Standard Gibbs Energies of Formation of the Ferro and Paramagnetic Phases of AlNd 2

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1 Standard Gibbs Energies of Formation of the Ferro and Paramagnetic Phases of AlNd 2 M. Morishita*, H. Yamamoto*, M. Kodera**, N. Nishimura**, S. Miura** and Y. Yamada*** *Department of Materials Science and Chemistry, University of Hyogo, Japan **Graduate Student of University of Hyogo *** Department of Electrical Engineering and Computer Science, University of Hyogo, Japan

2 Polymorphs and martensite phase transitions Magnetic and superconductive phase transitions Fig. Concept for the first and second order phase transition of a compound described in the text book by R. Swalin.

3 / kj m ol P resent study (α) P resent study (β) J acob 5 ),oxide T fg T em perature, T / K Fig. Standard Gibbs energies of formation of α- and β- NiMoO 4. (M. Morishita and A. Navrotsky: J. Am. Ceram. Soc., 86 (2003) 1927.)

4 Al:Free electrons originated from 3s and 3p components Nd:Strongly localized electrons composed of 4f component Interesting properties Wiring materials for liquid crystals Panels (Nd improves heat-resistance of Al wire) Candidate materials used for magneto - refreezegator Al 2 Nd(W.M.Swift and W.E.Wallace, 1968) Magnetic phase transition at 76.0K production Liquid nitrogen

5 Al-Nd binary system Al 11 Nd Nd 3,Al 3 Nd,Al 2 Nd, AlNd,AlNd 2,AlNd 3 Study on magnetic phase transition by measuring magnetization, M C p measurement Acid solution calorimetry Standard Gibbs Energies of Formation, f G T, of the Ferro and Paramagnetic Phases

6 1900 mass% Nd L Tempera ature, T/K βal 11 Nd (βnd) (Al) αal 11 Nd 3 Al 3 Nd Al 2 Nd AlNd AlNd 2 AlNd 3 (αnd) 300 Al mol% Nd Fig. Al-Nd Phase Diagram. Nd

7 Al Al Nd (AlNd (AlNd 2 ) Starting Materials : Pure Al and Nd Melting : Arc Melting Heat treatment : 673 K, 6 weeks XRD and EPMA C p, M, Solution calorimetry

8 dt CP = KW ( T Tb ) + P( t) dt Holder Sample Stage Heater Thermocouple (Cernox) Heat Capacity measurement by a relaxation method Fig. Appearance of apparatus for measurig Cp from 2K to 300 K.

9 30 p / J K-1 mol -1 C p Fig. Al Change in heat capacity,c p,with temperature,t,for Nd Al Nd Temperature, T / K

10 Ma agnetization, M / emu g H =10.2 koe /em u 2 g -2 M K 32K 34K 36K 38K 40K 42K 44K 46K 48K 50K Temperature, T / K H M / 0e g em u -1 Fig. Change in magnetization, M, with temperature,t,for Al Nd Al Nd Fig. Arrott Plot of Al Nd at K.

11 mix S T (Al Nd ) = 0 T C p (Al Nd ) T 0 T C p (Al) T dt dt T C p (Nd) T dt mix H T (Al Nd ) = mix H 298 (Al Nd ) + T 298 C p (Al Nd )dt T C p (Al)dT 298 T C p (Nd)dT 298 mix G T = mix H T T mix S T C p = Σ n = 1 n an T n J K -1 mol -1 (< 300 K)

12 Enthalpy of solution of mechanical mixture of pure substances 0.333Al+0.667Nd = 0.333Al aq Nd aq. (0.333Al+0.667Nd) [kj mol - 1 ] (1) sol H 298 Enthalpy of solution of intermediate phase compound Al Nd sol H = 0.333Al aq Nd aq. (Al Nd ) [kj mol - 1 ] (2) (1)-(2) (2) =(3) 0.333Al+0.667Nd = Al 0.667Nd} (Al Nd mix H 298 The measurement condition Solvent 5N-HCl 25.0(ml) quantity 1/1000mol (AlNd 2 :105.15mg) Enthalpy of mixing of intermediate phase sol H 298 sol H Enthalpy ] (3) of formation of intermetallic ) [kj mol - 1 ] (3) f H 298 (AlNd 2 ) = (Al Nd Al Nd ) = {0.333Al+ mix H [kj mol - 1 ] (4)

13 Fig. Schematic sketch of new Calvet-type type calorimeter.

14 Table Measured sol H 298 (0.333Al+0.667Nd) and (Al Nd ) (kj mol - 1 sol H 298 ). Measured solh (kj mol ) (kj mol - 1 ) 0.333Al+0.667Nd Al Nd Standard deviation Error(%) 0.333Al ± Nd Al Nd ±4.39 Table mix H and (kj mol - 1 mix H 298 f H 298 ) ±7.83 (Al f H Nd ) Ref. by Prof. G. (AlNd Borzone, 2 ) Z. Metallkd, ±23.49 (1993) mix H 298 (Al Nd ) / kj mol -1 = ±2 sol H AV

15 Fig. Measured enthalpy of mixing, mix H T, of Al Nd

16 Δm ix S T /J K -1 m ol T em perature, T /K Fig. Measured entropy of mixing, mix S T, of Al Nd

17 x G / kj m ol -1 T Δ m ix Al Nd Ferro Para Temperature, T/ K Fig. Gibbs energies of mixing, mix G T, of the ferro and paramagnetic Phases of Al Nd

18 Conclusion The f G T of the ferro and paramagnetic phases of AlNd 2 were directly determined by combining C p with the standard enthalpy of formation at 298 K. The G values indicate that the f T ferromagnetic phase is more stable than the paramagnetic phase below 37.8 K, and conversely above 37.8 K. The thermodynamic data confirm that 37.8 K is indeed the equilibrium magnetic phase transition temperature.

19 The measured magnetization by Li agreed well with our present study. (J. Alloys and Comp., 288(1999) Both of magnetizations by us and Li are half of the theoretically expected values of free Nd 3+ ion Li suggested at a possible magnetic structure proportion of the moments antiferromagnetically (J. Alloys and Comp., 288(1999) A ferrimagnetic state is another candidate

20 n µ Al = µ Al -µ Al = RT ln a Al µ Nd µ Al / kj mol Al 0.75 Nd 0.25 Al Nd Al N Nd Nd = µ Nd -µ Nd = RT ln a Nd kj mol -1 µ Nd / kj mol - 1 G Al Nd Al 0.5 Nd Al Nd K d0 0.2 ole0.4 fracti0.6 onnd Al NdMmix a-25.7 kj mol -1

21 The magnetization at low tempeararures under a magnetic field of 10.2 kos: 1.2 µb Theoretically expected value: 3.27 µb (free Nd 3+ ion ) Li suggested at a possible magnetic structure proportion of the moments antiferromagnetically (J. Alloys and Comp., 288(1999) A ferrimagnetic state is another candidate

22 Pioneer Studies on beyond Born-Oppenheimer Approximation I.L.Thomas, Phys. Rev., Vol.185 (1969) 90. L.J. Adamowicz, J. Chem. Phys., Vol.95 (1991) M. Cafiero, Phys. Rev. Lettt., Vol.89 (2002) H. Nakai, Chem. Phys. Lett., Vol.290 (1998) 437. U. Nagashima, J. Chem. Phys., Vol.124 (2006) 124. Nuclear Basis Wave Functions (NBFs) on the Basis of Zero Point Uncertain at 0 K Slater-type Functions (STFs) Explicit Correlated Gaussian Functions (ECG)

Determination of Standard Gibbs Energy of Formation of Al 2 Nd by Solution Calorimetry and Heat Capacity Measurement from Near Absolute Zero Kelvin

Materials Transactions, Vol. 47, No. 8 (26) pp. 244 to 248 #26 The Japan Institute of Metals Determination of Standard Gibbs Energy of Formation of Al 2 Nd by Solution Calorimetry and Heat Capacity Measurement