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Theory of the memory effect in thiourea . Defect density waves in modulated systems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lederer, Pascal Montambaux, Gilles Jamet, J. P. Chauvin, Maxime |
| Copyright Year | 2018 |
| Abstract | 2014 A simple Landau-Ginzburg theory is shown to account qualitatively and semi-quantitatively for the memory effect anomalies of the susceptibility and the birefringence in thiourea. The importance of the gradient amplitude coupling energy in thiourea is emphasized. The possibility of creating a defect-induced locked incommensurate phase around any arbitrary temperature within the modulated phase is demonstrated. Such a locked phase will appear as a consequence of the condensation of a periodic defect concentration if extrinsic mobile impurities are allowed to interact for a sufficient time with a static modulation. We briefly discuss some aspects of such defect density waves in the physics of modulated structures. J. Physique Lett. 45 (1984) L-627 L-637 15 JUIN 1984, Classification Physics Abstracts 61.70 64.70K 66.30J A new memory effect, characteristic of modulated structures, was recently observed in thiourea [1]. Similar observations in various other systems were subsequently reported [2-4]. The memory was proved in reference [1] to be a periodicity memory : a thiourea crystal is kept during a few minutes at a constant arbitrary temperature T* and constant field E * in the modulated part of the phase diagram, i.e. a point where the modulation wave vector is q* = q(T*, E *); a susceptibility anomaly is observed when after cooling the system and heating again in an external field, the trajectory of the system in the phase diagram crosses the line q(T, E) = q*. The interpretation of the effect described in [1] was based on the idea that a concentration of defects such as impurities, vacancies, dislocation, etc., with non zero mobility acquires a periodic component if allowed to interact for a sufficient time with a static modulation. In the following we use the word impurities as a generic name for extrinsic defects (as opposed to intrinsic defects of the modulated order parameter, such as solitons, vortex lines, etc.). New experimental results, obtained after a thiourea crystal was kept at a constant arbitrary (+) Associe au C.N.R.S. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019840045012062700 L-628 JOURNAL DE PHYSIQUE LETTRES temperature T* and zero field (with T* in the modulated part of the phase diagram) during a much longer time (about 15 hours) than, previously have been reported in part recently [5]. Figure la exhibits the observed effects on the susceptibility with increasing and decreasing T. Figure lb shows the birefringence anomaly (reported here for the first time). The susceptibility anomalies are very similar to the ones observed in the case of the commensurate phase [6] with q = b*/8 at fields higher than 500 V/mm. Accordingly, it was suggested in reference [5] that the wave vector was locked at the incommensurate value q* over a temperature interval AT 7-1.5 K. (In the case of Ref. [5] T* = 209.5 K; so that ?* ~ b*/7.15.) The reason for this locking is of course the extrinsic commensurability potential due to the periodic ordering of mobile defects during the « write-up » time. Fig. la. Relative difference ð,Xl/X between the normal susceptibility and the one with the memory effect for decreasing T, after a 15 hours stabilization time at T * = 209.6 K for decreasing T ; A/~// corresponds to the first experiment after the memory effect was « written-up ». The small amplitude curve ax2/x corresponds to a second experiment after the system has been allowed to relax partially by heating it up to 3 K above TB during 12 hours. From the ratio Ox2/~x~ we deduce that the relaxation time of the defects is of the order of 12 hours at T = TB + 3 K ~ 220 K. Fig.1 b. Relative difference b (tlnb~)/tlnb~ between the normal birefringence and the one with the memory effect for increasing T, after a 95 hours stabilization time at T = 198.1 K for increasing T ; this curve corresponds to the first experiment after the memory effect was written-up. The curve shown here is generic, and is similar to those obtained for different T*. The fact that T* here corresponds to q(T*) = b*/8 plays no role here : in zero field, there is no birefringence anomaly under a continuous temperature variation, and the modulation wave vector has no measurable anomaly, because there is no Umklapp term in zero field, as discussed in Refs. [6] and [11]. For details in experimental techniques, see Ref [11]. L-629 MEMORY EFFECT AND DEFECT DENSITY WAVES In this Letter, we want to give a very simple theoretical description of the susceptibility anomaly (Fig. 1) which strongly supports the notion of a Defect-Induced Locked Incommensurate phase. We predict that a suitably conducted neutron diffraction investigation should give direct evidence for this lock in. Our theory is based on the consideration of the Landau-Ginzburg free energy appropriate to pure thiourea [6-9] and on the changes in the susceptibility due to a forced lock-in of the modulation wave vector. 1. Free energy, susceptibility and birefringence. The standard Landau-Ginzburg functional appropriate to thiourea involves the component of the polarization along the ferroelectric axis Px(z) and its spatial derivatives along the anisotropy axis : E is the applied electric field ; Ao = (T T o)/C, B and y are positive constants and (X is negative. dPx 2 As discussed in [7a] and [8], the term proportional to Px dz accounts for the curvature of the q(T) curve below 7~ the disordered modulated transition temperature. In fact the curvature of the curves q(T, E) = const. is also well accounted for by this term. This is easily seen when the polarization wave is purely sinusoidal, that is, near enough the disordered-modulated transition line. We restrict our discussion to this case in the following. Then consider equation (1 ) with P x(z) = Po + 2P qcos qz. It becomes [8] |
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| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
