J. Phys. Chem. C 2008, 112, 17877–17882
17877
On the Low-Temperature Oxidation and Ultrathin Oxide Growth on Zirconium in the Presence of Atomic Oxygen: A Modeling Study Subramanian K. R. S. Sankaranarayanan* and Shriram Ramanathan HarVard School of Engineering and Applied Sciences, HarVard UniVersity, Cambridge, Massachusetts 02138 ReceiVed: June 2, 2008; ReVised Manuscript ReceiVed: August 20, 2008
Variable charge molecular dynamics simulations are used to investigate oxidation kinetics and nanoscale oxide growth on Zr(0001) surfaces due to atomic and molecular oxygen. Oxidation kinetics using atomic oxygen were significantly enhanced and resulted in an oxide scale with self-limiting thickness of ∼20-22 Å in the simulated low-temperature range of 300-600 K. This represented a 2-fold increase over molecular oxygen. Enhanced oxidation kinetics resulted from lowering of activation energy barrier by 0.46 eV in the case of atomic oxygen. Structural and dynamic correlations indicate that the oxide growth is primarily inward in both cases with oxygen diffusivities being ∼88% higher for oxidation in atomic oxygen. Our analysis indicated the formation of an oxide film with O/Zr ratio varying from 1.74 to 1.92 in the 300-600 K range in the presence of atomic oxygen, whereas that formed by natural oxidation was substoichiometric and oxygen deficient with O/Zr values varying from 1.42 to 1.57 in the 300-600 K temperature range. The simulation results are consistent with previously reported experimental investigations. I. Introduction Ultrathin metal oxides of zirconium and its alloys find applications as corrosion-resistant coatings,1 alternate gate dielectrics in advanced transistors,2 electrolyte membrane for advanced solid oxide fuel cells,3 and also as fuel cladding material for light-water nuclear reactors and pressure tube materials for heavy-water nuclear reactors.4 Such applications require precise control on the formation and quality of the oxide film. Recent experiments on oxide formation using activated oxygen have indicated dramatic enhancements in the rates of oxidation, which in turn has led to significant improvement in the quality as well as the electrical, optical, chemical, and mechanical properties of the oxide film formed.5-7 Additionally, hyperthermal oxidation of metals such as Zr is of great interest for space applications and requires a detailed understanding of the initial stages of oxide growth and morphology.8 One of the main constituents of thermosphere, where low Earth orbits (LEO) are located, is atomic oxygen. This atomic oxygen is formed mainly in the ionosphere through dissociation by UV radiation and impinges the space vehicles’ surface with incident flux of 1015-1016 atoms/cm2 s.9,10 Zirconium has been widely used as space-craft material and has been exposed to atomic oxygen in space on NASA’s Long Duration Exposure Facility.9 Understanding oxide growth mechanisms and kinetics in atomic oxygen is therefore of great scientific and technological interest. While there is limited experimental data differentiating the initial oxidation kinetics of different metals using atomic oxygen (O) and natural oxidation (O2), to the best of our knowledge, there are presently no theoretical models to explain these differences quantitatively.7,10-12 Low-temperature oxidation of metals has been less studied in comparison with the intermediate- and high-temperature oxidation regimes.13,14 Understanding differences in the low-temperature metal oxidation mechanism in the presence of O and O2 as well as the * Corresponding author. E-mail:
[email protected].
atomistic details of the growth kinetics, oxide microstructure, and the limiting thickness of the oxide films at nanoscale is hence of importance. In this work, the initial stages of oxidation of Zr(0001) surfaces at low temperatures by atomic oxygen species is investigated in detail and the differences in the oxidation mechanism, growth kinetics, and the nanoscale oxide structure formed between natural oxidation and activated oxygen are elucidated. We investigate the structural and dynamical correlation functions in the oxide film as well as the evolution of charges, self-limiting oxide thickness, atomic diffusivities, and local stresses for the two oxidation conditions. II. Computational Details The MD simulations are based on the modified charge transfer ionic potential (CTIP)15 model coupled with the embedded atom method (EAM)16 for modeling the metal/metal oxide systems. This potential model allows for variable and dynamic charge transfer between atoms and is capable of treating both metallic and ceramic systems as well as bond formation and bond breakage involved in oxidation processes. Such a charge transfer potential model (Streitz-Mintmire) has been previously used by Campbell et al. in their simulations of atomic and molecular oxidation of aluminum nanoclusters.17 The details of the potential model adopted in this work have been described in refs 15 and 18-20. The setup of the oxidation simulations are as follows: A slab of hexagonal close-packed (hcp) Zr containing approximately 500 atoms with dimensions (32 × 16 × 26 Å) was formed from an hcp unit cell. The surfaces were generated by artificially increasing the x-direction and introducing two vacuum slabs on each side of the metal substrate (Figure 1). This unit cell was repeated infinitely though 3-D space by applying periodic boundary conditions. This configuration allowed for accurate computation of the Coulomb interaction by the Ewald summation technique.21 The oxidation of the Zr metal substrates is
10.1021/jp804872u CCC: $40.75 2008 American Chemical Society Published on Web 10/23/2008
17878 J. Phys. Chem. C, Vol. 112, No. 46, 2008
Figure 1. Schematic showing the unit cell of substrate and the vacuum slabs surrounding it. The box length along the z-direction (Lz) is taken to be the same as the y-direction (Ly).
initiated by introducing either 100 O or 50 O2 molecules in the vacuum slab with their x-, y-, and z-positions chosen randomly. The oxygen number density is maintained constant at approximately 0.004/Å3 in both the cases. The velocities of O and O2 are chosen from a Maxwell-Boltzmann distribution corresponding to the required temperature. Additionally, reflecting boundary conditions are imposed on the atoms and molecules that might reach the simulation box limit. The equations of motion are integrated with time steps ∆t ) 1 fs for both shortrange and long-range forces. The atomic charges were updated every 100 time steps such that the electrostatic energy is minimized subject to the constraint of electroneutrality. Canonical MD simulations employing the Nose-Hoover thermostat is utilized to study low-temperature metal oxidation in the 300-600 K range. The MD simulations were stopped when fragments of oxide species are ejected into the gas phase owing to localized melting of the surfaces. In the present work, despite the use of the Nose-Hoover thermostat to dissipate heat, we observe that beyond 150-200 ps of simulation time, the oxide structure starts melting at the surface region. This is attributed to the accumulation of dissociated oxygen at the metal surface upon reaching the limiting regime, when their intake into the substrate is impeded. Such localized melting upon reaching the saturation thickness has also been observed in MD simulations of oxidation of Al and Al-Ni surfaces.20,22,23 III. Results and Discussion III.1. Oxidation Kinetics and Nanoscale Oxide Growth. The kinetics of nanoscale oxide growth on Zr(0001) surfaces using atomic and molecular oxygen is presented in this section. Figure 2 shows the evolution of the self-limiting oxide thickness for Zr oxidation performed using atomic oxygen and molecular oxygen respectively in the 300-600 K temperature range. The oxide film thickness shown in Figure 2 is defined as the distance between the x-positions of the outermost zirconium atoms and the innermost oxygen atom in the simulated substrates. The oxide thickness in both the cases shows an initial rapid increase followed by a slow growth phase. We find that the oxidation
Sankaranarayanan and Ramanathan and oxide growth kinetics at low temperatures is significantly enhanced in the presence of activated atomic oxygen. The selflimiting thickness of the oxide film formed using atomic and molecular oxygen correspond to approximately 2.1 and 1.0 nm, respectively, at 300 K. An increase in temperature from 300 to 600 K did not significantly alter the self-limiting oxide thickness formed in the two cases. However, it does increase the oxidation rate and results in an earlier onset of the saturating or slow growth rate regime. Such a significant enhancement in the oxidation kinetics and nanoscale oxide growth rate using atomic oxygen (13%) was also observed by Campbell et al. in their simulation study on aluminum nanocluster oxidation.17 The simulated oxidation kinetics of molecular oxidation can be compared with the experimental data available for lowtemperature natural oxidation of Zr surfaces. We find that the simulated self-limiting thickness of ∼ 1 nm agrees well with the 1.2 nm thickness obtained experimentally for O2 oxidation at 373 K by Jeurgens et al.24 Similarly, the simulated selflimiting thickness of the oxide film is also in good agreement with the experimentally determined average total oxide film thickness of ∼1-1.25 nm for oxidation of bare Zr substrate at 304 K and partial oxygen pressures of 1.3 × 10-7-1.3 × 10-5 Pa. In another investigation by Lyapin et al., the experimentally obtained oxide thickness after 1000 s of oxygen exposure time was found to vary from ∼1 to 2 nm in the 373-573 K range.25 As observed in our simulations, the initial stages of oxidation in their investigated temperature range were similar. The differences arise for film growth beyond 1.5 nm thickness for longer oxidation times much beyond 1000 s.26 However, such longer time scales are not accessible to the current MD simulations, making it difficult to make a direct comparison. As far as the atomic oxidation of Zr is concerned, to the best of our knowledge, there is no available experimental data in the simulated low-temperature range. However, the enhancement in oxidation kinetics as well as self-limiting thickness observed in our simulations is consistent with that observed for lowtemperature atomic oxidation of Ag and Si(110) surfaces.27-29 In both cases, the growth of the oxide scale on Zr surface is primarily inward and is attributed to the movement of anions toward the interior of the metal substrate (Figure 3). We find that the inward and the outward growth of the oxide saturate at 14.58 and 5.16 Å, respectively, for oxidation using atomic oxygen and 6.50 and 4.04 Å, respectively, for natural oxidation at 300 K. In both the cases, the inward growth saturates later than the outward. Furthermore, an initial layer-by-layer growth of the oxide is observed in the simulated temperature range for both the cases. This agrees well with reported experimental observations.30 Additionally, we have also studied the charge variation of surface atom for the two cases. For one such Zr
Figure 2. Variation of oxide film thickness with oxidation time in (a) O and (b) O2 environment at low temperatures.
Oxidation and Ultrathin Oxide Growth on Zirconium
J. Phys. Chem. C, Vol. 112, No. 46, 2008 17879
Figure 3. Inward and outward growth of the oxide film for (a) O and (b) O2 environment at 300 K. The oxide growth along the -y-axis represents the inward growth and that along the +y-axis represents the outward growth of the oxide film. The total oxide thickness resulting from the inward and outward oxide growth is also shown.
(
dL ) C exp dt
1 W0 - qaE + λL 2 kBT
)
(3.2)
where kB is the Boltzmann constant and C is a constant. The solution to the above equation yields a direct logarithmic growth law and is given by
L(t) )
( )
kBT ln[1 + µ(T)t] λ
(3.3)
The term µ(T) is a temperature-dependent term and is defined Figure 4. Variation of the structure term (λ) obtained by fitting the oxidation kinetic curves in Figure 2 to eq 3.6.
atom located at the metal surface, it took approximately 15 ps to become oxidized and attain charge values close to +3.0 e. Our simulation analysis indicates no significant difference between the charge variation with time for a similarly located surface atom in case of atomic and natural oxidation. The theory of low-temperature oxidation kinetics in ultrathin films may be utilized in conjunction with the simulation data derived from the oxidation kinetic curves shown in Figure 2 to get an estimate of the activation energy barrier for oxidation on Zr surfaces using O and O2. The expression for potential (W) to be overcome in the case of a field-assisted migration of an ion between two adjacent sites is given as31
1 W ) W0 - qaE + λL 2
(3.1)
In the above equation, W0 represents the intrinsic barrier for ionic jumps between two positions in the oxide film, q represents the charge on the ion, 2a represents the jump length, L is the oxide film thickness, and λ is a term that depends on the oxide structure. The second term on the right-hand side represents the lowering of the activation energy barrier by an electric field E across the oxide film, and the structure term (λ) represents structural changes in the oxide film associated with the film growth. One of the possible mechanisms for oxide growth involves ion movement via extended defects or structural channels in the oxide layer. As the oxide film thickens, ion entry into the oxide is considered to become more difficult because of a closing or consolidation of these channels. The activation energy is therefore larger for thicker oxide films and the change is proportional to the oxide film thickness. The resulting rate equation is given by31
by
( )
(
λ µ(T) ) C exp kBT
1 W0 - qaE 2 kBT
)
(3.4)
For large enough simulation times, i.e., µ(T)t > 1, eq 3.3 corresponds to a linear dependence of oxide thickness L(t) on ln(t) as shown below:
L(t) )
( )
( )
kBT kBT ln[µ(T)] + ln(t) λ λ
(3.5)
It is possible to compute the thickness of the oxide film at any given time instant as shown in Figure 2:
L(t) ) R ln(t) + β
(3.6)
Parameters R and β are defined by R ) kBT/λ and β ) kBT/λ ln[µ(T)]. After fitting the oxidation kinetic curves in Figure 2 to eq 3.6, the estimates of the two parameters R and β can be obtained. Utilizing these two parameters, it is possible to estimate the structure term λ and µ(T). For example, the variation in structure term λ with temperature T is shown in Figure 4 for the two surfaces. The structure term is a linear function of temperature and can be described by the following equations for oxidation in O and O2 environment, respectively.
λ ) 0.076T + 117 λ ) 0.11T + 38
(3.7) (3.8)
It can be seen from Figure 4 that the structure term λ is higher for O2 oxidation in comparison to atomic oxidation. On the basis of the activation energy defined by eq 3.1, increase in λ results in increasing the energy barrier required for oxidation. Hence, the increase in structure term results in reduced oxidation rates for natural oxidation. Similarly, the term µ(T)kBT/λ represents the Arrhenius dependence on the temperature, as seen in eq
17880 J. Phys. Chem. C, Vol. 112, No. 46, 2008
Sankaranarayanan and Ramanathan
Figure 5. Snapshots showing the enhancement in oxidation and resulting self-limiting thickness due to presence of atomic oxygen. (a) and (b) represent the oxide film thickness at 200 ps for O and O2 environments at 300 K. Zirconium atoms are shown in blue and oxygen in red.
3.4. The fits of µ(T)kBT/λ term to the inverse of temperature allow us to deduce the following equation for atomic and natural oxidation:
( (
) )
1 W0 - qaE 2 -1258 C exp ) exp + 2.77 kBT T
)
(3.9)
1 W0 - qaE 2 -337 ) exp C exp + 2.09 kBT T
)
(3.10)
(
(
Using the Arrhenius fits shown in eqs 3.9 and 3.10, it is possible to get an estimate of the term W0 - 1/2qaE. We find this to be 0.1084 ( 0.01 and 0.0290 ( 0.01 eV for atomic and natural oxidation, respectively. If the value of the electric field E is known, then it is possible to get the exact estimate of the energy barrier W0. The electric field lowers the energy barriers for the outward “hopping” of cations into and through interstices of the oxygen ion arrangement of the developing oxide film and is given by E ) Vk/L, where Vk represents the established potential and L represents the thickness of the oxide film. On the basis of the low-temperature oxidation studies of zirconium by Juergens et al., it is possible to get an estimate of the established kinetic potential (Vk ∼ 1.8 V).24,32 In the present simulations, the self-limiting oxide film thickness corresponding to atomic and natural oxidation corresponds to approximately 2 and 1 nm, respectively. Additionally, the average charge q of the zirconium atoms in the oxide film interior was found to be approximately 3.5e and 3.4e for O and O2 case, respectively. The jump distance was approximated from the first peak distance in the pair distribution function for Zr-Zr (∼ 3.2 and 3.4 Å for O and O2 case, respectively). The field term 1/2qaE was therefore found to be 0.504 and 1.04 eV for O and O2 oxidation, respectively. Thus, the activation energy barrier (W0) for O oxidation was found to be approximately 0.61 ( 0.01 eV, which was lower than that obtained for O2 oxidation 1.07 ( 0.01 eV. This is comparable with the experimentally obtained activation energies of 0.65 and 1.2 eV in the temperature range 873-1123 K for O and O2 oxidation of Zr.24 The decrease in the activation energy barrier appears to be responsible for the increased oxidation rates shown in Figure 2 and the enhanced self-limiting oxide thickness observed in Figure 5 for O oxidation when compared to O2. III.2. Oxide Scale Analysis. Structural and dynamical correlation analysis of the oxide structure indicates significant charge transfer to occur between the Zr and O atoms for both atomic and molecular oxidation (Figure 6). The Zr atoms are weakly charged close to the metal-oxide interface and greater than +3.5 e in the oxide interior, and a small decrease is also observed at the oxide-gas interface. Similarly, the oxygen atoms are weakly charged close to the oxide-gas interface and decrease to higher negative values in the oxide interior. The
Figure 6. Charge distribution in the Zr/O system taken at 150 ps of simulation time for atomic oxidation of Zr at 300 K. The charge distribution is shown as charge of each atom (e units where e ) 1.6 × 10-19 C) versus x-distance in the sample.
charges on oxygen atoms then decrease to lesser negative values close to the metal oxide interface. The reduction in magnitude of the oxygen charges near the oxide gas interface is attributed to the insufficient concentrations of cations to ionize the oxygen in the oxygen-rich surface region. Additionally, the oxygen charge close to the metal-oxide interface is also low, since they are ionized by cations that are weakly charged. Thus, the charge distribution in the metal oxide film is not homogeneous. We also calculated the atomic diffusivities based on the mean square displacements computed over 1 ps interval for oxidation at 300 K. Our analysis of the atomic diffusivities in the oxide region for O and O2 cases indicates that, during the first 100 ps, the diffusivity of oxygen is 21-88% higher for O oxidation. Upon reaching the self-limiting thickness, the oxygen diffusivities for O and O2 oxidation correspond to 5.1 × 10-9 and 3.1 × 10-9 cm2/s, respectively. Similarly, the diffusivity of Zr in the oxide region was also found to be higher for O than the O2 case. Furthermore, our analysis of diffusion of oxygen and zirconium atoms for the two cases indicates that the in-plane and out-of-plane components are about 40-60% higher (within 100 ps) for O oxidation at 300 K. While the higher in-plane diffusivities allow for increased self-limiting oxide thickness, the higher out-of-plane component causes uniformity in the oxide thickness and morphology in the case of O oxidation. This can be seen more clearly in the oxygen density profiles shown in Figure 7 for the two cases. We find that natural oxidation (O2) of Zr leads to a gradation of oxygen stoichiometry across the oxide thickness such that the oxygen density is low at the metal-oxide interface and higher at the oxide-gas interface. Thus, the oxide produced by natural oxidation is substoichiometric and oxygen-deficient. Oxidation using activated atomic oxygen produces a more uniform, stoichiometric, and thicker oxide film, which is crucial for good electrical performance.33 These results are in excellent agreement with the experimental observations of room temperature Zr oxidation.11
Oxidation and Ultrathin Oxide Growth on Zirconium
Figure 7. Atomic density profiles calculated for oxidation in O and O2 environments at 300 K.
We further find that the oxide scale formed in both cases is amorphous in nature. To the best of our knowledge, the differences between the amorphous oxide scale formed in the two cases are not known. We have analyzed the oxide structure using partial pair distribution functions (PDF), coordination numbers, and bond-angle distributions. Parts a and b of Figure 8 show the Zr-O PDF in the O and O2 oxide scale interior as well as the oxide-gas interface, respectively. It is seen that the position of the first peak in gZrO(r) gives the Zr-O bond length to be around 2.4 Å for O oxidation. On the other hand, the Zr-O PDF in the case of O2 oxidation shows a distribution of bond lengths from 2.16 to 2.4 Å in the oxide scales. The simulated bond lengths agree well with the reported average Zr-O bond lengths of 2.28 Å for oxide structure formed on Zr(0001).34 It can be seen that there is no significant difference in the Zr-O bond length for the oxide interior and oxide gas interface in both the cases. The corresponding coordination numbers for Zr, obtained by integrating gZrO(r) up to 3.2 Å, are 2.5 and 2.6 for O oxidation in the oxide interior and oxide-gas interface, respectively, and 3.1 and 3.4 for O2 oxidation in the oxide interior and oxide-gas interface, respectively. Parts c and d of Figure 8 show O-Zr-O bond-angle distribution in the interior of the oxide scales as well as the
J. Phys. Chem. C, Vol. 112, No. 46, 2008 17881 oxide-gas interface for Zr oxidation using O and O2, respectively. In case of O oxide scale, we find that there are two distinct peaks at 60° and 109° in the bond-angle distribution throughout the oxide structure. The peak at 109° is indicative of tetrahedrally coordinated structure. A slight shift in the peaks to smaller angles is observed at the oxide-gas interface, reflective of a decrease in the zirconium density. Similarly, at the metal-oxide interface the peaks shifted to slightly larger angles, owing to the decrease in oxygen density. On the other hand, the O-Zr-O bond-angle distribution in the O2 oxide scale shown in Figure 8d is very different from that of Figure 8c and has multiple peaks in both the oxide interior as well as the oxide-gas interface, reflecting the possibility of the existence of multiple nonstoichiometric oxide species. The substoichiometric oxide formation in the case of natural oxidation might be the result of the oxygen-deficient environment observed across the oxide scale (Figure 7). We further analyze the oxide film composition expressed as the average O/Zr ratio at different temperatures (300-600 K) for the two cases. The overall O/Zr ratio of the self-limiting oxide film increases with increasing temperature. For O, the O/Zr ratio saturates close to the stoichiometric ratio of 2 and varies from approximately 1.74 at 300 K to 1.92 at 600 K. On the other hand, the corresponding O/Zr ratio for the O2 oxide films are significantly lower than the stoichiometric ratio and varies from approximately 1.42 at 300 K to 1.57 at 600 K. This lower O/Zr ratio is attributed to slower oxidation kinetics, leading to O-deficiency of the oxide films, especially in the regions close to the metal/oxide interface. Such substoichiometric oxygen-deficient oxide films are known to have poor electrical conductivity, reduced corrosion resistance, as well as very poor thermal, chemical, and mechanical stability.31 For example, when the oxide scale of high-k materials such as ZrO2 becomes oxygen deficient, leakage currents increase drastically, leading to unwieldy power consumption and reduced device reliability. Similarly, oxygen-deficient ZrO2 also have increased O2- vacancy concentration in the oxide lattice, which causes increased ion diffusion through the oxide lattice, thereby
Figure 8. Pair distribution function for Zr-O calculated at 150 ps for oxidation in (a) O and (b) O2 environments at 300 K. The corresponding (O-Zr-O) bond angle distribution function in (c) O and (d) O2 environment at 300 K is also shown.
17882 J. Phys. Chem. C, Vol. 112, No. 46, 2008 drastically reducing its corrosion resistance. Oxidation using atomic oxygen thus provides a better alternative to natural oxidation toward developing ultrathin oxide films with stoichiometric metal/oxygen ratio and having superior material properties. IV. Conclusion In conclusion, we report the first variable-charge molecular dynamics simulation study of Zr oxidation by atomic (O) and molecular (O2) oxygen. These simulations include dynamic charge transfer among atoms and investigate the differences in oxidation kinetics, initial stages of zirconium oxide growth as well as the structure and morphology of the oxide films formed using O and O2. Structural analysis reveals enhanced selflimiting thickness using atomic oxygen (∼20 Å for O vs 10 Å for O2) for the oxide film obtained after 200 ps of simulation time at 300 K. The lower activation energy barrier for ion migration (∼0.62 eV for O vs 1.07 eV for O2) is likely responsible for the observed increase in the oxide growth kinetics using O. We find that the Zr and oxygen diffusivities in the oxide are about 40-60% higher for O than O2. The higher atomic diffusivities result in a more uniform oxide thickness as well as oxygen stoichiometry across the oxide film for oxidation using O. Analysis of the oxygen density profiles indicates a gradation in oxygen stoichiometry across the oxide film formed using O2. This results in a substoichiometric and oxygendeficient oxide which increases as we pass through the oxide from oxide-environment interface to regions close to the metal-oxide interface. The same is reflected in the calculated O/Zr composition ratio, bond lengths, and bond angle distribution functions. The simulation results of this work are in good agreement with experimental results on low-temperature Zr oxidation.11,24 Acknowledgment. The authors gratefully acknowledge the computational facilities provided by the research computing core at University of South Florida and CNS-NNIN at Harvard University. We also thank Dr. Julian Gale for providing the molecular dynamics code GULP 3.1 and Dr. Will Smith for providing DL_POLY 2.14, which are modified and used in the current research. Financial support from the Office of Naval Research is gratefully acknowledged. References and Notes (1) Holgado, J. P.; Perez-Sanchez, M.; Yubero, E.; Espinos, J. P.; Gonzalez-Elipe, A. R. Surf. Coat. Technol. 2002, 151, 449. (2) Kim, H.; Saraswat, K. C.; McIntyre, P. C. J. Mater. Res. 2005, 20, 3125.
Sankaranarayanan and Ramanathan (3) Shim, J. H.; Chao, C.-C.; Huang, H.; Prinz, F. B. Chem. Mater. 2007, 19, 3850. (4) Cox, B. J. Nucl. Mater. 2005, 336, 331. (5) Karthikeyan, A.; Ramanathan, S. Appl. Phys. Lett. 2007, 90, 093107. (6) Tsuchiyaa, M.; Ramanathan, S. Appl. Phys. Lett. 2008, 92, 033107. (7) Ramanathan, S.; Park, C.; McIntyre, P. J. Appl. Phys. 2002, 91, 4521. (8) Reddy, M. R. J. Mater. Sci. 1995, 30, 281. (9) Brodkin, J. S.; Sengupta, L. C.; Franzen, W.; Sagalyn, P. L. Thin Solid Films 1993, 234, 512. (10) Raspopov, S. A.; Gusakov, A. G.; Voropayev, A. G.; Vecher, A. A.; Zheludkevich, M. L.; Lukyanchenko, O. A.; Gritsovets, A. S.; Grishin, V. K. J. Chem. Soc., Faraday Trans. 1997, 93, 2113. (11) Ramanathan, S.; Chi, D.; Mcintyre, P. C.; Wetteland, C. J.; Tesmer, J. R. J. Electrochem. Soc. 2003, 150, F110. (12) Ramanathan, S.; McIntyre, P.; Luning, J.; Pianetta, P.; Muller, D. Philos. Mag. Lett. 2002, 82, 519. (13) Campbell, T.; Kalia, R. K.; Nakano, A.; Vashishta, P.; Ogata, S.; Rodgers, S. Phys. ReV. Lett. 1999, 82, 4866. (14) Chang, C.-L.; Ramanathan, S. J. Electrochem. Soc. 2007, 154, G160. (15) Zhou, X. W.; Wadley, H. N. G.; Johnson, R. A.; Larson, D. J.; Tabat, N.; Cerezo, A.; Petford-Long, A. K.; Smith, G. D. W.; Clifton, P. H.; Martens, R. L.; Kelly, T. F. Acta Mater. 2001, 49, 4005. (16) Finnis, M. W.; Sinclair, J. E. Philos. Mag. A 1984, 50, 45. (17) Campbell, T. J.; Aral, G.; Ogata, S.; Kalia, R. K.; Nakano, A.; Vashishta, P. Phys. ReV. B 2005, 71, 205413. (18) Zhou, X. W.; Wadley, H. N. G.; Filhol, J.-S.; Neurock, M. N. Phys. ReV. B 2004, 69, 035402. (19) Streitz, F. H.; Mintmire, J. W. Phys. ReV. B 1994, 50, 11996. (20) Sankaranarayanan, S. K. R. S.; Ramanathan, S. Phys. ReV. B 2008, 78, 085420. (21) Ewald, P. P. Ann. Phys. 1920, 369, 253. (22) Hasnaoui, A.; Politano, O.; Salazar, J. M.; Aral, G. Phys. ReV. B 2006, 73, 035427. (23) Hasnaoui, A.; Politano, O.; Salazar, J. M.; Aral, G.; Kalia, R. K.; Nakano, A.; Vashista, P. Surf. Sci. 2005, 579, 47. (24) Jeurgens, L.; Lyapin, A.; Mittemeijer, E. Surf. Interface Anal. 2006, 38, 727. (25) Lyapin, A.; Jeurgens, L. P. H.; Graat, P. C. J.; Mittemeijer, E. J. J. Appl. Phys. 2004, 96, 7126. (26) Lyapin, A.; Jeurgens, L. P. H.; Mittemeijer, E. J. Acta Mater. 2005, 53, 2925. (27) Kisa, M.; Li, L.; Yang, J.; Minton, T. K.; Stratton, W. G.; Voyles, P.; Chen, X.; van Benthem, K.; Pennycook, S. J. J. Spacecraft Rockets 2006, 43, 431. (28) Kisa, M.; Minton, T. K.; Yang, J. C. J. Appl. Phys. 2005, 97, 023520/1. (29) Zheludkevich, M. L.; Gusakov, A. G.; Voropaev, A. G.; Vecher, A. A.; Kozyrski, E. N.; Raspopov, S. A. Oxid. Met. 2004, 61, 39. (30) Zhang, C.-S.; Flinn, B. J.; Norton, P. R. Surf. Sci. 1992, 264, 1. (31) Lawless, K. R. Rep. Prog. Phys. 1974, 37, 231. (32) Jeurgens, L.; Lyapin, A.; Mittemeijer, E. Acta Mater. 2005, 53, 4871. (33) Ramanathan, S.; Muller, D.; Wilk, G. D.; Park, C.; Mcintyre, P. C. Appl. Phys. Lett. 2001, 79, 3311. (34) Wang, Y. M.; Li, Y. S.; Mitchell, K. A. R. Surf. Sci. 1995, 342, 272.
JP804872U
