Abstract
The systematic tuning of crystal lattice parameters to achieve improved kinematic compatibility between different phases is a broadly effective strategy for improving the reversibility, and lowering the hysteresis, of solid–solid phase transformations1,2,3,4,5,6,7,8,9,10,11. (Kinematic compatibility refers to the fitting together of the phases.) Here we present an apparently paradoxical example in which tuning to near perfect kinematic compatibility results in an unusually high degree of irreversibility. Specifically, when cooling the kinematically compatible ceramic (Zr/Hf)O2(YNb)O4 through its tetragonal-to-monoclinic phase transformation, the polycrystal slowly and steadily falls apart at its grain boundaries (a process we term weeping) or even explosively disintegrates. If instead we tune the lattice parameters to satisfy a stronger ‘equidistance’ condition (which additionally takes into account sample shape), the resulting material exhibits reversible behaviour with low hysteresis. These results show that a diversity of behaviours—from reversible at one extreme to explosive at the other—is possible in a chemically homogeneous ceramic system by manipulating conditions of compatibility in unexpected ways. These concepts could prove critical in the current search for a shape-memory oxide ceramic9,10,11,12.
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Data availability
The raw data that support the findings of this study are available at https://archive.materialscloud.org with the identifierhttps://doi.org/10.24435/materialscloud:6c-hk.
References
Chen, X., Srivastava, V., Dabade, V. & James, R. D. Study of the cofactor conditions: conditions of supercompatibility between phases. J. Mech. Phys. Solids 61, 2566–2587 (2013).
Chluba, C. et al. Ultralow-fatigue shape memory alloy films. Science 348, 1004–1007 (2015).
Delville, R. et al. Transmission electron microscopy study of phase compatibility in low hysteresis shape memory alloys. Philos. Mag. 90, 177–195 (2010).
Della Porta, F. On the cofactor conditions and further conditions of supercompatibility between phases. J. Mech. Phys. Solids 122, 27–53 (2019).
Niitsu, K., Kimura, Y., Omori, T. & Kainuma, R. Cryogenic superelasticity with large elastocaloric effect. NPG Asia Mater. 10, e457 (2018).
Zarnetta, R. et al. Identification of quaternary shape memory alloys with near-zero thermal hysteresis and unprecedented functional stability. Adv. Funct. Mater. 20, 1917–1923 (2010).
Gu, H., Bumke, L., Chluba, C., Quandt, E. & James, R. D. Phase engineering and supercompatibility of shape memory alloys. Mater. Today 21, 265–277 (2018).
Jetter, J. et al. Tuning crystallographic compatibility to enhance shape memory in ceramics. Phys. Rev. Mater. 3, 93603 (2019).
Wegner, M., Gu, H., James, R. D. & Quandt, E. Correlation between phase compatibility and efficient energy conversion in Zr-doped barium titanate. Sci. Rep. 10, 3496 (2020).
Liang, Y. G. et al. Tuning the hysteresis of a metal-insulator transition via lattice compatibility. Nat. Commun. 11, 3539 (2020).
Pang, E. L., McCandler, C. A. & Schuh, C. A. Reduced cracking in polycrystalline ZrO2-CeO2 shape-memory ceramics by meeting the cofactor conditions. Acta Mater. 177, 230–239 (2019).
Lai, A., Du, Z., Gan, C. L. & Schuh, C. A. Shape memory and superelastic ceramics at small scales. Science 341, 1505–1508 (2013).
Kohn, R. V. & Müller, S. Branching of twins near an austenite—twinned-martensite interface. Philos. Mag. A 66, 697–715 (1992).
Burkart, M. W. & Read, T. A. Diffusionless phase change in the indium-thallium system. Trans. Am. Inst. Min. Metall. Eng. 197, 1516–1524 (1953).
Ball, J. M. & James, R. D. in Analysis and Continuum Mechanics: a Collection of Papers Dedicated to J. Serrin on His Sixtieth Birthday 647–686 (Springer, 1989).
Yang, S. et al. A jumping shape memory alloy under heat. Sci. Rep. 6, 21754 (2016).
Yadava, K. et al. Extraordinary anisotropic thermal expansion in photosalient crystals. IUCrJ 7, 83–89 (2020).
Naumov, P., Chizhik, S., Panda, M. K., Nath, N. K. & Boldyreva, E. Mechanically responsive molecular crystals. Chem. Rev. 115, 12440–12490 (2015).
Tong, F. et al. Photomechanical molecular crystals and nanowire assemblies based on the [2+2] photodimerization of a phenylbutadiene derivative. J. Mater. Chem. C 8, 5036–5044 (2020).
Chandrasekar, S. & Chaudhri, M. M. The explosive disintegration of Prince Rupert’s drops. Philos. Mag. B 70, 1195–1218 (1994).
Gibbs, J.W. On the equilibrium of heterogeneous substances Vol. 1 (Longmans Green and Co., 1879)
Chen, X. et al. Direct observation of chemical short-range order in a medium-entropy alloy. Nature 592, 712–716 (2021).
Hayakawa, M., Kuntani, N. & Oka, M. Structural study on the tetragonal to monoclinic transformation in arc-melted ZrO2-2mol.%Y2O3—I. Experimental observations. Acta Metall. 37, 2223–2228 (1989).
Hayakawa, M. & Oka, M. Structural study on the tetragonal to monoclinic transformation in arc-melted ZrO2-2mol.%Y2O3—II. Quantitative analysis. Acta Metall. 37, 2229–2235 (1989).
Chen, X. & Song, Y. Structural Phase Transformation Web Tools (StrucTrans, 2014); http://www.structrans.org
Ball, J. M. & James, R. D. A characterization of plane strain. Proc. Math. Phys. Sci. 432, 93–99 (1991).
Acknowledgements
R.D.J. and H.G. were supported by the NSF (DMREF-1629026), the MURI programme (FA9550-18-1-0095 and FA9550-16-1-0566) and a Vannevar Bush Faculty Fellowship. R.D.J. also acknowledges a Mercator Fellowship for the support of this German–US collaboration. E.Q., J.R. and J.J. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) through a Reinhart Koselleck Project (313454214), and the project “Search for compatible zirconium oxide-based shape memory ceramics” (453203767). We thank N. Wolff for preliminary TEM measurements, and A. Mill for her assistance in the preparation of specimens for TEM investigation.
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Contributions
H.G. and J.R. contributed equally to the manuscript. J.R. synthesized and characterized the samples. E.Q., J.R. and J.J. designed the compositions and J.J. also aided in characterization. L.K. and A.L. contributed to our understanding of the chemical homogeneity in this system. H.G. and R.D.J. developed the theory of compatibility and identified the significance of the equidistance condition with input from all authors. R.D.J. wrote the manuscript with input from all authors. E.Q. and R.D.J. supervised the collaboration.
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Extended data figures and tables
Extended Data Fig. 1 Microstructure and grain size.
(a) SEM image of the sample y = 0.5 with monoclinic twin laminated microstructure, showing the untreated sample surface directly after sintering, and (b) the fractured surface of the same sample. (c) Typical transformed material from a weeping sample that shows separation at the grain boundaries.
Extended Data Fig. 2 Chemical homogeneity and absence of short-range ordering (crushed).
The micrographs of the microstructural and nanoscale investigations are TEM and HRTEM images as well as SAED and NBED patterns of the (Zr0.9 Hf0.1 O2)0.775 (Y0.5 Nb0.5 O2)0.225 (weeping) sample prepared by crushing. No additional reflections are observed in SAED and NBED patterns beyond those due to dynamical double diffraction. Also no additional reflections are seen in the FFT images.
Extended Data Fig. 3 Chemical homogeneity and absence of short-range ordering (FIB).
The micrographs of the microstructural and nanoscale analysis are HAADF-STEM and HAADF-HRSTEM images as well as SAED and NBED patterns of the (Zr0.9 Hf0.1 O2)0.775 (Y0.5 Nb0.5 O2)0.225 (weeping) sample, prepared by FIB. No additional reflections are observed in SAED, NBED patterns (only from dynamical double diffraction) as well as FFT images. Low-magnification HAADFM and atomic-scale HAADF micrographs are raw images, showing no significant intensity variation.
Extended Data Fig. 4 Chemical homogeneity, crushed sample.
Nanoscale chemical study of a (Zr0.9 Hf0.1 O2)0.775 (Y0.5 Nb0.5 O2)0.225 (weeping) sample, prepared by crushing. The images are HAADF-HRSTEM micrograph and high resolution EDX elemental maps, suggesting a uniform distribution of elements.
Extended Data Fig. 5 Chemical homogeneity, FIB sample.
Nanoscale chemical analysis of a (Zr0.9 Hf0.1 O2)0.775 (Y0.5 Nb0.5 O2)0.225 (weeping) sample prepared by FIB. The images are HAADF-HRSTEM micrograph and high resolution EDX elemental maps, suggesting a uniform distribution of elements.
Extended Data Fig. 6 Chemical homogeneity and structure at grain boundaries (FIB).
Nanoscale study and local chemical analysis of a grain boundary of a (Zr0.9 Hf0.1 O2)0.775 (Y0.5 Nb0.5 O2)0.225 (weeping) sample prepared by FIB. The micrographs are HAADF-STEM and HAADF-HRSTEM images as well as high resolution EDX elemental maps of the sample. Atomic-resolution HAADF micrographs are raw images, showing no significant intensity variation along the grain boundary (GB). The high resolution EDX maps suggest no significant element segregation at the grain boundary.
Extended Data Fig. 7 Structure by X-Ray Diffraction with Rietveld Refinement.
XRD diffraction pattern and calculated fit after Rietveld refinement (Top) with Topas software. The diagram at the bottom (Residual) shows the difference in intensity between the measured and calculated diffraction pattern. The sample in plot a) has a phase transformation above room temperature (RT) and is in the monoclinic phase, whereas the phase transformation of the sample in plot b) is below RT, so the pattern shows the tetragonal crystal structure. The low Rwp values, representing the goodness of the fit, indicate the quality of the Rietveld refinement. Temperature dependent measurements were conducted with a graphite domed heating stage. In c) the sample y = 0.9 is in its monoclinic phase, while in d) the measurement was taken at 415 °C following the monoclinic to tetragonal phase transition. The stage appears in the measured XRD pattern with additional peaks that were identified and excluded from the refinement done on the parameters of the physical phases. The resulting higher Rwp values compared to a) and b) can be explained by the reduced intensities due to limited transmissibility of the graphite dome used in these cases. Each measurement is refined up to 1000 times with different varied starting parameters with only the best fit being used for further calculations.
Extended Data Fig. 8 Temperature dependent XRD measurements.
Temperature dependent XRD measurement of the sample y = 0.8 with domed heating stage showing the phase transformation on heating and cooling. Upon heating, the characteristic tetragonal peak starts to grow at the austenitic start temperature and the monoclinic peaks are vanishing. At temperatures far above Af we force transformation of the residual phase. During cooling to 30 °C, we observe the reverse transformation (t-to-m) of the sample. These measurements are the basis to obtain the lattice parameter of the monoclinic and tetragonal phases by Rietveld refinement, to determine the temperature dependent change of these lattice parameters and to calculate the middle eigenvalues λ2 of the transformation stretch matrix for the lattice Correspondences 1a, 1b and 2.
Extended Data Fig. 9 Frame sequence of explosive behaviour.
In a sequence of frames, the Fig. shows the path of a jumping ceramic confined to a cylinder. This jump is also shown in Supplementary Video 2.
Supplementary information
Supplementary Information
This file contains Supplementary Sections 1–3 including equations for the analysis of compatibility and a heat transfer analysis and Tables 1–4.
Supplementary Video 1
A sample at a high Zr/Hf ratio exhibiting explosive behaviour on cooling to the transformation temperature. See the main text for details.
Supplementary Video 2
The path of a sample at a high Zr content exhibiting jumping, confined to a graduated cylinder. See also the main text and Extended Data Fig. 9.
Supplementary Video 3
A sample at a high Zr/Hf ratio that exhibits weeping (that is, steady falling apart at the grain boundaries). See also the main text and Fig. 2.
Supplementary Video 4
Reversible motion of the interface in the context of a general cooling protocol. The sample closely satisfies the equidistance condition. See the main text and the caption of Fig. 2.
Supplementary Video 5
This video shows reversible motion of an interface close up, so the interface position is clear. The sample closely satisfies the equidistance condition. See also the main text and the caption of Fig. 2.
Supplementary Video 6
A sample that was held at a temperature a little above the transformation temperature for 94 days, and then cooled to the point of transformation. This supports the arguments given in the Methods (“Possible rate effects”) on the absence of a significant rate effect.
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Gu, H., Rohmer, J., Jetter, J. et al. Exploding and weeping ceramics. Nature 599, 416–420 (2021). https://doi.org/10.1038/s41586-021-03975-5
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DOI: https://doi.org/10.1038/s41586-021-03975-5
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