Phase transition regulation, magnetocaloric effect, and abnormal thermal expansion

Lin Yuan; Hu Feng-Xia; Shen Bao-Gen

doi:10.7498/aps.72.20231118

Abstract

As a common phenomenon in nature, phase transition has received much attention for a long time. It has been applied to various fields, such as refrigeration, information and energy storage, and negative thermal expansion. Solid refrigeration technology based on magnetocaloric effect, electrocaloric effect, and mechanocaloric effect has the advantages of environmental protection, high efficiency, no noise, and easy miniaturization, and is expected to replace vapor compression technology. Among them, the magnetocaloric effect has the longest research history. However, the shortcomings of magnetocaloric effect driven by a single magnetic field limit its solid-state refrigeration application, such as insufficient amplitude of caloric effect, large hysteresis loss, and narrow refrigeration temperature span. To solve these problems, multifield tuning and multicaloric effect have come into people's sight. This paper introduces our recent research on improving the caloric effect by applying multifield, such as increasing entropy change, expanding transition temperature range, adjusting transition temperature, and reducing hysteresis losses. The thermodynamics of multifield and coupled-caloric effect are presented in the meantime. On the other hand, materials with abnormal thermal expansion (zero thermal expansion, negative thermal expansion) have important applications in precision manufacturing. The phase transition and lattice effect dominated by magnetic atoms in the giant magnetocaloric materials with strong magnetic-crystal coupling provide an ideal platform for exploring abnormal thermal expansion. This paper also introduces our recent research on abnormal thermal expansion in magnetocaloric materials, and looks forward to future relevant research.

Keywords:

Authors and contacts

1.
State Key Laboratory of Magnetism, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2.
Ningbo Institute of Materials Technology & Engineering, Chinese Academy of Sciences, Ningbo 315201, China
3.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
4.
Songshan Lake Materials Laboratory, Dongguan 523808, China

Corresponding author: Hu Feng-Xia, fxhu@iphy.ac.cn ; Shen Bao-Gen, shenbg@iphy.ac.cn

Funds: Project supported by the Science Center of the National Science Foundation of China (Grant No. 52088101), the National Natural Sciences Foundation of China (Grant Nos. 92263202, U23A20550, 51971240), the National Key Research and Development Program of China (Grant Nos. 2021YFB3501202, 2019YFA0704900, 2021YFA1400300, 2022YFB3505201), and the Strategic Priority Research Program B of Chinese Academy of Sciences (Grant No. XDB33030200).

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Cited By

图 1 LaFe_11.6Si_1.3化合物通过(a)核共振非弹X射线散射和(b)密度泛函理论计算得到的晶格熵随温度的变化曲线, 以及由此得到的(c)德拜温度Θ_D随温度的变化曲线^[71]; (d) 利用德拜近似得到的La(Fe_0.92Co_0.08)_11.9Si_1.1化合物的德拜温度Θ_D随温度的变化曲线^[31]

Figure 1. Temperature dependence of the experimental (a) and DFT-computed (b) vibrational entropy S_latt (T) of the Fe sublattice for LaFe_11.6Si_1.4 compound; (c) temperature dependence of the Debye temperature Θ_D of the LaFe_11.6Si_1.4 compound^[71]; (d) temperature dependence of Θ_D for La(Fe_0.92Co_0.08)_11.9Si_1.1 calculated using the Debye approximation^[31].

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图 2 La(Fe_0.92Co_0.08)_11.9Si_1.1化合物在不同压力下(a)磁热熵变 (磁场0—2 T, 0—5 T)和(b)压热熵变随温度的变化; (c)物理压力和H原子引入的化学压力对原子局域环境影响的对比示意图^[31]

Figure 2. For the La(Fe_0.92Co_0.08)_11.9Si_1.1 compound, (a) entropy change for the magnetic field changes of 0–2 T and 0–5 T under different pressures, and (b) entropy change for different pressure changes as a function of temperature; (c) schematic diagram indicating the variations of atomic local environments caused by physical pressure and chemical pressure^[31].

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图 3 (a) 不同物理压力下La(Fe_0.92Co_0.08)_11.9Si_1.1化合物晶胞体积随温度的变化曲线, 插图给出了相变过程中相对体积变化ΔV/V随压力的变化曲线; (b) 不同压力下中子衍射(531)^±特征峰的峰强计数随温度的变化曲线^[31]

Figure 3. (a) The lattice volume as a function of temperature for La(Fe_0.92Co_0.08)_11.9Si_1.1 compound under different pressures. Inset shows the relative volume change ΔV/V as a function of pressure; (b) neutron intensity (with error bars) of the (531)^± reflection as a function of temperature under different pressures^[31].

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图 4 0 kbar和9 kbar物理压力下La(Fe_0.92Co_0.08)_11.9Si_1.1化合物的顺磁态电子态密度在费米能级处的分布情况; 插图给出了0 kbar和9 kbar压力下的顺磁态总电子态密度曲线^[31]

Figure 4. The details of total density of states near the Fermi level E_F of La(Fe_0.92Co_0.08)_11.9Si_1.1 compound in the nonmagnetic state under pressures 0 and 9 kbar. The inset shows the total DOS in the nonmagnetic state, the Fermi energy is shifted to zero^[31].

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图 7 HoCuSi化合物不同物理压力下相变温度附近的等温磁化曲线　(a) 0 kbar, (b) 6.6 kbar, (c) 9.0 kbar; HoCuSi化合物在不同磁场变化、不同压力下的磁热熵变随温度的变化曲线 (d) 0—1 T, (e) 0—2 T, (f) 0—5 T^[32]

Figure 7. Magnetization isotherms of HoCuSi measured on increasing and decreasing fields under (a) 0 kbar, (b) 6.6 kbar, (c) 9.0 kbar, where the arrows indicate the ramping direction of magnetic field; entropy change under different pressures at (d) 0–1 T, (e) 0–2 T, and (f) 0–5 T magnetic field change^[32].

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图 5 HoCuSi化合物正弦波调制的反铁磁基态

Figure 5. The AFM ground state of HoCuSi compound with a sin wave modulation spin structure.

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图 6 (a)不同物理压力下HoCuSi化合物在0.01 T磁场时的升温(ZFC)和降温(FC)过程中的热磁曲线, 插图为不同物理压力下的磁化率倒数(1/χ)与温度的关系; (b) 基于(a)图中M-T曲线, 根据居里-外斯定律推导得到的有效磁矩M_eff以及顺磁居里温度θ_P压力依赖关系^[32]

Figure 6. (a) Temperature dependences of the ZFC and FC magnetizations for HoCuSi in a magnetic field of 0.01 T under different pressures. The inset shows 1/χ–T curves under different pressures; (b) the pressure dependences of paramagnetic Curie temperature θ_P and effective magnetic moment M_eff derived from the M-T curves in Fig.6(a)^[32].

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图 8 PrGa化合物在环境压力下晶胞参数随温度的变化曲线, 其中箭头指向自旋重取向温度T_SR和居里温度T_c (a) 晶胞参数a; (b) 晶胞参数b; (c) 晶胞参数c; (d) Pr³⁺的磁矩沿c轴(M_c)的投影^[81]

Figure 8. Temperature dependence of the lattice parameter (a) a, (b) b, (c) c, where the arrows indicate the positions of T_SR and T_c; (d) the projection of the magnetic moment along the c axis (M_c) ^[81].

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图 9 (a) 不同物理压力下PrGa化合物在0.5 T磁场时的升温(ZFC)和降温(FC)过程中的热磁曲线, 其中插图显示了T_SR和T_c与压力的关系; (b) PrGa化合物在5 T磁场下的磁化强度随温度的变化曲线, 插图给出了不同压力下的dM/dT曲线^[81]

Figure 9. (a) Temperature dependence of the ZFC and the FC magnetization for PrGa under a field 0.5 T, where the inset shows the dependence of T_SR and T_c on the application of pressure; (b) temperature dependence magnetization for PrGa under a field 5 T, where the inset shows the corresponding dM/dT curves under different pressures^[81].

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图 10 不同物理压力下PrGa化合物在磁场变化为0—1 T和0—5 T时的等温磁热熵变随温度的变化曲线^[81]

Figure 10. Temperature dependences of magnetic entropy change under 0 kbar, 3.5 kbar, 11.4 kbar for the field changes of 0–1 T and 0–5 T, respectively^[81].

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图 11 FeRh/PMN-PT异质结XRD图谱、球差电镜结果及PMN-PT多畴结构示意图　(a) FeRh(011)/(001)PMN-PT与(b) FeRh(001)/(011)PMN-PT异质结室温下的XRD图谱; (c) (001)PMN-PT单晶多畴结构示意图以及(d)不同铁电畴和FeRh畴在(001)面内晶胞参数示意图; (e) (011)PMN-PT单晶多畴结构示意; (f) FeRh(001)/(011)PMN-PT异质结横截面的球差电镜HAADF图像, 标尺是2 nm, 右侧展示了相应的α-FeRh、缓冲层和PMN-PT原子排列示意图; 界面附近(g) Fe (绿色)和(h) Pb (蓝色)的EDX元素分布图; (i)界面尖晶石结构缓冲层形成示意图, ABO₃钙钛矿结构的PMN-PT中Pb (红色原子)挥发, 产生空位, 与其相邻的原子偏移, 薄膜生长过程中界面处Fe原子渗入基片表面的空位中, 形成尖晶石结构的缓冲层^[33]

Figure 11. The XRD patterns of (a) FeRh(011)/(001)PMN-PT and (b) FeRh(001)/(011)PMN-PT heterostructure at room temperature; (c) configuration of spontaneous polarization vectors along body diagonals shown by arrows for (001)-oriented PMN-PT single crystal and (d) the projections of ferroelectric domains r1/r3 and r2/r4 in the (001)-plane and the corresponding FeRh domains in (011)-plane; (e) configuration of spontaneous polarization vectors along body diagonals shown by arrows for (011)-oriented PMN-PT single crystal; (f) cross-sectional STEM HAADF image of FeRh(001)/(011)PMN-PT heterostructure and the corresponding atomic arrangement of α-FeRh, buffer layer and PMN-PT; EDX mapping of (g) Fe (green) and (h) Pb (blue) element distribution at the interface, where the scale bar is 2 nm in length; (i) schematic diagram of spinel buffer layer formation. Pb atoms (red) in the ABO₃ perovskite PMN-PT volatilize at high temperature, and Pb vacancies appear, which give rise to the skewing of adjacent atoms. During film growth, Fe atoms at the interface permeate into Pb vacancies, facilitating the formation of a buffer layer with spinel structure^[33].

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图 12 (a) (011)FeRh/(001)PMN-PT异质结中在电场调控下FeRh薄膜0—5 T磁场的磁热熵变随温度的变化; (b) (001)FeRh/(011)PMN-PT异质结中在电场调控下FeRh薄膜0—5 T磁场的磁热熵变随温度的变化^[33]

Figure 12. The comparison of ΔS curves at 0–5 T under different electric field, where the corresponding refrigeration temperature spans are marked for (a) (011)FeRh/(001)PMN-PT and (b) (001)FeRh/(011)PMN-PT^[33].

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图 13 AMR 循环设计示意图　(a)磁场电场双场激励的AMR 循环示意图; (b)通过PMN-PT基片的铁电畴翻转/相变调控FeRh 薄膜的ΔS-T 曲线^[33]

Figure 13. Schematic diagram of AMR cycle: (a) Schematic diagram of dual field stimulated AMR cycle; (b) the ΔS-T curves of FeRh layer tuning by FE domains of PMN-PT substrates^[33].

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图 14 引入应变记忆效应的实验测量　(a) FeRh(001)/ PMN-PT(011)异质结测量模型示意图, 其中H和E分别表示施加的磁场和电场; (b) 在5 T和310 K下FeRh薄膜磁化强度随电场的变化曲线, A—B, 施加–6 kV/cm电场由基片引入的压应变使部分FM相转化为AFM相, 磁化强度下降, B—C, 移去–6 kV/cm电场, 应变记忆效应使磁化强度近似保持不变, C—D, 施加+6 kV/cm电场释放应变使部分AFM相回到FM相, 磁化强度上升, D—A, 移去+6 kV/cm电场, 应变记忆效应使磁化强度近似保持不变; (c) 零电场下前两圈磁场循环FeRh薄膜磁化强度随磁场的变化曲线; (d) 在5 T和0 T恒定磁场下施加脉冲电场FeRh薄膜磁化强度随磁场的变化曲线. 假设脉冲电场产生的应变更大, 路径6将沿路径6' 或路径6''. 可以看出, 由路径5—6, 5—6', 5—6''围成的面积远小于图(c)中3—4围成的面积甚至变成负的(路径5, 6, 6', 6''仅有磁场没有电场), 表示应变记忆效应导致的滞后损耗的非易失性大幅下降, 其来源于应变产生的机械功的补偿作用, 下部分的图对应于上述过程中磁场和电场随时间的变化曲线^[34]

Figure 14. Regulation of hysteresis loss by non-volatile strain: (a) Sketch of the FeRh/PMN-PT heterostructure; (b) the loop-like M–E curve measured at 5 T and 310 K; (c) M–H curves in the absence of electric field; (d) M–H curves with a pulse electric field 0 → – 6 → 0 kV/cm applied at 5 T. Supposing the produced strain could be larger, path 6 would be along path 6' or path 6'' instead, and then the enveloped area by path 5–6' or 5–6'' would approach zero or turn out to be inverse. Lower panel, an exploded diagram corresponds to the above processes^[34].

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图 15 FeRh层向Cu层和PMN-PT层热传导示意图　(a)以Cu为传热介质时, 有限元模拟得到的Cu层, FeRh层和PMN-PT层的温度随时间的变化结果; (b)热量从FeRh层传导到传热介质(Cu层)和PMN-PT基片层的示意图^[34]

Figure 15. Schematic diagram of heat flow from FeRh to Cu and PMN-PT: (a) Taking Cu as the heat medium, temperature evolution with time indicated by colors for the 3 layers of Cu, FeRh, and PMT-PT based on finite element simulation; (b) schematic diagram of heat flow from FeRh film to the heat transfer medium (Cu) and the PMN-PT substrates^[34].

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图 16 (a) 373 K, FeRh合金的温度和交变磁场的强度随时间的变化; (b) 373 K, FeRh合金在1.8 T磁场820次循环下绝热温变随时间的变化曲线; (c) α-FeRh相边界TEM图像, 右上角为选定区域的电子散射图谱; (d), (e)是与(c)相同区域的暗场TEM图谱, 其中(d), (e)分别允许FeRh$[0\overline{11}] $和γ-FeRh $[2\overline{41}] $ 散射点通过物镜孔径; (f) 不同频率下FeRh合金的功率密度SCP随温度的变化曲线, 插图为SCP峰值随频率的依赖曲线^[35]

Figure 16. (a) Temperature of FeRh alloys and the alternative magnetic field as a function of time at T = 373 K; (b) time dependence of adiabatic temperature change ΔT for FeRh alloys at 373 K under 820 cycles of 1.8 T magnetic field; (c) TEM image at the position of phase boundaries for α-FeRh, the inset shows the corresponding selected area electron diffraction (SAED) pattern; (d), (e) dark-field TEM images recorded from the same region as (c), where the diffraction spots of (d) α-FeRh $[0\overline{11}] $ and (e) γ-FeRh $[2\overline{41}] $ are allowed to pass through the hollow objective apertures; (f) temperature dependent SCP curves under different frequency, the inset shows the peak value of SCP as a function of frequency^[35].

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图 17 Ni₅₀Mn₃₅In₁₅合金　(a)耦合热熵变; (b)通过在不同压力下麦克斯韦关系计算得到的多卡熵变(黑色)和通过常压下磁热熵变与耦合热熵变的加和得到的多卡熵变(红色)^[36]

Figure 17. For Ni₅₀Mn₃₅In₁₅ alloy: (a) Two-dimensional plots of the coupled caloric effect ΔS_cp=$ \displaystyle\int _{0}^{{H}_{0}}\int _{0}^{{P}_{0}}\frac{\partial {\chi }_{12}}{\partial T}{\mathrm{d}}P{\mathrm{d}}H $ as a function of pressure and temperature under a magnetic field change of 5–0 T; (b) comparison of the entropy change at ambient pressure adjusted by the coupled effect [S_{0 GPa}(T, 5 T–0) + S_cp(T, P, 5 T–0), black curves] and magnetocaloric results at a specific pressure [S(T, P, 5 T–0), red curves] calculated using Maxwell’s relation^[36].

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图 18 环氧树脂粘结(a)前和(b)后各粉末样品的M–T曲线; 环氧树脂粘结压片的(c) Mn_0.97In_0.03CoGe, MnCo_0.98Cr_0.02Ge, (d) MnCoGe_0.99和MnCoGe_0.99In_0.01粉末样品的线性热膨胀系数^[52]

Figure 18. Temperature dependence of magnetization under a magnetic field of 0.3 T for (a) as-prepared and (b) bonded samples; temperature dependence of linear thermal expansions ΔL/L for bonded samples with compositions (c) Mn_0.97In_0.03CoGe, MnCo_0.98Cr_0.02Ge, and (d) MnCoGe_0.99, MnCoGe_0.99In_0.01^[52].

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图 19 MnCoGe_0.99In_0.01合金　(a) P5样品的扫描电子显微镜、高分辨透射电子显微镜和通过傅里叶变换得到的电子散射图像; (b)粘结的粉末样品和块材的线性热膨胀率, 颗粒尺寸: P1(10—20 μm), P4(2—5 μm), P3(1—2 μm)和P5(0.3—1.0 μm)^[53]

Figure 19. For MnCoGe_0.99In_0.01 alloy: (a) SEM image, high-resolution TEM image, and electron diffraction pattern from Fourier transform, P5 (0.3–1.0 μm), circled regions by the white line indicate the nanocrystallites; (b) linear thermal expansion $ {{\Delta }}L/L $ for the bonded particles compared with the bulk (the reference temperature is 390 K). Particle size: P1 (10–20 μm), P3 (2–5 μm), P4 (1–2 μm), and P5 (0.3–1 μm). The inset shows the morphology of the bonded particles^[53].

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图 20 Mn_0.87Fe_0.13NiGe合金的磁相图^[54]

Figure 20. Magnetic phase diagram of Mn_0.87Fe_0.13NiGe^[54].

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图 21 Mn_0.87Fe_0.13NiGe合金的(a)磁结构、晶体结构以及(b)负热膨胀行为; MnCoGe_0.99In_0.01合金的(c)磁结构、晶体结构以及(d)负热膨胀行为^[55]

Figure 21. The comparison between the magnetic structure, crystal structure, measured $ \Delta L/L $, and the calculated $ (\Delta L/L)_0$ = $( \Delta V/V)_3 $ for bonded (a), (b) Mn_0.87Fe_0.13NiGe and (c), (d) MnCoGe_0.99In_0.01^[55].

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图 22 Gd_x(Ho_0.5Dy0.5)_1–xCo₂合金体系的不同组分(x = 0, 0.1, 0.3, 0.5)在(a) 0—2 T和(b) 0—5 T磁场下的磁熵变随温度的变化^[98]

Figure 22. For Gd_x(Ho_0.5Dy_0.5)_1–xCo₂ compounds, entropy change ΔS under (a) 0–2 T and (b) 0–5 T magnetic field change for the samples with various Gd contents, x = 0, 0.1, 0.3, 0.5^[98].

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图 23 Gd_x(Dy_0.5Ho_0.5)_1–xCo₂合金体系(a)菱方亚铁磁结构和(b)立方顺磁结构的示意图, 其中箭头方向表示磁矩的方向; 该体系(c)x = 0和(d)x = 0.5的组分的变温XRD图谱, 该体系x = 0, 0.3, 0.5的组分的晶格体积(e)和晶格参数(f)随温度的变化, 其中线性热系数α_l和相应的操作间隔ΔT已标记^[98]

Figure 23. The sketches of (a) rhombohedral FIM and (b) cubic PM structure of Gd_x(Dy_0.5Ho_0.5)_1–xCo₂ compounds. Arrows indicate the directions of magnetic moments. The variable temperature XRD patterns around the cubic (311) and (222) peaks of Gd_x(Ho_0.5Dy_0.5)_1–xCo₂ for (c) x = 0 and (d) x = 0.5, where the blue balls marked on the peaks’ top and the lines guide eyes. Temperature dependence of (e) the lattice volume and (f) the lattice parameters for x = 0, 0.3, 0.5, where the linear thermal coefficients α_l and the corresponding operation intervals ΔT are marked^[98].

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