MAGNETOCALORIC MATERIALS

from Eq. (2.6) using temperature-dependent magnetization and spe- cific heat data. A summary of indirect measurement techniques to calculate the MCE was presented by Pecharsky & Gschneidner Jr.

(1999).

It should be pointed out that care must be taken when apply- ing indirect techniques to first-order transition materials, since dis- continuities in the MCE, latent heat and thermal hysteresis render the thermodynamic assumptions presented in Section 2.1 invalid. In this sense, the direct measurement approach to determineΔ𝑇ad be- comes more attractive for first-order materials. More detailed dis- cussions on the application of indirect characterization methods in first-order materials have been presented by Caron et al. (2009), Giguèrreet al.(1999), Moore et al.(2012), Smithet al.(2012).

2.2. Magnetocaloric materials 49

Ferromagnetic materials are classified according to their phase transition order either as (i) first-order or (ii) second-order. A sin- gle magnetic phase transition of a ferromagnetic material is con- sidered second-order, while a first-order phase transition involves latent heat. If a magnetic transition is accompanied by a structural transition, the magnetization change is discontinuous and the phase transition is first-order (Smithet al., 2012). Magnetocaloric mate- rials exhibiting a magneto-structural phase transition are consid- ered to have a ‘giant’ MCE due to a large, though narrow, peak inΔ𝑆(Pecharsky & Gschneidner, 1997). First-order transitions are normally accompanied by a thermal hysteresis, Δ𝑇_hys, which cor- responds to a different response of the material when subjected to heating and cooling, and is found around the transition tempera- ture. In principle, hysteresis is considered an undesirable effect in practical applications. A more detailed discussion on hysteresis re- lated phenomena is presented by Smithet al.(2012). An experimen- tal study was carried out by von Mooset al. (2014). Some magne- tocaloric compounds allow the possibility of tuning its𝑇_C by slight changes in their chemical composition; the MCE is graded from one temperature range to another. From an application point of view, this can be very interesting for it allows larger temperature spans to be reached in the so-called multistage AMRs (see Section 2.2.2).

In terms of Δ𝑇ad and Δ𝑆, the MCE does not scale linearly with the magnetic field, but with a power smaller than unity around the transition temperature. For second-order transition materials, this power is usually around2/3, i.e.Δ𝑇ad∝𝜇0𝐻^2/3, as predicted by the mean field theory (Oesterreicher & Parker, 1984). This rela- tionship, together with the influence of the demagnetization field is important in the design of the magnetic circuit, as will be detailed in Section 2.7.2.

Second-order materials have a reversible MCE (Bahl & Nielsen, 2009) while some first-order materials can have an irreversible MCE due to the hysteretic losses (Morrison et al., 2009). For materials exhibiting a reversible MCE, an important constraint forΔ𝑇_adupon magnetization and demagnetization is defined by Nielsenet al.(2010) as:

Δ𝑇_ad,mag(𝑇, 𝐻_i, 𝐻_f) =−Δ𝑇_ad,demag(𝑇 + Δ𝑇_ad,mag(𝑇, 𝐻_i, 𝐻_f), 𝐻_f, 𝐻_i) (2.8) The above relationship is also referred to as ‘theoretical de- magnetization’. For irreversible magnetocaloric materials, the equal- ity in Eq. (2.8) becomes an inequality due to the generation of

entropy so that:Δ𝑇_ad,mag>−Δ𝑇_ad,demag (Nielsenet al., 2010).

The ideal magnetocaloric material for refrigeration applica- tions at around room temperature should have the following char- acteristics: (i) a large MCE over an appropriate temperature range around room temperature, (ii) low magnetic and thermal hystere- ses, (iii) suitable thermal properties (high thermal conductivity and large thermal capacity) for optimal thermal behavior of the regene- rator, (iv) chemical stability to avoid corrosion, (v) suitable mechan- ical properties to simplify processing, (vi) low electrical resistance to minimize eddy currents (vii) environmentally friendly, and (viii) low raw material and fabrication costs (Gschneidner Jr. & Pecharsky, 2008; Sandeman, 2012).

The benchmark magnetocaloric material for applications at room temperature is gadolinium (Gd). Since the pioneering work of Brown (1976), Gd has been employed in most room-temperature magnetic refrigerators developed so far (Yu et al., 2010). It is the only element with 𝑇_C around room-temperature with a relatively large MCE. Nevertheless, the pursuit of suitable magnetocaloric working materials is one of the main challenges in magnetic re- frigeration research. Since the publication of the ‘giant’ MCE in Gd5Si2Ge2 by Pecharsky & Gschneidner (1997), several families of intermetallic compounds have been found to have similar charac- teristics. Among them, the most promising systems are the Fe2P (Teguset al., 2002) and NaZn13 (Fujieda et al., 2002) related com- pounds (see Section 2.2.2). Detailed reviews of magnetocaloric mate- rials for room-temperature applications were carried out by Pecharsky

& Gschneidner Jr. (2006), Brück (2007), Smithet al.(2012), Franco et al.(2012) and Liu et al.(2012).

2.2.1 Gadolinium (Gd)

Gadolinium (Gd) is the only pure element with a near room- temperature Curie temperature and a second-order phase transition from a ferromagnetic to a paramagnetic state. According to Bahl &

Nielsen (2009), the𝑇C of Gd ranges between 290 and 297 K for low magnetic fields, depending on the measuring technique employed and on the purity of the sample (Dan'kovet al., 1998).

Dan'kov et al. (1998) reported a maximum MCE of 3.8 K for an applied magnetic field of 1 T in extremely pure Gd samples.

While Benford & Brown (1981) reported a value of 3.6 K for the same applied magnetic field. Nevertheless,Δ𝑇_ad is lower in commer- cial grade Gd, which typically has a maximum MCE of 2.8 K/T at

2.2. Magnetocaloric materials 51

the Curie temperature for magnetic fields up to 2 T (approximately the maximum achievable magnetic field with permanent magnet ar- rays) (Spichkinet al., 2007). The point of maximumΔ𝑇_ad is close to the𝑇_C and increases withΔ𝐻 (Pecharsky et al., 2001).

Compiling experimental data from very pure Gd samples at high fields obtained by Pecharsky & Gschneidner Jr. (2006), Bahl &

Nielsen (2009) found the following relation between theΔ𝑇adof Gd and the internal magnetic field: Δ𝑇_ad[K] = 3.675 (𝜇₀𝐻[T])^0.7. On the other hand, for commercial grade Gd samples, the same authors obtained the following expression:Δ𝑇ad[K] = 2.85(5) (𝜇0𝐻[T])^0.78(3).

Gd is still the best performing magnetocaloric material avail- able for room-temperature applications due to its largeΔ𝑇ad, low 𝐶𝐻 and high thermal conductivity (Smith et al., 2012). Besides that, Gd has good chemical stability with commercial automotive antifreeze solutions (a mixture of distilled water, ethylene glycol and some corrosion inhibitors) (Engelbrecht et al., 2011). It also has good mechanical processing characteristics, being commercially available in a variety of shapes, including spheres and plates.

The typical magnetocaloric properties of Gd metal are shown in Fig. 4 for an applied magnetic field of 2 T. Fig. 4(a) shows the adiabatic temperature change, Δ𝑇_ad, and Fig. 4(b) the isothermal entropy change. The former peaks atΔ𝑇_ad∼5.7 K, while the latter peaks atΔ𝑆 ∼ 5.5^J/^kg.K(Gschneidner Jr. & Pecharsky, 2006).

Figure 4 – Magnetocaloric properties (a)Δ𝑇_adand (b)Δ𝑆 for a Gd for an applied magnetic field of 2 T (Pecharsky & Gschneidner Jr., 2006).

2.2.2 Promising magnetocaloric materials

After the discovery of the ‘giant’ MCE, the search for promis- ing magnetocaloric refrigerants focused on rare-earth compounds due to their high ordering temperatures. Intermetallic lanthanum- based compounds, such as La(Fe,Si)13, which crystallize in the NaZn13- type structure (1:13 phase) (Palstraet al., 1984), and the transition- metal-based compounds MnFe(P,As), which crystallize in the Fe2P- type structure (Tegus et al., 2002), are among the most promising magnetic refrigerants for near room-temperature magnetic cooling.

Detailed reviews of magnetocaloric materials for applications at room temperature have been carried out by Gschneidner Jr. et al. (2005), Liu et al. (2012), Franco et al. (2012) and Liu (2014).

Fig. 5 summarizes the maximum Δ𝑆 for different families of mag- netocaloric materials for a𝜇₀Δ𝐻 of 5 T, having Gd as a reference.

An interesting viewpoint paper about the search for new magne- tocaloric refrigerants has been written by Sandeman (2012).

Identifying Ways to Increase the Efficiency of Magnetocaloric Devices – Florianópolis, Brazil – April 15-19, 2013