ISSN 1063�7745, Crystallography Reports, 2014, Vol. 59, No. 2, pp. 252–257. © Pleiades Publishing, Inc., 2014.Original Russian Text © G.N. Mazo, M.Z. Galin, N.V. Lyskov, A.K. Ivanov�Schitz, 2014, published in Kristallografiya, 2014, Vol. 59, No. 2, pp. 290–296.

252

INTRODUCTION

In recent years, perovskite�like complex oxideswith a K2NiF4�type structure, which are mixed (elec�tronic and oxygen�ionic) conductors, have beenintensively studied. The composition of these com�pounds is often described by the formula А2ВО4, andtheir structure consists of perovskite АВО3 layers andAO (NaCl�type) layers alternating along the с axis [5].Complex oxides with Ni, Cu, or Co in the В siteexhibit a high thermochemical stability, their coeffi�cients of thermal expansion (CTEs) are close to thoseof traditional solid electrolytes, and the oxygen diffu�sivities correspond to those in perovskites [6–9]. Oxy�gen�ionic conductivity in the compounds of K2NiF4

structural type is implemented via the vacancy mech�anism in perovskite layers or through the diffusion ofinterstitial oxygen in АО layers [10–12].

To expand the class of electrode materials, themolecular dynamics (MD) method was used in [13] tostudy a new base cuprate: Pr2CuO4, in the structure ofwhich the CuO2 layer is combined with the fluoritePr2O2 layer. In this compound, the polyhedron of cop�per atom is a square (the Cu–O bond length is 1.98 Å)and the coordination environment of praseodymiumatoms has the form of a cube (Fig. 1a, structure T′). Atthe same time, it is known [14] that doping praseody�mium cuprate with a certain amount of strontiumleads to a structural change: PrSrCuO4 – δ acquires a Tstructure of the K2NiF4 type (Fig. 1b).

For copper atoms, an octahedron extended alongthe fourfold axis becomes a coordination polyhedron.

CuO6 octahedra with shared vertices in the equatorialplane form an infinite CuO2 layer (the Cu–O bondlength is 1.87 Å). Cations in the A site have a coordi�nation environment in the form of a nine�vertex poly�hedron [15].

Coordination polyhedra around copper atoms aredistorted mainly due to two factors. First, the Cu2+ ionis a typical Jahn–Teller ion (the extension of CuO6

octahedra in the axial direction removes the orbitaldegeneracy and lowers the energy of the system [16]).Second, the combination of NaCl�type and perovskitelayers in a unit cell inevitably changes the equilibriumbond lengths in the direction perpendicular to thecomposition plane [17].

In this study we demonstrate the possibilities ofcomputer simulation for establishing the relationshipbetween the crystal structure and oxygen mobility incomplex oxide PrSrCuO4–δ and determining thestructural mechanism of ion transport and transport(conduction) channels for oxygen anions.

COMPUTER SIMULATION

In this study we applied the MD method using theDL_POLY 2.20 package [18]. The calculation boxincluded 72 unit cells (6, 6, and 2 cells along the crys�tallographic directions a, b, and с, respectively) andcontained 965 atoms and 43 vacancies localized in theaxial positions of oxygen O2 (Fig. 1b). The composi�tion of the material is described by the formula

PHYSICAL PROPERTIES OF CRYSTALS

Computer Simulation of Ion Transport in a New Cathode Material PrSrCuO4 – δ

G. N. Mazoa, M. Z. Galinb, N. V. Lyskovb, and A. K. Ivanov�Schitzc

a Faculty of Chemistry, Moscow State University, Moscow, 119991 Russiab Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow region, 142432 Russia

c Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, 119333 Russiae�mail: alexey.k.ivanov@gmail.com

Received May 28, 2013

Abstract—Oxygen diffusion in the new class of cuprates Pr2 – xSrxCuO4 – δ (x = 1) with perovskite structurehas been simulated in the temperature range of 300–2100 K for the first time. A calculation has shown thepresence of anisotropy of oxygen motion: the oxygen transport in PrSrCuO3.7 in the temperature range of300–2100 K is mainly two�dimensional, with an activation energy of no more than 0.40 eV. The coefficientof thermal expansion of PrSrCuO3.7 (9.9 × 10–6 K–1 in the range 1300–2100 K) and the oxygen diffusivity init, which exceed the corresponding values for La2 – xSrxCuO4 – δ, indicate that this compound is promising asan electrode material with a mixed ionic�electronic conductivity for various electrochemical devices. Theresults expand the previous concepts of the oxygen�ion transport in complex cuprates.

DOI: 10.1134/S106377451402014X

CRYSTALLOGRAPHY REPORTS Vol. 59 No. 2 2014

COMPUTER SIMULATION OF ION TRANSPORT IN A NEW CATHODE MATERIAL 253

PrSrCuO3.7 (δ = 0.3); it was chosen based on theexperimental data [19].

The calculation was performed within the rigid�ionmodel [20]. The potential energy of the interactionbetween ions in the system was specified as the sum ofthe Coulomb (electrostatic) and short�range pairpotentials

, (1)

where rij is the distance between ions i and j; qi and qj

are the effective charges of these ions; Aij, ρij, and Cij

are the parameters of the short�range potential for par�ticles i and j; and ε0 is the permittivity.

The electrostatic contribution to the crystal latticeenergy was calculated by Ewald summation. Particularattention was paid to the choice of effective charges ofions. It was shown in [21] (using X�ray absorption nearedge structure (XANES) spectroscopy) that cupratesPr2CuO4 and PrSrCuO4 – δ with T' and T structures,respectively, contain praseodymium in only the oxida�tion state +3.0; therefore, the effective charge q(Pr) =+3.0 was chosen. The effective charge of oxygen wasretained invariable (q(O) = –1.925), as in the calcula�tion of Pr2CuO4 matrix [13]. The strontium chargeq(Sr) = +1.9 was chosen after a series of preliminarycalculations, which demonstrated the formation of themost stable structure with parameters close to thoseobtained by X�ray diffraction. It is known that copperatoms may have a variable oxidation state in cupratestructures; therefore, the charge of copper cations wasunambiguously determined from the electrical neu�trality condition after choosing the effective charges ofother atoms, q(Cu)= +2.2252.

60

( ) exp4

i j ij ijij ij

ij ij ij

q q r CV r A

r r

⎛ ⎞= + − −⎜ ⎟πε ρ⎝ ⎠

When calculating the short�range component ofthe potential energy, we restricted ourselves to consid�ering only cation–anion and anion–anion pairs [22,23]. The parameters of short�range interatomic poten�tial that were used are listed in Table 1.

In the initial configuration, ions were positioned inlattice sites and then the standard periodic boundaryconditions were imposed on the system. The cutoffradius rc was assumed to be a half�length of the shorteredge of the calculation box.

The atomic motion within the isothermal–isobaric(NPT) ensemble was calculated using the modifiedVerlet algorithm [20]. The chosen step of time integra�tion of the equations of motion was 0.1 fs. The calcu�lation was carried out in the temperature range of300–1200 K. At the initial instant, the velocities ofparticles in the box were assumed to be zero and thetemperature of the system was established at a speci�fied level. At each specific temperature, the system wasbrought to equilibrium (thermalization mode) for30 ps. The data array containing the coordinates andvelocities of all particles in the box was formed for70 ps (7 × 105 iterations) at temperatures of 300–1200 Kwith a step of 200 K.

Ol2Cu

A

O22

A

A

CuOl2

Ol2Cu

O2A

AO2

CuOl2

AO2

O22

A

Ol2Cu

O2A

Ol2Cu

(a) (b)

Fig. 1. Crystal structures (a) T' and (b) T.

Table 1. Parameters of the short�range interaction poten�tials [24, 25]

Type of i–j pair Aij, eV ρij, Å Cij, eV Å6

O–O 2000 0.2840 100

Pr–O 2055.35 0.3438 23.95

Cu–O 3950 0.2280 0

Sr–O 2000 0.3220 0

254

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MAZO et al.

The main information on the structural character�istics of the simulated system was obtained by calculat�ing and analyzing the radial pair correlation functions(RPCFs) gij(r) from the formula

, (2)

where is the average number of particles j in thespherical layer of thickness dr at a distance r from par�ticle i and ρ is the average atomic density of the system.

The mobility of particles in the crystal lattice wascharacterized using the mean�square displacement(MSD) functions

, (3)

where rk(t) is the coordinate of particle k at an instant t.

2

( )( )

4ij

ij

n rg r

r dr=

ρ π

ijn

[ ]22

1

1( ) ( ) (0)N

k k k

k

r t r t rN

=

= −∑

The time dependences of MSDs were approxi�mated by straight lines, the slope of which was used tocalculate the ion diffusivities Dk from the Einsteinrelation

, (4)

where l is the number of degrees of freedom (l = 1, 2,and 3 for one�, two�, and three�dimensional mecha�nisms of diffusion, respectively) and coefficient Bk

describes thermal oscillations of particles near theequilibrium position.

Particle trajectories in the model box were visuallyanalyzed with the use of the VMD 1.9.1 package [26].

RESULTS OF THE COMPUTER SIMULATION OF THE PrSrCuO3.7 SYSTEM AND DISCUSSION

Using the selected interaction parameters, we ana�lyzed the RPCFs for cation pairs (Fig. 2a) and calcu�lated the structural characteristics of the simulatedsystem. Note that, in view of the similarity of inter�atomic distances in Pr(Sr)–Pr(Sr) pairs for atomslocated in different crystallographic positions(Fig. 2b), the first peak is a superposition of threeclosely located peaks (Fig. 2a, insert). The third peakin the insert in Fig. 2a is the most diffuse one; it has thelowest amplitude and its characteristics yield the larg�est error in comparison with the experimental data.Nevertheless, as can be seen in Table 2, the calculatedand experimental values of interatomic distances arein good agreement.

Figure 3 shows the simulated temperature depen�dences of the unit�cell parameters for PrSrCuO3.7 andthe relative increase in volume. As can be seen inFig. 3a, the thermal expansion of the compound understudy is isotropic along the tetragonal unit�cell axes.

2( ) 2k k kr t lD t B= +

4

103

4

3.0 4.5

g Pr(

Sr)−

Pr(

Sr)

, r

4.03.5

3

2

1

0

r, Å

g Pr(

Sr)−

Pr(

Sr)

, r 3

2

1

098764 5

r, Åc

ab

(a) (b)

3.784

3.83

7

3.607

Fig. 2. (a) RPCFs for Pr(Sr)–Pr(Sr) pairs at 300 K and (b) the structure of PrSrCuO3.7. The insert in (a) shows the contour of thefirst peak as a superposition of three Gaussian peaks.

Table 2. Experimental and calculated interatomic distanc�es for PrSrCuO4 ⎯ δ with a crystal structure T at 300 K

Atomic pairs Experimental data, Å [14]

Calculated data, Å

Deviation, %

Pr(Sr)–Pr(Sr) 3.6674(18) 3.590(4) 2.1

3.7336(7) 3.812(3) 2.0

3.8373(13) 4.096(4) 6.7

Pr(Sr)–O1 2.6167(9) 2.518(7) 3.8

Pr(Sr)–O2 2.3891(24)2.6695(5)

2.458(3)2.639(1)

2.91.1

Cu–O1 1.8668(3) 1.824(2) 2.3

Cu–Cu 3.7336(7) 3.674(9) 1.6

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COMPUTER SIMULATION OF ION TRANSPORT IN A NEW CATHODE MATERIAL 255

The CTE(V1/3) value calculated from the temperaturedependence of the unit�cell volume (Fig. 3b) is(9.9 ±0.2) × 10–6 К–1

in the range of 1300–2100 K, which is

close to the value CTE = 10.5 × 10–6 K–1 of the solid

electrolyte ZrO2 + 8 mol % Y2O3 widely used in solidoxide fuel cells.

Figure 4 shows RPCF plots for some atomic pairs.In contrast to Pr2CuO4 [13], the behavior of the corre�

0.012

600 2200T, K

(IT −I700)/I700

800

0.010

0.008

0.006

0.004

0.002

0

200018001600140012001000

0.012

600 2200T, K

(VT −V700)/V700

800

0.010

0.008

0.006

0.004

0.002

0

200018001600140012001000

(6.0 ± 0.2) × 10−6 K−1

(9.9 ± 0.2) × 10−6 K−1

(a) (b)

Fig. 3. Temperature dependences of relative variations in (a) parameters а (filled square) and с (open triangle) of the PrSrCuO3.7unit cell and (b) the PrSrCuO3.7 unit�cell volume.

6

10r, Å

20

864

4

2

gPr(Sr)−O1, r

T, K30090015002100

6

10r, Å

20

864

4

2

gPr(Sr)−O2, r

(a) (b)

20

0 10r, Å

2 864

gСu−O1, r10

10r, Å

20

864

4

2

gСu−O2, r

(c) (d)

8

6

18

16

14

12

10

8

6

4

2

T, K30090015002100

T, K30090015002100

T, K30090015002100

Fig. 4. RPCFs for (a) Pr(Sr)–O1, (b) Pr(Sr)–O2, (c) Cu–O1, and (d) Cu–O2 pairs.

ac

256

CRYSTALLOGRAPHY REPORTS Vol. 59 No. 2 2014

MAZO et al.

lation functions with an increase in temperature doesnot indicate any disorder of the oxygen sublattice,since the RPCF curves exhibit basically only thespread of maxima and broadening of the correspond�ing peaks.

Nevertheless, the oxygen system becomes rathermobile, as follows from the analysis of the MSDs ofoxygen ions (Fig. 5a), since an increase in the MSDvalues in time indicates a translation character of oxy�gen motion. In addition, it can be seen in Fig. 5b thatthere is a pronounced anisotropy of oxygen displace�ments: the motion occurs mainly in the a–b plane.

The oxygen mobility was determined from the vari�ation of MSD as a function of time (at t > 10 ps) at dif�ferent temperatures from Eq. (4). The diffusivities inArrhenius coordinates are presented in Fig. 6. The

activation energy Еа varies from 0.14 to 0.40 eV, whichis much lower than Еа for Pr2CuO4 [13] but close to thecorresponding values for lanthanum and praseody�mium nickelates and cobaltates [9]. Note the higherdiffusivities of oxygen (especially in the range of 500–1000 K) for PrSrCuO3.7 as compared with the Pr2CuO4

matrix [13].

MD calculations allow one to gain deeper insightinto the mechanism of oxygen diffusion. As was men�tioned above, the oxygen mobility in the а–b plane(the diffusivity is 1.3 × 10–7 cm2 s–1 at 1500 K) is higherthan along the c axis (5.8 × 10–8 cm2 s–1), althoughoxygen vacancies are located in the Pr(Sr)–O layer.Following the motion of oxygen atoms, one can seethat oxygen atoms O1 spend most time in the CuO2

layer, with rare hops to the Pr(Sr)–O layer.

Figure 7 shows oxygen density profiles forPrSrCuO3.7. Oxygen ions of both types are involved inthe translational motion. Oxygen atoms O1 move basi�cally in the a–b plane; however, some of them canoccupy vacancies in the positions of oxygen O2 viahopping. The probability of motion of O1 oxygenatoms between O2 sites is extremely low; however,backward motion into O1 sites may occur. Generally,O2 atoms remain in their sites and undergo only ther�mal vibrations. At the same time, they may undergorare hops to the neighboring O1 sites and then partic�ipate in the diffusion motion in the a–b plane.

Our MD calculation showed that the oxygen trans�port in PrSrCuO3.7 in the temperature range of 300–1200 K is mainly two�dimensional with an activationenergy of no higher than 0.40 eV. The CTE ofPrSrCuO3.7 (9.9 × 10–6 К–1 in the range of 1300–2100 K) and the oxygen diffusivity exceeding that inLa2 – xSrxCuO4 – δ make this compound promising as acathode material with a mixed ionic–electronic con�

1.6

0 70t, pc

10 604030

⟨r2(t)⟩, Å2

T, K70015002100

(a)1.4

1.2

1.0

0.8

0.6

0.4

0.2

5020

0.4

0 70t, pc

10 604030

⟨r2(t)⟩, Å2(b)

0.3

0.2

0.1

5020

in the ab planealong the c axis

Fig. 5. MSDs of oxygen anions at (a) 700, 1500, and 2100 K and (b) at 1500 K in the a, b plane and along the c axis.

10−6

4 20104/T, K−1

6 181412 168 10

0.40 ± 0.04 eV

0.14 ± 0.02 eV

T, K5001000150020002500

10−7

10−6

D,

cm2 s

−1

bulk diffusion in the ab planealong the c axis

Fig. 6. Temperature dependence of oxygen diffusivity forPrSrCuO3.7.

CRYSTALLOGRAPHY REPORTS Vol. 59 No. 2 2014

COMPUTER SIMULATION OF ION TRANSPORT IN A NEW CATHODE MATERIAL 257

ductivity for various electrochemical devices, such asfuel cells and membranes for oxygen separation.

The results expand the concepts of oxygen�iontransport in complex cuprates [24, 27–29].

ACKNOWLEDGMENTS

This study was supported by the Russian Founda�tion for Basic Research, projects nos. 11�03�0875aand 11�08�01159a.

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Translated by E. Bondareva

с

а

б

а

CuOl2

O2Pr(Sr)

Pr(Sr)O2

CuOl2

Pr(Sr)O2

O2Pr(Sr)

CuOl2

O1

Pr(Sr)C

uO2

O1

Pr(Sr)C

uO2

O1

Pr(Sr)C

uO2

O1

Pr(Sr)C

uO2

(b)

(a)

Fig. 7. Calculated oxygen density profiles in PrSrCuO3.7(a) along the c axis and (b) in the 2 a–b plane at 1500 K.Squares indicate the initial positions of Pr(Sr) atoms andcircles indicate the positions of Cu atoms. The layers con�taining O1 and Pr(Sr)CuO2 atoms are selected in (b).