Thermodynamics of NdRhO3 and phase relations in thesystem Nd–Rh–O

K.T. Jacob a,n, Preeti Gupta a, Donglin Han b, Tetsuya Uda b

a Department of Materials Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, Indiab Department of Materials Science and Engineering, Kyoto University, Sakyo-ku, Kyoto 6068501, Japan

a r t i c l e i n f o

Article history:Received 2 August 2013Received in revised form17 September 2013Accepted 3 October 2013Available online 18 October 2013

Keywords:Phase equilibriaNdRhO3

Nd–Rh–O systemGibbs energyEnthalpy

a b s t r a c t

Phase equilibrium experiments indicate that NdRhO3 is the only ternary oxide in the system Nd–Rh–O at1273 K; it has orthorhombically-distorted perovskite structure. By employing a solid-state electroche-mical cell incorporating calcia-stabilized zirconia as the electrolyte, thermodynamic properties ofNdRhO3 are determined. The standard Gibbs energy of formation of NdRhO3 from its component binaryoxides in the temperature ranges from 900 to 1300 K can be expressed as: 1/2Rh2O3(ortho)þ1/2Nd2O3(hex)¼NdRhO3(ortho), Δf ðoxÞG

o= J mol�1ð7197Þ ¼ �66256þ5:64 ðT=KÞ.The decomposition temperature of NdRhO3 computed from extrapolated thermodynamic data is

1803 (74) K in pure oxygen and 1692 (74) K in air at standard pressure. Oxygen partial pressure–composition diagram and three-dimensional chemical potential diagram at 1273 K are developed fromthermodynamic data obtained in this study and auxiliary information from the literature. Equilibriumtemperature–composition phase diagrams at constant oxygen partial pressures are also constructed.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Rhodites of lanthanide elements are promising materials forcatalysis and electrochemistry [1–3]. LnRhO3 (Ln¼La, Dy, Gd, Lu) isused as a cathode in the photoelectrolysis of water [2,3]. LaRhO3

behaves as an active catalyst for the formation of linear alcoholsfrom synthetic gas [1]. Other catalytic and photocatalytic applica-tions of LnRhO3 are being explored. Macquart et al. [4] havesynthesized single crystals of LnRhO3 (Ln¼La, Pr, Nd, Sm, Eu, Tb)using K2CO3 flux and determined their crystal structures. Thecompounds have GdFeO3-type centrosymmetric distorted pervos-kite structure, which is orthorhombic and belongs to the spacegroup Pbnm. Taniguchi et al. [5] investigated electrical and magneticproperties of LnRhO3 (Ln¼rare earth except Ce and Pm). They foundthat LnRhO3 compounds are paramagnetic above 5 K. The resistivityof all LnRhO3 compounds exhibits semiconductor-like temperaturedependence. Recently, Yi et al. [6] have also confirmed paramag-netic state of NdRhO3 caused by the presence of Nd3þ ion. There isno information on phase relations in the ternary system Nd–Rh–Oand thermodynamic properties of NdRhO3 in the literature.

Because of potential applications in diverse fields, one of the aimsof this study is the establishment of an isothermal section of thephase diagram of the system Nd–Rh–O at 1273 K by equilibration

and phase analysis of quenched samples, employing optical andscanning electron microscopy (OM/SEM), powder X-ray diffraction(XRD), and energy dispersive spectroscopy (EDS). Based on ternaryphase relations, a solid-state electrochemical cell is designed tomeasure the thermodynamic properties of NdRhO3 in the tempera-ture range from 900 to 1300 K. Differential thermal analysis (DTA) isused to determine the decomposition temperature of ternary oxideNdRhO3. Different types of two-dimensional and three-dimensionalphase diagrams are developed using thermodynamic data.

2. Experimental methods

2.1. Materials

Spectroscopic grade Nd and Nd2O3 used in this study as startingmaterials were from Johnson Matthey Rare Earths Products, U.K.Nd2O3 was calcined under high-purity argon gas at 1273 K for 4 hbefore use. The structure confirmed by XRD analysis was hexagonal(A-type), with lattice parameters a¼0.3829 nm and c¼0.5999 nm.The metal atom had unusual sevenfold coordination in this struc-ture. Powders of Rh (99.95%) and Rh2O3 (99.9%, metal basis) wereobtained from Alfa Aesar. Rh2O3 was fired at 1273 K under high-purity oxygen gas for 24 h. The high-temperature low-pressureform of Rh2O3, often referred to as β-Rh2O3 or Rh2O3 (III), used inthis study had orthorhombic structure with lattice parametersa¼0.5148 nm, b¼0.5438 nm and c¼1.4693 nm. Octahedrally co-ordinated by O2� ions is Rh3þ ion. Each O2� ion is bonded to four

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n Corresponding author. Tel.: þ91 80 2293 2494; fax: þ91 80 2360 0472.E-mail addresses: katob@materials.iisc.ernet.in,

ktjacob@hotmail.com (K.T. Jacob).

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 43 (2013) 71–79

Rh3þ ions. In this structure pairs of RO6 octahedra share faces. Eachpair is connected to three others by edge sharing.

To prepare NdRhO3 an equimolar mixture of fine powders ofNd2O3 and Rh2O3 were ground together in ethanol, dried andpelletized for heat treatment at 1373 K under pure oxygen gas for48 h with several intermediate regrinding steps. The reaction wascompleted by heating further at 1573 K under flowing oxygen foranother 48 h. The formation of orthorhodite was confirmed byX-ray diffraction (XRD) technique. The lattice parameters of orthor-hombic NdRhO3 at room temperature were a¼0.5376 nm,b¼0.5754 nm and c¼0.7772 nm. The orthorhombic distortion isprobably caused by steric effects since aoc/√2ob.

2.2. Phase equilibrium studies at 1273 K

Phase relations in the system Nd–Rh–O were explored by equili-brating mixtures of pure metals and binary oxides at 1273 K, quench-ing in liquid nitrogen and phase identification at room temperature.The mixtures were compacted in a steel die at 150MPa beforeequilibration. The three samples containing only oxide phases wereequilibrated under pure oxygen atmosphere. These samples were firstheated to 1623 K for �8 h to initiate the reaction between the oxidesand then equilibrated for a total period of �144 h at 1273 K. Thesamples were quenched at regular intervals, ground to �325meshand repelletized six times during this period. The two samplescontaining a mixture of metal and oxide were pelletized and equili-brated in vacuum. The pellets, contained in closed alumina cruciblesand supported on sacrificial pellet of the same composition, wereplaced in quartz ampules which were evacuated and sealed. Thesamples were first heated to 1423 K for �8 h to initiate the reactionbetween metal and oxide and then equilibrated for a total period of�120 h at 1273 K. The phase compositions of the samples wereunaltered by further heat treatment. When there was no change inphase compositionwith time, attainment of equilibriumwas assumed.The average composition of the samples, materials used initially forthe preparation of each sample, and equilibrium phases identifiedafter quenching are listed in Table 1. Phase identification was doneusing optical and scanning electron microscopy (OM/SEM), energydispersive spectroscopy (EDS), and XRD. The average compositions ofthe samples used are marked in Fig. 1.

2.3. Electrochemical measurement

The reversible emf of the solid-state electrochemical cell,Pt-13%Rh, RhþNdRhO3þNd2O3//(CaO) ZrO2//Rh2O3þRh, Pt-13% Rh,was measured as a function of temperature in the range from 900to 1300 K. Right-hand side electrode is positive. Reference elec-trode on right-hand side and measuring electrodes on the leftwere separated by a calcia-stabilized zirconia (CSZ) tube whichserves as the solid electrolyte. In the temperature and oxygenpartial ranges encountered in this study, CSZ had oxygen iontransport number larger than 0.99. Both the electrodes wereconnected to measuring instruments with wires of Pt-13% Rh alloy.

The electrodes were contained in separate evacuated and sealedenclosures, which were separated by the impervious CSZ tube. Thedecomposition of Rh2O3 and NdRhO3 at high temperatures deter-mined the oxygen partial pressure over the reference and workingelectrodes, respectively. As the oxygen partial pressures over theelectrodes were substantial, closed systems are used to ensuregas–solid equilibrium. Since the apparatus and procedure used inthis study are almost identical to that described earlier [7,8], only aminimalist description is given here.

The measuring electrode was prepared by compacting a mix-ture of Nd2O3, NdRhO3 and Rh in the molar ratio 1:1.5:1 inside aclosed-end CSZ tube. NdRhO3 was taken in excess to establish byits decomposition the oxygen partial pressure in evacuated andsealed enclosure around the measuring electrode. A Pt-13% Rhwire, which functions as the electrode lead, was embedded in theelectrode mixture. A bell-shaped cover made of Pyrex was placedon the top of the CSZ tube. In order to seal the joint between theCSZ tube and the Pyrex bell, De-Khotinsky cement from CentralScientific Company (CENCO) was used. The CSZ tube and theattached bell were evacuated to a pressure of 0.1Pa and flame sealedunder vacuum.

The reference electrode was made by consolidating a mixtureof Rh and Rh2O3 in the molar ratio 1:1.5 in a CSZ crucible. Thecrucible was placed inside a silica tube closed at one end. The CSZtube inclosing the measuring electrode and the attached bell wereloaded on top of the reference electrode. The outer silica tube wasalso closed with a Pyrex cover using De-Khotinsky cement. Subse-quently, the chamber containing the reference electrode was evac-uated and sealed. The difference in oxygen partial pressure at thetwo electrodes at high-temperature was measured as an emf of thecell. Particle size of the powders used to make the electrodes variedfrom 3 to 25 μm. In this size range surface energy contribution isnegligible and the measured thermodynamic properties are essen-tially bulk properties [9].

The complete setup was suspended in a vertical resistancefurnace, with the electrodes located in the even temperature(71) K zone. The upper part of the cell with the cement sealswas at room temperature during measurement. In order tominimize the induced emf, a Faraday cage made from stainlesssteel foil was placed between the furnace and the cell assembly.The furnace temperature was controlled to (71) K and is mea-sured by a Pt/Pt-13%Rh thermocouple, checked against the melting

Table 1Results of phase equilibrium experiments at 1273 K under pure oxygen gas at0.1 MPa pressure.

Starting materials Average composition Equilibrium phases

XRh XNd XO

Nd2O3þRh2O3 0.10 0.30 0.60 Nd2O3þNdRhO3

Nd2O3þRh2O3 0.20 0.20 0.60 NdRhO3

Nd2O3þRh2O3 0.30 0.10 0.60 NdRhO3þRh2O3

Rh2O3þNd 0.32 0.21 0.47 Nd2O3þNdRhO3þ RhRh2O3þNdþRh 0.52 0.06 0.42 NdRhO3þRh2O3þRh

Fig. 1. Isothermal section of the phase diagram for the system Nd–Rh–O at 1273 K(cross marks denote the compositions of the samples equilibrated at high temperature).

K.T. Jacob et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 43 (2013) 71–7972

point of Au. High impedance (41012 Ω) digital voltmeter with thesensitivity of (70.01) mV was used to measure the cell emf.Electrochemical reversibility of the cell was ascertained by micro-coulometric titration in both directions by passing small directcurrent (�50 μA) using an external potential source for �5 min.The open circuit emf was monitored as a function of temperatureafter each titration. It gradually returned to the original value beforeeach titration indicating reversibility of the cell. Reproducibility ofemf on temperature cycling indicated thermal reversibility.

The electrodes were examined before and after emf measure-ment by X-ray diffraction (XRD), scanning electron microscopy(SEM) and energy dispersive spectroscopy (EDS). The phasecomposition of the electrodes was found to be unchanged duringhigh-temperature electrochemical measurements. The three-phase electrode consisting of Rh, NdRhO3 and Nd2O3 was stable inthe temperature range used in this study. Not observed was anyevidence of reaction between the electrodes and the solid electrolyte.

2.4. Thermogravimetric studies

Thermogravimetric analysis (TGA) and differential thermalanalysis (DTA) of NdRhO3 powder was carried out in air in thetemperature range from room temperature to 1773 K at a heatingrate of 10 K min�1 using a standard instrument, TG8120 (Rigaku,Japan).

3. Results and discussion

3.1. Phase relations

Results from phase equilibrium experiments on five samples,summarized in Table 1, are combined with information on thethree binary systems available in the literature [10] to draw theisothermal section of the phase diagram of the system Nd–Rh–O at1273 K shown in Fig. 1. Along the Nd–O binary only one stableoxide, Nd2O3, is found. In the Rh–O binary, Rh2O3 is the only stableoxide. Four stoichiometric (Nd3Rh2, Nd5Rh4, NdRh and NdRh3) andone nonstoichiometric (‘NdRh2’:0.66oXRho0.685) intermetallicphases are present along the Nd–Rh binary [10]. A liquid phaseexists in the composition range 0.007oXRho0.33 at 1273 K.

Only one stable ternary oxide is identified in this study alongthe Nd2O3–Rh2O3 join. It has GdFeO3-type centrosymmetric dis-torted pervoskite structure shown in Fig. 2. Situated in the cavityformed by tilted corner-sharing RhO6 octahedra are Nd3þ ions.There are eight O2� ions around Nd3þ that are at a distancesmaller than the nearest Nd3þ . But, there is another O2� ion just

beyond the nearest Nd3þ , so that the coordination around Nd3þ

may be considered as either eight or nine. The lattice parametersof NdRhO3 obtained in this study are in fair agreement with thedata reported in the literature [4]. Two three-phase triangles areidentified by experiment, Nd2O3þNdRhO3þRh and NdRhO3þRh2O3þRh. The tie-triangle with Nd2O3, NdRhO3 and Rh as cornersis useful for the measurement of Gibbs energy of formation ofNdRhO3. The oxygen chemical potential associated with this three-phase equilibrium is related to the stability of NdRhO3; greater thestability, the lower is the oxygen potential. Since metal Rh is foundto be in equilibrium with Nd2O3, it follows that Nd-rich liquidalloys and all five intermetallic phases would also be in equili-brium with Nd2O3. This is consistent with the fact that the Gibbsenergy of formation of Nd2O3 (�1446.37 kJ mol�1) is far morenegative than that of Rh2O3 (�37.38 kJ mol�1). There are ninethree-phase regions containing condensed phases: NdþNd–Rh(l)þNd2O3, Nd–Rh(l)þNd3Rh2þNd2O3, Nd3Rh2þNd5Rh4þNd2O3,Nd5Rh4þNdRhþNd2O3, NdRhþ ‘NdRh2’þNd2O3, ‘NdRh2’þNdRh3þNd2O3, NdRh3þRhþNd2O3, RhþNd2O3þNdRhO3, RhþNdRhO3þRh2O3. There are two three-phase fields where oxygen gas coexistswith two condensed phases: O2þNd2O3þNdRhO3, O2þNdRhO3þRh2O3. Two clearly visible two-phase regions involve alloys ofvariable composition, Nd–Rh (l) and ‘NdRh2’ in equilibrium withNd2O3. Other two phase regions are narrow and form the boundariesof three-phase fields.

3.2. Thermodynamic properties of NdRhO3

Reversible emf of the solid-state cell is plotted in Fig. 3 as afunction of temperature in the range from 900 to 1300 K. The emfis a linear function of temperature. The equation from least-squares regression analysis is:

E=mVð70:68Þ ¼ 288:9�0:0195 ðT=KÞ ð1Þ

The uncertainty limit corresponds to twice of the standarddeviation (2s). The estimated systematic errors in emf and tem-perature measurement are significantly lower than random error.The oxygen chemical potential at the right-hand reference electrodeis maintained by the dissociation of orthorhombic Rh2O3:

23Rh2O3 ¼

43RhþO2 ð2Þ

Fig. 2. A pictorial representation of GdFeO3-type centrosymmetric distorted per-voskite structure for ternary oxide NdRhO3.

Fig. 3. Temperature dependence of reversible emf of the solid-state electrochemi-cal cell.

K.T. Jacob et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 43 (2013) 71–79 73

The oxygen chemical potential of the reference electrode,which was measured earlier [11], can be represented as:

ΔμrO2=J mol�1ð780Þ ¼ �264243þ188 ðT=KÞ ð3Þ

At the left-hand measuring electrode the oxygen chemicalpotential is fixed by the equilibrium between the three condensedphases, Rh, Nd2O3 and NdRhO3:

43Rhþ 2

3Nd2O3þO2 ¼

43NdRhO3 ð4Þ

The oxygen chemical potential of the measuring electrode,computed from the emf using the Nernst equationðΔμr

02�Δμm02 ¼ �4FEÞ, is given by:

ΔμmO2= J mol�1ð7274Þ ¼ �352584þ195:53 ðT=KÞ ð5Þ

The cell reaction obtained by combining the two half-cell reac-tions is:

12Rh2O3ðorthoÞþ

12Nd2O3ðhexÞ ¼NdRhO3ðorthoÞ ð6Þ

The standard Gibbs energy of formation of NdRhO3 from thecomponent binary oxides, Nd2O3 with A-type hexagonal structureðP3m1Þ and high-temperature form of Rh2O3 having orthorhombiccorundum-related structure (Pbca), is given by:

Δrð6ÞGo= J mol�1ð7197Þ ¼ �ηFE¼ �66256þ5:64 ðT=KÞ ð7Þ

where η¼3 is the total number of electrons involved in theelectrode reaction per mole of NdRhO3, F is the Faraday constant,E is the reversible emf of the electrochemical cell and T is thetemperature in Kelvin. The temperature independent term in Eq.(7) gives the enthalpy of formation of NdRhO3 from its componentbinary oxides according to Eq. (6); �66.3 (70.44) kJ mol�1 at amean temperature of 1100 K. The entropy of formation of NdRhO3

from its component binary oxides is negative; �5.64 (70.39)J K�1 mol�1 at 1100 K. The small negative entropy of formation

from component oxides is consistent with the negative volumechange (ΔfðoxÞVo¼�2.25 mL mol�1) for the reaction at roomtemperature calculated from crystallographic data.

For calculating thermodynamic properties of NdRhO3 at298.15 K, heat capacity, enthalpy and entropy data for reactantsand products in Eq. (6) are required. Since heat capacity of NdRhO3

has not been measured, Neumann–Kopp rule is used for itsestimation. Although thermodynamic data for Nd2O3 is availablein the data compilations [12,13], they require revision in the lightof more recent information. Condfunke and Konning [14] reportedrefined data for standard enthalpy of formation of Nd2O3 at298.15 K. Heat content of Nd2O3 was measured by Pankratz et al.[15] in the temperature range from 400 to 1795 K. They found aminor thermal anomaly at 1395 K which was attributed to a phasetransformation (α-β). In the compilations of Pankratz [12] andKnacke et al. [13] a constant value of Co

P is assumed above 1395 K.Since this phase transformation cannot be reconciled with crystal-lographic data, the thermal anomaly is presumably caused byimpurities. In the reassessment of data for Nd2O3, a polynomialexpression based on data in the temperature range from 400 to1395 K is used to extrapolate Co

P to higher temperatures:

CoP= J K�1 mol�1 ¼ 107:8þ4:63� 10�2T�8:5� 10�6T2�8:45� 105T �2

ð8Þ

There is no change in the standard entropy of Nd2O3 at 298.15 Kgiven in the compilations [12,13]. Using the revised enthalpy offormation [14] and heat capacity, thermodynamic properties ofNd2O3 are reassessed and presented in Table 2.

The standard enthalpy of formation of NdRhO3 at 298.15 K fromelements in their normal standard states is assessed as Δf H

o298:15 K ¼

�1172:52ð71:6Þ kJ mol�1. The standard entropy of NdRhO3 at298.15 K is So ¼ �111:5ð70:41Þ J K�1 mol�1. The standard enthalpyof formation of Rh2O3, �405.53 (70.26) kJ mol�1, and the standardentropy of Rh2O3, 75.69 (70.5) J K�1 mol�1 at 298.15 K from Jacobet al. [16] are used in making the estimates for NdRhO3.

The oxygen potential corresponding to the decomposition ofNdRhO3 is given by Eq. (5). The decomposition temperature forNdRhO3 is 1803 (74) K in pure oxygen at standard pressure of

Table 2Thermochemical data for the reaction; 2Nd (cr, l)þ3/2 O2 (g)-Nd2O3 (cr).

T K CoP J K�1 mol�1 Ho

T �Ho298:15 kJ mol�1 So J K�1 mol�1 Δf H

o kJ mol�1 Δf Go kJ mol�1

298.15 111.343 0 158.589 �1806.9 �1719.809300 111.536 0.222 159.278 �1806.852 �1719.245400 119.679 1.245 192.581 �1804.707 �1689.633500 125.445 25.096 219.947 �1802.555 �1660.708600 130.173 38.136 243.263 �1800.488 �1632.251700 134.321 51.547 263.665 �1798.565 �1604.154800 138.079 65.304 281.870 �1796.861 �1576.401900 141.542 79.393 298.359 �1795.430 �1548.851

1000 144.755 93.794 313.466 �1794.321 �1521.4471100 147.747 108.490 327.432 �1793.594 �1494.1591128a 148.547 112.656 331.164 �1793.469 �1486.6071128 a 148.547 112.656 331.164 �1799.527 �1486.6251200 150.533 123.464 340.438 �1798.982 �1466.6081289 b 152.849 137.009 351.319 �1798.153 �1441.5271289 b 152.849 137.009 351.319 �1812.439 �1441.5731300 153.125 138.697 352.624 �1812.312 �1438.8831400 155.529 154.173 364.095 �1811.063 �1410.2071500 157.749 169.875 374.939 �1809.626 �1372.3011600 159.789 185.785 385.226 �1808.024 �1353.2571700 161.653 201.886 395.013 �1806.263 �1324.8951800 163.339 218.162 404.346 �1804.364 �1308.0011900 164.851 234.596 413.265 �1802.346 �1268.6052000 166.189 251.169 421.805 �1800.219 �1240.642

a 1128 K, transition point of Nd, ΔTrHo ¼ 3:03 kJ mol�1.

b 1289 K, melting point of Nd, ΔHo ¼ 7:143 kJ mol�1.

K.T. Jacob et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 43 (2013) 71–7974

PO2=Po ¼ 1. Decomposition in air at standard atmospheric pressure

occurs at 1692 (74) K.

3.3. Thermal analysis of NdRhO3 in air

Results of TGA and DTA analysis of NdRhO3 in air are shown inFig. 4. Heat flow, mass loss and temperature are plotted as afunction of time. The mass loss appears to occur in two stages. Thefirst phase, which starts at 1653 (77) K, is probably related to lossof excess oxygen in the perovskite. Since interstitial oxygen isenergetically unfavourable in the perovskite structure, the defectresponsible for oxygen nonstoichiometry is probably cation vacancy,with negative charge on excess oxygen ions compensated by thepresence of Rh4þ ions. RhO2 is stable up to 1035 K in pure oxygen atambient pressure [17] and Rh4þ exists in the spinel phase of thesystem Mg–Rh–O at 1373 K [18]. A-site vacancy is generally pre-ferred in perovskite structures rather than B-site vacancy. Since Nd/Rh ratio is unity, some Nd must move to the Rh site to give thedistribution: (Nd1�δ Vδ)A [Ndδ /2Rh(2�δ)/2]B O3. The defect reactioncan be written as:

32O2ðgÞ-NdRhO3þ2V‴NdþNdX

Rhþ6Rh�Rh ð9Þ

The second phase of mass loss starting at 1703 (77) K isrelated to the decomposition of stoichiometric NdRhO3 to Nd2O3

and Rh. The nonstoichiometric parameter δ in Nd1�δ RhO3 can beestimated as δ¼0.067 (70.02) from the relative mass changeassociated with the two stages of decomposition. Result of differ-ential thermogravimetric analysis (DTG), displayed as a function oftemperature in Fig. 5, is consistent with this interpretation. Thus, thedecomposition temperature of stoichiometric NdRhO3 from thermalanalysis obtained at a heating rate of 10 K min�1 is 1703 (77) K.Because of the dynamic nature of thermal analysis, true equilibriummay not be achieved at any temperature. The decompositiontemperature obtained during heating is expected to be severaldegrees above the equilibrium decomposition temperature. Thus,the decomposition temperature calculated from the extrapolatedthermodynamic data, 1692 (74) K, and that obtained from thermalanalysis are in reasonable consonance.

The oxygen excess in NdRhO3 was encountered only at hightemperatures and high oxygen pressures. The emf measurementswere conducted at lower temperatures in the range from 900 to1300 K. Since NdRhO3 was in equilibrium with metal Rh at themeasuring electrode, oxygen partial pressure was relatively low;PO2=P

o¼5.62�10�11 at 900 K and PO2=Po¼1.12�10�4 at 1300 K.

Because of the lower temperatures and reduced oxygen pressuresencountered during emf measurement, the non-stoichiometry ofNdRhO3 is insignificant and the data derived from emf measure-ments correspond to nearly stoichiometric composition.

3.4. Temperature-composition phase diagram at constant oxygenpartial pressures

A three-dimensional (3-D) temperature–composition phase dia-gram for system Nd–Rh–O, can be constructed at constant oxygenpartial pressures. The composition of each phase can be representedin the horizontal plane on equilateral triangle and temperaturealong the vertical axis. However, reading quantitative data fromsuch a diagram is difficult. Therefore, a two-dimensional (2-D) isconstructed by using metallic (or cationic) fraction, ηRh/(ηNdþηRh),ηi representing moles of component i, as the composition variable.Oxygen nonstoichiometry cannot be shown in such diagrams asoxygen is excluded from the composition parameter. Cation non-stoichiometry can be quantitatively depicted.

Temperature-composition diagrams at three oxygen partialpressures, PO2=P

o ¼ 1; PO2=Po ¼ 0:212, and PO2=P

o ¼ 10�6 are shownin Figs. 6–8, respectively, where Po ¼ 0:1 MPa is the standardpressure. At these oxygen pressures, Nd component is fully oxidized

Fig. 4. TGA, DTA and temperature of NdRhO3 as a function of time in air.

Fig. 5. Differential thermogravimetric analysis (DTG) of NdRhO3 as a function oftemperature in air.

K.T. Jacob et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 43 (2013) 71–79 75

to Nd2O3. Hence, alloy-oxide equilibria do not fall in the parametricrange displayed. Only three-phase equilibria associated with rela-tively high oxygen potentials fall in the domain of the diagram. Thistype of phase diagram is sensitive to oxygen partial pressure,although the sequence of phase stability remains essentially the

same at the different partial pressures. The difference between thedecomposition temperatures of NdRhO3 and Rh2O3 decreases some-what with decreasing oxygen partial pressure.

3.5. Computation of chemical potential diagrams for the systemNd–Rh–O at 1273 K

Thermodynamic data for various phases are necessary tocompute chemical potential diagrams. Reassessed thermodynamicdata for Nd2O3 is given in Table 2. Data for Rh2O3 is represented byEq. (3) [11,16]. Gibbs energy of formation for NdRhO3 obtained inthis study is given by Eq. (7). Using calorimetric data of Guo andKleppa [19] for enthalpy of formation of Nd5Rh4, NdRh, ‘NdRh2’

and NdRh3, Miedema's model [20] and Nd–Rh phase diagram [10],thermodynamic data for intermetallic phases in the binary systemNd–Rh are assessed. The entropy of formation of solid interme-tallic phases from pure metals in the solid state is assumed to bezero. The evaluated Gibbs energy of mixing for binary Nd–Rh ispresented Fig. 9 as a function of composition, relative pure solidmetal reference states. In the evaluation greater reliance is placedon measured calorimetric data and phase diagram information.The phase diagram constraints the composition dependence ofGibbs energy. The Gibbs energy of mixing for the liquid alloy at1273 K, relative to pure solid metals as reference state, can beapproximated by the sub-regular solution model [21]:

ΔmixG= J mol�1 ¼ RTðXNd ln XNdþXRh ln XRhÞþXNdXRhðΩNdXNdþΩRhXRhÞþ89XNdþ11450XRh ð10Þ

where XNd and XRh are mole fractions of Nd and Rh respectively,R is gas constant, T is temperature in Kelvin. The two sub-regularsolution parameters ΩNd and ΩRh are �275 kJ mol�1 and �175kJ mol�1, respectively. The last two terms on the right side ofEq. (10) together represent the Gibbs energy of a mechanicalmixture of pure liquid metals. The chemical potentials of Nd (ΔμNd)

Fig. 6. Temperature–composition phase diagram for the system Nd–Rh–O in pureoxygen; oxygen partial pressure (PO2 =P

o ¼ 1Þ; P1¼0.1 MPa.

Fig. 7. Temperature–composition phase diagram for the system Nd–Rh–O in air;oxygen partial pressure ðPO2 =P

o ¼ 0:212Þ, P1¼0.1 MPa.

Fig. 8. Temperature–composition phase diagram for the system Nd–Rh–O at lowoxygen partial pressureðPO2 =P

o ¼ 10�6Þ, P1¼0.1 MPa.

K.T. Jacob et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 43 (2013) 71–7976

and Rh (ΔμRh) are represented by the Eqs:

ΔμNd= J mol�1 ¼ RT ln XNdþX2Rhð2ΩNd�ΩRhÞþ2X3

RhðΩRh�ΩNdÞþ89

ð11Þ

ΔμRh= J mol�1 ¼ RT ln XRhþX2Ndð2ΩRh�ΩNdÞ

þ2X3NdðΩNd�ΩRhÞþ11450 ð12Þ

From the evaluated Gibb energy of mixing in Fig. 9, chemicalpotentials of Nd and Rh in various two-phase fields are obtainedusing the common-tangent-intercept method. Compositiondependence of chemical potentials is shown in Fig. 10. Thechemical potentials are constant in two-phase regions and areassumed to vary linearly with composition in the narrow non-stoichiometric range of intermetallic compounds. The chemicalpotential in liquid alloy varies non-linearly with composition asdescribed by Eqs. (11) and (12).

3.5.1. Logarithmic partial oxygen pressure–composition diagram at1273 K

Chemical potential of the volatile component can be easilycontrolled in systems containing two metals and a volatileelement. In the present case, the chemical potential of oxygencan be varied by controlling the composition of the gas phase, forexample by adjusting the ratio CO/CO2 or H2/H2O. Hence, oxygenpotential–composition diagrams at constant temperature are use-ful for synthesis of compounds and analysing phase stability underdifferent environments.

A two-dimensional (2-D) representation of oxygen partialpressure ½ log ðPO2=P

oÞ� as function of composition at 1273 K ispresented in Fig. 11. The oxygen partial pressure ½ log ðPO2=P

oÞ� isplotted on the vertical axis and the modified composition para-meter, ηRh/(ηNdþηRh), along the horizontal axis. Activity of Nd as afunction of composition in the binary system Nd–Rh is indispen-sible for the calculation of the oxygen potential corresponding tothe three-phase equilibria. When three condensed phases and agas phase (oxygen) coexist at equilibrium in a ternary system suchas Nd–Rh–O, the system is monovariant. Thus at a fixed tempera-ture, three condensed phases are in equilibrium at a unique partialpressure of oxygen. The three-phase equilibria are thereforerepresented by horizontal lines in the diagram. The alloy phasesare stable at low PO2 and oxide phases appear at higher PO2 .

The entire log ðPO2=PoÞ-composition diagram is divided into two

discrete regions. The large gap between these two regions isbridged by a break in the vertical axis of Fig. 11. Low oxygenpartial pressure region is linked with Nd–Rh alloy phases andNd2O3. In the high oxygen partial pressure region three-phaseequilibrium involves NdRhO3 and Nd2O3 or Rh2O3. At very lowoxygen partial pressure, only metallic phases of the binary Nd–Rhsystem exist. In fact, information on phase stability at very lowoxygen partial pressure displayed on this diagram is identical tothat available in the binary Nd–Rh phase diagram at the same

Fig. 9. Gibbs energy of mixing as a function of composition for the system Nd–Rhat 1273 K.

Fig. 10. Composition dependence of the calculated chemical potential of Rh and Ndin the system Nd–Rh at 1273 K.

Fig. 11. Logarithmic oxygen partial pressure ½ log ðPO2 =PoÞ� –composition diagram

for the system Nd–Rh–O at 1273 K, P1¼0.1 MPa.

K.T. Jacob et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 43 (2013) 71–79 77

temperature. On gradual increase in oxygen partial pressure, firstNd gets oxidized into Nd2O3. Thus, the first horizontal line at thebottom of the oxygen partial pressure–composition diagram sig-nifies the equilibrium between Nd, Nd-rich liquid alloy and Nd2O3.The area between the first and second horizontal lines representstwo-phase region involving Nd2O3 and liquid alloy. Progressiveoxidation of Nd in the alloy causes the appearance of the firstintermetallic phase Nd3Rh2 and three-phase equilibrium (Nd-richalloyþNd3Rh2þNd2O3). Oxidation of Nd in Nd3Rh2 brings aboutthe formation of the next intermetallic (Nd5Rh4) and establish-ment of the next three-phase equilibrium (Nd3Rh2þNd5Rh4þNd2O3). This process continues with the formation of successiveintermetallics deficient in Nd and the associated three-phaseequilibria. Finally, when all the Nd present in NdRh3 is oxidized,then metallic Rh is seen to coexist with Nd2O3. At significantlyhigher oxygen partial pressure, Rh combines with Nd2O3 andoxygen gas to form ternary oxide NdRhO3. The oxidation of Rhto Rh2O3 occurs at an oxygen potential higher than that for theformation of NdRhO3. At 1273 K the oxygen nonstoichiometry ofthe ternary oxide is likely to be negligible at high oxygenpressures.

There are two potential disadvantages with this type ofrepresentation. The first drawback is that an alloy and an oxidewith the same metallic or cationic fraction will fall on the samevertical line. However, since the stability fields of alloys and oxidesare well differentiated along the oxygen partial pressure axis, thisis not a major hurdle. The second disadvantage is that informationon oxygen nonstoichiometry cannot be displayed. Nevertheless,oxygen partial pressure–composition diagram provides usefulinformation regarding the oxygen pressure range for the stabilityof the various phases. The diagram is complementary to theconventional Gibbs triangle representation of the phase relationsin the ternary system (Fig. 1), where the composition of each phasecan be clearly depicted. The oxygen partial pressure–compositiondiagram shows phase evolution as oxygen potential over Nd–Rhalloys is increased. Gibbs triangle shows phase evolution as oxygenconcentration in Nd–Rh alloys is increased. All the topologicalrules of construction for conventional temperature-compositionbinary phase diagrams are applicable to the oxygen partialpressure–composition diagram demonstrated in Fig. 11.

A three-dimensional (3-D) oxygen partial pressure–composi-tion diagram can be constructed with Gibbs triangle at the base(X–Y plane) and logarithm of oxygen partial pressure along thevertical (Z) axis. However, it will be cumbersome to read dataaccurately from this type of diagram.

3.5.2. Three-dimensional chemical potential diagram at 1273 KIt is useful to know the variation of chemical potentials of Nd and

Rh along with oxygen potential in the system Nd–Rh–O. Theisothermal three-dimensional chemical potential diagram at 1273 Kis displayed in Fig. 12. The axis range for chemical potential of Rh issignificantly less than those for the other two components. Chemicalpotential of each component is plotted on a different orthogonal axis.Since the sum of the chemical potentials of the three componentsweighted by their corresponding stoichiometric coefficients is equalto the Gibbs energy of formation of the phase, the stability domain ofany stoichiometric phase is represented by a plane. Stoichiometry ofthe compound characterizes slope of the plane. Planes will havecurvature in the case of significant nonstoichiometry. Because of thecompressed scales used, the curvature is apparent in the figure onlyfor the surface representing liquid alloy. For a binary compound,slope is zero or infinite in one direction. A line, defined by theintersection of the two planes or surfaces, represents a two-phasefield. A point generated by the intersection of three planes orsurfaces represents a three-phase region.

It is apparent from Fig. 12 that the dominant phase over a widerange of chemical potentials is Nd2O3, with slopes ðdΔμO2

=dΔμNd ¼�1:333Þ and ðdΔμO2

=dΔμRh ¼ 0Þ. The intermetallics are repre-sented by vertical planes at low oxygen potentials. The width ofthe plane is a measure of the stability of the intermetallic. The planerepresenting NdRhO3 is restricted to the right top corner of thediagram where chemical potential of Rh and O2 are relatively highand chemical potential of Nd is very low. The slopes of the planerepresenting NdRhO3 are ðdΔμO2

=dΔμNd ¼ �0:667Þ and ðdΔμO2=

dΔμRh ¼ �0:667Þ. The stability domain of Rh2O3 lies above that ofthe ternary oxide NdRhO3. The plane representing Rh2O3 is parallelto the ΔμNd axis, with the slope ðdΔμO2

=dΔμRh ¼ �1:333Þ. The 3-Dchemical potential diagram gives an unambiguous geometric pic-ture of the stability domains of different phases in the chemicalpotential space.

4. Conclusions

The article reports the thermodynamic properties of NdRhO3

and phase relations in the system Nd–Rh–O at 1273 K, informationthat is unavailable in the literature. Presence of two three-phasefields, Nd2O3þNdRhO3þRh and NdRhO3þRh2O3þRh is con-firmed. The Nd�Rh alloy phases are in equilibrium with Nd2O3.

The standard Gibbs energy of formation of NdRhO3 from itsbinary component oxides Nd2O3 with A-type hexagonal structureand Rh2O3 with orthorhombic corundum-related structure isobtained from the emf of a solid-state electrochemical cell:

Δf ðoxÞGo= J mol�1ð7197Þ ¼ �66256þ5:64 ðT=KÞ

The standard enthalpy of formation of NdRhO3 at 298.15 Kfrom elements in their normal reference states is evaluated asΔf H

o298:15 K ¼ �1172:5ð71:6Þ kJ mol�1and the standard entropy

of NdRhO3 at 298.15 K as So298:15 K ¼ �111:5ð70:41Þ J K�1 mol�1.The oxygen potential for the decomposition of NdRhO3, measuredas a function of temperature, can be expressed as ΔμO2

= J mol�1

ð7274Þ ¼ �352584þ195:53 ðT=KÞThermodynamic data on intermetallic compounds in the binary

system Nd–Rh are evaluated based on calorimetric measurementsfor three compounds, Miedema's model and the phase diagram.Using available and estimated thermodynamic information for

Fig. 12. 3-D chemical potential diagram for the system Nd–Rh–O at 1273 K.

K.T. Jacob et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 43 (2013) 71–7978

various phases, phase relations in the system Nd–Rh–O arecomputed as a function of oxygen partial pressure at constanttemperature and as a function of temperature at constant oxygenpartial pressures. A three-dimensional chemical potential diagramis also established for Nd–Rh–O system at 1273 K. The thermo-dynamic data on NdRhO3 and the phase diagrams are useful forevaluating catalyst-support interactions, stability of the catalystunder different environments and for the design of catalystregeneration strategies.

Acknowledgement

K.T. Jacob is grateful to the Indian National Academy of Engi-neering for support as INAE Distinguished Professor. Preeti Guptathanks the University Grants Commission, India, for the award ofDr. D.S. Kothari Postdoctoral Fellowship.

Appendix A. Supplementary material

Supplementary data associated with this article can be found inthe online version at http://dx.doi.org/10.1016/j.calphad.2013.10.002.

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