Medium-range order in alkali metaphosphate glasses and melts investigated by reverse Monte Carlo simulations and diffraction analysis Sylvie Beaufils, 1 Laurent Cormier, 2 Monica Bionducci, 3 Claude Ecolivet, 1 Georges Calas, 2 Andre ´ Le Sauze, 4 and Roger Marchand 4 1 Groupe Matie `re Condense ´e et Mate ´riaux, UMR CNRS 6626, Universite ´ de Rennes I, 35042 Rennes Cedex, France 2 Laboratoire de Mine ´ralogie et Cristallographie, 4 Place Jussieu, 75252 Paris Cedex 05, France 3 Laboratoire Le ´on Brillouin C.E. Saclay, 91191 Gif sur Yvette, France 4 Laboratoire Verres et Ce ´ramiques, UMR CNRS 6512, Universite ´ de Rennes I, 35042 Rennes Cedex, France Received 19 December 2001; published 3 March 2003 Reverse Monte Carlo simulations have been performed on the alkali metaphosphate glasses Na 0.5 Li 0.5 PO 3 and LiPO 3 concerning structural experimental data obtained by neutron and x-ray diffraction at 300 K for both systems and versus temperature up to the melting point for the mixed composition. It appears that the contrast effect due to the negative scattering length of Li is not the only reason for the difference in the intensity of the prepeak observed in both systems. The main structural difference lies in the intermediate-range order, while the short-range order is quite similar in both systems. Moreover, it is shown that the intensity increase of the prepeak in the Na 0.5 Li 0.5 PO 3 structure factor is due to the partial structure factors of the PO 4 tetrahedron, sustaining the hypothesis of an ordering between several PO 4 tetrahedra and voids with temperature. DOI: 10.1103/PhysRevB.67.104201 PACS numbers: 61.43.Fs, 61.12.-q, 61.10.-i I. INTRODUCTION The structure of phosphate glasses has been extensively studied and the short-range order referred as SRO is rather well characterized in these compounds. 1–4 However, the question of the nature of the intermediate-range order re- ferred as IRO in such amorphous systems and its relation- ship to specific features in diffraction patterns is a more open subject. A peak emerging at low wave vector in the structure factor of amorphous systems, known as the prepeak, is sup- posed to be related to a certain organization at intermediate distances 10–20 Å in glasses. In many chalcogenide glasses, 5 in covalent amorphous systems such as SiO 2 Refs. 5, 6, and 27 and P 2 O 5 , 2,6 the prepeak appears at a wave vector Q 1 such as Q 1 r 1 2.5, where r 1 is the shortest inter- atomic distance. 7,8 In the family of phosphate glasses, this rule is roughly valid, with Q 1 =1.6 Å -1 , except for the se- ries of alkali metaphosphate glasses where Q 1 r 1 =1.6, with Q 1 =1.1 Å -1 . 4,9 We are interested by the eutectic composi- tion Na 0.5 Li 0.5 PO 3 , whose dynamic was previously characterized. 13,14 The structure has also been investigated between 300 K ( T g -215 K) and 800 K ( T m +53 K) by neu- tron diffraction and at 300 K by x-ray diffraction. 9 According to Eliott’s interpretation, 10–12 the prepeak in covalent sys- tems is mainly due to a contrast effect between dense and empty regions the latter centered around the cations of the amorphous structure. To check this hypothesis, it was inter- esting to emphasize this contrast. This was done by perform- ing the same kind of measurements on the metaphosphate composition LiPO 3 . Indeed, the Li neutron-scattering length is negative, which reinforces the contrast between cation centered regions and more dense regions. Simulations by the reverse Monte Carlo method have been performed on these two systems for all temperatures, which lead to several atomic configurations compatible with our experimental data and allows a detailed analysis of the partial structure factors in both systems. II. EXPERIMENT The two metaphosphate glass compositions were prepared by mixing NaPO 3 powder, liquid D 3 PO 4 85% in weight, and Li 2 CO 3 powder 99.94% 7 Li in adequate proportions. The melt was then heated to about 800 °C during 30 min. The glass transition temperature of Na 0.5 Li 0.5 PO 3 , obtained by differential scanning calorimetry, is T g =515 K, the melt- ing temperature is T m =747 K. The corresponding values for LiPO 3 are T g =588 K, T m =936 K. The samples were then crushed and placed in a cylindrical vanadium can where they were remelted. Neutron-scattering measurements were per- formed on the 7C2 spectrometer, located on the hot source of the Orphee reactor at Saclay. Diffraction patterns were col- lected using a 640-cell position-sensitive detector, covering an angular range of 128° in steps of 0.2°, with a neutron wavelength  =0.701 Å providing a momentum transfer range of  Q =0.6–16 Å -1 . A vanadium standard was used in order to calibrate the 640 detector cells with a relative precision better than 0.1%, and to obtain the absolute value of the standard intensity. The statistical error on the mea- sured intensity was of the order of 0.2%. Measurements were performed in a vanadium furnace at 300 K, 520 K ( =T g +5 K), 700 K, and 800 K ( T m +53 K) for Na 0.5 Li 0.5 PO 3 , and at 300 K for LiPO 3 . Conventional corrections were made in order to take into account effects of the furnace transmission 15 and multiple scattering. 16 Inelastic effects were corrected with the MCGR program. 17 wide angle x-ray scattering WAXS experiments were performed on a diffrac- tometer equipped for the Mo K radiation and a bent graph- ite monochromator Philips, PW1729. The intensity mea- surements were carried out by the  -2  step scanning method in the angular range 0.5° 2 q 140°, which corre- sponds to the Q range 0.8Q 16.6 Å -1 . The total counts accumulated at each measured point were not less than 10 000. The x-ray source was operating at a current of 35 mA and an accelerating voltage of 50 kV A standard treatment PHYSICAL REVIEW B 67, 104201 2003 0163-1829/2003/6710/1042017/$20.00 ©2003 The American Physical Society 67 104201-1