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Structure, magnetocaloric properties and thermodynamic modeling of enthalpies of formation of (Mn,X)-Co-Ge (X = Zr, Pd) alloys
Journal of Alloys and Compounds 796 (2019) 153e159
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Structure, magnetocaloric properties and thermodynamic modeling of enthalpies of formation of (Mn,X)-Co-Ge (X ¼ Zr, Pd) alloys b Piotr Ge˛ bara a, *, Zbigniew Sniadecki a b
Institute of Physics, Cze˛ stochowa University of Technology, Armii Krajowej 19 Av., 42-200 Cze˛ stochowa, Poland , Poland Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 November 2018 Received in revised form 2 April 2019 Accepted 30 April 2019 Available online 4 May 2019
Enthalpies of formation of (Mn,X)-Co-Ge (X ¼ Zr, Pd) system in different structural states were analyzed utilizing the semi-empirical Miedema's model combined with the geometric one. Substitution of Mn by Zr significantly improves glass forming ability of Mn-Co-Ge, with parent equiatomic alloy among them. Chosen half-Heusler alloys, which are thermodynamically stable for the mentioned elemental compositions, were obtained by arc-melting. The x-ray diffraction studies confirmed coexistence of orthorhombic NiTiSi-type and hexagonal Ni2In-type structures for parent MnCoGe alloy and (Zr, Pd)substituted samples. Thermomagnetic curves and magnetic isotherms allowed to reveal the Curie temperature TC and a magnetic entropy change DSM and allowed to analyze the influence of both substitutive elements. The Curie temperatures are equal to 293 K for MnCoGe, 278 K for Mn0.9Zr0.1CoGe alloy and 318 K for Mn0.9Pd0.1CoGe. The maximum magnetic entropy change DSM values, calculated for the change of external magnetic field of about 5 T, amount to 6.17, 2.94, and 11.11 J (kg K)1 for MnCoGe, Mn0.9Zr0.1CoGe and Mn0.9Pd0.1CoGe, respectively. Differences in magnetic characteristics of the analyzed alloys are mainly caused by the changes of extent of undergoing first order magnetostructural transition with Pd and Zr atoms substitution. The presence of Pd d moments is also beneficial for the enhancement of total magnetic moment and maximum value of magnetic entropy changes in Mn0.9Pd0.1CoGe alloy. © 2019 Elsevier B.V. All rights reserved.
Keywords: Heusler alloys Magnetocaloric effect Miedemas model
1. Introduction According to research of International Energy Agency, the energy consumed for cooling has risen drastically since 1990. Such situation is caused by permanent increase of a number of cooling devices basing on gas compression/expansion. An efficiency of such process is relatively low and reaches about 40% [1]. One of the cooling techniques with higher efficiency is based on intrinsic thermomagnetic property of magnetic material, which is well known today as magnetocaloric effect (MCE). A magnitude of the MCE can be expressed by adiabatic temperature change DTad or isothermal magnetic entropy change DSM. The MCE is observed in the vicinity of room temperature in some materials and intensive studies have been conducted on this group up to date, due to their potential application as an active magnetic regenerator in magnetic refrigerator. The main groups of materials which have been investigated for over twenty years are: (i) Gd [2] and its alloys (Gd5Si2Ge2
* Corresponding author. E-mail address: [email protected] (P. Ge˛ bara). https://doi.org/10.1016/j.jallcom.2019.04.341 0925-8388/© 2019 Elsevier B.V. All rights reserved.
[3] or Gd-based amorphous phases [4]), (ii) La(Fe,Si)13-type alloys [5e7], (iii) manganites [8,9] or (iv) Heusler alloys [10e12]. Relatively newly developed family of a room temperature magnetocaloric materials can be generally described as TM1-TM2-M, where TM1 and TM2 are transition metals, while M is a metalloid [13e16]. High values of DSM of TM1-TM2-M alloys are related to magnetostructural transition between high temperature paramagnetic phase (Ni2In-type) and low temperature ferromagnetic phase (TiNiSi-type). Indeed, the equiatomic TM1-TM2-M alloys are composed of the high temperature Ni2In-type hexagonal phase (P63/mmc space group) and low temperature TiNiSi-type orthorombic one (Pnma space group). Thermoelastic martensitic-like transition is observed in this group of alloys at 420 K [17]. Chemical composition of these alloys have been modified by Cr [18], Fe-Ni [19], Ga [20] and B or C [21], recently. The main long-term aim concerns the optimization of magnetic properties of half-Heusler alloys by substitution of Mn by Zr and Pd atoms and by the modification of microstructure by rapid quenching of molten alloy. At first, it was necessary to determine enthalpies of formation of (Mn,X)-Co-Ge (X ¼ Zr, Pd) to design compositions for further studies. We plan to synthesize samples in
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amorphous or partially amorphous state as precursors for crystallization of half-Heusler alloys. In this paper we calculate enthalpies of formation of (Mn,X)-Co-Ge (X ¼ Zr, Pd) in different structural states and analyze crystalline structure and magnetocaloric properties of chosen half-Heusler alloys in as-cast form, which will act as references in further studies.
DPHS, which is the product of chemical enthalpy and mismatch entropy [25]. Extrapolation of the thermodynamic properties of sub-binary systems was done using geometric model to determine the GFA of ternary and quaternary alloys. The calculations are described in more details in Refs. [25,26]. 3. Results and discussion
2. Experiment and calculations 3.1. Semi-empirical calculations of the enthalpies of formation The ingots were prepared by arc-melting of pure elements (Mn, Co, Ge, Zr, Pd) under a low pressure of inert gas (Ar). Samples were remelted several times to ensure their homogeneity. The structural analysis was done using Bruker D8 Advance diffractometer equipped with copper tube (CuKa) and semiconductor LynxEye detector. The X-ray diffraction data was refined by the Rietveld method using POWDERCELL 2.4 package [22]. Thermomagnetic curves and magnetic isotherms were measured using Quantum Design PPMS (VSM option) in magnetic field up to 5 T. The semi-empirical Miedema's model [23,24] was used to determine the enthalpies of formation. The emphasis was put on the calculations for amorphous phase and solid solution in each case, which would be complemental to vast number of literature data on intermetallic compounds. The most fundamental indicator of glass forming ability (GFA) is the enthalpy of formation of amorphous phase [fx]. The formation enthalpy of solid solution can be expressed using DHss . Other physical quantities and parameters were also calculated to indicate the difference of formation ability of phases which compete during the solidification process, namely (i) difference of formation enthalpies DHamss ¼ DHam DHss (ii) normalized mismatch entropy Ss/kB [25], which reflects the effect of atomic radius mismatch and (iii) glass forming ability parameter
Enthalpies of formation of amorphous phase, solid solution and differences between both quantities were calculated along with the normalized mismatch entropy and GFA parameter for Mn-Co-Ge, Zr-Co-Ge and Pd-Co-Ge ternaries. The results for Mn-Co-Ge system, treated in this paper as parent composition, are presented in Fig. 1 in the form of enthalpy-composition contour maps. Formation enthalpies of amorphous phase and solid solution are presented in Fig. 1a and b, respectively, while the difference of enthalpies DHamss in Fig. 1c. The most negative enthalpy values were obtained for Mn-Ge binaries in the vicinity of equiatomic composition, reaching almost 25 kJ/mol for Mn52Ge48. Such result can be justified by significant difference of Mn and Ge atomic radii, in comparison to Mn-Co and Co-Ge binaries, and by moderate values of interfacial enthalpy between all constituents. For the composition of interest in the present paper, equiatomic MnCoGe, DHam is equal to about 17.5 kJ/mol. Similar phase diagram was obtained for Mn-Co-Ge solid solutions (Fig. 1b), but the values of enthalpy of formation are slightly more negative than in the case of amorphous phase. This results in the positive values of DHamss in the whole composition range (Fig. 1c), indicating preferential formation of solid solution and reduced GFA. For MnCoGe
Fig. 1. Compositional dependences of formation enthalpy of amorphous phase DHam (a), formation enthalpy of solid solution DHss (b), their difference DHamss (c), normalized mismatch entropy Ss/kB (d) and glass forming ability parameter DPHS (e) for Mn-Co-Ge. Grey dots represent equiatomic MnCoGe composition.
P. Ge˛ bara, Z. Sniadecki / Journal of Alloys and Compounds 796 (2019) 153e159
composition, DHss and DHamss are equal to 20.7 kJ/mol and 3.2 kJ/mol, respectively. The normalized mismatch entropy (Fig. 1d) reflects the mismatch effect of atomic radii of constituents and for Mn-Co-Ge ternary alloys range from about 0 to 0.15. Mean value of Ss/kB calculated for a large group of ternary amorphous alloys by Takeuchi and Inoue [26] is equal to ~0.33. They have concluded that the critical value for the formation of amorphous phase is equal to 0.1 and the increase of the mismatch entropy facilitates the amorphization. The contour maps of formation enthalpy (Fig. 1a and b) and mismatch entropy (Fig. 1d) are consistent. It confirms the major impact of differences in atomic radii and limited influence of interfacial enthalpies. Described calculations took into account the topological disorder. GFA parameter denoted by DPHS add the chemical aspect by combining chemical enthalpy with Ss/kB. The calculated values are presented in Fig. 1e confirming the conclusions drawn before. In our case, an additional element does not promote the formation of glassy state and ternary alloys are still not favored to form the amorphous phase, which is in some manner in contradiction to one of the Inoue rules [27]. Fig. 2 shows the relation between mixing enthalpy DHchem and normalized mismatch entropy (Ss/kB) for the group of Mn-Co-Ge alloys. A marked area (between dashed lines described as Ss/kB ¼ 1 and log(Ss/
Fig. 2. Relation between log(Ss/kB) and DHchem for the Mn-Co-Ge system. Equiatomic MnCoGe composition is marked with a red dot. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
155
kB) ¼ log(2 102)x(DHchem/100 þ 1)) has been empirically determined as a glass forming region on the basis of a vast number of data by Takeuchi and Inoue [28]. Almost all of the alloys from MnCo-Ge family (with equiatomic MnCoGe, marked by red dot, among them) are on the verge of fulfilment of this GFA criterion, confirming low probability of formation of amorphous structure. This conclusion coincide with the earlier analysis. Substitution of Mn atoms by Zr in Mn-Co-Ge system changed the thermodynamic properties of the major part of analyzed alloys. Phase diagrams of formation enthalpies of amorphous phase and solid solution (refer to Fig. 1 in Supplementary material) are qualitatively very similar to those of Mn-Co-Ge. Nevertheless, enthalpies of formation are much more negative, mainly due to the values of interfacial enthalpy of Zr-Co and Zr-Ge binaries and relatively large atomic radius of zirconium. The lowest values of DHam and DHss of about 67 kJ/mol were reached for Zr48Ge52 and Zr49Ge51, respectively. In turn, DHam and DHss for equiatomic ZrCoGe are equal to about 50.9 kJ/mol and 43.4 kJ/mol, respectively. Increase of GFA after Zr substitution can be also confirmed by DHamss (Fig. 3a), Ss/kB (Fig. 3b) and DPHS (Fig. 3c). DHamss for ZrCo-Ge is negative in the large area of the phase diagram with the minimum of about 15.3 kJ/mol for Zr49Co51 alloy (Fig. 3c). Therefore, the criterion of GFA is also fulfilled in this case. Compositions close to the Co-Ge and Zr-Ge edges of phase diagram are suggested to form a solid solution rather than a glassy state. Moreover, Ss/kB exceeds the threshold value of 0.1 roughly for the same composition range, with the maximum of 0.31 reached for Zr41Co59, due to significant difference in atomic radii of both elements (rZr ¼ 1.60 Å, rCo ¼ 1.26 Å). The DPHS results differ from those presented in the previously described diagrams. Ternary Zr41Co42Ge17 with DPHS ¼ 13.8 kJ/mol is the composition with the highest GFA. Therefore, it is obvious in this case that an additional element promotes the amorphization in ternary alloys, as expected. For ZrCoGe, DPHS ¼ 12.7 kJ/mol and confirms the possibility of formation of fully amorphous alloy. Substitution of Pd in place of Mn in Mn-Co-Ge system does not change the thermodynamic properties significantly. Phase diagrams of formation enthalpies of amorphous phase and solid solution (refer to Fig. 2 in Supplementary material) qualitatively coincide with those of Mn-Co-Ge and Zr-Co-Ge, with the most negative values DHam ¼ 37.3 kJ/mol and DHss ¼ 41.9 kJ/mol for Pd49Ge51 and Pd50Ge50, respectively. Enthalpies of formation are more negative than those for Mn-Co-Ge but do not reach the level delineated by Zr-containing alloys. The main conclusion which should be drawn on the basis of DHamss contour map (Fig. 4a) is the positive value of the differential enthalpy for almost all compositions, except Co-Ge edge, where the values are still just slightly
Fig. 3. Compositional dependences of DHamss (a), Ss/kB (b) and DPHS (c) for Zr-Co-Ge. Grey dots represent equiatomic ZrCoGe composition.
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Fig. 4. Compositional dependences of DHamss (a), Ss/kB (b) and DPHS (c) for Pd-Co-Ge. Grey dots represent equiatomic PdCoGe composition.
negative. It indicates extremely low GFA at the expense of formation of solid solution. The normalized mismatch entropy reaches the maximum value of about 0.05, which is much lower than the threshold value of 0.1 [27]. DPHS is just slightly negative and equal to 1.1 kJ/mol for the equiatomic composition. The results described in this paragraph lead to the conclusion that the glass forming ability of Pd-Co-Ge is very low and the formation of solid solution would be preferred during synthesis. The differences of DHamss of Mn-Co-Ge and substituted systems are shown in Fig. 5 to give direct evidence of areas of phase diagram, where the glassy state formation is improved by Zr (Fig. 5a) or Pd (Fig. 5b). The regions where the enthalpies of Mn-CoGe and Zr/Pd-Co-Ge take lower values, are marked accordingly with Mn and Zr/Pd symbols. Black solid lines indicate the compositions where the enthalpies of both compared systems are of the
same value. Presented results confirm conclusion drawn in previous paragraphs, that Zr improves the GFA, while substitution of Pd insignificantly changes the thermodynamic parameters of Mn-CoGe, especially for the stoichiometry of interest (marked with a grey dot). Zirconium substitution decreases the initial DHamss value for Mn-Co-Ge system by 10.6 kJ/mol. The values of formation enthalpy of amorphous phase DHam , formation enthalpy of solid solution DHss , their difference DHamss , normalized mismatch entropy Ss/kB and glass forming ability parameter DPHS, were also calculated by us for the quaternary Mn0.9Zr0.1CoGe and Mn0.9Pd0.1CoGe alloys (Table 1). Presented results confirm the conclusions drawn from the particular phase diagrams, that Zr improves glass forming ability of Mn-Co-Ge alloys, while Pd is neutral in this sense, especially due to the atomic radii comparable to those of Co and Ge and negligibly small interfacial
Fig. 5. Phase diagrams exhibiting the difference of DHamss for Mn-Co-Ge and Zr/Pd-Co-Ge. The areas where Mn-Co-Ge is characterized by lower enthalpy values than Zr-Co-Ge (a) and Pd-Co-Ge (b) and the regions where the opposite relation holds, are marked accordingly with Mn and Zr/Pd symbols.
Table 1 Enthalpies of formation of amorphous phase DHam , of solid solution DHss , their difference DHamss , normalized mismatch entropy Ss/kB and glass forming ability parameter DPHS calculated for the ternary (Mn,Zr,Pd)CoGe and quaternary Mn0.9(Zr,Pd)0.1CoGe alloys.
MnCoGe ZrCoGe PdCoGe Mn0.9Zr0.1CoGe Mn0.9Pd0.1CoGe
DHam [kJ/mol]
DHss [kJ/mol]
DHamss [kJ/mol]
Ss/kB
DPHS [kJ/mol]
17.5 50.9 20.6 19.3 17.1
20.6 43.4 23.6 22.6 21.7
3.1 7.5 3.0 3.3 4.6
0.10 0.22 0.04 0.14 0.10
2.6 12.7 1.1 4.1 2.6
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enthalpy with Co. Mn0.9Zr0.1CoGe and Mn0.9Pd0.1CoGe were chosen for future investigations to check the influence of Pd and Zr on GFA experimentally and, if successful, to crystallize half-Heusler alloys from amorphous or partially amorphous precursors. Low content of Pd and Zr was maintained to avoid destabilization of expected phases, which would be appropriate from the point of view of magnetocaloric properties. As-cast samples synthesized on the present stage are characterized in details in the second part of the paper. This alloys will pose in the future as the reference for rapidly quenched samples. We should compare the calculated values of enthalpies of formation of amorphous alloys and solid solutions to those of intermetallic compounds, to have an overarching view. Due to coexistence of many different types of phases in half-Heusler alloys and chemical disorder in many cases, it is difficult to take into account all factors, which govern their thermodynamic properties and stability. Nevertheless, we compare enthalpies of formation of intermetallic compounds, which were calculated by Miedema's model for equiatomic binaries (Table 2) [24]. In the case of each binary system the enthalpy of formation of intermetallic compound is the most negative, comparing to the formation enthalpies of amorphous phase and solid solution. Nevertheless, we have to take into account rather small differences of mentioned quantities in most cases and the substitution effect, which favors the formation of glassy structure or solid solution (like in the case of high entropy alloys) instead of intermetallic phases. Moreover, we should not deny the benefits of kinetic factors, which additionally promote vitrification during rapid quenching.
3.2. Crystalline structure and magnetocaloric properties of halfHeusler alloys The x-ray diffraction patterns collected at room temperature for MnCoGe, Mn0.9Zr0.1CoGe and Mn0.9Pd0.1CoGe samples are shown in Fig. 6. The XRD pattern obtained for MnCoGe alloy revealed a coexistence of austenitic hexagonal Ni2In-type phase and small volume fraction of martensitic orthorhombic NiTiSi-type phase. The 10 at.% substitution of Mn by Pd caused an increase of orthorhombic phase content at the expense of hexagonal one. Such behavior suggests that Pd hampers formation of hexagonal phase. Moreover, the content of orthorhombic phase is relatively high and reaches up to 45 vol%, which allows us to state that Pd could stabilize the TiNiSi-type phase formation. Similar situation was observed in Zr-substituted sample. The coexistence of dominant hexagonal Ni2In-type (72 vol%) and orthorhombic phase was confirmed. The orthorhombic structure can be treated as a distorted hexagonal one [29]. The results of the Rietveld refinement were collected in Table 3. The values of lattice parameters calculated for MnCoGe alloy are
Table 2 Enthalpies of formation of amorphous phase DHam , solid solution DHss and intermetallic compounds DHinter in AB equiatomic binary systems. A
B
DH [kJ/mol] Co
Ge
Mn
DHam DHss DHinter [23] DHam DHss DHinter [23] DHam DHss DHinter [23]
Co
15 14 17 1 5 8
Ge
Mn
Zr
Pd
15 14 17
1 5 8 25 26 32
33 18 60 67 67 97 9 3 23
5 3 2 37 42 51 17 21 34
25 26 32
157
Fig. 6. X-ray diffraction patterns of MnCoGe, Mn0.9Pd0.1CoGe and Mn0.9Zr0.1CoGe alloys.
Table 3 The results of Rietveld refinement of the x-ray diffraction patterns of MnCoGe, Mn0.9Pd0.1CoGe and Mn0.9Zr0.1CoGe alloys. Alloy
Crystalline phase
Lattice parameter [Å] ± 0.001
a ¼ 4.070 c ¼ 5.281 Orthorhombic NiTiSi- type a ¼ 5.936 b ¼ 3.822 c ¼ 7.051 Mn0.9Pd0.1CoGe Hexagonal Ni2In- type a ¼ 4.081 c ¼ 5.286 Orthorhombic NiTiSi- type a ¼ 5.944 b ¼ 3.827 c ¼ 7.058 Mn0.9Zr0.1CoGe hexagonal Ni2In- type a ¼ 4.081 c ¼ 5.285 Orthorhombic NiTiSi- type a ¼ 5.941 b ¼ 3.827 c ¼ 7.055 MnCoGe
Hexagonal Ni2In- type
Volume fraction [%] 94 6
55 45
72 28
similar to those revealed by Li et al. [30]. Lattices of hexagonal and orthorhombic phases of Pd- and Zr-substituted samples are slightly expanded, due to the atomic radii of Pd (rPd ¼ 1.37 Å) and Zr (rZr ¼ 1.60 Å) overmatching Mn radius (rMn ¼ 1.18 Å). The increase of lattice parameters of hexagonal and orthorhombic phases is relatively small. It could suggest the occupation of Ge site (rGe ¼ 1.39 Å) instead of Co/Mn by large substitutive atoms. Nevertheless, more detailed analysis is needed to give a firm conclusion. The most important, it is evident that the phase constitution is preserved in both quaternary alloys with 10 at.% substitution of Mn atoms. It is believed that further adjustment of content of particular phases could be achieved by the optimization of initial state, for example by rapid quenching and subsequent annealing. In order to reveal the magnetic properties a temperature dependence of magnetization was measured (Fig. 7) in magnetic field of 0.1 T in three regimes: (i) during warming after zero field cooling (ZFC), (ii) during field cooling (FC) and (iii) during warming after cooling in field. The Curie temperature was determined from the temperature derivative of FC magnetization versus temperature plot, with estimated values of 293 ± 1, 278 ± 1 and 318 ± 1 K for MnCoGe, Mn0.9Zr0.1CoGe and Mn0.9Pd0.1CoGe, respectively. Moreover, for MnCoGe alloy and Pd-substituted sample, the temperature
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Fig. 8. Temperature dependences of magnetic entropy change of MnCoGe (a), Mn0.9Zr0.1CoGe (b) and Mn0.9Pd0.1CoGe (c) alloys.
isotherms collected over a wide range of temperatures. The calculations of magnetic entropy change DSM were made using thermomagnetic Maxwell relation [32]:
ðH
DSM ðT; DHÞ ¼ m0 0
Fig. 7. Temperature dependences of magnetization measured for Mn0.9Pd0.1CoGe and Mn0.9Zr0.1CoGe alloys in ZFC, FC and FCW regimes.
MnCoGe,
hysteresis between FC and FCW curves is clearly visible. Such behavior indirectly suggests an occurrence of first order phase transition in MnCoGe and Mn0.9Pd0.1CoGe alloys. In the case of Zrsubstituted sample, the temperature hysteresis is just slightly visible and the M(T) curves are less steep with broader transition range than for parent compound and Pd-substituted sample. Therefore we expect that the volume fraction undergoing first order phase transition is smaller in this case and magnetic properties more likely resemble those of system undergoing second order phase transition. The magnetocaloric effect (MCE), characterized by magnetic entropy change, was determined indirectly from magnetization
vMðT; HÞ vT
dH;
(1)
H
where T is temperature, m0 is magnetic permeability, H is magnetic field strength and M is magnetization. Peak of the DSM vs. T curves (Fig. 8) corresponds well with the Curie point of each alloy determined on the basis of thermomagnetic measurements. The maximum magnetic entropy change DSM values, calculated for the change of external magnetic field of ~5 T, amount to 6.17, 2.94 and 11.11 J (kg K)1 for MnCoGe, Mn0.9Zr0.1CoGe and Mn0.9Zr0.1CoGe, respectively. The smallest values of DSM are observed for the sample substituted by Zr. This is in accordance with the analysis of M(T) curves, where the first order magnetostructural phase transition was suggested to occur for parent alloy and Pd-substituted sample. On the other hand, almost two times higher value of magnetic entropy change, than for MnCoGe alloy, was measured for Pd-substituted sample. In this case, the dTFWHM value is relatively low. Low dTFWHM and high DSM are typical for the first order phase transition with consistent evidence in the form of thermal hysteresis characteristic for magnetostructural transition observed in M(T) curve measured for Mn0.9Pd0.1CoGe. The increase of maximum value of DSM, in comparison to parent compound, is connected with the enhancement of total magnetic moment of the alloy (bearing in mind the influence of undergoing magnetostructural transition also). This strengthening is related to additional magnetic moment on palladium atoms, as reported in
P. Ge˛ bara, Z. Sniadecki / Journal of Alloys and Compounds 796 (2019) 153e159 Table 4 Magnetic entropy change DSM and refrigerant capacity RC for MnCoGe, Mn0.9Zr0.1CoGe and Mn0.9Pd0.1CoGe alloys. Alloy
D(m0H) [T]
DSM [J (kg K)1]
RC [J kg1]
MnCoGe
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
1.22 2.65 3.89 5.05 6.17 0.66 1.35 1.97 2.42 2.94 2.02 4.33 6.68 8.83 11.11
38 80 129 160 193 33 78 121 177 219 39 86 131 209 238
Mn0.9Zr0.1CoGe
Mn0.9Pd0.1CoGe
P.G. would like to thank to Prof. Norbert Sczygiol e the Rector of Cze˛ stochowa University of Technology for financial support. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jallcom.2019.04.341. References
Tð hot
DSM ðT; HMAX ÞdT
mainly caused by the alteration of extent of the first order magnetostructural transition with Pd and Zr substitutions and by the presence of additional d moments of Pd introduced in Mn0.9Pd0.1CoGe. Acknowledgements
Ref. [31]. The values of the DSM revealed for the Mn0.9Pd0.1CoGe alloy are comparable to those obtained in Ref. [30]. Refrigerant capacity (RC) characterizes the amount of energy that can be gained from a kilogram of substance. RC was calculated using Wood-Potter equation [33]:
RCðdT; HMAX Þ ¼
159
(2)
Tcold
where RC is refrigerant capacity, dT ¼ Thot e Tcold is the temperature range of the thermodynamic cycle (dT corresponds to full width at half maximum of magnetic entropy change peak) and HMAX is the maximum value of external magnetic field. The magnetocaloric parameters determined for all studied samples are collected in Table 4. The highest RC was determined for Mn0.9Pd0.1CoGe alloy due to its enhanced DSM. It is noticeable that, in spite of large differences in maximum values of magnetic entropy changes, the values of RC are similar for the investigated alloys. Such results are governed by typical inverse proportion of DSM and dTFWHM, with the largest value of peak width for Zr-substituted alloy. 4. Conclusions The enthalpy of formation of intermetallic compound is the most negative in case of each analyzed system, comparing to the formation enthalpies of amorphous phase and solid solution. Nevertheless, substitution effect and kinetic factors can favor the formation of glassy structure during rapid solidification. Moreover, Zr improves the GFA, while substitution of Pd just slightly changes thermodynamics of Mn-Co-Ge, especially for equiatomic composition. The coexistence of TiNiSi-type and Ni2In-type phases was revealed for all studied samples. Moreover, palladium improved formation of orthorhombic TiNiSi-type phase. Zirconium substitution caused a decrease of the Curie temperature of MnCoGe alloy. In the case of Pd substitution, the increase of TC was revealed. The highest DSM was determined for the sample containing Pd. Reported differences in magnetic and magnetocaloric properties are
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Structure, magnetocaloric properties and thermodynamic modeling of enthalpies of formation of (Mn,X)-Co-Ge (X ¼ Zr, Pd) alloys b Piotr Ge˛ bara a, *, Zbigniew Sniadecki a b
Institute of Physics, Cze˛ stochowa University of Technology, Armii Krajowej 19 Av., 42-200 Cze˛ stochowa, Poland , Poland Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 November 2018 Received in revised form 2 April 2019 Accepted 30 April 2019 Available online 4 May 2019
Enthalpies of formation of (Mn,X)-Co-Ge (X ¼ Zr, Pd) system in different structural states were analyzed utilizing the semi-empirical Miedema's model combined with the geometric one. Substitution of Mn by Zr significantly improves glass forming ability of Mn-Co-Ge, with parent equiatomic alloy among them. Chosen half-Heusler alloys, which are thermodynamically stable for the mentioned elemental compositions, were obtained by arc-melting. The x-ray diffraction studies confirmed coexistence of orthorhombic NiTiSi-type and hexagonal Ni2In-type structures for parent MnCoGe alloy and (Zr, Pd)substituted samples. Thermomagnetic curves and magnetic isotherms allowed to reveal the Curie temperature TC and a magnetic entropy change DSM and allowed to analyze the influence of both substitutive elements. The Curie temperatures are equal to 293 K for MnCoGe, 278 K for Mn0.9Zr0.1CoGe alloy and 318 K for Mn0.9Pd0.1CoGe. The maximum magnetic entropy change DSM values, calculated for the change of external magnetic field of about 5 T, amount to 6.17, 2.94, and 11.11 J (kg K)1 for MnCoGe, Mn0.9Zr0.1CoGe and Mn0.9Pd0.1CoGe, respectively. Differences in magnetic characteristics of the analyzed alloys are mainly caused by the changes of extent of undergoing first order magnetostructural transition with Pd and Zr atoms substitution. The presence of Pd d moments is also beneficial for the enhancement of total magnetic moment and maximum value of magnetic entropy changes in Mn0.9Pd0.1CoGe alloy. © 2019 Elsevier B.V. All rights reserved.
Keywords: Heusler alloys Magnetocaloric effect Miedemas model
1. Introduction According to research of International Energy Agency, the energy consumed for cooling has risen drastically since 1990. Such situation is caused by permanent increase of a number of cooling devices basing on gas compression/expansion. An efficiency of such process is relatively low and reaches about 40% [1]. One of the cooling techniques with higher efficiency is based on intrinsic thermomagnetic property of magnetic material, which is well known today as magnetocaloric effect (MCE). A magnitude of the MCE can be expressed by adiabatic temperature change DTad or isothermal magnetic entropy change DSM. The MCE is observed in the vicinity of room temperature in some materials and intensive studies have been conducted on this group up to date, due to their potential application as an active magnetic regenerator in magnetic refrigerator. The main groups of materials which have been investigated for over twenty years are: (i) Gd [2] and its alloys (Gd5Si2Ge2
* Corresponding author. E-mail address: [email protected] (P. Ge˛ bara). https://doi.org/10.1016/j.jallcom.2019.04.341 0925-8388/© 2019 Elsevier B.V. All rights reserved.
[3] or Gd-based amorphous phases [4]), (ii) La(Fe,Si)13-type alloys [5e7], (iii) manganites [8,9] or (iv) Heusler alloys [10e12]. Relatively newly developed family of a room temperature magnetocaloric materials can be generally described as TM1-TM2-M, where TM1 and TM2 are transition metals, while M is a metalloid [13e16]. High values of DSM of TM1-TM2-M alloys are related to magnetostructural transition between high temperature paramagnetic phase (Ni2In-type) and low temperature ferromagnetic phase (TiNiSi-type). Indeed, the equiatomic TM1-TM2-M alloys are composed of the high temperature Ni2In-type hexagonal phase (P63/mmc space group) and low temperature TiNiSi-type orthorombic one (Pnma space group). Thermoelastic martensitic-like transition is observed in this group of alloys at 420 K [17]. Chemical composition of these alloys have been modified by Cr [18], Fe-Ni [19], Ga [20] and B or C [21], recently. The main long-term aim concerns the optimization of magnetic properties of half-Heusler alloys by substitution of Mn by Zr and Pd atoms and by the modification of microstructure by rapid quenching of molten alloy. At first, it was necessary to determine enthalpies of formation of (Mn,X)-Co-Ge (X ¼ Zr, Pd) to design compositions for further studies. We plan to synthesize samples in
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amorphous or partially amorphous state as precursors for crystallization of half-Heusler alloys. In this paper we calculate enthalpies of formation of (Mn,X)-Co-Ge (X ¼ Zr, Pd) in different structural states and analyze crystalline structure and magnetocaloric properties of chosen half-Heusler alloys in as-cast form, which will act as references in further studies.
DPHS, which is the product of chemical enthalpy and mismatch entropy [25]. Extrapolation of the thermodynamic properties of sub-binary systems was done using geometric model to determine the GFA of ternary and quaternary alloys. The calculations are described in more details in Refs. [25,26]. 3. Results and discussion
2. Experiment and calculations 3.1. Semi-empirical calculations of the enthalpies of formation The ingots were prepared by arc-melting of pure elements (Mn, Co, Ge, Zr, Pd) under a low pressure of inert gas (Ar). Samples were remelted several times to ensure their homogeneity. The structural analysis was done using Bruker D8 Advance diffractometer equipped with copper tube (CuKa) and semiconductor LynxEye detector. The X-ray diffraction data was refined by the Rietveld method using POWDERCELL 2.4 package [22]. Thermomagnetic curves and magnetic isotherms were measured using Quantum Design PPMS (VSM option) in magnetic field up to 5 T. The semi-empirical Miedema's model [23,24] was used to determine the enthalpies of formation. The emphasis was put on the calculations for amorphous phase and solid solution in each case, which would be complemental to vast number of literature data on intermetallic compounds. The most fundamental indicator of glass forming ability (GFA) is the enthalpy of formation of amorphous phase [fx]. The formation enthalpy of solid solution can be expressed using DHss . Other physical quantities and parameters were also calculated to indicate the difference of formation ability of phases which compete during the solidification process, namely (i) difference of formation enthalpies DHamss ¼ DHam DHss (ii) normalized mismatch entropy Ss/kB [25], which reflects the effect of atomic radius mismatch and (iii) glass forming ability parameter
Enthalpies of formation of amorphous phase, solid solution and differences between both quantities were calculated along with the normalized mismatch entropy and GFA parameter for Mn-Co-Ge, Zr-Co-Ge and Pd-Co-Ge ternaries. The results for Mn-Co-Ge system, treated in this paper as parent composition, are presented in Fig. 1 in the form of enthalpy-composition contour maps. Formation enthalpies of amorphous phase and solid solution are presented in Fig. 1a and b, respectively, while the difference of enthalpies DHamss in Fig. 1c. The most negative enthalpy values were obtained for Mn-Ge binaries in the vicinity of equiatomic composition, reaching almost 25 kJ/mol for Mn52Ge48. Such result can be justified by significant difference of Mn and Ge atomic radii, in comparison to Mn-Co and Co-Ge binaries, and by moderate values of interfacial enthalpy between all constituents. For the composition of interest in the present paper, equiatomic MnCoGe, DHam is equal to about 17.5 kJ/mol. Similar phase diagram was obtained for Mn-Co-Ge solid solutions (Fig. 1b), but the values of enthalpy of formation are slightly more negative than in the case of amorphous phase. This results in the positive values of DHamss in the whole composition range (Fig. 1c), indicating preferential formation of solid solution and reduced GFA. For MnCoGe
Fig. 1. Compositional dependences of formation enthalpy of amorphous phase DHam (a), formation enthalpy of solid solution DHss (b), their difference DHamss (c), normalized mismatch entropy Ss/kB (d) and glass forming ability parameter DPHS (e) for Mn-Co-Ge. Grey dots represent equiatomic MnCoGe composition.
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composition, DHss and DHamss are equal to 20.7 kJ/mol and 3.2 kJ/mol, respectively. The normalized mismatch entropy (Fig. 1d) reflects the mismatch effect of atomic radii of constituents and for Mn-Co-Ge ternary alloys range from about 0 to 0.15. Mean value of Ss/kB calculated for a large group of ternary amorphous alloys by Takeuchi and Inoue [26] is equal to ~0.33. They have concluded that the critical value for the formation of amorphous phase is equal to 0.1 and the increase of the mismatch entropy facilitates the amorphization. The contour maps of formation enthalpy (Fig. 1a and b) and mismatch entropy (Fig. 1d) are consistent. It confirms the major impact of differences in atomic radii and limited influence of interfacial enthalpies. Described calculations took into account the topological disorder. GFA parameter denoted by DPHS add the chemical aspect by combining chemical enthalpy with Ss/kB. The calculated values are presented in Fig. 1e confirming the conclusions drawn before. In our case, an additional element does not promote the formation of glassy state and ternary alloys are still not favored to form the amorphous phase, which is in some manner in contradiction to one of the Inoue rules [27]. Fig. 2 shows the relation between mixing enthalpy DHchem and normalized mismatch entropy (Ss/kB) for the group of Mn-Co-Ge alloys. A marked area (between dashed lines described as Ss/kB ¼ 1 and log(Ss/
Fig. 2. Relation between log(Ss/kB) and DHchem for the Mn-Co-Ge system. Equiatomic MnCoGe composition is marked with a red dot. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
155
kB) ¼ log(2 102)x(DHchem/100 þ 1)) has been empirically determined as a glass forming region on the basis of a vast number of data by Takeuchi and Inoue [28]. Almost all of the alloys from MnCo-Ge family (with equiatomic MnCoGe, marked by red dot, among them) are on the verge of fulfilment of this GFA criterion, confirming low probability of formation of amorphous structure. This conclusion coincide with the earlier analysis. Substitution of Mn atoms by Zr in Mn-Co-Ge system changed the thermodynamic properties of the major part of analyzed alloys. Phase diagrams of formation enthalpies of amorphous phase and solid solution (refer to Fig. 1 in Supplementary material) are qualitatively very similar to those of Mn-Co-Ge. Nevertheless, enthalpies of formation are much more negative, mainly due to the values of interfacial enthalpy of Zr-Co and Zr-Ge binaries and relatively large atomic radius of zirconium. The lowest values of DHam and DHss of about 67 kJ/mol were reached for Zr48Ge52 and Zr49Ge51, respectively. In turn, DHam and DHss for equiatomic ZrCoGe are equal to about 50.9 kJ/mol and 43.4 kJ/mol, respectively. Increase of GFA after Zr substitution can be also confirmed by DHamss (Fig. 3a), Ss/kB (Fig. 3b) and DPHS (Fig. 3c). DHamss for ZrCo-Ge is negative in the large area of the phase diagram with the minimum of about 15.3 kJ/mol for Zr49Co51 alloy (Fig. 3c). Therefore, the criterion of GFA is also fulfilled in this case. Compositions close to the Co-Ge and Zr-Ge edges of phase diagram are suggested to form a solid solution rather than a glassy state. Moreover, Ss/kB exceeds the threshold value of 0.1 roughly for the same composition range, with the maximum of 0.31 reached for Zr41Co59, due to significant difference in atomic radii of both elements (rZr ¼ 1.60 Å, rCo ¼ 1.26 Å). The DPHS results differ from those presented in the previously described diagrams. Ternary Zr41Co42Ge17 with DPHS ¼ 13.8 kJ/mol is the composition with the highest GFA. Therefore, it is obvious in this case that an additional element promotes the amorphization in ternary alloys, as expected. For ZrCoGe, DPHS ¼ 12.7 kJ/mol and confirms the possibility of formation of fully amorphous alloy. Substitution of Pd in place of Mn in Mn-Co-Ge system does not change the thermodynamic properties significantly. Phase diagrams of formation enthalpies of amorphous phase and solid solution (refer to Fig. 2 in Supplementary material) qualitatively coincide with those of Mn-Co-Ge and Zr-Co-Ge, with the most negative values DHam ¼ 37.3 kJ/mol and DHss ¼ 41.9 kJ/mol for Pd49Ge51 and Pd50Ge50, respectively. Enthalpies of formation are more negative than those for Mn-Co-Ge but do not reach the level delineated by Zr-containing alloys. The main conclusion which should be drawn on the basis of DHamss contour map (Fig. 4a) is the positive value of the differential enthalpy for almost all compositions, except Co-Ge edge, where the values are still just slightly
Fig. 3. Compositional dependences of DHamss (a), Ss/kB (b) and DPHS (c) for Zr-Co-Ge. Grey dots represent equiatomic ZrCoGe composition.
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156
Fig. 4. Compositional dependences of DHamss (a), Ss/kB (b) and DPHS (c) for Pd-Co-Ge. Grey dots represent equiatomic PdCoGe composition.
negative. It indicates extremely low GFA at the expense of formation of solid solution. The normalized mismatch entropy reaches the maximum value of about 0.05, which is much lower than the threshold value of 0.1 [27]. DPHS is just slightly negative and equal to 1.1 kJ/mol for the equiatomic composition. The results described in this paragraph lead to the conclusion that the glass forming ability of Pd-Co-Ge is very low and the formation of solid solution would be preferred during synthesis. The differences of DHamss of Mn-Co-Ge and substituted systems are shown in Fig. 5 to give direct evidence of areas of phase diagram, where the glassy state formation is improved by Zr (Fig. 5a) or Pd (Fig. 5b). The regions where the enthalpies of Mn-CoGe and Zr/Pd-Co-Ge take lower values, are marked accordingly with Mn and Zr/Pd symbols. Black solid lines indicate the compositions where the enthalpies of both compared systems are of the
same value. Presented results confirm conclusion drawn in previous paragraphs, that Zr improves the GFA, while substitution of Pd insignificantly changes the thermodynamic parameters of Mn-CoGe, especially for the stoichiometry of interest (marked with a grey dot). Zirconium substitution decreases the initial DHamss value for Mn-Co-Ge system by 10.6 kJ/mol. The values of formation enthalpy of amorphous phase DHam , formation enthalpy of solid solution DHss , their difference DHamss , normalized mismatch entropy Ss/kB and glass forming ability parameter DPHS, were also calculated by us for the quaternary Mn0.9Zr0.1CoGe and Mn0.9Pd0.1CoGe alloys (Table 1). Presented results confirm the conclusions drawn from the particular phase diagrams, that Zr improves glass forming ability of Mn-Co-Ge alloys, while Pd is neutral in this sense, especially due to the atomic radii comparable to those of Co and Ge and negligibly small interfacial
Fig. 5. Phase diagrams exhibiting the difference of DHamss for Mn-Co-Ge and Zr/Pd-Co-Ge. The areas where Mn-Co-Ge is characterized by lower enthalpy values than Zr-Co-Ge (a) and Pd-Co-Ge (b) and the regions where the opposite relation holds, are marked accordingly with Mn and Zr/Pd symbols.
Table 1 Enthalpies of formation of amorphous phase DHam , of solid solution DHss , their difference DHamss , normalized mismatch entropy Ss/kB and glass forming ability parameter DPHS calculated for the ternary (Mn,Zr,Pd)CoGe and quaternary Mn0.9(Zr,Pd)0.1CoGe alloys.
MnCoGe ZrCoGe PdCoGe Mn0.9Zr0.1CoGe Mn0.9Pd0.1CoGe
DHam [kJ/mol]
DHss [kJ/mol]
DHamss [kJ/mol]
Ss/kB
DPHS [kJ/mol]
17.5 50.9 20.6 19.3 17.1
20.6 43.4 23.6 22.6 21.7
3.1 7.5 3.0 3.3 4.6
0.10 0.22 0.04 0.14 0.10
2.6 12.7 1.1 4.1 2.6
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enthalpy with Co. Mn0.9Zr0.1CoGe and Mn0.9Pd0.1CoGe were chosen for future investigations to check the influence of Pd and Zr on GFA experimentally and, if successful, to crystallize half-Heusler alloys from amorphous or partially amorphous precursors. Low content of Pd and Zr was maintained to avoid destabilization of expected phases, which would be appropriate from the point of view of magnetocaloric properties. As-cast samples synthesized on the present stage are characterized in details in the second part of the paper. This alloys will pose in the future as the reference for rapidly quenched samples. We should compare the calculated values of enthalpies of formation of amorphous alloys and solid solutions to those of intermetallic compounds, to have an overarching view. Due to coexistence of many different types of phases in half-Heusler alloys and chemical disorder in many cases, it is difficult to take into account all factors, which govern their thermodynamic properties and stability. Nevertheless, we compare enthalpies of formation of intermetallic compounds, which were calculated by Miedema's model for equiatomic binaries (Table 2) [24]. In the case of each binary system the enthalpy of formation of intermetallic compound is the most negative, comparing to the formation enthalpies of amorphous phase and solid solution. Nevertheless, we have to take into account rather small differences of mentioned quantities in most cases and the substitution effect, which favors the formation of glassy structure or solid solution (like in the case of high entropy alloys) instead of intermetallic phases. Moreover, we should not deny the benefits of kinetic factors, which additionally promote vitrification during rapid quenching.
3.2. Crystalline structure and magnetocaloric properties of halfHeusler alloys The x-ray diffraction patterns collected at room temperature for MnCoGe, Mn0.9Zr0.1CoGe and Mn0.9Pd0.1CoGe samples are shown in Fig. 6. The XRD pattern obtained for MnCoGe alloy revealed a coexistence of austenitic hexagonal Ni2In-type phase and small volume fraction of martensitic orthorhombic NiTiSi-type phase. The 10 at.% substitution of Mn by Pd caused an increase of orthorhombic phase content at the expense of hexagonal one. Such behavior suggests that Pd hampers formation of hexagonal phase. Moreover, the content of orthorhombic phase is relatively high and reaches up to 45 vol%, which allows us to state that Pd could stabilize the TiNiSi-type phase formation. Similar situation was observed in Zr-substituted sample. The coexistence of dominant hexagonal Ni2In-type (72 vol%) and orthorhombic phase was confirmed. The orthorhombic structure can be treated as a distorted hexagonal one [29]. The results of the Rietveld refinement were collected in Table 3. The values of lattice parameters calculated for MnCoGe alloy are
Table 2 Enthalpies of formation of amorphous phase DHam , solid solution DHss and intermetallic compounds DHinter in AB equiatomic binary systems. A
B
DH [kJ/mol] Co
Ge
Mn
DHam DHss DHinter [23] DHam DHss DHinter [23] DHam DHss DHinter [23]
Co
15 14 17 1 5 8
Ge
Mn
Zr
Pd
15 14 17
1 5 8 25 26 32
33 18 60 67 67 97 9 3 23
5 3 2 37 42 51 17 21 34
25 26 32
157
Fig. 6. X-ray diffraction patterns of MnCoGe, Mn0.9Pd0.1CoGe and Mn0.9Zr0.1CoGe alloys.
Table 3 The results of Rietveld refinement of the x-ray diffraction patterns of MnCoGe, Mn0.9Pd0.1CoGe and Mn0.9Zr0.1CoGe alloys. Alloy
Crystalline phase
Lattice parameter [Å] ± 0.001
a ¼ 4.070 c ¼ 5.281 Orthorhombic NiTiSi- type a ¼ 5.936 b ¼ 3.822 c ¼ 7.051 Mn0.9Pd0.1CoGe Hexagonal Ni2In- type a ¼ 4.081 c ¼ 5.286 Orthorhombic NiTiSi- type a ¼ 5.944 b ¼ 3.827 c ¼ 7.058 Mn0.9Zr0.1CoGe hexagonal Ni2In- type a ¼ 4.081 c ¼ 5.285 Orthorhombic NiTiSi- type a ¼ 5.941 b ¼ 3.827 c ¼ 7.055 MnCoGe
Hexagonal Ni2In- type
Volume fraction [%] 94 6
55 45
72 28
similar to those revealed by Li et al. [30]. Lattices of hexagonal and orthorhombic phases of Pd- and Zr-substituted samples are slightly expanded, due to the atomic radii of Pd (rPd ¼ 1.37 Å) and Zr (rZr ¼ 1.60 Å) overmatching Mn radius (rMn ¼ 1.18 Å). The increase of lattice parameters of hexagonal and orthorhombic phases is relatively small. It could suggest the occupation of Ge site (rGe ¼ 1.39 Å) instead of Co/Mn by large substitutive atoms. Nevertheless, more detailed analysis is needed to give a firm conclusion. The most important, it is evident that the phase constitution is preserved in both quaternary alloys with 10 at.% substitution of Mn atoms. It is believed that further adjustment of content of particular phases could be achieved by the optimization of initial state, for example by rapid quenching and subsequent annealing. In order to reveal the magnetic properties a temperature dependence of magnetization was measured (Fig. 7) in magnetic field of 0.1 T in three regimes: (i) during warming after zero field cooling (ZFC), (ii) during field cooling (FC) and (iii) during warming after cooling in field. The Curie temperature was determined from the temperature derivative of FC magnetization versus temperature plot, with estimated values of 293 ± 1, 278 ± 1 and 318 ± 1 K for MnCoGe, Mn0.9Zr0.1CoGe and Mn0.9Pd0.1CoGe, respectively. Moreover, for MnCoGe alloy and Pd-substituted sample, the temperature
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Fig. 8. Temperature dependences of magnetic entropy change of MnCoGe (a), Mn0.9Zr0.1CoGe (b) and Mn0.9Pd0.1CoGe (c) alloys.
isotherms collected over a wide range of temperatures. The calculations of magnetic entropy change DSM were made using thermomagnetic Maxwell relation [32]:
ðH
DSM ðT; DHÞ ¼ m0 0
Fig. 7. Temperature dependences of magnetization measured for Mn0.9Pd0.1CoGe and Mn0.9Zr0.1CoGe alloys in ZFC, FC and FCW regimes.
MnCoGe,
hysteresis between FC and FCW curves is clearly visible. Such behavior indirectly suggests an occurrence of first order phase transition in MnCoGe and Mn0.9Pd0.1CoGe alloys. In the case of Zrsubstituted sample, the temperature hysteresis is just slightly visible and the M(T) curves are less steep with broader transition range than for parent compound and Pd-substituted sample. Therefore we expect that the volume fraction undergoing first order phase transition is smaller in this case and magnetic properties more likely resemble those of system undergoing second order phase transition. The magnetocaloric effect (MCE), characterized by magnetic entropy change, was determined indirectly from magnetization
vMðT; HÞ vT
dH;
(1)
H
where T is temperature, m0 is magnetic permeability, H is magnetic field strength and M is magnetization. Peak of the DSM vs. T curves (Fig. 8) corresponds well with the Curie point of each alloy determined on the basis of thermomagnetic measurements. The maximum magnetic entropy change DSM values, calculated for the change of external magnetic field of ~5 T, amount to 6.17, 2.94 and 11.11 J (kg K)1 for MnCoGe, Mn0.9Zr0.1CoGe and Mn0.9Zr0.1CoGe, respectively. The smallest values of DSM are observed for the sample substituted by Zr. This is in accordance with the analysis of M(T) curves, where the first order magnetostructural phase transition was suggested to occur for parent alloy and Pd-substituted sample. On the other hand, almost two times higher value of magnetic entropy change, than for MnCoGe alloy, was measured for Pd-substituted sample. In this case, the dTFWHM value is relatively low. Low dTFWHM and high DSM are typical for the first order phase transition with consistent evidence in the form of thermal hysteresis characteristic for magnetostructural transition observed in M(T) curve measured for Mn0.9Pd0.1CoGe. The increase of maximum value of DSM, in comparison to parent compound, is connected with the enhancement of total magnetic moment of the alloy (bearing in mind the influence of undergoing magnetostructural transition also). This strengthening is related to additional magnetic moment on palladium atoms, as reported in
P. Ge˛ bara, Z. Sniadecki / Journal of Alloys and Compounds 796 (2019) 153e159 Table 4 Magnetic entropy change DSM and refrigerant capacity RC for MnCoGe, Mn0.9Zr0.1CoGe and Mn0.9Pd0.1CoGe alloys. Alloy
D(m0H) [T]
DSM [J (kg K)1]
RC [J kg1]
MnCoGe
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
1.22 2.65 3.89 5.05 6.17 0.66 1.35 1.97 2.42 2.94 2.02 4.33 6.68 8.83 11.11
38 80 129 160 193 33 78 121 177 219 39 86 131 209 238
Mn0.9Zr0.1CoGe
Mn0.9Pd0.1CoGe
P.G. would like to thank to Prof. Norbert Sczygiol e the Rector of Cze˛ stochowa University of Technology for financial support. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jallcom.2019.04.341. References
Tð hot
DSM ðT; HMAX ÞdT
mainly caused by the alteration of extent of the first order magnetostructural transition with Pd and Zr substitutions and by the presence of additional d moments of Pd introduced in Mn0.9Pd0.1CoGe. Acknowledgements
Ref. [31]. The values of the DSM revealed for the Mn0.9Pd0.1CoGe alloy are comparable to those obtained in Ref. [30]. Refrigerant capacity (RC) characterizes the amount of energy that can be gained from a kilogram of substance. RC was calculated using Wood-Potter equation [33]:
RCðdT; HMAX Þ ¼
159
(2)
Tcold
where RC is refrigerant capacity, dT ¼ Thot e Tcold is the temperature range of the thermodynamic cycle (dT corresponds to full width at half maximum of magnetic entropy change peak) and HMAX is the maximum value of external magnetic field. The magnetocaloric parameters determined for all studied samples are collected in Table 4. The highest RC was determined for Mn0.9Pd0.1CoGe alloy due to its enhanced DSM. It is noticeable that, in spite of large differences in maximum values of magnetic entropy changes, the values of RC are similar for the investigated alloys. Such results are governed by typical inverse proportion of DSM and dTFWHM, with the largest value of peak width for Zr-substituted alloy. 4. Conclusions The enthalpy of formation of intermetallic compound is the most negative in case of each analyzed system, comparing to the formation enthalpies of amorphous phase and solid solution. Nevertheless, substitution effect and kinetic factors can favor the formation of glassy structure during rapid solidification. Moreover, Zr improves the GFA, while substitution of Pd just slightly changes thermodynamics of Mn-Co-Ge, especially for equiatomic composition. The coexistence of TiNiSi-type and Ni2In-type phases was revealed for all studied samples. Moreover, palladium improved formation of orthorhombic TiNiSi-type phase. Zirconium substitution caused a decrease of the Curie temperature of MnCoGe alloy. In the case of Pd substitution, the increase of TC was revealed. The highest DSM was determined for the sample containing Pd. Reported differences in magnetic and magnetocaloric properties are
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