W Bouzidi

K Nouri

T Bartoli

H Jaballah

S Ayadim

J Moscovici

L Bessais

Low Field Magnetocaloric Effect of PrCo 3 compounds

Keywords: numbers: 75.50.Bb, 75.50.Tt, 76.80.+y

Rare-earth-transition-metal intermetallics show very interesting magnetic properties for numerous applications (hard magnetic materials, magnetic refrigeration . . . ). This paper is devoted to the study of the structural, magnetic and magnetocaloric effect (MCE) of the intermetallic nanomaterials PrCo3, which derives from the PuNi3 type structure. This system crystallizes into the rhombohedral structure (R 3m space group). PrCo3 compound exhibits a second order ferro -paramagnetic transition at around 330 K. This 1:3 system, based on a stacked Pr2Co4 and PrCo5 units, has a magnetocaloric effect of 1.3 J/kg K at low field. In addition, we demonstrated that the MCE derived from phenomenological and experimental approaches were in agreement.

I. INTRODUCTION

Rare-earth-transition-metal (R -T ) intermetallic alloys are generally characterized by a high magnetic transition temperature and a single-axis (uniaxial) anisotropy. In addition, for a well optimized microstructure, they can show a high coercivity [START_REF] Cullity | Introduction to Magnetic Materials[END_REF][START_REF] Coey | [END_REF][3].

Several studies have focused on the magnetic properties of 4f rare-earth (R) and 3d transition metalbased (T ) intermetallics, both for their interesting magnetic properties and for their potential applications (permanent magnets, magnetostrictive actuators or sensors, magnetocaloric materials, high density magnetic recording, hydrogen storage . . . ).

RT y compounds are intergrowth phases (2 < y < 5). These compounds consist of a stack of units: the R 2 T 4 and RT 5 , that can also represented by [A 2 B 4 ] and [AB 5 ] units. RT y compounds are polymorphic phases, i.e. for the same composition, the system presents several possible structures. In this case, one obtains either the hexagonal structure (H) of space group P 6 3 /mmc or the rhombohedral structure (R) of space group R 3m. This binary RT y compounds can be described by the following equation [4,5]: y = (5n + 4)/(n + 2) with n = 0, 1, 2, 3, 4 . . ., n ≥ 0 is an integer representing the number of units [AB 5 ] in an elementary brick. In a general way, whatever y is, [A 2 B 4 ] + n[AB 5 ] can describe the elementary brick in this type of system. Thus, n = 1 corresponds to the stoichiometry RT 3 , n = 2, to the stoichiometry R 2 T 7 , and n = 3, to the stoichiometry R 5 T 19 . With the same rules, we find that n = 0 corresponds to the stoichiometry RT 2 , while n → ∞ corresponds to the stoichiometry RT 5 .

The magnetocaloric effect (MCE) in various magnetic * Corresponding author: bessais@icmpe.cnrs.fr materials has been extensively investigated experimentally and also theoretically, not only because of their potential applications for active magnetic refrigeration but also for understanding the fundamental properties of these materials. The intermetallic compounds were also studied for their MCE such as La(FeSiCo) 13 H, R 2 Fe 17 , and Gd 5 (GeSi) 4 [6][7][8][9][10][11][12][13][14][15][16][17][18][19].

The RCo 3 compounds are formed for all rare earths [20], their lattice parameters decrease with the rareearths atomic number, this is related to the contraction of the lanthanides [21] except for the special case of the CeCo 3 compound, where cerium has a smaller size than other rare earths [22].

Very few studies were devoted to magnetocaloric effect for RCo 3 compounds. The majority of R -T intermetallic compounds show a second order magnetic transition (SOMT) [17,[23][24][25][26]. However, the compounds that possess a SOMT exhibit negligible loss by thermal and magnetic hysteresis, which is a definite advantage for magnetic refrigeration.

In this work, we focused on the structural and magnetic properties of the intermetallic compound PrCo 3 prepared by high energy ball milling followed by a short heat treatment. We chose this compound because it has several potential advantages: (i) it is low cost and has better corrosion resistance than Gd which is the ideal candidate for the magnetocaloric effect. (ii) It does not exhibit thermal or magnetic hysteresis since it has a second order magnetic transition. (iii) In addition, this compound is a multifunctional material (magnetically hard, good hydrogen storage capacity and good magnetocaloric properties).

The crystal structure of this compound was found an inter-growth of MgZn 2 and CaCu 5 stacked structures. Furthermore, for the first time we studied the low-field magnetocaloric properties of the rhombohedral PrCo 3 PuNi 3 -type compound.

II. EXPERIMENT

PrCo 3 samples were prepared by melting praseodymium (99.9 wt%) and cobalt (99.9 wt%) in appropriate stoichiometric proportions.

A small excess of Pr was accounted for, in order to compensate some losses due to the volatile nature of the rare earth. The melting process was done by an electric arc furnace equipped with a W electrode under high-purity Ar atmosphere. In this process, the ingots obtained were remelted five times to achieve a better homogenization of the material.

The ingots were then subsequently processed into nanopowders by undergoing high energy ball milling for 5 hours in Ar atmosphere, using a Fritsch P7 planetary mill. The resulting powder was then wrapped in tantalum sheets and vacuum-sealed in a silica tube. Finally, the sealed tube was then placed in a furnace and heated at 1000 • C for 30 minutes. The thermal treatment was interrupted by quenching in cold water.

To identify the phases and describe the cell parameters of our compound, X-ray powder diffraction was carried out on a BRUKER diffractometer using Cu Kα radiation (λ = 1.5405 Å) with an internal silicon standard in order to insure an accuracy of ±10 -3 Å for the unitcell parameter. The intensities were measured at angles ranging from 2θ = 20 • to 80 • with a step size of 0.015 • . The Rietveld refinement of the diffractograms where then carried out using the FullProf computer code [27,28] in the supposition of the Thompson-Cox-Hastings line profile which allows the multiple-phase refinement in case of coexisting phases. The size of the diffraction domain in the sample was determined from the line pattern broadening, using the formula of Scherrer. The best refinement fit agreement is given by the usual agreement factors R B and χ 2 [3,29].

All the magnetic measurements such as Curie temperature T C and isothermal magnetic curves M (H) were measured on a differential sample magnetometer MAN-ICS in fields up to 15 kOe, on 10 mg powder samples.

III. RESULTS AND DISCUSSION

A. Structure analysis

It is important to emphasize that the structure of the PrCo 3 phase with a PuNi 3 -type structure is described by the stacking along the c-axis of the unit blocks PrCo 2 (MgCu 2 ) and PrCo 5 (CaCu 5 ) [30]. The AB 3 unit blocks are obtained by stacking the A 2 B 4 and AB 5 unit blocks three times. The block cell contains two non-equivalent crystallographic sites: Pr atoms in 3a and 6c sites, whereas, Co atoms in 3b, 6c and 18h sites.

X-ray diffractograms were refined using the FULL-PROF program with the Rietveld method using a Thompson-Cox-Hastings-pseudo-Voigt peak shape function [31][32][33]. As a measure of refinement quality, two fac- tors of agreement R B and χ 2 were used. The parameters of the unit cell were derived with Si standard (a = 5.4308 Å) leading to an accuracy of the unit cell parameters of ±1.10 -4 Å [34,35]. Fig. 1 shows the profile fit using the Rietveld analysis for the PrCo 3 compound. These results show that the sample is a single-phase with around 1% of a secondary phase. The diffraction peaks are indexed in the rhombohedral R 3m space group (PuNi3-type structure). In the table I, we have listed the best values of R B and χ 2 . The unit cell parameters (a= 5.0783(5) Å and c= 24.7943(9) Å) for PrCo 3 are in good agreement with the results found in the literature [36]. The atomic positions (x, y, z) and the occupation of the different Wyckoff positions of the compound PrCo 3 are grouped in table I.

B. Magnetic and magnetocaloric properties

Thermomagnetic properties

In this part, we will focus on intrinsic and extrinsic magnetic properties. The Curie temperature T C , is the intrinsic magnetic order transition. In intermetallics, constituted by rare-earth-transition-metal alloys, the magnetic transition temperature depends on three types of exchange interactions. The exchange interaction 3d -3d (J Co-Co ) between the moments of the Co sublattice, and the 4f -4f (Exchange (J Pr-Pr )) and the intersublattice 3d -4f exchange interaction (J Pr-Co )). We note that the 4f -4f rare earth interaction is expected to be low and negligible in comparison compared to the other two types of exchange interactions [37,[START_REF] Franse | Handbook of magnetic materials[END_REF].

The temperature dependency of the magnetization (Fig. 2) shows that T C is equal to 330 K determined by the calculation of the minima of the dM/dT derivative. This para-to ferromagnetic transition is due essentially to the predominance of the positive Co-Co exchange interactions 3d -3d [37,[START_REF] Franse | Handbook of magnetic materials[END_REF].

Phenomenological approach

To determine the MCE in the magnetic material PrCo 3 , a phenomenological model is used to simulate magnetization vs temperature curve, under a low magnetic field within the adiabatic conditions. It was demonstrated by the mean field theory that the magnetisation dependence on the temperature and on T C is given by [START_REF] Hamad | [END_REF]:

M (T ) = M fer -M par 2 tanh [δ(T C -T )] + T dM dT | T <T C + γ (1
) where M fer is an initial magnetization value at the ferro-paramagnetic transition for T < T C and M par is a final value of magnetization at the ferro-paramagnetic transition for T > T C . δ and γ parameters are given by the following two equations:

δ = 2( dM dT | T <T C -dM dT | T C ) M fer -M par γ = M fer + M par 2 - dM dT | T <T C .T C
where dM dT | T <T C represent the sensitivity of magnetization dM dT at ferromagnetic state and dM dT | T C is magnetization sensitivity dM dT at T C . Under adiabatic condition, the magnetic entropy change can be obtained by the integration of magnetization derivative as follow:

∆S M = -δ.H max M fer -M par 2 sech 2 [(δ(T C -T ))] + ( dM dT | T <T C ).H max (2)
Eq. 2 Shows that an observed relatively large magnetic entropy change is a consequence of high magnetization at ferromagnetic state and rapid drop in magnetization at T = T C . Hence, the peak of the magnetic entropy change ∆S max M can be calculated using the equation Eq. 2, in fact, for T C = T ∆S M =∆S max M , so, it is expressed as follow:

∆S max M = (-δ (M fer -M par ) 2 + ( dM dT | T <T C ))H max
The specific heat can be deduced from ∆S M , using the relation below[? ]: ∆C p = T δ∆S M δT Based on the above formula, heat capacity change ∆δC p , can be expressed as:

∆C p = -δ 2 .H max .T M fer -M par 2 sech 2 [(δ(T C -T ))] × tanh[δ(T C -T )]
(3) From this phenomenological model ∆S max M and ∆C p,H can be simply evaluated for PrCo 3 compound under magnetic field variation. Fig. 3 shows a good agreement between modeled and experimental magnetization variation with temperature for PrCo 3 , symbols represent experimental data, and the red line corresponds to modeled magnetization.

Moreover, Fig. 4 and Fig. 5 show ∆S M and ∆C p,H variation with temperature under a tow low magnetic fields , respectively. Predicted values of ∆S max M and ∆C p under tow relatively low magnetic field for PrCo 3 are determined as shown in Tab II. From Fig. 4 and Fig. 5 we can easily see that the increase of magnetic field causes an increase of ∆S M values from 0.13 J.(kg.K -1 ) to 0.27 J.(kg.K) -1 .

Experimental approach: magnetocaloric effect

The MCE shows the isotherm entropy change. For a constant pressure, the total entropy, S(T, H) is the combination of electronics (S el ), magnetic (S m ), and lattice (S lat ) [START_REF] Tishin | The magnetocaloric effect and its applications[END_REF]. It can be expressed as follows:

S(T, H) = S m (T, H) + S lat (T ) + S el (T )
We calculated the MCE in terms of the isothermal magnetic entropy change ∆S M using the magnetization isotherms measured at different temperatures. For PrCo3, we determined the isothermal magnetization between 310 and 355 K, under a weak magnetic field of 1.5 T. Fig. 6 illustrates the representative isothermal magnetization curves M (H, T ) of the intermetallic compound, recorded at various temperatures near T C . Analysis of Arrott's plots, M 2 versus H/M , obtained from the magnetic field dependency of isothermal magnetization, is shown in figure Fig. 7. Having in mind Banarjee criterion [50], the positive slope and linear behavior near T C confirm that the magnetic phase transition is of second order from the ferromagnetic to the paramagnetic state. The MCE has been investigated in terms of change in isothermal magnetic entropy ∆S M from the magnetisation isotherms obtained around T C . We calculate the change in magnetic entropy using Maxwell's thermodynamic relation, via this equation [START_REF] Pecharsky | Magnetocaloric effect from indirect measurements: Magnetization and heat capacity[END_REF]52]:

M ( A m 2 / k g ) µ 0 H ( T ) 3 1 0 K 3 1 5 K 3 2 0 K 3 2 5 K 3 3 0 K 3 3 5 K 3 4 0 K 3 4 5 K 3 5 0 K 3 5 5 K P r C o 3
T = 3 5 5 K T = 3 1 0 K 5 K M 2 ( ( A m 2 / k g ) 2 ) µ 0 H / M ( k g . T / A m 2 ) 3 1 0 K 3 1 5 K 3 2 0 K 3 2 5 K 3 3 0 K 3 3 5 K 3 4 0 K 3 4 5 K 3 5 0 K 3 5 5 K P r C o 3
∆S M (T, ∆H) = µ0Hmax 0 ∂S(T, H) ∂H T dH (4)
From Maxwell's thermodynamic relation

∂S(T, H) ∂H

T = ∂M (T, H) ∂T H (5)
We can finally obtain the equation of magnetic entropy variation :

∆S M (T, ∆H) = µ0Hmax 0 ∂M (T, H) ∂T H dH (6)
Based on the magnetization isotherm data, we can obtain indirectly the MCE [53]:

∆S M (T i , ∆H) = µ 0 i M i+1 -M i T i+1 -T i ∆H i (7)
Where µ 0 is the vacuum magnetic permeability, and M i , M i+1 are the magnetization values measured at T i and T i+1 in a field change of ∆H i [53]. From these calculations, we deduce the evolution of ∆S M with temperature and applied field. value is reached at T = T C . The maximum value is about 1.3 J/(kg.K) under a magnetic field of 0-1.5 T. It's important to note that the -∆S max M is high compared to other materials for magnetic refrigeration, such as Pr 2 Fe 17 (∆S = 2 J/(kg.K), µ 0 H = 1.5 T) [44], SmNi 5 (∆S = 1.2 J/(kg.K), µ 0 H = 1.5 T) [25] and GdNi 3 FeSi (∆S = 0.5 J/(kg.K), µ 0 H = 1.5 T) [46]. Table IV summarize the maximum in entropy change -∆S max M , Curie temperature and applied field for different intermetallic compound, developed for MCE application. The relative cooling power (RCP) is the second parameter for MCE characterization. We can deduce RCP, by application of the following equation based on magnetic entropy change [54,55]:

RCP = -∆S M δT F W HM (8)
The RCP is equal to 21 J/kg for the intermetallic PrCo3. Let's notice that, the high magnetic entropy change and the larger δT can provide a high RCP value.

In order to compare the predicted magnetic entropy change using the phenomenological approach and the magnetic entropy change obtained by experimental approach, both curves are plotted on the same figure. shows a good agreement between the two approaches, based on this result, the phenomenological model can be used to predict and describe the MCE of the intermetallic compounds.

IV. CONCLUSION

In this work we demonstrated that by using arc melting, PrCo 3 samples can be obtained faster than with other synthesis methods. The pure nanocrystalline phase PrCo 3 is finally obtained with a process consisting of high energy ball milling followed by a short heat treatment.

Rietveld refinement of XRD data confirmed the crystallization of the compound into rhombohedral PuNi 3 type structure (space group R 3m). The rare earth Pr atoms occupy both 3a and 6c crystallographic sites, whereas the Co atoms are placed on the sites 3b, 6c and 18h.

We also report new magnetic and magnetocaloric properties obtained for the first time for the nanocrystalline PrCo 3 : it exhibits a Curie temperature of 330 K and a maximum in entropy variation of 1.3 J/kg.K. From these measurements we also deduced its relative cooling power, which is approximately equal to 21 J/kg. We have deduced from the Arrott plots that the nature of its ferromagnetic to paramagnetic transition is of second order.

In addition, a theoretical approach was used that permit to successfully predict ∆S M , using a faster indirect method that delivers important information about the magnetocaloric properties of PrCo 3 compound. Due to its magnetic transition near ambient temperature, PrCo 3 can be a potential candidate, that could be optimized by targeted substitution to exhibit a large magnetocaloric effect.

Figure 1 .

 1 Figure 1. The Rietveld refinement of PrCo3

Figure 2 .

 2 Figure 2. Magnetization as a function of temperature for the PrCo3 compound. The TC is determined by the derivation method. The inset representation dM/dT vs. temperature

Figure 3 .

 3 Figure 3. Magnetization vs temperature for PrCo3 under tow low magnetic field.

Figure 4 .Figure 5 .

 45 Figure 4. Modeled magnetic entropy change (-∆SM ) versus temperature for the samples PrCo3 under tow low magnetic fields.

Figure 6 .

 6 Figure 6. Isotherm magnetization curves, M(H), for PrCo3 compound.

Figure 7 .

 7 Figure 7. The Arrott plots of PrCo3 compound.

Fig. 8

 8 represents the thermal variation of magnetic entropy change of PrCo3 compound. The -∆S max M increases with temperature evolution. -∆S max M

3 Figure 8 .

 38 Figure 8. Magnetic entropy change ∆SM versus temperature around the Curie temperature for PrCo3 compound

  Fig .9

Figure 9 .

 9 Figure 9. Phenomenological ∆SM versus experimental one around the Curie temperature for PrCo3 compound

Table I .

 I Unit cell parameters of the rhombohedral PrCo3 compound of P uNi3 type structure, space group R 3m.

	Parameters	value
	a( Å)	5.0783(5)
	c( Å)	24.7943(9)
	z(6c)Pr	0.1408(3)
	z(6c)Co 0.3331(5)
	x(18h)Co 0.4965(4)
	y(18h)Co 0.5034(6)
	z(18h)Co 0.0802(4)
	c/a	4.8915
	V ( Å) 3	551.417(2)
	RB	5.2
	χ 2	3.1

Table III .

 III M fer (Am 2 .(kg) -1 ), Mpar (Am 2 .(kg) -1 ), dM dT |T <T C (Am 2 .(kg.K) -1 ) and dM dT |T C (Am 2 .(kg.K) -1 ) determined from experimental M (T ) for PrCo3 µ0H (T) M fer Mpar dM dT |T <T C

		dM dT |T C
	0.13 22.74 11.6 -0.299	-1.24
	0.23 25.19 14.56 -0.334	-1.13

Table IV .

 IV Summary of magnetocaloric properties of PrCo3 compound compared with other magnetic materials.

	Compound	µ0H (T) TC (K) -∆S max M	J/(kg.K)	Ref.
	PrCo3	1.5	330	1.3	This work
	Pr2Co7 (P63/mmc)	1.5	600	1.1	[41]
	Pr2Co7 (R-3m)	1.5	580	3.7	[41]
	Pr5Co19	1.5	690	5.2	[42]
	Gd2Fe16Si	1.5	522	3.07	[18]
	Gd	1.5	293	3.8	[43]
	Pr2Fe17	1.5	285	2	[44]
	SmNi5	1.5	29	1.2	[25]
	SmNi	1.5	42	0.65	[45]
	GdNi3FeSi	1.5	168	0.5	[46]
	GdNi	2	69	8.9	[47]
	TbNi	2	67	11.5	[47]
	DyNi	1.5	61	2	[48]
	LaFe11.8Si1.2	1	186	3.1	[49]

The authors have no competing interests to declare that are relevant to the content of this article.

Funding

The authors did not receive support from any organization for the submitted work.

Data availability

All data generated or analyzed during this study are included in this published article .

DECLARATIONS

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Author Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by S. Ayadim, H. Jaballah, W. Bouzidi, K. Nouri and T. Bartoli. The first draft of the manuscript was written by W. Bouzidi, K. Nouri, T. Bartoli and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Conflicts of interests

The authors have no relevant financial or non-financial interests to disclose.


M Saidi

L Bessais
email: bessais@icmpe.cnrs.fr

M Jemmali

Review of the influence of copper and chromium substitution on crystal structure, magnetic properties and magnetocaloric effect of GdFe 2-x (Cu, Cr) x (x = 0, 0.1, 0.15 and 0.2) intermetallic compounds

Keywords: Intermetallic compounds, Magnetic materials, Magnetocaloric Effect

Review of the influence of copper and chromium substitution on crystal structure, magnetic properties and magnetocaloric effect of GdFe2(Cu, Cr) (x = 0, 0.1, 0.15 and 0.2) intermetallic compounds M. Saidi, Lotfi Bessais, M. Jemmali

Introduction

Over recent years, human consciousness about energy and environment has been highly emphasized. The toxic gases associated with global-warming, greenhouse effects and ozonedepleting gases, such as chlorofluorocarbons (CFCs), hydrofluoric carbons (HFCs) and ammonia (NH 3 ) [1,2] have posed a threat to human life, which limits the conventional gascompression (CGC) refrigerators. Thus, from an environmental conservation perspective, research on future refrigeration technologies is increasingly oriented toward other techniques, such as magnetic refrigeration (MR), based on the magnetocaloric effect (MCE) [3,4]. The principle of this effect is based on the reversible heating and cooling of a magnetic material after the application of a magnetic field variation [5,6]. In addition, magnetic refrigeration is becoming a promising technology to replace the conventional cooling technique, because it is much more compactly built due to the fact of taking solid substances as working materials. The key advantage of magnetic refrigeration is that it has ecological, economic and environmental benefits [START_REF] Trevizoli | Reference Module in Materials Science and Materials Engineering[END_REF][START_REF] Shi | [END_REF]9,10]. What is more, this technology doesn't cause atmospheric pollution or noise and it offers significantly more reliability and energy-efficient than the conventional refrigeration [11].

In this context, the intermetallic materials combining rareearth elements and transition metals with large magnetocaloric properties have attracted a considered attention owing to its potential application in the magnetic refrigeration (MR) technology [12,13,14,15,16,17,18,19,20,21,22,23,24].

Most of rare-earth transition-metals intermetallic compounds exhibit a second order magnetic transition (SOMT) [14,16,19,20,11]. Intermetallics that possess a SOMT generally exhibit negligible loss by thermal and magnetic hysteresis, consequently they could be a potential candidate for magnetic refrigeration.

In addition, many promising materials such as Gd 5 Si 2 Ge 2 [25,26] Mn 5 Ge 3-x Si x [27], and MnNiGa [28], have been broadly studied for their high magnetocaloric effect and their application as magnetic refrigerants.

Among numerous rare earth -transition metals-based intermetallic compounds, Laves-phases RM 2 (R stands for rare earth elements, and M stands for transition metals) compounds have been massively studied [29,30]. These phases crystallize in three structure types: MgCu 2 (C15) type structure, MgZn 2 (C14) type structure, and MgNi 2 type structure (C36) [31]. The RV 2 (R = Ti, Nb, Hf, and Ta) compounds present high melting point, good oxidation resistance, and high strength at elevated temperatures which make them available for hightemperature structural applications [32,33,34] and hydrogenstorage [35]. In addition, the rare earth Laves phases RCo 2 (R= Dy, Ho, Er) [36,37,38,39], TbCo 2 [40], GdCo 2 [41], and SmNi 2 [42] with cubic MgCu 2 -type structure (C15) exhibit attractive and useful properties such as significant anisotropic magnetostriction, large magnetovolume effect, and large magnetocaloric effect around the Curie temperature.

In the literature, GdFe 2 compound, which crystallizes in the cubic Laves-phase with MgCu 2 type structure, has been the subject of many investigations in the past few years [43,44,45]. These compounds are of considerable scientific and technological interests because of their excellent magnetic, electronic, elastic and thermal properties, due to the coexistence of complementary features of itinerant (3d) and localized (4 f ) electrons in these compounds.

In our previous papers [46,47], we have prepared a series of Gd-Fe-Cu and Gd-Fe-Cr alloys to determine the solid state phase equilibria in both ternary Gd-Fe-Cu and Gd-Fe-Cr systems at 800 • C, through the use of SEM-EDS and XRD techniques. The solid solutions GdFe 2-x Cu x and GdFe 2-x Cr x were identified to exist in these isothermal sections, respectively, which extended from about x = 0 to x = 0.2. This outcome opens the way in this experimental work, for investigating the effect of copper and chromium substitution for iron on the structural, magnetic, and magnetocaloric properties of the GdFe 2-x (Cu,Cr) x (x = 0, 0.1, 0.15 and 0.2 compounds.

Experimental section

Synthesis

Samples with the total mass of 0.5 g were prepared from gadolinium (99.99 wt.%), iron (99.99 wt.%), copper (99.99 wt.%) and chromium (99.99 wt.%) metals. Prior to the melting process, calculated amounts of the elements were precisely weighed on a microbalance. Then, alloys were produced by melting the constituents in stoichiometric quantities in an electric arc furnace, in water-cooled copper mold with the use of a non-consumable tungsten electrode under protective argon gas. A piece of zirconium was used to remove traces of oxygen. Each sample was re-melted and turned over four to five times to achieve complete fusion and to obtain homogeneous state. After the melting procedure, the final mass of each buttons was checked. The weight loss did not exceed 1% of the initial total mass [46,24]. After the melting procedure, the final mass of each buttons was checked. The weight loss did not exceed 1% of the initial total mass. After that, the melted samples were wrapped in Tantalum foil, vacuum-sealed in a quartz tube, and then annealed at 800 • C for seven days to ameliorate the atomic diffusion kinetics. The annealing process was ended by quenching the samples in cold water in order to preserve their high temperature state. Thereafter, each prepared ingot was milled by means of an agate mortar to prepare powders for the different measurements.

Characterizations and measurements

The microstructural examination and metallographic investigation of the samples were made by means of a Merlin Scanning electron microscopy (SEM) with a Silicon Drift Detector (SDD)-X-Max. Quantitative energy dispersive Xray spectroscopy (EDS) analysis was studied for quantitative phase analyses and composition measurement. Eventually, this characterization technique was performed to investigate the chemical composition and the morphological properties of the samples.

The crystallographic examination was performed by X-ray diffraction (XRD) patterns, recorded on a Bruker D8 diffractometer, using copper CuKα radiation (λ = 1.540562 Å). At room temperature, the data were registered over a 2θ ranging from 20 • to 80 • , with a step width of 0.015 • and counting rate of 13.5 s. The X-ray patterns of GdFe 2-x (Cu,Cr) x (x = 0, 0.1, 0.15 and 0.2) compounds was refined by the Rietveld method [48,49] using FULLPROF program [50,51,52,53,54,55] so as to identify the present phase and to determine the lattice parameters.

Magnetic properties were measured as a function of temperature and magnetic field using a DSM-8 MANICS differential magnetometer [53,54]. The temperature (T ) dependence of magnetization (M) for GdFe 2-x (Cu,Cr) x (x = 0, 0.1, 0.15 and 0.2) compounds was determined from 300 K to 800 K and in applied magnetic field of 0.12 T. The Curie temperature (T C ) for each sample was determined as the minima in the dM/dT plots [56]. The magnetocaloric parameters were evaluated using the magnetic measurements data.

Results and discussion

Structure analysis

The Laves-phases represent the largest group of intermetallic compounds. More than 1400 binary and ternary Laves-phases magnetocaloric effect of GdFe 2-x (Cu, Cr) x (x = 0, 0.1, 0.15 and 0.2) intermetallic compounds -3/11 were introduced in Pearsons Handbook of Crystallographic Data for Intermetallic Phases [START_REF] Villars | Pearsons handbook of crystallographic data for intermetallic phases[END_REF]. Laves-phases show a lot of interesting and useful properties such as excellent magnetic and magnetocaloric effects, corrosion and creep resistance properties. As a result, this class of intermetallics is strongly suggested for use as magneto-optical materials, hydrogen storage materials, magnetic and magnetocaloric materials [START_REF] Thoma | [END_REF]59,60]. These intermetallic phases are also named Friauf-Laves phases by Friauf who first studied the crystallographic their structures [61]. The stability of the AB 2 Laves-phase is ruled by the size ratio of atoms r A /r B equals: (3/2)1/2 = 1.225, where r A and r B are the average atomic radius of atoms occupying the A and B sites of the AB 2 crystal structure. These phases crystallize in three different kind of structure under the different conditions: the hexagonal type structure MgZn 2 (C14) and the double-hexagonal type structure MgNi 2 (C36) at high temperature, and the face centered cubic type structure MgCu 2 (C15) at low temperature [33].

The binary intermetallic compound GdFe 2 adopts the space group Fd 3m with the point symmetry O 7 h and the Pearson symbol cF24. This intermetallic compound belongs to the structure of the cubic Laves-phase MgCu 2 (C15) type. The gadolinium atoms have a face-centered structure and are structured relative to one another. However, the iron atoms are located in the corners of tetrahedral in the structure. This unit cell is formed by eight octants: gadolinium atoms occupy four octants, and the four iron tetrahedrons are located in the other four octants. The rare earth atoms Gd occupy the 8a Wyckoff site ( 18 , 1 8 , 1 8 ), and the transition metal atoms Fe are situated on the 16d site ( 12 , 1 2 , 1 2 ). The gadolinium atom is located at the center of a polyhedron named truncated tetrahedron formed by twelve iron atoms located in the corners. Besides, the iron atom at site 16d is surrounded by six iron atoms and six gadolinium ones. The lengths of Fe -Fe bonds are equal to 2,585 (2) Å, whereas that of Fe -Gd bonds are equal to 3.031 (4) Å as displayed in Figure 1. The detailed crystal structure of GdFe 2 compound and the coordination polyhedra for each Wyckoff site are shown in Figure 1. Iron and gadolinium atoms are drawn as yellow and pink circles, respectively.

The Rietveld refinement results of the X-ray diffraction patterns illustrate that the synthesized samples GdFe 2-x (Cu,Cr) x (x = 0, 0.1, 0.15 and 0.2) crystallize in the cubic MgCu 2 type structure (Fd 3m space group). We show in Figure 2 show that copper and chromium substitute partially iron on Wyckoff site 16d. During this substitution of Fe by Cu and Cr in the GdFe 2-x (Cu,Cr) x (x = 0, 0.1, 0.15 and 0.2), the same MgCu 2 -type structure was preserved. Table 1 summarizes the values of the crystallographic unit cell parameters, the reliability factors obtained from the best refinement, as well as the Gd, Fe, Cu and Cr occupation ratios.

The SEM-EDS analysis, which is in line with the results of the X-ray diffraction patterns, shows that all the prepared samples are single-phase. Figure 3 presents the SEM image micrograph of the GdFe 1.8 Cu 0.2 compound (as an example). The grey area shows that this sample consists only of the MgCu 2 -type structure without any impurity phase. The details of the measured compositions by EDS are listed as follows in Table 2.

In Figure 4, we plotted the variation of the cubic unit cell parameter (a) versus copper and chromium content x in the GdFe 2-x Cu x (x = 0, 0.1, 0.15 and 0.2) and GdFe 2-x Cr x (x = 0, 0.1, 0.15 and 0.2) compounds, respectively, obtained from the X-ray diffraction patterns refinement. The lattice parameter (a) of the GdFe 2 binary compound is equal to 7.430 Å. This value is in agreement with the value of 7.396 Å, previously reported by Buschow [62]. This slight difference of the lattice parameter could be due to the effect of the annealing step, or to the purity of the starting materials. From Figure 4, it can be seen that the lattice parameter (a) drop linearly with the increasing concentration of copper up to x = 0.2. This decrease is due to the smaller atomic radius size of copper (r = 1.45 Å) as compared to that of iron (r = 1.56 Å). On the contrary, a marked enhancement in the lattice parameter (a) was observed when increasing the chromium concentration (Figure 4). This expansion is due to the substitution of larger Cr atoms (r = 1.66 Å) for smaller Fe Let's notice that, I.A. Al-Omari et al. [43] showed that the lattice parameter (a) of GdFe 2-x Ti x (x = 0, 0.05, 0.10, 0.15, 0.20, and 0.30) compounds raise with the increase of Titanium content, since the radius of Ti atom is larger than that of Fe. Furthermore, for the YFe 2-x Al x (x=0.3, 0.5, 0.7) compounds, Z. Li et al. [63] reported that substituting aluminium for iron G d F e 1 , 8 C r 0 , 2 leads to a slight increase of the lattice parameters. In addition, B. Kotur et al. [64] indicated that the substitution of iron by larger atoms (Titanium, Vanadium, Molybdenum) resulted in great enhancement of the lattice parameters as well as the hydrogen capacity of the ErFe 2-x M x compounds.

M ( A m 2 / K g ) µ 0 H ( T ) 1 .8 1 .6 1 .4 1 .2 1 .0 0 .8 0 .6 0 .4 0 .0 0 .2 0
1 .8 1 .6 1 .4 1 .2 1 .0 0 .8 0 .6 0 .4 0 .0 M ( A m 2 / K g ) µ 0 H ( T ) 0 .2 ( b )

Magnetic properties

The magnetic transition temperatures of the GdFe 2-x (Cu,Cr) x (x = 0, 0.1, 0.15 and 0.2) compounds were identified by the temperature dependence of magnetization measurements M(T ) carried out in a low applied magnetic field of 0.12 T. All the studied samples present a sharp ferromagnetic-paramagnetic transition at Curie temperature. The plotted magnetization curves are illustrated in Figure 5. The values of the transition temperature T C is defined from the minimum of the temperature derivative of the magnetization, dM/dT versus temperature.

Review of the influence of copper and chromium substitution on crystal structure, magnetic properties and magnetocaloric effect of GdFe 2-x (Cu, Cr) x (x = 0, 0.1, 0.15 and 0.2) intermetallic compounds -6/11

Consequently, the substitution of Cu and Cr in the GdFe 2-x (Cu,Cr) x (x = 0, 0.1, 0.15 and 0.2) compounds has a striking effect on their magnetic ordering transition temperatures. From Figure 5, we can clearly see that T C drops with the increasing Cu and Cr content. We believe that this decrease is caused by the magnetic dilution that results from the replacement of magnetic iron atoms by non-magnetic copper and chromium atoms. Likewise, W. Steiner et al. [65] have studied the effect of Al substitution by Fe on magnetic and structural properties of Gd(Fe 1-x Al x ) 2 compounds. They showed that T C values decrease with increasing Al content from 795 K for GdFe 2 to 540 K for Gd(Fe 0.8 Al 0.2 ) 2 . Similarly, a previous study by N.H. Duc et al. [66] of the Gd(Fe,Ti) 2 compounds reveals that the increase of Ti concentration causes a gradual reduction in Curie temperature until 750 K for x = 0.1.

The M(H) curves at 300 K as a function of the applied magnetic field for different x values of GdFe 2-x Cu x and GdFe 2-x Cr x are shown respectively in Figure 6. From these curves, we have found that all the samples are magnetically ordered at 300 K and their magnetization depends on the copper and chromium concentration. Furthermore, the saturation magnetization M S was obtained by fitting the isothermal magnetization against magnetic field plots using the saturation approach law [67] :

M = M S 1 - b H 2
We notice that, M S decreases with the substitution of iron by Copper atoms as follows: 62.16 Am 2 /kg (2.99 µ B ) for x = 0; 54.26 Am 2 /kg (2.62 µ B ) for x = 0.1; 47.50 Am 2 /kg (2.29 µ B ) for x = 0.15 and 41.69 Am 2 /kg (2.01 µ B ) for x = 0.2. Likewise, the substitution of iron by chromium atoms has the effect of reducing M S as follows: 53.40 Am 2 /kg (2.56 µ B ) for x = 0.1, 44.33 Am 2 /kg (2.13 µ B ) for x = 0.15, and 37.99 Am 2 /kg (1.82 µ B ) for x = 0.2. Curie temperature and saturation magnetization values of the GdFe 2-x (Cu,Cr) x (x = 0, 0.1, 0.15 and 0.2) compounds are displayed in Table 3.

Magnetocaloric properties

The magnetic refrigeration (MR) based on the magnetocaloric effect (MCE) is of potential impact in both the field of sci-ence and technology due to their energy saving nature and environmental friendliness [START_REF] Trevizoli | Reference Module in Materials Science and Materials Engineering[END_REF][START_REF] Shi | [END_REF]9,10]. The MCE is an intrinsic property of magnetic materials and manifests itself in the heating or cooling of a magnetic material when undergoing a magnetic field. In this work, the magnetization isotherms M(H) for GdFe 2-x (Cu,Cr) x (x = 0, 0.1, 0.15 and 0.2) single crystal compounds were measured in a wide range of temperatures around magnetic transition temperature T C . Figure 7 presents the magnetization isotherms M(H) of the GdFe 2 , GdFe 1.8 Cu 0.2 and GdFe 1.8 Cr 0.2 compounds as an example.

It could be noted that magnetization increases slowly with the applied field above the Curie temperature resulting in the paramagnetic behavior of the compounds. However, below the Curie temperature, the magnetization rises rapidly with the applied magnetic field resulting in the ferromagnetic state of the compounds. The nature of magnetic phase transition of the GdFe 2-x (Cu,Cr) x (x = 0, 0.1, 0.15 and 0.2) compounds was identified by means of the Arrott-plots (µ 0 H/M vs. M 2 ) deduced from the magnetic field dependence of the isothermal magnetization. Arrottplots of GdFe 2 , GdFe 1.8 Cu 0.2 and GdFe 1.8 Cr 0.2 compounds are illustrated in Figure 8 as an example. In this Figure, there is neither S-shape curves nor negative slopes, which is indicative of a first order transition. However, in our experiment, we noted that these plots exhibit a positive slope demonstrating second-ordered phase characteristic of the ferromagnetic to paramagnetic transition as demonstrated by the Banerjee criterion [68].

To clarify the nature of the paramagnetic-ferromagnetic phase transition we used the Landau theory [69] and the Inoue-Shimizu model [70]. The magnetic free energy F can be expanded in power of magnetization M:

F(M, T ) = 1 2 a(T )M 2 + 1 4 b(T )M 4 + 1 6 c(T )M 6 +. . .-µ 0 HM
where a(T ), b(T ), and c(T ) are the Landau coefficients. The minimization of F(M, T ) with respect to M gives:

µ 0 H = a(T )M + b(T )M 3 + c(T )M 5
The coefficient a(T ) presents a minimum at T = T C , while the coefficient b(T ) can be positive, zero, or negative. When b(T C ) is positive or null the magnetic phase transition is of the second order, whereas, a first order magnetic phase transition occurs when b(T C ) is negative.

Figure 9 shows the evolution of the Landau coefficients a(T ) and b(T ) with the temperature for GdFe 1.8 Cu 0.2 compound. We clearly observed that b(T = T C ) = 0, which means that F(M, T ) is minimum that corresponds to M = 0 and consequently confirms the second order phase transition.

Magnetic compounds that show SOMT exhibit very low thermal and magnetic hysteresis. They could therefore be candidates for magnetic cooling.

The MCE of the samples is characterized by the isothermal magnetic entropy change ∆S(T ) as a function of temperature T and the applied magnetic field H. Indeed, the magnetic entropy change, ∆S(T ) was calculated through the numerical integration of the isothermal magnetization curves M(H, T ) between µ 0 H = 0 and µ 0 H = 1.56 T, employing the following Maxwell's thermodynamic formula [71]:

M ( A m 2 / K g ) m 0 H ( T ) 2 .0 1 .8 1 .6 1 .4 1 .2 1 .0 0 .8 0 .6 0 .4 0 .0 0 .2
∆S = µ 0 H 0 ( ∂ M ∂ T )dH ∆S(T i , ∆H) = µ 0 ∑ j M i+1 (T i+1 , H j ) -M i (T i , H j ) T i+1 -T i ∆H j
The magnetic entropy change plots measured at different temperatures under external field change for GdFe 2 , GdFe 1.8 Cu 0.2 and GdFe 1.8 Cr 0.2 compounds are illustrated in Figure 10. It is clearly seen that the maximum magnetic entropy change at the magnetic ordering temperature for the GdFe 2 reaching a value of ∆S max = 0.79 J/kg K at T C = 795 K leads to a pronounced increase as both copper and chromium content x increases. Meanwhile, the ∆S max for GdFe 2-x Cu x samples are slightly higher than those measured for alloys GdFe 2-x Cr x . For example, ∆S max value for the GdFe 1.8 Cu 0.2 sample is equal to 2.5 J/kg K, while ∆S max value achieved for the GdFe 1.8 Cr 0.2 sample is about 1.8 J/kg K.

The relative cooling power (RCP) is another crucial parameter that needs to be measured so as to determine the efficiency and the suitability of corresponding magnetocaloric materials for magnetic cooling. This factor is defined as the transferring of heat from the cold sink to the hot one in a refrigerant cycle. RCP is determined as a product of the full-width half maximum value in ∆S max ) curves and the maximum peak value of the entropy change, and is given by the below equation [72]:

RCP = -∆S Max × δ T FW HM
The field change dependence of the RCP for GdFe 2 , GdFe 1.8 Cu 0.2 and GdFe 1.8 Cr 0.2 compounds is summarized in the inset of Figure 10. The calculated -∆S max , and RCP parameters extracted from magnetocaloric study of all the studied compounds are listed in Table 4. From on this table, we can see that the RCP of GdFe 2-x Cu x (x= 0, 0.1, 0.15 and 0.2) compounds rise up monotonically as the copper concentration increases from 13.3 J/kg K to 44.3 J/kg K for x = 0 and x = 0.2, respectively. Similarly, the chromium substitution increases in effective way the RCP value of GdFe 2-x Cr x (x= 0, 0.1, 0.15 and 0.2) alloys. Because of the high value of Curie temperature, the GdFe 2-x (Cu,Cr) x alloys are qualified to be a significant candidate for magnetic refrigeration applications at high temperature (heat pump). The values of the magnetic entropy of the GdFe 2-x (Cu,Cr) x system are close to those determined in the R(Fe,Co) 2 system [73,74,75,76].

In order to improve the definition of the figure of merit and to make it more relevant, a new Temperature Averaged Entropy Change (TEC) parameter was proposed [77,78,79,80,81]. TEC can be derived using the following relation:

TEC(∆T H-C ) = 1 ∆T H-C max        T mid + ∆T H-C 2 T mid - ∆T H-C 2 |∆S M (T )|dT       
where ∆T H-C = T Hot -T Cold , T mid was chosen to optimize TEC(∆T H-C ). The calculated TEC values are given in Table 4.

We can notice, on the one hand, that the Temperature Averaged Entropy Change decreases with increasing ∆T H-C , and on the other hand, the substitution of Fe by Cr or Cu atoms increases the TEC value, in another words, the magnetocaloric efficiency is increased. In addition, the RCP parameter generally overestimate the magnetocaloric effect merit of intermetallics with a second-order phase transition.

Conclusion

The present paper explores the series of compounds GdFe 2-x (Cu, Cr) x (x= 0, 0.1, 0.15 and 0.2) with the aim of investigating their structural, magnetic and magnetocaloric properties. Room temperature X-ray powder diffraction analysis demonstrates that the crystal structure of all the synthesized compounds belongs to the cubic Laves-phase with MgCu 2 -type structure (Fd 3m space group). Indeed, the crystal structure of the parent compound GdFe 2 was found to stay conserved for all the melting alloys. The effect of substituting iron atoms in GdFe 2 with larger copper atom, leads to a rise in the lattice parameter a and the unit cell volume V . In contrast, these parameters decrease linearly with the increasing chromium atom. The study of the magnetic properties of the GdFe 2-x (Cu, Cr) x (x= 0, 0.1, 0.15 and 0.2) compounds revealed that the Curie temperature reduces with Cu and Cr substitutions. In fact, this decrease is due to the substitution of magnetic atoms by non-magnetic ones. The positive slopes of the Arrott plots for the substituted compounds indicate that the phase transition from ferromagnetic to paramagnetic state around T C undergo a second-order phase transition. Emphasis is mainly given to the study of magnetocaloric performances in the vicinity of magnetic phase transition in terms of the maximum magnetic entropy change and the relative cooling power. It is significant to note that a pronounced enhancement of the values of -∆S max and RCP of such substituted compounds occurs with the increase of copper and chromium content. A

Review of the influence of copper and chromium substitution on crystal structure, magnetic properties and magnetocaloric effect of GdFe 2-x (Cu, Cr) x (x = 0, 0.1, 0.15 and 0.2) intermetallic compounds -10/11

Mössbauer spectrometry study will be performed to confirm the structural properties and to determine the local magnetic moment per inequivalent crystallographic site. Moreover, abinitio calculations of the electronic structure will be carried out to determine the theoretical magnetic moments and hyperfine fields in order to compare them with those derived by Mössbauer spectrometry.

Figure 1 .

 1 Figure 1. Crystal structure of GdFe 2 and coordination polyhedra for each crystallographic site.

  the observed and calculated patterns as well as the difference profile of the GdFe 2 , GdFe 1.8 Cu 0.2 and GdFe 1.8 Cr 0.2 compounds as an example. The set of bars corresponds to the calculated positions of the Bragg peaks of the refined compounds. It is clear from Figure 2 that all compounds exhibit a perfect pure cubic single Laves-phase nature. The high quality of the refinement is corroborated by the low value of the fit indicator χ 2 and R B . It is noteworthy that the refinement analysis results

Figure 2 .

 2 Figure 2. The Rietveld refinement of the X-ray powder diffraction patterns of GdFe 2 , GdFe 1.8 Cu 0.2 and GdFe 1.8 Cr 0.2 compounds measured at room-temperature.

Figure 3 .

 3 Figure 3. Backscattered electron SEM image of the GdFe 1.8 Cu 0.2 compound.

Figure 4 .

 4 Figure 4. Variation of the lattice parameter a of (a) GdFe 2-x Cu x (x = 0, 0.1, 0.15 and 0.2) vs. Cu content and, (b) GdFe 2-x Cr x (x = 0, 0.1, 0.15 and 0.2) vs. Cr content.

Figure 5 .

 5 Figure 5. M(T) curves for (a) GdFe 2-x Cu x (x = 0, 0.1, 0.15 and 0.2) and, (b) GdFe 2-x Cr x (x = 0, 0.1, 0.15 and 0.2). Tne inset : dM/dT vs temperature.

Figure 6 .

 6 Figure 6. M(H) curves at T = 300 K for (a) GdFe 2-x Cu x (x = 0, 0.1, 0.15 and 0.2) and, (b) GdFe 2-x Cr x (x = 0, 0.1, 0.15 and 0.2) compounds.

  Review of the influence of copper and chromium substitution on crystal structure, magnetic properties and magnetocaloric effect of GdFe 2-x (Cu, Cr) x (x

Figure 7 .Figure 8 .Figure 9 .Figure 10 .

 78910 Figure 7. Isotherm magnetization curves M(H, T ) of (a) GdFe 2 , (b) GdFe 1.8 Cu 0.2 and (c) GdFe 1.8 Cr 0.2 compounds.

Table 1 .

 1 XRD

	62	1	0.950	0.050	-

analysis results obtained by Rietveld method on the GdFe 2-x (Cu, Cr) x (x = 0, 0.1, 0.15 and 0.2) compounds. Compounds a ( Å) V ( Å3 ) χ 2 R B Occupancy Gd(8a) Fe(16d) Cu(16d) Cr(16d) GdFe 2 7.430(2) 410.172(4) 1.97 2.91 1 1 --GdFe 1.9 Cu 0.1 7.397(5) 404.731(3) 1.57 2.

Table 2 .

 2 EDS results of the GdFe 2-x (Cu, Cr)

	x (x = 0, 0.1,

Table 3 .

 3 Values of Curie temperature and saturation magnetization for GdFe 2-x (Cu, Cr) x (x= 0, 0.1, 0.15 and 0.2)

	compounds.
	Compounds	T C (K) M S (Am 2 /kg)
	GdFe 2	795	62.16
	GdFe 1.9 Cu 0.1	760	54.26
	GdFe 1.85 Cu 0.15	745	47.50
	GdFe 1.8 Cu 0.2	720	41.69
	GdFe 1.9 Cr 0.1	780	53.40
	GdFe 1.85 Cr 0.15	766	44.33
	GdFe 1.8 Cr 0.2	757	37.99

Table 4 .

 4 Values of maximum entropy variation -∆S max , relative cooling power RCP, and Temperature Averaged Entropy Change (TEC) for ∆T H-C of 3 and 10 K, for GdFe 2-x (Cu, Cr) x (x= 0, 0.1, 0.15 and 0.2) compounds compared with other R(Fe,Co) 2 magnetic materials.Compounds µ 0 H(T) -∆S max (J/kg.K) RCP (J/kg) TEC(3) (J/kg.K) TEC(10) reference

	GdFe 2	1.5	0.79	13.3	1.46	1.15	This work
	GdFe 1.9 Cu 0.1	1.5	1.2	21.6			This work
	GdFe 1.85 Cu 0.15	1.5	1.4	31.7			This work
	GdFe 1.8 Cu 0.2	1.5	2.5	44.3	2.17	1.53	This work
	GdFe 1.9 Cr 0.1	1.5	0.9	14.8			This work
	GdFe 1.85 Cr 0.15	1.5	1.3	25.4			This work
	GdFe 1.8 Cr 0.2	1.5	1.8	36.8	2.85	2.12	This work
	HoFe 0.4 Co 1.6	1.5	0.5	-	-	-	[75]
	HoFe 0.14 Co 1.86	1.5	1.5	-	-	-	[75]
	ErFe 0.1 Co 1.9	1	3	-	-	-	[73]
	ErFe 0.2 Co 1.8	1	1	-	-	-	[73]
	TbFe 0.1 Co 1.9	5	3.5	-	-	-	[74]
	DyFe 0.08 Co 1.92	2	2.5	-	-	-	[76]

Review of the influence of copper and chromium substitution on crystal structure, magnetic properties and magnetocaloric effect of GdFe 2-x (Cu, Cr) x (x = 0, 0.1, 0.15 and 0.2) intermetallic compounds -2/11

Acknowledgments

This work was mainly supported by the CNRS, ICMPE, France, and the Tunisian Ministry of Higher Education and Scientific Research and Technology, LSME, University of Sfax, Tunisia.