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Heat capacities of several Co2YZ Heusler compounds
Thermochimica Acta 574 (2013) 79–84
Contents lists available at ScienceDirect
Thermochimica Acta journal homepage: www.elsevier.com/locate/tca
Heat capacities of several Co2 YZ Heusler compounds Ming Yin ∗ , Philip Nash, Song Chen Thermal Processing Technology Center, Illinois Institute of Technology (IIT), 10 West 32nd Street, Chicago, IL 60616, USA
a r t i c l e
i n f o
Article history: Received 17 August 2013 Received in revised form 1 October 2013 Accepted 4 October 2013 Available online 14 October 2013 Keywords: Heusler compound Heat content Heat capacity Heat of fusion Calorimetry
a b s t r a c t Heat contents of several Co2 -based Heusler compounds Co2 YZ (Y = Fe, Mn, Ti; Z = Al, Ga, Si, Ge, Sn) were measured from 500 K to 1500 K using a Setaram MTHC 96 drop calorimeter. Second order polynomials were adopted to fit the data and heat capacities were obtained by taking the derivatives with respect to temperature. Melting points were determined by differential scanning calorimetry (DSC) and measured heats of fusion were compared with those obtained from extrapolation of heat contents. Published by Elsevier B.V.
1. Introduction Heusler compounds [1,2] belong to a group of ternary intermetallics with the stoichiometric composition X2 YZ, in which X and Y are transition elements, and Z is usually a group III to V element. They have an L21 structure with the Pearson symbol cF16 and space group Fm-3m. Heusler compounds, of which there are several thousand, can have many interesting properties. The first discovered one, Cu2 MnAl [3] is ferromagnetic while none of the constituent elements is. Other examples of interesting properties are the ferrimagnet Mn2 VAl [4,5] which due to the internal spin compensation, has a rather small saturation magnetization and a fairly high Curie temperature which is desired for spintronics. Cu2 CeIn [6] can be applied to heavy fermion systems and Ni2 ZrGa [7] is a potential superconductor. Co2 YZ compounds are of special interest because they exhibit a wide range of magnetic properties with magnetic moments up to 6 B per unit cell, Curie temperatures up to 1100 K [8,9]. High tunnel magnetoresistance is observed in magnetic tunnel junctions based on Co2 FeSi [10]. Co2 MnZ alloys are proposed as half-metallic ferromagnets (HMF) with the presence of an energy gap at the Fermi level in one spin subband, and the metallic character of the density of states in the other subband, leading to 100% spin polarization, which are very promising materials for spintronics applications [11].
∗ Corresponding author. Tel.: +1 312 567 3203; fax: +1 312 567 8875; mobile: +1 312 394 0336. E-mail address: [email protected] (M. Yin). 0040-6031/$ – see front matter. Published by Elsevier B.V. http://dx.doi.org/10.1016/j.tca.2013.10.004
Thermodynamic data are of fundamental importance for alloy development through understanding of phase stability and equilibrium, establishing energy balances, calculating changes in enthalpies of reaction with temperature and so on. However, only limited thermodynamic data are available to help explore ternary Heusler systems. Fraga and Brandao [12] investigated low temperature (1.5–8.0 K) specific heat of Co2 MnSn using an adiabatic calorimeter with a mechanical heat switch. Graf et al. [13] studied the specific heat of Co2 TiAl from 0 K to 250 K both experimentally and theoretically and Umetsu et al. [14] measured the low temperature specific heats of Co2 MnGa and Co2 FeGa by a relaxation method. In this work, heat capacities of Co2 YZ (Y = Fe, Mn, Ti; Z = Al, Ga, Si, Ge, Sn) from 500 K to 1500 K were studied using a Setaram MTHC 96 drop calorimeter. 2. Experimental procedure/theory/calculation A single phase of B2 structure is confirmed in the Co2 MnAl alloy which was arc melted in an argon atmosphere and annealed in vacuum in a quartz tube at 700 K for 7 days. Co2 MnGe samples were obtained by arc melting and annealing at 773 K for 30 days. A single phase B2 structure was identified according to the measured XRD pattern as shown in Fig. 1 given that the weight loss during arc melting was up to 10% due to the spontaneous fracture of the sample on cooling while the overall composition did not change which was verified by the Energy Dispersive Spectrum. Since the size of the unit cell of an L21 structure is twice that of a B2 structure, the superlattice peak (0 0 2) in Fig. 1(a) would corresponds to (0 0 1) in Fig. 1(b). The other samples for the measurement of melting points and heat contents were synthesized at 1373 K in a Kleppa
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Fig. 1. XRD pattern of Co2 MnGe and enlarged characteristic peak, (a) simulated result of an L21 structure with superlattice peak (1 1 1) for L21 structure and superlattice peak (0 0 2) for B2 structure; (b) experimental result of a B2 structure with superlattice peak (0 0 1).
calorimeter [15]. Stoichiometric amounts of elemental powders were mixed and compressed into pellets of 0.1000 g each and dropped into the Kleppa calorimeter at 1373 K for 20 min and then cooled in flowing argon producing an as cooled structure. Co2 FeAl had a B2 structure while the other compounds had an L21 structure which was verified using X-ray diffraction (XRD) [16] with the presence of negligible amount of impurity if ever. Melting points were determined using a Setsys 1700 DSC with a heating rate of 5 K/min in an argon atmosphere. Pure Ag was used as the reference material. The area of the sample peaks were integrated and converted to J mole of atoms−1 using the heat of fusion of pure silver [17] as a standard. There is an obvious change of heat flow in the DSC curve of Co2 FeSi at 1510 K. Fig. 2 presents the partial DSC curve from 1400 K to 1570 K. The intersection of the baseline and tangent at the point of highest slope of the peak is defined as the onset point, the characteristic temperature of the transformation. Both the onset points of the peaks from heating curve and cooling curve were recorded and these were reasonably close to each other. Considering the propensity for undercooling, the onset points of the heating curves were considered to be more reliable. Due to the limit of the temperature range of the DSC, maximum 1610 K, melting points of Co2 FeAl, Co2 MnAl, Co2 TiAl, Co2 TiGa, Co2 TiSi and Co2 TiSn were not determined. Table 1 summarizes the measured melting points and heats of fusion. Samples and standard materials, NIST SRM sapphire, were dropped into the Setaram calorimeter alternately. The heat effect was integrated using the Setsoft software and compared with the standard value to obtain the heat contents. Details of the experimental procedure are described in [18]. The measured heat contents of Co2 FeGe from 588 K to 1553 K and corresponding standard deviation are listed in Table 2. The standard deviation is less than 6%. The heat content measured at
1373 K in the Kleppa calorimeter is also included for comparison [16]. Considering that the enthalpy of order–disorder and magnetic transformation is small (the integrated area of the peak from DSC result is less than 10% of heats of fusion), second order polynomials H = a · T 2 + b · T + c
(1)
were adopted to fit heat contents (H) of the solid phase [19] over the whole investigated temperature range in which T is the absolute temperature, and a, b, c are fitting parameters to be determined. Room temperature, 298.15 K, was chosen as the reference
Fig. 2. DSC curve of Co2 FeSi from 1400 K to 1570 K.
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Table 1 Melting points and heats of fusion of Co2 YZ (Y = Fe, Mn, Ti; Z = Al, Ga, Si, Ge, Sn). Compound
Onset pointa (K) Heating
Co2 FeAl Co2 FeGa Co2 FeSi Co2 FeGe Co2 MnAl Co2 MnSi Co2 MnGe Co2 MnSn Co2 TiAl Co2 TiGa Co2 TiSi Co2 TiSn a b
Heat of fusionb (kJ mole of atoms−1 )
Melting point (K) Cooling
1539 1510 1401
1562 1516 1439
1460 1353 1317
1433 1339 1320
This work >1592 1539 1510 1401 >1473 1460 1353 1317 >1556 >1595 >1597 >1596
Literature
1438 [21] 1346 [21] 1301 [22], 1250 [23]
DSC
Extrapolation
8.7 12.0 11.4
12.2
19.0 8.0 10.0
15.0 16.3
1460 [23]
The measured onset points are obtained in this work. The estimated uncertainty is ±3 K. Both types of heats of fusion are obtained in this work. The estimated uncertainty of the heat of fusion measured by the DSC is ±10%.
Table 2 Measured heat contents of Co2 FeGe from 588 K to 1553 K and fitted values. Temperature (K)a 588 689 791 892 994 1095 1197 1298 1373a 1374 1502 1553 a
Heat content (J mole of atoms−1 ) 8200 11,700 15,600 19,100 25,200 31,000 34,600 42,600 46,500 43,600 63,500 63,800
Standard deviation (J mole of atoms−1 ) 70 200 900 600 1100 800 1400 1900 1800 2500 2200 1500
Fitted heat content (J mole of atoms−1 ) 8210 11,800 15,800 20,100 24,800 29,900 35,300 41,100 45,600 45,700 62,800 64,500
Data from the Kleppa calorimetry measurement.
temperature. Thus, the temperature-intercept was set 298.15 K for H = 0. The following relationship between a, b and c is obeyed, 0 = a · 298.152 + b · 298.15 + c
(2)
Due to the limited amount of data, heat contents of liquid were fitted with a straight line. For Co2 FeGe and Co2 MnSi, heat
capacity (Cp ) of the liquid phase, i.e. slope of the straight line, was set 32.0 J K−1 mole of atoms−1 , a typical value for liquid metals [19,20]. Heat capacities were obtained by differentiating heat contents with respect to temperature. Cp = A · T + B
Fig. 3. Heat contents of Co2 TiGa from 572 K to 1475 K. The temperature-intercept is 298.15 K.
(3)
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Fig. 4. Heat contents of Co2 MnSi from 585 K to 1552 K.
Fig. 5. Partial DSC curves of Co2 FeGa, Co2 FeSi and Co2 MnSi from 800 K to 1200 K. Table 3 Summary of fitted parameters of heat contents of Co2 YZ (Y = Fe, Mn, Ti; Z = Al, Ga, Si, Ge, Sn). Compounds
Phase
Temperature range (K)
a
b
c
Adj-R2
Co2 FeAl Co2 FeGa Co2 FeSi Co2 FeGe
B2 L21 L21 L21 Liquid B2 L21 Liquid B2 Liquid L21 L21 L21 L21
585–1476 572–1475 584–1476 588–1375 1502–1553 673–1373 585–1374 1475–1552 588–1293 1377–1567 586–1476 572–1475 585–1476 584–1476
1.96E−2 1.90E−2 1.34E−2 1.79E−2
6.28E+0 8.86E+0 1.63E+1 1.25E+1 3.20E+1 2.45E+1 6.07E+0 3.20E+1 9.64E+0 3.31E+1 2.09E+1 2.05E+1 2.53E+1 2.18E+1
−3.62E+3 −4.33E+3 −6.06E+3 −5.32E+3 1.48E+4 −7.84E+3 −3.59E+3 1.62E+4 −4.59E+3 1.53E+4 −6.67E+3 −6.57E+3 −7.71E+3 −6.94E+3
0.9988 0.9986 0.9988 0.9986
Co2 MnAl Co2 MnSi Co2 MnGe Co2 TiAl Co2 TiGa Co2 TiSi Co2 TiSn
H = a · T 2 + b · T + c J/mole of atoms.
6.10E−3 2.00E−2 1.93E−2 4.90E−3 5.30E−3 1.94E−3 5.07E−3
0.9977 0.9992 0.9996 0.9987 0.9992 0.9985 0.9984
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Obviously, the following mathematical relationships are A = 2a obeyed.(4) B=b Fig. 3 shows the heat contents of Co2 TiGa as a function of temperature. It is representative of compounds that do not undergo solid–liquid phase transformation in the investigated temperature range. Heat contents of Co2 MnSi are shown in Fig. 4. The obvious discontinuity between 1400 K and 1500 K corresponds to the melting point, which agrees with the result from DSC (1460 K).
3. Discussion Melting points determined in this work are consistent with the literature values where available as compiled in Table 1. The results for Co2 MnSi and Co2 MnGe in this work are 1460 K and 1353 K respectively while those measured by Cheng et al. [21] using differential thermal analysis are 1438 K and 1346 K. Mavrodiev et al. [22] investigated Co2 MnSn using dilatometric and dynamical differential calorimetry and the result (1301 K) also agrees with this work (1317 K). Graf et al. [23] mentioned the higher melting temperature of Co2 TiSn (1460 K) in contrast to Co2 MnSn (1250 K) but did not specify the technique used to obtained the values. However, in this work, only a small peak was observed in Co2 TiSn at 1398 K which might be the melting of a small amount of binary impurity CoSn. Thus, we believe that the melting point of Co2 TiSn is beyond the temperature range of our calorimeter, i.e. higher than 1596 K, which is consistent with the result of compounds that are comprised of the same Y element Co2 TiZ (Z = Al, Ga, Si, Ge). Fig. 5 presents the partial DSC curves of Co2 FeGa, Co2 FeSi and Co2 MnSi from 800 K to 1200 K. There is a small exothermic peak (smaller than 5% of the integrated area of the heat of fusion) during cooling at 1110 K for Co2 FeGa which is close to the B2 to L21 transformation temperature measured by Kobayashi et al. [24] (1094 K). By coincidence, the Curie temperature of Co2 FeGa is also 1094 K which is confirmed by Umetsu et al. [25] (1093 K) using DSC and a vibrating sample magnetometer and agrees with the result found by Brown et al. [26] (Tc > 1100 K). The cause of the endothermic peak at 885 K is not known. The small peak (about 4% of the integrated area of the heat of fusion) of Co2 FeSi during cooling at 1039 K corresponds to the L21 to B2 transformation measured by Balke et al. [27] (1031 K). Another peak (about 8% of the integrated area of the heat of fusion) at 906 K is not reported in the literature. The absence of these small peaks on heating is likely due to the small heat effect. The peak (about 10% of the integrated area of the heat of fusion) in the DSC curve of Co2 MnSi at 1003 K presumably corresponds to the L21 to B2 transformation measured by Balke et al. [27] (1024 K). The construction of the Kleppa calorimeter and the Setaram calorimeter are very similar except that the thermocouples of the Kleppa calorimeter are embedded in the alumina core while that
Fig. 6. Comparison of heat contents at 1373 K from the Kleppa and the Setaram calorimeter. Dashed lines represent ±3 kJ mole of atoms−1 from equality.
of the Setaram calorimeter are exposed to the reaction chamber which makes the measurement precise but the thermocouples vulnerable. The very large thermal mass of the Kleppa calorimeter restricts the ability to modify the furnace temperature so it is maintained for long period of time at one temperature, typically 1373 K. The Setaram calorimeter temperature may be changed on a daily basis making it suitable for heat capacities determination. Despite the difference, heat contents at 1373 K from the two calorimeters used in this work are consistent with each other, as can be seen in Fig. 6. All data lie within the range of ±3 kJ mole of atoms−1 . The fitted parameters are compiled in Table 3. Adjusted residual sum of squares (adj-R2 ) is included to illustrate the goodness of fit to experimental points. For compounds of the same Y element, the fitted parameters are close to each other, especially when Z elements are in the same column in the periodic table. Derived heat capacities are listed in Table 4. According to Dulong-Petit law [28], heat capacities at room temperature (298.15 K) should be around 3R, i.e. 24.9 J K−1 mol−1 , in which R is the molar gas constant 8.31 J K−1 mol−1 . Of all the values, only Co2 FeAl and Co2 MnSi were outside the ±4 J K−1 mol−1 range. The reason for these exceptions is not clear. All the calculated heat capacities at 298.15 K are included in Table 4. Heats of fusion of Co2 FeGe, Co2 MnSi and Co2 MnGe were calculated by extrapolating heat contents of solid and liquid to the
Table 4 Summary of calculated parameters of heat capacities of Co2 YZ (Y = Fe, Mn, Ti; Z = Al, Ga, Si, Ge, Sn). Compounds
Phase
A
B
Heat capacities at 298.15 K (J K−1 mole of atoms−1 )
Co2 FeAl Co2 FeGa Co2 FeSi Co2 FeGe Co2 MnAl Co2 MnSi Co2 MnGe Co2 TiAl Co2 TiGa Co2 TiSi Co2 TiSn
B2 L21 L21 L21 B2 L21 B2 L21 L21 L21 L21
3.93E−2 3.80E−2 2.68E−2 3.59E−2 1.22E−2 4.00E−2 3.86E−2 9.80E−3 1.06E−2 3.88E−3 1.01E−2
6.28E+0 8.86E+0 1.63E+1 1.25E+1 2.45E+1 6.07E+0 9.64E+0 2.09E+1 2.05E+1 2.53E+1 2.18E+1
18.0 20.2 24.3 23.2 28.1 18.0 21.2 23.8 23.6 26.4 24.8
Cp = A·T + B J K−1 mole of atoms−1 .
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melting points and determining the difference, as shown in Table 1. The obtained values are compared with those measured by DSC and general agreement is observed. Data obtained by extrapolation should be more reliable since the measurement by DSC was a dynamic process. Also, the ratio of enthalpy to the integrated area is not necessarily independent of temperature, leading to errors due to the use of a standard element which melts at s substantially different temperature. 4. Conclusions Heat capacities of several Co2 -based Heusler compounds Co2 YZ (Y = Fe, Mn, Ti; Z = Al, Ga, Si, Ge, Sn) from 500 K to 1500 K were determined by differentiating the fitted second order polynomials of heat contents measured using the Setaram drop calorimeter with respect to temperature. The calculated values fit the Dulong-Petit law in general. Good agreement exists between the heat contents obtained from the Setaram drop calorimeter and the Kleppa drop calorimeter. Melting points were measured by DSC and are consistent with the results of heat contents and data from the literature. Acknowledgement This research is supported by NSF Grant #DMR0964812. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.tca.2013.10.004. References [1] T. Graf, C. Felser, S.S.P. Parkin, Simple rules for the understanding of Heusler compounds, Prog. Solid State Chem. 39 (2011) 1–50. [2] T. Graf, S.S.P. Parkin, C. Felser, Heusler compounds—a material class with exceptional properties, IEEE Trans. Magn. 47 (2011) 367–373. [3] F. Heusler, W. Starck, E. Haupt, Magnetic-chemical studies, Verh. Dtsch. Phys. Ges. 5 (1903) 219–223. [4] H. Itoh, T. Nakamichi, Y. Yamaguchi, N. Kazama, Neutron diffraction study of Heusler type alloy manganese-vanadium-aluminum (Mn0.47 V0.28 Al0.25 ), Trans. Japan Inst. Met. 24 (1983) 265–271. [5] T. Kubota, K. Kodama, T. Nakamura, Y. Sakuraba, M. Oogane, K. Takanashi, Y. Ando, Ferrimagnetism in epitaxially grown Mn2 VAl Heusler alloy investigated by means of soft X-ray magnetic circular dichroism, Appl. Phys. Lett. 95 (2009) 222503/1–222503/222503. [6] H. Nakamura, Y. Kitaoka, K. Asayama, Y. Onuki, T. Komatsubara, Observation of two phase transitions in the Heusler heavy fermion system CeInCu2 , J. Magn. Magn. Mater. 76/77 (1988) 467–468. [7] J. Winterlik, G.H. Fecher, C. Felser, M. Jourdan, K. Grube, F. Hardy, H. Von Löhneysen, K.L. Holman, R.J. Cava, Ni based superconductor: Heusler compound ZrNi2 Ga, Phys. Rev. B: Condens. Matter 78 (2008) 184506/1–184506/184506.
[8] S. Wurnehl, G.H. Fecher, H.C. Kandpal, V. Ksenofontov, C. Felser, H. Lin, Investigation of Co2 FeSi: the Heusler compound with highest Curie temperature and magnetic moment, Appl. Phys. Lett. 88 (2006) 032503/1–032503/32503. [9] B. Balke, S. Wurmehl, G.H. Fecher, C. Felser, C. Felser, M.C. Alves, F. Bernardi, J. Morais, Structural characterization of the Co2 FeZ (Z = Al, Si, Ga, and Ge) Heusler compounds by X-ray diffraction and extended X-ray absorption fine structure spectroscopy, Appl. Phys. Lett. 90 (2007) 172501/1–172501/172501. [10] Z. Gercsi, A. Rajanikanth, Y.K. Takahashi, K. Honob, M. Kikuchi, N. Tezuka, K. Inomata, Spin polarization of Co2 FeSi full Heusler alloy and tunneling magnetoresistance of its magnetic tunneling junctions, Appl. Phys. Lett. 89 (2006) 082512/1–082512/82512. [11] M.V. Yablonskikh, Y.M. Yarmoshenko, I.V. Solovyev, E.Z. Kurmaev, L.C. Duda, T. Schmitt, M. Magnuson, J. Nordgren, A. Moewes, Resonant L␣, X-ray emission and L3,2 X-ray absorption spectra of 3d metals in Co2 MnZ (Z = Al, Ga, Sn, Sb) Heusler alloys as an element-selective probe of spin character of valence band, J. Electron Spectrosc. Rel. Phenom. 144–147 (2005) 765–769. [12] G.L.F. Fraga, D.E. Brandao, Specific heat of X2 MnSn (X = Co, Ni, Pd, Cu), X2 MnIn (X = Ni, Pd) and Ni2 MnSb Heusler compounds, J. Magn. Magn. Mater. 102 (1991) 199–207. [13] T. Graf, G.H. Fecher, J. Barth, J. Winterlik, C. Felser, Electronic structure and transport properties of the Heusler compound Co2 TiAl, J. Phys. D: Appl. Phys. 42 (2009) 084003/1–084003/84003. [14] R.Y. Umetsu, N. Endo, A. Fujita, R. Kainuma, A. Sakuma, K. Fukamichi, K. Ishida, Electronic specific heat coefficient and magnetic properties of L21 phase in Co2 YGa (Y = Cr, Mn and Fe) Heusler alloys, J. Phys.: Conf. Ser. 200 (2010) 062036/1–062036/62036. [15] H. Su, P. Nash, Enthalpies of formation in the Al–Ni–Ru system by direct reaction synthesis calorimetry, J. Alloys Compd. 403 (2005) 217–222. [16] M. Yin, S. Chen, P. Nash, Enthalpies of formation of selected Co2 YZ Heusler compounds, J. Alloys Compd. 577 (2013) 49–56. [17] A.T. Dinsdale, SGTE data for pure elements, Calphad 15 (1991) 317–425. [18] R. Hu, P. Nash, Q. Chen, L. Zhang, Y. Du, Heat capacities of several Al–Ni–Ti compounds, Thermochim. Acta 486 (2009) 57–65. [19] J. Kaufman, H. Bernstein, Computer Calculations of Phase Diagrams, Academic Press, New York, 1970. [20] H.S. Tsien, The properties of pure liquids, J. Am. Rocket Soc. 23 (1953) 17–24. [21] S.F. Cheng, B. Nadgorny, K. Bussmann, E.E. Carpenter, B.N. Das, G. Trotter, M.P. Raphael, V.G. Harris, Growth and magnetic properties of single crystal Co2 MnX (X = Si, Ge) Heusler alloys, IEEE Trans. Magn. 37 (2001) 2176–2178. [22] G. Mavrodiev, S. Koneska, A. Szytula, Thermal expansion anomalies in the Heusler alloys Cu2 MnAl, Ni2 MnSn, Co2 MSn, Ni2 ZrSn and Ni2 ZrIn, J. Less Common Met. 159 (1990) L9–L12. [23] T. Graf, J. Barth, C.G.F. Blum, B. Balke, C. Felser, Phase-separation-induced changes in the magnetic and transport properties of the quaternary Heusler alloy Co2Mn1−x Tix Sn, Phys. Rev. B: Condens. Matter 82 (2011) 104420/1–104420/104420. [24] K. Kobayashi, R.Y. Umetsu, A. Fujita, K. Oikawa, R. Kainuma, K. Ishida, Magnetic properties and phase stability of half-metal-type Co2 Cr1−x Fex Ga alloys, J. Alloys Compd. 399 (2005) 60–63. [25] R.Y. Umetsu, K. Kobayashi, A. Fujita, K. Oikawa, R. Kainuma, K. Ishida, Halfmetallic properties of Co2 (Cr1−x Fex )Ga Heusler alloys, Phys. Rev. B 72 (2005) 214412/1–214412/214412. [26] P.J. Brown, K.U. Neumann, P.J. Webster, K.R.A. Ziebeck, The magnetization distributions in some Heusler alloys proposed as half-metallic ferromagnets, J. Phys.: Condens. Matter 12 (2000) 1827–1835. [27] B. Balke, G.H. Fecher, H.C. Kandpal, C. Felser, Properties of the quaternary halfmetal-type Heusler alloy Co2 Mn1−x Fex Si, Phys. Rev. B: Condens. Matter 74 (2006) 104405/1–104405/104405. [28] D.R. Gaskell, Introduction to the Thermodynamics of Materials, Third ed., Taylor & Francis, Washington, DC, 1995, pp. 112–114.
Contents lists available at ScienceDirect
Thermochimica Acta journal homepage: www.elsevier.com/locate/tca
Heat capacities of several Co2 YZ Heusler compounds Ming Yin ∗ , Philip Nash, Song Chen Thermal Processing Technology Center, Illinois Institute of Technology (IIT), 10 West 32nd Street, Chicago, IL 60616, USA
a r t i c l e
i n f o
Article history: Received 17 August 2013 Received in revised form 1 October 2013 Accepted 4 October 2013 Available online 14 October 2013 Keywords: Heusler compound Heat content Heat capacity Heat of fusion Calorimetry
a b s t r a c t Heat contents of several Co2 -based Heusler compounds Co2 YZ (Y = Fe, Mn, Ti; Z = Al, Ga, Si, Ge, Sn) were measured from 500 K to 1500 K using a Setaram MTHC 96 drop calorimeter. Second order polynomials were adopted to fit the data and heat capacities were obtained by taking the derivatives with respect to temperature. Melting points were determined by differential scanning calorimetry (DSC) and measured heats of fusion were compared with those obtained from extrapolation of heat contents. Published by Elsevier B.V.
1. Introduction Heusler compounds [1,2] belong to a group of ternary intermetallics with the stoichiometric composition X2 YZ, in which X and Y are transition elements, and Z is usually a group III to V element. They have an L21 structure with the Pearson symbol cF16 and space group Fm-3m. Heusler compounds, of which there are several thousand, can have many interesting properties. The first discovered one, Cu2 MnAl [3] is ferromagnetic while none of the constituent elements is. Other examples of interesting properties are the ferrimagnet Mn2 VAl [4,5] which due to the internal spin compensation, has a rather small saturation magnetization and a fairly high Curie temperature which is desired for spintronics. Cu2 CeIn [6] can be applied to heavy fermion systems and Ni2 ZrGa [7] is a potential superconductor. Co2 YZ compounds are of special interest because they exhibit a wide range of magnetic properties with magnetic moments up to 6 B per unit cell, Curie temperatures up to 1100 K [8,9]. High tunnel magnetoresistance is observed in magnetic tunnel junctions based on Co2 FeSi [10]. Co2 MnZ alloys are proposed as half-metallic ferromagnets (HMF) with the presence of an energy gap at the Fermi level in one spin subband, and the metallic character of the density of states in the other subband, leading to 100% spin polarization, which are very promising materials for spintronics applications [11].
∗ Corresponding author. Tel.: +1 312 567 3203; fax: +1 312 567 8875; mobile: +1 312 394 0336. E-mail address: [email protected] (M. Yin). 0040-6031/$ – see front matter. Published by Elsevier B.V. http://dx.doi.org/10.1016/j.tca.2013.10.004
Thermodynamic data are of fundamental importance for alloy development through understanding of phase stability and equilibrium, establishing energy balances, calculating changes in enthalpies of reaction with temperature and so on. However, only limited thermodynamic data are available to help explore ternary Heusler systems. Fraga and Brandao [12] investigated low temperature (1.5–8.0 K) specific heat of Co2 MnSn using an adiabatic calorimeter with a mechanical heat switch. Graf et al. [13] studied the specific heat of Co2 TiAl from 0 K to 250 K both experimentally and theoretically and Umetsu et al. [14] measured the low temperature specific heats of Co2 MnGa and Co2 FeGa by a relaxation method. In this work, heat capacities of Co2 YZ (Y = Fe, Mn, Ti; Z = Al, Ga, Si, Ge, Sn) from 500 K to 1500 K were studied using a Setaram MTHC 96 drop calorimeter. 2. Experimental procedure/theory/calculation A single phase of B2 structure is confirmed in the Co2 MnAl alloy which was arc melted in an argon atmosphere and annealed in vacuum in a quartz tube at 700 K for 7 days. Co2 MnGe samples were obtained by arc melting and annealing at 773 K for 30 days. A single phase B2 structure was identified according to the measured XRD pattern as shown in Fig. 1 given that the weight loss during arc melting was up to 10% due to the spontaneous fracture of the sample on cooling while the overall composition did not change which was verified by the Energy Dispersive Spectrum. Since the size of the unit cell of an L21 structure is twice that of a B2 structure, the superlattice peak (0 0 2) in Fig. 1(a) would corresponds to (0 0 1) in Fig. 1(b). The other samples for the measurement of melting points and heat contents were synthesized at 1373 K in a Kleppa
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Fig. 1. XRD pattern of Co2 MnGe and enlarged characteristic peak, (a) simulated result of an L21 structure with superlattice peak (1 1 1) for L21 structure and superlattice peak (0 0 2) for B2 structure; (b) experimental result of a B2 structure with superlattice peak (0 0 1).
calorimeter [15]. Stoichiometric amounts of elemental powders were mixed and compressed into pellets of 0.1000 g each and dropped into the Kleppa calorimeter at 1373 K for 20 min and then cooled in flowing argon producing an as cooled structure. Co2 FeAl had a B2 structure while the other compounds had an L21 structure which was verified using X-ray diffraction (XRD) [16] with the presence of negligible amount of impurity if ever. Melting points were determined using a Setsys 1700 DSC with a heating rate of 5 K/min in an argon atmosphere. Pure Ag was used as the reference material. The area of the sample peaks were integrated and converted to J mole of atoms−1 using the heat of fusion of pure silver [17] as a standard. There is an obvious change of heat flow in the DSC curve of Co2 FeSi at 1510 K. Fig. 2 presents the partial DSC curve from 1400 K to 1570 K. The intersection of the baseline and tangent at the point of highest slope of the peak is defined as the onset point, the characteristic temperature of the transformation. Both the onset points of the peaks from heating curve and cooling curve were recorded and these were reasonably close to each other. Considering the propensity for undercooling, the onset points of the heating curves were considered to be more reliable. Due to the limit of the temperature range of the DSC, maximum 1610 K, melting points of Co2 FeAl, Co2 MnAl, Co2 TiAl, Co2 TiGa, Co2 TiSi and Co2 TiSn were not determined. Table 1 summarizes the measured melting points and heats of fusion. Samples and standard materials, NIST SRM sapphire, were dropped into the Setaram calorimeter alternately. The heat effect was integrated using the Setsoft software and compared with the standard value to obtain the heat contents. Details of the experimental procedure are described in [18]. The measured heat contents of Co2 FeGe from 588 K to 1553 K and corresponding standard deviation are listed in Table 2. The standard deviation is less than 6%. The heat content measured at
1373 K in the Kleppa calorimeter is also included for comparison [16]. Considering that the enthalpy of order–disorder and magnetic transformation is small (the integrated area of the peak from DSC result is less than 10% of heats of fusion), second order polynomials H = a · T 2 + b · T + c
(1)
were adopted to fit heat contents (H) of the solid phase [19] over the whole investigated temperature range in which T is the absolute temperature, and a, b, c are fitting parameters to be determined. Room temperature, 298.15 K, was chosen as the reference
Fig. 2. DSC curve of Co2 FeSi from 1400 K to 1570 K.
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Table 1 Melting points and heats of fusion of Co2 YZ (Y = Fe, Mn, Ti; Z = Al, Ga, Si, Ge, Sn). Compound
Onset pointa (K) Heating
Co2 FeAl Co2 FeGa Co2 FeSi Co2 FeGe Co2 MnAl Co2 MnSi Co2 MnGe Co2 MnSn Co2 TiAl Co2 TiGa Co2 TiSi Co2 TiSn a b
Heat of fusionb (kJ mole of atoms−1 )
Melting point (K) Cooling
1539 1510 1401
1562 1516 1439
1460 1353 1317
1433 1339 1320
This work >1592 1539 1510 1401 >1473 1460 1353 1317 >1556 >1595 >1597 >1596
Literature
1438 [21] 1346 [21] 1301 [22], 1250 [23]
DSC
Extrapolation
8.7 12.0 11.4
12.2
19.0 8.0 10.0
15.0 16.3
1460 [23]
The measured onset points are obtained in this work. The estimated uncertainty is ±3 K. Both types of heats of fusion are obtained in this work. The estimated uncertainty of the heat of fusion measured by the DSC is ±10%.
Table 2 Measured heat contents of Co2 FeGe from 588 K to 1553 K and fitted values. Temperature (K)a 588 689 791 892 994 1095 1197 1298 1373a 1374 1502 1553 a
Heat content (J mole of atoms−1 ) 8200 11,700 15,600 19,100 25,200 31,000 34,600 42,600 46,500 43,600 63,500 63,800
Standard deviation (J mole of atoms−1 ) 70 200 900 600 1100 800 1400 1900 1800 2500 2200 1500
Fitted heat content (J mole of atoms−1 ) 8210 11,800 15,800 20,100 24,800 29,900 35,300 41,100 45,600 45,700 62,800 64,500
Data from the Kleppa calorimetry measurement.
temperature. Thus, the temperature-intercept was set 298.15 K for H = 0. The following relationship between a, b and c is obeyed, 0 = a · 298.152 + b · 298.15 + c
(2)
Due to the limited amount of data, heat contents of liquid were fitted with a straight line. For Co2 FeGe and Co2 MnSi, heat
capacity (Cp ) of the liquid phase, i.e. slope of the straight line, was set 32.0 J K−1 mole of atoms−1 , a typical value for liquid metals [19,20]. Heat capacities were obtained by differentiating heat contents with respect to temperature. Cp = A · T + B
Fig. 3. Heat contents of Co2 TiGa from 572 K to 1475 K. The temperature-intercept is 298.15 K.
(3)
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Fig. 4. Heat contents of Co2 MnSi from 585 K to 1552 K.
Fig. 5. Partial DSC curves of Co2 FeGa, Co2 FeSi and Co2 MnSi from 800 K to 1200 K. Table 3 Summary of fitted parameters of heat contents of Co2 YZ (Y = Fe, Mn, Ti; Z = Al, Ga, Si, Ge, Sn). Compounds
Phase
Temperature range (K)
a
b
c
Adj-R2
Co2 FeAl Co2 FeGa Co2 FeSi Co2 FeGe
B2 L21 L21 L21 Liquid B2 L21 Liquid B2 Liquid L21 L21 L21 L21
585–1476 572–1475 584–1476 588–1375 1502–1553 673–1373 585–1374 1475–1552 588–1293 1377–1567 586–1476 572–1475 585–1476 584–1476
1.96E−2 1.90E−2 1.34E−2 1.79E−2
6.28E+0 8.86E+0 1.63E+1 1.25E+1 3.20E+1 2.45E+1 6.07E+0 3.20E+1 9.64E+0 3.31E+1 2.09E+1 2.05E+1 2.53E+1 2.18E+1
−3.62E+3 −4.33E+3 −6.06E+3 −5.32E+3 1.48E+4 −7.84E+3 −3.59E+3 1.62E+4 −4.59E+3 1.53E+4 −6.67E+3 −6.57E+3 −7.71E+3 −6.94E+3
0.9988 0.9986 0.9988 0.9986
Co2 MnAl Co2 MnSi Co2 MnGe Co2 TiAl Co2 TiGa Co2 TiSi Co2 TiSn
H = a · T 2 + b · T + c J/mole of atoms.
6.10E−3 2.00E−2 1.93E−2 4.90E−3 5.30E−3 1.94E−3 5.07E−3
0.9977 0.9992 0.9996 0.9987 0.9992 0.9985 0.9984
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Obviously, the following mathematical relationships are A = 2a obeyed.(4) B=b Fig. 3 shows the heat contents of Co2 TiGa as a function of temperature. It is representative of compounds that do not undergo solid–liquid phase transformation in the investigated temperature range. Heat contents of Co2 MnSi are shown in Fig. 4. The obvious discontinuity between 1400 K and 1500 K corresponds to the melting point, which agrees with the result from DSC (1460 K).
3. Discussion Melting points determined in this work are consistent with the literature values where available as compiled in Table 1. The results for Co2 MnSi and Co2 MnGe in this work are 1460 K and 1353 K respectively while those measured by Cheng et al. [21] using differential thermal analysis are 1438 K and 1346 K. Mavrodiev et al. [22] investigated Co2 MnSn using dilatometric and dynamical differential calorimetry and the result (1301 K) also agrees with this work (1317 K). Graf et al. [23] mentioned the higher melting temperature of Co2 TiSn (1460 K) in contrast to Co2 MnSn (1250 K) but did not specify the technique used to obtained the values. However, in this work, only a small peak was observed in Co2 TiSn at 1398 K which might be the melting of a small amount of binary impurity CoSn. Thus, we believe that the melting point of Co2 TiSn is beyond the temperature range of our calorimeter, i.e. higher than 1596 K, which is consistent with the result of compounds that are comprised of the same Y element Co2 TiZ (Z = Al, Ga, Si, Ge). Fig. 5 presents the partial DSC curves of Co2 FeGa, Co2 FeSi and Co2 MnSi from 800 K to 1200 K. There is a small exothermic peak (smaller than 5% of the integrated area of the heat of fusion) during cooling at 1110 K for Co2 FeGa which is close to the B2 to L21 transformation temperature measured by Kobayashi et al. [24] (1094 K). By coincidence, the Curie temperature of Co2 FeGa is also 1094 K which is confirmed by Umetsu et al. [25] (1093 K) using DSC and a vibrating sample magnetometer and agrees with the result found by Brown et al. [26] (Tc > 1100 K). The cause of the endothermic peak at 885 K is not known. The small peak (about 4% of the integrated area of the heat of fusion) of Co2 FeSi during cooling at 1039 K corresponds to the L21 to B2 transformation measured by Balke et al. [27] (1031 K). Another peak (about 8% of the integrated area of the heat of fusion) at 906 K is not reported in the literature. The absence of these small peaks on heating is likely due to the small heat effect. The peak (about 10% of the integrated area of the heat of fusion) in the DSC curve of Co2 MnSi at 1003 K presumably corresponds to the L21 to B2 transformation measured by Balke et al. [27] (1024 K). The construction of the Kleppa calorimeter and the Setaram calorimeter are very similar except that the thermocouples of the Kleppa calorimeter are embedded in the alumina core while that
Fig. 6. Comparison of heat contents at 1373 K from the Kleppa and the Setaram calorimeter. Dashed lines represent ±3 kJ mole of atoms−1 from equality.
of the Setaram calorimeter are exposed to the reaction chamber which makes the measurement precise but the thermocouples vulnerable. The very large thermal mass of the Kleppa calorimeter restricts the ability to modify the furnace temperature so it is maintained for long period of time at one temperature, typically 1373 K. The Setaram calorimeter temperature may be changed on a daily basis making it suitable for heat capacities determination. Despite the difference, heat contents at 1373 K from the two calorimeters used in this work are consistent with each other, as can be seen in Fig. 6. All data lie within the range of ±3 kJ mole of atoms−1 . The fitted parameters are compiled in Table 3. Adjusted residual sum of squares (adj-R2 ) is included to illustrate the goodness of fit to experimental points. For compounds of the same Y element, the fitted parameters are close to each other, especially when Z elements are in the same column in the periodic table. Derived heat capacities are listed in Table 4. According to Dulong-Petit law [28], heat capacities at room temperature (298.15 K) should be around 3R, i.e. 24.9 J K−1 mol−1 , in which R is the molar gas constant 8.31 J K−1 mol−1 . Of all the values, only Co2 FeAl and Co2 MnSi were outside the ±4 J K−1 mol−1 range. The reason for these exceptions is not clear. All the calculated heat capacities at 298.15 K are included in Table 4. Heats of fusion of Co2 FeGe, Co2 MnSi and Co2 MnGe were calculated by extrapolating heat contents of solid and liquid to the
Table 4 Summary of calculated parameters of heat capacities of Co2 YZ (Y = Fe, Mn, Ti; Z = Al, Ga, Si, Ge, Sn). Compounds
Phase
A
B
Heat capacities at 298.15 K (J K−1 mole of atoms−1 )
Co2 FeAl Co2 FeGa Co2 FeSi Co2 FeGe Co2 MnAl Co2 MnSi Co2 MnGe Co2 TiAl Co2 TiGa Co2 TiSi Co2 TiSn
B2 L21 L21 L21 B2 L21 B2 L21 L21 L21 L21
3.93E−2 3.80E−2 2.68E−2 3.59E−2 1.22E−2 4.00E−2 3.86E−2 9.80E−3 1.06E−2 3.88E−3 1.01E−2
6.28E+0 8.86E+0 1.63E+1 1.25E+1 2.45E+1 6.07E+0 9.64E+0 2.09E+1 2.05E+1 2.53E+1 2.18E+1
18.0 20.2 24.3 23.2 28.1 18.0 21.2 23.8 23.6 26.4 24.8
Cp = A·T + B J K−1 mole of atoms−1 .
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melting points and determining the difference, as shown in Table 1. The obtained values are compared with those measured by DSC and general agreement is observed. Data obtained by extrapolation should be more reliable since the measurement by DSC was a dynamic process. Also, the ratio of enthalpy to the integrated area is not necessarily independent of temperature, leading to errors due to the use of a standard element which melts at s substantially different temperature. 4. Conclusions Heat capacities of several Co2 -based Heusler compounds Co2 YZ (Y = Fe, Mn, Ti; Z = Al, Ga, Si, Ge, Sn) from 500 K to 1500 K were determined by differentiating the fitted second order polynomials of heat contents measured using the Setaram drop calorimeter with respect to temperature. The calculated values fit the Dulong-Petit law in general. Good agreement exists between the heat contents obtained from the Setaram drop calorimeter and the Kleppa drop calorimeter. Melting points were measured by DSC and are consistent with the results of heat contents and data from the literature. Acknowledgement This research is supported by NSF Grant #DMR0964812. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.tca.2013.10.004. References [1] T. Graf, C. Felser, S.S.P. Parkin, Simple rules for the understanding of Heusler compounds, Prog. Solid State Chem. 39 (2011) 1–50. [2] T. Graf, S.S.P. Parkin, C. Felser, Heusler compounds—a material class with exceptional properties, IEEE Trans. Magn. 47 (2011) 367–373. [3] F. Heusler, W. Starck, E. Haupt, Magnetic-chemical studies, Verh. Dtsch. Phys. Ges. 5 (1903) 219–223. [4] H. Itoh, T. Nakamichi, Y. Yamaguchi, N. Kazama, Neutron diffraction study of Heusler type alloy manganese-vanadium-aluminum (Mn0.47 V0.28 Al0.25 ), Trans. Japan Inst. Met. 24 (1983) 265–271. [5] T. Kubota, K. Kodama, T. Nakamura, Y. Sakuraba, M. Oogane, K. Takanashi, Y. Ando, Ferrimagnetism in epitaxially grown Mn2 VAl Heusler alloy investigated by means of soft X-ray magnetic circular dichroism, Appl. Phys. Lett. 95 (2009) 222503/1–222503/222503. [6] H. Nakamura, Y. Kitaoka, K. Asayama, Y. Onuki, T. Komatsubara, Observation of two phase transitions in the Heusler heavy fermion system CeInCu2 , J. Magn. Magn. Mater. 76/77 (1988) 467–468. [7] J. Winterlik, G.H. Fecher, C. Felser, M. Jourdan, K. Grube, F. Hardy, H. Von Löhneysen, K.L. Holman, R.J. Cava, Ni based superconductor: Heusler compound ZrNi2 Ga, Phys. Rev. B: Condens. Matter 78 (2008) 184506/1–184506/184506.
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