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You may consider citing some of the following articles when using MuPRO to obtain results for your research article or presentation.


  1. Fei Xue, Yijia Gu, Linyun Liang, Yi Wang, and Long-Qing Chen. Orientations of low- energy domain walls in perovskites with oxygen octahedral tilts. Physical Review B, 90(22):220101, 2014.
  2. YL Li, SY Hu, ZK Liu, and LQ Chen. Effect of substrate constraint on the stability and evolution of ferroelectric domain structures in thin films. Acta materialia, 50(2):395– 411, 2002.
  3. YL Li, LE Cross, and LQ Chen. A phenomenological thermodynamic potential for BaTIO3 single crystals. Journal of Applied Physics, 98(6):064101, 2005.
  4. Guang Sheng, YL Li, JX Zhang, S Choudhury, QX Jia, Venkatraman Gopalan, Darrell G Schlom, ZK Liu, and LQ Chen. A modified landau–devonshire thermodynamic potential for strontium titanate. Applied Physics Letters, 96(23):232902, 2010.
  5. JX Zhang, YL Li, S Choudhury, LQ Chen, YH Chu, F Zavaliche, MP Cruz, R Ramesh, and QX Jia. Computer simulation of ferroelectric domain structures in epitaxial BiFeO3 thin films. Journal of Applied Physics, 103(9):094111, 2008.
  6. YL Li, SY Hu, ZK Liu, and LQ Chen. Effect of electrical boundary conditions on ferroelectric domain structures in thin films. Applied physics letters, 81(3):427–429, 2002.
  7. Yijia Gu, Zijian Hong, Jason Britson, and Long-Qing Chen. Nanoscale mechanical switching of ferroelectric polarization via flexoelectricity. Applied Physics Letters, 106(2):022904, 2015.


  1. X.-P. Wang, C. J. Garcia-Cervera, and W. E, “A Gauss–Seidel Projection Method for Mic romagnetics Simulations,"" J. Comput. Phys., vol. 171, no. 1, pp. 357–372, Jul. 2001.
  2. L.-Q. Chen and J. Shen, “Applications of semi-implicit Fourier-spectral method to phase field equations,"" Comput. Phys. Commun., vol. 108, no. 2–3, pp. 147–158, 1998.
  3. J. Zhang and L.-Q. Chen, “Phase-field microelasticity theory and micromagnetic simulations of domain structures in giant magnetostrictive materials”, Acta Mater., vol. 53, no. 9, pp. 2845–2855, May 2005.
  4. Y. Li, S. Y. Hu, Z.-K. Liu, and L.-Q. Chen, “Effect of substrate constraint on the stability and evolution of ferroelectric domain structures in thin films”, Acta Mater., vol. 50, pp. 395–411, 2002.
  5. S. Y. Hu and L.-Q. Chen, “A phase-field model for evolving microstructures with strong elastic inhomogeneity”, Acta Mater., vol. 49, no. 11, pp. 1879–1890, Jun. 2001.
  6. J.-M. Hu, T. N. Yang, L.-Q. Chen, and C.-W. Nan, “Engineering domain structures in nanoscale magnetic thin films via strain”, J. Appl. Phys., vol. 114, no. 16, p. 164303, 2013.

Effective Properties

  1. S.Y. Hu, L.Q. Chen, A phase-field model for evolving microstructures with strong elastic inhomogeneity, Acta Mater. 49 (2001) 1879.
  2. J.J. Wang, X.Q. Ma, Q. Li, J. Britson, L.Q. Chen, Phase transitions and domain structures of ferroelectric nanoparticles: Phase field model incorporating strong elastic and dielectric inhomogeneity, Acta Mater. 61 (2013) 7591.
  3. J. J. Wang, Y. Song, X. Q. Ma, L.-Q. Chen, and C.-W. Nan, Static magnetic solution in magnetic composites with arbitrary susceptibility inhomogeneity and anisotropy, J. Appl. Phys. 117 (2015) 043907.
  4. J. Z. Zhu, L. Q. Chen, J. Shen, and V. Tikare, Computing the Effective Diffusivity Using a Spectral Method, Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing, 2001. 311(1-2): p. 135-141
  5. Y. Cao, G. Sheng, J. X. Zhang, S. Choudhury, Y. L. Li, C. Randall, and L. Q. Chen, Piezoelectric response of single-crystal PbZr1-xTixO3 near morphotropic phase boundary predicted by phase-field simulation, Applied Physics Letters, 2010. 97(25): Art. No. 252904
  6. T. N. Yang, J.-M. Hu, C. W. Nan, and L. Q. Chen, Predicting effective magnetoelectric response in magnetic-ferroelectric composites via phase-field modeling, Applied Physics Letters, 2014. 104(5): Art. No. 052904


  1. Yanzhou Ji, Phase-field Modeling of Precipitation in Metallic Alloys: Morphology, Kinetics and Hardening Effects, PhD Thesis, Chapters 2 and 6, The Pennsylvania State University, Dec 2018.
  2. Yanzhou Ji and Long-Qing Chen, “Phase-field model of stoichiometric compounds and solution phases”, Acta Materialia 234 (2022) 118007