Nucleation barriers at corners for a cubic-to-tetragonal phase transformation

We are interested in the energetic cost of a martensitic inclusion of volume V in austenite for the cubic-to-tetragonal phase transformation. In contrast with the work of Knüpfer, Kohn and Otto (Commun. Pure Appl. Math.66 (2013), 867–904), we consider a domain with a corner and obtain a better scaling law for the minimal energy (Emin ∼ min(V2/3, V7/9)). Our predictions are in good agreement with physical experiments where nucleation of martensite is usually observed near the corners of the specimen.

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Ferroelectric Domain Structure of Pb(Zr.52Ti.48)03

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s1431927600000933 ◽

1980 ◽

Vol 38 ◽

pp. 214-215

Author(s):

E.K. Goo ◽

R.K. Mishra

Keyword(s):

Phase Transformation ◽

Domain Structure ◽

Tetragonal Phase ◽

Ferroelectric Domain ◽

Cubic Phase ◽

Ion Milling ◽

Thin Foils ◽

Ferroelectric Domain Structure ◽

Ferroelectric Domains

Ferroelectric domains are twins that are formed when PZT undergoes a phase transformation from a non-ferroelectric cubic phase to a ferroelectric tetragonal phase upon cooling below ∼375°C.,1 The tetragonal phase is spontaneously polarized in the direction of c-axis, making each twin a ferroelectric domain. Thin foils of polycrystalline Pb (Zr.52Ti.48)03 were made by ion milling and observed in the Philips EM301 with a double tilt stage.

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Phase transformation and preferred orientation in carboxylate derived ZrO2 thin films on silicon substates

Journal of Materials Research ◽

10.1557/jmr.1992.3065 ◽

1992 ◽

Vol 7 (11) ◽

pp. 3065-3071 ◽

Cited By ~ 4

Author(s):

Peir-Yung Chu ◽

Isabelle Campion ◽

Relva C. Buchanan

Keyword(s):

Thin Films ◽

Heat Treatment ◽

Phase Transformation ◽

Heating Rate ◽

Tetragonal Phase ◽

Monoclinic Phase ◽

Preferred Orientation ◽

Si Substrate ◽

Interfacial Diffusion ◽

Deposited Films

Phase transformation and preferred orientation in ZrO2 thin films, deposited on Si(111) and Si(100) substrates, and prepared by heat treatment from carboxylate solution precursors were investigated. The deposited films were amorphous below 450 °C, transforming gradually to the tetragonal and monoclinic phases on heating. The monoclinic phase developed from the tetragonal phase displacively, and exhibited a strong (111) preferred orientation at temperature as low as 550 °C. The degree of preferred orientation and the tetragonal-to-monoclinic phase transformation were controlled by heating rate, soak temperature, and time. Interfacial diffusion into the film from the Si substrate was negligible at 700 °C and became significant only at 900 °C, but for films thicker than 0.5 μm, overall preferred orientation exceeded 90%.

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Local atomic structure in tetragonal pure ZrO2nanopowders

Journal of Applied Crystallography ◽

10.1107/s0021889809054983 ◽

2010 ◽

Vol 43 (2) ◽

pp. 227-236 ◽

Cited By ~ 16

Author(s):

Leandro M. Acuña ◽

Diego G. Lamas ◽

Rodolfo O. Fuentes ◽

Ismael O. Fábregas ◽

Márcia C. A. Fantini ◽

...

Keyword(s):

Tetragonal Phase ◽

Local Structure ◽

X Ray Diffraction ◽

X Ray ◽

Atomic Structures ◽

Crystallite Sizes ◽

Exafs Study ◽

The Difference ◽

X Ray Absorption ◽

Good Agreement

The local atomic structures around the Zr atom of pure (undoped) ZrO2nanopowders with different average crystallite sizes, ranging from 7 to 40 nm, have been investigated. The nanopowders were synthesized by different wet-chemical routes, but all exhibit the high-temperature tetragonal phase stabilized at room temperature, as established by synchrotron radiation X-ray diffraction. The extended X-ray absorption fine structure (EXAFS) technique was applied to analyze the local structure around the Zr atoms. Several authors have studied this system using the EXAFS technique without obtaining a good agreement between crystallographic and EXAFS data. In this work, it is shown that the local structure of ZrO2nanopowders can be described by a model consisting of two oxygen subshells (4 + 4 atoms) with different Zr—O distances, in agreement with those independently determined by X-ray diffraction. However, the EXAFS study shows that the second oxygen subshell exhibits a Debye–Waller (DW) parameter much higher than that of the first oxygen subshell, a result that cannot be explained by the crystallographic model accepted for the tetragonal phase of zirconia-based materials. However, as proposed by other authors, the difference in the DW parameters between the two oxygen subshells around the Zr atoms can be explained by the existence of oxygen displacements perpendicular to thezdirection; these mainly affect the second oxygen subshell because of the directional character of the EXAFS DW parameter, in contradiction to the crystallographic value. It is also established that this model is similar to another model having three oxygen subshells, with a 4 + 2 + 2 distribution of atoms, with only one DW parameter for all oxygen subshells. Both models are in good agreement with the crystal structure determined by X-ray diffraction experiments.

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Effect of stress-induced phase transformation on the properties of polycrystalline zirconia containing metastable tetragonal phase

Journal of Materials Science ◽

10.1007/bf00553200 ◽

1978 ◽

Vol 13 (7) ◽

pp. 1464-1470 ◽

Cited By ~ 361

Author(s):

T. K. Gupta ◽

F. F. Lange ◽

J. H. Bechtold

Keyword(s):

Phase Transformation ◽

Tetragonal Phase

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Nucleation barriers for the cubic-to-tetragonal phase transformation in the absence of self-accommodation

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik ◽

10.1002/zamm.201800179 ◽

2018 ◽

Vol 99 (2) ◽

pp. e201800179 ◽

Cited By ~ 1

Author(s):

Hans Knüpfer ◽

Felix Otto

Keyword(s):

Phase Transformation ◽

Tetragonal Phase

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Microstrain and the Mechanism of the Reversible Monoclinic ⇌ Tetragonal Phase Transformation in Zirconia

Reactivity of Solids ◽

10.1007/978-1-4684-2340-2_63 ◽

1977 ◽

pp. 421-425

Author(s):

S. T. Buljan ◽

H. A. McKinstry ◽

V. S. Stubican

Keyword(s):

Phase Transformation ◽

Tetragonal Phase

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Residual Stress Analysis Considering Phase Transformation and Transformation Plasticity for Heat-Treated Large Size Shaft

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.725.647 ◽

2016 ◽

Vol 725 ◽

pp. 647-652 ◽

Cited By ~ 2

Author(s):

Yusuke Yanagisawa ◽

Yasuhiro Kishi ◽

Katsuhiko Sasaki

Keyword(s):

Heat Treatment ◽

Residual Stress ◽

Phase Transformation ◽

Air Cooling ◽

Water Cooling ◽

Stress Distributions ◽

Transformation Plasticity ◽

Large Size ◽

Heat Treated ◽

Good Agreement

The residual stress distributions of the forgings after both water-cooling and air-cooling were measured experimentally. The residual stress occurring during the heat-treatment was also simulated considering the phase transformation and the transformation plasticity. A comparison of the experiments with the simulations showed a good agreement. These results shows that the transformation plastic strain plays an important role in the heat treatment of large forged shafts.

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Mechanics of spontaneously formed nanoblisters trapped by transferred 2D crystals

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1801551115 ◽

2018 ◽

Vol 115 (31) ◽

pp. 7884-7889 ◽

Cited By ~ 38

Author(s):

Daniel A. Sanchez ◽

Zhaohe Dai ◽

Peng Wang ◽

Arturo Cantu-Chavez ◽

Christopher J. Brennan ◽

...

Keyword(s):

Scaling Law ◽

New Physics ◽

Adhesion Energy ◽

Work Of Adhesion ◽

Fourth Power ◽

Layered Systems ◽

Simple Scaling ◽

Dynamics Simulations ◽

2D Crystals ◽

Good Agreement

Layered systems of 2D crystals and heterostructures are widely explored for new physics and devices. In many cases, monolayer or few-layer 2D crystals are transferred to a target substrate including other 2D crystals, and nanometer-scale blisters form spontaneously between the 2D crystal and its substrate. Such nanoblisters are often recognized as an indicator of good adhesion, but there is no consensus on the contents inside the blisters. While gas-filled blisters have been modeled and measured by bulge tests, applying such models to spontaneously formed nanoblisters yielded unrealistically low adhesion energy values between the 2D crystal and its substrate. Typically, gas-filled blisters are fully deflated within hours or days. In contrast, we found that the height of the spontaneously formed nanoblisters dropped only by 20–30% after 3 mo, indicating that probably liquid instead of gas is trapped in them. We therefore developed a simple scaling law and a rigorous theoretical model for liquid-filled nanoblisters, which predicts that the interfacial work of adhesion is related to the fourth power of the aspect ratio of the nanoblister and depends on the surface tension of the liquid. Our model was verified by molecular dynamics simulations, and the adhesion energy values obtained for the measured nanoblisters are in good agreement with those reported in the literature. This model can be applied to estimate the pressure inside the nanoblisters and the work of adhesion for a variety of 2D interfaces, which provides important implications for the fabrication and deformability of 2D heterostructures and devices.

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