Bimodal phase percolation model for the structure of Ge-Se glasses and the existence of the intermediate phase Pierre Lucas, 1 Ellyn A. King, 1,2 Ozgur Gulbiten, 1 Jeffery L. Yarger, 3 Emmanuel Soignard, 3 and Bruno Bureau 2 1 Department of Materials Science and Engineering, University of Arizona, 4715 E. Fort Lowell Road, Tucson, Arizona 85712, USA 2 UMR CNRS 6226 Sciences Chimiques, Groupe Verres et Céramiques, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France 3 Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604, USA Received 19 October 2009; published 18 December 2009 A detailed nuclear magnetic resonance and Raman study of Ge x Se 1-x glasses indicate that the glass structure is composed of intertwined microdomains of GeSe 2 and Se n . Static nuclear magnetic resonance spectra of glasses ranging from 0  x  1 3 reveal the absence of Ge-Se-Se fragments in the structure. High temperature nuclear magnetic resonance showing considerable line narrowing confirms this observation. More importantly, the fraction of Se-Se-Se obtained by integration of nuclear magnetic resonance lines matches closely the percentage predicted for a bimodal phase model and is not consistent with the existence of Ge-Se-Se frag- ments. Raman spectra collected on the same glass also confirm the existence of GeSe 2 domains up to high selenium concentrations. The mobility of the Se n phase observed at high temperature while the GeSe 2 phase remains rigid is consistent with their respective underconstrained and overconstrained structural nature. The proposed bimodal phase percolation model is consistent with the original Phillips and Thorpe theory however it is clearly at odds with the intermediate phase model which predicts large amounts of Ge-Se-Se fragments in the structure. A calorimetric study performed over a wide range of cooling/heating rates shows a narrow composition dependence centered at r = 2.4 in contrast with the wide reversibility window observed by Modulated Differential Scanning Calorimetry. This suggests that the observation of the reversibility window associated with the intermediate phase in Ge-Se glasses could be an experimental artifact resulting from the use of a single modulation frequency. DOI: 10.1103/PhysRevB.80.214114 PACS numbers: 61.43.Dq, 81.05.Gc I. INTRODUCTION The structure of Ge x Se 1-x glasses has long been a source of controversy in the field of amorphous semiconductors. The structure of Ge x Se 1-x glasses in the range 0  x  1 3 was initially described using the chain crossing model CCM, whereby GeSe 4/2 tetrahedra are linked by Se chains whose length increases with Se content. 1,2 However, this model was quickly contradicted by the persistent observation of a Raman line near 213 cm -1 associated with Ge-Se-Ge sequences 3 and later assigned to structural fragments com- posed of corner- and edge-sharing tetrahedra. 4,5 The presence of edge-sharing tetrahedra in Se-rich glasses is not consistent with the CCM and in particular contradicts the existence of an “ordered phase” 1 at x = 0.2 GeSe 4  where all Ge atoms would be linked by a Se-Se doublet. More recently, the struc- ture of Ge x Se 1-x has been the object of intense modeling efforts centered on topological arguments involving counting constraints and atomic degrees of freedom. 6–14 An original model by Phillips and Thorp predicts an optimal glass for an average number of bonds per atom r = 2.4 corresponding to a topology where bond and angular constraints exactly equals the number of degrees of freedom in the structure. 6–8 This composition is characterized as the threshold between an underconstrained floppy phase for r  2.4 and an over- constrained rigid phase for r  2.4. The transition point r = 2.4 is thought to correspond to the composition at which the rigid phase percolates throughout the structure. This model was later refined by invoking the “self-organization” of the glassy network which results in a structure that re- mains rigid but unstressed over a wider range of composi- tions near r = 2.4. 15 The unstressed domain between the floppy and rigid phases was then termed the “intermediate phase.” Subsequently, models based on connecting structural fragments of different connectivity were developed to ratio- nalize the intermediate phase 11–14 and experimental measure- ments were performed to corroborate its existence. 10 In par- ticular, the nonreversible enthalpy obtained by Modulated Differential Scanning Calorimetry MDSC was shown to decrease in this domain. 10 In any case it was found that the structural origin of the intermediate phase requires the existence of Se-Se-Ge “isostatic” structural fragments in or- der to account for the “rigid but unstressed” nature of the network. 12–14 Among structural probes, solid state nuclear magnetic resonance constitutes a unique technique for examining the local environments of active elements in a qualitative and quantitative manner. But while silicate and phosphate glasses have been widely studied, chalcogenides and in particular selenides have received little attention due to the low nuclear magnetic resonance sensitivity of selenium. 16 Nevertheless, high quality spectra can be obtained using extended acquisi- tion times up to several days. 17,18 In this work, an extensive high-temperature nuclear magnetic resonance study shows evidence for a different structural model of Ge-Se glasses based on a bimodal percolation of Se n and GeSe 2 phases. It is shown that no significant amount of Se-Se-Ge fragments is present in the structure. These results are at odds with the existence of the intermediate phase. Calorimetric measure- ments on a series of Ge-Se glasses further suggest that the observation of the intermediate phase could be based on an experimental artifact. PHYSICAL REVIEW B 80, 214114 2009 1098-0121/2009/8021/2141148 ©2009 The American Physical Society 214114-1