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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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.
The authors declare no competing interests.
Peer review information Nature thanks Jian Luo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Extended data figures and tables
(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.
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.
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.
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.
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.
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.
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.
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.
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.
This file contains Supplementary Sections 1–3 including equations for the analysis of compatibility and a heat transfer analysis and Tables 1–4.
A sample at a high Zr/Hf ratio exhibiting explosive behaviour on cooling to the transformation temperature. See the main text for details.
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.
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.
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.
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.
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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