Thermodynamic properties of SrRuO3(s)

Journal of Alloys and Compounds 353 (2003) 263–268

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Thermodynamic properties of SrRuO 3 (s) Aparna Banerjee, R. Prasad*, V. Venugopal Fuel Chemistry Division, Bhabha Atomic Research Centre, Mumbai 400 085, India Received 29 September 2002; received in revised form 29 October 2002; accepted 29 October 2002

Abstract The enthalpy increment measurements and the standard molar Gibb’s energy of formation of SrRuO 3 (s) were measured using a high-temperature Calvet micro-calorimeter and a galvanic cell, respectively. The enthalpy increments can be represented by the polynomial expression: H 0 (T )2H 0 (298.15 K) (J mol 21 )5243517.21120.8T (K)10.898310 22 T 2 (K)119.97310 5 /T (K) [SrRuO 3 (s), 0 310.4#T (K)#798.8]. The heat capacity C p,m (T ), the first differential of H 0 (T )2H 0 (298.15 K) with respect to temperature is given by: 0 21 21 C p,m (SrRuO 3 , s, T ) (J mol K )5120.811.796310 22 T (K)219.97310 5 /T 2 (K). The standard Gibbs energy of formation of SrRuO 3 (s) has been determined by a galvanic cell using CaF 2 (s) as the solid electrolyte. The fluoride cell is represented by: (2)Pt / O 2 (g), hCaO(s)1CaF 2 (s)j / / CaF 2 / / hSrF 2 (s)1RuO 2 (s)1SrRuO 3 (s)j, O 2 (g) / Pt(1). The electromotive force (emf) of the above cell was measured as a function of temperature in the range from 894.4 to 1098 K. The standard Gibb’s energy of formation of SrRuO 3 (s) from elements in their standard state obtained by the fluoride cell can be given by: D f G 0 [SrRuO 3 (s)] / kJ mol 21 (62)52941.010.2586?(T / K) (894.4,T / K,1098). The slope and intercept of the above equation gives the entropy and enthalpy of formation of the compound at the average experimental temperature T av 5996.2 K. The heat capacity of SrRuO 3 (s) determined by Calvet calorimeter and the data obtained from fluoride cell were used to calculate the standard enthalpy and entropy of formation of the compound at 298.15 K. The second law method gives D f H 0 [SrRuO 3 (s), 298.15 K] and D f S 0 [SrRuO 3 (s), 298.15 K] of the compound from elements in their standard state to be 2955.0 kJ mol 21 and 111.04 J K 21 mol 21 , respectively.  2002 Elsevier Science B.V. All rights reserved. Keywords: Transition metal compounds; Enthalpy; Heat capacity; Calorimetry

1. Introduction Ruthenates display an exotic mix of magnetic and superconducting properties that are very sensitive to dimensionality of the system and chemical composition. The strontium ruthenates form Ruddlesden–Popper type complex oxides [1]. In the Ruddlesden–Popper series, that is, Sr n11 Ru n O 3n11 , n is the number of RuO 2 layers [2]. The interest in this family stems from the fact that ferromagnetic transforms into superconductivity as a function of number of RuO 2 (s) layers. The orthorhombic perovskite SrRuO 3 (s), corresponds to n5~ and is a ferromagnetic conductor [3–5]. In the double layered compound Sr 3 Ru 2 O 7 (s) where n52, metamagnetism has been observed [6,7], while Sr 2 RuO 4 (s) where n51 exhibits very low temperature oxide superconductivity at temperatures near 1 K [8,9]. SrRuO 3 (s) is an ideal electrode material for epitaxial ferroelectric device structures. It is *Corresponding author. Fax: 191-22-550-5151. E-mail address: [email protected] (R. Prasad).

used for the fabrication of dynamic random access memory (DRAM) capacitors [10]. It is also used in electro-optic devices [11]. Recently Stitzer et al. have described this family of oxides by the composite structure model [12]. The effect of structure of SrRuO 3 (s) on its electronic properties has been investigated by several workers [13,14]. Attention is focused primarily on structural investigations, magnetic and electrical properties of SrRuO 3 (s). However the thermodynamic properties of this compound needs investigation. Both strontium and ruthenium are formed in good yield during the fissioning of plutonium in fast breeder reactors. Understanding the thermodynamic properties of these ruthenates is important in understanding their behavior during operation, accident and in high temperature waste immobilization process. Hence it is important to determine the physico-chemical properties of SrRuO 3 (s) for its practical application in nuclear waste management, electronic device fabrication processes as well as long term reliability of these devices at high temperature and in corrosive environments. Mallika and Sreedharan [15] determined the Gibbs free energy of

0925-8388 / 02 / $ – see front matter  2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0925-8388(02)01210-0

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A. Banerjee et al. / Journal of Alloys and Compounds 353 (2003) 263–268

formation of SrRuO 3 (s) in the temperature range 991 to 1282 K over the coexisting phase field SrRuO 3 (s)1Ru(s)1 Sr 3 Ru 2 O 7 (s) using a solid oxide Galvanic cell. In the present study, the enthalpy increments of SrRuO 3 (s) were measured using a high temperature Calvet micro-calorimeter and the standard Gibbs energy of formation of SrRuO 3 (s) was determined by a galvanic cell using calcium fluoride as the solid electrolyte. Other thermodynamic parameters were evaluated from these experimental data.

2. Experimental SrRuO 3 (s) was prepared by heating a mixture of SrCO 3 (s) and RuO 2 (s) powders mixed in stoichiometric ratio and intimately ground in an agate mortar for several hours. The mixture was then heated in air in an alumina boat to 1473 K for 20 h. After a second grinding, the powder was pressed into pellets and heated in air for 24 h. The compound was then gradually cooled to room temperature [11]. Repeated heating and grinding was continued till the product was exclusively identified as SrRuO 3 (s) by X-ray diffraction (XRD).

2.1. Calvet calorimeter Enthalpy increment measurements of SrRuO 3 (s) were carried out using a Calvet calorimeter, Model HT-1000, supplied by Setaram of France. The calorimeter is based on the heat flow principle. The experimental assembly and procedure followed has been reported in an earlier publication [16]. The calorimeter consists of a massive fritted alumina block to maintain constant temperature. It has two compartments in the middle surrounded by Pt to (Pt110 mass percent Rh) thermopiles which are connected in opposition to nullify the thermal imbalance during the experiments. Two identical alumina tubes one end closed and gas tight, were introduced into these compartments. The other end of the alumina tubes were connected to a thermostated dropping mechanism or introducers. The samples were loaded into these introducers which were adapted to the equipment to maintain a controlled atmosphere in the alumina tubes. The sample introducer was maintained precisely at 298.15 K with the help of a bath circulator. To make measurements, a sample pellet of known mass was introduced into the sample-dropping device and when a steady baseline was achieved the sample was dropped into the calorimeter. The drop of the sample into the cell causes a change in the temperature of the cell which results in flow of heat from the cell to the block and vice-versa. This exchange of heat produces an electrical signal. This signal is amplified by a nano-volt amplifier and integrated to obtain the enthalpy change. An on-line computer for area integration carries out the acquisition and processing of data. The temperature of the

sample was monitored by a calibrated platinum resistance thermocouple (60.1 K). The calorimetric cells were evacuated and flushed with argon before dropping the sample. Drop experiments were carried out under a static argon atmosphere. At each experimental temperature, four samples were dropped alternately in the two compartments to determine the enthalpy increments. Thereafter the cells were emptied for the next experiment. The calibration factor of the calorimeter was determined by an electrical calibration method [17]. This was also checked at each experimental temperature, in each compartment alternately by dropping NIST standard reference material synthetic sapphire (SRM-720, Al 2 O 3 ). The characterized compound was pelletized into pellets of 3 mm diameter and 3 mm thickness under a pressure of 100 MPa and annealed in air at 600 K for several hours. These pellets were used for H 0 (T )2H 0 (298.15 K) measurements in the temperature range 310.4–798.8 K. The XRD pattern of SrRuO 3 (s) before and after the experiments remained the same indicating the stability of the oxides.

2.2. The fluoride cell assembly A stacked pellet assembly with the solid electrolyte and electrodes in the form of pellets and a common inert gas atmosphere over both electrodes was used for the construction of the fluoride cell as shown in Fig. 1. The pellets were placed in the following stacking sequence: reference electrode, CaF 2 (s) pellet and sample electrode inside an alumina cup with a hole in the center through which the lead of the platinum disc could be passed. This cup along with the pellets were spring loaded into a quartz tube one

Fig. 1. Schematic diagram of fluoride cell.

A. Banerjee et al. / Journal of Alloys and Compounds 353 (2003) 263–268

end of which could be attached to hooks which were provided in the flange. The flange was also provided with ‘O’ ring seal which could be tightened with the help of nuts and bolts. The entire set up was jacketed into another quartz tube to provide a leak proof atmosphere for the cell assembly. The cell assembly was evacuated to 10 23 Pa at ambient temperature for several hours to remove all surface adsorbed moisture. The cell was then filled with dry nitrogen gas, and kept under flowing nitrogen. The nitrogen gas was purified to remove hydrogen and moisture by passing it sequentially over hot cupric oxide and a couple of towers of anhydrous magnesium perchlorate. All connections were made by using oxygen free high conducting copper tube with brazed joints. The dried nitrogen gas contained about 100 ppm of oxygen and the flow rate was maintained at 1 dm 3 h 21 and provided the necessary gas atmosphere over the cell [18]. The cell was initially run using dry oxygen as the cover gas, flowing at the rate of 1 dm 3 h 21 . However in such a cell assembly it was found that over a period of time the electromotive force (emf) of the cell started drifting. This was due to formation of a fine black layer on the CaF 2 (s) pellet, causing the observed drift in the emf. Hence dry N 2 gas containing about 50–100 ppm of oxygen was used as the gaseous atmosphere over the cell. Using this cover gas drift in the emf was not observed. The outgoing cover gas was passed through a capillary tube immersed in silicone oil placed after the cell to protect the cell atmosphere from the atmosphere outside or in other words to prevent back-diffusion. The entire assembly was placed inside a vertical resistance furnace with the electrodes located in the even temperature zone of the furnace (61 K) and a calibrated chromel–alumel thermocouple located in the vicinity of the stacked pellet assembly was used to monitor the cell temperature. Optical grade single crystal of CaF 2 (s) (Harshaw / Filtrol, USA), dimensions 9 mm diameter33 mm thickness was used as the solid electrolyte. The reference electrode was made from an intimate mixture of CaO and CaF 2 in a 1:1 ratio and compacted into a cylindrical pellet of diameter 7 mm and thickness 2–3 mm at a pressure of 100 MPa. The sample pellet was made similarly by compaction and pelletisation of a mixture of SrF 2 (s)1RuO 2 (s)1SrRuO 3 (s) in the ratio of 1:1:1 into pellets of dimensions 7 mm diameter33 mm thickness at a pressure of 100 MPa. The emf of the cell was measured when the value of the emf was steady for 2–3 h using a Keithley electrometer Model614, with an input impedance greater than 10 14 ohms. The cell assembly was tested initially for the absence of asymmetric potential. The reproducibility of the emf data was verified by thermal cycling. The following cell configuration was employed in the present study: (2)Pt / O 2 (g), hCaO(s) 1 CaF 2 (s)j / / CaF 2 / / hSrF 2 (s) 1 RuO 2 (s) 1 SrRuO 3 (s)j, O 2 (g) / Pt( 1 )

(1)

The cell is written in such a manner that the right hand

265

electrode is positive. Measurements were carried out in the temperature range: 894.4–1098 K for the above cell. The X-ray diffraction pattern of the pellet after electrochemical measurements did not reveal any interaction between the equilibrium oxide phases.

3. Results and discussion

3.1. Enthalpy increment The H 0 (T )2H 0 (298.15 K) values for SrRuO 3 (s) obtained at different temperatures are given in Table 1 and shown in Fig. 2. Observed enthalpy increment data were least squares analyzed using the Shomate fit [19]. The boundary conditions used were: H 0 (T )2H 0 (298.15 K)50 and C 0p,m (298.15 K) equal to a known value. C 0p (298.15 K) for solid SrRuO 3 was estimated by the additive oxide method [20] and calculated to be 101.78 J K 21 mol 21 . This C 0p (298.15 K) value, was used as a starting value to fit the enthalpy increment data. Then the value was increased in steps until a close fit with the enthalpy increment data was obtained. A close fit was obtained for C 0p (298.15 K)5103.7 J K 21 mol 21 . H 0 (T )2H 0 (298.15 K) expression generated for SrRuO 3 (s) is given below: H 0 (T ) 2 H 0 (298.15 K) (J mol 21 ) 5 2 43517.2 1 120.8T (K) 1 0.898 3 10 22 T 2 (K) 1 19.97 3 10 5 /T (K) [SrRuO 3 (s), 310.4 # T (K) # 798.8]

(2)

The first differential of the above equation with respect to temperature gives the molar heat capacity, C 0p (T ) which is given by: C 0p (SrRuO 3 , s, T ) (J mol 21 K 21 ) 5 120.8 1 1.796 3 10 22 T (K) 2 19.97 3 10 5 /T 2 (K)

(3)

Table 1 Experimental enthalpy increments of SrRuO 3 (s) T (K)

H8(T )2H 0 (298.15 K) (J mol 21 )

310.4 369.6 381.0 448.6 461.8 477.2 500.4 514.9 555.1 626.9 666.9 702.0 714.3 763.4 779.5 798.8

1273.0 8047.0 9246.0 16804.0 18461.0 20286.0 23145.0 24848.0 29822.0 38344.0 43661.0 47808.0 49897.0 56381.0 59327.0 62481.0

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Table 3 The reversible emf of the cell: (2)Pt / O 2 (g), hCaO(s)1CaF 2 (s)j / / CaF 2 / / hSrF 2 (s)1RuO 2 (s)1SrRuO 3 (s)j, O 2 (g) / Pt(1) as a function of temperature T (K)

E (V)

T (K)

E (V)

894.4 915.5 927.9 934.6 949.5 965.7 979.7 994.8

0.1361 0.1401 0.1433 0.1465 0.1495 0.1520 0.1572 0.1592

1008.5 1022.6 1027.4 1037.3 1051.6 1079.5 1098.0

0.1626 0.1640 0.1688 0.1705 0.1730 0.1790 0.1840

3.2. Solid-state electrochemical measurements by fluoride cell The fluoride cell [1] was set up for measuring emf. The reversible emf of the cell is listed in Table 3, and the variation of emf as a function of temperature is shown in Fig. 3. The emf is a linear function of temperature, in the temperature range (894.4,T / K,1098): Fig. 2. Variation of [H 0 (T )2H 0 (298.15 K)] as a function of temperature.

E / V(64.12 3 10 24 ) 5 2 0.0745 1 2.353 3 10 24 ? (T / K) (4)

The enthalpy increment data for SrRuO 3 (s) has been reported for the first time. The standard molar entropy S 0 (298.15 K) for this compound was estimated by the Latimer entropy contribution of individual ions [20] which results in S 0 (298.15 K)5112.08 J K 21 mol 21 for SrRuO 3 (s). Based on these estimated data and the enthalpy increments measured the derived thermodynamic functions of SrRuO 3 (s) were calculated and the resulting values were extrapolated to 1000 K and given in Table 2.

The uncertainty quoted is the standard deviation in emf. The electrochemical reaction at the right hand side-working electrode can be written as: SrF 2 (s) 1 RuO 2 (s) 1 1 / 2O 2 (g) 1 2e 2 5 SrRuO 3 (s) 1 2F 2 (at the cathode)

(5)

The electrochemical reaction at the reference electrode on the left hand side of the cell can be written as:

Table 2 Derived thermodynamic functions of SrRuO 3 (s) T (K)

H 0T 2H 0298.15 (J mol 21 )

C 0p (J mol 21 K 21 )

S 0 (T ) (J mol 21 K 21 )

Free energy function (fef)a (J mol 21 K 21 )

300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0

191.6 5572.9 11236.9 17104.2 23127.5 29276.3 35530.6 41876.3 48303.5 54804.9 61374.9 68009.4 74705.2 81459.5 88270.5

104.1 110.8 115.5 119.0 121.8 124.1 126.0 127.7 129.3 130.7 132.1 133.3 134.5 135.6 136.8

112.8 129.4 144.7 158.3 170.9 182.7 193.5 203.7 213.3 222.2 230.7 238.8 246.4 253.7 260.7

112.1 113.4 116.4 120.3 124.7 129.5 134.4 139.3 144.3 149.2 154.0 158.7 163.4 167.9 172.4

a

fef5 2[G 0 (T )2H 0 (298.15 K)] /T.

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The net reaction given by Eq. (7) involves the transfer of two electrons. Hence from Nernst equation we get: D r G 0 (T ) 5 2 2FE

(9) 21

where, F is the Faraday constant 96486.4 C mol and the condensed phases are at unit activity. Combining Eqs. (4), (8) and (9) we get: D f G 0 (SrRuO 3 , s) / kJ mol 21 (62) 5 2 941.03 1 0.2586 (T / K) (894.4 , T / K , 1098)

Fig. 3. Variation of emf of the cell: (2)Pt / O 2 , hCaO(s)1CaF 2 (s)j / / CaF 2 / / hSrF 2 (s)1RuO 2 (s)1SrRuO 3 (s)j, O 2 / Pt(1) as a function of temperature.

CaO(s) 1 2F 2 5 CaF 2 (s) 1 1 / 2O 2 (g) 1 2e 2 (at the anode) (6) The overall cell reaction for the passage of two Faradays of electricity obtained by combining the two half cell reactions, is: SrF 2 (s) 1 CaO(s) 1 RuO 2 (s) 5 SrRuO 3 (s) 1 CaF 2 (s)

(7)

The standard Gibbs free energy change D r G 0 (T ) for the above reaction, can be obtained using the values of D f G 0 (CaO, s), D f G 0 (SrF 2 , s) and D f G 0 (CaF 2 , s) from Ref. [21], and D f G 0 (RuO 2 , s) from Kleykamp [22]: D r G 0 (T ) 5 D f G 0 (SrRuO 3 )(s) 1 D f G 0 [CaF 2 (s)] 2 D f G 0 [CaO(s)] 2 D f G 0 [SrF 2 (s)] 2 D f G 0 [RuO 2 (s)]

(8)

(10)

The error in D f G 0 (SrRuO 3 , s) includes the standard deviation in emf and the uncertainty in the data taken from literature. The slope and intercept of this least squares line corresponds respectively with the standard molar enthalpy and entropy of formation of SrRuO 3 (s) at the average experimental temperature (996.2 K). The enthalpy and entropy of formation of SrRuO 3 (s) at 298.15 K has been calculated by the second law method. Using the C 0p (T ) values obtained in this study and transition enthalpy values of Sr(s), and Ru(s) from Ref. [22], and O 2 (g) from Ref. [23], the second law value of D f H 0 (SrRuO 3 , s, 298.15 K) has been calculated as 2955.0 kJ mol 21 . The second law value of D f S 0 (SrRuO 3 , s, 298.15 K) has been calculated as 2111.04 J mol 21 . The Gibbs free energy values obtained in the present study, by fluoride cell differs from the values obtained by oxide cell [15] by about 50 kJ mol 21 as can be seen from Table 4. In order to determine D f G 0 (SrRuO 3 , s) by oxide cell it is necessary to determine the D f G 0 (Sr 3 Ru 2 O 7 , s) which in turn depends on the D f G 0 (Sr 2 RuO 4 , s). Thus the error in the D f G 0 (SrRuO 3 , s) will be large as errors are additive. However in order to determine D f G 0 (SrRuO 3 , s) in case of fluoride cell, 0 0 0 D f G (RuO 2 , s), D f G (SrF 2 , s), D f G (CaO, s) and 0 D f G (CaF 2 , s) are required and these values are taken from the literature which are well established.

4. Conclusion A high-temperature Calvet calorimeter was used to measure the enthalpy increments of SrRuO 3 (s) in the temperature range 310.4#T / K#798.8. The heat capacity of SrRuO 3 (s) was derived from experimental data of H 0 (T )2H 0 (298.15 K) (J mol 21 )5 243517.21120.8T (K)10.898310 22 T 2 (K)119.97310 5 /T (K). A solid

Table 4 Standard Gibbs free energy of formation of SrRuO 3 (s) from elements in their standard state: D f G 0 (SrRuO 3 , s, T ) (kJ mol 21 )5 A1BT (K) Ref.

[15] This study

T (K)

A (kJ mol 21 )

B (kJ mol 21 )

D f G 0 (kJ mol 21 ) 900 K

1000 K

1100 K

1200 K

(991–1282) (894.4–1098)

2985.7 2941.0

0.2519 0.2586

2759.0 2708.3

2737.8 2682.4

2708.6 2656.6

2683.4 2630.7

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state Galvanic cell using CaF 2 as the solid electrolyte was used to obtain the D f G 0 (SrRuO 3 , s) from elements in their standard state. D f G 0 (SrRuO 3 , s) calculated by least square regression analysis of the experimentally obtained emf data in this study and D f G 0 data of solid RuO 2 , SrF 2 , CaO and CaF 2 taken from the literature and can be represented by the equation: D f G 0 (SrRuO 3 , s) / kJ mol 21 (62.0)5 2 941.0310.2586 (T / K), in the temperature range (894.4, T / K,1098). A second law analysis gives the value of D f H 0 (SrRuO 3 , s, 298.15 K) as 2955.0 kJ mol 21 . The second law value of D f S 0 (SrRuO 3 , s, 298.15 K) has been 21 21 calculated as 2111.04 J K mol .

Acknowledgements The authors are grateful to Dr. K.D. Singh Mudher for assisting in X-ray diffraction analysis.

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