugation, electrostatic repulsion, and nature of the acid–base interactions on the catalytic surface.

Kinetic insights and environmental assessment for a sustainable seedless grape drying in China

Seedless grape drying is an energy-intensive postharvest process that significantly impacts the environmental sustainability of China’s grape industry. This study evaluated seedless grape drying kinetics, energy consumption, and life cycle assessment (LCA) at 40, 50, 60 and 70 °C air temperatures as variable heating conditions. Computational modelling validated against experiments revealed a strong temperature dependence in drying kinetics. Higher temperatures (70 °C) resulted in significantly faster drying times (around 630 min) compared to lower temperatures (40 °C, around 1380 min). However, this came at the cost of high energy consumption values. Interestingly, energy reductions were noticeable above 60 °C due to significantly shortened drying times. The minimum energy required at given temperatures, with an air velocity of 2.5 m·s−1 and a relative humidity of 30 %, was 138.3 MJ at 40 °C, while the maximum was 198.1 MJ at 60 °C. Similar trends were observed in the overall LCA impact values, where convective drying contributed over 90 % of the global warming potential (GWP) across all scenarios. Energy consumption emerged as the primary impact driver, followed by slighter transport and agricultural production contributions. A multi-criteria analysis using the weighted sum method identified the 70 °C scenario as most favourable in balancing short-time drying, moderate energy use and low GWP impacts. This integrated approach demonstrates the potential for optimising the trade-off between drying performance and environmental impacts, which could advance low-carbon drying technologies and develop more sustainable food production systems.

NH3/C2H6 and NH3/C2H5OH oxidation in a shock tube: Multi-speciation measurement, uncertainty analysis, and kinetic modeling

This study examines NH3, NO, and CO profiles during NH3/C2H6 and NH3/C2H5OH oxidation in a shock tube using laser absorption spectroscopy at 1317–1957 K and ∼2.8 bar, with 5–20% C2H6 or C2H5OH, equivalence ratios of 0.5/1.0/1.5, and a 0.9 argon dilution ratio. Metrological uncertainty analysis on mole fractions have been performed. A novel dynamic uncertainty methodology is proposed to time-resolved speciation profiles. From the experimental measurements, the promotional effect on ammonia ignition by C2H6 or C2H5OH is identical under investigated conditions. The multi-speciation profiles demonstrate reasonable relations among the consumption of NH3 and the formation of NO and CO, which show strong temperature and equivalence ratio dependence. An updated PTB-NH3/C2 1.1 mechanism accurately predicts ignition delay times and speciation profiles. Sensitivity analysis reveals NH3 chemistry’s significant control, with NH3+O2/H/OH and N2H2+M reactions being critical at >1300 K, and HO2 interactions being pivotal at 800–1200 K. The reactions related to N2H2 and N-C chemistries dominate for fuel-rich mixtures at high temperatures, resulting in a reverse equivalence ratio dependence on IDTs, namely fuel-rich mixtures exhibit the lowest reactivity. The N-C chemistries, particularly the pronounced reaction pathway of HCN→CN→NCO→HNCO→CO play a crucial role in maintaining the CO level constant after reaching its peak position under fuel-rich conditions·NH3 consumption pathways shift from NH2→H2NO→HNO→NO→NO2→N2O→N2 at intermediate temperatures to NH3→NH2→NH→N(HNO)→NO→(N2O)N2 at high temperatures. The C2-additives participate in the oxidation process by introducing additional OH/H/CH3 radicals, thereby facilitating the reactive radical pool and developing the N-C intersystem-crossing pathways. In summary, the extensive multi-speciation data, metrological uncertainty analysis, mechanism validation and development, together with comprehensive kinetic modelling can be valuable resources for further studies of ammonia combustion.

On the Strong Composition Dependence of the Martensitic Transformation Temperature and Heat in Shape Memory Alloys.

General derivation of the well-known Ren-Otsuka relationship, 1αdTodx=-αβ (where To, x, α and β(>0) are the transformation temperature and composition, as well as the composition and temperature coefficient of the critical shear constant, c', respectively) for shape memory alloys, SMAs, is provided based on the similarity of interatomic potentials in the framework of dimensional analysis. A new dimensionless variable, tox=ToxTmx, describing the phonon softening (where Tm is the melting point) is introduced. The dimensionless values of the heat of transformation, ΔH, and entropy, ΔS, as well as the elastic constants c', c44, and A=c44c' are universal functions of to(x) and have the same constant values at to(0) within sub-classes of host SMAs having the same type of crystal symmetry change during martensitic transformation. The ratio of dtodx and α has the same constant value for all members of a given sub-class, and relative increase in c' with increasing composition should be compensated by the same decrease in to. In the generalized Ren-Otsuka relationship, the anisotropy factor A appears instead of c', and α as well as β are the differences between the corresponding coefficients for the c44 and c' elastic constants. The obtained linear relationship between h and to rationalizes the observed empirical linear relationships between the heat of transformation measured by differential scanning calorimetry (DSC) (QA⟶M) and the martensite start temperature, Ms.