Birefringence and order parameter of ammonium bromide

Egert, G.; Jahn, I.R.; Renz, Diemo

doi:10.1016/0038-1098(71)90562-x

Cited by 44 publications

(3 citation statements)

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“…However, this transition has a small first order component. In bulk experiments the temperature dependence of the order parameter was observed with an exponent of (3 = 0.25 [13]. This is less than the Ising value (3 = 0.32 and probably due to the first order component.…”

mentioning

confidence: 79%

Near-surface x-ray critical scattering from aNH4Br (11¯0) surface

1993

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We present the first observations of near-surface critical phenomena of a phase transition in a molecular solid showing both an order-disorder and a strong displacive component. The surface xray scattering experiments were performed on an NH 4 Br single crystal (T c = 235 K). For the order parameter they show a crossover from a power law with the bulk critical exponent f3 -0.3 ± 0.05 to a surface behavior with exponent 0i = 0.8 ± 0.1. Prom the diffuse intensity we have determined the critical exponents 77u = 1.3 ± 0.15, v -0.5 ± 0.15 and the correlation length ^ = 4 db 0.5 A.PACS numbers: 61.50. Ks, 61.10.Lx, 64.70.Kb In the past few years there has been great interest in the critical behavior of phase transitions in the nearsurface region. The broken translational symmetry at the surface leads to a modified criticality [1,2]. There are three possible types of phase transitions induced by the surface: (i) the "ordinary" transition with the same transition temperatures in the bulk and at the surface, (ii) the "extraordinary" case where the ordering of the surface occurs at a higher temperature ("surface transition") than in the bulk, and (iii) the "special" transition representing a multicritical point separating the types mentioned above. For each of these transitions new surface-related critical exponents occur. However, the length scale of the critical fluctuations remains to be the bulk correlation length £. In the case of the ordinary transition there is only one additional exponent, while the other surface exponents can be expressed as combinations of the new one and the bulk values via scaling relations. In theoretical studies many detailed predictions have been made also introducing new methods for precision determinations of critical parameters [1,3]. For experimental investigations of critical phenomena at surfaces Dietrich and Wagner proposed x-ray and neutron diffraction [4]. A detailed review of both theoretical and experimental aspects concerning the surface scattering is given by Dosch [5].So far the experiments were concentrated on magnetic systems and order-disorder transitions in alloys. The first observations of the temperature behavior of the surface order parameter have been made on the magnetization of Ni surfaces by Celotta et al. [6] and Alvarado et al. [7]. Especially the latter yielded the predicted power law with the critical exponent j3\ = 0.825 ± 0.04. Surface x-ray scattering investigations on the order-disorder transitions in CU3AU and, more related to second order phase transitions, Fe3Al were carried out by Dosch and co-workers [8,9] and verified the theoretical predictions even better. In particular, all surface exponents could be determined independently and the scaling relations could be tested [9]. Furthermore, Toennies and Vollmer [10] performed a helium atom scattering study on a KMnF 3 surface. For this structural (distortive) phase transition their experiment yielded (3\ = 0.63 ± 0.03. This exponent is too small for an ordinary transition in the Heisenberg model but in r...

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confidence: 79%

Near-surface x-ray critical scattering from aNH4Br (11¯0) surface

1993

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“…At the same time, we exclude the induction of local polarity due to change in symmetry while d.c. is acting. On the other hand, it is known that ∆n~q 2 , where q is an order parameter [31]. In the investigated crystal, the P S is the order parameter, therefore, the presence of birefringence above T C indicates once again that the phase is polar.…”

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confidence: 90%

Phase Transitions and Local Polarity above TC in a PbZr0.87Ti0.13O3 Single Crystal

et al. 2020

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Solid solutions of PbZr1−xTixO3 (PZT) are one of the most widely used piezoelectric materials with perovskite structure. Despite the decades of research, the phase diagram of PZT reported in 1971 has not been resolved yet. Recently, it turned out that single crystals of good quality of these solid solutions can be grown. By means of top-seeded solution growth (TSSG) technique, we succeeded to grow a single PbZr0.87Ti0.13O3 crystal. Hence, a partial verification of the diagram could be performed through investigations of the optical, dielectric, pyroelectric and elastic properties of this crystal, in a wide temperature range. The obtained results confirmed that the PbZr0.87Ti0.13O3 crystal undergoes a sequence of phase transitions, such as those observed in ceramics of similar chemical composition. However, additional anomalies of investigated physical properties were observed and discussed. Moreover, the influence of electric field on optical properties has been investigated for the first time and has proven the existence of local polar character of the phase above TC in a limited temperature range.

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“…For order-disorder transitions the birefringence is proportional to the square of the order parameter if the crystal symmetry changes at the transition (Egert, Jahn & Renz, 1971). A log-log plot between 295 and 418 K in Fig.…”

Section: Methodsmentioning

confidence: 99%

The layered perovskites (C₃H₇NH₃)₂MnCl₄(PAMC) and (C₂H₅NH₃)₂MnCl₄(EAMC): birefringence studies and the symmetry of the commensurately modulated ε phase of PAMC

Brunskill¹,

Depmeier²

1982

Acta Cryst Sect A

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INFORMATION THEORY AS A BASIS FOR THE MAXIMUM DETERMINANTstructure-factor magnitudes are obtained from experiment. Nevertheless, the extrapolation of data, in both cases, corresponds to determination of an analytic function whose squared modulus is a function of maximum entropy measure. The definition for entropy measure is that given by Ponsonby (1973), parallel form and shown to be equivalent. With only the restrictions that (electron) density be positive, and that matrices and determinants be of small enough order to be positive definite, the two equivalent formulations yield identical results and provide an informationtheoretic interpretation of the maximum determinant.v V being the unit-cell volume. Ponsonby emphasizes that this is strictly only a measure of relative entropy of the real power spectrum of an underlying signal. In this sense maximum H' corresponds to maximum entropy measure p(r) = Ig(r)l z, and a maximum-entropy distribution function for Gh, the transform of g(r). Equation (6) AbstractBy measuring the birefringence on (001) platelets of PAMC as a function of temperature, previously determined phase transitions have been confirmed. Large effects were measured on passing through the normal-incommensurate ~ --, y transition and through the normal-commensurate ~ --, e transition, whereas the commensurate-normal e--, 6 and the incommen-* Bis(n-propylammonium) tetrachloromanganate.

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Birefringence and order parameter of ammonium bromide

Cited by 44 publications

References 8 publications

Near-surface x-ray critical scattering from aNH4Br (11¯0) surface

Near-surface x-ray critical scattering from aNH4Br (11¯0) surface

Phase Transitions and Local Polarity above TC in a PbZr0.87Ti0.13O3 Single Crystal

The layered perovskites (C₃H₇NH₃)₂MnCl₄(PAMC) and (C₂H₅NH₃)₂MnCl₄(EAMC): birefringence studies and the symmetry of the commensurately modulated ε phase of PAMC

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Birefringence and order parameter of ammonium bromide

Cited by 44 publications

References 8 publications

Near-surface x-ray critical scattering from aNH4Br (11¯0) surface

Near-surface x-ray critical scattering from aNH4Br (11¯0) surface

Phase Transitions and Local Polarity above TC in a PbZr0.87Ti0.13O3 Single Crystal

The layered perovskites (C3H7NH3)2MnCl4(PAMC) and (C2H5NH3)2MnCl4(EAMC): birefringence studies and the symmetry of the commensurately modulated ε phase of PAMC

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The layered perovskites (C₃H₇NH₃)₂MnCl₄(PAMC) and (C₂H₅NH₃)₂MnCl₄(EAMC): birefringence studies and the symmetry of the commensurately modulated ε phase of PAMC