research article thermodynamic properties of la...

Research ArticleThermodynamic Properties of La

1minus119909Sm

119909CoO3

Rasna Thakur and N K Gaur

Superconductivity Research Lab Department of Physics Barkatullah University Bhopal 462026 India

Correspondence should be addressed to RasnaThakur rasnathakuryahoocom

Received 29 May 2014 Accepted 11 September 2014 Published 29 September 2014

Academic Editor Franz Demmel

Copyright copy 2014 R Thakur and N K Gaur This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

We have investigated the bulk modulus and thermal properties of La1minus119909

Sm119909CoO3(0 le 119909 le 02) at temperatures 1K le 119879 le

300K probably for the first time by incorporating the effect of lattice distortions using the modified rigid ion model (MRIM)The calculated specific heat thermal expansion bulk modulus and other thermal properties reproduce well with the availableexperimental data implying that MRIM represents properly the nature of the pure and doped cobaltate The specific heats arefound to increase with temperature and decrease with concentration (x) for the present The increase in Debye temperature (120579

119863)

indicates an anomalous softening of the lattice specific heat because increase inT3-term in the specific heat occurs with the decreaseof concentration (x)

1 IntroductionCobaltites of rare-earth elements with the chemical formulaLnCoO

3are important agile and multifunctional materials

which are very promising for high temperature oxygenseparation membranes and cathodes in solid oxide fuel cells(SOFCs) heterogeneous catalysts and gas sensors [1 2] TheLaCoO

3ceramic is at present the best studied representative

of the rare-earth cobaltite family LaCoO3exhibits two spin

state transitions as the temperature increasesThe first transi-tion is from low temperature low spin (LS) to intermediatespin (IS) state near 100K characterized by a steep jump ofmagnetization at the transition [3ndash5] and the second oneis from IS to high spin (HS) state leading to an insulator-metal (I-M) transition around 500K [3 5] Throughoutthe ACoO

3series only LaCoO

3has been analyzed with

rhombohedral symmetry [6] the rest of the members of thefamily with the ionic radius of the rare-earth smaller than theionic radius of La exhibit an orthorhombic crystallographicstructure [7] A structural transition from rhombohedral(1198773119862) to orthorhombic (Pbnm) symmetry with Sm dopinglevel 119909 gt 008 is found from the X-ray diffraction data inLa1minus119909

Sm119909CoO3[8]

Recently we have applied the modified rigid ion model(MRIM) to study the specific heat of cobaltates and mangan-ites [9 10] Motivated from the applicability and versatility ofMRIMwe have appliedMRIM to investigate the temperature

dependence of the specific heat thermal expansion and elas-tic and thermal properties of La

1minus119909Sm119909CoO3(0 le 119909 le 02)

It is found that the model is successful in describing temp-erature dependent (1 K lt 119879 lt 300K) specific heat (119862) cohe-sive energy (120601) molecular force constant (119891) Reststrahlenfrequency (120592) Debye temperature (120579

119863) and Gruneisen

parameter (120574) of La1minus119909

Sm119909CoO3(0 le 119909 le 02) The various

properties in La1minus119909

Sm119909CoO3(0 le 119909 le 02) are affected by the

exchange of the A ions due to their different ionic radii Thepaper is organized in the following way

The computational details of model formalism are givenin Section 2 In Section 3 we discuss the elastic and thermalproperties of La

1minus119909Sm119909CoO3(0 le 119909 le 02) The calculated

results are compared with the available experimental resultsin the same section Finally in Section 4 the findings of thepresent study are concluded

2 Formalism of MRIMThe effective interionic potential corresponding to the mod-ified rigid ion model (MRIM) frame work is expressed as[9 10]

120601 (119903) = minus1198902

2sum

1198961198961015840

1198851198961198851198961015840119903minus1

1198961198961015840 minussum

1198961198961015840

1198621198961198961015840119903minus6

1198961198961015840

+ [1198991198941198871198941205731198961198961015840 exp

(119903119896+ 1199031198961015840 minus 1199031198961198961015840)

120588119894

+1198991015840

119894

2119887119894

Hindawi Publishing CorporationInternational Journal of MetalsVolume 2014 Article ID 616525 5 pageshttpdxdoiorg1011552014616525

2 International Journal of Metals

Table 1 Values of average cation radius at A-site tolerance factor critical radius and model parameters of La1minus119909

Sm119909CoO3(00 le 119909 le 02)

Compound 119903A (A) Tolerance factor (119905) 119903cr (A)Model parameters

(A-site) 1198871times 10minus19 (J) 120588

1(A) 119887

2times 10minus19 (J) 120588

2(A)

LaCoO3 1360 09958 09148 1662 1114 0225 0404La098Sm002CoO3 1357 09953 09159 1636 1105 0222 0399La096Sm004CoO3 1355 09947 09164 1605 1095 0219 0394La094Sm006CoO3 1352 09941 09168 1596 1093 0218 0392La092Sm008CoO3 1350 09936 09168 1551 1071 0213 0383La088Sm012CoO3 1205 09420 10102 1317 1757 0197 0364La084Sm016CoO3 1202 09413 10143 1288 1751 0192 0355La080Sm020CoO3 1199 09407 10169 1269 1751 0190 0351

119 126 133

0

80

160

240

320

Bulk modulusSize mismatch

Tolerance factorA-site variance

Ionic radius at A-site (A)

La1minusxSmxCoO3

Bulk

mod

ulus

(GPa

) siz

em

ismat

ch (times

10)

tole

ranc

e fac

tor

(times10

2)

and

A-sit

e var

ianc

e (times10)

Figure 1 The variation of bulk modulus size mismatch tolerancefactor and A-site variance of La

1minus119909Sm119909CoO3(00 le 119909 le 20) with

the radius of A-site cation

times [120573119896119896exp

(2119903119896minus 119903119896119896)

120588119894

+ 12057311989610158401198961015840 exp

(21199031198961015840 minus 11990311989610158401198961015840)

120588119894

]]

(1)

Here first term is attractive long range (LR) coulomb inter-actions energy The second term represents the contribu-tions of van der Waals (vdW) attraction for the dipole-dipole interaction and is determined by using the Slater-Kirkwood Variational (SKV) method [11] The third termis short range (SR) overlap repulsive energy represented bythe Hafemeister-Flygare-type (HF) interaction extended upto the second neighbour In (1) 119903

1198961198961015840 represents separation

between the nearest neighbours while 119903119896119896and 11990311989610158401198961015840 appearing

in the next terms are the second neighbour separation 119903119896

(1199031198961015840) is the ionic radii of 119896 (1198961015840) ion 119899 (1198991015840) is the number

of nearest (next nearest neighbour) ions The summation isperformed over all the 1198961198961015840 ions 119887

119894and 120588

119894are the hardness

and range parameters for the 119894th cation-anion pair (119894 = 1 2)respectively and 120573

1198961198961015840 is the Pauling coefficient [12] expressed

as

1205731198961198961015840 = 1 + (

119885119896

119873119896

) + (1198851198961015840

1198731198961015840

) (2)

with 119885119896(1198851198961015840) and 119873

119896(1198731198961015840) as the valence and number of

electrons in the outermost orbit of 119896 (1198961015840) ions respectivelyThe model parameters (hardness and range) are determinedfrom the equilibrium condition

[119889120601 (119903)

119889119903]

119903=1199030

= 0 (3)

and the bulk modulus

119861 =1

91198701199030

[1198892120601 (119903)

1198891199032

]

119903=1199030

(4)

The symbol 119870 is the crystal structure constant 1199030is the

equilibrium nearest neighbor distance of the basic perovskitecell and 119861 is the bulk modulus The cohesive energy forLa1minus119909

Sm119909CoO3(0 le 119909 le 02) is calculated using (1)

and other thermal properties such as the Debye temperature(120579119863) Reststrahlen frequency (120592) molecular force constant

(119891) Gruneisen parameter (120574) specific heat (119862) and thermalexpansion (120572) are computed using the expressions given in[9 10] The results are thus obtained and discussed below

3 Results and Discussion

31 Model Parameters The values of input data like unit cellparameters and interionic distances for Sm doped LaCoO

3

are taken from [8] for the evaluation of model parameters(1198871 1205881) and (119887

2 1205882) corresponding to the ion pairs Co3+-O2minus

and La3+Sm3+-O2The values of model parameters (1198871 1198872 1205881

and 1205882) are listed in Table 1 The tolerance factor 119905(119905 = (119903A +

119903119874)2(119903B + 119903

119874)) for these compounds is reported in Table 1

which satisfies the condition that 119905 for a stable perovskitephase is above 084 [16] Depending on the composition ofthe perovskite critical radius (119903cr) can be calculated by using(5) (Table 1) which describes the maximum size of themobileion to pass through Consider

119903cr =1198860((34) 119886

0minus radic2119903B) + 119903

2

B minus 1199032

A

2 (119903A minus 119903B) + radic21198860

(5)

International Journal of Metals 3

Table 2 Values of bulk modulus cohesive and thermal properties of La1minus119909

Sm119909CoO3(00 le 119909 le 02)

Compound 119861119879(GPa) Cohesive property Thermal property

120601 (eV)MRIM

120601 (eV)Kapustinskii Eqn 119891 (Nm) 120592 (THz) 120579

119863(K) 120574

LaCoO3 1806 minus1485 minus1475 3520 940 4519 308La098Sm002CoO3 1842 minus1488 minus1479 3587 949 4560 312La096Sm004CoO3 1878 minus1492 minus1482 3656 957 4602 315La094Sm006CoO3 1895 minus1494 minus1484 3685 961 4619 317La092Sm008CoO3 1959 minus1500 minus1489 3805 976 4691 323La088Sm012CoO3 2111 minus1514 minus1505 4123 102 4879 340La084Sm016CoO3 2175 minus1517 minus1511 4250 103 4951 347La080Sm020CoO3 2213 minus1521 minus1515 4325 104 4991 352Others 180a minus14454b 480careference [13] breference [14] and creference [15]

where 119903A and 119903B are the radius of the A ion and B ion respec-tively and 119886

0corresponds to the lattice parameter (11988113)

The condition that critical radius does not exceed 105 A [17]for typical perovskite material is satisfied in our compoundsThe values of ionic radii and atomic compressibility for La3+Sm3+ Co3+ and O2minus are taken from [18 19] We defined thevariance of the LaSm ionic radii as a function of 119909 1205902 =

sum(1199091198941199032

119894minus1199032

A) Here119909119894 119903119894 and 119903A are the fractional occupanciesthe effective ionic radii of cation of La and Sm and theaveraged ionic radius (119903A = (1 minus 119909)119903R3+ + 119909119903A3+) respectivelyThe effect of ionic radii on tolerance factor andA-site varianceis shown in Figure 1 In La

1minus119909Sm119909CoO3 the A-site cation

radius reduces with decrease in 119909 and the buckling of Co-O-Co angle progressively increases with 119909 which leads toincreased distortions of the lattice Here we have computedthe bulk modulus (119861) on the basis of Atoms in Molecules(AIM) theory [20]which emphasizes the partitioning of staticthermophysical properties in condensed systems into atomicor group distributionsThe computed values of bulkmodulusfor La

1minus119909Sm119909CoO3(002 le 119909 le 02) are in good agreement

with value predicted by Cornelius et al [13]

32 Cohesive Energy The cohesive energy (120601) is a measureof the strength of forces that bind atoms together in the solidstates and is descriptive in studying the phase stability Thecohesive energy of Sm doped LaCoO

3is computed using

(1) and is reported in Table 2 The negative value of the 120601

indicates that these compounds are stable at ambient tem-peratureThe calculated cohesive energy of La

1minus119909Sm119909CoO3is

quite comparable with the reported value of the lattice energyfor SmCoO

3 minus14454 eV [14] The variation of the cohesive

energy (120601) of La1minus119909

Sm119909CoO3(0 le 119909 le 02) as a function of

A-site ionic radius is displayed Figure 2 Further to ascertainthe validity of the MRIM we have used the generalizedKapustinskii equation [21] The lattice energy obtained usingthe Kapustinskii equation is close to the MRIM Accordingto generalized Kapustinskii equation the lattice energies ofcrystals with multiple ions are given as

UKJmolminus1 = minus12139

⟨119903⟩(1 minus

120588

⟨119903⟩)sum119899

1198961199112

119896 (6)

119 126 133Ionic radius at A-site (A)

La1minusxSmxCoO3

minus152

minus150

minus148

120601(e

V)

Figure 2 Variation of cohesive energy with radius of A-site cationfor La

1minus119909Sm119909CoO3(00 le 119909 le 20)

where ⟨119903⟩ = weighted mean cation-anion radius sum and 120588 isthe average value of model parameters 120588

1and 1205882

33 Thermal Properties We have also predicted the molec-ular force constant (119891) Reststrahlen frequency (120592) andGruneisen parameter (120574) for Sm doped LaCoO

3(Table 2)

In the Debye approach we consider the vibrations of thecollective positive ion lattice with respect to the negative ionlattice The frequency of vibration obtained by this modelis also reported here as Reststrahlen frequency This is clearfrom Table 2 that as the Sm doping increases the Reststrahlenfrequency increases The Debye temperature estimated forthe analysis of specific heat is also reported in Table 2 Ourcalculated values of Debye temperature for La

1minus119909Sm119909CoO3

(002 le 119909 le 02) are close to reported value of LaCoO3

which is 480K [15] Since the ionic radius of Sm is larger thanthat of La the bulk modulus and other thermal propertiessystematically increase with increasing 119909 (Table 2) We have


334 335 336 337440

460

480

500La1minusxSmxCoO3

Molar volume (cm3)

120579D

(K)

Figure 3 Variation of Debye temperature (120579119863) for La


(00 le 119909 le 20) withmolar volume (cm3) of the basic perovskite cell

displayed the variation of the Debye temperature (120579119863) of Sm

doped LaCoO3as a function of molar volume in Figure 3

and the 120579119863is observed to be increasing with increasing basic

perovskite molar cell volume

34 Specific Heat and Thermal Expansion The specific heatin the normal state of the material is usually approximated bythe contribution of the lattice specific heat The temperaturedependence (10 K le 119879 le 300K) of specific heat forLa1minus119909

Sm119909CoO3(0 le 119909 le 02) is computed as displayed

in Figure 4 We find that when the temperature is below300K the specific heat (Figure 4) is strongly dependent ontemperature which is due to the anharmonic approximationHowever at higher temperatures the anharmonic effect on119862is suppressed and 119862 is almost constant at high temperatureThe computed results on specific heat for LaCoO

3compared

with the experimental work of Tsubouchi et al [22] intemperature range (10 K le 119879 le 300K) are displayed inthe inset of Figure 4 The calculated dependence of 119862 ontemperature does not show any anomalous behavior and isin good agreement with the other experimental data [22]

Encouraged by the specific heat results we tried tocompute the thermal expansion coefficient (120572) as a functionof temperature using the well-known relation 120572 = 120574119862119861

119879119881

where 119861119879 119881 and 119862 are the isothermal bulk modulus unit

formula volume and specific heat at constant volume respec-tively and 120574 is the Gruneisen parameter It is important tonote that in Figure 5 (for 10 K) that thermal expansion showsa significant decrease due to the doping of Sm in LaCoO

3

Our results on volume thermal expansion coefficients willcertainly serve as a guide to experimental workers in future

4 Conclusion

On the basis of an overall discussion it may be concludedthat the description of the thermodynamic properties of Sm

100 200 300

00 002004 006008 012016 020

0

50

100

150

200

0 100 200 3000

50

100

T (K)

C(J

mol

e K)

C(J

mol

e K)

Experimental

Calculated

T (K)

LaCoO3

Figure 4The variation of calculated specific heat of La1minus119909

Sm119909CoO3

(00 le 119909 le 02) as a function of temperature (10 le 119879 le

300K)The curves of higher cation doping are shifted upward by 10 Jeach from the preceding curve for clarity Inset shows the specificheat of LaCoO

3in the temperature interval (10 K le 119879 le 300K)

and its comparison with the experimental values [22] The solidline (mdash) and open square (◻) represent the model calculation andexperimental curve respectively

000 005 010 015 02035

40

45

50

55

Sm doping ()

La1minusxSmxCoO3

120572(10minus8

Kminus1)

Figure 5 The variation of thermal expansion (120572) with composition(119909) in La

1minus119909Sm119909CoO3(00 le 119909 le 02) at 10 K

doped LaCoO3given by us is remarkable in view of the inher-

ent simplicity and less parametric nature of themodified rigidion model (MRIM) Our results are probably the first reportsof specific heat and thermal expansion at these temperaturesfor La

1minus119909Sm119909CoO3(002 le 119909 le 02) To the best of our

knowledge the values on bulk modulus cohesive and lattice


thermal properties for La1minus119909

Sm119909CoO3(00 le 119909 le 02)

have not yet been measured or calculated hence our resultscan serve as a prediction for future investigations

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

Theauthors are thankful to theUniversityGrant Commission(UGC) New Delhi for providing the financial support

References

[1] T Inagaki K Miura H Yoshida et al ldquoHigh-performanceelectrodes for reduced temperature solid oxide fuel cells withdoped lanthanum gallate electrolyte II La(Sr)CoO

3cathoderdquo

Journal of Power Sources vol 86 no 1-2 pp 347ndash351 2000[2] C H Chen H J M Bouwmeester R H E Van Doom

H Kruidhof and A J Burggraaf ldquoOxygen permeation ofLa03Sr07CoO3minus120575

rdquo Solid State Ionics vol 98 no 1-2 pp 7ndash131997

[3] S Yamaguchi Y Okimoto H Taniguchi and Y Tokura ldquoSpin-state transition and high-spin polarons in LaCoO

3rdquo Physical

Review B Condensed Matter and Materials Physics vol 53 no6 pp R2926ndashR2929 1996

[4] Y Kobayashi N Fujiwara S Murata K Asai and H YasuokaldquoNuclear-spin relaxation of 59Co correlated with the spin-statetransitions in LaCoO

3rdquo Physical Review BmdashCondensed Matter

and Materials Physics vol 62 no 1 pp 410ndash414 2000[5] M Senarıs-Rodrıguez and J Goodenough ldquoLaCoO

3revisitedrdquo

Journal of Solid State Chemistry vol 116 no 2 pp 224ndash231 1995[6] P G Radaelli and S W Cheong ldquoStructural phenomena

associated with the spin-state transition in LaCoO3rdquo Physical

Review B vol 66 Article ID 094408 2002[7] J A Alonso M J Martınez-Lope C de La Calle and V

Pomjakushin ldquoPreparation and structural study from neutrondiffraction data of RCoO

3(R = Pr Tb Dy Ho Er Tm Yb Lu)

perovskitesrdquo Journal of Materials Chemistry vol 16 pp 1555ndash1560 2006

[8] J R Sun R W Li and B G Shen ldquoSpin-state transition inLa1minus119909

Sm119909CoO3perovskitesrdquo Journal Of Applied Physics vol 89

p 1331 2001[9] R Thakur R K Thakur and N K Gaur ldquoThermophysical

properties of Pr1minus119909

Ca119909CoO3rdquoThermochimica Acta vol 550 pp

53ndash58 2012[10] R K Thakur S Samatham N Kaurav V Ganesan N K Gaur

and G S Okram ldquoDielectric magnetic and thermodynamicproperties of Y

1minus119909Sr119909MnO

3(x = 01 and 02)rdquo Journal of Applied

Physics vol 112 no 10 Article ID 104115 2012[11] J C Slater and J G Kirkwood ldquoThe van der waals forces in

gasesrdquo Physical Review vol 37 no 6 pp 682ndash697 1931[12] L Pauling Nature of the Chemical Bond Cornell University

Press Ithaca NY USA 1945[13] A L Cornelius S Kletz and J S Schilling ldquoSimple model for

estimating the anisotropic compressibility of high temperaturesuperconductorsrdquo Physica C vol 197 no 3-4 pp 209ndash223 1992

[14] M A Farhan and M J Akhtar ldquoNegative pressure drivenphase transformation in Sr doped SmCoO

3rdquo Journal of Physics

Condensed Matter vol 22 no 7 Article ID 075402 2010

[15] C He H Zheng J F Mitchell M L Foo R J Cava and CLeighton ldquoLow temperature Schottky anomalies in the specificheat of LaCoO

3 defect-stabilized finite spin statesrdquo Applied

Physics Letters vol 94 no 10 Article ID 102514 2009[16] C-M Fang and R Ahuja ldquoStructures and stability of ABO

3

orthorhombic perovskites at the Earthrsquos mantle conditionsfrom first-principles theoryrdquo Physics of the Earth and PlanetaryInteriors vol 157 no 1-2 pp 1ndash7 2006

[17] M Mogensen D Lybye N Bonanos P V Hendriksen and FW Poulsen ldquoFactors controlling the oxide ion conductivity offluorite and perovskite structured oxidesrdquo Solid State Ionics vol174 no 1ndash4 pp 279ndash286 2004

[18] R D Shannon ldquoRevised effective ionic radii and systematicstudies of interatomic distances in halides and chalcogenidesrdquoActa Crystallographica Section A vol 32 pp 751ndash767 1976

[19] C Kittel Introduction to Solid State Physics Wiley New YorkNY USA 5th edition 1976

[20] A M Pendas A Costales M A Blanco J M Recio and VLuana ldquoLocal compressibilities in crystalsrdquo Physical Review Bvol 62 Article ID 13970 2000

[21] L Glasser ldquoLattice energies of crystals with multiple ions ageneralized Kapustinskii equationrdquo Inorganic Chemistry vol34 no 20 pp 4935ndash4936 1995

[22] S Tsubouchi T Kyomen M Itoh and M Oguni ldquoKinetics ofthe multiferroic switching in MnWO

4rdquo Physical Review B vol

69 Article ID 144406 2004

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


Table 1 Values of average cation radius at A-site tolerance factor critical radius and model parameters of La1minus119909

Sm119909CoO3(00 le 119909 le 02)

Compound 119903A (A) Tolerance factor (119905) 119903cr (A)Model parameters

(A-site) 1198871times 10minus19 (J) 120588

1(A) 119887

2times 10minus19 (J) 120588

2(A)

LaCoO3 1360 09958 09148 1662 1114 0225 0404La098Sm002CoO3 1357 09953 09159 1636 1105 0222 0399La096Sm004CoO3 1355 09947 09164 1605 1095 0219 0394La094Sm006CoO3 1352 09941 09168 1596 1093 0218 0392La092Sm008CoO3 1350 09936 09168 1551 1071 0213 0383La088Sm012CoO3 1205 09420 10102 1317 1757 0197 0364La084Sm016CoO3 1202 09413 10143 1288 1751 0192 0355La080Sm020CoO3 1199 09407 10169 1269 1751 0190 0351

119 126 133

0

80

160

240

320

Bulk modulusSize mismatch

Tolerance factorA-site variance

Ionic radius at A-site (A)

La1minusxSmxCoO3

Bulk

mod

ulus

(GPa

) siz

em

ismat

ch (times

10)

tole

ranc

e fac

tor

(times10

2)

and

A-sit

e var

ianc

e (times10)

Figure 1 The variation of bulk modulus size mismatch tolerancefactor and A-site variance of La

1minus119909Sm119909CoO3(00 le 119909 le 20) with

the radius of A-site cation

times [120573119896119896exp

(2119903119896minus 119903119896119896)

120588119894

+ 12057311989610158401198961015840 exp

(21199031198961015840 minus 11990311989610158401198961015840)

120588119894

]]

(1)

Here first term is attractive long range (LR) coulomb inter-actions energy The second term represents the contribu-tions of van der Waals (vdW) attraction for the dipole-dipole interaction and is determined by using the Slater-Kirkwood Variational (SKV) method [11] The third termis short range (SR) overlap repulsive energy represented bythe Hafemeister-Flygare-type (HF) interaction extended upto the second neighbour In (1) 119903

1198961198961015840 represents separation

between the nearest neighbours while 119903119896119896and 11990311989610158401198961015840 appearing

in the next terms are the second neighbour separation 119903119896

(1199031198961015840) is the ionic radii of 119896 (1198961015840) ion 119899 (1198991015840) is the number

of nearest (next nearest neighbour) ions The summation isperformed over all the 1198961198961015840 ions 119887

119894and 120588

119894are the hardness

and range parameters for the 119894th cation-anion pair (119894 = 1 2)respectively and 120573

1198961198961015840 is the Pauling coefficient [12] expressed

as

1205731198961198961015840 = 1 + (

119885119896

119873119896

) + (1198851198961015840

1198731198961015840

) (2)

with 119885119896(1198851198961015840) and 119873

119896(1198731198961015840) as the valence and number of

electrons in the outermost orbit of 119896 (1198961015840) ions respectivelyThe model parameters (hardness and range) are determinedfrom the equilibrium condition

[119889120601 (119903)

119889119903]

119903=1199030

= 0 (3)

and the bulk modulus

119861 =1

91198701199030

[1198892120601 (119903)

1198891199032

]

119903=1199030

(4)

The symbol 119870 is the crystal structure constant 1199030is the

equilibrium nearest neighbor distance of the basic perovskitecell and 119861 is the bulk modulus The cohesive energy forLa1minus119909

Sm119909CoO3(0 le 119909 le 02) is calculated using (1)

and other thermal properties such as the Debye temperature(120579119863) Reststrahlen frequency (120592) molecular force constant

(119891) Gruneisen parameter (120574) specific heat (119862) and thermalexpansion (120572) are computed using the expressions given in[9 10] The results are thus obtained and discussed below

3 Results and Discussion

31 Model Parameters The values of input data like unit cellparameters and interionic distances for Sm doped LaCoO

3

are taken from [8] for the evaluation of model parameters(1198871 1205881) and (119887

2 1205882) corresponding to the ion pairs Co3+-O2minus

and La3+Sm3+-O2The values of model parameters (1198871 1198872 1205881

and 1205882) are listed in Table 1 The tolerance factor 119905(119905 = (119903A +

119903119874)2(119903B + 119903

119874)) for these compounds is reported in Table 1

which satisfies the condition that 119905 for a stable perovskitephase is above 084 [16] Depending on the composition ofthe perovskite critical radius (119903cr) can be calculated by using(5) (Table 1) which describes the maximum size of themobileion to pass through Consider

119903cr =1198860((34) 119886

0minus radic2119903B) + 119903

2

B minus 1199032

A

2 (119903A minus 119903B) + radic21198860

(5)



Sm119909CoO3(00 le 119909 le 02)


120601 (eV)MRIM


119863(K) 120574





sum(1199091198941199032

119894minus1199032







3is computed using










⟨119903⟩(1 minus

120588

⟨119903⟩)sum119899

1198961199112

119896 (6)


La1minusxSmxCoO3

minus152

minus150

minus148

120601(e

V)


1minus119909Sm119909CoO3(00 le 119909 le 20)


1and 1205882


3(Table 2)






334 335 336 337440

460

480

500La1minusxSmxCoO3

Molar volume (cm3)

120579D

(K)











3compared



119879119881



3


4 Conclusion


100 200 300

00 002004 006008 012016 020

0

50

100

150

200

0 100 200 3000

50

100

T (K)

C(J

mol

e K)

C(J

mol

e K)

Experimental

Calculated

T (K)

LaCoO3


Sm119909CoO3





000 005 010 015 02035

40

45

50

55

Sm doping ()

La1minusxSmxCoO3

120572(10minus8

Kminus1)









Sm119909CoO3(00 le 119909 le 02)




Acknowledgment


References


3cathoderdquo





3rdquo Physical





3revisitedrdquo


























3









69 Article ID 144406 2004








CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Sm119909CoO3(00 le 119909 le 02)


120601 (eV)MRIM


119863(K) 120574





sum(1199091198941199032

119894minus1199032







3is computed using










⟨119903⟩(1 minus

120588

⟨119903⟩)sum119899

1198961199112

119896 (6)


La1minusxSmxCoO3

minus152

minus150

minus148

120601(e

V)


1minus119909Sm119909CoO3(00 le 119909 le 20)


1and 1205882


3(Table 2)






334 335 336 337440

460

480

500La1minusxSmxCoO3

Molar volume (cm3)

120579D

(K)











3compared



119879119881



3


4 Conclusion


100 200 300

00 002004 006008 012016 020

0

50

100

150

200

0 100 200 3000

50

100

T (K)

C(J

mol

e K)

C(J

mol

e K)

Experimental

Calculated

T (K)

LaCoO3


Sm119909CoO3





000 005 010 015 02035

40

45

50

55

Sm doping ()

La1minusxSmxCoO3

120572(10minus8

Kminus1)









Sm119909CoO3(00 le 119909 le 02)




Acknowledgment


References


3cathoderdquo





3rdquo Physical





3revisitedrdquo


























3









69 Article ID 144406 2004








CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




334 335 336 337440

460

480

500La1minusxSmxCoO3

Molar volume (cm3)

120579D

(K)











3compared



119879119881



3


4 Conclusion


100 200 300

00 002004 006008 012016 020

0

50

100

150

200

0 100 200 3000

50

100

T (K)

C(J

mol

e K)

C(J

mol

e K)

Experimental

Calculated

T (K)

LaCoO3


Sm119909CoO3





000 005 010 015 02035

40

45

50

55

Sm doping ()

La1minusxSmxCoO3

120572(10minus8

Kminus1)









Sm119909CoO3(00 le 119909 le 02)




Acknowledgment


References


3cathoderdquo





3rdquo Physical





3revisitedrdquo


























3









69 Article ID 144406 2004








CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Sm119909CoO3(00 le 119909 le 02)




Acknowledgment


References


3cathoderdquo





3rdquo Physical





3revisitedrdquo


























3









69 Article ID 144406 2004








CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



research article thermodynamic properties of la...

Documents