Citation: | YU Jidong, YAO Songlin, WU Qiang. Advances of Phase Field Modeling of Martensitic Phase Transformation[J]. Chinese Journal of High Pressure Physics, 2021, 35(4): 040109. doi: 10.11858/gywlxb.20210772 |
[1] |
CHEN L Q. Phase-field models for microstructure evolution [J]. Annual Review of Materials Research, 2002, 32: 113–140. doi: 10.1146/annurev.matsci.32.112001.132041
|
[2] |
LOGINOVA I S, SINGER H M. The phase field technique for modeling multiphase materials [J]. Reports on Progress in Physics, 2008, 71(10): 106501. doi: 10.1088/0034-4885/71/10/106501
|
[3] |
EMMERICH H. Advances of and by phase-field modelling in condensed-matter physics [J]. Advances in Physics, 2008, 57(1): 1–87. doi: 10.1080/00018730701822522
|
[4] |
STEINBACH I. Phase-field models in materials science [J]. Modelling and Simulation in Materials Science and Engineering, 2009, 17(7): 073001. doi: 10.1088/0965-0393/17/7/073001
|
[5] |
WANG Y Z, LI J. Phase field modeling of defects and deformation [J]. Acta Materialia, 2010, 58(4): 1212–1235. doi: 10.1016/j.actamat.2009.10.041
|
[6] |
BOETTINGER W J, WARREN J A, BECKERMANN C, et al. Phase-field simulation of solidification [J]. Annual Review of Materials Research, 2002, 32: 163–194. doi: 10.1146/annurev.matsci.32.101901.155803
|
[7] |
WANG Y, KHACHATURYAN A G. Three-dimensional field model and computer modeling of martensitic transformations [J]. Acta Materialia, 1997, 45(2): 759–773. doi: 10.1016/S1359-6454(96)00180-2
|
[8] |
WANG Y Z, KHACHATURYAN A G. Multi-scale phase field approach to martensitic transformations [J]. Materials Science and Engineering: A, 2006, 438/439/440: 55–63. doi: 10.1016/j.msea.2006.04.123
|
[9] |
MAMIVAND M, ZAEEM M A, KADIRI H E. A review on phase field modeling of martensitic phase transformation [J]. Computational Materials Science, 2013, 77: 304–311. doi: 10.1016/j.commatsci.2013.04.059
|
[10] |
DENG Y, GAMMER C, CISTON J, et al. Hierarchically-structured large superelastic deformation in ferroelastic-ferroelectrics [J]. Acta Materialia, 2019, 181: 501–509. doi: 10.1016/j.actamat.2019.10.018
|
[11] |
CLAYTON J D, KNAP J. A phase field model of deformation twinning: nonlinear theory and numerical simulations [J]. Physica D: Nonlinear Phenomena, 2011, 240(9/10): 841–858. doi: 10.1016/j.physd.2010.12.012
|
[12] |
LIU G S, MO H X, WANG J, et al. Coupled crystal plasticity finite element-phase field model with kinetics-controlled twinning mechanism for hexagonal metals [J]. Acta Materialia, 2021, 202: 399–416. doi: 10.1016/j.actamat.2020.11.002
|
[13] |
WANG L Y, LIU Z L, ZHUANG Z. Developing micro-scale crystal plasticity model based on phase field theory for modeling dislocations in heteroepitaxial structures [J]. International Journal of Plasticity, 2016, 81: 267–283. doi: 10.1016/j.ijplas.2016.01.010
|
[14] |
ALBRECHT C, HUNTER A, KUMAR A, et al. A phase field model for dislocations in hexagonal close packed crystals [J]. Journal of the Mechanics and Physics of Solids, 2020, 137: 103823. doi: 10.1016/j.jmps.2019.103823
|
[15] |
BOURDIN B, FRANCFORT G A, MARIGO J J. The variational approach to fracture [M]. Berlin: Springer Verlag, 2008.
|
[16] |
MIEHE C, HOFACKER M, WELSCHINGER F. A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits [J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(45/46/47/48): 2765–2778. doi: 10.1016/j.cma.2010.04.011
|
[17] |
REZAEI S, MIANROODI J R, BREPOLS T, et al. Direction-dependent fracture in solids: atomistically calibrated phase-field and cohesive zone model [J]. Journal of the Mechanics and Physics of Solids, 2021, 147: 104253. doi: 10.1016/j.jmps.2020.104253
|
[18] |
WANG T, YE X, LIU Z L, et al. Modeling the dynamic and quasi-static compression-shear failure of brittle materials by explicit phase field method [J]. Computational Mechanics, 2019, 64(6): 1537–1556. doi: 10.1007/s00466-019-01733-z
|
[19] |
WANG T, YE X, LIU Z L, et al. A phase-field model of thermo-elastic coupled brittle fracture with explicit time integration [J]. Computational Mechanics, 2020, 65(5): 1305–1321. doi: 10.1007/s00466-020-01820-6
|
[20] |
BALL J M, JAMES R D. Fine phase mixtures as minimizers of energy [J]. Archive for Rational Mechanics and Analysis, 1987, 100(1): 13–52. doi: 10.1007/BF00281246
|
[21] |
BALL J M, JAMES R D. Proposed experimental tests of a theory of fine microstructure and the two-well problem [J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1992, 338(1650): 389–450. doi: 10.1098/rsta.1992.0013
|
[22] |
KOHN R V. The relaxation of a double-well energy [J]. Continuum Mechanics and Thermodynamics, 1991, 3(3): 193–236. doi: 10.1007/BF01135336
|
[23] |
BHATTACHARYA K. Microstructure of martensite [M]. Oxford: Oxford University Press, 2004.
|
[24] |
唐志平. 冲击相变[M]. 北京: 科学出版社, 2008: 87.
|
[25] |
WEN Y H, WANG Y, BENDERSKY L A, et al. Microstructural evolution during the α2→α2 + O transformation in Ti-Al-Nb alloys: phase-field simulation and experimental validation [J]. Acta Materialia, 2000, 48(16): 4125–4135. doi: 10.1016/S1359-6454(00)00186-5
|
[26] |
ARTEMEV A, JIN Y, KHACHATURYAN A G. Three-dimensional phase field model of proper martensitic transformation [J]. Acta Materialia, 2001, 49(7): 1165–1177. doi: 10.1016/S1359-6454(01)00021-0
|
[27] |
RAO W F, KHACHATURYAN A G. Phase field theory of proper displacive phase transformations: structural anisotropy and directional flexibility, a vector model, and the transformation kinetics [J]. Acta Materialia, 2011, 59(11): 4494–4503. doi: 10.1016/j.actamat.2011.03.072
|
[28] |
JAVANBAKHT M, ADAEI M. Investigating the effect of elastic anisotropy on martensitic phase transformations at the nanoscale [J]. Computational Materials Science, 2019, 167: 168–182. doi: 10.1016/j.commatsci.2019.05.047
|
[29] |
XIE X, KANG G Z, KAN Q H, et al. Phase-field theory based finite element simulation on thermo-mechanical cyclic deformation of polycrystalline super-elastic NiTi shape memory alloy [J]. Computational Materials Science, 2020, 184: 109899. doi: 10.1016/j.commatsci.2020.109899
|
[30] |
WANG D, LIANG Q L, ZHAO S S, et al. Phase field simulation of martensitic transformation in pre-strained nanocomposite shape memory alloys [J]. Acta Materialia, 2019, 164: 99–109. doi: 10.1016/j.actamat.2018.10.030
|
[31] |
LEVITAS V I, LEVIN V A, ZINGERMAN K M, et al. Displacive phase transitions at large strains: phase-field theory and simulations [J]. Physical Review Letters, 2009, 103(2): 025702. doi: 10.1103/PhysRevLett.103.025702
|
[32] |
VAN DER WAALS J D. The thermodynamic theory capillarity under the hypothesis of a continuous variation of density [J]. Verhandelingen van de Koninklijke Academie voor Wetenschappen, 1893, 1: 1–56.
|
[33] |
GIBBS J W. A method of geometrical representation of the thermodynamic properties of substances by means of surfaces [J]. Transactions of the Connecticut Academy, 1873, 2: 382–404.
|
[34] |
CAHN J W, HILLIARD J E. Free energy of a nonuniform system. I. interfacial free energy [J]. The Journal of Chemical Physics, 1957, 28(2): 258. doi: 10.1063/1.1744102
|
[35] |
ALLEN S M, CAHN J W. A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening [J]. Acta Metallurgica, 1979, 27(6): 1085–1095. doi: 10.1016/0001-6160(79)90196-2
|
[36] |
KOBAYASHI H, ODE M, KIM S G, et al. Phase-field model for solidification of ternary alloys coupled with thermodynamic database [J]. Scripta Materialia, 2003, 48(6): 689–694. doi: 10.1016/S1359-6462(02)00557-2
|
[37] |
SEOL D J, HU S Y, LI Y L, et al. Computer simulation of spinodal decomposition in constrained films [J]. Acta Materialia, 2003, 51(17): 5173–5185. doi: 10.1016/S1359-6454(03)00378-1
|
[38] |
WANG Y, JIN Y M, CUITIÑO A M, et al. Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations [J]. Acta Materialia, 2001, 49(10): 1847–1857. doi: 10.1016/S1359-6454(01)00075-1
|
[39] |
CAHN J W, HAN S C, MCFADDEN G B. Anisotropy of interfaces in an ordered hcp binary alloy [J]. Journal of Statistical Physics, 1999, 95(5/6): 1337–1360. doi: 10.1023/A:1004583324097
|
[40] |
OGATA S, LI J, YIP S. Ideal pure shear strength of aluminum and copper [J]. Science, 2002, 298(5594): 807–811. doi: 10.1126/science.1076652
|
[41] |
OGATA S, LI J, YIP S. Energy landscape of deformation twinning in bcc and fcc metals [J]. Physical Review B, 2005, 71(22): 224102. doi: 10.1103/PhysRevB.71.224102
|
[42] |
SHEN C, LI J, WANG Y Z. Finding critical nucleus in solid-state transformations [J]. Metallurgical and Materials Transactions A, 2008, 39(5): 976–983. doi: 10.1007/s11661-007-9302-7
|
[43] |
KARMA A, RAPPEL W J. Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics [J]. Physical Review E, 1996, 53(4): R3017. doi: 10.1103/PhysRevE.53.R3017
|
[44] |
KARMA A, RAPPEL W J. Quantitative phase-field modeling of dendritic growth in two and three dimensions [J]. Physical Review E, 1998, 57(4): 4323–4349. doi: 10.1103/PhysRevE.57.4323
|
[45] |
FINEL A, BOUAR Y L, DABAS B, et al. Sharp phase field method [J]. Physical Review Letters, 2018, 121(2): 025501. doi: 10.1103/PhysRevLett.121.025501
|
[46] |
PROVATAS N, GOLDENFELD N, DANTZIG J. Efficient computation of dendritic microstructures using adaptive mesh refinement [J]. Physical Review Letters, 1998, 80(15): 3308–3311. doi: 10.1103/PhysRevLett.80.3308
|
[47] |
JEONG D, KIM J. Fast and accurate adaptive finite difference method for dendritic growth [J]. Computer Physics Communications, 2019, 236: 95–103. doi: 10.1016/j.cpc.2018.10.020
|
[48] |
LEVITAS V I, IDESMAN A V, PRESTON D L. Microscale simulation of martensitic microstructure evolution [J]. Physical Review Letters, 2004, 93(10): 105701. doi: 10.1103/PhysRevLett.93.105701
|
[49] |
STEINBACH I, APEL M. Multi phase field model for solid state transformation with elastic strain [J]. Physica D: Nonlinear Phenomena, 2006, 217(2): 153–160. doi: 10.1016/j.physd.2006.04.001
|
[50] |
LEVITAS V I, ESFAHANI S E, GHAMARIAN I. Scale-free modeling of coupled evolution of discrete dislocation bands and multivariant martensitic microstructure [J]. Physical Review Letters, 2018, 121(20): 205701. doi: 10.1103/PhysRevLett.121.205701
|
[51] |
ABBOUD H, KOSSEIFI C A, CHEHAB J P. A stabilized bi-grid method for Allen-Cahn equation in finite elements [J]. Computational and Applied Mathematics, 2019, 38(2): 35. doi: 10.1007/S40314-019-0781-0
|
[52] |
徐祖耀. 材料相变[M]. 北京: 高等教育出版社, 2013: 352.
|
[53] |
BHATTACHARYA K, CONTI S, ZANZOTTO G, et al. Crystal symmetry and the reversibility of martensitic transformations [J]. Nature, 2004, 428(6978): 55–59. doi: 10.1038/nature02378
|
[54] |
SOEJIMA Y, MOTOMURA S, MITSUHARA M, et al. In situ scanning electron microscopy study of the thermoelastic martensitic transformation in Ti-Ni shape memory alloy [J]. Acta Materialia, 2016, 103: 352–360. doi: 10.1016/j.actamat.2015.10.017
|
[55] |
WANG S J, SUI M L, CHEN Y T, et al. Microstructural fingerprints of phase transitions in shock-loaded iron [J]. Scientific Reports, 2013, 3: 1086. doi: 10.1038/srep01086
|
[56] |
FALK F. One-dimensional model of shape memory alloys [J]. Archives of Mechanics, 1983, 35(1): 63–84.
|
[57] |
FALK F, KONOPKA P. Three-dimensional Landau theory describing the martensitic phase transformation of shape-memory alloys [J]. Journal of Physics: Condensed Matter, 1990, 2(1): 61–77. doi: 10.1088/0953-8984/2/1/005
|
[58] |
JACOBS A E, CURNOE S H, DESAI R C. Simulations of cubic-tetragonal ferroelastics [J]. Physical Review B, 2003, 68(22): 224104. doi: 10.1103/PhysRevB.68.224104
|
[59] |
CAHN J W, KALONJI G. Symmetry in solid state transformation morphology [M]. Warrendale, USA, 1981.
|
[60] |
VEDANTAM S, ABEYARATNE R. A Helmholtz free-energy function for a Cu-Al-Ni shape memory alloy [J]. International Journal of Non-Linear Mechanics, 2005, 40(2/3): 177–193. doi: 10.1016/j.ijnonlinmec.2004.05.005
|
[61] |
SHCHYGLO O, SALMAN U, FINEL A. Martensitic phase transformations in Ni-Ti-based shape memory alloys: the Landau theory [J]. Acta Materialia, 2012, 60(19): 6784–6792. doi: 10.1016/j.actamat.2012.08.056
|
[62] |
LEVITAS V I, PRESTON D L. Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. I. austenite ↔ martensite [J]. Physical Review B, 2002, 66(13): 134206. doi: 10.1103/PhysRevB.66.134206
|
[63] |
LEVITAS V I, PRESTON D L. Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. II. multivariant phase transformations and stress space analysis [J]. Physical Review B, 2002, 66(13): 134207. doi: 10.1103/PhysRevB.66.134207
|
[64] |
SHE H, LIU Y L, WANG B. Phase field simulation of heterogeneous cubic→tetragonal martensite nucleation [J]. International Journal of Solids and Structures, 2013, 50(7/8): 1187–1191. doi: 10.1016/j.ijsolstr.2012.12.020
|
[65] |
GOMEZ H, BURES M, MOURE A. A review on computational modelling of phase-transition problems [J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2019, 377(2143): 20180203. doi: 10.1098/RSTA.2018.0203
|
[66] |
WEN Y H, WANG Y, CHEN L Q. Effect of elastic interaction on the formation of a complex multi-domain microstructural pattern during a coherent hexagonal to orthorhombic transformation [J]. Acta Materialia, 1999, 47(17): 4375–4386. doi: 10.1016/S1359-6454(99)00247-5
|
[67] |
WEN Y H, WANG Y, CHEN L Q. Phase-field simulation of domain structure evolution during a coherent hexagonal-to-orthorhombic transformation [J]. Philosophical Magazine A, 2000, 80(9): 1967–1982. doi: 10.1080/01418610008212146
|
[68] |
DEVILLE S, GUÉNIN G, CHEVALIER J. Martensitic transformation in zirconia: Part I. nanometer scale prediction and measurement of transformation induced relief [J]. Acta Materialia, 2004, 52(19): 5697–5707. doi: 10.1016/j.actamat.2004.08.034
|
[69] |
BAIN E C. The nature of martensite [J]. Trans. AIME, 1924, 70: 25–46.
|
[70] |
VATTRÉ A, DENOUAL C. Polymorphism of iron at high pressure: a 3D phase-field model for displacive transitions with finite elastoplastic deformations [J]. Journal of the Mechanics and Physics of Solids, 2016, 92: 1–27. doi: 10.1016/J.JMPS.2016.01.016
|
[71] |
DENOUAL C, CAUCCI A M, SOULARD L, et al. Phase-field reaction-pathway kinetics of martensitic transformations in a model Fe3Ni alloy [J]. Physical Review Letters, 2010, 105(3): 035703. doi: 10.1103/PhysRevLett.105.035703
|
[72] |
DENOUAL C, VATTRÉ A. A phase field approach with a reaction pathways-based potential to model reconstructive martensitic transformations with a large number of variants [J]. Journal of the Mechanics and Physics of Solids, 2016, 90: 91–107. doi: 10.1016/j.jmps.2016.02.022
|
[73] |
VATTRÉ A, DENOUAL C. Continuum nonlinear dynamics of unstable shock waves induced by structural phase transformations in iron [J]. Journal of the Mechanics and Physics of Solids, 2019, 131: 387–403. doi: 10.1016/j.jmps.2019.07.012
|
[74] |
HOMAYONIFAR M, MOSLER J. Efficient modeling of microstructure evolution in magnesium by energy minimization [J]. International Journal of Plasticity, 2012, 28(1): 1–20. doi: 10.1016/j.ijplas.2011.05.011
|
[75] |
CLAYTON J D. Nonlinear Eulerian thermoelasticity for anisotropic crystals [J]. Journal of the Mechanics and Physics of Solids, 2013, 61(10): 1983–2014. doi: 10.1016/j.jmps.2013.05.009
|
[76] |
OLSON G B, ROITBURD A L. Martensitic nucleation [M]//OLSON G B, OWEN W S. Martensite. Materials Park, Ohio: ASM International, 1992: 149.
|
[77] |
HENNIG R G, TRINKLE D R, BOUCHET J, et al. Impurities block the α to ω martensitic transformation in titanium [J]. Nature Materials, 2005, 4(2): 129–133. doi: 10.1038/nmat1292
|
[78] |
CASPERSEN K J, CARTER E A. Finding transition states for crystalline solid-solid phase transformations [J]. Proceedings of the National Academy of Sciences of the United States of America, 2005, 102(19): 6738–6743. doi: 10.1073/pnas.0408127102
|
[79] |
DUPÉ B, AMADON B, PELLEGRINI Y P, et al. Mechanism for the α→ε phase transition in iron [J]. Physical Review B, 2013, 87(2): 024103. doi: 10.1103/PhysRevB.87.024103
|
[80] |
BAKHTIARI S, LIU J Z, LIU Y N, et al. Monoclinic angle, shear response, and minimum energy pathways of NiTiCu martensite phases from ab initio calculations [J]. Acta Materialia, 2019, 178: 59–67. doi: 10.1016/j.actamat.2019.07.050
|
[81] |
GAO Y P, SHI R P, NIE J F, et al. Group theory description of transformation pathway degeneracy in structural phase transformations [J]. Acta Materialia, 2016, 109: 353–363. doi: 10.1016/j.actamat.2016.01.027
|
[82] |
GAO Y P, WANG Y Z. Hidden pathway during fcc to bcc/bct transformations: crystallographic origin of slip martensite in steels [J]. Physical Review Materials, 2018, 2(9): 093611. doi: 10.1103/PhysRevMaterials.2.093611
|
[83] |
ZHANG T L, WANG D, WANG Y Z. Novel transformation pathway and heterogeneous precipitate microstructure in Ti-alloys [J]. Acta Materialia, 2020, 196: 409–417. doi: 10.1016/j.actamat.2020.06.048
|
[84] |
GAO Y P. Symmetry and pathway analyses of the twinning modes in Ni-Ti shape memory alloys [J]. Materialia, 2019, 6: 100320. doi: 10.1016/j.mtla.2019.100320
|
[85] |
GAO Y P, ZHENG Y F, FRASER H, et al. Intrinsic coupling between twinning plasticity and transformation plasticity in metastable β Ti-alloys: a symmetry and pathway analysis [J]. Acta Materialia, 2020, 196: 488–504. doi: 10.1016/j.actamat.2020.07.020
|
[86] |
OLSON G B. Computational design of hierarchically structured materials [J]. Science, 1997, 277(5330): 1237–1242. doi: 10.1126/science.277.5330.1237
|
[87] |
CISSÉ C, ZAEEM M A. A phase-field model for non-isothermal phase transformation and plasticity in polycrystalline yttria-stabilized tetragonal zirconia [J]. Acta Materialia, 2020, 191: 111–123. doi: 10.1016/j.actamat.2020.03.025
|
[88] |
WEI S L, KIM J W, CANN J L, et al. Plastic strain-induced sequential martensitic transformation [J]. Scripta Materialia, 2020, 185: 36–41. doi: 10.1016/j.scriptamat.2020.03.060
|
[89] |
LEVITAS V I. High pressure phase transformations revisited [J]. Journal of Physics: Condensed Matter, 2018, 30(16): 163001. doi: 10.1088/1361-648X/aab4b0
|
[90] |
XU Y, MING P B, CHEN J. A phase field framework for dynamic adiabatic shear banding [J]. Journal of the Mechanics and Physics of Solids, 2020, 135: 103810. doi: 10.1016/j.jmps.2019.103810
|
[91] |
JAVANBAKHT M, LEVITAS V I. Phase field simulations of plastic strain-induced phase transformations under high pressure and large shear [J]. Physical Review B, 2016, 94(21): 214104. doi: 10.1103/PhysRevB.94.214104
|
[92] |
GUO X H, SHI S Q, MA X Q. Elastoplastic phase field model for microstructure evolution [J]. Applied Physics Letters, 2005, 87(22): 221910. doi: 10.1063/1.2138358
|
[93] |
PARANJAPE H M, MANCHIRAJU S, ANDERSON P M. A phase field-finite element approach to model the interaction between phase transformations and plasticity in shape memory alloys [J]. International Journal of Plasticity, 2016, 80: 1–18. doi: 10.1016/j.ijplas.2015.12.007
|
[94] |
KUNDIN J, RAABE D, EMMERICH H. A phase-field model for incoherent martensitic transformations including plastic accommodation processes in the austenite [J]. Journal of the Mechanics and Physics of Solids, 2011, 59(10): 2082–2102. doi: 10.1016/j.jmps.2011.07.001
|
[95] |
ESFAHANI S E, GHAMARIAN I, LEVITAS V I. Strain-induced multivariant martensitic transformations: a scale-independent simulation of interaction between localized shear bands and microstructure [J]. Acta Materialia, 2020, 196: 430–443. doi: 10.1016/j.actamat.2020.06.059
|
[96] |
SCHMITT R, KUHN C, MÜLLER R, et al. Crystal plasticity and martensitic transformations: a phase field approach [J]. Technische Mechanik, 2014, 34(1): 23–38. doi: 10.24352/UB.OVGU-2017-051
|
[97] |
ROTERS F, EISENLOHR P, HANTCHERLI L, et al. Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications [J]. Acta Materialia, 2010, 58(4): 1152–1211. doi: 10.1016/j.actamat.2009.10.058
|
[98] |
RICE J R. Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity [J]. Journal of the Mechanics and Physics of Solids, 1971, 19(6): 433–455. doi: 10.1016/0022-5096(71)90010-X
|
[99] |
MA A, ROTERS F. A constitutive model for fcc single crystals based on dislocation densities and its application to uniaxial compression of aluminium single crystals [J]. Acta Materialia, 2004, 52(12): 3603–3612. doi: 10.1016/j.actamat.2004.04.012
|
[100] |
YAO S L, YU J D, CUI Y N, et al. Revisiting the power law characteristics of the plastic shock front under shock loading [J]. Physical Review Letters, 2021, 126(8): 085503. doi: 10.1103/PhysRevLett.126.085503
|