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Theoretical investigation on the surface and morphological properties of lead nickelate multiferroics: vacancy dependency

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Abstract

In the context of the development of materials, morphology control represents an important tool for tuning their properties, thus enabling their application on photocatalysis, energy conversion and other areas. In this work, DFT/B3LYP methodology was carried out to investigate the surface structure and the electronic, ferroelectric and magnetic properties of low index surfaces of the multiferroic PbNiO3 material at the R3c crystalline phase. The results indicate that the surface energy increases in the following the order (110) < (012) < (111) < (001) < (101) < (100). These results allow us to predict the available morphologies, finding that six theoretical morphologies correspond to those reported experimentally, while nine morphologies have not yet been reported experimentally. The properties of the exposed surfaces for each morphology can be associated with the number of oxygen vacancies (V0), and the presence of uncoordinated [NiO6] and [PbO6] clusters.

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References

  1. Jian J, Jiang G, van de Krol R, Wei B, Wang H (2018) Recent advances in rational engineering of multinary semiconductors for photoelectrochemical hydrogen generation. Nano Energy 51:457–480

    CAS  Google Scholar 

  2. Sekhar KC, Silva JPB, Kamakshi K, Pereira M, Gomes MJM (2013) Semiconductor layer thickness impact on optical and resistive switching behavior of pulsed laser deposited BaTiO3/ZnO heterostructures. Appl Phys Lett 102:212903–212907

    Google Scholar 

  3. Tian Y-F, Hu S-J, Yan S-S, Mei L-M (2013) Oxide magnetic semiconductors: materials, properties, and devices. Chin Phys B 22:088505–088521

    Google Scholar 

  4. Bonafos C, Carrada M, Benassayag G, Schamm-Chardon S, Groenen J, Paillard V, Pecassou B, Claverie A, Dimitrakis P, Kapetanakis E, Ioannou-Sougleridis V, Normand P, Sahu B, Slaoui A (2012) Si and Ge nanocrystals for future memory devices. Mater Sci Semicond Process 15:615–626

    CAS  Google Scholar 

  5. Jang JS, Kim HG, Lee JS (2012) Heterojunction semiconductors: a strategy to develop efficient photocatalytic materials for visible light water splitting. Catal Today 185:270–277

    CAS  Google Scholar 

  6. Meyer BK, Polity A, Reppin D, Becker M, Hering P, Klar PJ, Sander T, Reindl C, Benz J, Eickhoff M, Heiliger C, Heinemann M, Bläsing J, Krost A, Shokovets S, Müller C, Ronning C (2012) Binary copper oxide semiconductors: from materials towards devices. Phys Status Solidi (b) 249:1487–1509

    CAS  Google Scholar 

  7. Ozgur U, Hofstetter D, Morkoc H (2010) ZnO devices and applications: a review of current status and future prospects. Proc IEEE 98:1255–1268

    CAS  Google Scholar 

  8. Orton J (2009) The story of semiconductors, 2nd edn. Oxford University Press, Nova York

    Google Scholar 

  9. Ashrafi A, Jagadish C (2007) Review of zincblende ZnO: stability of metastable ZnO phases. J Appl Phys 102:071101–071112

    Google Scholar 

  10. Klingshirn C (2007) ZnO: material, physics and applications. ChemPhysChem 8:782–803

    CAS  Google Scholar 

  11. Awschalom DD, Flatte ME (2007) Challenges for semiconductor spintronics. Nat Phys 3:153–159

    CAS  Google Scholar 

  12. Baltz V, Manchon A, Tsoi M, Moriyama T, Ono T, Tserkovnyak Y (2018) Antiferromagnetic spintronics. Rev Mod Phys 90:015005–015062

    CAS  Google Scholar 

  13. Lebrun R, Ross A, Bender SA, Qaiumzadeh A, Baldrati L, Cramer J, Brataas A, Duine RA, Kläui M (2018) Tunable long-distance spin transport in a crystalline antiferromagnetic iron oxide. Nature 561:222–225

    CAS  Google Scholar 

  14. Li X, Yang J (2016) First-principles design of spintronics materials. Natl Sci Rev 3:365–381

    CAS  Google Scholar 

  15. Sergio T, Marta G, Sophie D, Clément B, Karim B, Sophie C, Cyrile D, Eric J, Pierre S, Richard M, Frédéric P (2016) Self-assembled monolayers based spintronics: from ferromagnetic surface functionalization to spin-dependent transport. J Phys Condens Matter 28:094010–1–094010-11

    Google Scholar 

  16. Sando D, Barthélémy A, Bibes M (2014) BiFeO3 epitaxial thin films and devices: past, present and future. J Phys Condens Matter 26:473201–473223

    CAS  Google Scholar 

  17. Fusil S, Garcia V, Barthélémy A, Bibes M (2014) Magnetoelectric devices for spintronics. Annu Rev Mater Res 44:91–116

    CAS  Google Scholar 

  18. Fabian J, Matos-Abiague A, Ertler C, Stano P, Žutić I (2007) Semiconductor spintronics. Acta Phys Slovaca 57:565–907

    CAS  Google Scholar 

  19. Felser C, Fecher Gerhard H, Balke B (2007) Spintronics: a challenge for materials science and solid-state chemistry. Angew Chem Int Ed 46:668–699

    CAS  Google Scholar 

  20. Je-Geun P, Manh Duc L, Jaehong J, Sanghyun L (2014) Structure and spin dynamics of multiferroic BiFeO3. J Phys Condens Matter 26:433202–433236

    Google Scholar 

  21. Silva J, Reyes A, Esparza H, Camacho H, Fuentes L (2011) BiFeO3: a review on synthesis, doping and crystal structure. Integr Ferroelectr 126:47–59

    CAS  Google Scholar 

  22. Liu K, Fan H, Ren P, Yang C (2011) Structural, electronic and optical properties of BiFeO3 studied by first-principles. J Alloy Compd 509:1901–1905

    CAS  Google Scholar 

  23. Tian H, Kuang X-Y, Mao A-J, Zhao H-J, Li H, Kuang F-G (2015) Comparing hydrostatic-pressure- and epitaxial-strain-induced phase transitions in multiferroic PbNiO3 from first principles. Solid State Commun 203:75–80

    CAS  Google Scholar 

  24. Hao XF, Stroppa A, Barone P, Filippetti A, Franchini C, Picozzi S (2014) Structural and ferroelectric transitions in magnetic nickelate PbNiO3. New J Phys 16:015030–015050

    Google Scholar 

  25. Wang W, Wang S, He D, Xu J-A (2014) Pressure induced phase transition of PbNiO3 from LiNbO3-type to perovskite. Solid State Commun 196:8–12

    CAS  Google Scholar 

  26. Erkişi A, Yıldırım EK, Gökoğlu G (2014) Electronic structure and magnetic properties of PbMO3 (M = Fe Co, Ni) magnetic perovskites: an ab initio study. Int J Mod Phys B 28:1450205–1450214

    Google Scholar 

  27. Hao XF, Stroppa A, Picozzi S, Filippetti A, Franchini C (2012) Exceptionally large room-temperature ferroelectric polarization in the PbNiO3 multiferroic nickelate: first-principles study. Phys Rev B 86:014116–014120

    Google Scholar 

  28. Inaguma Y, Tanaka K, Tsuchiya T, Mori D, Katsumata T, Ohba T, Hiraki K-I, Takahashi T, Saitoh H (2011) Synthesis, structural transformation, thermal stability, valence state, and magnetic and electronic properties of PbNiO3 with perovskite- and LiNbO3 type structures. J Am Chem Soc 133:16920–16929

    CAS  Google Scholar 

  29. Chen SW, Huang MJ, Lin PA, Jeng HT, Lee JM, Haw SC, Chen SA, Lin HJ, Lu KT, Chen DP, Dou SX, Wang XL, Chen JM (2013) Orbital structure of FeTiO3 ilmenite investigated with polarization-dependent X-ray absorption spectroscopy and band structure calculations. Appl Phys Lett 102:042107–042112

    Google Scholar 

  30. Chikoidze E, Tchelidze T, Popova E, Maso P, Ponjavidze N, Keller N, Dumont Y (2013) Conductivity type inversion in wide band gap antiferromagnetic FeTiO3. Appl Phys Lett 102:122112–122116

    Google Scholar 

  31. Wu X, Steinle-Neumann G, Narygina O, McCammon C, Dubrovinsky L (2010) In situ high-pressure study of LiNbO3-type FeTiO3: X-ray diffraction and Mossbauer spectroscopy. High Press Res 30:395–405

    CAS  Google Scholar 

  32. Xin C, Wang Y, Sui Y, Wang Y, Wang X, Zhao K, Liu Z, Li B, Liu X (2014) Electronic, magnetic and multiferroic properties of magnetoelectric NiTiO3. J Alloy Compd 613:401–406

    CAS  Google Scholar 

  33. Varga T, Droubay TC, Bowden ME, Colby RJ, Manandhar S, Shutthanandan V, Hu D, Kabius BC, Apra E, Shelton WA, Chambers SA (2013) Coexistence of weak ferromagnetism and polar lattice distortion in epitaxial NiTiO3 thin films of the LiNbO3-type structure. J Vac Sci Technol B Nanotechnol Microelectron Mater Process Meas Phenom 31:030603–1–030603-5

    Google Scholar 

  34. Salvador P, Gutierrez C, Goodenough JB (1982) Photoresponse of n-type semiconductor NiTiO3. Appl Phys Lett 40:188–190

    CAS  Google Scholar 

  35. Zhu X (2009) Recent patents on perovskite ferroelectric nanostructures. Recent Pat Nanotechnol 3:42–45

    CAS  Google Scholar 

  36. Yang YC, Song C, Wang XH, Zeng F, Pan F (2008) Giant piezoelectric d33 coefficient in ferroelectric vanadium doped ZnO films. Appl Phys Lett 92:012907–1–012907-3

    Google Scholar 

  37. Chen Z-X, Chen Y, Jiang Y-S (2001) DFT study on ferroelectricity of BaTiO3. J Phys Chem B 105:5766–5771

    CAS  Google Scholar 

  38. Dragan D (1998) Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics. Rep Prog Phys 61:1267–1326

    Google Scholar 

  39. Scott JF (2013) Room-temperature multiferroic magnetoelectrics. NPG Asia Mater 5:e72-1–e72-11

    Google Scholar 

  40. Scott JF (2007) Data storage: multiferroic memories. Nat Mater 6:256–257

    CAS  Google Scholar 

  41. Eerenstein W, Mathur ND, Scott JF (2006) Multiferroic and magnetoelectric materials. Nature 442:759–765

    CAS  Google Scholar 

  42. Vaz CAF (2012) Electric field control of magnetism in multiferroic heterostructures. J Phys Condens Matter 24:333201–333229

    CAS  Google Scholar 

  43. Setter N, Damjanovic D, Eng L, Fox G, Gevorgian S, Hong S, Kingon A, Kohlstedt H, Park NY, Stephenson GB, Stolitchnov I, Taganstev AK, Taylor DV, Yamada T, Streiffer S (2006) Ferroelectric thin films: review of materials, properties, and applications. J Appl Phys 100:051606–051651

    Google Scholar 

  44. Lacerda LHDS, Ribeiro RAP, de Lazaro SR (2019) Magnetic, electronic, ferroelectric, structural and topological analysis of AlFeO3, FeAlO3, FeVO3, BiFeO3 and PbFeO3 materials: theoretical evidences of magnetoelectric coupling. J Magn Magn Mater 480:199–208

    CAS  Google Scholar 

  45. Lacerda LHDS, de Lazaro SR (2019) DFT simulations to clarify the molecular origin of magnetoelectric coupling in R3c materials based on Fe. New J Chem 43:10610–10617

    CAS  Google Scholar 

  46. Lacerda LHS, de Lazaro SR (2018) Multiferroism and magnetic ordering in new NiBO3 (B = Ti, Ge, Zr, Sn, Hf and Pb) materials: a DFT study. J Magn Magn Mater 465:412–420

    CAS  Google Scholar 

  47. Lacerda LHDS, de Lazaro SR (2018) Improvement of multiferroic property and change of magnetic ordering in new ANiO3 (A = Ti, Ge, Zr, Sn, Hf and Pb). Comput Mater Sci 153:228–234

    CAS  Google Scholar 

  48. Ribeiro RAP, Lacerda LHS, Longo E, Andrés J, de Lazaro SR (2019) Towards enhancing the magnetic properties by morphology control of ATiO3 (A = Mn, Fe, Ni) multiferroic materials. J Magn Magn Mater 475:544–549

    CAS  Google Scholar 

  49. Murtaza T, Ali J, Khan MS, Asokan K (2018) Structural, electrical and magnetic properties of multiferroic BiFeO3–SrTiO3 composites. J Mater Sci Mater Electron 29:2110–2119

    CAS  Google Scholar 

  50. Alyeksyei A, Bai Y, Lu Q, Zhao S (2018) The regulation of magnetoelectric coupling and magnetic exchange bias effects in La doped Bi5Ti3FeO15 multiferroic films. Mater Lett 213:114–117

    CAS  Google Scholar 

  51. Jain A, Panwar AK, Jha AK (2018) Significant enhancement in structural, dielectric, piezoelectric and ferromagnetic properties of Ba0.9Sr0.1Zr0.1Ti0.9O3–CoFe2O4 multiferroic composites. Mater Res Bull 100:367–376

    CAS  Google Scholar 

  52. Bharathkumar S, Sakar M, Ponpandian N, Balakumar S (2018) Dual oxidation state induced oxygen vacancies in Pr substituted BiFeO3 compounds: an effective material activation strategy to enhance the magnetic and visible light-driven photocatalytic properties. Mater Res Bull 101:107–115

    CAS  Google Scholar 

  53. Sarkar T, Elizabeth S, Anil Kumar PS (2018) Enhanced magnetization and reduced leakage current by Zr substitution in multiferroic ScMnO3. J Magn Magn Mater 448:266–273

    CAS  Google Scholar 

  54. Suresh P, Vijaya Laxmi K, Anil Kumar PS (2018) Enhanced room temperature multiferroic characteristics in hexagonal LuFe1xNixO3 (x = 0−0.3) nanoparticles. J Magn Magn Mater 448:117–122

    CAS  Google Scholar 

  55. Ge W, Rahman A, Cheng H, Zhang M, Liu J, Zhang Z, Ye B (2018) Probing the role of cation vacancies on the ferromagnetism of La-doped BiFeO3 ceramics. J Magn Magn Mater 449:401–405

    CAS  Google Scholar 

  56. Teixeira MM, de Oliveira RC, Oliveira MC, Pontes Ribeiro RA, de Lazaro SR, Li MS, Chiquito AJ, Gracia L, Andrés J, Longo E (2018) Computational chemistry meets experiments for explaining the geometry, electronic structure, and optical properties of Ca10V6O25. Inorg Chem 57:15489–15499

    CAS  Google Scholar 

  57. Ribeiro RAP, de Lazaro SR, Gracia L, Longo E, Andrés J (2018) Theoretical approach for determining the relation between the morphology and surface magnetism of Co3O4. J Magn Magn Mater 453:262–267

    CAS  Google Scholar 

  58. Ribeiro RAP, Andrés J, Longo E, Lazaro SR (2018) Magnetism and multiferroic properties at MnTiO3 surfaces: a DFT study. Appl Surf Sci 452:463–472

    CAS  Google Scholar 

  59. Ribeiro RAP, Longo E, Andrés J, de Lazaro SR (2018) A DFT investigation of the role of oxygen vacancies on the structural, electronic and magnetic properties of ATiO3 (A = Mn, Fe, Ni) multiferroic materials. Phys Chem Chem Phys 20:28382–28392

    CAS  Google Scholar 

  60. Oliveira MC, Ribeiro RAP, Gracia L, de Lazaro SR, de Assis M, Oliva M, Rosa ILV, Gurgel MFDC, Longo E, Andrés J (2018) Experimental and theoretical study of the energetic, morphological, and photoluminescence properties of CaZrO3:Eu3+. CrystEngComm 20:5519–5530

    CAS  Google Scholar 

  61. Tasker PW (1979) The stability of ionic crystal surfaces. J Phys C Solid State Phys 12:4977–4984

    CAS  Google Scholar 

  62. Dai Y, Gao Q, Cui C, Yang L, Li C, Li X (2018) Role of ferroelectric/ferromagnetic layers on the ferroelectric properties of magnetoelectric composite films derived by chemical solution deposition. Mater Res Bull 99:424–428

    CAS  Google Scholar 

  63. Dai J-Q, Xu J-W, Zhu J-H (2017) Thermodynamic stability of BiFeO3 (0001) surfaces from ab initio theory. ACS Appl Mater Interfaces 9:3168–3177

    CAS  Google Scholar 

  64. Ribeiro RAP, de Lazaro SR, Pianaro SA (2015) Density functional theory applied to magnetic materials: Mn3O4 at different hybrid functionals. J Magn Magn Mater 391:166–171

    CAS  Google Scholar 

  65. Chartier A, D’Arco P, Dovesi R, Saunders VR (1999) Ab initio Hartree–Fock investigation of the structural, electronic, and magnetic properties of Mn3O4. Phys Rev B 60:14042–14048

    CAS  Google Scholar 

  66. Feng X, Harrison NM (2004) Magnetic coupling constants from a hybrid density functional with 35% Hartree–Fock exchange. Phys Rev B 70:092402–092405

    Google Scholar 

  67. Becke AD (2014) Perspective: fifty years of density-functional theory in chemical physics. J Chem Phys 140:18A301–18A320

    Google Scholar 

  68. Dovesi R, Erba A, Orlando R, Zicovich-Wilson CM, Civalleri B, Maschio L, Rérat M, Casassa S, Baima J, Salustro S, Kirtman B (2018) Quantum-mechanical condensed matter simulations with CRYSTAL. Wiley Interdiscip Rev Comput Mol Sci 8:e1360-1–e1360-36

    Google Scholar 

  69. Towler MD, Allan NL, Harrison NM, Saunders VR, Mackrodt WC, Aprà E (1994) Ab initio study of MnO and NiO. Phys Rev B 50:5041–5054

    CAS  Google Scholar 

  70. Ferrari AM, Pisani C (2006) An ab initio periodic study of NiO supported at the Pd (100) surface. Part 1: the perfect epitaxial monolayer. J Phys Chem B 110:7909–7917

    CAS  Google Scholar 

  71. Zagorac D, Doll K, Schön JC, Jansen M (2012) Sterically active electron pairs in lead sulfide? An investigation of the electronic and vibrational properties of PbS in the transition region between the rock salt and the α-GeTe-type modifications. Chem Eur J 18:10929–10936

    CAS  Google Scholar 

  72. Monkhorst HJ, Pack JD (1976) Special points for Brillouin-zone integrations. Phys Rev B 13:5188–5192

    Google Scholar 

  73. Pisani C, Dovesi R, Roetti C (1988) Hartree–Fock ab initio treatment of crystalline systems. Springer, Berlin

    Google Scholar 

  74. Toyoda M, Yamauchi K, Oguchi T (2013) Ab initio study of magnetic coupling in CaCu3B4O12 (B = Ti, Ge, Zr, and Sn). Phys Rev B Condens Matter Mater Phys 87:224430–224437

    Google Scholar 

  75. Liechtenstein AI, Katsnelson MI, Antropov VP, Gubanov VA (1987) Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys. J Magn Magn Mater 67:65–74

    CAS  Google Scholar 

  76. Dzyaloshinsky I (1958) A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J Phys Chem Solids 4:241–255

    CAS  Google Scholar 

  77. Moriya T (1960) Anisotropic superexchange interaction and weak ferromagnetism. Phys Rev 120:91–98

    CAS  Google Scholar 

  78. Sergienko IA, Dagotto E (2006) Role of the Dzyaloshinskii–Moriya interaction in multiferroic perovskites. Phys Rev B 73:094434–094438

    Google Scholar 

  79. Fennie CJ (2008) Ferroelectrically induced weak ferromagnetism by design. Phys Rev Lett 100:167203–167206

    Google Scholar 

  80. Rabe KM, Ghosez P (2007) Physics of ferroelectrics: a modern perspective. Springer, Berlin, pp 117–174

    Google Scholar 

  81. Donnerberg HJ, Tomlinson SM, Catlow CRA (1991) Defects in LiNbO3-II. Computer simulation. J Phys Chem Solids 52:201–210

    CAS  Google Scholar 

  82. Schirmer OF, Thiemann O, Wöhlecke M (1991) Defects in LiNbO3-I. Experimental aspects. J Phys Chem Solids 52:185–200

    CAS  Google Scholar 

  83. Nassau K, Levinstein HJ, Loiacono GM (1996) Ferroelectric lithium niobate. 1. Growth, domain structure, dislocations and etching. J Phys Chem Solids 27:983–988

    Google Scholar 

  84. Nassau K, Levinstein HJ, Loiacono GM (1966) Ferroelectric lithium niobate. 2. Preparation of single domain crystals. J Phys Chem Solids 27:989–996

    CAS  Google Scholar 

  85. Abrahams SC, Levinstein HJ, Reddy JM (1966) Ferroelectric lithium niobate. 5. Polycrystal X-ray diffraction study between 24° and 1200°C. J Phys Chem Solids 27:1019–1026

    CAS  Google Scholar 

  86. Benedek NA, Fennie CJ (2013) Why are there so few perovskite ferroelectrics? J Phys Chem C 117:13339–13349

    CAS  Google Scholar 

  87. Varga T, Kumar A, Vlahos E, Denev S, Park M, Hong S, Sanehira T, Wang Y, Fennie CJ, Streiffer SK, Ke X, Schiffer P, Gopalan V, Mitchell JF (2009) Coexistence of weak ferromagnetism and ferroelectricity in the high pressure LiNbO3-type phase of FeTiO3. Phys Rev Lett 103:047601-1–047601-4

    Google Scholar 

  88. Gao N, Quan C, Ma Y, Han Y, Wu Z, Mao W, Zhang J, Yang J, Li X, Huang W (2016) Experimental and first principles investigation of the multiferroics BiFeO3 and Bi0.9Ca0.1FeO3: structure, electronic, optical and magnetic properties. Phys B 481:45–52

    CAS  Google Scholar 

  89. Gu Y, Zhao J, Zhang W, Zheng H, Liu L, Chen W (2017) Structural transformation and multiferroic properties of Sm and Ti co-doped BiFeO3 ceramics with Fe vacancies. Ceram Int 43:14666–14671

    CAS  Google Scholar 

  90. Shu H, Ma Y, Wang Z, Mao W, Chu L, Yang J, Wu Q, Min Y, Song R, Li X (2017) Structural, optical and multiferroic properties of (Nd, Zn)-Co-doped BiFeO3 nanoparticles. J Supercond Novel Magn 30:3027–3034

    CAS  Google Scholar 

  91. Das A, De S, Bandyopadhyay S, Chatterjee S, Das D (2017) Magnetic, dielectric and magnetoelectric properties of BiFeO3–CoFe2O4 nanocomposites. J Alloy Compd 697:353–360

    CAS  Google Scholar 

  92. Yu J, Zhou P, Li Q (2013) New insight into the enhanced visible-light photocatalytic activities of B-, C- and B/C-doped anatase TiO2 by first-principles. Phys Chem Chem Phys 15:12040–12047

    CAS  Google Scholar 

  93. Zhou P, Yu J, Wang Y (2013) The new understanding on photocatalytic mechanism of visible-light response NS codoped anatase TiO2 by first-principles. Appl Catal B 142–143:45–53

    Google Scholar 

  94. Ma X, Dai Y, Guo M, Huang B (2012) The role of effective mass of carrier in the photocatalytic behavior of silver halide-based Ag@AgX (X = Cl, Br, I): a theoretical study. ChemPhysChem 13:2304–2309

    CAS  Google Scholar 

  95. Soares GB, Ribeiro RAP, de Lazaro SR, Ribeiro C (2016) Photoelectrochemical and theoretical investigation of the photocatalytic activity of TiO2:N. RSC Adv 6:89687–89698

    CAS  Google Scholar 

  96. Picard J, Cerf R (2006) The Wulff crystal in Ising and percolation models: Ecole d’Eté de Probabilités de Saint-Flour XXXIV - 2004. Springer, Berlin

    Google Scholar 

  97. Wulff G (1901) Zur Frage der Geschwindigkeit des Wachstums und der Auflösung der Krystallflagen. Zeitschrift für Krystallographie und Mineralogie 34:449–530

    CAS  Google Scholar 

  98. Barmparis GD, Lodziana Z, Lopez N, Remediakis IN (2015) Nanoparticle shapes by using Wulff constructions and first-principles calculations. Beilstein J Nanotechnol 6:361–368

    Google Scholar 

  99. Andrés J, Gracia L, Gouveia AF, Ferrer MM, Longo E (2015) Effects of surface stability on the morphological transformation of metals and metal oxides as investigated by first-principles calculations. Nanotechnology 26:405703-1–405703-11

    Google Scholar 

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Acknowledgements

The authors acknowledge support from CAPES, CNPq, Fundação Araucária (Financing Project 009/2017) and the High-Performance Computing Laboratory (LCAD) from Ponta Grossa State University for their computational facilities acquired through FINEP CT-INFRA/2013 support.

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da Silveira Lacerda, L.H., de Lazaro, S.R. Theoretical investigation on the surface and morphological properties of lead nickelate multiferroics: vacancy dependency. J Mater Sci 55, 6875–6890 (2020). https://doi.org/10.1007/s10853-020-04526-5

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