A method for calculating the magnetic-driven lattice entropy change of magnetocrystalline coupling materials

Abstract

The present invention discloses a method for calculating the magnetic-driven lattice entropy change of a magnetocrystalline coupling material, including: determining the volume fraction λ(H) of the high-field phase structure at each magnetic field during the phase transition process of the magnetocrystalline coupling material; respectively obtaining the Debye temperatures of the zero-field phase and the high-field phase of the magnetocrystalline coupling material, and calculating the lattice entropy of its zero-field phase and high-field phase according to the Debye model; establishing a two-phase coexistence model of the zero-field phase and the high-field phase, and calculating the lattice entropy S L (H) of the material at different magnetic fields in the phase transition temperature range under isothermal conditions; calculating the magnetic-driven lattice entropy change ΔS L (H) of the magnetocrystalline coupling material at each magnetic field during the phase transition process, determining the minimum magnetic field required for ΔS L (H) to tend to saturation, and finding out the temperature range where the maximum lattice entropy change is located. The present invention provides necessary solutions for constructing strong magnetocrystalline coupling, increasing the total entropy change, reducing the driving magnetic field, and determining the optimal refrigeration working temperature range in magnetic refrigeration materials.

Description

Technical Field

[0001] The present invention relates to the field of magnetic refrigeration materials, and more specifically to a method for calculating the magnetic-driven lattice entropy change of magnetocrystalline coupling materials. Background Art

[0002] In recent years, new solid-state refrigeration technologies represented by magnetic refrigeration have been increasingly emphasized by countries around the world due to their advantages such as environmental friendliness, low carbon, high efficiency, stability, reliability, light weight, and low noise. Magnetic refrigeration is a refrigeration method based on the magnetocaloric effect of materials, that is, under the action of a changing magnetic field, the arrangement of magnetic moments of magnetic materials changes accordingly, resulting in the release and absorption of heat by the materials themselves. Through reasonable cycle design, refrigeration can ultimately be achieved.

[0003] All along, first-order magnetic phase change materials with magnetocrystalline coupling characteristics have been considered as the main candidate working fluids for magnetic refrigeration. The magnetocrystalline coupling in such materials is manifested as the simultaneous occurrence of crystal structure phase change (or sudden change of lattice constant) during magnetic phase change, that is, the occurrence of magnetostructural coupling phase change (or magnetoelastic phase change). Due to the drastic changes in magnetization intensity and lattice order near the phase change point, the phase change in such materials is easily driven by different physical fields such as magnetic field, pressure, or temperature, showing rich magnetocaloric, piezocaloric, elastocaloric, magnetic shape memory, and negative thermal expansion effects. We know that the total entropy change of magnetocrystalline coupling materials under magnetic field drive is mainly composed of the magnetic entropy change ΔS M (H) caused by magnetic order change and the lattice entropy change ΔS L (H) caused by lattice order change. However, we note that the maximum molar magnetic entropy Rln(2J + 1) (R is the gas constant) in the material is limited by the total angular momentum quantum number J. Even when using rare-earth magnetic materials with high J as refrigeration working fluids, the pure magnetic entropy change shown is very limited. And the lattice entropy change is usually associated with the volume change accompanying the phase change of magnetic materials, and there is no theoretical upper limit. Therefore, maximizing the excavation of lattice entropy is one of the important means to improve the magnetic refrigeration performance of magnetocrystalline coupling alloys.

[0004] Currently, the research on lattice entropy change mostly adopts the method of temperature-driven phase transition. The existing problems mainly include: (1) This kind of method only calculates the lattice entropy change between two stable phase structures before and after the phase transition. Therefore, we cannot obtain the lattice entropy change when the phase transition has not ended (such as when two phases coexist); (2) The magnetization history during the magnetic phase transition is not considered, so the magnitude of the magnetic-driven lattice entropy change and the minimum magnetic field required for the lattice entropy change to reach saturation cannot be directly determined. In fact, after the magnetic-driven structural phase transition is completed at a specific temperature, the lattice entropy no longer changes. Therefore, there is no need to blindly use a very strong magnetic field to drive the lattice entropy change. Sometimes a relatively small magnetic field can make the lattice entropy change reach saturation. Therefore, it is necessary to develop a calculation method that can determine the magnetic-driven lattice entropy change of magnetocrystalline coupling materials to provide necessary solutions for improving the magnetic refrigeration performance of magnetocrystalline coupling alloys. Summary of the Invention

[0005] The purpose of the present invention is to provide a two-phase coexistence model for calculating the magnitude of the lattice entropy change driven by different magnetic fields during the phase transition of magnetocrystalline coupling materials, and to determine the minimum magnetic field required for the lattice entropy change to reach saturation and the temperature range where the maximum lattice entropy change of the material is located.

[0006] The technical solution adopted by the present invention is as follows: A method for calculating the magnetic-driven lattice entropy change of magnetocrystalline coupling materials includes the following specific steps:

[0007] Step 1, determine the volume fraction λ(H) of the high-field phase structure under each magnetic field during the phase transition of the magnetocrystalline coupling material;

[0008] Step 2, respectively obtain the Debye temperatures of the zero-field phase and the high-field phase of the magnetocrystalline coupling material and Calculate their lattice entropies of the zero-field phase and the high-field phase according to the Debye model and

[0009] Step 3, establish a two-phase coexistence model of the zero-field phase and the high-field phase, and calculate the lattice entropy S L (H) of the material at different magnetic fields in the phase transition temperature range under isothermal conditions;

[0010] Step 4, calculate the magnetic-driven lattice entropy change ΔS L (H) of the magnetocrystalline coupling material during the phase transition under each magnetic field, determine the minimum magnetic field required for ΔS L (H) to tend to saturation, and find the temperature range where the maximum lattice entropy change is located.

[0011] Furthermore, in Step 1, the volume fraction of the high-field phase structure of the magnetocrystalline coupling material during the phase transition can be obtained by methods such as magnetic field X-ray diffraction spectrum, magnetic field neutron diffraction spectrum, or phase field simulation.

[0012] Further, in step 2, according to the lattice entropy calculation formula of the Debye model, the lattice entropy of the magnetocrystalline coupling material in the zero-field phase and the high-field phase is calculated. and The lattice entropy calculation formula based on the Debye model is as follows:

[0013]

[0014] where N is the number of atoms in the material chemical formula, k B is the Boltzmann constant, T is the temperature, Θ D is the Debye temperature of the material, e is the base of the natural logarithm, and its value is 2.718; x is the integration variable, and its upper and lower limits are 0 and Θ D / T respectively.

[0015] Further, in step 3, in the phase transition temperature range, if the applied magnetic field is 0, at this time the magnetocrystalline coupling material is completely in the zero-field phase structure, then the lattice free energy of the material is denoted as When the applied magnetic field is strong enough, the material is completely transformed into the high-field phase structure, and the lattice free energy of the material is written as At a lower magnetic field H, the phase transition of the material has not ended and it is in the coexistence region of the low-field phase and the high-field phase. Suppose the volume fraction of the high-field phase contained in the material at this time is λ(H) (0 ≤ λ(H) ≤ 1), then the corresponding lattice free energy of the high-field phase in the material is The lattice free energy of the zero-field phase is Therefore, the total lattice free energy F L (H) of the material in the two-phase coexistence region at a lower magnetic field H is:

[0016]

[0017] where λ(H) is the volume fraction of the high-field phase structure of the material, and are the lattice free energies of the zero-field phase structure and the high-field phase structure of the material respectively. The lattice entropy can be obtained from Then, at a magnetic field H, the total lattice entropy S L (H) of the material in the two-phase coexistence region is:

[0018]

[0019] where λ(H) is the volume fraction of the high-field phase structure of the material, and are the lattice entropies of the zero-field phase structure and the high-field phase structure of the material respectively. Therefore, the lattice entropy S L (H) of the magnetocrystalline coupling material at different magnetic fields in the phase transition temperature range can be calculated by establishing a two-phase coexistence model.

[0020] Further, in step 4, during the field increasing process, the magnetic-driven lattice entropy change ΔS L (H) in the phase transition temperature range is the difference between the lattice entropy at each magnetic field and the lattice entropy at zero field; during the field decreasing process, the magnetic-driven lattice entropy change ΔS L (H) in the phase transition temperature range is the difference between the lattice entropy at each magnetic field and the lattice entropy at the saturation field.

[0021] Advantages of the present invention:

[0022] (1) The present invention provides a method for calculating the magnetic-driven lattice entropy change of a magnetocrystalline coupling material. It can be seen from the calculated data that the lattice entropy change of the magnetocrystalline coupling material is related to the magnetization history of the material and the temperature environment it is in.

[0023] For example, during the field increasing process, when the embodiment is at 6.1 K, only a 2 T magnetic field is required to drive the lattice entropy change to approach saturation, and at 15 K, a lower external magnetic field is needed, and the lattice entropy change value at 1.5 T is basically close to the saturation value. Similarly, at 25 K, the material can obtain a lattice entropy change of -18.49 Jkg -1 K -1 in a 2 T magnetic field. Further increasing the magnetic field can gradually drive the lattice entropy change to the saturation value of -23.72 Jkg -1 K -1 . It can be seen from these calculation results that sometimes we do not need a large magnetic field to drive the entropy change value of the material, and a relatively high lattice entropy change can be exploited at a lower magnetic field, thus obtaining good low-field magnetocaloric performance. In addition, it can also be seen that the saturated lattice entropy changes at different temperature points in the phase transition interval of the embodiment are not the same, and the performance is optimal in the temperature range near 25 K. Therefore, by adopting the technical solution of the present invention, not only can a large entropy change at low field be exploited, but also the optimal working temperature range can be determined.

[0024] (2) Traditional methods can only calculate the lattice entropy change between two stable phases before and after the phase transition. The present invention overcomes this limitation, can calculate the lattice entropy change at each stage of the magnetic field-driven phase transition process, and can determine the minimum magnetic field required for the lattice entropy change to reach saturation and the temperature range where the maximum lattice entropy change of the material is located. It avoids the waste of resources caused by blindly increasing the working magnetic field, achieving the purpose of energy conservation, efficiency improvement, green carbon reduction. The present invention can provide useful information for optimizing magnetocaloric performance such as constructing strong magnetocrystalline coupling, increasing the total entropy change, reducing the driving magnetic field, and determining the optimal working temperature range, thus strongly promoting the development of magnetocaloric technology forward and realizing a new revolution in green and environmental-friendly refrigeration technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a flow chart of a calculation method for calculating the magnetic-driven lattice entropy change of a magnetocrystalline coupling material according to the present invention.

[0026] Figure 2(a) shows the curves of lattice entropy versus magnetic field during the field-increasing and field-decreasing processes at a temperature of 6.1 K; Figure 2(b) shows the curves of lattice entropy change versus magnetic field during the field-increasing and field-decreasing processes at a temperature of 6.1 K.

[0027] Figure 3(a) shows the curves of lattice entropy versus magnetic field during the field-increasing and field-decreasing processes at a temperature of 15 K; Figure 3(b) shows the curves of lattice entropy change versus magnetic field during the field-increasing and field-decreasing processes at a temperature of 15 K.

[0028] Figure 4(a) shows the curves of lattice entropy versus magnetic field during the field-increasing and field-decreasing processes at a temperature of 25 K; Figure 4(b) shows the curves of lattice entropy change versus magnetic field during the field-increasing and field-decreasing processes at a temperature of 25 K. Specific Embodiments

[0029] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0030] As Figure 1 shown, a method for calculating the magnetic-driven lattice entropy change of a magnetocrystalline coupling material includes the following specific steps:

[0031] Step 1: Determine the volume fraction of the high-field phase structure at each magnetic field during the phase transition process of the magnetocrystalline coupling material;

[0032] In the embodiment of the present invention, the selected material is Gd 5 Ge 4 alloy. The Gd 5 Ge 4 alloy undergoes a magnetic structure coupling phase transition from a zero-field antiferromagnetic state to a high-field ferromagnetic state under the drive of a magnetic field. Among them, the volume fraction data of the high-field phase structure at each magnetic field at temperatures of 6.1 K and 25 K are derived from the article "Magnetic-Field-Induced Structural Transformation and the Nature of the Giant Magnetocaloric Effect in Gd 5 Ge 4 " published in the journal "Physical Review Letters" in 2003, issue 91: 197204 (V.K. Pecharsky, A.P. Holm, K.A. Gschneidner, R. Rink, Massive magnetic-field-induced structural transformation in Gd 5 Ge 4and the nature of the giant magnetocaloric effect, Phys. Rev. Lett., 91 197204 (2003)), the volume fraction data of the high-field phase structure at each magnetic field at 15 K is from the article "In-situ structural studies in magnetic fields from 0 to 35 kOe between 2.2 and 315 K by X-ray powder diffractometer" published in the journal "Review of Scientific Instruments" in 2004, volume 75: 1081 - 1088 (A.P. Holm, V.K. Pecharsky, K.A. Gschneidner, R. Rink, M.N. Jirmanus, X-ray powder diffractometer for in situ structural studies in magnetic fields from 0 to 35 kOe between 2.2 and 315 K, Rev. Sci. Instrum., 75 1081 - 1088 (2004)).

[0033] Step 2: Obtain the Debye temperatures of the zero-field phase and the high-field phase of the magnetocrystalline coupling material respectively and Calculate the lattice entropies of its zero-field phase and high-field phase according to the Debye model and

[0034] The Debye temperature of the zero-field phase in the embodiment The Debye temperature of the high-field phase The data is from the article "Electrical resistivity, electronic heat capacity, and electronic structure of Gd" published in the journal "Physical Review B" in 2001 5 Ge 4 , Phys. Rev. B, 64 235103 (2001)) (E.M. Levin, V.K. Pecharsky, K.A. Gschneidner, G.J. Miller, Electrical resistivity, electronic heat capacity, and electronic structure of Gd 5 Ge 4 , Phys. Rev. B, 64 235103 (2001)).

[0035] According to the lattice entropy calculation formula of the Debye model, use numerical calculation methods to calculate the lattice entropies of the embodiment in the zero-field phase and the high-field phase respectively and The lattice entropy calculation formula based on the Debye model is as follows:

[0036]

[0037] Among them, N is the number of atoms in the chemical formula of the embodiment; k B is the Boltzmann constant; T is the temperature; Θ D is the Debye temperature of the embodiment; e is the base of the natural logarithm, and its value is 2.718; x is the integration variable, and its upper and lower limits are 0 and Θ D / T.

[0038] Step 3: Establish a two-phase coexistence model of the zero-field phase and the high-field phase, and calculate the lattice entropy S L (H) of the material at different magnetic fields in the phase transition temperature range under isothermal conditions. The model is as follows:

[0039]

[0040] Among them, λ(H) is the volume fraction of the high-field phase structure of the embodiment, and are the lattice entropies of the zero-field phase structure and the high-field phase structure of the embodiment respectively. The lattice entropy S L (H) at each magnetic field during the phase transition process is calculated as shown in Table 1: Table 1 Lattice entropy of each magnetic field during the phase transition process of the embodiment under isothermal conditions

[0041]

[0042] Step 4: Calculate the magnetic-field-driven lattice entropy change at each magnetic field during the phase transition process of the magnetocrystalline coupling material, determine the minimum magnetic field required for the lattice entropy change to tend to saturation, and find the temperature range where the maximum lattice entropy change occurs.

[0043] During the field-increasing process, the magnetic-field-driven lattice entropy change ΔS L (H) of the embodiment in the phase transition temperature range is the difference between the lattice entropy at each magnetic field and the lattice entropy at zero field. During the field-decreasing process, the magnetic-field-driven lattice entropy change ΔS L (H) of the embodiment in the phase transition temperature range is the difference between the lattice entropy at each magnetic field and the lattice entropy at the saturation field. The calculation results of the lattice entropy change driven by different magnetic fields of the embodiment under isothermal conditions of 6.1K, 15K, and 25K are shown in Table 2:

[0044] Table 2 Lattice entropy change at different magnetic fields during the phase transition process of the embodiment under isothermal conditions

[0045]

[0046] As can be seen from FIGS. 2(a) and 2(b), during the field-increasing process at 6.1 K, the lattice entropy of the example remains unchanged below 1 T magnetic field. As the magnetic field increases, the lattice entropy shows a sharp drop in the range of 1 - 2 T, indicating that the crystal structure change of the example under the magnetic field drive causes a drastic magneto-structural coupling phase transition. Further increasing the magnetic field, the lattice entropy of the example stabilizes at 2.5 T, and at this time, the magnetic field-driven lattice entropy change reaches the saturation value of -0.47 Jkg -1 K -1 。When the magnetic field is removed, its crystal structure still maintains a high content of high-field structure. Therefore, the lattice entropy remains almost unchanged during the field-decreasing process.

[0047] As can be seen from FIGS. 3(a) and 3(b), during the field-increasing process at 15 K, in the range of 0 - 0.5 T, the lattice entropy of the example remains stable. As the magnetic field increases, its lattice entropy begins to decrease and basically approaches the saturation value at 1.5 T. Further increasing the magnetic field, the lattice entropy of the example completely stabilizes at 2 T, and at this time, the magnetic field-driven lattice entropy change reaches the saturation value of -6.99 Jkg -1 K -1 。The field-decreasing process from 3.5 - 1 T at 15 K has the same characteristics as that at 6.1 K. Its crystal structure maintains a high content of high-field structure, and the lattice entropy remains almost unchanged when the magnetic field is decreased. However, different from the field-decreasing process at 6.1 K, when the magnetic field is further decreased, part of the high-field phase structure of the example transforms into the zero-field phase structure, causing its lattice entropy to increase. It increases from 2.80 Jkg at 3.5 T -1 K -1 to 6.39 Jkg at 0 T -1 K -1 , that is, it increases by 3.59 Jkg after the magnetic field is completely removed -1 K -1 。

[0048] As can be seen from FIGS. 4(a) and 4(b), during the field-increasing process at 25 K, the lattice entropy of the example remains stable below 1 T magnetic field. Further increasing the magnetic field, the lattice entropy begins to decrease and gradually approaches saturation at 2 T. At this time, the lattice entropy change value can reach -18.49 Jkg -1 K -1 。When the magnetic field is increased to 2.5 T, the structure phase transition of the example is completed, and the lattice entropy change can reach the saturation value of -22.31 Jkg -1 K -1 。Different from the field-decreasing processes at 6.1 K and 15 K, at 25 K, the lattice entropy of the example increases from 15.35 Jkg at 1.5 T -1 K -1 to 35.68 Jkg at 0 T -1 K -1, indicating that the lattice entropy of the embodiment at 25K has good recoverability. In fact, when the magnetic field is completely removed from 3.5T at this time, the crystal structure of the embodiment can almost return to the zero-field structure, resulting in an increase in lattice entropy of 22.76 Jkg -1 K -1 , which also indicates that the embodiment at 25K has excellent demagnetization endothermic effect.

[0049] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the magnetic-driven lattice entropy change of a magnetocrystalline coupling material, Characterized in that: It includes the following specific steps: Step 1, determine the volume fraction λ(H) of the high-field phase structure under each magnetic field during the phase transition process of the magnetocrystalline coupling material; Step 2, obtain the Debye temperatures of the zero-field phase and the high-field phase of the magnetocrystalline coupling material respectively and The zero-field phase is the ZF phase, and the high-field phase is the HF phase. Calculate the lattice entropy of its zero-field phase and high-field phase according to the Debye model and Step 3: Establish a two-phase coexistence model of the zero-field phase and the high-field phase, and calculate the lattice entropy S(H) of the material at different magnetic fields in the phase transition temperature range under isothermal conditions; L (H); Step 4, calculate the magnetic-field-driven lattice entropy change ΔS L (H) during the phase transition process of the magnetocrystalline coupling material, and determine the minimum magnetic field required for ΔS L (H) to tend to saturation, and find out the temperature range where the maximum lattice entropy change is located; In step 3, in the phase transition temperature range, if the externally applied magnetic field is 0, at this time the magnetocrystalline coupling material is completely in the zero-field phase structure, then the lattice free energy of the material is denoted as When the externally applied magnetic field is strong enough, the material is completely transformed into the high-field phase structure, and at this time the lattice free energy of the material is written as Under a relatively low magnetic field H, the phase transition of the material has not ended and it is in the coexistence region of the low-field phase and the high-field phase; Let the volume fraction of the high-field phase contained in the material at this time be λ(H), where 0 ≤ λ(H) ≤ 1. Then the lattice free energy of the corresponding high-field phase in the material is The lattice free energy of the zero-field phase is Therefore, when the material is in the two-phase coexistence region at a lower magnetic field H, the total lattice free energy F L (H) is as follows: where λ(H) is the volume fraction of the high-field phase structure of the material, and are the lattice free energies of the zero-field phase structure and the high-field phase structure of the material, respectively; the lattice entropy is obtained from , then when the material is in the two-phase coexistence region under the magnetic field H, the total lattice entropy S L (H) is: where λ(H) is the volume fraction of the high-field phase structure of the material, and are the lattice entropies of the zero-field phase structure and the high-field phase structure of the material, respectively; thus, by establishing a two-phase coexistence model, the lattice entropy S L (H) of the magnetocrystalline coupling material at different magnetic fields in the phase transition temperature range can be calculated.

2. The method for calculating the magnetic-driven lattice entropy change of a magnetocrystalline coupling material according to claim 1, Characterized in that: In the said Step 1, the volume fraction of the high-field phase structure of the magnetocrystalline coupling material during the phase transition process is obtained by magnetic field X-ray diffraction spectrum, magnetic field neutron diffraction spectrum or phase field simulation method.

3. The method for calculating the magnetic-driven lattice entropy change of a magnetocrystalline coupling material according to claim 1, Characterized in that: In the step 2, according to the lattice entropy calculation formula of the Debye model, the lattice entropy of the magnetocrystalline coupling material in the zero-field phase and the high-field phase is calculated. and The lattice entropy calculation formula based on the Debye model is as follows: where N is the number of atoms in the material chemical formula; k B is the Boltzmann constant; T is the temperature; Θ D is the Debye temperature of the material; e is the base of the natural logarithm, with a value of 2.718; x is the integration variable, and its upper and lower limits are 0 and Θ D / T, respectively.

4. The method for calculating the magnetic-driven lattice entropy change of a magnetocrystalline coupling material according to claim 1, Characterized in that: In the step 4, during the field increasing process, the magnetic-driven lattice entropy change ΔS L (H) is the difference between the lattice entropy at each magnetic field and the lattice entropy at zero field; during the field decreasing process, the magnetic-driven lattice entropy change ΔS L (H) is the difference between the lattice entropy at each magnetic field and the lattice entropy at the saturation field.

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