Molar volume minimum and adaptative rigid networks in relationship with the intermediate phase in glasses C. Bourgel, 1,2 M. Micoulaut, 3 M. Malki, 1,2 and P. Simon 1,2 1 CNRS, UPR 3079 CEMHTI, 1D Avenue de la Recherche Scientifique, 45071 Orléans Cedex 02, France 2 Université d’Orléans (Polytech’Orléans, Faculté des Sciences), BP 6749, 45072 Orléans Cedex 02, France 3 Laboratoire de Physique Théorique de la Matière Condensée, UPMC-Paris 6, CNRS UMR 7600, Boite Postale 121 4, Place Jussieu, 75252 Paris Cedex 05, France Received 17 June 2008; revised manuscript received 8 September 2008; published 21 January 2009 We propose that the molar volume minimum observed in barium silicate glasses 1- xSiO 2 - xBaO is related to the onset of an adaptative rigid glassy network. We obtain in the compositional window 29%  x  33% a dramatic decrease in stressed rigid local units from the Raman analysis and at x =31% the onset of barium ionic conduction. A random bond model J. Barré et al., Phys. Rev. Lett. 94, 208701 2005 and constraint counting algorithms permit defining of the free energy of the system, and analyzing of the elastic nature of three compositional ranges of interest: a stressed rigid phase at low x, a flexible phase at high x, and a stress-free intermediate phase where space filling is optimized. DOI: 10.1103/PhysRevB.79.024201 PACS numbers: 61.43.Fs, 63.50.-x I. INTRODUCTION The molar volume of binary-alloy liquids and glasses does not always display a monotonic behavior with alloy composition. For instance, molar volume minima have been reported for a certain number of glassy systems that under- score the tendency of a network to densify its structure in selected compositional ranges. 1 While this is a rather well documented and debated issue in alkali germanates, 2 little is known about the same tendency in silicate glasses and liquids 3 although the precise knowledge and the origin of compositional trends in molar volume have some obvious implications in geochemistry and Earth Sciences in general. In the literature, a principle for compactness optimum has been invoked from an elegant argument stating that a me- chanical stability 4 is reached when the number density of mechanical constraints n c arising from interatomic bond- bending and bond-stretching forces equals the number of de- grees of freedom. This mechanical stability criterion has been later identified with a rigidity transition 5 at which the number density of low-frequency floppy modes f =3- n c vanishes. It implies that the volume contraction is linked with tight bonding and shorter bond lengths when the num- ber density of constraints matches exactly the number of de- grees of freedom. However, space-filling tendency is obvi- ously the consequence of a collective behavior and cannot be simply handled from global or mean-field approaches. 4,5 In chalcogenide network glasses, it has been observed that space-filling compositional windows 6,7 were correlated with thermally reversing windows or rigid intermediate phases IP obtained from complex heat-flow measurements at the glass transition. 8 These windows are located around the net- work mean coordination number r ¯ = 2.4, and are found be- tween the flexible where n c  3 and the stressed rigid phase n c  3 of glasses. 9–13 Do such correlations exist in other types of networks such as the oxides or ionic conductors? Recent molecular- dynamics simulations of densified silicas have shown 14,15 that the balance between two structural mechanisms accom- modating low flexible and high stressed rigid pressure applications could lead to a space-filling window, clearly re- lated with a pressure-induced rigidity transition. Here it is shown that the correlation between space-filling windows and the intermediate phase also exist in rigidity induced by composition for an archetypal silicate system, the barium based glass. Our results therefore underscore the commonal- ity of the physics driving the formation of intermediate phases in covalent-chalcogenide and ionic-oxide glasses, and the way composition and pressure space-filling windows can be achieved. We describe experimental and theoretical results on barium silicates of the form 1- xSiO 2 - xBaO from Raman spectroscopy, ionic conduction, and a random bond model, 11 which show that the observed molar volume minimum is located in the intermediate phase which results from the net- work adaptation leading to a rigid and almost stress-free net- work within the compositional window 29%  x  33%. In this respect, barium silicates display very common features with chalcogenide network glasses. Beyond this main issue, the present paper shows also how the intermediate phase in glasses can be detected when its most obvious signature from heat-flow measurements cannot be provided. Barium sili- cates and geological glasses in general have glass transition temperatures that exceed by far the highest accessible tem- perature of the calorimetric setup 8 used for the heat-flow measurements. One has therefore to find alternative experi- mental signatures for the intermediate phase in these peculiar high-temperature glassy systems. Barium silicate glasses and melts have received little attention compared to alkali sili- cates although the role of alkaline-earth silicates tends to be even more important as network modifiers in natural systems than alkali metals. Any new insight into the structure, the thermal behavior, and/or the electrical transport behavior is therefore welcome. The present paper is organized as follows: in Sec. II, we show the molar volume results, and describe the experimen- tal data obtained in Raman scattering and conductivity mea- surements together with the estimate of the total number den- PHYSICAL REVIEW B 79, 024201 2009 1098-0121/2009/792/0242018 ©2009 The American Physical Society 024201-1