On the observation of critical indices of primary and secondary order parameters using birefringence

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Abstract
The forms of the birefringence change at phase transitions are discussed for four types of phase transition: (i) ferrodistortive, (ii) cubic systems with an n-dimensional soft mode and order parameter, (iii) cubic systems with a one-dimensional soft mode occurring at n q0 points, and (iv) tetragonal magnetic systems (in which there is no crystallographic symmetry change at the phase transition). The birefringence is shown to vary as ( pi ) for case (i); as the secondary parameter ( pi alpha pi alpha )-(1/n) sigma alpha ( pi alpha pi alpha ) for case (ii); as ( pi )2 for case (iii); and as the energy for case (iv). The advantage of birefringence is that it is not sensitive to fluctuations, while the disadvantages are that one must work with a single-domain single crystal of a transparent substance.