The interpretation of HAUP measurements: a study of the systematic errors

Abstract

Please be advised that this information was generated on 2018-05-10 and may be subject to change. j Phys. d : Appl. Phys. 28 (1995) 1195-1211. Printed in the UK T h e i n t e r p r e t a t i o n o f h a u p m e a s u r e m e n t s : a s t u d y o f t h e s y s t e m a t i c e r r o r sM IntroductionThe merits of the high-accuracy universal polarimeter (HAUP), introduced by Kobayashi and Uesu (1983), lie in the possibility of measuring very accurately and simultaneously the optical activity and birefringence of crystals. In addition, the rotation of the optical indicatrix is detected with a high sensitivity. The measurements require optically transparent, birefringent platelets of single crystals, with flat (polished) plane-parallel faces. It is very important to perform the measurements as a function of some external parameter in order to separate systematic errors from the optical properties, In the experiments described in this paper, the wavelength k of the light is the external parameter* Additional parameters can be temperature, electric fields (electro-optics) or magnetic fields (magneto-optics).The presence and nature of structural phase transitions can often be revealed by the birefringence (Ivanov 1991, Gehring 1977). The point symmetry of a specific phase can be studied by measuring the optical activity in several directions in a crystal, since optical activity is a tensorial property, which is sensitive to the symmetry (Nye 1985). The HAUP is, therefore, a powerful instrument in crystal optics.A very interesting problem in this field is encountered for incommensurately modulated crystals, with a centrosymmetric paraelectric phase (Cummins 1990). The incommensurate phase is often a (small) periodic deformation of the centrosymmetric paraelectric phase. The wavelengths of the periodic deformation is incommensurate with the lattice of the average structure. Therefore, the lattice translational symmetry is broken in at least one direction. Of course, the question arises of whether this phase can be optically active, because optical activity is forbidden in a centrosymmetric crystal (Nye 1985 In order to exclude the possibility that these differences are caused by the way of measuring or the way of interpreting the measurements, we feel . it necessary to reconsider very precisely the working principles of the HAUP method. In this paper, we re-derive rigorously the HAUP intensity formula (section 2 ). Experiments have been performed both on a centrosymmetric crystal with zero optical activity and on the non-centrosymmetric room-temperature phase of quartz, which has a large optical activity (section 3). In section 4 the obtained results are used to re consider critically the fitting procedures with which the optical properties are extracted from the measurements. Moreover, in section 5, the behaviour and origin of the systematic errors will be studied thoroughly. The quality and sensitivity of HAUP measurements is addressed in section 6 . For all aspects of the HAUP method, we discuss and take into accoun...

Influence of incommensurate modulation on the optical properties of the solid solution ((CH3)4<

“…Note that ( pϪa) is a constant with a magnitude in the order of 10 Ϫ4 . 12,20 Therefore, it is clear that k, and consequently G 33 , is nonzero already in the paraelastic phase. It has been explained in the Introduction that one can expect this, because the centrosymmetry is broken by the complete miscibility of Br and Cl.…”

“…9 This was done with a high-accuracy universal polarimeter ͑HAUP͒ that is very well suited for this purpose. [9][10][11][12] In the case of ((CH 3 ) 4 N) 2 CuCl 4 a rotation of the optical indicatrix was detected in the incommensurate phase, which contradicts an orthorhombic symmetry. In addition, ͑small͒ optical activity was found which contradicts the presence of an inversion center.…”

“…12 Both the so-called ⌬⌰ correction and the ⌬Y correction were carried out. The latter reduces the magnitude of the ␦Y error, typical in the HAUP method, to the order of 10 Ϫ5 or smaller.…”

“…However, it is well known from other experiments that (pϪa) has a magnitude in the order of 10 Ϫ4 . 12,20 One can, therefore, estimate the gyration by neglecting ( pϪa) in the case that the value of (pϪa)ϩ2k is much larger than 10 Ϫ4 . Furthermore, the measurements provide the values of it is possible to find the rotation of the optical indicatrix with a large accuracy.…”

“…In the measurements as a function of temperature at least two extinction directions 12 were measured, in order to determine the rotation of the indicatrix with a large accuracy. 19 The temperature was left to stabilize for about half an hour after each change of its value, because we have learned from previous experiments that shorter stabilization times can lead to irreproducible results.…”