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The relationship between intermediate-range order in glasses and discernible features in the static structure factor

The relationship between intermediate-range order in glasses and discernible features in the static structure factor

ELSEVIER Physica B 234-236 (1997) 448--449 The relationship between intermediate-range order in glasses and discernible features in the static struc...

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ELSEVIER

Physica B 234-236 (1997) 448--449

The relationship between intermediate-range order in glasses and discernible features in the static structure factor R. Fayos a,*, F.J. Bermejo a, J. Dawidowski a, H.E. Fischer b, M.A.

Gonzfilez b

alnstituto de Estructura de la Materia, CSIC, Serrano 123, Madrid E-28006, Spain blnstitut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France

Abstract

The relationship between intermediate-range order in glasses and discernible features in the diffraction pattern of glassy materials is demonstrated experimentally by a direct comparison of the static-structure factors of a material in its liquid, stable crystal, rotator-phase crystal, orientational glass and amorphous phases. The orientationally disordered crystalline phases appear as an intermediate ordering stage between the stable crystal and the glassy solid. Keywords: Amorphous materials; Diffraction; Correlation lengths

The origin of the first sharp diffraction peak (FSDP) in the molecular-scale static-structure factor S ( Q ) of disordered materials has been a matter of debate [1] stemming from the possible identification of this feature as a reciprocal space manifestation of intermediate-range order (IRO), namely, the presence of stereo-regularities involving atoms located beyond the first coordination shell. Previous efforts [2,3] have never produced any widely accepted evidence showing that the characteristic parameters of such a peak, such as its position in wave number Qp or its width AQ, could be directly related to quantities such as characteristic distances and/or coherence lengths or to any other construct better suited for the description of order in non-periodic arrays. The debate has mostly been centered on the identification of some feature in D ( r ) describing the spatial extent of correlations in real space (interpreted as a "correlation length" Rc=2rt/AQ) with some distinguishable feature in the FSDP or any other portion of S(Q). We have recently shown that there exists at least one material, ethanol [4], which by means of mild * Corresponding author.

thermal treatment can be prepared in situ in its liquid, glass, stable (monoclinic) crystal, rotator-phase crystal (RP) and orientational glass (OG) obtained by freezing of the rotational degrees of freedom. A series of diffraction experiments, using the D4 and D2B diffractometers of the ILL, monitored all the phase transformations by following the changes in the position, shape and width of the FSDP. As shown by a set of I ( Q ) diffraction patterns for glassy, rotatorphase and stable crystal forms of ethanol shown in Fig. 1, the first intense peak of the RP crystal lies at a wave vector rather close to where the glass shows its maximum, whereas the monoclinic stable crystal form shows only two sets of composite peaks at some 1.55 and 1.80 A -1, that is on either sides of the momentum transfers where glass, liquid and RP or OG solids show their maxima. The RP and OG crystals show a progression of five Bragg peaks, which index as a BCC crystal structure with a lattice constant of about 5.32 A at 105 K, which shows a remarkable dependence on temperature leading to a thermal expansion coefficient of some 2.6 x 10 - 4 K -1 i.e. of the same order of magnitude of those shown by amorphous materials.

0921-4526/97/$17.00 © 1997 Elsevier ScienceB.V. All rights reserved Pll S092 1-4526(96)01006-X

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R. Fayos et al. IPhysica B 234-236 (1997) 448~449 8 6

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r (A) Fig. 2. D(r) correlation functions for the monoclinic (a), OG (b), and RP crystals (c), glass (d) and normal liquid (6). The curve superimposed to (b) shows the result of a calculation of the intermolecular part of D(r) in a model of 512 BCC unit cells assuming a complete decorrelation of orientations. The functions have been shifted by two-unit increments.

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Fig. 1. The I(Q) patterns for the glass at T=5 K the RP at 105 K and the monoclinic crystal at the same temperature. The inset shows the reflections at 2.33, 2.87, 3.31 and 3.70A -~. A comparison o f the static D ( r ) pair-correlation functions derived from inversion o f the structure factors measured at D4B is shown in Fig. 2. The curves pertaining to the RP and O G phases show a low-period oscillation from around 4.6/1 onwards with an average period o f about 3.74(8 ) A. This comes rather close to that derived from the position o f the main Bragg peak ( ~ 3.8 A), and its origin was investigated by means o f a calculation o f such a correlation function for a model o f a BCC crystal where the molecular orientations are completely uncorrelated, the result also

shown in Fig. 2. On the other hand, the persistence o f such an oscillation agrees with the narrow width o f the Bragg (1 1 0) peak in both RP and OG. A look at the D ( r ) function o f glass (and liquid) shows that the period and phase o f its long-Q oscillations are rather close to those o f the RP and OG solids, especially if one accounts for the smaller density o f glass and the shorter persistence length (the oscillation dies away above some 18 A). As a matter o f fact, such a persistence (or "coherence length", Re) turns out to be not far from that o f about 20 A estimated from the width o f the glass FSDP. The present results thus provide direct, model-free evidence o f the relevance o f parameters characterizing the FSDP o f glassy matter as true indicators o f order at scales beyond first neighbours.

References

[1] P.S. Salmon, Proc. Roy. Soc. London A 445 (1994) 351 and references therein. [2] S.C. Moss and D.L. Price, in: Physics of Disordered Materials, eds., D. Adler et al. (Plenum, New York, 1985) p. 77; S.R. Elliot, Phys. Rev. Lett. 67 (1991) 711; A.P. Sokolov, A. Kisliuk, M. Soltwisch and D. Quitmann, Phys. Rev. Lett. 69 (1992) 1540. [3] J. B16try, Phil. Mag. B 62 (1990) 469. [4] A. Srinivasan, F.J. Bermejo, A. de AndrOs, J. Dawidowski, J. Zfifiiga and A. Criado, Phys. Rev. B 53 (1996) 8172.