@article{fancher_burch_patala_dickey_2022, title={Implications of gnomonic distortion on electron backscatter diffraction and transmission Kikuchi diffraction}, volume={1}, ISSN={["1365-2818"]}, url={https://app.dimensions.ai/details/publication/pub.1143660520}, DOI={10.1111/jmi.13077}, abstractNote={Abstract}, number={2}, journal={JOURNAL OF MICROSCOPY}, author={Fancher, Chris M. and Burch, Matthew J. and Patala, Srikanth and Dickey, Elizabeth C.}, year={2022}, month={Jan} }
 @article{kadambi_abdeljawad_patala_2020, title={A phase-field approach for modeling equilibrium solute segregation at the interphase boundary in binary alloys}, volume={175}, url={https://doi.org/10.1016/j.commatsci.2020.109533}, DOI={10.1016/j.commatsci.2020.109533}, abstractNote={A number of experimental and theoretical findings in age hardening alloys suggest that specific solute elements preferentially segregate to and reduce the energy of the interphase boundary (IB). This segregation mechanism can stabilize the precipitation microstructure against coarsening, allowing higher operating temperatures in structural applications. Herein, we present a phase field model of solute segregation to IBs that separate matrix and precipitate phases in binary alloys. The proposed modeling framework is capable of capturing bulk thermodynamics and interfacial free energies, while also accounting for various mass transport mechanisms. Analytical equilibrium solutions of one-dimensional systems are presented, and excess IB quantities are evaluated independent of the Gibbs dividing surface convention. With the aid of the parallel tangent construction, IB segregation isotherms are established in terms of the alloy composition and the model parameters describing the free energy functions. Under the regular solution approximation, computational studies elucidating the dependence of the IB energy and segregation levels on temperature and free energy model parameters are presented. We show that the model is consistent with the Gibbs adsorption equation; therefore, it is possible to compare the adsorption behavior predicted by the model parameters with experiments and atomistic simulations. Future work on extending the model to ternary alloys, and incorporating the effect of elastic interactions on IB segregation is expected.}, journal={Computational Materials Science}, publisher={Elsevier BV}, author={Kadambi, Sourabh B. and Abdeljawad, Fadi and Patala, Srikanth}, year={2020}, month={Apr}, pages={109533} }
 @article{guziewski_banadaki_patala_coleman_2020, title={Application of Monte Carlo techniques to grain boundary structure optimization in silicon and silicon-carbide}, volume={182}, url={https://doi.org/10.1016/j.commatsci.2020.109771}, DOI={10.1016/j.commatsci.2020.109771}, abstractNote={While classical atomistic simulations are commonly used to study energetically favorable structures of grain boundaries, the determination of these structures oftentimes comes at a significant computational cost for each grain boundary surveyed. This arises from the need to sample many microscopic degrees of freedom within the grain boundary even when the five macroscopic degrees of freedom are known. Recent work has proposed the use of a Monte Carlo approach to grain boundary optimization, in which atoms are iteratively added or removed from the grain boundary region and the resultant structure accepted or rejected according to the Metropolis criterion. This enables the rapid sampling of microscopic degrees of freedom, thus decreasing the computational costs required to find minimum energy structures. However thus far, this approach has only been applied to single element, metallic systems of the bcc and fcc structure. This work expands the Monte Carlo grain boundary optimization approach to ceramic systems, considering the more complex diamond cubic (Silicon) and zinc blende (multi-element Silicon Carbide) crystal structures. The novel contributions of this article involve modifications to the Monte Carlo approach necessary for systems with multiple elements and covalent bonding, which results a complex energy landscape with significantly more local minima. The Monte Carlo algorithm is applied to a variety of symmetric tilt and twist grain boundaries, and the determined minimum energy structures are found to be in good agreement with literature. The algorithm also samples over a range of non-equilibrium grain boundary structures, allowing for a quantification of the metastability of grain boundaries. These results raise the possibility of expanding the Monte Carlo approach to other material systems and its use as a robust tool in better characterizing grain boundaries and other interfaces.}, journal={Computational Materials Science}, publisher={Elsevier BV}, author={Guziewski, Matthew and Banadaki, Arash D. and Patala, Srikanth and Coleman, Shawn P.}, year={2020}, month={Sep}, pages={109771} }
 @article{kadambi_abdeljawad_patala_2020, title={Interphase boundary segregation and precipitate coarsening resistance in ternary alloys: An analytic phase-field model describing chemical effects}, volume={197}, url={https://doi.org/10.1016/j.actamat.2020.06.052}, DOI={10.1016/j.actamat.2020.06.052}, abstractNote={Many experimental and first principles studies on precipitation hardening alloys show that segregation of elemental species to the matrix-precipitate interphase boundary (IB) reduces the boundary's energy. This segregation mechanism can thermally stabilize the microstructure against precipitate coarsening processes and allow for higher operating temperatures in structural applications. In this paper, we develop a phase-field modeling framework to describe IB solute segregation in ternary alloys. The interfacial thermodynamics is effectively described by defining an IB phase with a characteristic free energy-concentration dependence. Equilibrium for the IB phase is established via the parallel tangent plane construction, analogous to classical treatments for segregation to free surfaces and grain boundaries. Analytic steady-steady solutions elucidating the dependence of IB properties on bulk phase composition, temperature and model parameters are derived for a one-dimensional system. Analytic relations for the classical thermodynamic quantities–IB energy and relative solute excess–are derived and the Gibbs adsorption equation is shown to hold; therefore, predictions of the model can be compared with experiments and atomistic simulations. An application of the model is demonstrated for Zn segregation to Mg/Mg2Sn using representative IB parameters. A two-particle coarsening simulation of IB segregation is performed: the result demonstrates enhanced coarsening resistance of the ternary alloy relative to the binary alloy.}, journal={Acta Materialia}, publisher={Elsevier BV}, author={Kadambi, Sourabh B and Abdeljawad, Fadi and Patala, Srikanth}, year={2020}, month={Sep}, pages={283–299} }
 @article{chowdhury_zhuang_coleman_patala_bair_2020, title={Quantum Materials for Energy-Efficient Computing}, volume={72}, ISSN={["1543-1851"]}, DOI={10.1007/s11837-020-04293-3}, number={9}, journal={JOM}, author={Chowdhury, Sugata and Zhuang, Houlong and Coleman, Shawn and Patala, Srikanth and Bair, Jacob}, year={2020}, month={Sep}, pages={3147–3148} }
 @article{chowdhury_zhuang_coleman_patala_bair_2020, title={Quantum Materials for Energy-Efficient Computing (vol 72, pg 3147, 2020)}, volume={72}, ISSN={["1543-1851"]}, DOI={10.1007/s11837-020-04431-x}, abstractNote={This correction is to update the authors’ affiliations. They appear correctly here.}, number={12}, journal={JOM}, author={Chowdhury, Sugata and Zhuang, Houlong and Coleman, Shawn and Patala, Srikanth and Bair, Jacob}, year={2020}, month={Dec}, pages={4721–4721} }
 @article{thomas_patala_2020, title={Vacancy diffusion in multi-principal element alloys: The role of chemical disorder in the ordered lattice}, volume={196}, url={https://doi.org/10.1016/j.actamat.2020.06.022}, DOI={10.1016/j.actamat.2020.06.022}, abstractNote={Many of the purported virtues of Multi-Principal Element Alloys (MPEAs), such as corrosion, high-temperature oxidation and irradiation resistance, are highly sensitive to vacancy diffusivity. Similarly, solute interdiffusion is governed by vacancy diffusion. It is also often unclear whether MPEAs are truly stable or effectively stabilized by slow interdiffusion. The considerable composition space afforded to these alloys makes optimizing for desired properties a daunting task; theoretical and computational tools are necessary to guide alloy development. For diffusion, such tools depend on both a knowledge of the vacancy migration barriers within a given alloy and an understanding of how these barriers influence vacancy diffusivity. We present a generalized theory of vacancy diffusion in rugged energy landscapes, paired with Kinetic Monte Carlo simulations of MPEA vacancy diffusion. The barrier energy statistics are informed by nudged elastic band calculations in the equiatomic CoNiCrFeMn alloy. Theory and simulations show that vacancy diffusion in solid-solution MPEAs is not necessarily sluggish, but can potentially be tuned, and that trap models are an insufficient explanation for sluggish diffusion in the CoNiCrFeMn HEA. These results also show that any model that endeavors to faithfully represent diffusion-related phenomena must account for the full nature of the energy landscape, not just the migration barriers.}, journal={Acta Materialia}, publisher={Elsevier BV}, author={Thomas, Spencer L. and Patala, Srikanth}, year={2020}, month={Sep}, pages={144–153} }
 @article{maldonis_banadaki_patala_voyles_2019, title={Short-range order structure motifs learned from an atomistic model of a Zr50Cu45Al5 metallic glass}, volume={175}, ISSN={["1873-2453"]}, url={https://doi.org/10.1016/j.actamat.2019.05.002}, DOI={10.1016/j.actamat.2019.05.002}, abstractNote={The structural motifs of a Zr50Cu45Al5 metallic glass were learned from atomistic models using a new structure analysis method called motif extraction that employs point-pattern matching and machine learning clustering techniques. The motifs are the nearest-neighbor building blocks of the glass and reveal a well-defined hierarchy of structures as a function of coordination number. Some of the motifs are icosahedral or quasi-icosahedral in structure, while others take on the structure of the most close-packed geometries for each coordination number. These results set the stage for developing clearer structure-property connections in metallic glasses. Motif extraction can be applied to any disordered material to identify its structural motifs without the need for human input.}, journal={ACTA MATERIALIA}, publisher={Elsevier BV}, author={Maldonis, Jason J. and Banadaki, Arash Dehghan and Patala, Srikanth and Voyles, Paul M.}, year={2019}, month={Aug}, pages={35–45} }
 @article{patala_2019, title={Understanding grain boundaries - The role of crystallography, structural descriptors and machine learning}, volume={162}, ISSN={["1879-0801"]}, url={https://doi.org/10.1016/j.commatsci.2019.02.047}, DOI={10.1016/j.commatsci.2019.02.047}, abstractNote={Grain boundaries (GBs) influence a wide array of physical properties in polycrystalline materials and play an important role in governing microstructural evolution under extreme environments. While the importance of interfaces is well documented, their properties are among the least understood of all the defect types present in engineering material systems. This is due to the vast configurational space of interfaces, resulting in a diverse range of structures and properties. The complexity associated with GB structures is related to the different crystallographic degrees of freedom – the misorientation, the boundary-plane orientation and the relative translations between the adjoining crystals. These unique challenges can be addressed by leveraging high-throughput simulations of GB properties and developing machine learning algorithms grounded in the concepts of bicrystallography of interfaces. To demystify the relationships between crystallography and properties, the symmetry aspects of GBs are reviewed with an emphasis on boundary-plane orientations and disconnection line defects. To quantify structure-property relationships, recent advances in describing GB structures using the polyhedral unit model and the gaussian-based approximation of local atomic environments are discussed. Finally, examples of predicting GB structure-property relationships using machine learning techniques are summarized. As part of a special issue, the goal of this review article is to motivate machine learning strategies that are informed by bicrystallography and novel structural descriptors for developing reliable crystallography-structure-property relationships for grain boundaries.}, journal={COMPUTATIONAL MATERIALS SCIENCE}, publisher={Elsevier BV}, author={Patala, Srikanth}, year={2019}, month={May}, pages={281–294} }
 @article{banadaki_tschopp_patala_2018, title={An efficient Monte Carlo algorithm for determining the minimum energy structures of metallic grain boundaries}, volume={155}, ISSN={["1879-0801"]}, url={https://doi.org/10.1016/j.commatsci.2018.09.017}, DOI={10.1016/j.commatsci.2018.09.017}, abstractNote={Sampling minimum energy grain boundary (GB) structures in the five-dimensional crystallographic phase space can provide much-needed insight into how GB crystallography affects various interfacial properties. However, the complexity and number of parameters involved often limits the extent of this exploration to a small set of interfaces. In this article, we present a fast Monte Carlo scheme for generating zero-Kelvin, low energy GB structures in the five-dimensional crystallographic phase space. The Monte Carlo trial moves include removal and insertion of atoms in the GB region, which create a diverse set of GB configurations and result in a rapid convergence to the low energy structure. We have validated the robustness of this approach by simulating over 1184 tilt, twist, and mixed character GBs in both fcc (Aluminum and Nickel) and bcc (α-Iron) metallic systems.}, journal={COMPUTATIONAL MATERIALS SCIENCE}, publisher={Elsevier BV}, author={Banadaki, Arash Dehghan and Tschopp, Mark A. and Patala, Srikanth}, year={2018}, month={Dec}, pages={466–475} }
 @article{banadaki_patala_2017, title={A three-dimensional polyhedral unit model for grain boundary structure in fcc metals}, volume={3}, ISSN={["2057-3960"]}, url={https://doi.org/10.1038/s41524-017-0016-0}, DOI={10.1038/s41524-017-0016-0}, abstractNote={Abstract}, number={1}, journal={NPJ COMPUTATIONAL MATERIALS}, publisher={Springer Nature}, author={Banadaki, Arash Dehghan and Patala, Srikanth}, year={2017}, month={Mar} }
 @article{patala_2017, title={Approximating coincidence - turning a new page for bicrystallography}, volume={73}, ISSN={["2053-2733"]}, DOI={10.1107/s2053273317003321}, abstractNote={Most materials used in engineering applications are polycrystalline, i.e. they consist of many single-crystal grains that come together to form bulk polycrystalline microstructures. In these polycrystals, the least understood defect types are the interfaces, which are present at the intersections of abutting grains with distinct lattice orientations. Since the individual grains have an underlying lattice structure and correspond to specific space-group symmetries, the properties of interfaces are analysed by first decoding the crystallographic aspects of the two overlapping crystals (i.e. a bicrystal). This framework, known as bicrystallography (Pond & Vlachavas, 1983), relies on group-theoretical aspects of discrete lattices for determining the symmetries and the possible defect characteristics of interfaces (Sutton & Balluffi, 1995). One of the key concepts introduced in bicrystallography is the theory of the coincidence site lattice (CSL), which has played a major role in classifying experimentally observed interfaces in a wide array of inorganic polycrystalline material systems. The CSL corresponds to the ‘intersection lattice’ formed by overlapping two misoriented lattices (Grimmer, 1976). Associated with each CSL is the number, defined as the ratio of the volumes of the primitive unit cell of the CSL and the underlying single-crystal lattice. Therefore, quantifies the extent of overlap between the two misoriented lattices. An example of this is shown in Fig. 1(a) for a two-dimensional square lattice, where the two overlapping lattices are rotated by 1⁄4 2 tan ð1=3Þ 36:87 with respect to each other. The CSL obtained has an area five times the original lattice, and hence = 5. From an experimental perspective, the algorithm for determining the value of an interface is straightforward. First, the lattice orientations of the adjoining grains are measured through orientation imaging microscopy either in the scanning (Schwartz et al., 2009) or the transmission mode (Trimby, 2012; Caswell et al., 2009). The misorientation matrix M is then computed and is determined by the least positive integer such that M is an integral matrix. However, this algorithm is very sensitive to the precision with which the lattice orientations are measured. For example, shown in Fig. 1(b) is the bicrystal pattern obtained with a misorientation of 1⁄4 2 tan ð18=53Þ 1⁄4 37:52 . As is evident from this illustration, while the pattern changes ever so slightly from the = 5 bicrystal, the value associated with 1⁄4 37:52 is 3133. This large difference in stems from the fact that the CSL theory relies on the exact coincidence of lattice points. Therefore, a small error in the experimentally measured misorientation matrix can lead to a large deviation in the computed of the interface. This issue is particularly troublesome for interfaces in low-symmetry crystal systems where a priori enumeration of generating misorientations does not exist. In this issue, Runnels presents a physically intuitive and mathematically elegant framework to overcome the challenges of the discrete nature of the CSL theory (Runnels, 2017). The central idea developed in this article is that can be computed by determining the extent of overlap between the atomic density fields of the two overlapping lattices. First, instead of representing atoms as a discrete set of points, they are expressed using continuous functions representing their probability densities. The functions used to represent the atomic density are called mollifiers (Friedrichs, 1944) and have unique properties that simplify the mathematics underlying the computation of the extent of overlap between two lattice fields. Bump functions such as those shown in Fig. 1 of ISSN 2053-2733}, journal={ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES}, author={Patala, Srikanth}, year={2017}, month={Mar}, pages={85–86} }
 @article{burch_fancher_patala_de graef_dickey_2017, title={Mapping 180° polar domains using electron backscatter diffraction and dynamical scattering simulations}, volume={173}, ISSN={0304-3991}, url={http://dx.doi.org/10.1016/j.ultramic.2016.11.013}, DOI={10.1016/j.ultramic.2016.11.013}, abstractNote={A novel technique, which directly and nondestructively maps polar domains using electron backscatter diffraction (EBSD) is described and demonstrated. Through dynamical diffraction simulations and quantitative comparison to experimental EBSD patterns, the absolute orientation of a non-centrosymmetric crystal can be determined. With this information, the polar domains of a material can be mapped. The technique is demonstrated by mapping the non-ferroelastic, or 180°, ferroelectric domains in periodically poled LiNbO3 single crystals. Further, the authors demonstrate the possibility of mapping polarity using this technique in other polar materials system.}, journal={Ultramicroscopy}, publisher={Elsevier BV}, author={Burch, Matthew J. and Fancher, Chris M. and Patala, Srikanth and De Graef, Marc and Dickey, Elizabeth C.}, year={2017}, month={Feb}, pages={47–51} }
 @article{kadambi_patala_2017, title={Thermodynamic stabilization of precipitates through interface segregation: Chemical effects}, volume={1}, ISSN={["2475-9953"]}, DOI={10.1103/physrevmaterials.1.043604}, abstractNote={Precipitation hardening, which relies on a high density of intermetallic precipitates, is a commonly utilized technique for strengthening structural alloys. Structural alloys are commonly strengthened through a high density of small size intermetallic precipitates. At high temperatures, however, the precipitates coarsen to reduce the excess energy of the interface, resulting in a significant reduction in the strengthening provided by the precipitates. In certain ternary alloys, the secondary solute segregates to the interface and results in the formation of a high density of nanosize precipitates that provide enhanced strength and are resistant to coarsening. To understand the chemical effects involved, and to identify such systems, we develop a thermodynamic model using the framework of the regular nanocrystalline solution model. For various global compositions, temperatures and thermodynamic parameters, equilibrium configuration of Mg-Sn-Zn alloy is evaluated by minimizing the Gibbs free energy function with respect to the region-specific (bulk solid-solution, interface and precipitate) concentrations and sizes. The results show that Mg$_2$Sn precipitates can be stabilized to nanoscale sizes through Zn segregation to Mg/Mg$_2$Sn interface, and the precipitates can be stabilized against coarsening at high-temperatures by providing a larger Zn concentration in the system. Together with the inclusion of elastic strain energy effects and the input of computationally informed interface thermodynamic parameters in the future, the model is expected to provide a more realistic prediction of segregation and precipitate stabilization in ternary alloys of structural importance.}, number={4}, journal={PHYSICAL REVIEW MATERIALS}, author={Kadambi, Sourabh B. and Patala, Srikanth}, year={2017}, month={Sep} }
 @article{seita_volpi_patala_mccue_schuh_diamanti_erlebacher_demkowicz_2016, title={A high-throughput technique for determining grain boundary character non-destructively in microstructures with through-thickness grains}, volume={2}, ISSN={2057-3960}, url={http://dx.doi.org/10.1038/NPJCOMPUMATS.2016.16}, DOI={10.1038/NPJCOMPUMATS.2016.16}, abstractNote={Abstract}, number={1}, journal={npj Computational Materials}, publisher={Springer Science and Business Media LLC}, author={Seita, Matteo and Volpi, Marco and Patala, Srikanth and McCue, Ian and Schuh, Christopher A and Diamanti, Maria Vittoria and Erlebacher, Jonah and Demkowicz, Michael J}, year={2016}, month={Jun} }
 @article{banadaki_patala_2016, title={A simple faceting model for the interfacial and cleavage energies of Sigma 3 grain boundaries in the complete boundary plane orientation space}, volume={112}, ISSN={["1879-0801"]}, DOI={10.1016/j.commatsci.2015.09.062}, abstractNote={Interfacial energies play a crucial role in the evolution of polycrystalline microstructures both in structural and functional materials. From a crystallographic perspective, the energy landscape depends both on the misorientation and the boundary-plane orientation of grain boundaries (GBs). Traditionally, however, GB structure–property relationships have been investigated primarily for interfaces with twist or tilt character and with an emphasis on the role of misorientation. In this article, we introduce an automated routine for simulating the minimum energy structures for general GBs. The important role of the boundary-plane orientation is elucidated by simulating 297 distinct Aluminum Σ3 GBs that adequately sample the fundamental zone of the plane orientation space. It is observed that while the energy varies significantly as a function of the boundary-plane orientation, the variation is also smooth and without cusps in the fundamental zone. In this article, a simple energy function, motivated by the two-dimensional faceting model for interface structures, is proposed for the free-surfaces and the Σ3 GBs in Aluminum. The energy function consists of only three fitting parameters and predicts the energy landscape surprisingly well. It is anticipated that this model may be extended to represent the energies of GBs corresponding to higher Σ-misorientations. Finally, as an application of the faceting model for interfaces, the theoretical cleavage energies for Σ3 GBs in Aluminum have been computed. It has been observed that, contrary to conventional wisdom, the Σ3(111) twin boundary does not exhibit the highest cleavage energy and these results are expected to have consequences for grain boundary engineering.}, journal={COMPUTATIONAL MATERIALS SCIENCE}, author={Banadaki, Arash Dehghan and Patala, Srikanth}, year={2016}, month={Feb}, pages={147–160} }
 @article{burch_fancher_patala_dickey_2016, title={Imaging 180° Polarization Reversal in Ferroelectric Oxides with Electron Backscatter Diffraction}, volume={22}, ISSN={1431-9276 1435-8115}, url={http://dx.doi.org/10.1017/S1431927616009958}, DOI={10.1017/S1431927616009958}, abstractNote={A ferroelectric material’s permittivity is dependent on the extrinsic contribution of domain wall displacement during the application of an external field, which can involve the motion of both 90° and 180° domain walls. Directly quantifying non-180° domain structures through diffraction based techniques is generally straightforward; as the diffraction condition will be different from one side of a domain wall to the other, reflecting the rotation of the unit-cell and resulting in an easily quantifiable metric to determine location of domain wall [1]. Identifying 180° ferroelectric domains is more difficult, as Friedel’s law states that the intensity of a diffracting plane and its inverse will be equal. Fortunately, Friedel’s law is broken for dynamical scattering in a non-centrosymmetric crystal system, which is necessary for ferroelectricity. This has led to techniques such as convergent beam electron diffraction (CBED) being utilized for the characterization of 180° domain structures [1]. More recently, electron backscatter diffraction (EBSD) has been utilized to map 90° domain structures in ferroelectric oxides [2]. However, utilizing EBSD for imaging 180° domains has not been possible before, due to limitations in simulating dynamical EBSD patterns. Recently, however, De Graef has developed dynamical diffraction simulation software for EBSD, which we have used to map 180° polarization reversal in ferroelectric oxides [3]. In}, number={S3}, journal={Microscopy and Microanalysis}, publisher={Cambridge University Press (CUP)}, author={Burch, Matthew J. and Fancher, Chris M. and Patala, Srikanth and Dickey, Elizabeth C.}, year={2016}, month={Jul}, pages={1822–1823} }
 @article{banadaki_patala_2015, title={An efficient algorithm for computing the primitive bases of a general lattice plane}, volume={48}, DOI={10.1107/s1600576715004446}, abstractNote={The atomistic structures of interfaces and their properties are profoundly influenced by the underlying crystallographic symmetries. Whereas the theory of bicrystallography helps in understanding the symmetries of interfaces, an efficient methodology for computing the primitive basis vectors of the two-dimensional lattice of an interface does not exist. In this article, an algorithm for computing the basis vectors for a plane with Miller indices (hkl) in an arbitrary lattice system is presented. This technique is expected to become a routine tool for both computational and experimental analysis of interface structures.}, number={2}, journal={J Appl Cryst}, publisher={International Union of Crystallography (IUCr)}, author={Banadaki, Arash D. and Patala, Srikanth}, year={2015}, month={Mar}, pages={585–588} }
 @article{homer_patala_priedeman_2015, title={Grain Boundary Plane Orientation Fundamental Zones and Structure-Property Relationships}, volume={5}, ISSN={["2045-2322"]}, DOI={10.1038/srep15476}, abstractNote={Abstract}, journal={SCIENTIFIC REPORTS}, author={Homer, Eric R. and Patala, Srikanth and Priedeman, Jonathan L.}, year={2015}, month={Oct} }
 @article{patala_marks_cruz_2013, title={Elastic Strain Energy Effects in Faceted Decahedral Nanoparticles}, volume={117}, DOI={10.1021/jp310045g}, abstractNote={Decahedral morphology, with re-entrant surface modifications, is one of the common structures observed in nanoparticles. These motifs, although thermodynamically stable only at very small size ranges, have been experimentally observed to grow up to much larger sizes (100 nm to several micrometers). Whereas the surface energy plays an important role, the contributions of the elastic strain energy are nonnegligible at larger sizes and the effect of stress relaxation due to re-entrant surface faceting is poorly understood. In this article, the volumetric strain energy due to the disclination defect is computed using finite element analysis and the relaxation due to the formation of re-entrant surfaces is shown. Contrary to conventional wisdom, the disclination strain energy is shown to be a nontrivial function of the geometry and in general increases with increasing aspect ratio. The computed strain energies also result in approximately 50% increase in the stability regime than the previously reported result...}, number={3}, journal={Journal of Physical Chemistry C}, author={Patala, Srikanth and Marks, Laurence D. and Cruz, Monica Olvera}, year={2013}, pages={1485–1494} }
 @article{patala_schuh_2013, title={Representation of single-axis grain boundary functions}, volume={61}, DOI={10.1016/j.actamat.2013.01.067}, abstractNote={The ability to describe continuous functions on the space of grain boundary parameters is crucial for investigating the functional relations between the structure and the properties of interfaces, in analogy to the way that continuous distribution functions for orientations (i.e. texture information) have been used extensively in the optimization of polycrystalline microstructures. Here we develop a rigorous framework for the description of continuous functions for a subset of the five-parameter grain boundary space, called the “single-axis grain boundary” space. This space consists of all the boundary plane orientations for misorientations confined to a single axis, and is relevant to the method of presenting boundary plane statistics in widespread current use. We establish the topological equivalence between the single-axis grain boundary space and the 3-sphere, which in turn enables the use of hyperspherical harmonics as basis functions to construct continuous functions. These functions enable the representation of statistical distributions and the construction of functional forms for the structure–property relationships of grain boundaries.}, number={8}, journal={Acta Materialia}, author={Patala, Srikanth and Schuh, Christopher A.}, year={2013}, pages={3068–3081} }
 @article{patala_schuh_2013, title={Symmetries in the representation of grain boundary-plane distributions}, volume={93}, DOI={10.1080/14786435.2012.722700}, abstractNote={Symmetries play a crucial role in the theoretical analysis and visualization of the five macroscopic grain boundary parameters, including the misorientation (three parameters) and the orientation of the boundary-plane (two parameters). The symmetry aspects of the misorientation spaces are very well documented and in this article all possible boundary-plane symmetries are enumerated for the 32 crystallographic point groups. It is observed that the boundary-plane spaces exhibit a wide variety of point group symmetries, which depend both on the crystallographic point group and on the corresponding misorientation (i.e. location in the fundamental zone). The list of symmetries presented here should serve as a guide for graphical representations of not only the distributions of boundary-plane orientations but also for the representation of boundary-plane related properties such as energy, mobility etc.}, number={5}, journal={Philosophical Magazine}, author={Patala, Srikanth and Schuh, Christopher A.}, year={2013}, pages={524–573} }
 @article{patala_marks_cruz_2013, title={Thermodynamic Analysis of Multiply Twinned Particles: Surface Stress Effects}, volume={4}, DOI={10.1021/jz401496d}, abstractNote={In nanoparticle technologies, such as SERS, fuel cell catalysis and data storage, icosahedral and decahedral nanoparticles, owing to their defect structure, provide higher functionality than their single-crystal Wulff counterparts. However, precise control on the yield of multiply twinned structures during solution synthesis has been challenging. In particular, it is difficult to synthesize icosahedral structures due to the high volumetric strain energy associated with the disclination defects and the transition to decahedral morphologies. In this Letter, we elucidate the role of surface stresses in influencing the thermodynamic stability of multiply twinned particles. Increasing the surface stresses inhibits the formation of decahedral structures and increases the likelihood of synthesizing metastable icosahedral particles. Analogously, large decahedral particles may be stabilized by decreasing the surface stresses. Therefore, by tailoring the solution chemistry to influence the surface stresses, greater...}, number={18}, journal={J. Phys. Chem. Lett.}, publisher={American Chemical Society (ACS)}, author={Patala, Srikanth and Marks, Laurence D. and Cruz, Monica Olvera}, year={2013}, month={Sep}, pages={3089–3094} }
 @article{patala_mason_schuh_2012, title={Improved representations of misorientation information for grain boundary science and engineering}, volume={57}, DOI={10.1016/j.pmatsci.2012.04.002}, abstractNote={For every class of polycrystalline materials, the scientific study of grain boundaries as well as the increasingly widespread practice of grain boundary engineering rely heavily on visual representation for the analysis of boundary statistics and their connectivity. Traditional methods of grain boundary representation drastically simplify misorientations into discrete categories such as coincidence vs. non-coincidence boundaries, special vs. general boundaries, and low- vs. high-angle boundaries. Such rudimentary methods are used either because there has historically been no suitable mathematical structure with which to represent the relevant grain boundary information, or, where there are existing methods they are extremely unintuitive and cumbersome to use. This review summarizes recent developments that significantly advance our ability to represent a critical part of the grain boundary space: the misorientation information. Two specific topics are reviewed in detail, each of which has recently enjoyed the development of an intuitive and rigorous framework for grain boundary representation: (i) the mathematical and graphical representation of grain boundary misorientation statistics, and (ii) colorized maps or micrographs of grain boundary misorientation. At the outset, conventions for parameterization of misorientations, projections of misorientation information into lower dimensions, and sectioning schemes for the misorientation space are established. Then, the recently developed hyperspherical harmonic formulation for the description of orientation distributions is extended to represent grain boundary statistics. This allows an intuitive representation of the distribution functions using the axis–angle parameterization that is physically related to the boundary structure. Finally, recently developed coloring schemes for grain boundaries are presented and the color legends for interpreting misorientation information are provided. This allows micrographs or maps of grain boundaries to be presented in a colorized form which, at a glance, reveals all of the misorientation information in an entire grain boundary network, as well as the connectivity among different boundary misorientations. These new and improved methods of representing grain boundary misorientation information are expected to be powerful tools for grain boundary network analysis as the practice of grain boundary engineering becomes a routine component of the materials design paradigm.}, number={8}, journal={Progress in Materials Science}, author={Patala, Srikanth and Mason, Jeremy K. and Schuh, Christopher A.}, year={2012}, pages={1383–1425} }
 @article{patala_schuh_2011, title={A continuous and one-to-one coloring scheme for misorientations}, volume={59}, DOI={10.1016/j.actamat.2010.09.058}, abstractNote={Grain boundaries and their networks have profound influence over properties and structure evolution in every class of polycrystalline materials. Despite recent advances in characterization techniques, there remain fundamental problems in representing grain boundary network information; existing methods neglect the full complexity of misorientation information and often rely on boundary classification schemes of dubious physical significance. This situation has arisen in part because grain boundary misorientations have no known mapping to a simple Euclidean space; conventional wisdom suggests that the misorientation space is equivalent to the rotation space, which is known to require five variables for a continuous one-to-one mapping. In this paper, we show that, contrary to this expectation, the misorientation spaces for homophase misorientations for the 432 point group can indeed be mapped to three-dimensional Euclidean space. With this advance, we show that grain boundary networks can now be "colored", with every color uniquely reflecting the full misorientation information of every boundary in the network.}, number={2}, journal={Acta Materialia}, author={Patala, Srikanth and Schuh, Christopher A.}, year={2011}, pages={554–562} }
 @article{patala_schuh_2011, title={The topology of homophase misorientation spaces}, volume={91}, DOI={10.1080/14786435.2010.541169}, abstractNote={Homophase misorientation spaces are investigated with a focus on the effect of symmetry operations on their topology and their minimum embedding dimensions in Euclidean space. Whereas the topology of rotation space is well established and requires a minimum of five variables for a one-to-one and continuous mapping, the spaces of orientations and misorientations are quotient spaces of the rotation space and are obtained by applying various equivalence relations. The equivalence relations for orientation spaces only involve the rotational symmetries of the underlying crystals. These spaces are classified under the three-dimensional manifolds called the spherical 3-manifolds, which have a non-trivial fundamental group, are not simply connected spaces, and do not embed in three-dimensional Euclidean space. In the case of homophase misorientation spaces, however, in addition to rotational symmetry operations there is a further ‘grain exchange symmetry’, which is shown to simplify the topology considerably. In some important cases this symmetry also reduces the number of Euclidean dimensions required to embed these misorientation spaces. The homophase misorientation spaces for the dihedral point groups D 2(222), D 4(422) and D 6(622), the tetrahedral point group T(23), and the octahedral group O(432) are all found to be embeddable in only three dimensions, two dimensions less than required for rotations. Hence, these misorientation systems can be represented using three variables in a one-to-one and continuous manner.}, number={10}, journal={Philosophical Magazine}, author={Patala, S and Schuh, CA}, year={2011}, pages={1489–1508} }
 @article{patala_schuh_2010, title={Topology of Homophase Grain Boundaries in Two-Dimensional Crystals: The Role of Grain Exchange Symmetry}, volume={17}, number={1}, journal={Cmc-Computers Materials & Continua}, author={Patala, S. and Schuh, C. A.}, year={2010}, pages={1–17} }