Authors: Radel Gimaev1, Dmitry Kopeliovich2, Yury Spichkin2 and Alexander Tishin2,3
1 - National Research Center "Kurchatov Institute", 123182, Moscow, Russia
2 - Advanced Magnetic Technologies and Consulting LLC, Troitsk, Moscow, Russia
3 - Faculty of Physics, M.V. Lomonosov Moscow State University, 119991 Moscow, Russia
Published in "Journal of Magnetism and Magnetic Materials" №459 (2018).
Abstract.
The adiabatic temperature change, magnetization, heat capacity and thermal conductivity coefficient of a set of commercial purity heavy rare earth metals were measured. The temperature and magnetic field dependences of the adiabatic temperature change and magnetization were measured by direct and induction methods, respectively, in dynamic mode closely corresponding to the operational conditions of working magnetic refrigerators. The temperature dependences of the heat capacity and thermal conductivity coefficient in a constant magnetic field were measured by adiabatic calorimetry and steady-state methods. The obtained experimental results were compared with the literature data on high-purity heavy rare earths magnetothermal properties. The possible effect of the material purity on magnetic refrigerators parameters and ability to use the commercial purity materials in such devices are discussed.
1 Introduction
Rare earth (RE) metals and their alloys are of great interest to researchers, especially from the point of view of the physics of magnetic phenomena. The reason for the active research of heavy RE materials is their exceptional magnetic and magnetothermal properties, which has contributed to our understanding of the physics of magnetic phenomena. In addition, studying of the properties of RE metals has practical importance. These metals are used in many fields of technology. Some of the practical applications are connected with the large magnetocaloric effect (MCE) in Gd and its alloys. Today Gd is used in prototypes of magnetic refrigerators [1–7]. Additionally, a number of articles presenting the medical applications of MCE have been published [8,9]. Magnetocaloric properties of other heavy RE metals do not find the practical applications. However, studying of their magnetic and magnetothermal properties are interesting for elucidation of fundamental basics of magnetism in RE.
The highest values of adiabatic temperature change (ΔT) and largest and sharpest jumps in temperature dependences of magnetization (M), heat capacity (C) and thermal conductivity coefficient (k) are observed in high-purity materials. A number of experimental results for polycrystalline and single-crystalline heavy RE metals with high purity are presented in [10–16]. The preparation of high-purity materials is a time-consuming procedure and greatly affects the final cost of materials. At the same time, for a real magnetic refrigerator, a large amount of magnetocaloric materials are required. Current developed prototypes of magnetic refrigerators use up to 2.8 kg of magnetocaloric materials, such as Gd, GdEr, GdTb, GdDy, GdY as a working body [1–7]. Therefore, the commercial magnetic refrigerators will be packed with polycrystalline materials with commercial purity (about 99.5 at. %) and therefore investigation of these materials is of great interest. The main objective of this work is to detect the possible effects of the commercial purity of heavy RE materials on the parameters of magnetic refrigerators. The steps for this are as follows: (1) complex study of magnetocaloric properties of Gd and Tb samples for and (2) comparison of measurement results with literature data for RE metals of different purity.
2 Materials and methods
Polycrystalline samples of heavy RE metals Gd and Tb had commercial purity (99.5 at. %). Each sample was cut to four different pieces with dimensions of 9mm × 4mm × 1mm (for MCE measurements), 3mm × 1mm × 1mm (for magnetization measurements), 4mm × 4mm × 5mm (for heat capacity measurements) and 4mm × 2mm × 20mm (for thermal conductivity measurements).
Measurements of MCE, magnetization, heat capacity and thermal conductivity were made using universal setup for measurements of magnetization and magnetothermal properties (AMT&C LLC, Russia). A schematic drawing of this setup is showed in Fig. 1(e). The experimental setup includes the following main parts:
- Halbach-type magnetic field source (3) remotely controlled by PC;
- Liquid nitrogen Dewar (1);
- Data acquisition and measurements control system based on temperature controller, digital voltmeters and power supply, remotely controlled by PC with measurements software;
- Four measuring inserts with different sample holders for measurements of temperature and magnetic field dependences of the adiabatic temperature change (Fig. 1(a)), temperature and field dependences of the magnetization (Fig (b)), temperature dependences of heat capacity (Fig. 1(c)) and temperature dependences of thermal conductivity coefficient (Fig. 1(d)) in constant magnetic field.
Fig. 1. Sample holders of measuring inserts for (a) MCE measurements, (b) magnetization measurements, (c) heat capacity measurements and (d) thermal conductivity measurements; (e) schematic drawing of universal setup for measurements of magnetization and magnetothermal properties.
Each of the four sample holders contained a resistive temperature sensor and heater connected to PID temperature controller for temperature stabilization and control. The magnetic field was measured by either Hall sensor (ΔT(H,T), C(T), k(T) measurements) or measuring coil (M(H,T) measurements). The adiabatic temperature change ΔT was measured by differential thermocouple. For heat capacity and thermal conductivity the resistive temperature sensor was used. The inserts for heat capacity and thermal conductivity measurements contained a measuring heater thermally connected to the sample.
The measuring inserts were placed inside the outer case, which then was evacuated to vacuum of 10-3 torr.
The universal setup created by AMT&C LLC allows for fully automatic measurements of MCE, heat capacity, magnetization and thermal conductivity coefficient of magnetic materials in the temperature range of 80 K – 360 K and for changing or static magnetic fields up to 1.8 T.
Direct MCE measurements were conducted at constant stabilized temperatures in changing magnetic field. Adiabatic temperature change and magnetic field were synchronously measured during the changing magnetic field. Thus, two time-varying signals (temperature and field) and one stable value (stabilized temperature of sample) were recorded in the MCE measurements. Measurements of adiabatic temperature change were conducted in a dynamic mode, when the ΔT and H values simultaneously and continuously are recorded in changing magnetic field. In addition, the method presented allows one to conduct the measurements during several changing magnetic field cycles.
Heat capacity measurements were performed by the adiabatic method, which consist of recording the time-varying temperature of the sample after pulsed heating. If the sample is in adiabatic conditions, after heat pulse the heat capacity (C) is obtained from the values of temperature increase (ΔTC) and the heat transferred to the sample (ΔQC):
The heat capacity measurements were conducted in constant magnetic field. Thus, in the heat capacity measurements, two time-varying signals (temperature and heater current) and one stable value (magnetic field) were recorded.
The thermal conductivity was measured by steady-state method [11]. In this method, the steady heat flow through the sample was created by the heater mounted on the “hot” side of the sample and copper heat sink on the “cold” side. The heat flow (ΔQk/Δt) can be determined as:
where k is thermal conductivity coefficient, A is cross-sectional area of sample, ΔTk is the temperature difference between hot and cold sides of sample, L is length of the sample. Thus, the temperature difference and heat flow, which equals to heater power, can be measured and the thermal conductivity coefficient is obtained by formula (2). The two time-varying values (temperature and heater current) and one stable value (magnetic field) were recorded.
Magnetization was measured using an induction method [12]. The sample holder (Fig. 1b) includes two identical coils. The sample is mounted inside one of these coils and placed in a changing magnetic field. The magnetization is measured by detecting the current induced in the coil due to the changing magnetic moment of the sample. The second coil is used to subtract the signal induced by the changing magnetic field on the coil from the signal of the coil with sample. Additionally, the magnetic field is measured by the second coil. Thus, in magnetization measurements two time-varying values (magnetization and magnetic field) and one stable value (temperature) are recorded.
Because each measured signal is time-varying or at constant voltage, the measurements of different properties were conducted using the universal setup presented above. Thereby, in the universal setup for measurements of magnetization and magnetothermal properties, the same hardware (except for measuring inserts) was used for different measurements: MCE, heat capacity, thermal conductivity coefficient and magnetization. It is important in complex investigation of magnetocaloric effect to conduct measurements of different properties under the same conditions for the same samples. Such measurements can be made in one universal measuring setup. The measurements control, data acquisition, representation and saving are provided by four control programs developed on the LabVIEW platform.
3 Results and discussion.
For comparison of the magnetocaloric response of commercial polycrystalline materials and high-purity samples, three main parameters can be investigated and discussed: adiabatic temperature change ΔT, isothermal magnetic entropy change ΔSM and relative cooling power RCP(S). In the present work the ΔT was measured directly using a universal setup. The temperature dependences of ΔSM were calculated indirectly from isothermal M(H) curves using the Maxwell relation:
The M(H) curves were experimentally measured using universal setup for measurements of magnetization and magnetothermal properties.
Fig. 2 shows the experimental ΔT(H) curves for commercial Gd (a) and Tb (b) at temperatures in the vicinity of magnetic phase transition and was measured directly as magnetic field was increased up to 1.8 T.
Fig. 2. The ΔT(H) dependences of polycrystalline Gd and Tb with commercial purity, the inserts display the ΔT(T) curves (blue circles) obtained from measurements for a field change of 1.8 T and literature data [12,17] for high purity (99.96 wt.%) samples (black lines).
Curves display similar behavior: adiabatic temperature change is increased nonlinearly and reaches the maximum value of 4 K at 292.7 K for Gd and 6.4 K at 231.4 K for Tb. By comparing this dependences with the ΔT(T) curves for high-purity (99.98 wt. %) Gd and Tb presented in [12,17] it can be seen that dependences for commercial samples have more linear character and about 15 % lower maximum values of ΔT: 4 K and 4.8 K for commercial and high-purity Gd, 6.4 K and 7.2 for commercial and high-purity Tb, for at H=1.8 T respectively. Results of direct MCE measurements under conditions in real magnetic refrigerator were also presented in [18]. It was shown that the efficiency of magnetic refrigerators can be improved by increasing of frequencies of operating cycles in case of Gd as a working body.
The field dependences of magnetization are showed at fig. 3. Magnetization measurements were conducted at dynamic mode, when magnetic field was changed during several field cycles.
Fig. 3. The M(H) dependences of polycrystalline Gd and Tb with commercial purity.
Isothermal magnetic entropy change was calculated from magnetization dependences using relation (3).
The temperature dependences of isothermal magnetic entropy change are displayed in fig. 4.
Fig. 4. The ΔSM(T) dependences of Gd (a) and Tb (b) with commercial purity (solid lines) and high-purity (dashed lines). Data for high-purity materials are obtained from [11,19]
Comparing with the high purity materials the maximal ΔSM value is about 18% lower.
The RCP(S) values were obtained as RCP(S) = (ΔSM)MAX × TFWHM, where (ΔSM)MAX is a maximum value in temperature dependence of isothermal magnetic entropy change and TFWHM is full-width at a half maximum.
RCP(S) values (fig. 5) for high-purity samples were about 12% larger comparing with commercial samples. It is important to note, that although the maximal values in ΔSM(T) dependences are smaller for commercial materials, the curves are wider and the TFWHM values are greater for commercial Gd and Tb samples. Due to this fact, the difference between RCP(S) it not large. As an example, the determination of the RCP(S) for commercial and high-purity Gd for 0 – 1.8 T field rise is shown at fig. 6. Additionally, fig. 6 shows that the increasing of materials purity leads to increase the maximal value of ΔSM. At the same time, the materials with lower purity (99.5 at.%) display the wider ΔSM(T) peak (FWHM is 41 K for commercial purity and 37 K for high-purity Gd in fig. 6). It should be noted that the wider ΔSM(T) peak leads not only to increase the efficiency of magnetocaloric material (RCP(S) value), but also to broadening of its working range in magnetic refrigeration.
Fig. 5. The RCP(S) at different magnetic field changes for Gd (a) and Tb (b) with commercial purity (red points and line) and high-purity (black points and line). Data for high-purity materials are obtained from [10,11,19].
RCP(S) values (fig. 5) for high-purity samples were about 12% larger comparing with commercial samples. It is important to note, that although the maximal values in ΔSM(T) dependences are smaller for commercial materials, the curves are wider and the TFWHM values are greater for commercial Gd and Tb samples. Due to this fact, the difference between RCP(S) it not large. As an example, the determination of the RCP(S) for commercial and high-purity Gd for 0 – 1.8 T field rise is shown at fig. 6. Additionally, fig. 6 shows that the increasing of materials purity leads to increase the maximal value of ΔSM. At the same time, the materials with lower purity (99.5 at.%) display the wider ΔSM(T) peak (FWHM is 41 K for commercial purity and 37 K for high-purity Gd in fig. 6). It should be noted that the wider ΔSM(T) peak leads not only to increase the efficiency of magnetocaloric material (RCP(S) value), but also to broadening of its working range in magnetic refrigeration.
Fig. 6. The RCP(S) values determination for Gd of high-purity (black) and commercial purity (red) at magnetic field changing of 0 – 1.8 T. Data for high-purity materials are obtained from [19].
Heat capacity was measured for Gd commercial sample at zero magnetic field. Obtained results show that the jump near Curie temperature is more sharply for high-purity material. For complex MCE investigation it is important to conduct a different measurements in the same conditions. As can be seen from fig. 7 the Gd has the sharp jump thus the small differences at the conditions can lead to large disagreements between data of heat capacity measurements and adiabatic temperature change, which connected by relation:
Fig. 7. C(T) at zero magnetic field measured for commercial (open circles) and high-purity Gd (dashed line).
Thermal conductivity measurements were made at room temperature for Gd sample. The measurements of thermal conductivity at room temperature given the value of 9.8 W/K*m for commercial Gd. This value is insignificantly lower (2 %) than for high-purity single-crystalline Gd [20].
The comparison of main magnetocaloric parameters adiabatic temperature change, isothermal magnetic entropy change and RCP(S) for commercial and high-purity Gd and Tb shows that the values for high-purity materials are larger to about 15 % for ΔT, 18 % for ΔSM and 12 % for RCP(S). For more representative comparison of the efficiency of magnetocaloric material in magnetic refrigeration the RCP(S) values should be considered. This is due to the fact, that RCP(S) includes both maximal value of magnetocaloric parameter and its width on the temperature dependence. Thus, numeric value RCP(S) directly shows the efficiency of the magnetocaloric material in magnetic refrigeration and can be used as a numeric parameter of magnetocaloric material’s efficiency. Taking it into consideration Gd and Tb display the degradation of 12% of its efficiency with decreasing of purity from 99.98 at.% to 99.5 at.%. At the same time, the preparation of high-purity materials is significantly more expensive procedure. Thus, the wide using of magnetic refrigerators will be apparently connected with magnetocaloric materials of commercial purity. The issue about using the commercial purity materials is compromise between the cost of magnetic refrigerator and its efficiency.
4 Conclusion.
The complex study of magnetocaloric properties generally includes the direct measurements of adiabatic temperature change and measurements of magnetization and heat capacity. It is important to measure the different properties under the same conditions using the same samples. The best solution is to measure the different properties in one universal setup.
For practical applications of MCE in magnetic refrigeration, it is important to make measurements under the same conditions as those in magnetic refrigerators- with changing magnetic field during several magnetic field cycles.
The measurements of adiabatic temperature change, magnetization, heat capacity and thermal conductivity were made for polycrystalline Gd and Tb with commercial purity. Fully automatic measurements of these properties were conducted under identical conditions using the same samples in a universal setup for magnetization and magnetothermal measurements. Measurements of adiabatic temperature change and magnetization were conducted in a dynamic mode. It is important to note that the Gd and Tb samples were measured in conditions close to those of a working body in a magnetic refrigerator. Isothermal magnetic entropy change and relative cooling power values were obtained from magnetization data.
Comparison of the obtained results for polycrystalline commercial samples with results of high-purity samples shows that using high-purity samples in magnetic refrigerators allows an increase in efficiency of up to 12 %. Improvement of the purity of the material leads to an increase of the RSP(S) value to 12%. At the same time, material with lower purity (99.5 at.%) shows a wider peak on ΔSM(T) dependence. Thus, commercial purity materials have a more comprehensive working temperature range for use in magnetic refrigeration.
Work at Advanced Magnetic Technologies and Consulting LLC is supported by Skolkovo Foundation, Russia. Authors acknowledge support by the AMT&C Group Ltd., UK.
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