Journal of Alloys and Compounds 591 (2014) 170–173
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Standard molar enthalpy of formation of FeGe(s) and FeGe2(s) intermetallic compounds S. Phapale a, R. Mishra a,⇑, D. Chattaraj b, P. Samui b, P. Sengupta c, P.K. Mishra d a
Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India Product Development Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India c Material Science Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India d Technical Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India b
a r t i c l e
i n f o
Article history: Received 14 October 2013 Received in revised form 17 December 2013 Accepted 22 December 2013 Available online 3 January 2014 Keywords: Iron germanium alloy Enthalpy of formation Calorimetry
a b s t r a c t Thermodynamics plays an important role in predicting long term stability of the materials under different reactive conditions. The present paper describes determination of standard molar enthalpies of formation of FeGe(s) and FeGe2(s) compounds employing a high temperature solution calorimeter. The reaction enthalpies of Fe(s), Ge(s), FeGe(s) and FeGe2(s) in liquid Sn at 986 K were measured using a Calvet calorimeter. The standard molar enthalpy of formation of the compounds at 298 K (DfH298 ) were calculated using the measured reaction enthalpy data. The values of DfH298 of FeGe(s) and FeGe2(s) at 298 K were found to 15.56 ± 0.92 and 36.89 ± 1.17 kJ mol1, respectively. The standard molar enthalpy of formation of FeGe(s) and FeGe2(s) at 298 K obtained experimentally has been compared with the calculated values derived using Vienna ab initio simulation package (VASP). Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction The phase diagram of binary Fe–Ge system comprises several phases with large homogeneity range, many critical points and order–disorder phase transitions . Out of many phases in this system, FeGe and FeGe2 are the only two line compounds having negligible homogeneity range and have been at the focus of attention for their interesting magnetic properties. The cubic iron monogermanide, FeGe , is a non-centrosymmetric cubic helimagnet (B20-type structure) with Curie temperature at around 280 K. The ground state of this magnetic phase consists of long-range helical modulations with periods up to several hundred unit-cells. It has been predicted that there is a possibility of formation of magnetic vortices in non-centro-symmetric ferromagnets [3,4] and cubic helimagnets in this compound and this has triggered an intensive quest for exotic states [5–9]. Jartych et al.  have investigated thermal stability and hyperﬁne interactions of mechanically alloyed Fe–Ge phases. Thermodynamics plays an important role in predicting long term stability of the materials under different reactive conditions. However, detail information on thermodynamic stabilities of these phases is not available. In the present paper, we report standard molar enthalpy of formation of FeGe(s) and FeGe2(s) compounds determined by calorimetric technique. The
⇑ Corresponding author. Tel.: +91 22 2559 2460; fax: +91 22 2550 5151. E-mail address: [email protected]
(R. Mishra). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.12.196
enthalpy of formation data obtained from calorimetric measurements has been veriﬁed by ab initio calculations. 2. Experimental FeGe(s) and FeGe2(s) were prepared by reacting appropriate amounts of the Fe(s) (purity 99.9%) and Ge(s) (6N pure) metal powders. The metal powders were thoroughly mixed in an agate mortar under acetone and dried. The homogeneously mixed powders were pressed into pellets and sealed in evacuated quart ampoules at 106 mbar pressure. The quartz ampoule containing Fe and Ge in molar ratio 1:1 and 1:2 were heated for 2 weeks at 700 °C and 800 °C respectively which is about 40 °C below their respective peritectic decomposition temperatures. The samples were then homogenized by intermediate grinding and heated again in a similar fashion for two more weeks. The samples were reground. The compounds were characterized for their phase purity using a Philips X-ray diffractometer (Model PW-1820). The standard molar enthalpies of formation of FeGe(s) and FeGe2(s) compounds were determined by measuring the enthalpy change for the reaction of FeGe and FeGe2 compounds and their component metal such as Fe(s) and Ge(s) in high purity (99.99, Alfa Aesar) liquid Sn solvent at 986 K using a Setaram Calvet calorimeter, Model HT-1000. The calorimeter has an isothermal alumina block which contains two identical one-end closed alumina cells surrounded by a series of thermopiles. The temperature of the isothermal block was measured using a Pt–Pt 10% Rh thermocouple (±0.1 K). The heat ﬂow between the isothermal block and either of the cells was recorded in the form of a millivolt signal. The details of the experimental measurements have been described elsewhere . The heat calibration was carried out using a synthetic sapphire [NIST SRM-720]. About 3 g of Sn solvent was taken in each of the two identical quartz tubes which act as a protective lining and having outer diameter (OD) matching exactly with the alumina reaction cell for proper thermal contact. The reaction cell assembly was slowly lowered into the calorimeter and the calorimeter was programmed up to 986 K at a heating rate of 0.5 K/min and maintained at 986 ± 0.05 K during the whole experiment. The reaction tubes were equilibrated inside the chamber for
S. Phapale et al. / Journal of Alloys and Compounds 591 (2014) 170–173 sufﬁciently long time till a steady base line for heat ﬂux signal was achieved. The slope of the base line of the differential heat ﬂow signal was nearly zero since the heat effect due to any small loss of the volatile components, will get nulliﬁed as the same effect was present in the sample and reference cells. Small pellets containing few milligrams of the reactants were dropped from room temperature to the reaction cell containing liquid solvent maintained at 986 K and the corresponding enthalpy change was determined by integrating the heat ﬂow signal with respect to time. The time required for the completion of the reaction was determined by recording the heat ﬂow signal (J/g) for different time interval. The reaction time was concluded when a steady base line was achieved and the values of reaction enthalpy obtained as a function of time converged into a constant value. For each dissolution experiment the reaction time was determined and the heat ﬂow signals recorded for the same time period for all experiments. Similarly, for each experiment fresh solvent was used so that the similar dilution condition was maintained. The amount of the reactant dropped into solvent was chosen in such a manner that the concentration of Fe and Ge remained well below 1 atom%. The inﬁnite dilution condition was established by repeating the dissolution experiments on a same lot of the solvent. The consistency in the values of the reaction per unit mass of the reactants is indicative of the fact that the inﬁnite dilution condition was maintained during the measurements. After each measurement the sample was slowly withdrawn from the calorimeter chamber and allowed to cool to room temperature. The frozen liquid was characterized by XRD and EDX analysis to know the uniform distribution of solute in the solvent and evolution of the phase in the solvent matrix. 2.1. Computational details Computational studies on FeGe(s) and FeGe2(s) compounds reported here was performed using Vienna simulation package (VASP) , which implements Density Functional Theory (DFT). The plane wave based pseudo-potential method was used for the total energy calculations. The exchange correlation energy was described under the generalized gradient approximation (GGA) of Perdew–Burke– Ernzerhof (PBE) scheme, respectively. The energy cut off for the plane wave basis set was ﬁxed to 500 eV. Ground state atomic geometries were obtained by minimizing the Hellman–Feynman forces using the conjugate gradient method. The force on each ion was minimized up to 5 meV/Å. The k-point meshes were constructed using the Monkhorst–Pack scheme and the 9 9 9 k-point mesh was used for the primitive cell for Brillouin zone sampling.
3. Results and discussion Figs. 1 and 2 give the XRD patterns of FeGe(s) and FeGe2(s) prepared by the direct reaction of Fe and Ge powder at 973 and 1073 K respectively. The compound FeGe crystallizes in the hexagonal type structure with space group P6/mmm (No. 191). The observed cell parameters are found to be a = 5.002 Å, c = 4.053 Å as compare to the reported value of. a = 5.003 Å, c = 4.055 Å [JCPDF No. 170228] The XRD lines for FeGe2 could be indexed with a tetragonal crystal lattice with unit cell constants a = 5.906 Å, c = 4.955 Å and space group I4/mcm (No. 140), against the reported value of a = 5.908, c = 4.957 [JCPDF No. 25-0357]. No impurity lines due to the starting materials Fe and Ge or any other phases could be observed in XRD pattern of the above two compounds. Differential thermal analysis of FeGe and FeGe2 sample showed two broad endothermic peaks at 748 °C and 840 °C indicating
Fig. 1. XRD plot of FeGe sample.
Fig. 2. XRD plot of FeGe2 sample.
peritectic decomposition of FeGe and FeGe2 which is in agreement with the reported phase diagram of Fe–Ge system . Electron probe microscope analysis (EPMA) results of the sample indicate the presence of homogenous single phase material which iron to germanium atomic ratio 1:1 and 1:2 respectively for FeGe and FeGe2 compounds. No other impurity phases could be identiﬁed in the above sample. Fig. 3(a–d) gives the heat ﬂow signal for the dropping of Fe(s), Ge(s), FeGe(s) and FeGe2(s) samples from room temperature to liquid Sn solvent maintained at 986 K. In each case endothermic signal was observed. The completion of the reaction between solute and the solvent was monitored by recording the heat ﬂow signal for different time intervals (10, 15, 30, 45 and 60, 90, 120, 150, 180, 210 and 240 min). The overall heat effects for dissolution of samples in liquid Sn solvent were calculated using the SETSOFT software supplied along with the instrument. The rate of dissolution of Fe, Ge, FeGe and FeGe2 in liquid Sn at 986 K has been compared in Fig. 4(a–d). From Fig. 4 it can be observed that the time taken for the complete dissolution of Fe, Ge, FeGe and FeGe2 in liquid Sn at 986 K (i.e. time at which enthalpy change per gm of the sample saturates) is 45, 60, 165 and 209 min respectively. Since the reaction enthalpy of solute with the solvent was determined by integrating the heat ﬂow versus time signal over a long period, corrections for the heat effect due to base shift recorded under exactly similar conditions were applied in all these cases. Fig. 3a gives enthalpy change measured as a function of time for the dropping 17.9 mg of Fe measured at 986 K. A steady base line in
Fig. 3. (a–d) Plots of heat ﬂow versus time for dissolution of Fe(s), Ge(s), FeGe(s) and FeGe2(s) in liquid Sn at 986 K.
S. Phapale et al. / Journal of Alloys and Compounds 591 (2014) 170–173
Fig. 4. (a–d) Plot of enthalpy of dissolution versus time for Fe(s), Ge(s), FeGe(s) and FeGe2(s) in liquid Sn at 986 K.
the heat ﬂow signal was observed after 60 min of sample dropping where no signiﬁcant change in the heat ﬂow values could be noticed. The enthalpy change for the dissolution was found to
increase with time and got stabilized after 1 h. From the phase diagram of binary Fe–Sn system at 986 K it could be inferred that for Sn-rich composition with less than 1 at% Fe forms a homogeneous liquid phase and hence it is assumed here that a homogeneous liquid phase is formed in the dissolution process. The average enthalpy change for Fe(s) dropping is found to be 25.22 ± 0.40 kJ mol1. This enthalpy change was attributed to the sum of the heat effects due to the enthalpy increment for heating Fe(s) from 298 K to 986 K and the heat effect due to dissolution of Fe(s) with the solvent at 986 K. The heat effect for the enthalpy increment for Fe(s) was obtained from the integration of heat capacity equation i.e. R 986 DH ¼ 298 CpFe;s dT, using reference data . The value of the enthalpy increment for Fe is found to be 28.26 kJ mol1. Subtracting this enthalpy increment value from the total measured enthalpy change, the heat effect due to dissolution of Fe(s) was calculated. The enthalpy of dissolution (DHdissolution) of Fe(s) in liquid Sn solvent at 986 K was found to be 3.04 ± 0.40 kJ mol1. The reaction enthalpy for Ge(s), FeGe(s) and FeGe2(s) were determined following exactly similar procedure. Fig. 3b gives the heat ﬂow versus time plot for dropping of Ge(s) in the solvent. It can be observed that in this case also immediately after the dropping an endothermic peak was obtained. The average enthalpy change for Ge(s) dropping is found to be 53.37 ± 0.69 kJ mol1. The nature of the heat effect can be similarly explained by the
Fig. 5. (a and b) SEM pictures for the frozen Sn alloy containing FeGe and FeGe2 samples respectively, obtained after the calorimetric reaction.
Table 1 Molar enthalpies of dissolution of Fe(s), Ge(s), FeGe(s) and FeGe2(s) in 3 g of liquid Sn solvent at T = 986 K; m denotes the mass of the sample dissolved; DH is the measured energy change per unit mass and DHT is the molar enthalpy of solution. Compound
DH (J g1)
DHT (kJ mol1)
DHincrement (kJ mol1)
Fe(s) At. wt. = 55.845
17.90 30.13 34.36
460 447 448
25.69 24.97 25.02 Avg: 25.22 ± 0.40
3.04 ± 0.40
Ge(s) Mol. wt. = 72.61
14.9 31.4 38.5
741 740 724
53.80 53.73 52.57 Avg: 53.37 ± 0.69
35.93 ± 0.69
FeGe(s) Mol. wt. = 128.455
26.9 21.1 21.6
699 695 702
89.79 89.28 90.17 Avg: 89.75 ± 0.45
48.55 ± 0.45
FeGe2(s) Mol. wt. = 201.065
37.01 36.67 32.4
789 794 791
158.64 159.65 159.04 Avg: 159.11 ± 0.51
105.71 ± 0.51
S. Phapale et al. / Journal of Alloys and Compounds 591 (2014) 170–173 Table 2 Reaction scheme for the standard molar enthalpy of formation of FeGe(s) and FeGe2(s) (M(sln) = dilute solution of species M in 3 g liquid Sn solvent maintained at 986 K, (Df H298 (FeGe, s) = DH1 + DH3 + DH4 and Df H298 (FeGe2, s) = DH2 + DH3 + 2DH4). Reaction
D Hi (kJ mol1)
FeGe(s, 298 K) + (sln, 986 K) = Fe(sln, 986 K) + Ge(sln, 986 K) FeGe2(s, 298 K) + (sln, 986 K) = Fe(sln, 986 K) + 2Ge(sln, 986 K) Fe(s, 298 K) + (sln, 986 K) = Fe(sln, 986 K) 2Ge(s, 298 K) + (sln, 986 K) = Ge(sln, 986 K) Fe(s, 298 K) + Ge(s, 298 K) = FeGe(s, 298 K)
48.55 ± 0.45
105.71 ± 0.51
D H3 D H4 Df H298
3.04 ± 0.40 35.93 ± 0.69 15.56 ± 0.92
Fe(s, 298 K) + 2Ge(s, 298 K) = FeGe2(s, 298 K)
36.89 ± 1.17
enthalpy increment for heating of Ge(s) from 298 K to 986 K and also by the heat effects due to dissolution of Ge(s) with the solvent at 986 K. Subtracting this enthalpy increment value from the measured enthalpy change, the enthalpy of dissolution (DHdissolution) of Ge(s) in liquid Sn solvent at 986 K was found to be 35.93 ± 0.69 kJ mol1. Fig. 3c and d gives heat ﬂow versus time signals for FeGe(s) and FeGe2(s). In these two compounds also single endothermic peaks were observed. The average enthalpy change for FeGe(s) and FeGe2(s) dropping were found to be 89.75 ± 0.45 and 159.11 ± 0.51 kJ mol1, respectively. In absence of heat capacity information on FeGe(s) and FeGe2(s), the contributions due to enthalpy increment for the heating of the sample from room temperature to 986 k were experimentally determined. The average values of enthalpy increment for FeGe and FeGe2 are found to be 41.2 and 53.4 kJ mol1 respectively. Hence, the corresponding heats of dissolution (DHdissolution) are 48.55 ± 0.45 and 105.71 ± 0.51 kJ mol1, respectively. The frozen products from each calorimetric measurement were analyzed for the uniform distribution of Fe and Ge elements in the Sn matrix employing SEM/EDX technique. Fig. 5a and b gives SEM pictures of the frozen products containing Sn alloys with dissolved FeGe and FeGe2 samples, obtained after the reaction. The darker spots shown in these pictures represent lighter elements Fe and Ge. Analysis of the EDX results indicates that Fe and Ge atoms are uniformly distributed in the whole solvent matrix. 3.1. Standard enthalpy of formation of FeGe(s) and FeGe2(s) (experimental)
Hence, the enthalpy of formation of FeGe(s) and FeGe2(s) from the elements at 0 K can be calculated using the following equations:
Df HðFeGe;0 KÞ ¼ Etot ðFeGe;0 KÞ Etot ðFe;0 KÞ Etot ðGe;0 KÞ
Df HðFeGe2 ;0 KÞ ¼ Etot ðFeGe2 ;0 KÞ Etot ðFe;0 KÞ 2 Etot ðGe;0 KÞ
The enthalpy of formation of FeGe(s) and FeGe2(s) at 0 K were calculated as 31.75 kJ mol1 and 54.74 kJ mol1, respectively. It can be observed that the standard enthalpy of formation of FeGe(s) and FeGe2(s) derived from calorimetric measurements and the results obtained from ab initio calculations at 0 K are on expected lines. In the absence of data on heat capacity of FeGe and FeGe2 in the temperature range of 0–298 K, we have calculated the heat capacity of the compounds. The values of the enthalpy increment from 0 K to 298 K calculated using the relation R 298 CpdT are found to be 11.6 and 12.6 kJ mol1for FeGe and FeGe2 0 respectively. Considering the above enthalpy increment values, the enthalpy of formation of FeGe and FeGe2 at 298 K are calculated and found to be 20.15 and 42.0 kJ mol1 respectively. These values are comparable to the experimentally determined values, viz., 15.65 ± 0.92 and 36.89 ± 1.17 kJ mol1. Here, we would like to mention that the above calculation was carried out considering only the lattice contribution to the heat capacity. However, the magnetic and electronic contributions to the heat capacities values, if added, the calculated values will be further closer to the experimental results. 4. Summary In summary, we have prepared FeGe(s) and FeGe2(s) alloys by heating metal powders in evacuated quartz ampoules. The materials were characterized by XRD, DTA, SEM and EPMA techniques. The standard molar enthalpy of formation of FeGe(s) and FeGe2(s) at 298 K (DfH298 ) were determined by measuring the reaction enthalpy of Fe(s), Ge(s), FeGe(s) and FeGe2(s) in liquid Sn solvent at 986 K employing high temperature Calvet calorimeter. The values of DfH298 of FeGe(s) and FeGe2(s) at 298 K were found to be 15.56 ± 0.92and 36.89 ± 1.17 kJ mol1, respectively. References
The standard molar enthalpies of formation of FeGe(s) and FeGe2(s) were derived using the thermochemical cycles given in Tables 1 and 2, respectively. The values for molar enthalpies of dissolution (DHdissolution) of FeGe(s), FeGe2(s), Fe(s) and Ge(s) were used to derive the standard molar enthalpy of formation of FeGe(s) and FeGe2(s) at 298 K. The values are found to be 15.56 ± 0.92 and 36.89 ± 1.17 kJ mol1, respectively. 3.2. Standard enthalpy of formation of FeGe(s) and FeGe2(s) (calculation) The formation of FeGe(s) and FeGe2(s) from its constituent elements is described by the chemical reactions:
FeðsÞ þ GeðsÞ ¼ FeGeðsÞ
FeðsÞ þ 2GeðsÞ ¼ FeGe2 ðsÞ
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