Structures and energetics of low-index stoichiometric BiPO4 surfaces

CrystEngComm ◽  
2019 ◽  
Vol 21 (32) ◽  
pp. 4730-4739 ◽  
Author(s):  
Yuan Xu ◽  
Xinguo Ma ◽  
Jisong Hu ◽  
Ang Xu ◽  
Zhuoran Wang ◽  
...  
Keyword(s):  
Wulff Shape

Four low-index surfaces of monazite BiPO4 in the Wulff shape are investigated.

On Uniqueness of the Wulff Shape for Cellular Automata

1991 ◽  
Vol 14 (1) ◽  
pp. 75-89
Author(s):  
Paweł Wlaź
Keyword(s):  
Cellular Automata ◽  
Large Class ◽  
Growth Function ◽  
Wulff Shape ◽  
Transition Rules

In this paper, ordered transition rules are investigated. Such rules describe an increment of mono-crystals and for every rule one can calculate so called Wulff Shape. It is shown that for some large class of these rules, there exists at most one growth function which generates a given Wulff Shape.

scholarly journals The Wulff shape as the asymptotic limit of a growing crystalline interface

1997 ◽  
Vol 1 (3) ◽  
pp. 560-571 ◽  
Author(s):  
Stanley Osher ◽  
Barry Merriman
Keyword(s):  
Asymptotic Limit ◽  
Wulff Shape

scholarly journals Wulff shape of strontium titanate nanocuboids

2015 ◽  
Vol 632 ◽  
pp. L22-L25 ◽  
Author(s):  
Lawrence Crosby ◽  
James Enterkin ◽  
Federico Rabuffetti ◽  
Kenneth Poeppelmeier ◽  
Laurence Marks
Keyword(s):  
Strontium Titanate ◽  
Wulff Shape

scholarly journals Quasicrystals and the Wulff-Shape

1999 ◽  
Vol 21 (3) ◽  
pp. 421-436 ◽  
Author(s):  
K. Böröczky ◽  
U. Schnell
Keyword(s):  
Wulff Shape

scholarly journals STABILITY OF CRYSTALLINE EVOLUTIONS

2005 ◽  
Vol 15 (06) ◽  
pp. 921-937 ◽  
Author(s):  
MATTEO NOVAGA ◽  
EMANUELE PAOLINI
Keyword(s):  
Integral Curve ◽  
Jacobian Matrix ◽  
Convex Polyhedra ◽  
Wulff Shape ◽  
Stability Properties ◽  
Fixed Volume ◽  
The Stability

In this paper we analyze the stability properties of the Wulff-shape in the crystalline flow. It is well known that the Wulff-shape evolves self-similarly, and eventually shrinks to a point. We consider the flow restricted to the set of convex polyhedra, we show that the crystalline evolutions may be viewed, after a proper rescaling, as an integral curve in the space of polyhedra with fixed volume, and we compute the Jacobian matrix of this field. If the eigenvalues of such a matrix have real part different from zero, we can determine if the Wulff-shape is stable or unstable, i.e. if all the evolutions starting close enough to the Wulff-shape converge or not, after rescaling, to the Wulff-shape itself.

The Wulff Shape of Alumina: III, Undoped Alumina

2004 ◽  
Vol 85 (3) ◽  
pp. 611-622 ◽  
Author(s):  
Mikito Kitayama ◽  
Andreas M. Glaeser
Keyword(s):  
Wulff Shape

A note on the stability of the Wulff shape

2006 ◽  
Vol 87 (3) ◽  
pp. 272-279 ◽  
Author(s):  
Sven Winklmann
Keyword(s):  
Wulff Shape ◽  
The Stability

Some characterizations of the Wulff shape

2010 ◽  
Vol 348 (17-18) ◽  
pp. 997-1000 ◽  
Author(s):  
Leyla Onat
Keyword(s):  
Wulff Shape
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