Thermodynamic properties of Ln1−xSrxCoO3 (Ln = Pr, Nd, Sm and Dy)

Accepted Manuscript Thermodynamic properties of Ln1-xSrxCoO3 (Ln=Pr, Nd, Sm and Dy) Rasna Thakur, Rajesh K. Thakur, N.K. Gaur PII:

S0925-8388(15)31609-1

DOI:

10.1016/j.jallcom.2015.11.053

Reference:

JALCOM 35908

To appear in:

Journal of Alloys and Compounds

Received Date: 6 July 2015 Revised Date:

4 November 2015

Accepted Date: 7 November 2015

Please cite this article as: R. Thakur, R.K. Thakur, N.K. Gaur, Thermodynamic properties of Ln1xSrxCoO3 (Ln=Pr, Nd, Sm and Dy), Journal of Alloys and Compounds (2015), doi: 10.1016/ j.jallcom.2015.11.053. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Thermodynamic properties of Ln1-xSrxCoO3 (Ln=Pr, Nd, Sm and Dy) Rasna Thakur*, Rajesh K. Thakur, and N.K. Gaur

*[email protected] Corresponding author- Rasna Thakur

Barkatullah University, Bhopal 462026, India.

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Address: Superconductivity Research Lab, Department of Physics,

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Department of Physics, Barkatullah University, 462026, Bhopal, India

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Tel. No.: +91-755-2491821, Fax no.: +91-755-2491823

Abstract

We have investigated the thermodynamic properties of Ln1-xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) perovskites using modified rigid ion model (MRIM) and a novel atomistic approach of Atoms in Molecules (AIM) theory. The effect of Sr doping on lattice specific heat and thermal expansion coefficient as a function of temperature (1 K ≤ T ≤ 300 K) are reported probably for the first time. The

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MRIM results on thermal expansion coefficient of Sr doped LnCoO3 (Ln= Pr, Nd, Sm and Dy) suggest that higher Sr doping may not be applicable to solid oxide fuel cell. Besides, we have reported bulk modulus (B), cohesive energy (ϕ), molecular force constant (f), Reststrahlen frequency (υ), Debye temperature (θD), Gruneisen parameter (γ) and specific heat. It is found that the present model has a

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promise to predict the thermodynamic properties of other perovskites as well.

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Keywords: Specific heat, Thermal expansion, Cohesive energy, Cobaltates

1. Introduction

Doped cobaltate perovskites Ln1-xAxCoO3 (Ln =La, rare earth and A= Ca, Sr, Ba), have a unique 6 e g0 , feature among some other perovskites, which change the spin state of the Co3+ (low-spin LS: t2g 5 4 6 6 4 e1g , high-spin HS: t2g e g2 ,) and Co4+(LS: t2g e g0 , IS: t2g e g0 HS, t2g e g2 ,) ions. intermediate-spin IS: t2g

The spin states of undoped LnCoO3 exhibit a gradual crossover with increasing temperature from the low-spin (LS) state to the intermediate-spin (IS) state or to the high-spin (HS) state. Upon doping A2+ ions into LnCoO3, some of trivalent Co ions become tetravalent, and these also contain a mixture of 1

ACCEPTED MANUSCRIPT low and higher spin states. Apart from the LnCoO3, other important Ln1-xAxCoO3 (Ln3+= Pr3+, Nd3+, Sm3+and Dy3+) are also known to exhibit interesting magnetic and electrical properties [1-5]. Among the cobaltates of the Pr1-xAxCoO3 series, Pr0.5Sr0.5CoO3 stands out for unusual magnetic properties [6]. Two phase transitions at TA=120 K and TC=226 K were detected in studying its magnetic properties

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[7]. The transition at TC is related to ferromagnetic disordering, while the nature of the transition at TA is not clearly understood at present second but may correspond to a ferromagnetic transition or an alteration of the ferromagnetic state associated with orbital ordering. Both transitions are manifested in the temperature dependence of the specific heat, but only the transition at TC is manifested as a change in the slope of the temperature dependence of the electric resistance. The series, Nd1-xSrxCoO3

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(0.1≤x≤0.5) also shows unusual magnetic properties [8, 9]. The temperature dependence of the magnetization differs from that expected for a simple ferromagnet. The magnetization sharply increases

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for the samples with x=0.2, 0.3 and 0.5 at Curie temperatures 70, 155 and 240K, respectively, followed by a subsequent decrease at temperatures lower than TF~20, 40 and 70K, respectively [9]. SmCoO3 is an important member of the cobaltate family due to its excellent gas sensing abilities, low temperature magnetic behavior and giant magnetoresistance [10]. Doping of Sr ion at Sm in SmCoO3 results in enhanced electrical and ionic conductivities along with better optical properties [4]. The crystal lattice symmetry is orthorhombic [6, 11] for Ln1–xSrxCoO3 (Ln=Pr and Nd). The structural analyses [3, 4] on

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Sm1−xSrxCoO3 at room temperature revealed structure changes from orthorhombic for x ≤ 0.5 to cubic symmetry, for x ≥0.6. In contrast, for Dy1-xSrxCoO3 cubic pcrovskite structure exists in the range of x = 0.6-0.9 [4]

However, the physical properties of Ln1-xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) are still

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unknown and have received little attention so far. In view of the above it was thought to examine the effect of the partial substitution of the A-site cation i.e. Pr, Nd, Sm and Dy by Sr in Ln1−xSrxCoO3 on

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the specific heat, thermal expansion coefficient, bulk modulus (BT), cohesive energy (ϕ), molecular force constant (f), Reststrahlen frequency (υ), Debye temperature (θD) and Gruneisen parameter (γ). The present paper is organized as follows. In section 2 the computational details of model formalism are given to calculate the thermal properties and elastic moduli.

We present the results and related discussions about the thermal

properties in section 3. Concluding remarks are given in Section 4.

2. Formalism The effective interionic potential corresponding to the modified rigid ion model (MRIM) frame work [12, 13] is expressed as: 2

ACCEPTED MANUSCRIPT φ (r ) = −

e2 2

∑Z

k

Z k ' rkk− 1' −

kk '

∑C

−6 kk ' kk '

r

+

∑nbβ

kk '

n' + i bi [β kk exp {(2 rk − rkk 2

i i

kk '

exp {(rk + rk ' − rkk ' ) ρ i }

i

.

(1)

) ρ i } + β k ' k ' exp {(2 rk ' − rk ' k ' ) ρ i }]

Here, first term is attractive long range (LR) coulomb interactions energy. The second term represents

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the contributions of van der Waals (vdW) attraction for the dipole-dipole interaction and is determined by using the Slater-Kirkwood Variational (SKV) method [14]. The third term is short range (SR) overlap repulsive energy represented by the Hafemeister–Flygare-type (HF) interaction extended up to the second neighbor. In expression (1), other symbols involved are the same as those defined in our earlier respectively and βikk′ is the Pauling coefficient [15] given by

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β i kk ' = 1 + ( Z k / N k ) + ( Z k ' / N k ' ) ,

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papers [12, 13]. bi and ρi are the hardness and range parameters for the ith cation–anion pair (i = 1, 2)

(2)

Zk (Zk′) and Nk (Nk′) are the valence and the number of electrons in the outermost orbit of the k (k′) ion respectively. The contributions of van der Waals (vdW) attraction for the dipole-dipole interaction is determined by using Slater- Kirkwood Variational (SKV) method [14] −6 , φkVdW k ′ = Ckk ′rkk '

and C = 3eh α α (α / N )1/ 2 +(α / N )1/ 2  kk ′ 4πm k k ′  k k k′ k′  

(3)

.

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

−1

Here e and m are the charge and mass of the electron respectively. αk (αk′) is the polarizability of k (k') ion. Nk (Nk') are the effective number of electrons responsible for the polarization of k (k') ion. The

[dφ

dr ]r =r0 = 0 ,

and the bulk modulus

[

]

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model parameters, hardness (b) and range (ρ) are determined from the equilibrium condition. (4)

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B = 1 9 Kr0 d 2φ dr 2 r = r , 0

(5)

Where K is the crystal structure-dependent constant and r0 is the equilibrium nearest neighbor distance. The expressions for calculating the thermodynamic properties like Debye temperature (θD), Reststrahlen frequency (υ), molecular force constant (f), Gruneisen parameter (γ), specific heat (C) and thermal expansion (α) are taken from our earlier papers [12-13]. Equations (4) and (5) have been used to compute the model parameters which are used to calculate the cohesive and thermal properties of these Sr doped cobaltates. The results are thus obtained and discussed below.

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ACCEPTED MANUSCRIPT 3. Computed Results and Discussion 3.1 Model parameters Using the input data and the vdW coefficients (Ckk′) calculated from the SKV method [1-5, 14] the model parameters ((b1, ρ1) and (b2, ρ2)) corresponding to the ionic bonds Co-O and Ln/Sr–O (Ln=Pr,

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Nd, Sm and Dy) for different compositions (0≤ x ≤ 1) and temperatures 1 K ≤ T ≤ 300 K have been calculated using equations (4) and (5) for Ln1-xSrxCoO3 (Ln=Pr, Nd, Sm and Dy). Using these model parameters listed in Table 1, the values of φ, f , υ, θD and γ are computed and depicted in tables 2 (below transition) and 3 (above transition) for Ln1-xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) respectively. The decreasing trend of the model parameters with decrease in doping content (x)

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indicates the slight distortion of the perfect octahedra and subsequent decrease in the strength of the crystal together.

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The simplest approach to account for variations of physical property with A site composition is to consider a quasi random distribution of hard sphere cations over the A type sites. This has traditionally been parameterized through the average A cation radius , often expressed as the Goldschmidt tolerance factor t: t=

rA + rO

2 (rCo + rO )

,

(6)

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where rCo and r0 are the cobalt and oxide ion radii, respectively. Shannon’s ionic radii [16] were used in this study for the calculation of tolerance factor and an ionic radius in a crystal structure can be varied with change of both a coordination number and a charge valence of each ion. For the calculation of the tolerance factor fin these systems, the calculation of ionic radius of Co ion is important. As mentioned

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in [3], the charge valence of Co3+ (0.545 Å (LS), 0.560 Å (IS), 0.610 Å (HS), 6th coordinated) can be changed into Co4+ (0.53 Å, 6th coordinated) in proportion to the amount of acceptors. An average

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radius value for Co ions was used in consideration of a change of charge valences due to Sr dopant amount. The larger ionic radius of Sr2+ ion in Ln1-xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) system could cause a small distorted crystal structure owing to a large tolerance factor. Then this small distortion can enhance electronic-hole conduction by means of decreasing the charge-transfer gap. The tolerance factor for these compounds is reported in Table 1 which satisfies the condition that t for a stable perovskite phase is above 0.84 [17]. It is noted from the inspection of Table 1 that with increasing concentration (x) the tolerance factor t increases, which suggests that buckling of octahedral network becomes smaller as x increases [18]. We have displayed the variation of tolerance factor of (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) in Fig. 1 against A-site cation radius.

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ACCEPTED MANUSCRIPT The physical properties of cobaltate are sensitive both to the average A-site (Ln3+ and Sr2+) cations radius and cobaltate valency. The another crucial factor which is observed to be controlling the properties of doped cobaltate is the size mismatch (Fig. 1) of cations at A-site, represented by the cations-size disorder parameter, σ 2 =

∑

y i ri 2 − < rA > 2 , where yi, ri and are the

i

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fractional occupancies, ionic radii of the i cation and average A-site cation radius respectively.

The effective radius of the triangular cavity formed by two A-site cations and one B-site cation which is the narrowest pass for the oxygen ion migration, is reported here as the critical radius (rcr) (Table 1). Depending on the composition of the perovskite, critical radius (rcr) can be calculated by

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using Eqn. 7 which describes the maximum size of the mobile ion to pass through:

(7)

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3  a o  a o − 2 rB  + rB2 − rA2 4  , rcr =  2 (rA − rB ) + 2 a o

where rA and rB are the radius of the A ion and B ion, respectively, and a 0 corresponds to the lattice parameter (V1/3). Because the lattice parameter a is dependent on the size of rA and rB, the critical radius rcr is a complicated function of both rA and rB. In material design, it is always need to know how the cation size influences the value of the critical radius, which can provide guideline for the doping ion selection. In other words, it is desired to get the monotonicity of rcr with respect to rA and rB. Generally,

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the critical radius does not exceed 1.05 Å [19] while the ionic radius of oxygen is 1.4 Å [16], i.e. it is a crucial factor controlling the oxygen ion transport. The critical radius for these compounds is reported

materials.

3.2 Cohesive energy

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in Table 1 which satisfies the condition that rcr must be less than 1.05 Å [19] for typical perovskite

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Cohesive energy (φ) can be considered as a measure of a structure’s overall chemical stability. Here, we have calculated the cohesive energy of Ln1-xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) compounds using Eqn. (1) and then reported them in Tables 2, 3. The calculated cohesive energy shows the magnitude of cohesion in these compounds and indicates a measure of strength of the forces binding atoms together in solids. The cohesive energy is therefore expected to change in the same trend as the bulk modulus, which represents the strength to the volume change and is related to the overall atomic binding properties of the materials. The negative values of cohesive energy show the stability of these compounds. Here, it is noted that the compounds with the lowest cohesive energy (Table 2, 3) have tolerance factors closes to 1 which suggest that the greater the degree of ion-size match, the lesser the 5

ACCEPTED MANUSCRIPT tightly bound the structure needs to be in order to stay together. We have also calculated the lattice energies of these compounds using the generalized Kapustinskii equation [20] which uses the ionic strength of the crystal defined as, t

I = −(1 2 )∑ nk z k2 ,

(8)

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k

where t is the number of the type of ions in the formula unit, each of number nk and charge zk. In our calculations the value of the ionic strength for the LnCoO3 compounds is found to be 16 and this value decreases slightly with Sr doping. According to the generalized Kapustinskii equation the lattice energies of crystals with multiple ions are given as, 1213.9  1 − ρ  ∑ nk z k2 . r  r 

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U (kJmol −1 ) −1 = −

(9)

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Here is the weighted mean cation–anion radius sum and ρ is taken as the average of model parameters ρ1 and ρ2. The value of the lattice energy estimated using the empirical Kapustinskii equation is found to be in good agreement with our low temperature calculated values, giving further confidence to the validity of our model. It can be inferred from the cohesive energy results (Table 2, 3) that the stability of doped compounds is somewhat less compared to that of the parent compound, and this can be correlated with the observed distortions of the lattice compared to the parent compound.

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Our calculated values of cohesive energy for Ln1-xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) is comparable to the reported value (-144.54 eV) by Farhan et al. [3] below transition temperature. The

3.3 Bulk modulus

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results on cohesive properties indicate enhanced stability above the transition temperature (Table 3).

There are several methods in determining elastic properties in perovskites, but due to the small changes

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of the unit cell dimensions, the accuracy of determining bulk modulus always has been unpredictable. Here, the bulk modulus is calculated on the basis of Atoms in molecules (AIM) theory [21] which emphasizes the partitioning of static thermodynamic properties in condensed systems into atomic or group contributions. The values obtained are represented as B0 in Tables 2. We considered the effect of charge and size mismatch along with the octahedral distortions due to Jahn-Teller effect on the bulk modulus of the compounds. The formal expression for calculating the Jahn-Teller (JT) distortions is taken as: ∆

JT

=

N

(1 / N ) ∑ (d i − < d > ) / < d > )

2

,

(10)

i

6

ACCEPTED MANUSCRIPT where is the average value of di bond distances in BON octahedral. The expression for the cation size and charge mismatch (Fig. 1) at the A-site and B-site is:  (1 − x A )rA + x A rA' )  ,  (1 − x A )rCo3+ + x A rCo 4+ ) 

σm = 

(11)

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where x A is the concentration of the rare earth cation of radius rA' at the A-site and rA is the radius of the Sr2+ cation. rCo3+ is the radius of Co3+ ion in valence state III and rCo 4+ is the radius of Co4+ ion in valence state IV. Similarly replacing the radius rA (rA’) with Ln3+ /Sr2+(Ln=Pr3+, Nd3+, Sm3+ and Dy3+) charge at the A-site and rCo with the valence of Co3+ and Co4+ at the B-site, the charge mismatch can

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also be calculated. The effect of buckling of super-exchange angle Co-O-Co on distortions of the unit cell is calculated as,

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φ S = cos < ω >= cos(π − < θ > ) / 2 ,

(12)

where average tilting of the BO6 octahedra is < ω > and < θ > is the average super-exchange angle Co-O-Co. The expression for the bulk modulus of the distorted perovskite cobaltate is: BT =

K S B0σ m cos ω , exp (∆ JT )σ C

(13)

where KS is the spin order-dependent constant of proportionality, and its value is less than 1 for the

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ferromagnetic state and more than 1 for paramagnetic state, B0 is the bulk modulus for undistorted structure calculated on the basis of AIM theory, σm is the size mismatch, σc is the charge mismatch, ∆JT is JT distortion of CoO6 octahedra and cos ω is the effect of buckling of the Co-O-Co angle. Bulk

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modulus of the distorted structure is listed in Table 3 as BT which takes effect of all the distortions. The calculated value of bulk modulus 243.5 GPa and 255.2 GPa for NdCoO3 and SmCoO3 are in good agreement with the reported value of 230 GPa for NdCoO3 and 255.2 GPa for SmCoO3 by Zhou et al.

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and Farhan et al. [22, 3] whereas our reports on bulk modulus of Sr doped LnCoO3 (Ln=Pr, Nd, Sm and Dy) are probably the first reports on them. The present values of bulk modulus and the others [2223, 3] are found in reasonable agreements. We have displayed the variation of the bulk modulus of Sr doped compounds as a function of molar volume in Fig. 2. It is observed that the bulk modulus decreases with the increasing basic perovskite molar cell volume. Similar variation of the bulk modulus with the cell volume were observed also also by Cohen et al. [24] and Shein et al. [25] for alkaline earth chalcogenides, ionic halides and transition metal diborides. Furthermore, we found that in the compounds investigated here, the bulk modulus exhibit a linear relationship when plotted against molar volume of the basic perovskite cell, but fall on different straight lines (Fig. 2 (a-b)) according to the A7

ACCEPTED MANUSCRIPT site radius of the compounds. The bulk modulus is expected to exhibit the explicit dependences on concentration (x) and A-site ionic radii. The bulk modulus of these compounds is higher above the transition temperature (TN) due to the linearly increasing lattice distortions in these phase compared to

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the bulk modulus below transition temperature (TN). 3.4 Thermal Properties

We have also calculated the thermal properties of Ln1-xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1). The thermal properties provide us interesting information about the substance. The Debye temperature (θD) reflects its structure stability, the strength of bonds between its separate elements, structure defects

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availability and its density. It is to be noted from table 2, 3 that the Debye temperatures of Sr doped compounds are less than the Debye temperature of LnCoO3 (Ln= Pr, Nd, Sm and Dy) and in turn it can

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be predicted that the specific heat of Sr doped compounds is higher. It can also be observed from Table 2, 3 that the Debye temperature decreases with increasing Sr concentration in the eg orbital. The Debye temperatures and other thermal properties of Sr doped cobaltates are reported in Table 2, 3, and compared with the available data [26]. In Fig. 3 the calculated Debye temperatures are plotted with tolerance factor. On inspection of Fig. 3 it is observed that the tolerance factor increases down the series the Debye temperature decreases monotonically. With the above-deduced values of θD, the

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change in θD with x indicates that a reduction of T3 term in the specific heat occurs with the elevated values of x. To explain the variation of θD with the Sr substitution, we tried to analyse our results in the framework of Double Exchange (DE) interaction with electron-lattice interaction. The change of the Co-O distance induced by substitution of the Ln (Ln=Pr, Nd, Sm and Dy) site by Sr decreases θD.

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Henceforth, the x dependence of θD in Ln1-xSrxCoO3 (Ln=Pr, Nd, Sm and Dy) suggests that increased Sr doping drives the system effectively far from the weak electron-phonon coupling region. Usually,

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the Debye temperature is a function of temperature that varies from technique to technique. Here, it is to be noted that the Debye temperature used for calculating the low temperature specific heat is quite different from the Debye temperature at which the specific heat reaches its saturation value. In order to access the relative merit of the present potential we have calculated the molecular force constant (f) for the pure and doped cobaltate compounds. Since, the restrahalen frequency is directly proportional to the molecular force constant (f) therefore both of them vary with the temperature accordingly for these compounds. The Reststrahlen frequency (υ) and molecular force constant (f) (Table 2, 3) could not be compared due to lack of experimental data in literature. A precise experimental analysis of these two thermal properties is needed to verify the results of present calculations. Here it is to be noted that reststrahlen frequency is higher above TN phase and it gives higher Debye temperature. In turn, the 8

ACCEPTED MANUSCRIPT lattice specific heat above transition temperature is expected to reduce. The Gruneisen parameter (γ) arising from vibrational modes has been determined from measurements of the Debye temperature, θD. The value of the Gruneisen parameter (γ) below TN seems to be reasonable since its value lies between 2 and 3 as reported earlier [27]. The Gruneisen parameter is above 3 for most of the compounds above

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TN, which indicates the enhanced anharmonic effects. These properties have been computed with the help of model parameters and have been listed in Table 2, 3. Due to the lack of experimental data, we have compared them with available data.

3.5 Specific heat and thermal expansion

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The specific heat is one of the instructive probes to elucidate the strong electron–phonon coupling mechanism. Therefore we have computed the specific heat for Ln1-xSrxCoO3 (Ln=Pr, Nd and Sm, Dy

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and 0≤ x ≤ 1) over the temperature range 1 K ≤T≤ 300 K and the results are displayed in Fig. 4-9. These values are compared with the available experimental data in subsequent figures. It is important to note that the specific heats show a significant increase (as shown in Fig. 4 for 10 K) due to the doping of Sr in LnCoO3 (Ln=Pr, Nd, Sm and Dy) perovskite. It is also established that, for compounds whose low temperature (LT) Debye temperature is different from the high temperature (HT) Debye temperature, a Debye model with one Debye temperature (LT) does not account for all of the specific

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heat, as the contribution of optical phonons at higher temperature cannot be neglected. Therefore the specific heat for Pr1-xSrxCoO3 (x=0 and 0.5) is computed using two Debye temperatures, as θD below TN is different from Debye temperature above TN. Specific heat in temperature range 10 K ≤T≤ 300 K for PrCoO3 is displayed in Fig. 5. Our computed results are compared with the experimentally

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measured data obtained by Tsubouchi et al. [28] with a relaxation method using PPMS. The specific heat at low temperature (i.e., up to 50 K) increase gradually and then increases sharply up to room

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temperature and at low temperature below 50 K, we observed a softening in specific heat which indicates the strong electron-phonon interaction in PrCoO3. Heat capacity in temperature range 10 K ≤T≤ 300 K for Pr1-xSrxCoO3 (0 ≤x≤ 0.5) is displayed in the inset of Fig. 5. The specific heat of Pr1xSrxCoO3

(0.1 ≤x≤ 0.5) could not be compared due to lack of experimental data but it follows a

systematic trend and exhibit features which are consistent with those revealed by the measured specific heat curves available for pure PrCoO3 and doped PrCoO3 [28]. Besides, the temperature evolution of the lattice specific heat of Pr0.5Sr0.5CoO3 over the temperature range 10K ≤ T ≤ 300K (Fig. 6) shows good match with the experimental values of Mahendiran et al. [7] with softening in specific heat at low temperatures. A sharp peak observed in the experimental specific heat curve [7] at around ≈ 226 K and 9

ACCEPTED MANUSCRIPT 120 K in Fig. 6, corresponding to the ferromagnetic transition and second ferromagnetic transition or an alteration of the ferromagnetic state associated with orbital ordering. Since, our computations take into account only the phonon contribution to the specific heat, therefore, anomalies (Fig 6), arising due to orbital ordering and spin state transitions are not revealed from our computed specific heat results.

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The inset of Fig. 6 shows C/T, plotted as a function of temperature (T). Fig. 7(a-h) shows the calculated specific heat of Nd1-xSrxCoO3 with one HT Debye temperature and its comparison with experimental values [29]. Our computed specific heats are in satisfactory agreement with experimental values of Morchshakov et al. [29]. The calculated specific heat for Nd1xSrxCoO3

(x=0.05 and 0.4) are slightly higher than the experimental values for temperature

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100K≤T≤240K, which indicates that our model has slightly underestimated the Debye temperature for these concentrations (x). The temperature dependence (1K≤T≤21K) of specific heat for Nd0.7Sr0.3CoO3

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is computed as displayed in the inset of Fig. 7(f) and compared with the experimental data of Jirak et al. [30].

Further, we have also studied the temperature dependent evolution of the lattice specific heat of Ln1-xSrxCoO3 (Ln=Sm and Dy) over the temperature range 10K≤ T≤ 300K and displayed in Fig. 8 (ab). It can be clearly noticed from Fig. 8 that, specific heat increases strongly with increase in temperature at low temperatures and becomes nearly constant at higher temperatures 300 K. Our results

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on specific heat for Ln1-xSrxCoO3 (Ln=Sm and Dy), are probably the first report on them hence our comment on their reliability is restricted until the experimental report on them. It is interesting to note from Fig. 8 that the overall shape of specific heat is generally consistent with available data for other Sr doped cobaltates [31].

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Furthermore, the specific heat obtained using LT and HT Debye temperature for cubic SrCoO3 is also presented. The calculated low temperature values of specific heat for SrCoO3 after adding the

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electronic specific heat contribution i.e. 46 mJ/mole-K2 [32] as a constant offset value to our lattice specific heat is shown in Fig. 9(a). To the best of our knowledge, the experimental data for x=1.0 at low temperature is not available; therefore the specific heat variations for SrCoO3 is compared with experimental data available for oxygen deficient SrCoO3 [32]. We have also computed the specific heat of SrCoO3 for temperature 10K ≤ T ≤ 300K and shown in Fig. 9 (b). At room temperature, the C value reaches approximately 124.46 J mol−1K−1 (Fig. 9(b)). This makes about 99.68% of the saturated lattice heat taking into account the Dulong-Petit high-temperature limit C=15 NkB~ 125 J mol−1K−1 in ABO3 perovskites. In this paper the effect of the A-site substitution in Ln1−xSrxCoO3 (Ln=Pr, Nd and Sm, Dy and 0≤ x ≤ 1) perovskites on the thermal expansion coefficient is computed by using the well known 10

ACCEPTED MANUSCRIPT relation α = γC BV where B, V, C are the isothermal bulk modulus, unit formula volume and specific heat at constant volume respectively and γ is the Gruneisen parameter. Moreover, the potential of these compounds for an application in solid oxide fuel cells (SOFC) is evaluated. It has been found that cobaltates are mixed ionic–electronic conductors and are very attractive candidates for cathodes of

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solid oxide fuel cells (SOFC). The thermal expansion of the material used in SOFC must be equal that of the electrolyte yttria-stabilized zirconia (YSZ). The main drawback of cobaltates as cathodes for SOFC is the very high coefficient of thermal expansion [33] compared to the electrolyte YSZ [34]. On doping Sr (0.0 ≤ x ≤ 1.0) in LnCoO3 at 10 K, the thermal expansion increases monotonically with concentration (x) as shown in Fig. 10(a-d). The thermal expansion values follow the same trend as

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found in specific heat. The increase in thermal expansion may be associated with transition of Co3+ from a low spin to intermediate or high spin (HS) state. Co3+ ions with IS state in a cubic crystal field

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are highly Jahn-Teller-active ions, i.e., the surrounding oxygen octahedron is distorted to lift the energetic degeneracy of the eg levels. Since the Jahn-Teller distortions are closely connected with the orbitals of the Co3+ ions, a change in orbital ordering will probably change the lattice parameters and may possibly lead to an increase of the thermal expansion. Similar variation of the thermal expansion with the marginal increase on Sr2+ substitution was observed previously for manganites and chromate [35, 36]. Our calculated value of 20.9 ×10-6 (K-1) for thermal expansion of Pr0.7Sr0.3CoO3 at 300K is

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closer to the reported values of 18.8 ×10-6 (K-1) for oxygen deficient Pr0.7Sr0.3CoO3-δ reported by Tietz et al. [33]. It can be noticed from Table 3 that the values of thermal expansion of Sm1-xSrxCoO3 and Dy1-xSrxCoO3 at room temperature are closer to the Tu et al. data [4]. For better applications of these materials it is to be kept in mind that an A site substitution in a Co perovskite does not seem to be

EP

promising in order to reduce the thermal expansion. A replacement of B site (Co ions) by other

AC C

transition metals (Mn, Cu, Ga etc.) ions may help to reduce the thermal expansion coefficient.

4. Conclusion

A detailed description of the theoretical investigation for the specific heat, thermal expansion, elastic and thermodynamic properties for the present Ln1−xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) perovskites has been presented in this paper. The MRIM results on bulk modulus shows a decreasing linear trend with increasing concentration (x) of Sr and volume. It is concluded from the elastic properties results obtained from MRIM that it is quite obvious that the bulk modulus reflecting the elastic property can be expressed in terms of various distortions. The Debye temperature for Ln1−xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) perovskites decreases with increasing doping level of 11

ACCEPTED MANUSCRIPT Sr. The specific heat correspondingly increases with increasing doping level. Here, our results are probably the first reports on the specific heat for Ln1−xSrxCoO3 (Ln= Pr, Nd, Sm, Dy and 0.05≤x≤1) at these temperatures and compositions. Besides, the thermal expansion coefficient (TEC) study reveal weaker thermal compatiblility of Ln1−xSrxCoO3 (Ln= Pr, Nd, Sm and Dy) as electrode with electrolyte

RI PT

yttria-stabilized zirconia (10.5×10-6K-1) in SOFC application. A good agreement between the present MRIM results and the experimental values reported by different workers [3, 4, 7, 22, 23, 26-32] has been found. Further investigations are in progress to improve the compatibility towards the electrolyte by B-site doping, without resulting in a great decrease in electrochemical properties. The method presented in this work will be helpful to material scientists for finding new materials with desired

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elastic and thermal properties among a series of structurally complex compounds.

M AN U

Acknowledgements

The authors are thankful to the M.P.C.S.T. Bhopal for providing the financial support. One of us RT is thankful to UGC, New Delhi for the award of Post Doctoral Fellowship.

References

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H.Y. Tu, Y. Takeda, N. Imanishi, O. Yamamoto, Solid State Ionics 100 (1997) 283.

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I.O. Troyanchuk, D.V. Karpinskii, A.N. Chobot, D.G. Voietsekhovich, V.M. Dobryanskii,

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[3]

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JETP letters 84 (2006) 151.

Hiroyasu Masuda, Toshiaki Fujita, Takeshi Miyashita, Minoru Soda, Yukio Yasui, Yoshiaki Kobayashi, Masatoshi Sato, J. Phys. Soc. Japan, 72 (2003) 873–878.

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R. Ganguly, A. Maignan, C. Martin, M. Hervieu, B. Raveau, J. Phys.: Condens. Matter 14 (2002) 8595.

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D. D. Stauffer and C. Leighton, Phys. Rev. B 70 (2004) 214414. C. R. Michel, E. Delgado, G. Santillan, A. H. Martinez, A. Chavez-Chavez, Mater. Res. Bull. 42 (2007) 84.

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A. Ghoshray, B. Bandyopadhyay, K. Ghoshray, V. Morchshakov, K. Barner, I.O. Troyanchuk, H. Nakamura, T. Kohara, G.Y. Liu, G.H. Rao, Phys. Rev. B 69 (2004) 064424.

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Rajesh K. Thakur, Rasna Thakur, S. Shanmukhrao Samatham, N. Kaurav, N.K. Gaur, V. Ganesan, G.S. Okram, J. Appl. Phys. 112 (2012) 104115.

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K. Leinenweber, Y. Wang, T. Yagi, H. Yusa, Am. Mineral. 79 (1994) 197.

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K. Knizek, Z. Jirak, J. Hejtmanek, M. Veverka, M. Marysko, G. Maris, T. T. M. Palstra, Eur.

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Phys. J. B. 47 (2005) 213. [19]

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[14]

R. Thakur, R.K. Thakur, N.K. Gaur, Thermochim. Acta 584 (2014) 79-82.; R. Thakur, A. Srivastava, R.K. Thakur, N.K. Gaur, J. Alloys and Compd. 516 (2012) 58-64. J.C. Slater and J.G. Kirkwood, Phys. Rev. 37 (1931) 682.

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[13]

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[29]

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AC C

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[33]

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ACCEPTED MANUSCRIPT [34]

F. Tietz, in: P. Vincenzini (Ed.), Proceedings of the 9th Cimtec-World Forum on New Materials 61 (1999).

[35]

S. Slilomsak, D.P. Schilling, H.U. Anderson, in: S.C. Singhal (Ed.): Proceedings of the 1st International Symposium on SOFC, Electro Chemical Society Incorporation, New Jersey, USA,

EP

TE D

M AN U

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M.D. Mathews, B.R. Ambekar, A.K. Tyagi, Thermochim. Acta 390 (2002) 61.

AC C

[36]

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129 (1989).

Figure Captions

14

ACCEPTED MANUSCRIPT

Fig.1. Variation of size mismatch, charge mismatch, tolerance factor and A-site varaince for

Ln1−xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) perovskites with the radius of A-site cation. Fig. 2. Variation of bulk modulus of (a) LnCoO3 (Ln=Pr, Nd, Sm, Dy) and (b) Ln1−xSrxCoO3 (Ln=Pr,

RI PT

Nd, Sm, Dy and 0.5≤ x ≤ 1) perovskites with molar volume (cm3) of the basic perovskite cell. The solid line is a guide, to depict the linear variation.

Fig. 3. Variation of Debye temperature with tolerance factor for (a) Pr1−xSrxCoO3 (0≤ x ≤ 0.5), (b)

SC

Nd1−xSrxCoO3 (0≤ x ≤ 0.5), (c) Sm1−xSrxCoO3 (0≤ x ≤ 1) and (d) Dy1−xSrxCoO3 (0≤ x ≤ 0.9)

M AN U

perovskites.

Fig. 4. The variation of computed specific heat (C) with composition (x) for (a) Pr1−xSrxCoO3 (0≤ x ≤

0.5), (b) Nd1−xSrxCoO3 (0≤ x ≤ 0.5), (c) Sm1−xSrxCoO3 (0≤ x ≤ 1) and (d) Dy1−xSrxCoO3 (0≤ x ≤ 0.9) perovskites at 10 K.

Fig. 5. The variation of computed specific heat of PrCoO3 as a function of temperature (10 K ≤ T ≤ 300

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K) and its comparison with experimental values of Tsubouchi et al. [28]. The solid line with dark circle (–●–) and open circle (○) represent the model calculation and experimental values respectively. Inset shows calculated specific heat as a function of temperature (10K ≤ T ≤ 300 K) for Pr1−xSrxCoO3 (0≤ x

EP

≤ 1).

Fig. 6. The variation of specific heat of Pr0.5Sr0.5CoO3 as a function of temperature (10 K ≤ T ≤ 300 K)

AC C

and its comparison with experimental values of Mahendiran et al. [7]. The dark triangle (▲) and dark square (■) represent the model calculation and experimental values respectively. Inset shows calculated C/T as a function of temperature (10K ≤ T ≤ 300 K).

Fig. 7. (a-h) The variation of specific heat of Nd1−xSrxCoO3 (x=0.05, 0.1, 0.15, 0.2, 0.4 and 0.5) as a

function of temperature (10 K ≤ T ≤ 300 K) and its comparison with experimental values of Morchshakov et al. [29]. The solid line (–) and open triangle (∆) represent the model calculation and experimental values respectively. Variation of specific heat of Nd0.7Sr0.3CoO3 is compared with experimental values of Jirak et al. [30]. Inset shows the variation of specific heat of Nd0.7Sr0.3CoO3 as a

15

ACCEPTED MANUSCRIPT function of temperature (10 K ≤ T ≤ 21 K) and its comparison with experimental values of Jirak et al. [30].

Fig. 8. The variation of computed specific heat of (a) Sm1−xSrxCoO3 (0≤ x ≤ 1) and (b) Dy1−xSrxCoO3

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(0≤ x ≤ 0.9) as a function of temperature (10 K ≤ T ≤ 300 K). Fig. 9. The variation of (a) C/T versus T2 of SrCoO3 and its comparison with experimental values of

Balamurugan et al. [31]. The solid line with dark triangle (–▲–) and dark square (■) represent the model calculation and experimental values respectively and (b) the variation of specific heat of SrCoO3

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as a function of temperature (10 K ≤ T ≤ 300 K).

M AN U

Fig. 10. The variation of thermal expansion coefficient (α) with composition (x) for (a) Pr1−xSrxCoO3

(0≤ x ≤ 0.5), (b) Nd1−xSrxCoO3 (0≤ x ≤ 0.5), (c) Sm1−xSrxCoO3 (0≤ x ≤ 1) and (d) Dy1−xSrxCoO3 (0≤ x

AC C

EP

TE D

≤ 0.9) perovskites at 10 K.

16

ACCEPTED MANUSCRIPT Table1. Values of average size of the ions at the rare-earth site (rA), the size variance of the ions at the

rare-earth site (σ2), tolerance factor (t), critical radius (rcr) and model parameters of Ln1−xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) perovskites. rA (Å) (A-site)

Variance

PrCoO3 Pr0.9Sr0.1CoO3 Pr0.8Sr0.2CoO3 Pr0.7Sr0.3CoO3 Pr0.6Sr0.4CoO3 Pr0.5Sr0.5CoO3

1.179 1.192 1.205 1.218 1.231 1.244

0.00 0.00154 0.00274 0.00360 0.00412 0.00429

NdCoO3 Nd0.95Sr0.05CoO3 Nd0.90Sr0.10CoO3 Nd0.85Sr0.15CoO3 Nd0.80Sr0.20CoO3

1.163 1.170 1.177 1.185 1.192

0.00 0.00102 0.00194 0.00275 0.00345

b1x10-19 (J) (Å) (Co-O) Pr1-xSrxCoO3 (0.0 ≤ x ≤ 0.5) 0.9306 1.0186 1.321 0.9367 1.0110 1.413 0.9429 1.0082 1.476 0.9491 1.0058 1.526 0.9553 0.9983 1.599 0.9616 0.9922 1.789 Nd1-xSrxCoO3 (0.0 ≤ x ≤ 0.5) 0.9248 1.0179 1.252 0.9282 1.0166 1.284 0.9315 1.0155 1.313 0.9349 1.0149 1.369 0.9383 1.0135 1.431

Nd0.70Sr0.30CoO3

1.207

0.00454

0.9450

1.0070

Nd0.60Sr0.40CoO3

1.222

0.00518

0.9518

Nd0.50Sr0.50CoO3

1.237

0.00540

0.9587

ρ1 (Å) (Co-O)

ρ2 (Å) (Ln/Sr-O)

RI PT

2

b2 x10-19 (J) (Ln/Sr-O)

rcr

1.451 1.491 1.520 1.553 1.588 2.075

0.194 0.200 0.205 0.209 0.218 0.235

0.347 0.360 0.370 0.381 0.399 0.427

1.791 1.818 1.845 1.873 1.910

0.187 0.190 0.192 0.196 0.201

0.339 0.340 0.347 0.353 0.362

1.512

1.950

0.208

0.377

0.9980

1.582

1.968

0.215

0.390

0.9924

1.670

1.993

0.221

0.401

1.134

1.976

0.181

0.329

SC

σ (Å ) 2

Tolerance factor (t)

M AN U

Compound

Sm1-xSrxCoO3 (0.0 ≤ x ≤ 1.0) 1.132

0.00

Sm0.9Sr0.1CoO3

1.149

0.00285

0.9214

1.0224

1.217

1.979

0.189

0.345

Sm0.8Sr0.2CoO3

1.167

0.00507

0.9293

1.0255

1.295

2.000

0.192

0.352

Sm0.7Sr0.3CoO3

1.185

0.00665

0.9372

1.0166

1.363

2.001

0.197

0.361

Sm0.6Sr0.4CoO3

1.203

0.00760

0.9451

1.0081

1.454

2.005

0.205

0.376

Sm0.5Sr0.5CoO3

1.221

0.00792

0.9530

0.9992

1.536

2.011

0.211

0.385

Sm0.4Sr0.6CoO3

1.360

0.00960

1.000

0.9116

1.686

2.019

0.223

0.408

Sm0.3Sr0.7CoO3

1.380

0.00840

1.001

0.9075

1.842

2.112

0.230

0.415

Sm0.2Sr0.8CoO3

1.400

0.00640

1.002

0.9077

2.056

2.213

0.240

0.426

Sm0.1Sr0.9CoO3

1.420

0.00360

1.003

0.8969

2.295

2.313

0.254

0.441

SrCoO3

1.440

0.00

1.020

2.410

2.422

0.327

0.573

EP

AC C

DyCoO3

0.9136

1.0317

TE D

SmCoO3

Dy1-xSrxCoO3 (0.0 ≤ x ≤ 0.9)

1.083

0.00

0.8959

1.0453

0.996

0.907

0.167

0.246

Dy0.4Sr0.6CoO3

1.219

0.01236

0.9538

1.0078

1.548

1.666

0.208

0.382

Dy0.3Sr0.7CoO3

1.242

0.01082

0.9636

0.9996

1.757

1.707

0.223

0.407

Dy0.2Sr0.8CoO3

1.264

0.00824

0.9734

0.9930

1.968

1.744

0.238

0.430

Dy0.1Sr0.9CoO3

1.287

0.00463

0.9832

0.9865

2.169

1.768

0.249

0.452

17

ACCEPTED MANUSCRIPT Table 2. Values of cohesive and thermal properties of Ln1−xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) perovskites at low temperature (i.e. below transition temperature). f φ (eV) υ (Kapustins (N/m) (THz) kii) Pr1-xSrxCoO3 (0.0 ≤ x ≤ 0.5) -139.4 22.67 7.52 -138.5 20.85 7.27 -137.6 19.24 7.05 -136.8 17.84 6.85 -135.8 16.46 6.65 -134.7 15.22 6.47

PrCoO3 Pr0.9Sr0.1CoO3 Pr0.8Sr0.2CoO3 Pr0.7Sr0.3CoO3 Pr0.6Sr0.4CoO3 Pr0.5Sr0.5CoO3 Others

118.1 108.1 99.81 91.53 84.24 77.81

NdCoO3 Nd0.95Sr0.05CoO3 Nd0.90Sr0.10CoO3 Nd0.85Sr0.15CoO3 Nd0.80Sr0.20CoO3

123.4 117.7 112.4 107.5 102.9

-141.4 -140.3 -139.4 -138.4 -137.6 -136.6 -144.54a Nd1-xSrxCoO3 (0.0 ≤ x ≤ 0.5) -142.4 -140.4 23.56 -141.8 -139.9 22.55 -141.3 -139.4 21.62 -140.7 -139.0 20.73 -140.2 -138.5 19.88

Nd0.70Sr0.30CoO3

94.16

-139.2

-137.4

Nd0.60Sr0.40CoO3

86.18

-138.2

Nd0.50Sr0.50CoO3

79.31

-137.1

Others

-144.54

γ

361.5 349.6 338.8 329.4 319.7 310.7

2.31 2.20 2.09 2.00 1.90 1.81 (2-3)b

7.63 7.49 7.37 7.25 7.13

366.6 360.3 354.3 348.5 342.9

2.35 2.29 2.23 2.18 2.13

18.25

6.90

331.8

2.02

-136.1

16.72

6.68

320.9

1.91

-135.1

15.43

6.49

311.8

1.82

M AN U

c

θD

(Κ)

RI PT

φ (eV) (MRIM)

SC

B (GPa)

Compound

(2-3)d

120.8

-142.1

-139.9

22.93

7.46

358.6

2.29

Sm0.9Sr0.1CoO3

120.5

-141.2

-138.8

21.03

7.21

346.6

2.17

Sm0.8Sr0.2CoO3

102.2

-140.1

-138.6

19.72

7.05

338.8

2.11

Sm0.7Sr0.3CoO3

93.78

-139.2

-137.4

18.14

6.83

328.3

2.00

Sm0.6Sr0.4CoO3

86.23

-138.3

-136.3

16.73

6.63

318.8

1.91

Sm0.5Sr0.5CoO3

79.37

-137.2

-135.1

15.42

6.44

309.8

1.81

Sm0.4Sr0.6CoO3

60.69

-132.1

-129.4

11.81

5.71

274.6

1.54

Sm0.3Sr0.7CoO3

55.93

-130.9

-128.5

10.94

5.58

268.4

1.47

AC C

TE D

SmCoO3

EP

Sm1-xSrxCoO3 (0.0 ≤ x ≤ 1.0)

Sm0.2Sr0.8CoO3

51.91

-129.8

-127.8

10.24

5.48

263.4

1.41

Sm0.1Sr0.9CoO3

47.71

-128.7

-126.3

9.38

5.33

256.4

1.33

SrCoO3

43.37

-127.5

-126.3

8.50

4.48

215.6

1.21

Others

e

(2-3)f

-144.54

Dy1-xSrxCoO3 (0.0 ≤ x ≤ 0.9)

DyCoO3

140.1

-146.5

-146.6

27.54

8.09

385.4

2.51

Dy0.4Sr0.6CoO3

78.32

-137.7

-136.3

15.30

6.44

309.4

1.81

Dy0.3Sr0.7CoO3

71.41

-136.3

-134.7

13.99

6.25

300.7

1.71

Dy0.2Sr0.8CoO3

65.35

-135.0

-133.3

12.85

6.10

293.3

1.63

Dy0.1Sr0.9CoO3

59.91

-133.7

131.8

11.82

5.97

286.9

1.05

Others a

-144.54

g

f Ref. [3], bRef. [27],cRef. [3], dRef. [27], eRef. [3],18 Ref. [27], gRef. [3], hRef. [27]

(2-3)h

ACCEPTED MANUSCRIPT Table 3. Values of cohesive and thermal properties of Ln1−xSrxCoO3 (Ln=Pr, Nd, Sm, Dy and 0≤ x ≤ 1) perovskites at high temperature (i.e. above transition temperature). φ (eV)

B (GPa)

φ (eV)

f (N/m)

(MRIM) (Kapustinskii) Pr1-xSrxCoO3 (0.0 ≤ x ≤ 0.5) -154.1 -155.6 43.92

υ

θD

(THz)

(Κ)

γ

α×10 10−6 (Κ−1) Cal. Others

228.8

10.47

503.2

3.50

20.1

-

217.7 209.8

-153.8 -153.7

-155.5 -154.8

41.98 40.67

10.32 10.25

496.1 492.7

3.40 3.32

20.6 20.7

-

Pr0.7Sr0.3CoO3 Pr0.6Sr0.4CoO3

201.6 190.6

-153.6 -153.3

-154.7 -154.1

39.30 37.26

10.18 10.01

488.9 480.9

3.25 3.12

20.9 21.3

18.8d -

Pr0.5Sr0.5CoO3 Others

174.1 211.8a

-153.1

-153.9

34.07

9.68

464.8 480b

2.94 (2-3)c

22.1

-

NdCoO3

243.5

Nd1-xSrxCoO3 (0.0 ≤ x ≤ 0.5) -154.3 -155.6 46.48

10.72

515.1

3.62

19.7

-

Nd0.95Sr0.05CoO3 Nd0.90Sr0.10CoO3

237.3 231.4

-154.2 -154.2

-155.2 -154.8

45.45 44.48

10.64 10.58

511.5 508.2

3.57 3.52

19.9 20.2

-

Nd0.85Sr0.15CoO3 Nd0.80Sr0.20CoO3

225.8 217.7

-154.1 -153.7

-154.7 -153.5

43.51 42.07

10.51 10.38

504.9 498.8

3.46 3.39

20.3 20.5

-

Nd0.70Sr0.30CoO3

206.7

-153.6

Nd0.60Sr0.40CoO3

198.5

-153.5

Nd0.50Sr0.50CoO3

191.4

Others

e

230 , 212.4

-153.2 f

SC

RI PT

PrCoO3 Pr0.9Sr0.1CoO3 Pr0.8Sr0.2CoO3

M AN U

Compound

-153.4

40.08

10.23

491.7

3.27

20.7

-

-153.3

38.53

10.14

487.1

3.18

21.0

-

-153.1

37.25

10.08

484.4

3.10

21.6

-

480

g

Sm1-xSrxCoO3 (0.0 ≤ x ≤ 1.0) 255.2

-155.8

Sm0.9Sr0.1CoO3

241.5

-155.8

Sm0.8Sr0.2CoO3

228.9

-155.7

Sm0.7Sr0.3CoO3

221.9

Sm0.6Sr0.4CoO3

210.5

Sm0.5Sr0.5CoO3

204.2

Sm0.4Sr0.6CoO3

189.6

Sm0.3Sr0.7CoO3

182.0

Sm0.2Sr0.8CoO3

170.9

Sm0.1Sr0.9CoO3

162.9

SrCoO3

160.6

Others

10.85

521.2

3.69

19.4

24.0m

-156.5

45.95

10.66

512.2

3.55

19.9

22.2 m

-156.5

44.19

10.55

507.2

3.49

20.2

20.5 m

-155.9

42.94

10.51

505.0

3.41

20.3

19.5 m

-155.6

-155.7

40.83

10.36

498.0

3.29

20.6

19.6 m

-155.5

-155.6

39.67

10.34

496.8

3.22

20.7

20.5 m

-155.4

-155.6

36.90

10.10

485.4

3.06

21.1

22.0 m

-155.3

-155.5

35.60

10.00

483.6

3.00

21.3

20.4 m

-156.2

-155.4

33.72

9.95

478.0

2.92

21.7

19.2 m

-156.1

-155.3

32.03

9.86

473.8

2.81

21.9

21.0 m

-147.4

31.49

8.70

417.9

2.75

EP

255.2 , 217.8

48.45

-155.6

-148.9

i

AC C

h

-156.7

TE D

SmCoO3

-144.54

j

480

(2-3)

-

l

Dy1-xSrxCoO3 (0.0 ≤ x ≤ 0.9)

DyCoO3

271.9

-159.3

-159.8

58.61

11.75

564.3

4.14

19.4

Dy0.4Sr0.6CoO3

206.1

-157.1

-157.5

40.28

10.45

502.0

3.25

19.8

16.3p

Dy0.3Sr0.7CoO3

187.9

-156.3

-156.6

36.83

10.15

487.8

3.07

20.8

17.1p

Dy0.2Sr0.8CoO3

173.1

-155.5

-155.8

34.05

0.994

477.4

2.93

21.6

19.0p

Dy0.1Sr0.9CoO3

161.2

-154.9

-155.2

31.83

0.979

470.8

2.81

22.0

22.0p

480n

(2-3)o

Others a

22.1

k

Ref. [23], bRef. [26], cRef. [27], dRef. [32], eRef. [22], fRef. [23], gRef. [26],hRef. [3], iRef. [23],jRef. [3], kRef. [26], lRef. [27], Ref. [4], nRef. [26], oRef. [27], pRef. [4]

m

19

ACCEPTED MANUSCRIPT

Pr1-xSrxCoO3

50

0 Size mismatch Charge mismatch Tolerance factor A-site variance

Sm1-xSrxCoO3

50

0 1.1

Nd1-xSrxCoO3 100

(b)

Size mismatch Charge mismatch Tolerance factor A-site variance

Dy1-xSrxCoO3

SC

100

(a)

M AN U

150

150

Size mismatch Charge mismatch Tolerance factor A-site variance

RI PT

100

Size mismatch Charge mismatch Tolerance factor A-site variance

1.2

1.3

1.4

1.1

A-site cation radius (Å)

EP

TE D

20

0 150

50

(d) 0 1.2

1.3

A-site cation radius (Å)

Figure 1

50

100

(c)

AC C

2

Size mismatch (×10), Charge mismatch (×10 ), 2 4 Tolerance factor (×10 ) and Varaince (×10 )

150

ACCEPTED MANUSCRIPT

(b)

Sm

Pr

RI PT

Nd

200

200 Sr

150 31.5 32.4 33.3 3 Molar volume (cm )

32

33 34 3 Molar volume (cm )

M AN U

150 30.6

SC

Pr-Sr Nd-Sr Sm-Sr Dy-Sr

EP

TE D

Figure 2

AC C

Bulk modulud (GPa)

250

250

(a)

Dy

21

35

ACCEPTED MANUSCRIPT

0.94

0.94

0.96

Nd1-xSrxCoO3

Pr1-xSrxCoO3

500

510

RI PT

500

480 (a)

460

490

(b) Sm1-xSrxCoO3

Dy1-xSrxCoO3 560

500

520

450 (c)

400 0.90 0.95 1.00

(d)

SC

Debye temperature (K)

0.96 0.92

480

0.88 0.92 0.96 1.00

Tolerance factor

M AN U

Tolerance factor

AC C

EP

TE D

Figure 3

22

ACCEPTED MANUSCRIPT

0.10 Nd1-xSrxCoO3

Pr1-xSrxCoO3

0.084

0.09

0.072

(a)

(b)

0.10

0.07 Sm1-xSrxCoO3

Dy1-xSrxCoO3

SC

C (J/mole K)

0.08

RI PT

0.078

0.09

M AN U

0.12

(c)

0.0

0.4 0.8 % Sr doping

1.2

Figure 4

AC C

EP

TE D

0.06

23

0.0

0.08

0.06 (d)

0.4 0.8 % Sr doping

ACCEPTED MANUSCRIPT

LT cal. HT cal. Exp. 200

Pr1-xSrxCoO3 100

0

0

0

0.0 0.2 0.4

50

100

100

200 T (K)

200

M AN U

T (K)

AC C

EP

TE D

Figure 5

24

0.1 0.3 0.5

300

SC

50

150

RI PT

100

PrCoO3

C (J/mole K)

C (J/mole K)

150

300

50

0.6 0.4 0.2

Pr0.5Sr0.5CoO3 0.0

0

100

200 T (K)

200 T (K)

300

M AN U

0

100

SC

100

RI PT

Pr0.5Sr0.5CoO3

LT cal. HT cal. Exp. C/T (J/mole K 2)

C (J/mole K)

ACCEPTED MANUSCRIPT

AC C

EP

TE D

Figure 6

25

300

ACCEPTED MANUSCRIPT

50 Exp. Cal.

0

(c)

0.10

Exp. Cal.

(d)

0.15

50

200

100

100

50

50

100

100

50

50

0

100

200

0 300

T (K)

(g)

100

200

T (K)

EP

TE D

Figure 7

26

150

(f)

100

Exp. Cal.

0

50 0

(h)

0.5

Exp. Cal.

M AN U

T (K)

0 0

4 Cal. 3 Exp. 2 1 0.3 0 0 5 10 15 20 T (K)

Exp. 0.3 Cal.

0

0

Exp. Cal.

Cal.

100

(e)

0.4

100

0 0

150 0.2

AC C

C (J/mole K)

100

150

C (J/mole K)

(b)

0.05

RI PT

(a)

0.0

SC

150

Cal.

100

200

T (K)

100 50

0 300

200

150

150

100

100 50 0

0.8

100

0.0 0.2 0.4 0.6 0.9

200 T (K)

0.1 0.3 0.5 0.7 1.0

50

Dy1-xSrxCoO3

(b)

0.0 0.6 0.7 0.8 0.9

RI PT

(a)

Sm1-xSrxCoO3

M AN U

C (J/mole K)

250

SC

ACCEPTED MANUSCRIPT

300

AC C

EP

TE D

Figure 8

27

0

100

200 T (K)

300

ACCEPTED MANUSCRIPT

0.15 SrCoO3

(b)

SrCoO3

Exp. Cal.

0.05 100

200 2 2 T (K )

300

400

50

0

0

M AN U

0

RI PT

0.10

100

SC

C (J/mole K)

2

C/T (J/mole K )

150

(a)

AC C

EP

TE D

Figure 9

28

100

Cal. Classical limit

200 T (K)

300

ACCEPTED MANUSCRIPT

Pr1-xSrxCoO3

Nd1-xSrxCoO3

RI PT

0.5

0.4

(a)

(b)

0.3 Sm1-xSrxCoO3 Dy1-xSrxCoO3 0.6 0.5 0.4 0.3 (c) (d) 0.2 0.0 0.4 0.8 1.2 0.0 0.4 0.8 % Sr doping % Sr doping

0.3

0.4

M AN U

SC

-7

-1

α (10 K )

0.4

AC C

EP

TE D

Figure 10

29

0.3 0.2

ACCEPTED MANUSCRIPT

Highlights •

Probably the first report on the specific heat and thermal expansion in Ln1-xSrxCoO3 (Ln=Pr, Nd, Sm and Dy) perovskite. Effect of lattice distortions on bulk modulus and thermal properties is presented.

•

Thermal properties are computed using the MRIM probably for the first time.

•

The negative values of cohesive energy show the stability of these compounds.

AC C

EP

TE D

M AN U

SC

RI PT

•