Lattice Entropy Changes Research Articles

Giant magnetocaloric effect in the Co-doped Tb5Si2Ge2 by establishing magnetostructural coupling

The magnetostructural coupling materials exhibit excellent magnetocaloric properties, making them ideal candidates for magnetic refrigerants. Tb5Si2Ge2 reveals diverse phase transition behaviors, but its structural and magnetic phase transitions are decoupled, which restricts its potential applications in magnetic refrigeration technology. Here, we demonstrate that upon the addition of Co into the Ge site of Tb5Si2Ge2, the compound can obtain a strong magnetostructural coupling between the structural and the magnetic transition, which can significantly improve the magnetocaloric properties. It is observed that the magnetic entropy change under a magnetic field change of 5 T is increased from − 18.30 Jkg−1K−1 to − 31.34 Jkg−1K−1 after adding the magnetic element Co into the compound. The temperature-averaged entropy change (TEC) at the working range of 3 K under 1 T is also improved 2.1 times, exhibiting an enhanced low-field magnetocaloric performance. In addition, theoretical calculations show that a large lattice entropy change of 21.5 Jkg−1K−1 can be achieved after the magnetostructural transformation in the Co-doped compound. The results demonstrate that Co doping can be used to construct a stable magnetostructural transition, transforming Tb5Si2Ge2 into an excellent magnetic refrigerant.

Magnetic field-dependent lattice entropy change in Gd5Ge4

The total entropy change in the first-order magnetic phase transition materials is mainly composed of lattice entropy change (LEC) and magnetic entropy change (MEC). Generally, the MEC is limited by the total angular momentum quantum number, while the LEC is related to the volume change associated with phase transition and it can be easily regulated. Therefore, maximizing LEC is considered as an effective means to improve the refrigeration performance. However, the current research methods only calculate the LEC between two stable phases after phase transition, whereas the LEC during phase transformation is not fully clarified. Here, the mixed Debye temperature (MDT) model and the mixed lattice entropy (MLE) model are proposed based on the two-phase coexistence mechanism for calculating the LEC during the magnetic field-driven phase transition in Gd5Ge4. Both models indicate that the lattice entropy strongly depends on the applied magnetic field during phase transformation. According to the MLE model, which shows better accuracy, a large LEC up to –22.31 Jkg-1K−1 at 25 K can be exerted in Gd5Ge4 by a relatively small magnetic field of 2.5 T. Our proposed theoretical models are helpful for designing high-performance magnetic refrigerants.

Irradiation engineered lattice distortion in Ti-Ni shape memory alloy achieving enhanced elastocaloric effect

Large lattice distortion is the design idea to obtain a high elastocaloric effect of shape memory alloys. In the present work, a new method of He ion irradiation is used to obtain a large lattice distortion, resulting in a 6.5 K of adiabatic temperature in Ti-Ni microwires, compared to the 2.9 K of the unirradiated sample. In addition, the isothermal entropy change is 68 J/kg·K at 293 K, which is twice as high as that of unirradiated alternatives. The microwires have a larger unit cell lattice distortion after irradiation across the stress-induced martensite transformation, therefore, the irradiated sample has a larger lattice entropy change, resulting in the improvement of the phase transformation entropy change. This is the main reason that the elastocaloric effect of Ti-Ni shape memory microwires is significantly improved after He ion irradiation. This method will provide a new idea for the design of colossal elastocaloric effect materials and provide the possibility for the application of solid-state refrigeration.

Sign of lattice and spin entropy change during phase transition in giant magnetocaloric materials

<p indent=0mm>Solid-state refrigeration based on the magnetocaloric effect (MCE) has garnered worldwide attention because of its superior energy conservation and environment friendliness. A common feature of giant magnetocaloric materials is the simultaneous magnetic and lattice transitions, while some of them undergo negative expansion, i.e., lattice contraction, during the transition from the ferromagnetic (FM) to the paramagnetic (PM) phase. Generally, a larger lattice volume indicates softer phonons and therefore a larger phonon entropy. However, experimental and theoretical studies have shown that there are great differences in the mechanism of phonon modes for different materials. In particular, the strengthening or softening of the phonon vibration mode during magnetic phase transition determines the magnitude and sign of lattice entropy change. Therefore, for the giant MCE materials with negative thermal expansion, whether the sign of lattice and spin entropy change is the same or the opposite has always been controversial. Combined with previous studies of nuclear resonance inelastic X-ray scattering (NRIXS), and by means of heat flow measurements and Debye theory calculations, we have clarified the sign of lattice and spin entropy change of giant magnetocaloric La(Fe, Si)₁₃-based compounds and MM<italic></italic>X alloys with negative thermal expansion. Results show that the lattice and spin entropy changes retain the same sign for La(Fe, Si)₁₃-based compounds and MM′X (M, M′ = transition element, X = main element) alloys, which conforms to the principle of entropy increase. This work is helpful in fully understanding the intrinsic mechanism of giant magnetocaloric effect and its multi-field regulation for magnetostructural/magnetoelastic materials with negative thermal expansion during phase transition.

The sign of lattice and spin entropy change in the giant magnetocaloric materials with negative lattice expansions

Solid-state refrigeration based on the magnetocaloric effect (MCE) has garnered worldwide attention because of its superior energy conservation and its environmentally friendly impact. Many materials exhibiting magnetostructural/magnetoelastic transitions have been identified by their giant MCE as promising refrigerants. The common feature of these materials is their simultaneous magnetic and lattice transitions; some also undergo negative expansions, i.e., lattice contractions, along with a ferromagnetic (FM) to paramagnetic (PM) transition. For these materials, whether the signs of lattice and spin entropy change are the same or opposite has become a controversial issue, noting that a larger unit cell volume usually indicates softer phonons and therefore a bigger phonon entropy. On the basis of our experiments and published data, we demonstrate that the lattice and spin entropy changes retain the same sign at least for La(Fe,Si)13-based compounds and MM’X alloys with giant MCE, for which the lattice undergoes negative expansion along with a FM to PM transition on heating. The clarification of the sign of lattice entropy change in the total entropy change is of particular importance for a comprehensive understanding of new materials with giant magnetocaloric effect and their design.

Neutron diffraction study on hydrostatic pressure regulated magnetostructural transition and magnetocaloric effect in MnNi1 – xFexSi1 – yGey alloys

Ni2In-type hexagonal compounds MM′X (M, M′ = transition metals, X = main element) involving magnetostructural transition (MST) have attracted much attention due to their giant magnetocaloric effect (MCE). Physical pressure, as an effective method, has been used to adjust the MST and the resultant MCE. Enhanced and diminished MCEs by hydrostatic pressure were both reported previously, but the underlying mechanism is unclear. Here, we report our neutron diffraction study on MST and MCE regulated by hydrostatic pressure in MnNi1 – xFexSi1 – yGey alloys. Careful refinements indicate that the martensitic phase shows a linear ferromagnetic structure with spin moment confined on Mn sites, which remains almost unchanged at pressures lower than 5 kbar even though slight compressions of Mn–Mn bond lengths can be identified. The MST keeps sharp under pressures lower than 5 kbar, while the derived volume change (ΔV/V) across MST reduces 7%, i.e., from 2.84% (0 kbar) to 2.63% (2.1 kbar), due to the effect of pressure on two-phase coexistence. Accordingly, the estimated lattice entropy change (ΔSLatt) based on the Debye approximation reduces by 10% from 37.1 J/kg K (0 kbar) to 33.5 J/kg K (2.1 kbar). These ΔSLatt values, driven by temperature, are all somewhat larger than the magnetic entropy change driven by a 5 T magnetic field. This result may imply that a magnetic field of 5 T is not sufficient for the MST to complete. As the pressure reaches 5 kbar, the MST notably slows down. This may originate from the extended temperature region of two-phase coexistence but not the decoupling of MST.

Carbon deficiency-induced changes of structure and magnetism of Mn3SnC

Crystal structure, magnetoelastic coupling, magnetization and magnetocaloric effects of Mn3SnC0.94 and Mn3SnC0.81 were investigated. Temperature-dependent high-resolution X-ray diffraction measurements showed that a larger carbon deficiency of Mn3SnC0.81 reduces lattice distortions more significantly than it reduces the lattice parameter. Resonant ultrasound spectroscopy measurements showed that the larger carbon deficiency has no effect on the lattice stiffening across a ferromagnetic transition, whereas it reduces the lattice softening across a low-temperature transition. Magnetic measurements showed that the larger carbon deficiency doubles high-field magnetization and improves the refrigeration capacity. It is suggested that the larger carbon deficiency of Mn3SnC0.81 weakens antiferromagnetic interactions more significantly than it enhances ferromagnetic interactions. However, the magnetocaloric effect of each sample includes a contribution from the lattice entropy change, which is not sensitive to the carbon deficiency.

Magnetostructural phase transitions and magnetocaloric effect in Mn(As,P) compounds and their composites

The magnetostructural phase transition in Mn(As,P) compounds was studied by a combination of X-ray diffraction on single crystals and by the magnetisation measurements. The mentioned transition is accompanied by anisotropic deformation of the crystal lattice, magnetisation hopping and heat evolving due to a large magnetocaloric effect (MCE). It is shown that this transition is a transformation from the hexagonal ferromagnetic to the orthorhombic paramagnetic phase at heating above the Curie temperature (TC). The values of the magnetic and lattice entropy changes at phase transition are obtained and the adiabatic temperature change is estimated in the frame of Clapeyron-Clausius relations. It is found that the MCE in the magnetic field 140 kOe reaches the value of 13.5 K. It is shown that a superparamagnetic structure (as a conglomerate of microscale areas) is formed above Curie temperature in zero magnetic field. On the other hand at the temperatures above the TC the ferromagnetic state is induced by magnetic fields exceeding the certain critical value Hcr while the above-mentioned superparamagnetic state is destroyed by the same magnetic fields. The magnetic properties of the bulk Mn(As,P) and the polymeric composite based on Mn(As,P) compound are compared.

Magnetic and lattice entropy change across martensite transition of Ni-Mn-Sn melt spun ribbons: Key factors in magnetic refrigeration

Ni45Mn44Sn11 melt spun ribbons have been prepared by melt spinning technique. A single austenite L21 phase with lattice constant 5.945 Å is confirmed at room temperature. The first order martensite transition is observed from calorimetric, electronic transport and magnetic measurements in our Ni45Mn44Sn11 melt spun ribbon sample. The change in lattice entropy due to martensite transformation is found to be nearly 15 J kg−1 K−1 from calorimetric data, both for heating and cooling cycle. A noticeable shift (−7.5 K) of reverse martensite transition for the application of 8 T magnetic field has been clearly observed from temperature dependent resistivity measurement. Field induced transformation of martensite phase to austenite phase has also been noticed directly from the field dependent isothermal resistivity data inside martensite transition regime. As a result large negative magnetoresistance of 38% has been observed at 265 K. Sharp increase of magnetization, on heating, near reverse martensite transition is also observed due to transformation of weak magnetic martensite phase to ferromagnetic austenite phase. Isothermal magnetization data show magnetic hysteresis near the martensite transition regime due to difference in austenite and martensite phase fraction between increasing and decreasing field. A maximum positive magnetic entropy change of 7.2 J kg−1 K−1 is observed for the field change of 5 T. Magnetic hysteresis and refrigerant capacity are the important parameters for magnetic refrigerant material. The maximum value of magnetic hysteresis loss is 16.6 J kg−1. However, the net refrigerant capacity is found to be 30.4 J kg−1 for Ni45Mn44Sn11 melt spun ribbon sample. The adiabatic temperature change is found to be of −2.68 K for application of 5 T magnetic field at 276 K.

Temperature and magnetic field dependent martensite transformation in Al doped Ni-Mn-Sn disorder alloys and its effects on magnetoresistance and magnetocaloric effect near room temperature

Ferromagnetic shape memory alloys Ni45Mn44Sn11-xAlx (x = 1, 2) were prepared by arc melting technique. The martensite transition, which is first order in nature, has been clearly observed through magnetic, differential scanning calorimetry and electronic transport measurements. Magnetic path dependent very large magnetic entropy change (19 Jkg−1K−1 and 14 Jkg−1K−1 obtained from decreasing and increasing field magnetization data, respectively) due to sharp increase of magnetization from weak magnetic martensite phase to ferromagnetic austenite phase has been observed for Ni45Mn44Sn10Al1 alloy. However, the observed large magnetic entropy change in Ni45Mn44Sn9Al2 alloy (20.6 Jkg−1K−1 and 19.2 Jkg−1K−1 obtained from decreasing and increasing field magnetization data, respectively) are found to be not much dependent on magnetic path. Thermal path dependent large negative magneto-resistance (∼ −15% and −24% at 288(C) K and 288(W) K, respectively, for 8 T applied magnetic field), due to difference in austenite and martensite phase fraction, has been found inside the martensite transition regime for Ni45Mn44Sn10Al1 alloy. From calorimertic measurement, the lattice entropy change for Ni45Mn44Sn10Al1 alloy due to the martensite transition has been observed to be nearly 55 Jkg−1K−1. The maximum adiabatic temperature change for Ni45Mn44Sn10Al1 and Ni45Mn44Sn9Al2 alloy are found to be −2.7 K and −1.2 K, respectively, for the change of magnetic field of 5 T. Magnetic field dependent isothermal resistivity does not change much outside the martensite transition temperature. Large decrease in resistivity by applied magnetic field has been observed inside martensite transition because of field induced conversion of martensite to austenite phase. The decreasing field isothermal magnetization and resistivity data do not follow increasing field data for having more austenite phase fraction than the field increasing path.

Impact of lattice dynamics on the phase stability of metamagnetic FeRh: Bulk and thin films

We present phonon dispersions, element-resolved vibrational density of states (VDOS) and corresponding thermodynamic properties obtained by a combination of density functional theory (DFT) and nuclear resonant inelastic X-ray scattering (NRIXS) across the metamagnetic transition of B2 FeRh in the bulk material and thin epitaxial films. We see distinct differences in the VDOS of the antiferromagnetic (AF) and ferromagnetic (FM) phase which provide a microscopic proof of strong spin-phonon coupling in FeRh. The FM VDOS exhibits a particular sensitivity to the slight tetragonal distortions present in epitaxial films, which is not encountered in the AF phase. This results in a notable change in lattice entropy, which is important for the comparison between thin film and bulk results. Our calculations confirm the recently reported lattice instability in the AF phase. The imaginary frequencies at the $X$-point depend critically on the Fe magnetic moment and atomic volume. Analyzing these non vibrational modes leads to the discovery of a stable monoclinic ground state structure which is robustly predicted from DFT but not verified in our thin film experiments. Specific heat, entropy and free energy calculated within the quasiharmonic approximation suggest that the new phase is possibly suppressed because of its relatively smaller lattice entropy. In the bulk phase, lattice degrees of freedom contribute with the same sign and in similar magnitude to the isostructural AF-FM phase transition as the electronic and magnetic subsystems and therefore needs to be included in thermodynamic modeling.

A combined thermodynamics and first principles study of the electronic, lattice and magnetic contributions to the magnetocaloric effect in La0.75Ca0.25MnO3

Manganites with the formula La1−xCaxMnO3 for 0.2 < x < 0.5 undergo a magnetic field driven transition from a paramagnetic to ferromagnetic state, which is accompanied by changes in the lattice and electronic structure. An isotropic expansion of the La0.75Ca0.25MnO3 cell at the phase transition has been observed experimentally. It is expected that there will be a large entropy change at the transition due to its first order nature. Doped lanthanum manganite (LMO) is therefore of interest as the active component in a magnetocaloric cooling device. However, the maximum obtained value for the entropy change in Ca-doped manganites merely reaches a moderate value in the field of a permanent magnet. The present theoretical work aims to shed light on this discrepancy. A combination of finite temperature statistical mechanics and first principles theory is applied to determine individual contributions to the total entropy change of the system by treating the electronic, lattice and magnetic components independently. Hybrid-exchange density functional (B3LYP) calculations and Monte Carlo simulations are performed for La0.75Ca0.25MnO3. Through the analysis of individual entropy contributions, it is found that the electronic and lattice entropy changes oppose the magnetic entropy change. The results highlighted in the present work demonstrate how the electronic and vibrational entropy contributions can have a deleterious effect on the total entropy change and thus the potential cooling power of doped LMO in a magnetocaloric device.

Experimental and theoretical investigations of the magnetocaloric effect of Ni2.15Mn0.85−xCuxGa (x=0.05,0.07) alloys

Magnetocaloric effects of Ni2.15Mn0.85−xCuxGa (x=0.05,0.07) alloys were investigated with both experimental and theoretical approaches. The experiments show that these alloys have large entropy changes and refrigeration capacities with the field change of 2T. Further theoretical analysis indicates that both magnetic entropy changes and lattice entropy changes have the same sign during heating, while the main entropy change arises from the magnetic entropy change.

Making the most of the magnetic and lattice entropy changes

Recent discoveries of novel materials exhibiting a magnetocaloric effect that is strongly enhanced by the magnetoelastic coupling—the so-called giant magnetocaloric effect materials—stimulated an unprecedented expansion of research related both to the fundamentals of the phenomenon and potential future applications of these materials in continuous magnetic cooling near room temperature. The subject of this work is twofold. On one hand, systems exhibiting the giant magnetocaloric effect may be prone to hysteresis, and may exist in nonequilibrium, phase-separated states, thus requiring a special care when their intrinsic physical properties are of interest. On the other hand, in order to harvest most of the magnetocaloric potential of a specific compound, both the magnetic and lattice degrees of freedom of the material must be precisely controlled.

Magnetocaloric effect in 4d itinerant ferromagnet SrRuO 3

The magnetocaloric effect (MCE) in 4d itinerant ferromagnet SrRuO 3 prepared by conventional ceramic processing has been investigated using superconducting quantum interference device (SQUID). SrRuO 3 material exhibits magnetic entropy change Δ S M = −2.5 J/kg K and adiabatic temperature change Δ T ad = 3.1 K at an applied field of 6.5 T and near Curie temperature (∼160 K). Based on the analysis of Debye approximation, the lattice entropy change reaches Δ S L = 0.34 J/kg K and is 12% of total entropy changes. The present work demonstrates the importance of the lattice entropy change in SrRuO 3 material with second-order phase transition since the large change in lattice volume exhibits near Curie temperature.

Entropy changes associated with the first-order magnetic transition in LaFe13−xSix

Entropy changes accompanying a first-order magnetic transition have been studied for the intermetallic alloys LaFe13−xSix. An expression of the entropy change due to lattice expansion/contraction is derived based on the general thermodynamics theory. Combining it with the structural/magnetic measurements, and the mean-field-theory analyses, changes in magnetic, lattice, and electronic entropies are estimated. It is found that although magnetic entropy change is dominant, lattice entropy change is comparably large and cancels out most of the magnetic one. In contrast, electronic entropy change is negligibly small.

Entropy changes due to the first-order phase transition in the Gd5SixGe4−x system

Entropy changes due to magnetostructrual phase transition in Gd5SixGe4−x intermetallics have been studied based on a systematic analysis of experiment data and mean-field theory calculations. It is found that the magnetic and lattice entropy changes have the same sign. Further analysis indicates that the main entropy change (∼60%–∼80%) comes from the field-induced change of the magnetic order, while the rest arise from the entropy difference of the two crystallographic modifications joined by the structural transition, probably due to the variation of the lattice vibration mode. The present work reveals the importance of lattice entropy for a system experiencing a first-order transition.

Magnetic refrigerator–heat pump

For almost half a century low‐temperature physicists have been exploiting the adiabatic demagnetization of paramagnetic materials to achieve temperatures near absolute zero. Until recently the potential utility of the magnetic cycle for refrigeration and heat pumping near room temperature has not been taken seriously for two reasons: First of all, the degree of magnetic order achievable in paramagnetic materials at practical field strength becomes very small at room temperature. Thus the entropy change that pumps heat when magnetic fields are applied and withdrawn becomes too small to be useful. Furthermore, by 20 K the lattice entropy changes of typical paramagnetic salts and the magnetic entropy changes from which they must be subtracted in a Carnot refrigeration cycle are comparable.

Mechanism for the First-Order Magnetic Transition in the FeRh System

Measurements of the field dependence of the critical temperature (Tcrit) for the first-order antiferromagnetic-ferromagnetic transition in FeRh established that the total entropy change (ΔST) at Tcrit is much larger than the change in lattice entropy (ΔSL). Doping experiments (Pd, Pt, or Ir) showed that ΔST−ΔSL=ΔS varies almost linearly with Tcrit. Apparently the transition involves a change in the electronic density of states and thus in the electronic entropy, S=γTcrit, where γ is the electronic heat coefficient. To test this mechanism, low-temperature specific-heat measurements were made on several compositions in the Fe(Rh, Pd) system. The compositions and γ values are Fe53Rh47 (59 μJ/g·°K2), Fe51Rh49 (60 μJ/g·°K2), Fe48Rh46Pd6 (64 μJ/g·°K2), Fe49Rh51 (16 μJ/g·°K2), and Fe48Rh49Pd3 (31 μJ/g·°K2). The first three are ferromagnetic at T=0; the latter two are antiferromagnetic with Tcrit of 310° and 210°K, respectively. The insensitivity of γ to Fe concentration in the ferromagnetic samples suggests a broad peak in the d-band at the Fermi surface. The resulting entropy changes, ΔS=(γF−γA)Tcrit, agree with Kouvel's measurements and confirm the electron gas entropy as the main driving force for the transition.

Unusual Nature of the Abrupt Magnetic Transition in FeRh and Its Pseudobinary Variants

Previous measurements of the critical temperature (Tcrit) for the first-order antiferromagnetic-ferromagnetic transition in FeRh as a function of magnetic field have established that the total entropy change at the transition (ΔS) is much larger than the estimated change in lattice entropy (ΔS)lat. This study has now been extended to pseudobinary variants of FeRh where the Rh is partially replaced by Pd, Pt, or Ir, resulting in a large decrease or increase of Tcrit from its value (about 330°K) for FeRh. In each case, a value for ΔS was deduced from the measured field dependence of Tcrit. The difference between each ΔS and an estimated (ΔS)lat value, when plotted vs Tcrit, defines a smooth curve with a maximum at about 500°K, which is just below the Curie points of these alloys. It is therefore concluded that ΔS−(ΔS)lat represents an entropy change of magnetic origin. This anomalous change in magnetic entropy is attributed to thermal excitation of the Rh moments which in the ferromagnetic state are induced by the net exchange field from neighboring Fe moments; in the antiferromagnetic state this net exchange field vanishes, and the induced Rh moments and their contribution to the entropy go essentially to zero.