Article pubs.acs.org/JPCC
Standard Gibbs Energies of Formation of the Ferro- and Paramagnetic Phases of AlNd3 Masao Morishita,*,† Keiichiro Ikeda,‡ Naoto Nishimura,‡ Seiji Miura,‡ and Yoshihiro Yamada§ †
Department of Materials Science and Chemistry, ‡Graduate Student, and §Department of Electrical Engineering and Computer Sciences, University of Hyogo, Japan ABSTRACT: The standard Gibbs energies of formation, ΔfG°m,T, below and above the critical temperatures of polymorphs, magnetic, and superconductive phase transitions are necessary to clarify the driving forces for such phase transitions. However, they have remained unsolved due to experimental difficulties. In the present study, the ΔfG°m,T values of the ferro- and paramagnetic phases of AlNd3 were directly determined. The standard entropy of formation, ΔfSm,T ° , was determined from the heat capacity, Cp,m ° , from 2 to 300 K. The standard enthalpies of formation, ΔfH°m,T, were determined by combining C°p,m with the standard enthalpy of formation at 298 K, ΔfHm,298 ° , obtained by acid-solution calorimetry. The magnetization, M, was measured by a magnetic balance. The ΔfGm,T ° values obtained by combining the ΔfSm,T ° and ΔfHm,T ° values indicate that the phase transition occurs at 73.47 K, i.e., the Curie point, consistent with the spontaneous magnetization from para- to ferromagnetic phases clarified by measuring M. The ΔfG°m,T function for the ferromagnetic phase is more stable than the paramagnetic phase below the Curie point and conversely over the Curie point, indicating that the driving force for the magnetic phase transition can be defined by the difference in ΔfGm,T ° between the former and the latter. Such a driving force appears to be a measure for materials design for magnetic refrigerants. phase diagram of the Al−Nd binary system,4 there are six compounds: Al11Nd3, Al3Nd, Al2Nd, AlNd, AlNd2, and AlNd3. Kissell and Wallace5 measured the magnetization, M, of AlNd at 2−300 K and reported that the antiferromagnetic phase is found below 25 K. Li6 measured the M of AlNd2 at 2−300 K and reported that spontaneous magnetization is observed below 50 K. Regarding AlNd3 scoped in the present study, Borzone et al. measured standard enthalpies of formation at 298 K, ΔfH°298, of AlNd3 by the direct reaction method.7 However, the standard Gibbs energies of formation, ΔfG°T, and M of AlNd3 have not yet been investigated. In our present study, the standard enthalpy of ° , of AlNd3 at 298 K was determined by acid formation, ΔfHm,298 solution calorimetry in a similar way to the Mg−Zn compounds8−12 and AlNd22 in our previous studies. The standard entropy of formation at 298 K, ΔfS°m,298, of AlNd3 was ° , in a determined by measuring the heat capacity, Cp,m temperature range from 2 to 300 K by a recently developed relaxation method.13−15 Furthermore, the standard Gibbs energy of formation as a function of temperature was obtained from C°p,m and ΔfHm,298 ° . To confirm the magnetic phase transition, the magnetization, M, was measured by a magnetic balance. Finally, the thermodynamic basis of the magnetic phase transition of AlNd3 was clarified from the obtained ΔfG°m,T which indicated the driving force for the magnetic phase transition. Such a driving
1. INTRODUCTION The standard Gibbs energies of formation, ΔfG°m,T, below and above the critical temperatures, Tc, of polymorphs, magnetic, and superconductive phase transitions are necessary to clarify the driving forces for such phase transitions. However, they have remained unsolved due to experimental difficulties. Previously, one of our authors, Morishita, directly investigated the thermodynamic properties of not only the α and β polymorphs of NiMoO41 but also the ferro- and paramagnetic phases of AlNd2 by calorimetry.2 The ΔfG°m,T values of the α and β polymorphs of NiMoO4 were determined by combining drop solution calorimetry into molten sodium molybdate with measurement of heat capacity, C°p,m, from very low (2 K) to high temperatures.1 The ΔfG°m,T values indicate that the α phase is more stable than the β phase below 1000 K and conversely above 1000 K, consistent with the observed first-order phase transition.1 The ΔfG°m,T values of the ferro- and paramagnetic phases of AlNd2 were determined by combining acid solution calorimetry with measuring the Cp,m ° values.2 The ΔfGm,T ° values indicate that the ferromagnetic phase is more stable than the paramagnetic phase below 39.59 K and conversely above 39.59 K, consistent with the observed λ type phase transition.2 It is well-known that there are oxides which reveal the superconductive phase transition in liquid nitrogen. To put such superconductors to practical use, a refrigeration technique for keeping liquid nitrogen below its boiling point (=77.2 K) should be developed at the same time. Recently, magnetic refrigeration has been studied as effective low-temperature refrigeration.3 The Al−Nd binary system appears to be important to search for the magnetic refrigerants for refrigerating liquid nitrogen. In the © 2012 American Chemical Society
Received: February 8, 2012 Revised: August 22, 2012 Published: August 24, 2012 20489
dx.doi.org/10.1021/jp301259n | J. Phys. Chem. C 2012, 116, 20489−20495
The Journal of Physical Chemistry C
Article
force appears to be a measure for materials design for magnetic refrigerants.
° T (Al 0.25Nd 0.75) Δf Sm, =
2. EXPERIMENTAL SECTION Commercial Al plate (99.99%, Nilaco Co., Japan) and Nd blocks (99.9%, HPCI Co., Japan) were used as starting materials. Since formulation for one mole atoms is convenient to construct thermodynamic cycles for measurements and compare the thermodynamic properties of compounds, AlNd3 is rewritten as Al0.25Nd0.75. Al0.25Nd0.75 was prepared by arc-melting with a tungsten electrode in an argon (99.99%) atmosphere. After melting, the sample was sealed under vacuum in a silica tube at room temperature and then subjected to a homogenizing treatment at 673 K for 3 weeks. Excess addition of 2 mol % of Nd, which was determined from prior experiments, was necessary to prepare Al0.25Nd0.75 since the evaporation loss of Al and oxidation loss of Nd were counter-balanced during arcmelting and heat treatment. The composition of the sample was confirmed by an electron microprobe analyzer (EPMA, JEOL, JXA-8900R). It was homogeneous and single phase. The average of the atomic ratios of Al and Nd of five analyses was 24.99 and 75.05 mol %, respectively. The mean standard deviation, σ, of the five analyses was ±0.55 mol %. The sample was shown to be a single phase by X-ray diffraction measurements, corresponding to the reference datum.16 Therefore, the sample constituent was found to be stoichiometric Al0.25Nd0.75. Table 1 shows the thermodynamic cycle to determine ΔfH°m,298 of Al0.25Nd0.75. ΔfH°m,298 of Al0.25Nd0.75 was defined as the
∫0
dT − 0.25 × T T C p°,m(Nd) C p°,m(Al) dT − 0.75 × dT 0 T T
T
∫
(1)
n
C °p ,m =
∑ anT n
J K−1 (mol of atoms)−1 (
