Materials Science on a Single Defect Level - Dimensions of Complexity

The statement that a materials functionality is controlled by defects is perhaps the most recognized paradigm of materials science, solid state electrochemistry, and condensed physics alike. Defects define the electronic and transport functionality of semiconductors, strength of structural materials, and operational life times of energy storage and conversion devices. From a more fundamental perspective, interplay between defects and long-range elastic, magnetic, and electrostatic interactions gives rise to often unique properties of ferroelectric relaxors, spin glasses, and martensites. Correspondingly, a quantitative atomic-level understanding of materials functionality on the level of single structural defect will bring a paradigm shift in materials science from largely phenomenological development to the knowledge-driven design and optimization.

The atomic and electronic structure of defects is now well-amenable to the set of (scanning) transmission electron microscopy imaging methods [1]. However, the functionality on a single defect level, were it thermal phase transitions, bias-induced polarization switching or electrochemical reactions, or strain-induced mechanical or ferroelastic phenomena, presents a heftier challenge. Application of global stimulus in the form of temperature variation or uniform magnetic or electric field activates phase transition at all defects present in system simultaneously. Consequently, macroscopic and imaging studies will reveal the effect only of the strongest defects.

For example, polarization switching activated at a single defect site in a ferroelectric capacitor structure will quickly propagate through the material volume, precluding probing defect functionality in adjacent volumes. Remarkably, using the traditional nanoscience approach of material confinement in the form of nanodots, wires, or films will generally not allow isolating or identifying a defect – since newly formed surfaces and edges then provide new defect sites!

Figure 1. Confinement of electric, thermal, or strain field by the scanning probe microscopy tip allows localizing transformation in a small volume of materials that can include no defects or well-defined single defects. If the dual challenge of quantitative probing of associated transformations in the nanoscale volume and defect identification is met, this approach will allow probing structure-property relationship on single-defect level.

An alternative approach for probing materials functionality actively pursued by Oak Ridge National Laboratory group (imaging.ornl.gov) in close collaboration with Scanning Transmission Electron Microscopy group (stem.ornl.gov) is the use of field confinement rather then material confinement. In these experiments, the SPM tip focuses an electric or thermal field in a nanometer of material, inducing local transformations. In parallel, measured dynamic strain, resonance frequency shift, or quality factor of the cantilever (piezoresponse force microscopy, electrochemical strain microscopy) or tip-surface current (conductive AFM) provides information on processes in the material (polarization, domain size, ionic motion, second phase formation, melting) induced by local stimuli. The uniqueness of this approach is that transformation can be probed in material volumes containing no or single individual extended defects, paving a pathway for studying phase transformations and electrochemical reactions on a single defect level.

However, the simplicity of the concept is belied by the surprising complexity of experimental techniques required to probe mesoscopic defect functionality. Indeed, the hardware platforms for these studies can be realized on 30,000+ SPMs worldwide. However, these studies require drastic improvement in capability to collect and analyze multidimensional data sets, well beyond state of the art (2D imaging or 3D spectroscopic imaging) in the field. This argument can be exemplified as follows:

• The spatial scanning necessitates data acquisition over a 2D dense grid of points
• The probing local transformation requires sweeping local stimulus (tip bias or temperature) while measuring the response
• All first order phase transitions are hysteretic and hence are history dependent. This necessitates first order reversal curve type studies, effectively increasing dimensionality of the data (e.g. probing Preisach densities)
• First order phase transition often possess slow time dynamics, necessitating probing kinetic hysteresis (and differentiating it from thermodynamics) by measuring response as a function of time
• The detection of force-based SPMs necessitates probing response in a frequency band around resonance (since resonant frequency can be position dependent and single-frequency methods fail to capture these changes[2]).

Overall, these requirements necessitate 4D, 5D, and 6D datasets (0.5 – 30 GB image) size, and bring forth the obvious challenges of data storage, dimensionality reduction, visualization, and interpretation. The development of these multidimensional SPMs has been a focus of research activity at ORNL Center for Nanophase Materials sciences, with many of relevant examples of probing ferroelectric polarization switching and phase transitions, electrochemical reactions in Li-ion and oxygen conductors, and local glass and melting transition temperatures summarized in recent reviews [3,4]. In particular, for materials with artificially engineered defect structures polarization switching can be probed on a single defect level and directly compared to the results of phase-field modeling, providing the first example of phase transition probed and understood on a single defect level [5]. The recent emergence of electrochemical strain microscopy (ESM)[6,7] holds the promise for extending these approaches for probing gas-solid reactions, electorcatalysis and ionic dynamics in materials such as Li-ion and Li-air batteries, fuel cells, and memristive electronics.

The second key challenge is the collection of atomic level structural information of the defect, the task best achieved by advanced electron microscopy tools. This approach is exemplified in Fig. 2, illustrating the first example of polarization switching is a multiferroic material induced by a biased SPM probe [8].The future will see the combination of the local SPM excitation with focused X-ray and electron microscopy probes.

Figure 2. (a) Artistic vision of combined (scanning) transmission electron microscopy – scanning probe microscope experiment. Here, (S)TEM provides atomic level structural and electronic information on changes in material induced by field confined by an SPM probe. (b) Ferroelectric domain switching in the STEM geometry. Data courtesy of A. Borisevich and H.J. Chang and similar to that in Ref. [6].

Overall, the presence and interactions of multiple structural defects mediated by long-range elastic, electrostatic, and ionic concentration fields are the origins of complexity of real-world materials. The SPM field confinement approach allows exploring materials functionality on the single defects level. While hardware platforms are readily available, quantitative studies require a significant increase in complexity and dimensionality of data acquisition and analysis. Perhaps this illustrates the conservation laws of complexity – we cannot make things simpler, we can only shift complexity between materials and measurements.

Research supported by the U.S. Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division and partially performed at the Center for Nanophase Materials Sciences (SVK), a DOE-BES user facility.

References

1. S.J. Pennycook and P.D. Nellist (Eds.), Scanning Transmission Electron Microscopy: Imaging and Analysis, Springer 2011
2. S. Jesse, S.V. Kalinin, R. Proksch, A.P. Baddorf, and B.J. Rodriguez, The band excitation method in scanning probe microscopy for rapid mapping of energy dissipation on the nanoscale, Nanotechnology 18, 435503 (2007).
3. S.V. Kalinin, A.N. Morozovska, L.Q. Chen, and B.J. Rodriguez, Local polarization dynamics in ferroelectric materials, Rep. Prog. Phys. 73, 056502 (2010).
4. S. Jesse and S.V. Kalinin, Band excitation in scanning probe microscopy: Sines of change, J. Phys. D 44, 464006 (2011).
5. B.J. Rodriguez, S. Choudhury, Y.H. Chu, A. Bhattacharyya, S. Jesse, K. Seal, A.P. Baddorf, R. Ramesh, L.Q. Chen, and S.V. Kalinin, Unraveling Deterministic Mesoscopic Polarization Switching Mechanisms: Spatially Resolved Studies of a Tilt Grain Boundary in Bismuth Ferrite, Adv. Func. Mat. 19, 2053 (2009).
6. N. Balke, S. Jesse, A.N. Morozovska, E. Eliseev, D.W. Chung, Y. Kim, L. Adamczyk, R.E. Garcia, N. Dudney, and S.V. Kalinin, Nanoscale mapping of ion diffusion in a lithium-ion battery cathode, Nature Nanotechnology 5, 749 (2010).
7. A. Kumar, F. Ciucci, A.N. Morozovska, S.V. Kalinin, and S. Jesse, Measuring oxygen reduction/evolution reactions on the nanoscale, Nature Chemistry 3, 707 (2011).
8. H.J. Chang, S.V. Kalinin, S. Yang, P. Yu, S. Bhattacharya, P.P. Wu, N. Balke, S. Jesse, L.Q. Chen, R. Ramesh, S.J. Pennycook, and A.Y. Borisevich, Watching domains grow: In-situ studies of polarization switching by combined scanning probe and scanning transmission electron microscopy, J. Appl. Phys. 110, 052014 (2011).