Journal Home > Volume 12 , Issue 5

Chemical doping is a normal strategy to tune thermal expansion coefficient (TEC) of ceramics in engineering applications, but the resultant TEC values usually follow Vegard’s law, as doping does not modify the nature of chemical bonding in ceramics and its anharmonicity. In this paper, we report abnormal TEC behavior in (Nd1−xDyx)2Zr2O7 ceramics, where the TEC values remarkably exceed the values predicted by Vegard’s law and even exceed the values obtained for two constituents Nd2Zr2O7 and Dy2Zr2O7. In addition to a reduction in lattice energy with an increasing molar fraction of Dy (x) value, we attribute the additional increase in the TEC to the high concentration of Dy dopants in a pyrochlore (P) region, which can soften low-lying optical phonon modes and induce strongly avoided crossing with acoustic phonon branches and enhanced anharmonicity. We believe that this finding can provide a new route to break through the restriction imposed by the conventional Vegard’s law on the TEC values and bring new opportunities for thermal barrier coatings (TBCs) or ceramic/metal composites towards realizing minimized thermal mismatch and prolonged service life during thermal cycling.


menu
Abstract
Full text
Outline
Electronic supplementary material
About this article

Abnormal thermal expansion coefficients in (Nd1−xDyx)2Zr2O7 pyrochlore: The effect of low-lying optical phonons

Show Author's information Zesheng Yanga,Yi Lia,b,Wei PanaChunlei Wana( )
State Key Laboratory of New Ceramics & Fine Processing, Tsinghua University, Beijing 100084, China
College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China

† Zesheng Yang and Yi Li contributed equally to this work.

Abstract

Chemical doping is a normal strategy to tune thermal expansion coefficient (TEC) of ceramics in engineering applications, but the resultant TEC values usually follow Vegard’s law, as doping does not modify the nature of chemical bonding in ceramics and its anharmonicity. In this paper, we report abnormal TEC behavior in (Nd1−xDyx)2Zr2O7 ceramics, where the TEC values remarkably exceed the values predicted by Vegard’s law and even exceed the values obtained for two constituents Nd2Zr2O7 and Dy2Zr2O7. In addition to a reduction in lattice energy with an increasing molar fraction of Dy (x) value, we attribute the additional increase in the TEC to the high concentration of Dy dopants in a pyrochlore (P) region, which can soften low-lying optical phonon modes and induce strongly avoided crossing with acoustic phonon branches and enhanced anharmonicity. We believe that this finding can provide a new route to break through the restriction imposed by the conventional Vegard’s law on the TEC values and bring new opportunities for thermal barrier coatings (TBCs) or ceramic/metal composites towards realizing minimized thermal mismatch and prolonged service life during thermal cycling.

Keywords: first-principles calculations, thermal expansion, thermal barrier coating (TBC), avoided crossing

References(47)

[1]
Lu TC, Yang J, Suo Z, et al. Matrix cracking in intermetallic composites caused by thermal expansion mismatch. Acta Metall Mater 1991, 39: 1883–1890.
[2]
Fitzpatrick ME, Hutchings MT, Withers PJ. Separation of macroscopic, elastic mismatch and thermal expansion misfit stresses in metal matrix composite quenched plates from neutron diffraction measurements. Acta Mater 1997, 45: 4867–4876.
[3]
Martena M, Botto D, Fino P, et al. Modelling of TBC system failure: Stress distribution as a function of TGO thickness and thermal expansion mismatch. Eng Fail Anal 2006, 13: 409–426.
[4]
Wei ZY, Meng GH, Chen L, et al. Progress in ceramic materials and structure design toward advanced thermal barrier coatings. J Adv Ceram 2022, 11: 985–1068.
[5]
Vaßen R, Jarligo MO, Steinke T, et al. Overview on advanced thermal barrier coatings. Surf Coat Technol 2010, 205: 938–942.
[6]
Cao XQ, Vassen R, Stoever D. Ceramic materials for thermal barrier coatings. J Eur Ceram Soc 2004, 24: 1–10.
[7]
Schlichting KW, Padture NP, Jordan EH, et al. Failure modes in plasma-sprayed thermal barrier coatings. Mater Sci Eng 2003, 342: 120–130.
[8]
Wu J, Wei XZ, Padture NP, et al. Low-thermal-conductivity rare-earth zirconates for potential thermal-barrier-coating applications. J Am Ceram Soc 2002, 85: 3031–3035.
[9]
Liu DB, Shi BL, Geng LY, et al. High-entropy rare-earth zirconate ceramics with low thermal conductivity for advanced thermal-barrier coatings. J Adv Ceram 2022, 11: 961–973.
[10]
Wang YH, Ma Z, Liu L, et al. Reaction products of Sm2Zr2O7 with calcium–magnesium–aluminum–silicate (CMAS) and their evolution. J Adv Ceram 2021, 10: 1389–1397.
[11]
Feng J, Xiao B, Zhou R, et al. Thermal expansions of Ln2Zr2O7 (Ln = La, Nd, Sm, and Gd) pyrochlore. J Appl Phys 2012, 111: 103535.
[12]
Zhu JT, Wei MY, Xu J, et al. Influence of order–disorder transition on the mechanical and thermophysical properties of A2B2O7 high-entropy ceramics. J Adv Ceram 2022, 11: 1222–1234.
[13]
Lehmann H, Pitzer D, Pracht G, et al. Thermal conductivity and thermal expansion coefficients of the lanthanum rare-earth-element zirconate system. J Am Ceram Soc 2003, 86: 1338–1344.
[14]
Ren XR, Wan CL, Zhao M, et al. Mechanical and thermal properties of fine-grained quasi-eutectoid (La1−xYbx)2Zr2O7 ceramics. J Eur Ceram Soc 2015, 35: 3145–3154.
[15]
Liu ZG, Ouyang JH, Zhou Y. Preparation and thermophysical properties of (NdxGd1−x)2Zr2O7 ceramics. J Mater Sci 2008, 43: 3596–3603.
[16]
Liu ZG, Ouyang JH, Zhou Y, et al. Densification, structure, and thermophysical properties of ytterbium–gadolinium zirconate ceramics. Int J Appl Ceram Technol 2009, 6: 485–491.
[17]
Yang J, Zhao M, Zhang L, et al. Pronounced enhancement of thermal expansion coefficients of rare-earth zirconate by cerium doping. Scripta Mater 2018, 153: 1–5.
[18]
Wan CL, Qu ZX, Du AB, et al. Influence of B site substituent Ti on the structure and thermophysical properties of A2B2O7-type pyrochlore Gd2Zr2O7. Acta Mater 2009, 57: 4782–4789.
[19]
Qu ZX, Wan CL, Pan W. Thermal expansion and defect chemistry of MgO-doped Sm2Zr2O7. Chem Mater 2007, 19: 4913–4918.
[20]
Guo L, Zhang Y, Wang CM, et al. Phase structure evolution and thermal expansion variation of Sc2O3 doped Nd2Zr2O7 ceramics. Mater Design 2015, 82: 114–118.
[21]
Guo L, Li BW, Cheng YX, et al. Composition optimization, high-temperature stability, and thermal cycling performance of Sc-doped Gd2Zr2O7 thermal barrier coatings: Theoretical and experimental studies. J Adv Ceram 2022, 11: 454–469.
[22]
Christensen M, Abrahamsen AB, Christensen NB, et al. Avoided crossing of rattler modes in thermoelectric materials. Nat Mater 2008, 7: 811–815.
[23]
Rodríguez-Carvajal J. FullProf. Available at https://cdifx.univ-rennes1.fr/fps/fp_rennes.pdf, 2000.
[24]
Liang YJ, Che YC, Liu XX, et al. Manual of Practical Inorganic Matter Thermodynamics. Shenyang, China: Northeastern University Press, 1993. (in Chinese)
[25]
Kresse G, Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 1996, 54: 11169–11186.
[26]
Kresse G, Hafner J. Ab initio molecular dynamics for liquid metals. Phys Rev B 1993, 47: 558–561.
[27]
Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 1999, 59: 1758–1775.
[28]
Shu XY, Qing Q, Wen MF, et al. Experimentally and theoretically revealing the co-doping effects of Ce–Sr in Gd2Zr2O7. Langmuir 2022, 38: 11529–11538.
[29]
Togo A, Tanaka I. First principles phonon calculations in materials science. Scripta Mater 2015, 108: 1–5.
[30]
Begg BD, Hess NJ, McCready DE, et al. Heavy-ion irradiation effects in Gd2(Ti2−xZrx)O7 pyrochlores. J Nucl Mater 2001, 289: 188–193.
[31]
Sayed FN, Grover V, Bhattacharyya K, et al. Sm2−xDyxZr2O7 pyrochlores: Probing order–disorder dynamics and multifunctionality. Inorg Chem 2011, 50: 2354–2365.
[32]
Shannon RD. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Cryst 1976, 32: 751–767.
[33]
Mandal BP, Banerji A, Sathe V, et al. Order–disorder transition in Nd2−yGdyZr2O7 pyrochlore solid solution: An X-ray diffraction and Raman spectroscopic study. J Solid State Chem 2007, 180: 2643–2648.
[34]
Scheetz BE, White WB. Characterization of anion disorder in zirconate A2B2O7 compounds by Raman spectroscopy. J Am Ceram Soc 1979, 62: 468–470.
[35]
Wan CL, Qu ZX, Du AB, et al. Order–disorder transition and unconventional thermal conductivities of the (Sm1−xYbx)2Zr2O7 series. J Am Ceram Soc 2011, 94: 592–596.
[36]
Zhou L, Huang ZY, Qi JQ, et al. Thermal-driven fluorite–pyrochlore–fluorite phase transitions of Gd2Zr2O7 ceramics probed in large range of sintering temperature. Metall Mater Trans A 2016, 47: 623–630.
[37]
Guo L, Li MZ, Zhang Y, et al. Improved toughness and thermal expansion of non-stoichiometry Gd2−xZr2+xO7+x/2 ceramics for thermal barrier coating application. J Mater Sci Technol 2016, 32: 28–33.
[38]
Kittel C, McEuen P. Introduction to Solid State Physics, 7th edn. New York, USA: John Wiley & Sons, 1996.
[39]
Momma K, Izumi F. VESTA: A three-dimensional visualization system for electronic and structural analysis. J Appl Cryst 2008, 41: 653–658.
[40]
Barker WW, White PS, Knop O. Pyrochlores. X. Madelung energies of pyrochlores and defect fluorites. Can J Chem 1976, 54: 2316–2334.
[41]
Pannetier J. Energie electrostatique des reseaux pyrochlore. J Phys Chem Solids 1973, 34: 583–589. (in French)
[42]
Hess NJ, Begg BD, Conradson SD, et al. Spectroscopic investigations of the structural phase transition in Gd2(Ti1−yZry)2O7 pyrochlores. J Phys Chem B 2002, 106: 4663–4677.
[43]
Zhang SY, Li HL, Zhou SH, et al. Estimation thermal expansion coefficient from lattice energy for inorganic crystals. Jpn J Appl Phys 2006, 45: 8801.
[44]
Lan GQ, Ouyang B, Xu YS, et al. Predictions of thermal expansion coefficients of rare-earth zirconate pyrochlores: A quasi-harmonic approximation based on stable phonon modes. J Appl Phys 2016, 119: 235103.
[45]
Lan GQ, Ouyang B, Song J. The role of low-lying optical phonons in lattice thermal conductance of rare-earth pyrochlores: A first-principle study. Acta Mater 2015, 91: 304–317.
[46]
Tadano T, Gohda Y, Tsuneyuki S. Impact of rattlers on thermal conductivity of a thermoelectric clathrate: A first-principles study. Phys Rev Lett 2015, 114: 095501.
[47]
Wan CL, Zhang W, Wang YF, et al. Glass-like thermal conductivity in ytterbium-doped lanthanum zirconate pyrochlore. Acta Mater 2010, 58: 6166–6172.
File
JAC0734_ESM.pdf (248.7 KB)
Publication history
Copyright
Acknowledgements
Rights and permissions

Publication history

Received: 12 December 2022
Revised: 24 January 2023
Accepted: 20 February 2023
Published: 11 April 2023
Issue date: May 2023

Copyright

© The Author(s) 2023.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 52022042), the National Key R&D Program of China (No. 2021YFB3702300), and National Science and Technology Major Project (No. J2019-VII-0008-0148).

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Return