Molecular dynamics simulation of oxygen ion diffusion in Ba2In2O5

ELSEVIER

Molecular

dynamics simulation of oxygen ion diffusion Ba,In,O,

in

Abstract Molecular dynamics simulation was employed to study oxygen ion diffusion in Ba,ln,O, with bro~vnmillurite structure. When the system was heated. the original orthorhombic cell changed to a tetragonal cell at 2300 K. Inspection of the structure revdtxl that oxygen ions jump from their original sites to the nearest vacant sites. The dill‘usion was restricted li)r the sites arounci the tetrahedrally coordinated In ion, resulting in highly an&tropic diffusion on the (I(’ plant. At 4600 K it further transformed to an oxygen disordered cubic perovskite structure. in bvhich all oxygen ions contributed to diffusion. The predicted transition \I;I~ consistent with the observed transition to a fast oxide-ion conductor for this compounci. although predicted temperature \V;LS overestimated. The effect of composition on the transition was studied by simulating the AzB20, (A’ ’ = Ha. Sr. Ca: B’ ’ = Al. Fe, In) systems. From these results, oxide-ion conductors Lvith lower transition temperatures could be predicted.

1. Introduction A Brownmillerite

(Ca,AlFeO,)

structure

can be re-

garded as an oxygen-deficient perovskite structure [I]. In the structure, oxygen vacancies ( C;, in Fig. 1) arc ordered in lines parallel to (IOI), resulting in tctrahedral coordination for half of the (Al, Fe) ions. Because a sixth of the oxygen sites in the corresponding perovskite structure are vacant, this material could be a candidate for a fast oxygen ion conductor. Goodenough et al. [2] have indeed observed a first-order transition to a fast oxide-ion conductor at 930°C for Ba,In,O, which adapts brownmillerite structure at ambient temperature. More recently Sr,ScAlO, [3] and Ba,GdIn, , Ga,O, [4] have been reported as fast oxide-ion conductors. Shin et al. [5] have reported that SrzFezO, with brownmillerite structure transforms to an oxygen disordered cubic perovskite structure above 700°C. However the details of the diffusion mechanism and its relation with the struc-

* Corresponding Earth’s

Interior.

author. Okqama

Present University.

address: Misasa,

Institute Tottori

for

Study 687~01.

of the

Japan.

tural transition of the compound have not been reported to date. The purpose of the present study is to obtain an insight into the mechanisms of the oxygen ion diffusion in Ba~In205. We employed the molecular dynamics (MD) simulation technique for this purpose. The MD simulation has been used to study the diffusion behavior of the superionic conductors [h]. However no MD study has been reported for compounds with brownmillerite structure. In order to examine the effect of composition on the transition behavior, we extended the simulation to A,B,O, (A = Ba, Sr. Ca: B = Al. Fe. In) systems as well.

2. Experimental

procedure

In the present study. a MD simulation program (MXDORTO and MXDTRICL). developed by Prof. K. Kawamuru of Tokyo Institute of Technology, was employed [7]. The MD simulation procedure was similar to our previous study or ACu02 [Xl. We used a full ionic two-body potential with Born-Mayer-type short-range repulsion term. as shown below, I(i) = cj,(/,‘r,, +.tjh, + h,) exp[(cc,+ (1,+ /‘,,I (h, + h,)] OY31-5107

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37

The first term is for electrostatic potential between ions i and j separated by r,,. having formal charges of cl; and L!,. respectively. The second term is for repulsive potential and ,f;, is a constant. Repulsion parameters (cl;. h,) for ions used in this simulation were taken from Kunz and Armbruster [9]. The total number of atoms in a simulated cell was 324 (containing 9 unit cells; 3~1. Ih, 3c). The initial internal coordinate for each ion was taken from that of Ca,FeAlO, [I]. and was relaxed at 300 K. In order to study the structure at high temperatures, the system was heated up to 5000 K with a heating rate of 0.5 K/step (total 10J steps). At temperatures near the transitions, constant temperature MD runs were also performed in order to obtain details of oxygen ion diffusion behavior.

3. Results

b

and discussion

To our knowledge. the structure of Ba#,O, is not refined. We performed a 5000-step simulation at 300 K to relax the initial structure [I] with fixed cell parameters, as observed for Ba,ln,O, (u = 0.61 I, b = 1.6816 and c = 0.5992 nm) [2]. The structure was stable during the simulation and each ion moved slightly from the initial position. We simulated a powder X-ray diffraction pattern using the obtained structure. The pattern matched quite well with that observed, supporting the MD-derived structure. When the system was further relaxed, without constraining the cell parameters at 300 K and 0.1 MPa (i.e., constant-pressure MD simulation), the N- and c-axes expanded whereas the h-axis shrunk during the simulation with final cell parameters of LI= 0.6255, h = 1.6588 and c = 0.6077 nm. The differences between the observed and simulated cell parameters were less than 3%. Better agreement will be achieved by adjusting potential parameters in Eq. I, once the structure of Ba,In,O, is refined.

In order to study the structure at high temperatures. the system was heated to 5000 K. Fig. 2 shows the reduced cell parameters of the corresponding cubic perovskite (i.e., U’ = ‘~~‘2, b’ = b!4, and c’ = (,/,I?) during heating. At temperatures below 2300 K, the cell parameters linearly increased with increasing temperature. At around 2300 K, the cell parameters changed drastically. and above the temperature. coalescence of N’- and cl-axes was observed (i.e.. a tetragonal cell), Above 4600 K the b’-axis further coalesced with other

Fig. I. Ba,ln,05 kvith brownmillerite structure viewed from the ;xOOI \ direction. Iridium ions take both octahedral and tetrahedral coordlnations in this structure. For clarity. Ba ions are not shoan. Oxygen vacancy (I;,) is indicated by X. In the corresponding pcrwhkite structure.

this

vacancy

ih occupied.

axes (i.e., a cubic cell). It should be noted that the tetragonal and cubic cells described here are inferred from the cell parameters, not directly from the symmetry of the simulated system. Since the oxygen ions are diffusing in the cell. it was difficult to define the symmetry of the system. Very long duration simulation is necessary to define the time-averaged position for oxygen in the system. In order to observe the oxygen ion diffusion behavior. the mean-square-displacement (msd) of oxygen ions was monitored during the heating. We noted a sudden 0.450

E c 0.445 \ LQJ 0.440 ‘;E 0.435 E % .g s $

0.430 0.425 0.420 0.415

300

1 I...’ 800

I 1300

I I... 180023002800

~...~...~I..~.I,...1....1., 3300

Temperature

380043004800

/K

Fig. 2. Reduced cell parameters of Ba,ln205. which corresponds to the cubic perovskitc cell. as a function of temperature. Initial orthorhombic cell transforms to a tetragonal cell aboLe 2300 K. and to a cubic cell above 4600 K.

48

Fig. 3. Ionic trajectories of Ba11n20~ in a unit cell biwcd (001) direction (stereo image). Solid and light lines show of In and 0 ions. respectively. Circles shoa’ the positions

from the trajectories of ions at

300

K. Oxygen

K. See

Fig.

I for

reference

of each

site.

(A)

At

2300

ions at 01 sites migrate to oxygen vncancie~ I I’,,). (B) At 5000 K. All oxygen ions are diffusing at this temperature. Note that oxygen ions mostly stay in the oxygen sites (01, 01. 03 and V,,).

increase in the msd at the orthorhombic,‘tetragonal transition, suggesting the start of the oxygen ion diffusion at the transition. Goodenough et al. [2] observed a first-order transition to a fast oxide-ion conductor for this compound at 930°C. Although the simulated transition temperature is about 1000 K higher than that of the observed. the transition to the phase with oxygen ion diffusion is consistent with the observations.

In order to inspect the diffusion process(es) in the tetragonal phase, the trajectories of ions at 2300 K were shown in Fig. 3(A). It can be seen that the oxygen ions at 02 site (Fig. I) migrated to the nearest oxygen vacancy sites (V,,), whereas Ba and In ions were vibrating at their original positions. We noted that the oxygen ions that first migrated were always the ions at the 02 site. Then the oxygen ions at the 03 site could migrate to the C’(, site or now vacant 02 site. However, we have never observed the migration of the oxygen ions at 01 site in the tetragonal phase. Since 02, 03 and V(, sites are placed around the In2 ion, the oxygen ion diffusion is restricted in each In2-tetrahedra containing layer (layer A in Fig. I). This is because the

oxygen ion callnot pass the layers made of the 01 site (layer B in Fig. 1). This causes an anisotropic diffusion on layer A (i.e., (a’ in-plane diffusion). In the original brownmillerite structure, the oxygen vacancies are lined parallel to (101). However now the vacancies are distributed randomly on the layer A. resulting in the tetragonal cell. Thus the oxygen ion diffusion and the orthorhombic,~tetragonal transition are interrelated. The trajectories of ions at 5000 K were shown in Fig. 3(B). Unlike Fig. 3(A), the oxygen ions at the 01 site are now migrating, thus the anisotropy observed at lower temperatures disappeared. The trajectories of the oxygen ions reveal that the ions mostly stay at the oxygen sites (01. 02, 03 and C’(,) of the corresponding perovskite structure, between migration. Thus the structure could be regarded as a cubic perovskite with partial oxygen occupancies (5’6) at 01. 02, 03 and V(, sites. No structural study of Ba,In,O, has been reported to date. therefore. we are not able to compare expcrimental results, at present. Shin ct al. [5] reported the transition from brownmillerite to a cubic perovskite structure for Sr,Fe,O, at 700°C as noted before. Our simulation of this compound revealed that the original brownmillerite structure transforms to a cubic perovskite structure at 3900 K. without passing the intermediate tetragonal phase observed for Ba,In,O,. The simulated transition is consistent with the observed transition. although again the transition temperature was overestimated. Nevertheless the difference of structural transition behavior suggests that the transition might be affected by the size of cations in the structure (i.e., Ba versus Sr). Thus the effects of composition on the transition and oxygen ion diffusion in the brownmillerite structure are discussed in the next section. 3.4. Sittlultrtions ,fh A,B,OS (A = Bu. St-, CU: B = Al, FL’, III) Using the same procedure as described above, A,B,OT (A’+ = Ba. Sr, Ca; B3+ = Al, Fe’+, In) systems are simulated up to 5000 K. The results are summarized in Table I. We noted three relationships between the structural property and composition. First, if ionic radius of the A-site cation (r,) is large relative to that of the B-site cation (r,%). the structure is unstable as observed for Ba?Al,O, and Sr,Al,O,. Indeed no brownmillerite phase was reported for these compositions. Table I suggests that rA,‘rH should be in the range of 1.6 to 2.1 for stabilization of the structure. Second, the tetragonal phase was observed only when the A-site is occupied by the Ba ion. Third, in genera1 the temperature (T,) where oxygen diffusion starts, decreases with increasing r,, ‘rH. These results suggest simple rule for a lower transition temperature oxygen ion conductor with brownmillerite structure. That is keep ~),II’,~ as

49

Camp.

T’!L (K)

Transition

Ba,AI?O, BalFeZOT Ba21n20i

1200 2600

Unstable Ortho tetra Ortho tetra

Sr,Al,O, Sr2Fe20< Sr21n20~ Cn2A120, Ca,Fe,O,

3900 41700 3600 4600 4x0

Ca,ln,O, “ Defined h Ionic

as the radii

taken

temperature from

where Shanon

msd and

Observed

Remarks

No No Yes

2.7 7.2 1.8

Unstable Ortho cubic Ortho cubic Ortho cubic Ortho’cubic

No Yes Yes Yes Yes

2.4 I.9 I.6 7. I I.7

Ortho

No

I .4

cubic

exceeded

Preuitt

cubic cubic

7-, = 1300 0 C Tr. Stable

K at 970

at high

K P

5 x IO- 1 nm’.

[IO].

high as possible unless it becomes unstable. Reported oxygen ion conductors [Z-4] seem to satisfy this rule. Therefore MD simulation can be used to predict the stability and the transition behavior of the candidate compound with this structure, prior to the ‘real’ experiment. Finally reasons for the overestimation of the transition temperature are considered. The potential parameters used in the simulation are not optimized for A2B20,. In order to improve the potentials, structural and thermodynamic data of A,B,O, must be included for the parameter-refinement procedure. However, these data are scare at the moment. The potential form (Eq. 1) used in this study might be too simple. Incorporation of covalency in terms of fractional charges and three-body terms would improve the simulation. Another possible reason is that the simulation was performed on the perfect crystal without any extrinsic defects (though it does contain intrinsic oxygen vacancies). It is well known that MD simulation always overestimates melting temperature, when no surface (defect) is considered. Nevertheless further experimental and computational studies are necessary to improve the simulation.

Acknowledgements The authors thank Professor K. Kawamura for supplying his molecular dynamics simulation programs.

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