BaF2 Heterolayer

Jan 5, 2009 - Dirk Zahn*, Oliver Hochrein, Xiangxin Guo and Joachim Maier*. Max-Planck Institut für Chemische Physik fester Stoffe, Nöthnitzerstrass...
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J. Phys. Chem. C 2009, 113, 1315–1319

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Molecular Dynamics Modeling of Nanoscale CaF2/BaF2 Heterolayer Structures Dirk Zahn,*,†,‡ Oliver Hochrein,† Xiangxin Guo,§,| and Joachim Maier*,§,| Max-Planck Institut fu¨r Chemische Physik fester Stoffe, No¨thnitzerstrasse 40, D-01187 Dresden, Germany, Max-Planck-Institut fu¨r Festko¨rperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany ReceiVed: September 30, 2008; ReVised Manuscript ReceiVed: NoVember 10, 2008

We present a transferable technique for the preparation of atomistic models mimicking ion conductor heterolayers grown by molecular beam epitaxy. On this basis, CaF2/BaF2 sandwich structures involving (100), (110), and (111) interfaces were explored. Our molecular dynamics simulations reveal a close interplay of interface-driven lattice deformation and resulting dislocations with the fluoride ion redistribution and local conductivity. From this, an interfacial core region of about 1 nm thickness can be assessed, accompanied by a space charge zone in BaF2 that is, however, three times thicker. Significant conductivity effects owing to charge carrier redistribution are found, which are closely related to the experimental results on this system. Introduction The peculiar characteristics of ion transport in confined systems have opened a new perspective to manipulate ionic conductivity in solids.1–12 In recent years, heterolayers of CaF2 and BaF2 have evolved to a model system for demonstrating size effects in nanoionics.13 The molecular beam epitaxy technique allows the preparation of ionic heterolayers exhibiting individual layer thicknesses down to only a few nanometers. Extensive experimental work has been done for investigating ionic conductivities both parallel and perpendicular to the interfaces.14–17 To complement the experimental efforts, a series of molecular dynamics simulations were aimed at ionic conductivities of CaF2/BaF2 heterostructures.18–21 Unlike studies related to bulk CaF2 or BaF2 alone,22 the modeling of heterostructures typically relies on assumptions on the interface structure. The most straightforward approach to model preparation is to attach singlecrystalline CaF2 and BaF2 layers to form a sandwich structure. In the study of Nomura and Kobayashi, both compounds were forced on a single lattice.18 While this in principle corresponds to a heterolayer system, lattice relaxation by dislocation formation remains elusive to such simulation models. Adams and Tan explored the relaxation of a CaF2 and BaF2 heterolayer system initially prepared as uniform 2D and 3D lattices.21 From this the formation of stacking faults through rotation of the layers was observed. While this work is still biased from its initial preparation, it demonstrates the importance of structural relaxation for the assessment of realistic heterolayer model systems. In attempt to circumvent prejudicing the CaF2-BaF2 interfaces, Sayle et al. prepared heterostructures by amorphization and recrystallization.19,20 In this model the relaxation procedure leads to nanopolycrystalline structures. The latter comprise structural features (dislocations, (100) and (111) interface patches) which are also observed in the sandwiches of crystalline layers grown by molecular beam epitaxy.13 However, the overall * Corresponding authors. † Max-Planck Institut fu¨r Chemische Physik fester Stoffe. ‡ Tel.: +49 (0) 351 4646 4205. Fax: +49 (0) 351 4646 4002. E-mail: [email protected]. § Max-Planck-Institut fu¨r Festko¨rperforschung. | E-mail: [email protected] and [email protected].

Figure 1. Illustration of the optimization scheme based on repeated heating and annealing cycles. The initial (100) sandwich structure (left) is heated to 1000 K in order to induce the melting of the fluoride sublattice in both the BaF2 and the CaF2 lamella (middle). Ion mobility is then reduced by gradually reducing temperature until a lowtemperature structure (right) is obtained. Convergence was checked from repeated heating/cooling cycles and comparison of the distribution of the fluoride ions as illustrated in Figure 3. The interface structure (highlighted in red) is illustrated in more detail in Figure 2.

structure, i.e., polycrystallinity and the collectivity of dislocations, differs considerably from the experimentally prepared heterolayers. In the present work, we report on a somewhat similar molecular dynamics simulation approach, which is, however, aimed at modeling the heterolayer structures in close concordance to the structures grown by molecular beam epitaxy. This allows direct comparison to local aspects as observed from transmission electron microscopy, and macroscopic properties like charge carrier concentration and conductivity profiles as elaborated by Maier and co-workers.13–17,23 Simulation Details. Three independent simulation models were investigated. Periodic boundary conditions were used for

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Figure 2. Top: projections of the simulation model perpendicular to the interfaces of the (100) and (111) BaF2-CaF2 heterolayer structures, respectively. For better clarity calcium and barium ions are not shown. The fluoride ions are colored in red and yellow accounting for tetrahedral (regular lattice sites) and other nearest neighbor coordination (interstitials), respectively. The core region of the (100) interface comprises the interfacial F- layer (2) and the adjacent F- layers at the surface of the BaF2 (1) and CaF2 (3) blocks, respectively. Bottom: analogous illustration of the (110) interfaces from two different perspectives. Refer to Figure 3 for a quantitative analysis of the excess charge arising from the average numbers of interstitials and vacancies in each layer.

all simulations described in the following. The initial model of the (100) heterolayer structure was prepared by attaching two single-crystalline blocks of CaF2 (15 × 17 × 17 unit cells) and BaF2 (13 × 15 × 15 unit cells). These dimensions were chosen in order to match the two crystallites of different lattice constants within a periodic supercell (17 × 5.46 Å ≈ 15 × 6.15 Å). Analogous considerations were taken for the preparation of the starting models of the (110) and (111) sandwich structures after rotation of the unit cell according to

{} { } {} { } (001) a b f (1j10) c (110)

and

a (011j) b f (11j0) , c (111)

respectively.

For each heterolayer system, the area of the interface roughly corresponds to 10 × 10 nm, while the thickness of each layer was chosen to be about 8 nm. The total number of ions amounts to 87 120, 89 190, and 85 473 for the modeling of [100]-, [110]-, and [111]-oriented heterolayers, respectively. The ionic interactions are modeled by the force field of Sayle et al.19 Ewald summation is used to calculate the Coulomb interactions. For the molecular dynamics simulations, a time step of 2 fs was found to be appropriate. Constant pressure (1 atm) is applied by allowing anisotropic shape deformation of the simulation cell. Temperature ranges from 0 to 1000 K are devised in intervals of 100 K, which are explored from subsequent 100 ps runs. Results and Discussion The initially prepared CaF2/BaF2 heterolayer structures correspond to noninteracting single-crystalline blocks. On the basis of these naive starting points, more realistic model systems were generated by a simulated annealing-type procedure. This encompasses several heating and cooling cycles for promoting ionic mobility and annealing to obtain relaxed structures, respectively. Each cycle is based on a series of molecular dynamics simulation runs applying constant pressure (1 atm)

and heating/cooling rates of 1 K/ps. As a consequence of the limited time scales of the molecular dynamics simulations, the heating/cooling rates must be chosen rather large compared to the experiments. The mechanistic analysis presented in the following is therefore checked for consistency on the basis of several heating/cooling cycles. The relaxation process may be nicely illustrated by comparing simulation snapshots taken during the first heating/cooling cycle (Figure 1). During a 1 ns molecular dynamics run, the initial structure is heated from 0 to 1000 K. This degree of thermalization allows fluoride conductivity throughout the whole simulation system. On the other hand, the cationic sublattices remain in the solid state and experience only small, yet important, distortions as discussed below. Upon cooling of the simulation system, the distribution of the fluoride ions differs significantly from the initial structure. The fluoride concentration profiles were therefore chosen as indicators for exploring the convergence of the heating/annealing procedure, which required two to three cycles for all sandwich structures studied. In the optimized heterolayer models, the CaF2 and BaF2 lattices are locally deformed in order to accommodate the structural mismatch at the interface between both layers. From Figure 2, the organization of dislocations may be observed in full agreement with experimental findings based on transmission electron microscopy (available for the (111) sandwich only).23 Moreover, a peculiar interplay of lattice distortion and the dislocations with the local arrangement of the fluoride ions is observed. This gives rise to significant effects on ionic conductivity as discussed in the following. Fluoride density profiles computed for slices perpendicular to the (100), (110), and (111) interfaces are shown in Figures 3a-c, respectively. Two superimposing effects need to be considered for the rationalization of the concentration profiles: (i) The interfacial core effect related to the local atomistic structure (lattice distortion and dislocations) of the BaF2/CaF2 contact. This effect arises from the different chemical Fpotentials near the dislocations and in the adjacent layers next

Nanoscale CaF2/BaF2 Heterolayer Structures

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Figure 4. Distribution of cation-cation distances calculated for several (100) layers of the (100) CaF2-BaF2 heterolayer model as obtained after relaxation and annealing to 300 K. The cation-cation distances in bulk CaF2 and BaF2 are shown in blue and green, respectively. The black curve corresponds to the distance distribution at the CaF2-BaF2 interface, whereas the distance profile a single (100) layer above/below the interface is illustrated in red.

Figure 3. (a) Density profile of the fluoride ions along the [100] direction as obtained from a snapshot of the 800 K simulation run. The inset highlights the core region of the interface (see also Figure 2). At the interface the fluoride density is lower than the average of the two bulk values (dashed line). This accounts for a displacement of fluoride ions (in average 0.15/nm2) into the BaF2 layer adjacent to the (100) interface. Moreover, about 0.025% F- donation (on average per (100) layer, not visible in the Figure) from the bulk BaF2 phase to the interface was observed. The overall F- donation from the BaF2 bulk phase to the interfaces is accumulated from roughly 10 (100) layers and amounts to about 0.04/nm2. (b) Density profile of the fluoride ions along the [111] direction as obtained from a snapshot of the 800 K simulation run. At the interface the fluoride density is lower than the average of the two bulk values (dashed line). This accounts for a donation of fluoride ions (on average 0.5/nm2) from the interface into the adjacent (111) layers. The average donation of F- ions from the bulk BaF2 layer to the interface was found as about 0.075% per (111) layer. The inset highlights the charge distribution of the BaF2 bulk region for the randomly chosen snapshot. The overall F- donation from the BaF2 bulk phase to the interfaces is accumulated from roughly 10 (111) layers and amounts to an average of about 0.25/nm2. (c) Density profile of the fluoride ions along the [110] direction as obtained from a snapshot of the 800 K simulation run. Unlike the (100) and (111) sandwich models, the sandwich of (110) layers exhibits no interfacial fluoride layers. The core interfacial region is there much larger compared to the (100) and (111) interfaces (see also Figure 2). The donation of fluoride ions (on average 0.6/nm2) reflects ion transfer from the surface of the CaF2 block to the adjacent BaF2 layers. The donation of F- ions from the bulk BaF2 layer to the interface was found as about 0.1% per (110) layer. The overall F- donation from the BaF2 bulk phase to the interfaces is accumulated from roughly 10 (111) layers and amounts to an average of about 0.3/nm2.

Figure 5. Profile of the spacing of the (100) layers of the BaF2-CaF2-BaF2 heterolayer structure at 300 K. Qualitatively similar distortions are observed for the (110) and (111) sandwich models. The core region of the interface is marked according to the layers illustrated in Figures 2 and 3a.

to the interface. Figures 3a-c indicate charge adsorption at the contact plane at the expense of a counter charge in adjacent space charge regions. In fluoride systems, this process has been assumed to occur in micro- and nanocrystalline CaF2 and nonannealed CaF2/BaF2 interfaces.24,25,27 (ii) The redistribution of the mobile ionic species because of the different standard chemical potentials of fluoride interstitials/Vacancies in BaF2 and CaF2, involving space charge zones in both materials. This mechanism was considered to be dominant in the annealed CaF2/ BaF2 heterostructures.13,16 In principle, both aspects are accessible to our simulations. While the atomistic models are particularly suited for exploring the local interfacial core effect originating from specific atomic constellations, the investigation of the redistribution of fluoride ions near the bulk center suffers from limited statistics due to limited simulation time scales. This particularly applies to ion transport in the less conductive CaF2 phase. In the (100) and (111) heterolayer structures, the BaF2/CaF2 slabs are separated by an interfacial layer of fluoride ions, as seen in Figure 2 (and also becomes obvious later in Figure 3a). The columns denoted by 1, 2, 3 have to be considered as a region with varied structure (varied standard chemical potential) and are subsumed under the interfacial core (see also below, Figure 5). These layers may be attributed to neither of the two bulk phases. An estimate of the local fluoride concentration in

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Figure 6. (a) Profile of the ion conductivity for the (100) heterolayer model at 800 K. The local conductivity was calculated on the basis of individual (100) layers for which the mean-square displacement of the fluoride ions were explored from 100 ps runs. The dashed and the dotted lines indicate the conductivity in bulk BaF2 and CaF2 as obtained from experiments, respectively.13 The core region of the interface is marked according to the layers illustrated in Figures 2 and 3a. Refer to the text for a discussion of the conductivity profile. (b) Same as (a) but for the (111) heterolayer model. (c) Same as (a) but for the (110) heterolayer model.

the electroneutral stage could hence be the arithmetic average of the bulk values (dashed lines in Figures 3a, b). In that core region we observe a significant F- excess; this is essentially due to the excess in column 1. For the (110) heterolayer structure, no interfacial layer of fluoride ions is available. This dissimilarity arises as a consequence of the different lattice cuttings. The core region extends over a greater distance, as also seen by the concentration profile illustrated in Figure 3c. (In the core region, the fluoride concentration is reduced in the interfacial CaF2 layer, whereas the interfacial BaF2 layer and, to an even larger extent, the BaF2 layer adjacent to the interface exhibit an increase in fluoride concentration.)

Zahn et al. Apart from the dislocations shown in Figure 2, the rationalization of the interfacial core effect should also involve local lattice distortions as illustrated in Figures 4 and 5. By the example of the (100) interface, the different lattice spacing in the bulk and at the interface was calculated. The occurrence profile of cation-cation distances in different (100) layers is shown in Figure 4. Parallel to the interface, only the contact layers of Ba2+ and Ca2+ ions exhibit strong distortions compared to the bulk. Normal to the interface, changes in the spacing of (100) layers are observed at much larger range (Figure 5). We furthermore calculated the ionic conductivity on the basis of the mean-square displacements sampled for individual layers, separately. As illustrated in Figures 6a-c, the interfaces dramatically affect the ionic conductivity over length scales of up to about 2 nm. However, also beyond this distance from the interface, ionic conductivity is observed to be much larger than the bulk level. This phenomenon may be attributed to the increased concentration of fluoride vacancies in the BaF2 slabs as suggested on the basis of the space charge and Gouy-Chapman models.16,17 The steep increase very close to the geometric boundary is attributed to vacancies enriched at/near the dislocation cores. While F- interstitials are even more abundant in the core region, the interstitials are pinned and do not contribute to the ionic conductivity. Indeed, the conductivity profile may be taken as proportional to the local concentration of F- vacancies. Mapping this by a laterally homogeneous situation, the profile is not far from a Gouy-Chapman model with a debye length of 2.5 nm. This length was calculated on the basis of the adsorbed charges and assuming the intrinsic disorder predicted by the Frenkel constant given in ref 26. The corresponding space charge potential would be 430 mV. In the CaF2 layer (debye length of ∼16 nm) the thermodynamic model predicts an increase of F- interstitials which could not be observed from the molecular dynamics simulations. This may be attributed to the much smaller mobility in CaF2 which necessitates waiting times that are too long to be covered by the molecular dynamics simulations. How far this kinetic hindering causes the donation of fluoride ions from the BaF2 layer to be halted by the interface and how far the interfacial core effect corresponds to local equilibrium cannot be detailed here. Note that both effects, the charge absorption by core and adsorption by a neighboring phase, have been described in ref 27 and have both been experimentally verified. The interfacial core effect is well established in polycrystalline systems (e.g., CaF2, AgCl, SrTiO3) as well as at heterophases (e.g., BaF2/ Al2O3, AgCl/Al2O3). In the context of the heterostructures, the core effect was also considered, but especially for nonannealed samples. Arguments that favor the bilateral redistribution for the annealed heterostructures are the independence of the interfacial crystallography and the better fitting of the perpendicular measurements.14,16 From our simulations, the average depletion of fluoride ions in the center of the BaF2 slabs was found to vary from 0.025% to 0.1% depending on the type of the interface. As already mentioned, in the experiments fluoride donation and ionic conductivities are independent of the interface type (only (111) and (110) were explored so far). This discrepancy again hints at shortcomings of the molecular dynamics simulations which can only partially describe the concentration relaxation according to the effect of different chemical potentials. Indeed, as the migration of fluoride interstitials into the CaF2 slab is elusive, only the interplay of the chemical potentials of the BaF2 layer and the interfacial core can be observed.

Nanoscale CaF2/BaF2 Heterolayer Structures Unlike the mean-field models which are based on the dynamical equilibrium of all ion transfer processes, the healing/ annealing cycles cannot account for long-term annealing (as accessible to dedicated experiments). While other structural features appear reasonably converged, insufficient relaxation applies to the CaF2 layer, for which ionic mobility is much smaller compared to BaF2. In terms of the interfacial structures, our model exhibits only dislocations that are physically necessary to accommodate the two single-crystalline layers of different lattice constants, similar to long-term annealed BaF2/ CaF2 heterolayers. Moreover, the molecular dynamics calculations here correspond to the Gouy-Chapman situation because of the high investigated temperature (800 K) and the absence of impurities in the model systems. However, in terms of the conductivity properties, the molecular dynamics simulations indicate a stronger role of the interfacial core characterized by F- transfer from BaF2 to the interface, preceding the equilibrium phase transfer process. Conclusion Atomistic models of CaF2/BaF2 heterolayers involving (100), (110), and (111) interfaces were explored. Our molecular dynamics simulations are based on naive starting structures which were optimized from several heating/annealing cycles. As a consequence, cationic lattice distortion, dislocations, and its interplay with local accumulation/depletion of the mobile ionic species are investigated in an unbiased manner. The two phenomena which account for the fluoride concentration profile and local ionic conductivity were addressed. Apart from a fluoride donation from BaF2 to CaF2 driven by different chemical standard potentials, the present work offers profound insights into the adsorption effect of the interface structure. This interfacial core effect may superimpose the donation of fluoride ions from the BaF2 layer to the CaF2 layer. But it may also be the precursor of a final equilibration. The fact that the excess fluoride ions are essentially accumulated at the interface may be related to the much lower ionic mobility in CaF2. Nevertheless, the molecular dynamics simulations provide qualitative insights into the mechanisms governing ionic conductivity in CaF2/BaF2 heterolayers in concordance to the experiments. In

J. Phys. Chem. C, Vol. 113, No. 4, 2009 1319 particular, the conductivity enhancement caused by the enrichment of mobile fluoride vacancies in the space charge zones of BaF2 is very close to the experimental results. Acknowledgment. D.Z. gratefully acknowledges highperformance computing resources provided by the ZIH Dresden. References and Notes (1) J.Maier, J. Nat. Mater. 2005, 4, 805. (2) Tuller, H. L. Solid State Ionics 2000, 131, 142. (3) Schoonman, J. Solid State Ionics 2005, 135, 5. (4) Zhukovskii, Y. F.; Balaya, P.; Kotomin, E. A.; Maier, J. Phys. ReV. Lett. 2006, 96, 058302. (5) Tscho¨pe, A.; Sommer, E.; Birringer, R. Solid State Ionics 2001, 139, 255. (6) Chiang, Y.-M.; Lavik, E. B.; Kosacki, I.; Tuller, H. L.; Ying, J. Y. Appl. Phys. Lett. 1996, 69, 185. (7) Kim, S.; Maier, J. J. Electrochem. Soc. 2002, 149, J73. (8) Balaya, P.; Jamnik, J.; Fleig, J.; Maier, J. Appl. Phys. Lett. 2006, 88, 062109. (9) Guo, X.; Pithan, C.; Ohly, C.; Jia, C.-L.; Dornseiffer, J.; Haegel, F.-H.; Waser, R. Appl. Phys. Lett. 2005, 86, 082110. (10) Peters, A.; Korte, C.; Hesse, D.; Zakharov, N.; Janek, J. Solid State Ionics 2007, 178, 67. (11) Li, H.; Richter, G.; Maier, J. AdV. Mater. 2003, 15, 736. (12) Guo, Y.-G.; Lee, J.-S.; Maier, J. AdV. Mater. 2005, 17, 2815. (13) Sata, N.; Eberman, K.; Eberl, K.; Maier, J. Nature 2000, 408, 946. (14) Guo, X. X.; Sata, N.; Maier, J. Electrochim. Acta 2004, 49, 1091. (15) Guo, X. X.; Maier, J. Surf. Sci. 2004, 549, 211. (16) Guo, X. X.; Matei, I.; Lee, J. S.; Maier, J. Appl. Phys. Lett. 2007, 91, 103102. (17) Guo, X. X.; Matei, I.; Jamnik, J.; Lee, J.-S.; Maier, J. Phys. ReV. B 2007, 76, 125429. (18) Nomura, K.; Kobayashi, M. Ionics 2003, 9, 64. (19) Sayle, D. C.; Doig, J. A.; Parker, S. C.; Watson, G. W. Chem. Commun. 2003, 1804. (20) Sayle, D. C.; Doig, J. A.; Parker, S. C.; Watson, G. W. Phys. Chem. Chem. Phys. 2005, 7, 16. (21) Adams, S.; Tan, E. S. Solid State Ionics 2008, 179, 33. (22) Hochrein, O.; Zahn D. Solid State Ionics, in press. (23) Jin-Phillipp, N. Y.; Sata, N.; Maier, J.; Scheu, C.; Hahn, K.; Kelsch, M.; Ru¨hle, M. J. Chem. Phys. 2004, 120, 2375. (24) Puin, W.; Rodewald, S.; Ramlau, R.; Heitjans, P.; Maier, J. Solid State Ionics 2000, 131, 159. (25) Saito, Y.; Maier, J. J. Electrochem. Soc. 1995, 142, 3078. (26) Guo, X. X.; Maier J. Submitted for publication, 2008. (27) Guo, X. X.; Maier J. Submitted for publication, 2008.

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