Curie group

The Curie groups or continuous point groups are all those point groups that have at least one continuous rotational symmetry . They are named after Pierre Curie , who used them to describe the symmetry of electric and magnetic fields. There are seven Curie groups divided into two systems.

The seven Curie groups

The cylindrical system

The cylinders or cones given as examples are finite bodies. They are rotated or twisted in such a way that the axes of these bodies remain unchanged in any case.

Hermann Mauguin symbol	Hermann Mauguin short symbol	Schoenflies icon	possible physical properties	example
${\displaystyle A_{\infty }}$	${\displaystyle \infty }$	${\displaystyle C_{\infty }}$	optically active, enantiomorphic, piezoelectric, pyroelectrically polar	rotating cone
${\displaystyle {\frac {A_{\infty }}{M}}C}$	${\displaystyle {\bar {\infty }}}$	${\displaystyle C_{\infty h},\,S_{\infty },\,C_{\infty i}}$		rotating cylinder
${\displaystyle A_{\infty }\infty A_{2}}$	${\displaystyle \infty 2}$	${\displaystyle D_{\infty }}$	optically active, enantiomorphic, piezoelectric	Cylinder that is exposed to torsional forces of opposite magnitude
${\displaystyle A_{\infty }M}$	${\displaystyle \infty m}$	${\displaystyle C_{\infty v}}$	piezoelectric, pyroelectric	standing cone
${\displaystyle {\frac {A_{\infty }}{M}}{\frac {\infty A_{2}}{\infty M}}C}$	${\displaystyle {\bar {\infty }}m}$	${\displaystyle D_{\infty h};D_{\infty d}}$		standing cylinder

|

The spherical system

Hermann Mauguin symbol	Hermann Mauguin short symbol	Schönflies symbol	possible physical properties	example
${\displaystyle \infty A_{\infty }}$	${\displaystyle 2\infty }$	${\displaystyle \ K}$	optically active, enantiomorphic	sphere filled with an optically active liquid
${\displaystyle \infty {\frac {A_{\infty }}{M}}C}$	${\displaystyle m{\bar {\infty }}}$	${\displaystyle \ K_{h}}$		sphere filled with an isotropic liquid

Applications

The Curie groups are used to describe the symmetry of fields. This is required when applying the Curie principle to determine the properties of a body in a field.

literature

• Will Kleber , Hans-Joachim Bautsch , Joachim Bohm : Introduction to crystallography. 19th, improved edition. Edited by Joachim Bohm and Detlef Klimm. Oldenbourg Wissenschaftsverlag, Munich 2010, ISBN 978-3-486-59075-3 .

Web links

• The cylindrical system (IUCr / engl.)
• The spherical system (IUCr / engl.)

Individual evidence

1. ↑ Pierre Curie: Sur la symétrie dans les phénomènes physiques, symétrie d'un champ électrique et d'un champ magnétique. In: Journal de Physique théorique et appliquée. Ser. 3, Vol. 3, No. 1, 1894, pp. 393-415, doi : 10.1051 / jphystap: 018940030039300 .