Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings | Paper Citation Record

Observation ef48b2c5-d62b-45db-86fa-d98c47a4d6b3 · outbound

This paper cites Phase transitions and equation of state of Zirconium under high pressure.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Phase transitions and equation of state of Zirconium under high pressure

Reference 1

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This paper cites Phase-field approach for stress-and temperature-induced phase transformations that satisfies lattice instability conditions.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Phase-field approach for stress-and temperature-induced phase transformations that satisfies lattice instability conditions

Reference 2

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This paper cites Finite-strain scale-free phase-field approach to multivariant marten- sitic phase transformations with stress-dependent effective thresholds.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Finite-strain scale-free phase-field approach to multivariant marten- sitic phase transformations with stress-dependent effective thresholds

Reference 4

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This paper cites Simulations of multivariant Si I to Si II phase transformation in polycrystalline silicon with finite-strain scale-free phase-field approach.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Simulations of multivariant Si I to Si II phase transformation in polycrystalline silicon with finite-strain scale-free phase-field approach

Reference 5

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This paper cites Omega phase transformation–morphologies and mechanisms.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Omega phase transformation–morphologies and mechanisms

Reference 6

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This paper cites Bangerth, R.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Bangerth, R

Reference 7

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This paper cites Phase transitions in solids under high pressure.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Phase transitions in solids under high pressure

Reference 8

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Observation 99b8069c-a714-4765-8ec3-54e9435c25fa · outbound

This paper cites Effect of hydrostatic pressure on the kinetics of α–ω phase transformation in Zirconium.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Effect of hydrostatic pressure on the kinetics of α–ω phase transformation in Zirconium

Reference 9

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This paper cites C´ aceres and P.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings C´ aceres and P

Reference 10

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Observation b3c43dd4-c9e2-48ef-a973-fbf51d83eaec · outbound

This paper cites Quantitative kinetic rules for plastic strain-induced α-ω phase transformation in Zr under high pressure.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Quantitative kinetic rules for plastic strain-induced α-ω phase transformation in Zr under high pressure

Reference 11

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Observation a2d29b60-6210-4e96-aba4-f2fa9e76fe9e · outbound

This paper cites Allotropic phase transformation of pure Zirconium by high-pressure torsion.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Allotropic phase transformation of pure Zirconium by high-pressure torsion

Reference 12

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This paper cites Pressure-induced α→ ω transition in Titanium metal: a systematic study of the effects of uniaxial stress.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Pressure-induced α→ ω transition in Titanium metal: a systematic study of the effects of uniaxial stress

Reference 13

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This paper cites Microscale phase field modeling of the martensitic transformation during cyclic loading of NiTi single crystal.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Microscale phase field modeling of the martensitic transformation during cyclic loading of NiTi single crystal

Reference 14

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This paper cites Strain-induced multivariant martensitic transformations: A scale-independent simulation of interaction between localized shear bands and mi- crostructure.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Strain-induced multivariant martensitic transformations: A scale-independent simulation of interaction between localized shear bands and mi- crostructure

Reference 15

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This paper cites Pandey Sorb Yesudhas Feng Lin, Valery I.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Pandey Sorb Yesudhas Feng Lin, Valery I

Reference 16

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Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Unresolved cited work

Reference 17

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Observation ff00e47b-d7d1-47a1-938c-3e9c40ee38a6 · outbound

This paper cites Phase transitions in high-purity Zirconium under dynamic compression.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Phase transitions in high-purity Zirconium under dynamic compression

Reference 18

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Observation e0bf093d-b6a9-4d74-ae5d-6f846d6656f0 · outbound

This paper cites Phase transitions in Zr at sub-nanosecond time scales.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Phase transitions in Zr at sub-nanosecond time scales

Reference 19

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Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Unresolved cited work

Reference 20

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This paper cites Finite element simulations of martensitic phase transitions and microstructures based on a strain softening model.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Finite element simulations of martensitic phase transitions and microstructures based on a strain softening model

Reference 21

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Observation 3ab0881f-ca9f-4c10-b5a7-d2777576e205 · outbound

This paper cites Role of twinning on the omega-phase transformation and stability in Zirconium.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Role of twinning on the omega-phase transformation and stability in Zirconium

Reference 22

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Observation 6f0a33e9-3080-4af0-a496-09e1e4c6d384 · outbound

This paper cites Effect of dislo- cation slip and deformation twinning on the high-pressure phase transformation in Zirconium.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Effect of dislo- cation slip and deformation twinning on the high-pressure phase transformation in Zirconium

Reference 23

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This paper cites Some relations for finite inelastic deformation of microheterogeneous materials with moving discontinuity surfaces.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Some relations for finite inelastic deformation of microheterogeneous materials with moving discontinuity surfaces

Reference 24

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This paper cites High-pressure mechanochemistry: conceptual multiscale theory and interpretation of experiments.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings High-pressure mechanochemistry: conceptual multiscale theory and interpretation of experiments

Reference 25

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This paper cites Phase field approach for stress-and temperature-induced phase transformations that satisfies lattice instability conditions.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Phase field approach for stress-and temperature-induced phase transformations that satisfies lattice instability conditions

Reference 26

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This paper cites High pressure phase transformations revisited.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings High pressure phase transformations revisited

Reference 27

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This paper cites High-Pressure Phase Transformations under Severe Plastic Deformation by Torsion in Rotational Anvils.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings High-Pressure Phase Transformations under Severe Plastic Deformation by Torsion in Rotational Anvils

Reference 28

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This paper cites Phase transformations, fracture, and other structural changes in inelastic materials.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Phase transformations, fracture, and other structural changes in inelastic materials

Reference 29

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This paper cites Recent in situ experimental and theoretical advances in severe plastic deformations, strain-induced phase transformations, and microstructure evolution under high pressure.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Recent in situ experimental and theoretical advances in severe plastic deformations, strain-induced phase transformations, and microstructure evolution under high pressure

Reference 30

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This paper cites Athermal resistance to interface motion in the phase-field theory of microstructure evolution.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Athermal resistance to interface motion in the phase-field theory of microstructure evolution

Reference 31

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This paper cites Three-dimensional Landau theory for multi- variant stress-induced martensitic phase transformations.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Three-dimensional Landau theory for multi- variant stress-induced martensitic phase transformations

Reference 32

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This paper cites Microscale simulation of martensitic microstructure evolution.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Microscale simulation of martensitic microstructure evolution

Reference 33

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Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Unresolved cited work

Reference 34

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This paper cites Levitas, Hao Chen, and Liming Xiong.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Levitas, Hao Chen, and Liming Xiong

Reference 35

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This paper cites Levitas, Hao Chen, and Liming Xiong.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Levitas, Hao Chen, and Liming Xiong

Reference 36

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This paper cites Levitas, S.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Levitas, S

Reference 37

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This paper cites Tensorial stress-plastic strain fields in α-ω Zr mixture, transformation kinetics, and friction in diamond-anvil cell.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Tensorial stress-plastic strain fields in α-ω Zr mixture, transformation kinetics, and friction in diamond-anvil cell

Reference 38

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This paper cites Grain growth phenomenon during pressure-induced phase transformations at room temperature.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Grain growth phenomenon during pressure-induced phase transformations at room temperature

Reference 39

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This paper cites Rules for the crystallite size and dislocation density evolution in phases during α-ω transformation in zr under high- pressure and severe plastic flow.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Rules for the crystallite size and dislocation density evolution in phases during α-ω transformation in zr under high- pressure and severe plastic flow

Reference 40

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This paper cites Revisiting the High-Pressure Behaviors of Zirconium: Nonhydrostaticity Promoting the Phase Transitions and Absence of the Isostructural Phase Transition in β-Zirconium.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Revisiting the High-Pressure Behaviors of Zirconium: Nonhydrostaticity Promoting the Phase Transitions and Absence of the Isostructural Phase Transition in β-Zirconium

Reference 41

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This paper cites In situ quantitative study of plastic strain-induced phase transfor- mations under high pressure: Example for ultra-pure Zr.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings In situ quantitative study of plastic strain-induced phase transfor- mations under high pressure: Example for ultra-pure Zr

Reference 42

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This paper cites In situ study of microstructure evolution andα→ω phase transition in annealed and pre-deformed Zr under hydrostatic loading.Journal of Applied Physics , 136(11):115901, 2024.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings In situ study of microstructure evolution andα→ω phase transition in annealed and pre-deformed Zr under hydrostatic loading.Journal of Applied Physics , 136(11):115901, 2024

Reference 43

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Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Unresolved cited work

Reference 44

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Observation b8d9a56a-e677-479e-ae22-bd3ada1c3c36 · outbound

This paper cites Real time study of grain enlargement in zirconium under room-temperature compression across the α to ω phase transition.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Real time study of grain enlargement in zirconium under room-temperature compression across the α to ω phase transition

Reference 45

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Observation bf0cbc1f-43d5-4be5-8e25-b104b654accb · outbound

This paper cites Classification of the critical resolved shear stress in the hexagonal-close-packed materials by atomic simulation: Application to α-Zirconium and α-Titanium.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Classification of the critical resolved shear stress in the hexagonal-close-packed materials by atomic simulation: Application to α-Zirconium and α-Titanium

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:04.037896Z

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Observation 0f5190f4-4f3b-4f08-95f6-4b531964f498 · outbound

This paper cites Omega phase in materials.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Omega phase in materials

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:04.026890Z

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Observation 79e06c3d-d050-4686-be3f-251d67610fb7 · outbound

This paper cites Microscopic and crystallographic aspects of retained omega phase in shock- loaded Zirconium and its formation mechanism.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Microscopic and crystallographic aspects of retained omega phase in shock- loaded Zirconium and its formation mechanism

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:04.015006Z

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Observation ae5cef08-5719-42e9-9479-0f8b39752afc · outbound

This paper cites Orientation dependency of the α to ω plus beta transformation in commercially pure Zirconium by high-pressure torsion.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Orientation dependency of the α to ω plus beta transformation in commercially pure Zirconium by high-pressure torsion

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:04.003554Z

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Observation a77121de-737e-4bdb-8bb5-2b4e81ee6b50 · outbound

This paper cites Picosecond dynamics of a shock-driven displacive phase transformation in Zr.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Picosecond dynamics of a shock-driven displacive phase transformation in Zr

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:03.992495Z

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Observation 9c2d4518-b3d3-4d6a-be69-7a40af05f382 · outbound

This paper cites Microstructural evolution in Zirco- nium based alloys.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Microstructural evolution in Zirco- nium based alloys

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:03.981257Z

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Observation 2dd3a1a7-9740-4ec4-a341-401215310bbf · outbound

This paper cites Effects of intersti- tial impurities on the high pressure martensitic α to ω structural transformation and grain growth in Zirconium.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Effects of intersti- tial impurities on the high pressure martensitic α to ω structural transformation and grain growth in Zirconium

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:03.970472Z

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Observation 757c80fe-f192-41a8-b929-21271cdf9745 · outbound

This paper cites First-principles calculations of phase transition, elas- ticity, and thermodynamic properties for TiZr alloy.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings First-principles calculations of phase transition, elas- ticity, and thermodynamic properties for TiZr alloy

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:03.958065Z

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Observation e068b76f-dab9-4d0f-b2d6-a055c21a443e · outbound

This paper cites Orientation rela- tions during the α-ω phase transition of zirconium: In situ texture observations at high pressure and temperature.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Orientation rela- tions during the α-ω phase transition of zirconium: In situ texture observations at high pressure and temperature

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:03.946235Z

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Observation 939b3e81-9f0f-43e4-a12c-2a8299c0aa6a · outbound

This paper cites Three- dimensional phase-field modeling of martensitic microstructure evolution in steels.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Three- dimensional phase-field modeling of martensitic microstructure evolution in steels

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:03.934585Z

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Observation 2ef268bc-82bf-42a4-92b4-caa9ef7108f6 · outbound

This paper cites α–ω and ω–α phase transformations in Zirconium under hydrostatic pressure: A 3D mesoscale study.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings α–ω and ω–α phase transformations in Zirconium under hydrostatic pressure: A 3D mesoscale study

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:03.922779Z

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Observation 84641329-a9a6-412b-9c69-b70a31057850 · outbound

This paper cites Lattice instability during solid-solid structural transformations under a general applied stress tensor: Example of Si I → Si II with metallization.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Lattice instability during solid-solid structural transformations under a general applied stress tensor: Example of Si I → Si II with metallization

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:03.910893Z

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Observation 9d011b75-5899-4f8a-ac31-297596cb371a · outbound

This paper cites Understanding controversies in the α-ω and ω-β phase transformations of Zirconium from nonhydrostatic thermodynamics.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Understanding controversies in the α-ω and ω-β phase transformations of Zirconium from nonhydrostatic thermodynamics

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:03.898286Z

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Observation 2c952d2a-2d6f-4705-b36a-67c2180674fe · outbound

This paper cites α–ω conversion in Titanium and Zirconium during shear deformation under pressure.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings α–ω conversion in Titanium and Zirconium during shear deformation under pressure

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:03.777648Z

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Observation 0e32c001-72ea-407a-972e-a92f839b5f62 · outbound

This paper cites Devel- oping an interatomic potential for martensitic phase transformations in Zirconium by machine learning.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings Devel- oping an interatomic potential for martensitic phase transformations in Zirconium by machine learning

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:03.765382Z

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Observation e9d35b10-8082-45fa-99c7-1f7accb70773 · outbound

This paper cites hcp →ω phase transition mechanisms in shocked Zirconium: A machine learning based atomic simulation study.

Analytical and Scale-Free Phase-Field Studies of $\alpha$ to $\omega$ Phase Transformation in Single Crystal Zirconium under Nonhydrostatic Loadings hcp →ω phase transition mechanisms in shocked Zirconium: A machine learning based atomic simulation study

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:35:03.752137Z

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