Paper Research: Magnetocaloric Effect and Crystalline Materials for Magnetic Refrigeration

Transcription

1 1-1 Paper Research: Magnetocaloric Effect and Crystalline Materials for Magnetic Refrigeration Xinkai Qiu Keywords Magnetic entropy, magnetocaloric effect, crystalline, phase transition. Abstract In recent years, applying the magnetocaloric effect to refrigeration as an alternative for the vapor-compression refrigerator has raised interest in research on magnetocaloric response materials. This paper will mainly focus on the crystalline materials which have been reported in the past two decades. A critical review of the potential candidates, especially rare earth-free materials, is provided.

2 List of Content I. Introduction II. Crystalline materials containing rare earth elements A. Laves Phases B. La[Fe(Si,Al)] 13 family C. Gd 5 (Si,Ge) 4 family D. Ferromagnetic lanthanum manganites E. Other crystalline compounds containing rare earth metals III. Rare earth-free materials A. Heusler alloys B. Mn-TM-(Si, Ge) compounds C. (Mn, TM) 5 X 3 compounds D. MnAs alloys E. FeRh alloys F. Other rare earth-free crystalline compounds IV. Discussion over potential candidates V. Summary and conclusion Acknowledgment References

3 I. Introduction The magnetocaloric effect is defined as the reversible temperature change of a magnetic material upon the application or removal of a magnetic field [1]. In Franco s review, the first reported discovery is attributed to the German physicist E. Warburg in 1881 [2]. But doubt remains as some suggest that the discovery of the effect should be attributed to the French physicist P. Weiss and Swiss physicist A. Piccard in 1917 [3,4]. After the fundamental principle was suggested by P. Debye in 1926 and W. Giaoque in 1927, it immediately drew attention to another possibility of lowering temperature. In fact, the magnetocaloric effect has been employed to achieve ultralow temperature in research laboratories. However, society is not satisfied with this narrow application as energy has already become an inevitable problem. The most commonly used refrigerator units follow the principle of the reverse Carnot cycle which is based on the compression and expansion of gas and yield only 40% of the ideal efficiency with the best of their kind. In comparison, if the magnetocaloric effect could be applied in commercial use, the efficiency of the refrigerator will rise to 60% which helps a lot in energy saving. Furthermore, unlike vapor-compression refrigerators, no refrigerant gases are required in magnetic refrigerators, which contribute to ozone layer protection and will be considered as environmentally friendly. In recent years, several models of magnetic refrigerators were successfully built to prove that this technology is feasible [5-8]. But as the researchers tried to meet the requirements for conventional use, they started to come across all kinds of problems. Thermal and magnetic hysteresis is always a challenge for materials that exhibit the magnetocaloric effect. Another particular challenge is that a high performance device requires a better refrigerant whose potential of being selected as candidate will be discussed in this article. A typical magnetic refrigeration cycle is analogous to the reverse Carnot cycle. The refrigerant, which is the working material, starts in thermal equilibrium in an adiabatic environment (Figure 1a). Figure 1. The four stages of a magnetic refrigeration cycle: (a) adiabatic magnetization, (b) remove heat, (c) adiabatic demagnetization, and (d) cool refrigerator contents [1]. In the stage of adiabatic magnetization, an increasing external magnetic field causes the magnetic moments of the atoms to align parallel, thereby decreasing the magnetic entropy and increasing the lattice entropy accordingly. As a result, the temperature of the magnetocaloric material increases. In the later stage, a heat transfer fluid is employed to remove the heat by cooling the material back to its initial temperature. Depending on the target temperature, the choice of fluid varies. In order to achieve ultra-low temperature, liquid helium is required. Usually, water is commonly chosen for working close to room temperature. During the heat removal stage, the magnetic field is held constant to prevent the magnetic moments from changing. After the magnetocaloric material is sufficiently cooled, it will be separated from the liquid. In 1

4 adiabatic demagnetization, the magnetic field is decreased so that the lattice entropy decreases as well as the temperature. Later on, the magnetic field is held constant again to prevent the refrigerant from heating as it will be placed in thermal contact with the environment to transfer heat since the working material is cooler than the environment. By performing these four stages cyclically, one is able to construct a magnetic refrigerator. In order to characterize a magnetocaloric material, a list of standards including parameters needs to be established. The most straightforward parameter is the adiabatic temperature change ΔT ad, which is defined as the temperature change of the material when adiabatically magnetized/demagnetized. Furthermore, the magnetic entropy change ΔS M also plays a role in the characterization of a candidate. It is quite intuitive that a suitable candidate for magnetic refrigeration should have a large ΔS M. In Franco s review, Equations 1 and 2 are provided to explain the connections among ΔT ad, ΔS M and temperature T. Equation 1 to the transition temperature, which is largely dependent on the order of the transition. According to Pecharsky s description, c p shows a discontinuity at the transition temperature if it is a second-order magnetic transition, which is smeared out by the applied magnetic field, as shown in Figure 2 [9]. Figure 2. The heat capacity of ErAl 2 measured in 0 and 5 T magnetic fields [9]. For first-order magnetic transitions, c p shows a divergence at the transition temperature. Pecharsky reported that in the case of DyCo 2, the divergence is strongly smeared out, as shown in Figure 3 [10]. The peak in c p exhibits a shift to different temperatures by the application of the magnetic field [11]. Equation 2 In these equations, µ 0 is the permeability of free space and H max is the maximum applied magnetic field. Usually c p is assumed to be field independent and Equation 1 can be replaced by. Equation 3 We are not interested in the change of c p when the temperature range is far away from the transition temperature since the magnetocaloric effect is small. However, the behavior of c p is different in the range closer Figure 3. The heat capacity in the vicinity of the first order phase transformation of polycrystalline DyCo 2 [10]. 2

5 In general, Equation 3 shows that materials with second-order transitions have greater potential than those with first-order transitions since the change of applied field has less effect on c p than the former. The third quantity that we care about is the amount of heat that can be transferred from the material s hot end to cold end, or more specifically, between its hot and cold reservoirs. Franco defined this as the refrigerant capacity RC as follows:, Equation 4 where T hot and T cold refer to the hot and cold reservoirs [1]. These temperatures are usually measured using the full width at half maximum of the peak. Everything looks fine since we have all these parameters to help us identify suitable candidates. However, problems still remain as the considerations above do not help us to distinguish the suitability of better first-order transition materials from other second-order transition materials. It is possible that a first-order material yields larger ΔT ad and ΔS M but has a narrow peak width with respect to temperature, which restricts the usage of the material [12]. Additionally, to identify whether a magnetocaloric material is capable of practical use, engineers need to take other factors into consideration, such as corrosion resistance and mechanical properties. Besides achieving ultralow temperature or refrigeration close to room temperature, recent papers have suggested a wide range of other applications including energy harvesting through thermomagnetic transitions [13] and the development of microfluidic pumps [14]. In 2011, Reis proposed using the oscillating magnetocaloric effect of diamagnetic materials as highly sensible sensors for magnetic field [15]. In theoretical research, the magnetocaloric effect also helps in revealing the characteristics of phase transitions [16,17]. This is a critical review of the available materials for magnetic refrigeration. We identify two main categories of crystalline materials based on whether or not they contain rare earth elements. Figure 4 gives a good example in explaining how groups of materials are classified. The absolute value of the maximum magnetic entropy change is shown as a function of temperature; every group of these crystalline materials shows different behaviour and thus gives us a straightforward way of identifying the magnetocaloric materials with the best performance for a particular application. Figure 4. Maximum magnetic entropy change for ΔH=5 T versus peak temperature for different families of magnetocaloric materials [1]. II. Crystalline Materials Containing Rare Earth Metals. In this section, we will discuss the family of crystalline materials containing rare earth metals. Crystalline systems can be divided into different groups depending on the crystal structures exhibited near the phase transition temperature. Generally, crystalline materials containing rare earth elements can be placed in several 3

6 groups: Laves phases, La(Fe,Si) 13 intermetallics and their derivatives, gadolinium germanium silicides (5:4 stoichiometry) and their derivatives, ferromagnetic lanthanum manganites, and other crystalline intermetallic compounds containing rare earth elements. A. Laves phases. Laves phases with stoichiometry AB 2 crystallize in three types of structures including the cubic MgCu 2 -type, hexagonal MgZn 2 -type and hexagonal MgNi 2 -type. Among these three, only the cubic phase where A is a rare earth metal (including Sc and Y) and B is generally a transition metal (other elements such as Al, Ga and Ge can also be present) is capable of the magnetocaloric effect [1]. In the cubic Laves the thermal variation of the magnetic entropy change, which is shown in Figure 5. As we can see, YFe 2 D 4.2 gives the largest magnetic entropy change among the three materials and in general all three show a declining trend when the applied magnetic field decreases. Together with the data in Figure 6, we can conclude that YFe 2 D 4.2 gives the best performance below the metamagnetic transition temperature of K. However, comparing with La(Fe 1-x Si x ) 13, which can reach JK -1 kg -1 in magnetic entropy change, YFe 2 D 4.2 is not as good and this system requires further development. phases (space group Fd m), rare earth atoms form a diamond lattice at the center and other B atoms surround this lattice to form a tetrahedron. In the case where the B atoms are transition metals, two magnetic sublattices can be formed, one by the magnetic rare earth atoms and the other by itinerant electron magnetism due to the transition metals. Taking Co on the B-site for example, the two magnetic sublattices couple parallel for light rare earth elements. In this way, Pr, Nd, Pm and Sm introduce ferromagnetism into Laves phases. On the other hand, heavy rare earth elements such as Gd, Tb, Dy, Ho and Er will make the sublattices couple antiparallel to form ferrimagnets. In 2009, Paul-Boncour and Mazet reported that the monoclinic compound YFe 2 D 4.2, which has a large reversible entropy change up to ΔS M =-10.83JK -1 kg -1 for a field variation of 5 T, would be a good candidate for magnetic refrigeration applications [18]. Powder samples of YFe 2 H 4.2 and Y 0.5 Tb 0.5 Fe 2 D 4.2 were also measured to find 4

7 Figure 5. Thermal variation of the magnetic entropy change [18]. Figure 7. Temperature dependence of magnetic entropy change in HoCuSi for different magnetic field changes [19]. B. La[Fe(Si,Al)] 13 family. In Shen s review, the La-Fe binary phase diagram shows an immiscible system, in which no intermetallic compounds form. By adding small amounts of Si or Al, it allows the compounds to form a ferromagnetic face-centered-cubic NaZn13-type structure (space group Fm c) containing 112 atoms per Figure 6. Magnetization curves at 0.03 T recorded upon cooling [18]. In 2010, Chen found that HoCuSi undergoes a field-induced first order metamagnetic transition from antiferromagnetic to ferromagnetic states below the Néel temperature[19]. Figure 7 shows a large magnetic entropy change up to 33.1 JK -1 kg -1, which is comparable to that of the La(Fe 1-x Si x ) 13 family in the literature. The refrigerant capacity was reported to be 385 J/kg. However, the low transition temperature (7K) restricts the application of this material to ultralow temperature. Additionally, the time-consuming production and low yield would be a challenge on its way to practical use. unit cell [20]. In 2001 Hu reported that a compound LaFe 11.4 Si 1.6 with the cubic NaZn 13 -type structure shows a reversible magnetic phase transition at a Curie temperature of approximately 208 K [21]. The magnetic entropy change reaches 19.4 JK -1 kg -1 under a field of 5 T, which exceeds that of most other materials previously reported as magnetocaloric candidates (Figure 8). Another feature that makes it a promising material for practical use is that the transition temperature is much closer to room temperature compared with other reported materials. The large entropy change is ascribed to the sharp change of magnetization, which is caused by a large negative lattice expansion at the Curie temperature. An asymmetrical broadening of the peak with increasing field is also observed from Figure 8, which results from the field-induced itinerant-electron metamagnetic transition 5

8 from the paramagnetic to ferromagnetic state above the Curie temperature. Figure 8. Magnetic entropy change of LaFe 11.4 Si 1.6 for magnetic field changes of 0 to 1.0 to 2 T, and 0 to 5 T. For comparison, data for LaFe 10.4 Si 2.6 under 2 T are also presented [21]. The addition of Al instead of Si is less effective in stabilizing the NaZn13-type structure according to the literature [20]. There is a reported compound La(Fe 0.98 Co 0.02 ) 11.7 Al 1.3 that shows comparable results with ΔS M =-11JK -1 kg -1 and T c =200 K in a field of 5 T. compositional changes such as substituting different elements for Si or Ge will destroy the magnetocaloric effect and shift the Curie temperature closer to room temperature. However, as an exception, the substitution of Ga preserves the magnetocaloric effect [24]. In 2010, Prabahar showed that the partial substitution of Nb in Gd 5 Si 2-x Ge 2-x Nb 2x alloys increases the Curie temperature, magnetic entropy and refrigerant capacity [39]. As we can see in Figure 9, by controlling the proportion of Nb in the composition range (0 2x 0.1), the magnetocaloric effect of the alloy can be strongly enhanced (ΔS M =-9.8 JK -1 kg -1 ). This could be because the substitution of Nb results in a low volume fraction of a second Gd 5 Si 3 -type phase which leads to the enhancement. Moreover, with increasing applied magnetic field, we can predict that this alloy will show a larger change in magnetic entropy. However, the refrigerant capacity of 98 J/kg is not comparable with that of the La[Fe(Si,Al)] 13 family. C. Gd 5 (Si,Ge) 4 family These systems belong to the A 5 B 4 family, where A is a rare earth element. They experience a magnetostructural first-order phase transition between two polymorphic structures: the orthorhombic Gd 5 Si 4 -type and Sm 5 Ge 4 -type structures (space group Pnma), which are the parent structures of binary Gd 5 Si 4 and Gd 5 Ge 4, respectively [1,22]. The representative of this family that is of interest for the magnetocaloric effect is Gd 5 Ge 2 Si 2, reported by Pecharsky in 1997 [23], with a magnetic entropy change of 18.5 JK -1 kg -1 and an adiabatic temperature change of 15 K in an applied field of 5 T. It is believed that Figure 9. Magnetic entropy change of Gd 5 Si 2-x Ge 2-x Nb 2x alloys for a magnetic field change of 2 T [39]. D. Ferromagnetic lanthanum manganites The ferromagnetic lanthanum manganites considered for magnetic refrigeration are usually derived from LaMnO 3. In the review by Phan in 2007, it is described that excess 6

9 oxygen, La deficiency or the substitution of a non-trivalent rare earth ion leads to the appearance of mixed valence Mn ions and to ferromagnetic coupling between Mn 3+ and Mn 4+ ions via the double-exchange mechanism [25]. Here we have a look at the first reported study on lanthanum manganites for the magnetocaloric effect [26]. The measurements were done by Morelli et al. on LaMnO 3 films doped with Ca, Ba or Sr. These films exhibit paramagnetic-to-ferromagnetic phase transitions at 250, 300 and 350 K respectively. However, the magnetic entropy changes were five times smaller than for both Gd 5 (Si,Ge) 4 and the La[Fe(Si,Al)] 13 family. Further improvement may be focused on the film morphology and composition to obtain an increase in magnetization and magnetic entropy change. E. Other crystalline compounds containing rare earth metals There are a large number of other crystalline compounds which have been developed for the application of magnetic refrigeration. Here we will discuss a few of them. In a review by Brȕck, the LaMn 2-x Fe x Ge 2 alloys (space group I /mmm) exhibit Curie transitions between K and K. These alloys crystallize in the tetragonal ThCr 2 Si 2 -type structure and the Curie temperature gradually decreases with increasing Fe concentration as x changes from 0.10 to 0.20 [27]. The magnetic entropy is considerably low with a value of approximately 1 JK -1 kg -1. Another example is Pr 2 Fe 17, prepared by high-energy ball milling, which adopts the Th 2 Zn 17 -type rhombohedral crystal structure [28]. The magnetic entropy change decreases from 6.3 to 4.5 JK-1kg-1 under an applied field of 5 T after the milling process. Additionally, the width of the ΔS M curve is substantially enlarged, which leads to an enhanced refrigerant capacity. III. Rare Earth-Free Crystalline Materials This section discusses candidate materials in the following order: Heusler alloys, Mn-TM-Si-Ge compounds (TM = transition metals), (Mn, TM) 5 X 3 compounds, MnAs alloys, MnFePAs alloys, FeRh alloys and other rare earth-free alloys. A. Heusler alloys Heusler alloys are defined as ordered intermetallics with the generic formula X 2 YZ (BiF 3 -type structure) in which the three components occupy the crystallographically nonequivalent positions of the space group Fm m [1]. X and Y are 3d elements and Z is a IIIA-VA group element. The magnetism of these alloys is usually dependent on the X or Y element. Hu reported a large magnetic entropy change in Ni 52.6 Mn 23.1 Ga 24.3 single crystals in 2001 [29]. The obtained magnetic entropy change reached 18.0 JK -1 kg -1 under an applied field of 5 T (Figure 10). Another interesting result is that this value increased by 4.0 JK -1 kg -1 for each 1 T increase in field (Figure 11). The larger magnetic entropy change can be attributed to the abrupt change of magnetization when a first-order martensitic transition takes place. 7

10 under an applied field of 5 T and becomes larger with increasing field. This is referred to as the giant inverse magnetocaloric effect and has its origin in a martensitic phase transformation that modifies the magnetic exchange interactions through the change in lattice parameters. Such a transformation leads to the occurrence of magnetically inhomogeneous states near the magnetic transformation temperature, which implies that the inverse magnetocaloric effect exists only in the martensite phase. Figure 10. Magnetic entropy change as a function of temperature under different applied fields along the c-axis of the martensite phase [29]. Figure 11. The dependence of the peak value of magnetic entropy on applied field along the c axis of the martensite phase[29]. Another interesting result was obtained by Krenke in 2005 [30]. An inverse magnetocaloric effect was found in Ni-Mn-Sn alloys, which means that applying a magnetic field adiabatically, rather than removing it, causes the sample to cool. This material exhibits a moderate entropy increase when the field is applied, but with the opposite sign (Figure 12). The value can reach 18 JK -1 kg -1 Figure 12. Entropy change for x=0.15 and x=0.13 in Ni 0.50 Mn 0.50 x Sn x [30]. 8

11 This interesting property has led to a suggested application also in an inverse style. Instead of cooling, it could be used as a heat-sink for heat generated when a conventional magnetocaloric material is magnetized before cooling by adiabatic demagnetization. B. Mn-TM-(Si, Ge) compounds. Song Lin et al. reported the structural and magnetic properties of MnFe 1-x Co x Ge compounds [31]. These compounds crystallize in the hexagonal Ni 2 In-type crystal structure for x 0.8 and in the orthorhombic NiTiSi-type structure for x>0.8. The Curie temperature increases with increasing x. A maximum magnetic entropy change of 9 JK -1 kg -1 was measured for x=0.8 for a field change from 0 to 5 T at approximately 289 K (Figure 13). Although the refrigerant capacity was not provided, we can clearly see potential for application in magnetic refrigeration. from 0 to 2 T and 5 T [31]. C. (Mn, TM) 5 X 3 compounds All these compounds crystallize in the hexagonal Mn 5 Si 3 -type structure (space group P6 3 /mcm). Songlin et al. reported that with Si as the X element, the antiferromagnetic ordering temperature of Mn 5-x Fe x Si 3 shifts to higher temperature with increasing Fe content [32]. In general, the compound Mn 5 Si 3 is an antiferromagnet with a field-induced transition. However, with x=4 and 5, ferromagnetic order was found. The measured magnetic entropy was fairly low with a value of about 3 JK -1 kg -1 at 58 K under an applied field of 5 T. D. MnAs alloys MnAs is rarely considered as a suitable candidate for magnetic refrigerant due to its toxic nature. Between 2004 and 2007, several papers reported on the colossal magnetocaloric effect (magnetic entropy change above the theoretical magnetic limit). One of these examples is provided by de Campos in 2006 [33]. Mn 1-x Fe x As shows the colossal magnetocaloric effect under ambient pressure (Figure 14). This material could operate in the temperature range from 310 K to 285 K, a very important temperature interval for domestic and industrial applications. However, a large thermal hysteresis is also observed which would bring a big challenge if applied in practice. Figure 13. Magnetic entropy change of the MnFe 1-x Co x Ge compounds in a field change 9

12 Figure 14. The colossal effect for Mn 1-x Fe x As as a function of temperature and Fe content for a magnetic field variation of 5 T [33]. Another example was given in 2002, when MnFeP 0.45 As 0.55 was reported to have a Curie temperature of about 300 K which allows magnetic refrigeration at room temperature [34]. The magnetic entropy change reaches 14.5 JK -1 kg -1 and 18 JK -1 kg -1 for field changes of 2 T and 5 T, respectively (Figure 15). The refrigerant capacity is also comparable with Gd 5 Ge 2 Si 2. Nevertheless, the use of As would certainly be an important question regarding the safety of the material. Figure 15. Magnetic entropy changes of MnFeP 0.45 As 0.55, Gd and Gd 5 Ge 2 Si 2 [34]. E. FeRh alloys The first study on FeRh alloys was done by Annaorazov et al. in 1992 [35]. The measurement on Fe 49 Rh 51 alloys showed a large magnetic entropy change whichup to about 22 JK -1 kg -1 under an applied field of 1.95 T at 300 K. The refrigerant capacity was also significant compared to other materials at the time with a value of Jkg -1 T -1. However, a lack of reproducibility of the initial results pointed to an irreversible character of the giant magnetocaloric effect in the system. In Gschneidner s review, he suggested that the irreversible behaviour of the magnetocaloric effect in this family is associated with the nature of the first-order phase transformation, which in this case is a magnetic order-order transformation [40]. Another reason might be its high sensitivity to processing history which increases the difficulty of obtaining reproducible results. Recently, Manekar and Roy suggested that for a refrigeration cycle using this system, the first field increasing/decreasing cycle at hot temperature should be isothermal. Afterwards, an increase in adiabatic field could be applied [36]. F. Other rare earth-free crystalline compounds In 2007, Rong and Liu reported that Fe x Pt 100-x (x=78-88) alloys have a phase transition from the disordered γ phase to the ordered α phase during cooling, while the reverse process takes place during heating [37]. Additionally, magnetic fields also induce a phase transition from the γ phase to the α phase near the transition temperature. The temperature- and magnetic-field-induced phase transitions give rise to a huge negative thermal expansion and thus a giant magnetic entropy change which is up to 39.8 JK -1 kg -1 with x=79 at around 250 K in an applied field of 7 T (Figure 16). This result is significant although the problem of thermal hysteresis again becomes an obstacle for further use. 10

13 Figure 16. Magnetic entropy change of Fe 79 Pt 21 and Fe 80 Pt 20 alloys for magnetic field changes of 0-2 T, 0-5 T and 0-7 T with (a) increasing field and (b) decreasing field, [37]. IV. Discussion of Potential Candidates Rare earth elements such as La, Gd have been a vital part in the design and production of high performance magnets for magnetic refrigeration. However, considering he stock of rare earth resources, the need driven by the market is expanding at such a high speed that society is concerned about the future of high performance magnets and thus looking for alternatives for rare earth elements has become more important in recent years. This is not an easy task. The previous sections on crystalline materials for magnetic refrigeration clearly show that materials containing rare earth elements usually have better performance in magnetic entropy change and refrigerant capacity, which are the important parameters for the selection of candidates. However, we need to see that some rare earth-free materials such as FeRh alloys and Heusler alloys have comparable parameters and a wider range of applications such as heat sinks and ultra-low temperature refrigerants. One possible direction of looking for potential rare earth-free materials is to form structures known to exhibit the magnetocaloric effect using other ingredients. Researchers have found that tetrataenite, which is formed by Fe and Ni and is abundant in meteorites, has good magnetization properties. It is possible that by doping with different elements, Fe and Ni may be fused to form such a structure without the need for extreme conditions like in outer space. Diamond, which has been successfully produced under high temperature (usually over 2000 ), high pressure ( atm) and a reductive atmosphere, might give us a lead in the synthesis of tetrataenite. However, these minerals are formed over millions of years in nature, and the possibility of shortening the time scale would be a future challenge. Nanoparticles may be another option. Usually carbon would not be a suitable choice in the fabrication of magnets. However, nanoparticles containing carbon may have the possibility of enhancing magnetic performance. It has been reported that superparamagnetic nanoparticles can be better magnetocaloric materials than paramagnetic materials due to their enlarged magnetic moments [41]. However, the peak usually spreads over a larger span of temperatures which can sometimes give a higher refrigerant capacity [43]. One inspiration is that Mn 3 GaC exhibited an inverse giant magnetocaloric effect associated with an antiferromagnetic to ferromagnetic transition at 165 K, with a magnetic entropy change of 15 JK -1 kg -1 under an applied field of 2 T [38]. Comparing to bulk samples, nanostructured materials may not show obvious advantages because nanostructuring can lead to a decrease in the magnetocaloric effect due to a broadened phase transition peak [42]. Models have been proposed to explain how other factors such as particle size, particle concentration, interactions between particles and anisotropy play a role in the magnetocaloric response. V. Summary and Conclusion The analysis of the crystalline materials considered here can be summarized in Table 1. Currently, the best performing magnetocaloric material is the Gd 5 (Si,Ge) 4 family, which are capable of working at room temperature. Heusler alloys also have potential but the 11

14 problem of hysteresis is a big challenge for Magnetic refrigeration is a promising applications. For ultra-low temperature, Laves phases including HoCuSi have a working technology as an alternative to current vapor-compression refrigerators and meets temperature close to 7 K. It should be noted today s energy saving requirements. that Ni-Mn-Sn alloys display the inverse Crystalline materials that show the magnetocaloric effect, which can be used as a heat sink for refrigeration. Another factor is magnetocaloric effect have good potential for applications and the families of candidates cost. Although rare earth-free materials have been greatly developed in recent years. generally have lower prices compared to rare earth elements, the use of Rh would also cost Crystalline materials containing rare-earth elements generally have advantages over rare a lot in production. earth-free materials. However, further Group T c (K) ΔS M (JK -1 kg -1 ) RC (Jkg -1 ) Applications Containing rare earth Laves Phases YFe 2 D 4.2 : HoCuSi: Refrigeration to ultra-low temperature La[Fe(Si,Al)] 13 LaFe 11.4 Si 1.6 : Refrigeration family close to room temperature Gd 5 (Si,Ge) 4 family Gd 5 Si 2-x Ge 2-x Nb 2x : Refrigeration at room temperature Ferromagnetic LaMnO 3 : 150 ~-2 - lanthanum manganites Rare earth-free Heusler alloys Ni 52.6 Mn 23.1 Ga 24.3 :~ Refrigeration at 300 room temperature Ni-Mn-Sn Heat sink alloys:300 Mn-TM-(Si, Ge) compounds Refrigeration at room temperature (Mn, TM) 5 X compounds MnAs alloys ~ Refrigeration at room temperature FeRh alloys Refrigeration at room temperature Table 1. Comparison of different families of materials. 12

15 improvements in rare earth-free materials may bring them to a better position in the magnetic refrigeration applications. Acknowledgment Supervisor: Prof. G. Blake 13

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19 Notes i 1-1 Sep 28, 2014, 21:30, Erik Van der Giessen - focussed, fairly clear and arriving at specific set of (useful) conclusions - scientific writing (equations, referencing) can be further improved Report generated by GoodReader