Maksimova, E.M.

Zamkovskaya, A.I.

SocioEconomic Challenges Journal (Sumy State University)

СЕКЦІЯ 1: Теоретична та ФЕЕ :: 2015 
експериментальна фізика 
36 
Visualization of Thermal Crystals Expansion 
 
Maksimova E.М., PhD, Zamkovskaya A.I., student 
V.I. Vernadsky Crimean Federal University, Simferopol 
 
Thermal properties of crystals can be visualized using the indicatory 
surfaces of thermal expansion. Radius-vector of this surface is proportional 
to the size of the relative lengthening of crystal in this direction at heating. 
The form and orientation of the indicatory surfaces of thermal expansion of 
the crystals is related to their symmetry according Neumann's Principle: for 
the crystals of the highest category – a sphere, fig.1(а); for the middle 
category – spheroid, fig.1(b); for the lowest category – a triaxial ellipsoid, 
fig.1. 
  
 
Figure 1 – The indicatory surface of thermal expansion of sphalerite (a), α-
quartz (b) and brookite (c), constructed in Mathcad 
application package.  
 
There are a small number of materials, which in some directions have 
negative coefficients of thermal expansion (for example: calcite, graphite). 
In such crystals there are directions, which are not exposed to temperatures 
– cones of zero expansion. 
 
1. W.A. Wooster, Tensors and group theory for the physical properties of 
crystals (Oxford: Claredon Press: 1973). 
2. N.V. Perelomova, M.M. Tagiyeva, Book of problems in crystal physics 
(Moscow: Science: 1982).  


Visualization of Thermal Crystals Expansion

https://essuir.sumdu.edu.ua/bitstream/123456789/40672/1/Maksimova_thermal%20expansion.pdf

Visualization of Thermal Crystals Expansion

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SocioEconomic Challenges Journal (Sumy State University)