NANO LETTERS
Mechanically Controlled, Seeded Formation of a Nanoscale Metastable Phase in Ionic Compounds
2004 Vol. 4, No. 9 1769-1773
James W. Palko,†,‡ Murat Durandurdu,† and John Kieffer*,† Department of Materials Science and Engineering, UniVersity of Michigan, Ann Arbor, Michigan 48109, and Department of Materials Science and Engineering, UniVersity of Illinois, Urbana-Champaign, Illinois 61801 Received May 30, 2004; Revised Manuscript Received July 14, 2004
ABSTRACT Like in epitaxial and hetero-epitaxial growth, the structural order at internal grain boundaries may be used to control the nature of new phases that nucleate at such an interface. We demonstrate this concept via computer simulation. We predict the templated nucleation of a new metastable phase at the (310) symmetric tilt grain boundary in both NaCl and LiCl when subject to an external mechanical constraint. The level of applied stress allows one to control the extent to which this metastable phase grows with nanoscale precision. This interfacial seeding of structural transitions has potential to produce functionally patterned materials for novel logic and sensing devices.
In the realm of nanotechnology, where materials are assembled at a level that provides only limited access by experiments, and considering the continuously increasing precision with which novel materials must be synthesized, the predictive capabilities of materials simulation are a key asset for successful materials design. One method employed to synthesize nanostructured materials is patterned selfassembly, as achieved through templating.1-3 Templates promote spatially selective growth by displaying structural or chemical affinity toward the material deposited from a solution (or other incongruent ambient medium). As shown here, the basic premise of templating may also be applied to the transformation between two well-ordered crystalline phases, and the resulting dynamical and reversible structural transition can serve as the functional basis of the material. The case in point is a controlled transformation of alkali halides from the NaCl-structured form to a new-found metastable hexagonal polymorph. A particular grain boundary plays the role of the template that mediates the transition from the stable cubic rock salt phase of these ionic solids into the metastable hexagonal modification, thereby avoiding the alternative path leading to fracture. Using both classical molecular dynamics (MD) simulations and ab initio density functional theory calculations, we describe, for the first time, the physical properties of this hexagonal phase in NaCl and examine this mediated transformation mechanism. * Corresponding author. E-mail
[email protected], Phone (734) 7635671, Fax (734) 763-4788. † University of Michigan. ‡ University of Illinois. 10.1021/nl0491879 CCC: $27.50 Published on Web 08/10/2004
© 2004 American Chemical Society
The resulting hexagonal structure has the symmetry P63/ mmc, which is identical to that of R-boron nitride. As may be expected, this phase shows a high contrast in many of its physical properties compared to the cubic phase, as well as a high degree of anisotropy, suggesting a broad range of applications, e.g., optical and acoustic devices that take advantage of reflections at the interface and interference within the transformed layer. While this hexagonal phase has never been observed experimentally for alkali halides, evidence for the existence of structures with hexagonal symmetry in highly ionic systems has been reported in prior computational studies. For example, in simulations of heteroepitaxial growth of ultrathin films on rock salt-structured, largely ionic materials (CaO and MgO), hexagonal structures developed in surface layers in order to accommodate the dilatational strain in the films resulting from the lattice mismatches.4,5 Moreover, ab initio calculations, have shown that hexagonal configurations are stable as small clusters of alkaline earth oxides6,7 and alkali halides8 and metastable in bulk MgO.9 In our simulations, significant formation of the hexagonal phase is for the first time achieved by subjecting the starting material to a uniaxial strain normal to a particular grain boundary, which contains a slightly deformed building block of the hexagonal phase and thereby provides the seed for further transformation. In this novel approach, the level of applied stress provides tremendous control over the extent of transformation. Using MD simulations performed with the LAMMPS code,10,11 we studied the transformation behavior in both NaCl and LiCl to examine the effect of the cation-to-anion
Figure 1. Expansion of (310) tilt grain boundary into hexagonal phase. (a) Stress-strain curve with stress normal to the grain boundary. Negative magnitudes correspond to tensile stresses. Percentage of atoms with 5-fold coordination is determined from the number of atoms with exactly 5 neighbors of opposite type within 4.0 Å. (b)-(d) Snapshots of grain boundary at indicated strains.
radius ratio. We also varied the nature of the grain boundary that serves as the nucleation site for the transformation to include (310), (510), and (710) symmetric tilt boundaries. Transformation to the hexagonal phase is observed only for the (310) symmetric tilt boundary, which for NaCl is that described by Chen and Kalonji (Figure 1b).12 An important characteristic of this boundary is the presence of two distorted six-membered rings that form channels along the grain boundary. In the case of LiCl, this same structure for the (310) grain boundary is stable in our calculations at elevated temperature and pressure (e.g., 10 GPa and 600 K), while at ambient conditions the structure suggested by Duffy and Tasker for NiO, in which oppositely charged ions on the cusps of the adjacent surface steps directly confront each other, is slightly more stable.13 We applied fully periodic boundaries to the simulation cell, requiring two grain boundaries per cell. (We observe the same transformations in systems with free surfaces, except that the phase boundary is distorted near these surfaces.) The potential energy was calculated as the sum of rigid ion pair potentials with a Born-Mayer repulsive term.14 The specific values for the potential parameters used here are based on a genetic algorithm optimization by Reardon.15,16 The ions were assigned their full charges (qCation ) 1, qAnion ) -1). This form of potential has proven to be very effective in the simulation of interfaces and defects in alkali-halides and other rock salt-structured materials.4,5,12,17 A particle mesh Ewald (PME) method was employed to lessen the expense in dealing with long-range electrostatic interactions.18 The Nose-Hoover barostat19 was used to attain constant normal stress on the required faces, while the temperature was 1770
maintained using velocity rescaling. The total number of atoms in the tensile simulations is 78 400. Dimensions of the initial cells are 25 × 12 × 6 nm and 23 × 11 × 5 nm for NaCl and LiCl, respectively. The cell is strained at a constant rate normal to the grain boundaries and held at a constant compressive stress of 1 atm in all directions perpendicular to that. The system temperature is maintained at 300 K. Figure 1a shows a plot of the stress versus strain normal to the grain boundary for NaCl and LiCl. The degree of transformation may be quantified by the number of atoms with 5-fold coordination, which is also shown in Figure 1a. A small number (∼4%) of the atoms in the initial configuration are 5-fold coordinated. These are located in the grain boundaries. At first, this number increases slightly with increasing tension. The onset of substantial transformation to the hexagonal phase is marked by a rapid increase in the rate of change in the number of 5-fold coordinated atoms, as well as by minima in the stress strain curves for NaCl and LiCl at ∼5%, ∼1 GPa and ∼4.5%, 800 MPa, respectively. This apparent decrease in transformation stress from NaCl to LiCl is consistent with previous ab initio calculations, indicating that the stability of hexagonal alkali-halide clusters improves with decreasing cation-to-anion size ratio.8 After onset, the stress required for further transformation drops off in a roughly linear fashion. The true strain rate for these simulations was 5 × 108 /s. A simulation at 2 × 108 /s in LiCl shows a similar transformation stress. Figure 1b-d shows a sequence of snapshots at the state points indicated in Figure 1a, illustrating the expansion of the hexagonal phase from the grain boundary in NaCl. A movie of the transformation Nano Lett., Vol. 4, No. 9, 2004
Figure 3. (a) Unit cell of hexagonal phase showing electronic structure. Isodensity surfaces correspond to 0.0065 e-/Bohr3. (b) Three-point correlations for the hexagonal phase in the NaCl system expanded by 16% under uniaxial tensile stress. The contours represent the isointensity lines of the probability density for finding an atom at a distance r from a central atom, while the line connecting these two atoms forms an angle θ relative to a reference direction. The probability density is calculated for each atom at the origin and by choosing each of its neighbors (of opposite type) to define a possible reference direction. The resulting distribution is then normalized per atom and unit volume sampled for possible neighbors within a 5 Å radius. Crosses show the (r,θ) locations of atoms expected for an ideal unstressed structure, the size being proportional to the expected frequency. To aid the interpretation of the diagram, the dotted lines and cartoon atoms highlight the locations of atoms belonging to one hexagonal ring in the basal plane.
Figure 2. (a) Energy-volume and Gibbs free energy-pressure curves from ab initio calculations for NaCl and (b) LiCl. (c) Infrared spectra for cubic and hexagonal phases in NaCl from MD simulations (normalized by the zero frequency intensity).
is available as Supporting Information. Upon reversing the applied strain, the structure of the transformed domains fully reverts to the initial rock salt configuration, following essentially the same path in the stress-strain diagram as during forward transformation. Simulations have also been conducted with vacancies near the grain boundary as possible crack nucleation centers. For ∼0.4% vacancies in the grain boundary region of LiCl, the system behaves essentially the same as the defect-free system. The stability of both cubic and hexagonal phases for NaCl and LiCl is further investigated using ab initio density functional theory calculations performed with the ABINIT code.20,21 Both structures were relaxed at zero pressure, Nano Lett., Vol. 4, No. 9, 2004
allowing the atomic coordinates, lattice constants, and lattice angles to change independently. The hexagonal phase is found to be metastable at zero pressure. While a minor amount of deformation does take place during the relaxation, it is hardly perceptible to visual inspection and does not break the hexagonal symmetry. To further explore the stability range of the structures against isotropic deformation, they were each optimized at several volumes and fit to BirchMurnaghan equations of state. Energy-volume curves for the structures are given in Figure 2a and b. The Gibbs free energy curves of the hexagonal phase for NaCl and LiCl (also shown in Figure 2a and b) cross that of the stable cubic phase at a pressure of about -2 GPa (i.e., in the tensile regime), indicating the phase transformation points. The total energy calculations were undertaken using density functional theory within the local density approximation to electron exchange correlation.22 The Kohn-Sham orbitals were expanded on a plane wave basis set, and an energy cutoff of 40 Hartree (Ha) was employed. We adopted the normconserving pseudopotentials generated within the scheme developed by Troullier-Martins.23 Sixty-four special k-points were used for Brillouin-zone integration. The electron density was also calculated and found to segregate into a highly spherical distribution around the Cl- ions (Figure 3a), thus supporting the use of the rigid ion model in the MD simulations. The transformed phase has a primitive hexagonal unit cell of the space group (P63/mmc) with two molecular units (i.e., 2 NaCl) per unit cell (Figure 3a). Further MD simulations were conducted on this metastable phase at a hydrostatic pressure of 1 atm and 300 K, assuming orthogonal periodic boundary conditions. The off-diagonal elements of the stress tensor remained negligibly small throughout the simulation, implying that shear deformations are not significant in the system under these conditions. As described above, the 1771
Table 1. Simulated Properties of NaCl Phases at 1 atm and 300 Ka
rbasal (nm)b raxial (nm)b raxial/rbasal b Elat (kJ/mol)c C11 (GPa)d C33 (GPa)d C44 (GPa)d C66 (GPa)d C12 (GPa)d C13 (GPa)d
hexagonal phase
cubic phase
0.271+/-0.001 0.279+/-0.001 1.03+/-0.01 -771.3+/-0.1 26.1 38.8 11.6 2.8 20.4 12.5
0.2809+/-0.0003 0.2809+/-0.0003 1 -777.5+/-0.1 45.7 45.7 15.1 15.1 16.1 16.1
a All values obtained from MD simulations. b r basal and raxial are the nearest neighbor separations within the basal plane and along the axial direction, respectively. c Elat corresponds to the lattice energy. d Elastic constants have been determined based on a ∼1% expansion at a strain rate of 5 × 107 /s. For constants where more than one determination was made, the total spread was found to be less than 2.5%. For C66 this would correspond to an error of up to 20%.
stability of the structure toward shear deformation was in fact verified using ab initio calculations. The static properties of this structure, using NaCl as an example, are summarized in Table 1. The ratio of nearest neighbor separation normal to and within the basal plane (raxial/rbasal) is 1.03 ( 0.01. The lattice energy of the hexagonal phase is 0.8% higher than that of the cubic phase. The structure of the hexagonal phase in the stressed state corresponds closely to the ideal structure determined from simulation at ambient conditions, as demonstrated by the three-point correlations among close neighbors (Figure 3b). Thus, the strain is primarily accommodated by continued transformation to the hexagonal phase without substantial deformation of the structure. Based on our calculations, a significant change in physical properties is associated with this structural change. Given the clear delineation of the phase boundary, a pronounced spatial contrast in mechanical and dielectric behaviors can be achieved with this stress-induced reversible transformation. The relatively open structure in the basal plane compared to the linear structure along the c axis (identical to the alternating ion strings along [001] in the cubic phase) leads to very strong elastic anisotropy (Table 1). Particularly striking is the extremely low shear modulus in the basal plane, C66, which is more than 4 times smaller than C44. This indicates a propensity for transformation back to the cubic phase under shear in the basal plane. The ionic contribution to the dielectric constants of the hexagonal phase also shows significant anisotropy ((K3/ K1)Ionic ) 1.1) and, as would be expected from the lower density, is on average 20% smaller than that of the cubic phase. The hexagonal structure also shows pleochroism in the infrared region, as indicated by the IR absorption spectrum (Figure 2c). The primary vibrational frequency (transverse optical mode, TO) in the axial direction is similar to the cubic phase, but the second, higher-frequency peak (longitudinal, LO) is shifted to lower frequency. The TO peak in the basal plane is at significantly higher frequency than 1772
in the cubic phase, but there is no clear LO peak. Instead, there is a gradually stepped shoulder on the high-frequency side of the TO peak. Because of the significant differences in the properties of the cubic and hexagonal phases, the stark spatial contrast in phase character, and the high degree of control that can be exerted with regard to the extent of conversion, such transformations based on engineered nucleation may provide for a number of novel applications. Examples of devices that might utilize this technology include solid-state optic and acoustic switches, sensors, and filters based on the high contrasts at the phase boundaries and the anisotropy of the hexagonal phase. For example, one could fabricate micromirror arrays that are based on the reflection at multiple interfaces. The reflection strength, both in terms of total magnitude and spectral character, could be tuned by varying the extent of transformation, as controlled via thermal expansion or piezoelectric actuation. Furthermore, the idea of extending templating to “traditional” crystalline phase transformations opens up tremendous opportunities for materials design based on engineered transitions. Although high symmetry grain boundaries in alkali halides constitute a well characterized system for studying these processes, it is likely that other materials (e.g., MgO) are better suited for such applications, and in addition to grain boundaries, heteroepitaxial interfaces may be equally if not more useful as templates in nucleating these mechanically induced transformations. Acknowledgment. The work of J.W.P. was partially supported by the Fannie and John Hertz Foundation Fellowship. Supporting Information Available: A movie of the transformation from the cubic to the hexagonal phase in NaCl. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Lewis, D. W.; Willock, D. J.; Catlow, C. R. A.; Thomas, J. M.; Hutchings, G. J. Nature 1996, 382, 604-606. (2) Aizenberg, J.; Black, A. J.; Whitesides, G. M. Nature 1999, 398, 495-498. (3) Goldberger, J.; He, R. R.; Zhang, Y. F.; Lee, S. W.; Yan, H. Q.; Choi, H. J.; Yang, P. D. Nature 2003, 422, 599-602. (4) Sayle, D. C. J. Mater. Chem. 1999, 9, 607-616. (5) Sayle, D. C.; Catlow, C. R. A.; Dulamita, N.; Healy, M. J. F.; Maicaneanu, S. A.; Slater, B.; Watson, G. W. Mol. Simul. 2002, 28, 683-725. (6) Recio, J. M.; Pandey, R.; Ayuela, A.; Kunz, A. B. J. Chem. Phys. 1993, 98, 4783-4792. (7) Bawa, F.; Panas, I. Phys. Chem. Chem. Phys. 2002, 4, 103-108. (8) Aguado, A.; Ayuela, A.; Lopez, J. M.; Alonso, J. A. Phys. ReV. B 1997, 56, 15353-15360. (9) Limpijumnong, S.; Lambrecht, W. R. L. Phys. ReV. B 2001, 63, 104103. (10) Plimpton, S. J. Comput. Phys. 1995, 117, 1-19. (11) Plimpton, S. J.; Pollock, R.; Stevens, M. In Eighth SIAM Conference on Parallel Processing for Scientific Computing; SIAM: Minneapolis, 1997. (12) Chen, L.-Q.; Kalonji, G. Philos. Mag. A 1992, 66, 11-26. (13) Duffy, D. M.; Tasker, P. W. Philos. Mag. A 1983, 47, 817-825. (14) Fumi, F. G.; Tosi, M. P. J. Phys. Chem. Solids 1964, 25, 31-43. (15) Reardon, B. J.; Kieffer, J. Philos. Mag. B 1998, 77, 907-924. Nano Lett., Vol. 4, No. 9, 2004
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