Vibrational Entropy Change Research Articles

Temperature-dependent lattice dynamics study on phase stability, martensitic transformation mechanism, and vibrational entropy properties of B2-type Ni–Mn–Ti Heusler alloy

The all-d-metal Ni–Mn–Ti Heusler alloy with its good mechanical properties and colossal caloric effects has attracted significant attention for mechanocaloric refrigeration. However, the phase stability of the B2-type disordered structure at finite temperatures and the physical origin of large phase transformation entropy change in theoretical calculation remain unclear. In view of thermal and strongly anharmonic effects, we combined the first-principles and temperature dependent effective potential calculations to systematically study the phase stability, martensitic transformation mechanism, and vibrational entropy properties of B2 partial disordered structures for Ni8Mn5Ti3 and Ni8Mn6Ti2. Our results showed the austenitic structures of Ni8Mn5Ti3 and Ni8Mn6Ti2 both exhibit antiferromagnetic interaction behaviors at targeted temperatures, resolving the contradiction between previous calculations and experiments. By the analysis of phonon dispersion relations and Helmholtz free energies at low and high temperatures, we provided a deeper explanation for the underlying mechanism of martensitic transformation. Meanwhile, the phase transformation temperatures and vibrational entropy changes were accurately predicted compared with the experiment results. Specifically, we demonstrated that the large vibrational entropy change of Ni–Mn–Ti material originates from the contributions of both the tetragonal distortion ratio and volume change, which provides important theoretical guidance and has great practical significance for designing the solid-state material with large vibrational entropy change in the application of solid-state refrigeration.

Colossal barocaloric effect of the spin-crossover compound {Fe(pz)2(BH3CN)2} near room temperature

As one of the most likely alternatives to traditional vapor compression refrigeration technology, solid refrigeration technology based on the barocaloric effect (BCE) has attracted extensive attention in recent years. Spin-crossover (SCO) compounds are considered suitable for working at low driving pressures due to high-pressure sensitivity and small hysteresis width. However, the entropy change (ΔSSCO) of the SCO compound is smaller than that of other excellent barocaloric materials (plastic crystals and two-dimensional perovskites). Here, we report the BCE of the SCO compound {Fe(pz)2(BH3CN)2} (pz = pyrazine) with a smaller molar mass and a third source of entropy change besides electron and vibrational entropy changes. Compound {Fe(pz)2(BH3CN)2} exhibits high pressure sensitivity (dT1/2dP= 20.2 K kbar−1) as well as entropy change (ΔSSCO= 202 J kg−1 K−1). The maximum values of reversible isothermal entropy change (ΔSit,rev,max) and adiabatic temperature change (ΔTad,rev,max) at 1 kbar are only 103 J kg−1 K−1 and ∼0 K, respectively, due to the hysteresis behavior. However, at sufficiently high driving pressures, ΔSit,rev,max exceeds 200 J kg−1 K−1, and ΔTad,rev,max can reach ∼47 K, which exceeds all SCO compounds reported in BCE studies and is comparable to some plastic-crystalline and two-dimensional perovskite barocaloric materials. The excellent BCE of the SCO compound {Fe(pz)2(BH3CN)2} is mainly due to its small molar mass, which makes the unit mass compound exhibit higher ΔSSCO, while the introduction of the third source of entropy change—the reorientation entropy change (ΔSreo), only plays a small role. This is expected to promote the practical application of SCO compounds as barocaloric refrigerants.

Accurate prediction of chemical short-range order and its effect on thermodynamic, structural, and electronic properties of disordered alloys: Exemplified in Cu3Au

Electronic-structure methods based on density-functional theory (DFT) were used to directly quantify the effect of chemical short-range order (SRO) on thermodynamic, structural, and electronic properties of archetypal face-centered-cubic (fcc) Cu3Au alloy. We show that SRO can be tuned to alter bonding and lattice dynamics (i.e., phonons) and detail how these properties are changed with SRO. Thermodynamically favorable SRO improves phase stability of Cu3Au from − 0.0343 eV-atom−1 to −0.0682 eV-atom−1. We use DFT-based linear-response theory to predict SRO and its electronic origin, and accurately estimate the transition temperature, ordering instability (L12), and Warren-Cowley SRO parameters, observed in experiments. The accurate prediction of real-space SRO gives an edge over computationally and resource intensive approches such as Monte-Carlo methods or experiments, which will enable large-scale molecular dynamic simulations by providing supercells with optimized SRO. We also analyze phonon dispersion and estimate the vibrational entropy changes in Cu3Au (from 9kB at 300–6kB at 100 K). We establish from SRO analysis that exclusion of chemical interactions may lead to a skewed view of true properties in chemically complex alloys. The first-principles methods described here are applicable to any arbitrary complex solid-solution alloys, including multi-principal-element alloys, so hold promise for designing technologically useful materials.

Vibrational dynamics in the undercooled liquid of ultra-fragile metallic glasses

The lattice vibrational dynamics in ultra-fragile Pt57Cu23P20 and Pt60Cu20P20 glasses were investigated using in situ inelastic neutron scattering to measure the evolution of the phonon density of states (DOS) through the glass transition, into the undercooled liquid phase, and through crystallization. The phonon DOS curves are remarkably similar for the undercooled liquids and the amorphous solids. The vibrational entropy was obtained with these phonon DOS curves, and changes in vibrational entropy caused by the glass transition are less than 0.05kB/atom. For these highly fragile metal/metalloid glasses, the excess vibrational entropy of the undercooled liquid is about 0.5–1.5 J mol−1 K−1, compared to 0.1 J mol−1 K−1 reported earlier for stronger Cu–Zr glasses. Our work suggests that, consistent with our previous report for less fragile metallic glasses, the fraction of the total excess entropy that is vibrational is small, and the discontinuity in excess entropy at the glass transition is mainly due to configurational entropy.

Dynamics in the ordered and disordered phases of barocaloric adamantane.

High-entropy order-disorder phase transitions can be used for efficient and eco-friendly barocaloric solid-state cooling. Here the barocaloric effect is reported in an archetypal plastic crystal, adamantane. Adamantane has a colossal isothermally reversible entropy change of 106 J K-1 kg-1. Extremely low hysteresis means that this can be accessed at pressure differences less than 200 bar. Configurational entropy can only account for about 40% of the total entropy change; the remainder is due to vibrational effects. Using neutron spectroscopy and supercell lattice dynamics calculations, it is found that this vibrational entropy change is mainly caused by softening in the high-entropy phase of acoustic modes that correspond to molecular rotations. We attribute this difference in the dynamics to the contrast between an 'interlocked' state in the low-entropy phase and sphere-like behaviour in the high-entropy phase. Although adamantane is a simple van der Waals solid with near-spherical molecules, this approach can be leveraged for the design of more complex barocaloric molecular crystals. Moreover, this study shows that supercell lattice dynamics calculations can accurately map the effect of orientational disorder on the phonon spectrum, paving the way for studying the vibrational entropy, thermal conductivity, and other thermodynamic effects in more complex materials.

Energy-entropy multiscale cell correlation method to predict toluene-water log P in the SAMPL9 challenge.

The energy-entropy multiscale cell correlation (EE-MCC) method is used to calculate toluene-water log P values of 16 drug molecules in the SAMPL9 physical properties challenge. EE-MCC calculates the free energy, energy and entropy from molecular dynamics (MD) simulations of the water and toluene solutions. Specifically, MCC evaluates entropy by partitioning the system into cells of correlated atoms at multiple length scales and further partitioning the local coordinates into energy wells, yielding vibrational and topographical terms from the energy-well sizes and probabilities. The log P values calculated by EE-MCC using three 200 ns MD simulations have a mean average error of 0.82 and standard error of the mean of 0.97 versus experiment, which is comparable with the best methods entered in SAMPL9. The main contribution to log P is from energy. Less polar drugs have more favourable energies of transfer. The entropy of transfer consists of increased solute vibrational and conformational terms in toluene due to weaker interactions, fewer solute positions in the larger-molecule solvent, reduced water vibrational entropy, negligible change in toluene vibrational entropy, and gains in solvent orientational entropy. The solvent entropy contributions here may be slightly underestimated because software limitations and statistical fluctuations meant that only the first shell could be included while averaged over the whole solution. Nonetheless, such issues will be addressed in future software to offer a general method to calculate entropy directly from MD simulation and to provide molecular understanding or guide system design.

Structural and ITC Characterization of Peptide-Protein Binding: Thermodynamic Consequences of Cyclization Constraints, a Case Study on Vascular Endothelial Growth Factor Ligands.

Macrocyclization constraints are widely used in the design of protein ligands to stabilize their bioactive conformation and increase their affinities. However, the resulting changes in binding entropy can be puzzling and uncorrelated to affinity gains. Here, the thermodynamic (Isothermal Titration Calorimetry) and structural (X‐ray, NMR and CD) analysis of a complete series of lactam‐bridged peptide ligands of the vascular endothelial growth factor, and their unconstrained analogs are reported. It is shown that differences in thermodynamics arise mainly from the folding energy of the peptide upon binding. The systematic reduction in conformational entropy penalty due to helix pre‐organization can be counterbalanced by an unfavorable vibrational entropy change if the constraints are too rigid. The gain in configurational entropy partially escapes the enthalpy/entropy compensation and leads to an improvement in affinity. The precision of the analytical ITC method makes this study a possible benchmark for constrained peptides optimization.

Kinematic Vibrational Entropy Assessment and Analysis of SARS CoV-2 Main Protease.

The three-dimensional conformations of a protein influence its function and select for the ligands it can interact with. The total free energy change during protein-ligand complex formation includes enthalphic and entropic components, which together report on the binding affinity and conformational states of the complex. However, determining the entropic contribution is computationally burdensome. Here, we apply kinematic flexibility analysis (KFA) to efficiently estimate vibrational frequencies from static protein and protein-ligand structures. The vibrational frequencies, in turn, determine the vibrational entropies of the structures and their complexes. Our estimates of the vibrational entropy change caused by ligand binding compare favorably to values obtained from a dynamic Normal Mode Analysis (NMA). Higher correlation factors can be achieved by increasing the distance cutoff in the potential energy model. Furthermore, we apply our new method to analyze the entropy changes of the SARS CoV-2 main protease when binding with different ligand inhibitors, which is relevant for the design of potential drugs.

Origin of Ferroelectricity in Two Prototypical Hybrid Organic-Inorganic Perovskites.

Hybrid organic-inorganic perovskite (HOIP) ferroelectrics are attracting considerable interest because of their high performance, ease of synthesis, and lightweight. However, the intrinsic thermodynamic origins of their ferroelectric transitions remain insufficiently understood. Here, we identify the nature of the ferroelectric phase transitions in displacive [(CH3)2NH2][Mn(N3)3] and order-disorder type [(CH3)2NH2][Mn(HCOO)3] via spatially resolved structural analysis and ab initio lattice dynamics calculations. Our results demonstrate that the vibrational entropy change of the extended perovskite lattice drives the ferroelectric transition in the former and also contributes importantly to that of the latter along with the rotational entropy change of the A-site. This finding not only reveals the delicate atomic dynamics in ferroelectric HOIPs but also highlights that both the local and extended fluctuation of the hybrid perovskite lattice can be manipulated for creating ferroelectricity by taking advantages of their abundant atomic, electronic, and phononic degrees of freedom.

Change in vibrational entropy with change in protein volume estimated with mode Grüneisen parameters.

For a small adjustment in average volume, due to a change in state of a protein or other macromolecule at constant temperature, the change in vibrational entropy is related to the mode Grüneisen parameters, which relate shifts in frequency to a small volume change. We report here values of mode Grüneisen parameters computed for two hydrated proteins, cytochrome c and myoglobin, which exhibit trends with mode frequency resembling those of glassy systems. We use the mode Grüneisen parameters to relate volumetric thermal expansion to previously computed values of the isothermal compressibility for several proteins. We also estimate changes in vibrational entropy resulting from the change in volume upon ligand bonding of myoglobin and the homodimeric hemoglobin from Scapharca inaequivalvis (HbI). We compare estimates of the change in entropy upon ligation obtained in terms of mode Grüneisen parameters with the results of normal mode analysis for myoglobin and earlier molecular dynamics simulations of HbI. The results illustrate how small changes in average volume can yield changes in entropy that contribute to ligand binding and allostery.

Molecular thermodynamic understanding of transport behavior of CO2 at the ionic liquids‐electrode interface

AbstractThe transport behavior of CO2 at the ionic liquids (ILs)‐electrode interface was revealed from the thermodynamic view via molecular dynamics simulations. The hopping and self‐diffusive mechanisms were identified in the interfacial and bulk region, and thereafter a hopping‐diffusion model was developed to evaluate the transport resistance of CO2 from bulk to the interface. Meanwhile, the vibrational spectrum and entropy change of CO2 at the interface were calculated using the thermodynamic analysis method. For ILs with the same cation ([Emim]+), both transport resistance and entropy decrease follow the order: [BF4]− < [AC]− < [NO3]−, indicating [BF4]− possesses the faster CO2 transport efficiency across the electrical double layer. Furthermore, the methyl substitution effect on transport and thermodynamic properties was clarified, indicating the coupling relation between the transport process and thermodynamic advantage. These findings can lay the ground for the molecule design of ILs‐electrode interface in the applications in the chemical engineering field.

Influence of hydrogenation on the vibrational density of states of magnetocaloric LaFe11.4Si1.6H1.6

We report on the impact of magnetoelastic coupling on the magnetocaloric properties of LaFe$_{11.4}$Si$_{1.6}$H$_{1.6}$ in terms of the vibrational density of states, which we determined with $^{57}$Fe nuclear resonant inelastic X-ray scattering measurements and with density-functional-theory based first-principles calculations in the ferromagnetic low-temperature and paramagnetic high-temperature phase. In experiments and calculations, we observe pronounced differences in the shape of the Fe-partial VDOS between non-hydrogenated and hydrogenated samples. This shows that hydrogen does not only shift the temperature of the first-order phase transition, but also affects the elastic response of the Fe-subsystem significantly. In turn, the anomalous redshift of the Fe VDOS, observed by going to the low-volume PM phase, survives hydrogenation. As a consequence, the change in the Fe specific vibrational entropy $\Delta S_\mathrm{lat}$ across the phase transition has the same sign as the magnetic and electronic contribution. DFT calculations show that the same mechanism, which is a consequence of the itinerant electron metamagnetism associated with the Fe subsystem, is effective in both the hydrogenated and he hydrogen-free compounds. Although reduced by 50 % as compared to the hydrogen-free system, the measured change $\Delta S_\mathrm{lat}$ of 3.2\pm1.9 J/kgK across the FM to PM transition contributes with 35 % significantly and cooperatively to the total isothermal entropy change $\Delta S_\mathrm{iso}$. Hydrogenation is observed to induce an overall blueshift of the Fe-VDOS with respect to the H-free compound; this effect, together with the enhanced Debye temperature observed, is a fingerprint of the hardening of the Fe sublattice by hydrogen incorporation. In addition, the mean Debye velocity of sound of LaFe$_{11.4}$Si$_{1.6}$H$_{1.6}$ was determined from the NRIXS and the DFT data.

New Insight on the Interface between Polythiophene and Semiconductors via Molecular Dynamics Simulations.

Polythiophene is considered as an effective dry adhesive and is promising to be a conductive adhesive due to its excellent properties. Here, we used steered molecular dynamics to investigate the interfacial strength between polythiophene and various semiconductors with similar structures including silicon, silicon carbide, and diamond. Energy decomposition was done to have a detailed insight into the adhesive mechanism. Particularly, we laid stress on the entropy difference of the polythiophene chain in different systems. Van der Waals interaction and electrostatic interaction both positively contributed to the adhesion between polythiophene and semiconductors, while the entropy change of polythiophene, including vibrational entropy change and conformational entropy change, weakened the adhesion to some extent. Our results indicated that the combined effect of these three factors made the adhesion between polythiophene and silicon carbide the strongest among the systems we studied. Additionally, it was found that such adhesion was scarcely influenced by temperature. This simple polythiophene-semiconductor interfacial study can help optimize the choice of the semiconductor when applying the polythiophene adhesive.

Electronic Property and Negative Thermal Expansion Behavior of Si136-xGex (x = 8, 32, 40, 104) Clathrate Solid Solution from First Principles.

We present the electronic and vibrational studies on Si136-xGex (x = 8, 32, 40, 104) alloys, using the local density approximation (LDA) scheme. We find that a “nearly-direct” band gap exists in the band structure of Si104Ge32 and Si96Ge40, when compared with the similarly reported results obtained using a different computational code. The calculated electronic density of state (EDOS) profiles for the valence band remain nearly identical and independent of the Ge concentration (x = 32, 40, 104) even though some variation is found in the lower conduction band (tail part) as composition x is tuned from 8 (or 40) to 104. The negative thermal expansion (NTE) phenomenon is explored using quasi-harmonic approximation (QHA), which takes the volume dependence of the vibrational mode frequencies into consideration, while neglecting the temperature effect on phonon anharmonicity. Determined macroscopic Grüneisen parameter trends show negative values in the low temperature regime (1 K < T < 115 K), indicating the NTE behavior found in Si128Ge8 is analogous to the experimental result for Si136. Meanwhile, calculations for the ratio of the vibrational entropy change to the volume change at several characteristic temperatures reconfirm the existence of NTE in Si128Ge8 and Si104Ge32.

Isostructural phase transition of fcc Ce: Molecular dynamics simulations

Ce is a rare earth element in the periodic table. In the range of low temperature and low pressure, there are two face-centered-cubic (FCC) phases (&lt;i&gt;α&lt;/i&gt;-Ce and &lt;i&gt;γ&lt;/i&gt;-Ce) and a double-hexagonal-close-packed phase (&lt;i&gt;β&lt;/i&gt;-Ce) for metallic Ce. At ambient temperature and about 0.7 GPa pressure, Ce undergoes &lt;i&gt;γ&lt;/i&gt;→&lt;i&gt;α&lt;/i&gt; phase transition with a volume shrink of 14%–17% discontinuously. In this paper, an embedded-atom method (EAM) potential compatible for &lt;i&gt;α&lt;/i&gt;-Ce and &lt;i&gt;γ&lt;/i&gt;-Ce was developed. This EAM potential has been employed to study several basic properties of cerium in these two FCC phases, such as equilibrium lattice constants, cohesive energies, and elastic constants. These results showed good accordance with experiments and first principle calculations. The lattice defects have been studied with the formation energy calculations of vacancies, interstitials, surfaces, stacking faults, and twinning defects in &lt;i&gt;α&lt;/i&gt;-Ce and &lt;i&gt;γ&lt;/i&gt;-Ce lattice. The lattice dynamics of &lt;i&gt;α&lt;/i&gt;-Ce and &lt;i&gt;γ&lt;/i&gt;-Ce have been analyzed using our EAM potential. The lattice vibrational entropy was calculated and plotted as functions of temperature for each phases. The vibrational entropy change across the &lt;i&gt;α&lt;/i&gt;-&lt;i&gt;γ&lt;/i&gt; phase transition showed to be ~0.67 &lt;i&gt;k&lt;/i&gt;&lt;sub&gt;&lt;i&gt;B&lt;/i&gt;&lt;/sub&gt; per atom at ambient temperature. Using molecular dynamics simulation with our EAM potential, several isotherms and radial distribution functions were calculated. These isotherms and radial distribution functions demonstrate a first order phase transition between two FCC structures, corresponding to &lt;i&gt;α&lt;/i&gt;-Ce and &lt;i&gt;γ&lt;/i&gt;-Ce, with a critical point sets at &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;c&lt;/sub&gt;≈550 K and &lt;i&gt;P&lt;/i&gt;&lt;sub&gt;c&lt;/sub&gt;≈1.21 GPa. Thus the newly developed EAM potential could provide a reasonable description of FCC Ce and its &lt;i&gt;α&lt;/i&gt;-&lt;i&gt;γ&lt;/i&gt; phase transition within the scale of classical molecular dynamics simulation.

Magnetocaloric effect enhancement driven by intrinsic defects in a Ni45Co5Mn35Sn15 alloy

The influence of mechanically-induced defects on the magnetostructural properties is analyzed in a Ni-Co-Mn-Sn alloy subjected to soft milling and subsequent annealing treatments. It is found that, opposite to what occurs in Ni-Mn-Sn ternary alloys, the annealing treatment affects the magnetic properties in a different way in martensite and in austenite. In particular, the saturation magnetization significantly increases in martensite after annealing whereas just a very slight variation is observed in austenite. This leads to the interesting fact that the presence of microstructural defects, far for worsening, makes the magnetocaloric effect to be higher in the as-milled state than after annealing. This behavior is explained as the result of the combination of the effect of defects on the Mn-Mn distance, the effect of Co on the magnetic exchange coupling between Mn atoms, and the effect of defects on the vibrational entropy change at the martensitic transformation.

An Unusual Phase Transition Driven by Vibrational Entropy Changes in a Hybrid Organic–Inorganic Perovskite

The driving forces for the phase transitions of ABX3 hybrid organic-inorganic perovskites have been limited to the octahedral tilting, order-disorder, and displacement. Now, a complex structural phase transition has been explored in a HOIP, [CH3 NH3 ][Mn(N3 )3 ], based on structural characterizations and ab initio lattice dynamics calculations. This unusual first-order phase transition between two ordered phases at about 265 K is primarily driven by changes in the collective atomic vibrations of the whole lattice, along with concurrent molecular displacements and an unusual octahedral tilting. A significant entropy difference (4.35 J K-1 mol-1 ) is observed between the low- and high-temperature structures induced by such atomic vibrations, which plays a main role in driving the transition. This finding offers an alternative pathway for designing new ferroic phase transitions and related physical properties in HOIPs and other hybrid crystals.

An Unusual Phase Transition Driven by Vibrational Entropy Changes in a Hybrid Organic–Inorganic Perovskite

AbstractThe driving forces for the phase transitions of ABX3 hybrid organic–inorganic perovskites have been limited to the octahedral tilting, order–disorder, and displacement. Now, a complex structural phase transition has been explored in a HOIP, [CH3NH3][Mn(N3)3], based on structural characterizations and ab initio lattice dynamics calculations. This unusual first‐order phase transition between two ordered phases at about 265 K is primarily driven by changes in the collective atomic vibrations of the whole lattice, along with concurrent molecular displacements and an unusual octahedral tilting. A significant entropy difference (4.35 J K−1 mol−1) is observed between the low‐ and high‐temperature structures induced by such atomic vibrations, which plays a main role in driving the transition. This finding offers an alternative pathway for designing new ferroic phase transitions and related physical properties in HOIPs and other hybrid crystals.

DynaMut: predicting the impact of mutations on protein conformation, flexibility and stability.

Proteins are highly dynamic molecules, whose function is intrinsically linked to their molecular motions. Despite the pivotal role of protein dynamics, their computational simulation cost has led to most structure-based approaches for assessing the impact of mutations on protein structure and function relying upon static structures. Here we present DynaMut, a web server implementing two distinct, well established normal mode approaches, which can be used to analyze and visualize protein dynamics by sampling conformations and assess the impact of mutations on protein dynamics and stability resulting from vibrational entropy changes. DynaMut integrates our graph-based signatures along with normal mode dynamics to generate a consensus prediction of the impact of a mutation on protein stability. We demonstrate our approach outperforms alternative approaches to predict the effects of mutations on protein stability and flexibility (P-value < 0.001), achieving a correlation of up to 0.70 on blind tests. DynaMut also provides a comprehensive suite for protein motion and flexibility analysis and visualization via a freely available, user friendly web server at http://biosig.unimelb.edu.au/dynamut/.

Lattice dynamics across the magnetic transition in(Mn,Fe)1.95(P,Si)

The lattice dynamics in MnFe0.95Si0.50P0.50 were investigated experimentally using Fe57 nuclear inelastic scattering and inelastic x-ray scattering across the first-order magnetic transition which occurs close to room temperature. The lattice dynamics characterization was supported by a macroscopic magnetic characterization, an x-ray diffraction study, and a hyperfine interactions characterization using Mossbauer spectroscopy. The Fe specific and the x-ray generalized density of phonon states were obtained both in the ferromagnetic and in the paramagnetic state. A prominent shift, 2meV at 20meV, in the x-ray generalized density of phonon states across the first-order magnetic transition, that involves vibrations with essentially Fe character, is revealed corroborated by a change in the local environment quantified in the isomer shift and the quadrupole splitting. Above 35meV the vibrational modes are practically insensitive to the magnetic transition. The entropy change induced by a 1T magnetic field across the magnetic transition, ∼10J/K/kg, is only a fraction of the Fe vibrational entropy change, 62(21)J/K/kg.