# Study of High-Temperature Behaviour of ZnO by Ab Initio Molecular Dynamics Simulations and X-ray Absorption Spectroscopy

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## Abstract

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## 1. Introduction

## 2. Experimental Details

## 3. Computational Details

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AIMD | Ab Initio Molecular Dynamics |

BADF | Bond Angle Distribution Functions |

DFT | Density Functional Theory |

EXAFS | Extended X-ray Absorption Fine Structure |

FT | Fourier Transform |

MS | Multiple-Scattering |

MSD | Mean-Square Displacements |

MSRD | Mean-Square Relative Displacements |

Pair Distribution Function | |

RMC | Reverse Monte Carlo |

## References

- Özgür, U.; Alivov, Y.I.; Liu, C.; Teke, A.; Reshchikov, M.A.; Doğan, S.; Avrutin, V.; Cho, S.J.; Morkoç, H. A comprehensive review of ZnO materials and devices. J. Appl. Phys.
**2005**, 98, 041301. [Google Scholar] [CrossRef] [Green Version] - Janotti, A.; de Walle, C.G.V. Fundamentals of zinc oxide as a semiconductor. Rep. Prog. Phys.
**2009**, 72, 126501. [Google Scholar] [CrossRef] [Green Version] - Lee, K.M.; Lai, C.W.; Ngai, K.S.; Juan, J.C. Recent developments of zinc oxide based photocatalyst in water treatment technology: A review. Water Res.
**2016**, 88, 428–448. [Google Scholar] [CrossRef] [PubMed] - Tereshchenko, A.; Bechelany, M.; Viter, R.; Khranovskyy, V.; Smyntyna, V.; Starodub, N.; Yakimova, R. Optical biosensors based on ZnO nanostructures: Advantages and perspectives. A review. Sens. Actuat. B-Chem.
**2016**, 229, 664–677. [Google Scholar] [CrossRef] [Green Version] - Gurylev, V.; Perng, T.P. Defect engineering of ZnO: Review on oxygen and zinc vacancies. J. Eur. Ceram. Soc.
**2021**, 41, 4977–4996. [Google Scholar] [CrossRef] - Rasmidi, R.; Duinong, M.; Chee, F.P. Radiation damage effects on zinc oxide (ZnO) based semiconductor devices—A review. Rad. Phys. Chem.
**2021**, 184, 109455. [Google Scholar] [CrossRef] - Verma, R.; Pathak, S.; Srivastava, A.K.; Prawer, S.; Tomljenovic-Hanic, S. ZnO nanomaterials: Green synthesis, toxicity evaluation and new insights in biomedical applications. J. Alloys Compd.
**2021**, 876, 160175. [Google Scholar] [CrossRef] - Abrahams, S.C.; Bernstein, J.L. Remeasurement of the structure of hexagonal ZnO. Acta Crystallogr. B
**1969**, 25, 1233–1236. [Google Scholar] [CrossRef] - Reeber, R.R. Lattice parameters of ZnO from 4.2
^{∘}to 296^{∘}K. J. Appl. Phys.**1970**, 41, 5063–5066. [Google Scholar] [CrossRef] - Karzel, H.; Potzel, W.; Köfferlein, M.; Schiessl, W.; Steiner, M.; Hiller, U.; Kalvius, G.M.; Mitchell, D.W.; Das, T.P.; Blaha, P.; et al. Lattice dynamics and hyperfine interactions in ZnO and ZnSe at high external pressures. Phys. Rev. B
**1996**, 53, 11425–11438. [Google Scholar] [CrossRef] - Dal Corso, A.; Posternak, M.; Resta, R.; Baldereschi, A. Ab initio study of piezoelectricity and spontaneous polarization in ZnO. Phys. Rev. B
**1994**, 50, 10715–10721. [Google Scholar] [CrossRef] [PubMed] - Wang, Z. Novel nanostructures of ZnO for nanoscale photonics, optoelectronics, piezoelectricity, and sensing. Appl. Phys. A
**2007**, 88, 7–15. [Google Scholar] [CrossRef] - Hsiao, C.C.; Huang, K.Y.; Hu, Y.C. Fabrication of a ZnO Pyroelectric Sensor. Sensors
**2008**, 8, 185–192. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bdikin, I.K.; Gracio, J.; Ayouchi, R.; Schwarz, R.; Kholkin, A.L. Local piezoelectric properties of ZnO thin films prepared by RF-plasma-assisted pulsed-laser deposition method. Nanotechnology
**2010**, 21, 235703. [Google Scholar] [CrossRef] [PubMed] - Yang, Y.; Guo, W.; Pradel, K.C.; Zhu, G.; Zhou, Y.; Zhang, Y.; Hu, Y.; Lin, L.; Wang, Z.L. Pyroelectric Nanogenerators for Harvesting Thermoelectric Energy. Nano Lett.
**2012**, 12, 2833–2838. [Google Scholar] [CrossRef] - Goel, S.; Kumar, B. A review on piezo-/ferro-electric properties of morphologically diverse ZnO nanostructures. J. Alloys Compd.
**2020**, 816, 152491. [Google Scholar] [CrossRef] - Schulz, H.; Thiemann, K. Structure parameters and polarity of the wurtzite type compounds SiC-2H and ZnO. Solid State Commun.
**1979**, 32, 783–785. [Google Scholar] [CrossRef] - Kihara, K.; Donnay, G. Anharmonic thermal vibrations in ZnO. Can. Mineral.
**1985**, 23, 647–654. [Google Scholar] - Albertsson, J.; Abrahams, S.C.; Kvick, Å. Atomic displacement, anharmonic thermal vibration, expansivity and pyroelectric coefficient thermal dependences in ZnO. Acta Crystallogr. B
**1989**, 45, 34–40. [Google Scholar] [CrossRef] - Serrano, J.; Manjón, F.J.; Romero, A.H.; Ivanov, A.; Cardona, M.; Lauck, R.; Bosak, A.; Krisch, M. Phonon dispersion relations of zinc oxide: Inelastic neutron scattering and ab initio calculations. Phys. Rev. B
**2010**, 81, 174304. [Google Scholar] [CrossRef] [Green Version] - Wu, X.; Lee, J.; Varshney, V.; Wohlwend, J.L.; Roy, A.K.; Luo, T. Thermal Conductivity of Wurtzite Zinc-Oxide from First-Principles Lattice Dynamics—A Comparative Study with Gallium Nitride. Sci. Rep.
**2016**, 6, 22504. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Timoshenko, J.; Anspoks, A.; Kalinko, A.; Kuzmin, A. Temperature dependence of the local structure and lattice dynamics of wurtzite-type ZnO. Acta Mater.
**2014**, 79, 194–202. [Google Scholar] [CrossRef] [Green Version] - Kuzmin, A.; Anspoks, A.; Kalinko, A.; Timoshenko, J. The use of X-ray absorption spectra for validation of classical force-field models. Z. Phys. Chem.
**2016**, 230, 537–549. [Google Scholar] [CrossRef] - Lewis, G.V.; Catlow, C.R.A. Potential models for ionic oxides. J. Phys. C Solid State Phys.
**1985**, 18, 1149–1161. [Google Scholar] [CrossRef] - Zaoui, A.; Sekkal, W. Pressure-induced softening of shear modes in wurtzite ZnO: A theoretical study. Phys. Rev. B
**2002**, 66, 174106. [Google Scholar] [CrossRef] - Kulkarni, A.J.; Zhou, M.; Ke, F.J. Orientation and size dependence of the elastic properties of zinc oxide nanobelts. Nanotechnology
**2005**, 16, 2749–2756. [Google Scholar] [CrossRef] [Green Version] - Klementiev, K.; Norén, K.; Carlson, S.; Clauss, K.G.V.S.; Persson, I. The BALDER Beamline at the MAX IV Laboratory. J. Phys. Conf. Ser.
**2016**, 712, 012023. [Google Scholar] [CrossRef] [Green Version] - VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Comput. Phys. Commun.
**2005**, 167, 103–128. [Google Scholar] [CrossRef] [Green Version] - Kühne, T.D.; Iannuzzi, M.; Ben, M.D.; Rybkin, V.V.; Seewald, P.; Stein, F.; Laino, T.; Khaliullin, R.Z.; Schütt, O.; Schiffmann, F.; et al. CP2K: An Electronic Structure and Molecular Dynamics Software Package—Quickstep: Efficient and Accurate Electronic Structure Calculations. J. Chem. Phys.
**2020**, 152, 194103. [Google Scholar] [CrossRef] - CP2K Developers Group. 2000–2021. Available online: https://www.cp2k.org (accessed on 5 August 2021).
- Perdew, J.P.; Ruzsinszky, A.; Csonka, G.I.; Vydrov, O.A.; Scuseria, G.E.; Constantin, L.A.; Zhou, X.; Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett.
**2008**, 100, 136406. [Google Scholar] [CrossRef] [Green Version] - Krack, M. Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals. Theor. Chem. Acc.
**2005**, 114, 145–152. [Google Scholar] [CrossRef] [Green Version] - VandeVondele, J.; Hutter, J. Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. J. Chem. Phys.
**2007**, 127, 114105. [Google Scholar] [CrossRef] [Green Version] - Kuzmin, A.; Timoshenko, J.; Kalinko, A.; Jonane, I.; Anspoks, A. Treatment of disorder effects in X-ray absorption spectra beyond the conventional approach. Rad. Phys. Chem.
**2020**, 175. [Google Scholar] [CrossRef] [Green Version] - Bocharov, D.; Krack, M.; Rafalskij, Y.; Kuzmin, A.; Purans, J. Ab initio molecular dynamics simulations of negative thermal expansion in ScF
_{3}: The effect of the supercell size. Comput. Mater. Sci.**2020**, 171, 109198. [Google Scholar] [CrossRef] - Anisimov, V.I.; Zaanen, J.; Andersen, O.K. Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B
**1991**, 44, 943–954. [Google Scholar] [CrossRef] [Green Version] - Dudarev, S.L.; Manh, D.N.; Sutton, A.P. Effect of Mott-Hubbard correlations on the electronic structure and structural stability of uranium dioxide. Philos. Mag. B
**1997**, 75, 613–628. [Google Scholar] [CrossRef] - Rabone, J.; Krack, M. A procedure for bypassing metastable states in local basis set DFT+U calculations and its application to uranium dioxide surfaces. Comput. Mater. Sci.
**2013**, 71, 157–164. [Google Scholar] [CrossRef] - Kuzmin, A.; Chaboy, J. EXAFS and XANES analysis of oxides at the nanoscale. IUCrJ
**2014**, 1, 571–589. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kuzmin, A.; Evarestov, R.A. Quantum mechanics–molecular dynamics approach to the interpretation of X-ray absorption spectra. J. Phys. Condens. Matter
**2009**, 21, 055401. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ankudinov, A.L.; Ravel, B.; Rehr, J.J.; Conradson, S.D. Real-space multiple-scattering calculation and interpretation of X-ray-absorption near-edge structure. Phys. Rev. B
**1998**, 58, 7565–7576. [Google Scholar] [CrossRef] [Green Version] - Rehr, J.J.; Albers, R.C. Theoretical approaches to X-ray absorption fine structure. Rev. Mod. Phys.
**2000**, 72, 621–654. [Google Scholar] [CrossRef] - Hedin, L.; Lundqvist, S. Explicit local exchange-correlation potentials. J. Phys. C Solid State Phys.
**1971**, 4, 2064. [Google Scholar] [CrossRef] - Shalimov, A.; Paszkowicz, W.; Grasza, K.; Skupiński, P.; Mycielski, A.; Bak-Misiuk, J. X-ray characterisation of a bulk ZnO crystal. Phys. Status Solidi B
**2007**, 244, 1573–1577. [Google Scholar] [CrossRef] - Booth, C.H.; Bridges, F.; Bauer, E.D.; Li, G.G.; Boyce, J.B.; Claeson, T.; Chu, C.W.; Xiong, Q. XAFS measurements of negatively correlated atomic displacements in HgBa
_{2}CuO_{4+δ}. Phys. Rev. B**1995**, 52, R15745. [Google Scholar] [CrossRef] [PubMed] - Jeong, I.K.; Heffner, R.H.; Graf, M.J.; Bilinge, S.J.L. Lattice dynamics and correlated atomic motion from the atomic pair distribution function. Phys. Rev. B
**2003**, 67, 104301. [Google Scholar] [CrossRef] [Green Version] - Sapelkin, A.V.; Bayliss, S.C. Distance dependence of mean-square relative displacements in EXAFS. Phys. Rev. B
**2002**, 65, 172104. [Google Scholar] [CrossRef] - Jonane, I.; Lazdins, K.; Timoshenko, J.; Kuzmin, A.; Purans, J.; Vladimirov, P.; Gräning, T.; Hoffmann, J. Temperature-dependent EXAFS study of the local structure and lattice dynamics in cubic Y
_{2}O_{3}. J. Synchrotron Rad.**2016**, 23, 510–518. [Google Scholar] [CrossRef] - Jonane, I.; Anspoks, A.; Kuzmin, A. Advanced approach to the local structure reconstruction and theory validation on the example of the W L
_{3}-edge extended X-ray absorption fine structure of tungsten. Model. Simul. Mater. Sci. Eng.**2018**, 26, 025004. [Google Scholar] [CrossRef] [Green Version] - Sevillano, E.; Meuth, H.; Rehr, J.J. Extended X-ray absorption fine structure Debye-Waller factors. I. Monatomic crystals. Phys. Rev. B
**1979**, 20, 4908–4911. [Google Scholar] [CrossRef]

**Figure 1.**The crystal structure of wurtzite-type ZnO: a supercell 6a × 4b × 4c used in AIMD simulations is shown. The unit cell is indicated by thick black lines.

**Figure 2.**Comparison of the experimental (black curves) and AIMD calculated (red curves) Zn K-edge EXAFS spectra and their Fourier transforms (FTs) at 300, 600, 900 and 1200 K. The AIMD calculations were performed in the NpT ensemble. The curves are shifted vertically for clarity.

**Figure 3.**Atomic pair distribution functions (PDFs) around absorbing Zn atom obtained from AIMD calculations in the NpT ensemble at 300, 600, 900 and 1200 K. Vertical lines show crystallographic distances in wurtzite-type ZnO at 300 K from [19].

**Figure 4.**Left panel: Dependence of the Zn–O (solid symbols) and Zn–Zn (open symbols) MSRDs $\sigma {(T,r)}^{2}$ on distance R and temperature T in wurtzite-type ZnO evaluated from AIMD calculations at 300 K (circles), 600 K (squares), 900 K (diamonds) and 1200 K (triangles) in the NpT ensemble. Horizontal lines show asymptotic behaviour of MSRDs for distant shells. Right panel: Temperature dependence of MSRD factors for the nearest and distant Zn–O and Zn–Zn atom pairs in w-ZnO. Solid and dashed lines are fits by the Einstein model with the characteristic temperature ${\theta}_{\mathrm{E}}$ for Zn–O and Zn–Zn atom pairs, correspondingly.

**Figure 5.**Bond angle distribution functions (BADFs) O–Zn–O and Zn–O–Zn within and between ZnO${}_{4}$ tetrahedra, respectively, calculated by AIMD. Dashed (solid) curves correspond to the O–Zn–O and Zn–O–Zn angles within the $ab$ plane (along the c axis). Vertical lines indicate the positions of the distribution maxima at 300 K.

**Table 1.**The average lattice parameters for ZnO obtained from AIMD simulations using the NpT ensemble vs. the experimental values from [19].

AIMD | Experiment | |||
---|---|---|---|---|

Temperature (K) | a (Å) | c (Å) | a (Å) | c (Å) |

300 | 3.258 | 5.220 | 3.24992 (5) | 5.20658 (8) |

600 | 3.265 | 5.231 | 3.25682 (5) | 5.21251 (8) |

900 | 3.272 | 5.243 | 3.26480 (5) | 5.21939 (8) |

1200 | 3.281 | 5.257 |

**Table 2.**Temperature dependence of the mean-square displacements (MSDs) for oxygen and zinc atoms in ZnO, estimated from the asymptotic behaviour of MSRDs at large distances.

T (K) | MSD (O) (Å${}^{2}$) | MSD (Zn) (Å${}^{2}$) |
---|---|---|

300 | 0.0054 (4) | 0.0072 (4) |

600 | 0.010 (3) | 0.014 (3) |

900 | 0.018 (5) | 0.024 (5) |

1200 | 0.024 (6) | 0.033 (6) |

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**MDPI and ACS Style**

Bocharov, D.; Pudza, I.; Klementiev, K.; Krack, M.; Kuzmin, A.
Study of High-Temperature Behaviour of ZnO by Ab Initio Molecular Dynamics Simulations and X-ray Absorption Spectroscopy. *Materials* **2021**, *14*, 5206.
https://doi.org/10.3390/ma14185206

**AMA Style**

Bocharov D, Pudza I, Klementiev K, Krack M, Kuzmin A.
Study of High-Temperature Behaviour of ZnO by Ab Initio Molecular Dynamics Simulations and X-ray Absorption Spectroscopy. *Materials*. 2021; 14(18):5206.
https://doi.org/10.3390/ma14185206

**Chicago/Turabian Style**

Bocharov, Dmitry, Inga Pudza, Konstantin Klementiev, Matthias Krack, and Alexei Kuzmin.
2021. "Study of High-Temperature Behaviour of ZnO by Ab Initio Molecular Dynamics Simulations and X-ray Absorption Spectroscopy" *Materials* 14, no. 18: 5206.
https://doi.org/10.3390/ma14185206