Non-local temperature-dependent phase-field models for non-isothermal phase transitions

2007 ◽  
Vol 76 (1) ◽  
pp. 197-210 ◽  
Author(s):  
Pavel Krejčí ◽  
Elisabetta Rocca ◽  
Jürgen Sprekels
Keyword(s):  
Phase Transitions ◽  
Phase Field ◽  
Local Temperature ◽  
Temperature Dependent ◽  
Phase Field Models ◽  
Non Local

Mathematical Models for Solid-Solid Phase Transitions Driven by Configurational Forces

2013 ◽  
Vol 774-776 ◽  
pp. 488-492
Author(s):  
Pei Cheng Zhu
Keyword(s):  
Phase Transitions ◽  
Mathematical Models ◽  
Shape Memory ◽  
Phase Field ◽  
Mean Curvature ◽  
Solid Phase ◽  
Configurational Forces ◽  
Two Phase ◽  
Phase Field Models ◽  
Martensitic Phase Transformations

Two phase-field models for solid-solid phase transitions driven by configurational forces are reviewed, and the formulation of the models is briefly presented for the non-conserved case, as an example. Applications include martensitic phase transformations in, e.g., shape memory alloys and sintering in ceramic producing. They are compared with two other famous models for phase transitions that are driven by mean curvature.

scholarly journals Phase-field modelling and computing for a large number of phases

2019 ◽  
Vol 53 (3) ◽  
pp. 805-832
Author(s):  
Élie Bretin ◽  
Roland Denis ◽  
Jacques-Olivier Lachaud ◽  
Édouard Oudet
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Representation ◽  
High Resolution Data ◽  
Phase Field Models ◽  
Efficient Storage ◽  
Non Local ◽  
Discretization Point ◽  
Field Approaches

We propose a framework to represent a partition that evolves under mean curvature flows and volume constraints. Its principle follows a phase-field representation for each region of the partition, as well as classical Allen–Cahn equations for its evolution. We focus on the evolution and on the optimization of problems involving high resolution data with many regions in the partition. In this context, standard phase-field approaches require a lot of memory (one image per region) and computation timings increase at least as fast as the number of regions. We propose a more efficient storage strategy with a dedicated multi-image representation that retains only significant phase field values at each discretization point. We show that this strategy alone is unfortunately inefficient with classical phase field models. This is due to non local terms and low convergence rate. We therefore introduce and analyze an improved phase field model that localizes each phase field around its associated region, and which fully benefits of our storage strategy. To demonstrate the efficiency of the new multiphase field framework, we apply it to the famous 3D honeycomb problem and the conjecture of Weaire–Phelan’s tiling.

On the nature of the phase transitions of aluminosilicate perrhenate sodalite

2020 ◽  
Vol 235 (6-7) ◽  
pp. 213-223
Author(s):  
Hilke Petersen ◽  
Lars Robben ◽  
Thorsten M. Gesing
Keyword(s):  
Raman Spectroscopy ◽  
Phase Transitions ◽  
Decomposition Temperature ◽  
Second Phase ◽  
Structure Property ◽  
X Ray Diffraction ◽  
Temperature Dependent ◽  
Two Phase ◽  
Structure Property Relationships ◽  
Heat Capacity Measurements

AbstractThe temperature-dependent structure-property relationships of the aluminosilicate perrhenate sodalite |Na8(ReO4)2|[AlSiO4]6 (ReO4-SOD) were analysed via powder X-ray diffraction (PXRD), Raman spectroscopy and heat capacity measurements. ReO4-SOD shows two phase transitions in the investigated temperature range (13 K < T < 1480 K). The first one at 218.6(1) K is correlated to the transition of dynamically ordered $P\overline{4}3n$ (> 218.6(1 K) to a statically disordered (<218.6(1) K) SOD template in $P\overline{4}3n$. The loss of the dynamics of the template anion during cooling causes an increase of disorder, indicated by an unusual intensity decrease of the 011-reflection and an increase of the Re-O2 bond length with decreasing temperature. Additionally, Raman spectroscopy shows a distortion of the ReO4 anion. Upon heating the thermal expansion of the sodalite cage originated in the tilt-mechanism causes the second phase transition at 442(1) K resulting in a symmetry-increase from $P\overline{4}3n$ to $Pm\overline{3}n$, the structure with the sodalites full framework expansion. Noteworthy is the high decomposition temperature of 1320(10) K.

scholarly journals Creating polar antivortex in PbTiO3/SrTiO3 superlattice

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Adeel Y. Abid ◽  
Yuanwei Sun ◽  
Xu Hou ◽  
Congbing Tan ◽  
Xiangli Zhong ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Phase Field ◽  
Driving Force ◽  
Topological Phase ◽  
Phase Field Simulation ◽  
Topological Structures ◽  
Field Simulation ◽  
Condensed Matters ◽  
Topological Phase Transitions ◽  
Insight Into

AbstractNontrivial topological structures offer a rich playground in condensed matters and promise alternative device configurations for post-Moore electronics. While recently a number of polar topologies have been discovered in confined ferroelectric PbTiO3 within artificially engineered PbTiO3/SrTiO3 superlattices, little attention was paid to possible topological polar structures in SrTiO3. Here we successfully create previously unrealized polar antivortices within the SrTiO3 of PbTiO3/SrTiO3 superlattices, accomplished by carefully engineering their thicknesses guided by phase-field simulation. Field- and thermal-induced Kosterlitz–Thouless-like topological phase transitions have also been demonstrated, and it was discovered that the driving force for antivortex formation is electrostatic instead of elastic. This work completes an important missing link in polar topologies, expands the reaches of topological structures, and offers insight into searching and manipulating polar textures.

Temperature-induced structural phase transitions in RERhSn (RE = Y, Gd-Tm, Lu)

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Simon Engelbert ◽  
Rolf-Dieter Hoffmann ◽  
Jutta Kösters ◽  
Steffen Klenner ◽  
Rainer Pöttgen
Keyword(s):  
Rare Earth ◽  
Phase Transitions ◽  
Driving Force ◽  
Room Temperature ◽  
Structural Phase ◽  
Structural Phase Transitions ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
Temperature Dependent ◽  
X Ray

Abstract The structures of the equiatomic stannides RERhSn with the smaller rare earth elements Y, Gd-Tm and Lu were reinvestigated on the basis of temperature-dependent single crystal X-ray diffraction data. GdRhSn crystallizes with the aristotype ZrNiAl at 293 and 90 K. For RE = Y, Tb, Ho and Er the HP-CeRuSn type (approximant with space group R3m) is already formed at room temperature, while DyRhSn adopts the HP-CeRuSn type below 280 K. TmRhSn and LuRhSn show incommensurate modulated variants with superspace groups P31m(1/3; 1/3; γ) 000 (No. 157.1.23.1) (γ = 3/8 for TmRhSn and γ = 2/5 for LuRhSn). The driving force for superstructure formation (modulation) is a strengthening of Rh–Sn bonding. The modulation is expressed in a 119Sn Mössbauer spectrum of DyRhSn at 78 K through line broadening.

scholarly journals Spectral Approximation of Fractional PDEs in Image Processing and Phase Field Modeling

2017 ◽  
Vol 17 (4) ◽  
pp. 661-678 ◽  
Author(s):  
Harbir Antil ◽  
Sören Bartels
Keyword(s):  
Image Processing ◽  
Phase Field ◽  
Differential Operators ◽  
Mathematical Tool ◽  
Phase Field Models ◽  
Field Modeling ◽  
Regularity Properties ◽  
Fractional Pdes ◽  
Fractional Differential ◽  
Fractional Differential Operators

AbstractFractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The numerical solution of corresponding model problems via a spectral method is analyzed. Its efficiency and features of the model problems are illustrated by numerical experiments.

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