Symmetry-Adapted Distortion Modes as Descriptors for Materials Informatics

  • Prasanna V. Balachandran
  • Nicole A. Benedek
  • James M. Rondinelli
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 225)


In this paper, we explore the application of symmetry-mode analysis for establishing structure-property relationships. The approach involves describing a distorted (low-symmetry) structure as arising from a (high-symmetry) parent structure with one or more static symmetry-breaking structural distortions. The analysis utilizes crystal structure data of parent and distorted phase as input and decomposes the distorted structure in terms of symmetry-adapted distortion-modes. These distortion-modes serves as the descriptors for materials informatics. We illustrate the potential impact of these descriptors using perovskite nickelates as an example and show that it provides a useful construct beyond the traditional tolerance factor paradigm found in perovskites to understand the atomic scale origin of physical properties, specifically how unit cell level modifications correlate with macroscopic functionality.


Tolerance Factor Ground State Structure Material Informatics Distortion Mode Antiferromagnetic Phase Transition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



P.V.B. acknowledges funding support from the Los Alamos National Laboratory (LANL) Laboratory Directed Research and Development (LDRD) DR (#20140013DR) on Materials Informatics. J.M.R. acknowledges funding support from the NSF (DMR-1454688).


  1. 1.
    E.S. Machlin, T.P. Chow, J.C. Phillips, Structural stability of suboctet simple binary compounds. Phys. Rev. Lett. 38, 1292–1295 (1977)CrossRefGoogle Scholar
  2. 2.
    J.R. Chelikowsky, J.C. Phillips, Quantum-defect theory of heats of formation and structural transition energies of liquid and solid simple metal alloys and compounds. Phys. Rev. B 17, 2453–2477 (1978)CrossRefGoogle Scholar
  3. 3.
    P.B. Littlewood, Structure and bonding in narrow gap semiconductors. Crit. Rev. Solid State Mater. Sci. 11(3), 229–285 (1983)CrossRefGoogle Scholar
  4. 4.
    A. Zunger, Systematization of the stable crystal structure of all \({\rm {AB}}\)-type binary compounds: a pseudopotential orbital-radii approach. Phys. Rev. B 22, 5839–5872 (1980)CrossRefGoogle Scholar
  5. 5.
    T.R. Paudel, A. Zakutayev, S. Lany, M. d’Avezac, A. Zunger, Doping rules and doping prototypes in A\(_2\)BO\(_4\) spinel oxides. Adv. Funct. Mater. 21(23), 4493–4501 (2011)CrossRefGoogle Scholar
  6. 6.
    P.V. Balachandran, S.R. Broderick, K. Rajan, Identifying the inorganic gene for high-temperature piezoelectric perovskites through statistical learning. Proc. R. Soc. A: Math. Phys. Eng. Sci. 467(2132), 2271–2290 (2011)CrossRefGoogle Scholar
  7. 7.
    J. Yan, P. Gorai, B. Ortiz, S. Miller, S.A. Barnett, T. Mason, V. Stevanovic, E.S. Toberer, Material descriptors for predicting thermoelectric performance. Energy Environ. Sci. 8, 983–994 (2015)CrossRefGoogle Scholar
  8. 8.
    B. Meredig, C. Wolverton, Dissolving the periodic table in cubic zirconia: data mining to discover chemical trends. Chem. Mater. 26(6), 1985–1991 (2014)CrossRefGoogle Scholar
  9. 9.
    L.M. Ghiringhelli, J. Vybiral, S.V. Levchenko, C. Draxl, M. Scheffler, Big data of materials science: critical role of the descriptor. Phys. Rev. Lett. 114, 105503 (2015)CrossRefGoogle Scholar
  10. 10.
    T. Das, T. Lookman, M.M. Bandi, A minimal description of morphological hierarchy in two-dimensional aggregates. Soft Matter 11, 6740–6746 (2015)Google Scholar
  11. 11.
    B.J. Campbell, H.T. Stokes, D.E. Tanner, D.M. Hatch, ISODISPLACE: a web-based tool for exploring structural distortions. J. Appl. Crystallogr. 39(4), 607–614 (2006)CrossRefGoogle Scholar
  12. 12.
    C.J. Howard, H.T. Stokes, Group-theoretical analysis of octahedral tilting in perovskites. Acta Crystallogr. Sect. B 54(6), 782–789 (1998)CrossRefGoogle Scholar
  13. 13.
    J.M. Perez-Mato, D. Orobengoa, M.I. Aroyo, Mode crystallography of distorted structures. Acta Crystallogr. Sect. A 66(5), 558–590, (2010).
  14. 14.
    D. Orobengoa, C. Capillas, M.I. Aroyo, J.M. Perez-Mato, AMPLIMODES: symmetry-mode analysis on the bilbao crystallographic server. J. Appl. Crystallogr. 42(5), 820–833 (2009)CrossRefGoogle Scholar
  15. 15.
    P.V. Balachandran, J.M. Rondinelli, Interplay of octahedral rotations and breathing distortions in charge-ordering perovskite oxides. Phys. Rev. B 88, 054101 (2013)CrossRefGoogle Scholar
  16. 16.
    I.C. Tung, P.V. Balachandran, J. Liu, B.A. Gray, E.A. Karapetrova, J.H. Lee, J. Chakhalian, M.J. Bedzyk, J.M. Rondinelli, J.W. Freeland, Connecting bulk symmetry and orbital polarization in strained RNiO\(_{3}\) ultrathin films. Phys. Rev. B 88, 205112 (2013)CrossRefGoogle Scholar
  17. 17.
    J. Tolédano, P. Tolédano, The Landau Theory of Phase Transitions. (World Scientific, Singapore, 1987)Google Scholar
  18. 18.
    N.A. Benedek, C.J. Fennie, Why are there so few perovskite ferroelectrics?. J. Phys. Chem. C 117(26), 13339–13349 (2013)Google Scholar
  19. 19.
    A. Cammarata, J.M. Rondinelli, Contributions of correlated acentric atomic displacements to the nonlinear second harmonic generation and response. ACS Photonics 1(2), 96–100 (2014)CrossRefGoogle Scholar
  20. 20.
    R.D. Shannon, Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. Sect. A 32, 751–767 (1976)CrossRefGoogle Scholar
  21. 21.
    G. Catalan, Progress in perovskite nickelate research. Phase Trans. 81, 729–749 (2008)CrossRefGoogle Scholar
  22. 22.
    J. Chakhalian, J.M. Rondinelli, J. Liu, B.A. Gray, M. Kareev, E.J. Moon, N. Prasai, J.L. Cohn, M. Varela, I.C. Tung, M.J. Bedzyk, S.G. Altendorf, F. Strigari, B. Dabrowski, L.H. Tjeng, P.J. Ryan, J.W. Freeland, Asymmetric orbital-lattice interactions in ultrathin correlated oxide films. Phys. Rev. Lett. 107, 116805 (2011)CrossRefGoogle Scholar
  23. 23.
    J.M. Rondinelli, S.J. May, J.W. Freeland, Control of octahedral connectivity in perovskite oxide heterostructures: an emerging route to multifunctional materials discovery. MRS Bull. 37, 261–270 (2012)CrossRefGoogle Scholar
  24. 24.
    M. Ringnér, What is principal component analysis? Nat. Biotech. 26(3), 303–304 (2008)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Prasanna V. Balachandran
    • 1
  • Nicole A. Benedek
    • 2
  • James M. Rondinelli
    • 3
  1. 1.Theoretical Division, Los Alamos National LaboratoryLos AlamosUSA
  2. 2.Department of Materials Science and EngineeringCornell UniversityIthacaUSA
  3. 3.Department of Materials Science and EngineeringNorthwestern UniversityEvanstonUSA

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