The Modeling of the Lyapunov's Exponents for Incommensurate Superstructures, Which Is a Spontaneous Deformation as a Parameter of Order

Author(s):  
S. Sveleba ◽  
I. Katerynchuk ◽  
I. Kunyo ◽  
I. Karpa

In this paper an extensive study is reported of the very remarkable, and thus far apparently unique, case of the deformation in three dimensions of protocatechuic acid, to which attention was drawn many years ago by Otto Lehmann. The deformations are spontaneous, and are probably due to progressive gliding of the lattice planes, which exist in two configurations, one stable and the other unstable, the latter being the condition of the long prismatic rods when they first form. Such a prism presently deforms into a zigzag crystal, with stable and unstable sections in alternation which, with continuation of the deformation, becomes again straight, but now in the stable configuration. The bending is progressive, like that of an umbrella case, pendant from the end of an oblique cane pointed down, when the latter is pushed into it. The movements are so rapid that motion pictures, made with a microscope, were necessary for the observation of certain stages of the deformation. The deformations have been shown to many chemists and physicists during the past decade or more, none of whom had ever seen or heard of this remarkable type of crystal movement. The deformations are usually observed as the warm saturated solution cools, but they also occur after the crystal has been dried for many hours.


2019 ◽  
Vol 100 (14) ◽  
Author(s):  
Kostiantyn V. Yershov ◽  
Volodymyr P. Kravchuk ◽  
Denis D. Sheka ◽  
Jeroen van den Brink ◽  
Yuri Gaididei

1955 ◽  
Vol 10 (11) ◽  
pp. 942-952 ◽  
Author(s):  
Wataru Kinase ◽  
Hidetoshi Takahashi

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