Structure of high-temperature fluid selenium J. Y. Raty Laboratoire de Physique de la Matie `re Condense ´e B5, Universite ´ de Lie `ge, B4000 Sart-Tilman, Belgium A. Sau ` l Centre de Recherche sur les Me ´canismes de la Croissance Cristalline, CNRS, Campus de Luminy, Case 913, F13288 Marseille, Cedex 09, France J. P. Gaspard Laboratoire de Physique de la Matie `re Condense ´e B5, Universite ´ de Lie `ge, B4000 Sart-Tilman, Belgium C. Bichara Centre de Thermodynamique et de Microcalorime ´trie, CNRS, 26 rue du 141e `me R.I.A., F13331 Marseille, Cedex 3, France Received 11 December 1998 A semiempirical tight-binding energy model is developed for selenium. It includes s and p electrons as well as an empirical description of the dispersion forces that proves necessary at the liquid densities under study. The band-structure parameters are obtained by fitting ab initio calculations. The simulated liquid structures are in very good agreement with the most recent x-ray scattering and extended x-ray absorption fine-structure experiments in a broad temperature and density range. The Monte Carlo simulations performed show that the complex liquid structures observed result from the breaking and branching of the selenium chains. The total coordination number is shown to result from the balance between one-, two-, and threefold coordinated atoms. The role of these defects is discussed in relationship with the electrical conductivity of the liquid, i.e., the semiconductor-metal and metal-nonmetal transitions observed at high pressures. S0163-18299903228-2 I. INTRODUCTION Unlike tellurium, liquid selenium is a semiconductor in a broad temperature range above the melting temperature ( T m =490 K. At high temperature ( T 1500 K and high pressure ( P 600 bars, in a range where its density around 0.0250 atom Å -3 ) is significantly lower than the density of crystalline selenium 0.0367 atom Å -3 ), liquid selenium eventually becomes metallic. 1,2 This behavior is rather unex- pected for two reasons. First, expanded fluids generally ex- hibit a lower electrical conductivity at lower densities. 3 Sec- ond, according to various recent extended x-ray absorption fine-structure 4 EXAFS and x-ray scattering 5,6 measure- ments on the liquid phase, the number of first neighbors, or coordination number denoted CN in the following is slightly lower in the metallic state than in the semiconduct- ing state, in contrast with the CN of liquid tellurium that increases above 2 upon melting into a metallic phase. 7,8 . Dis- regarding allotropes, the crystalline structures of solid sele- nium and tellurium are very similar, made by stacking heli- cal chains, and result from a Peierls distortion of a simple cubic structure. 9 They are semiconductors or semimetals be- cause the Peierls distortion opens a gap in the electronic density of states DOS at the Fermi level. The effect of pressure on Peierls distorted structures is to reduce the gap in the DOS by increasing the number of first neighbors. 9 The effect of the temperature cannot be addressed in a general way because the entropic contribution to the free energy that could counterbalance the energy difference between Peierls distorted and undistorted structures depends on each particu- lar case. It is to be noted that the increase of electrical con- ductivity in liquid selenium takes place at high pressures, but in a region where its density is lower than that of the semi- conducting state, in the low-temperature liquid, at lower pressure. Thus, the abovementioned mechanism of reducing the electronic gap by increasing the density and the number of first neighbors does not play a role, and the origin of the metallic character of fluid selenium at high pressure and tem- perature is still an open question. The large number of papers on this subject, initiated by the experimental results of Tamura 10 and co-workers on the atomic structure of the liq- uid, is an indication of the complexity of the problem. The theoretical understanding of the process is hindered by the nature of the bonding in selenium that makes it diffi- cult to obtain realistic disordered atomic structures from computer simulations. The bonds within the chains are cova- lent, with a contribution to the bonding energy of the order of 2 eV/atom, whereas the bonds between the chains are an order of magnitude weaker, in an energy range where the long-range dispersion forces are no longer negligible. This difficulty makes the simulation of liquid selenium a chal- lenging problem from both the structural and electronic points of view. This problem has been tackled by various techniques in the last few years. An empirical model of the atomic interactions by means of two- and three-body forces has been proposed. 11 It yields correct solid-state properties, including the vibrational density of states, 12 but its transfer- ability to disordered phases of different connectivities and densities is questionable. Ab initio calculations 13–15 of the atomic and electronic structure offer a more promising ap- proach but are facing two problems. As pointed out by Kresse et al. 16 the local-density approximation LDA of the density-functional theory fails to stabilize the correct crystal- line structure, and generalized gradient corrections beyond PHYSICAL REVIEW B 15 JULY 1999-II VOLUME 60, NUMBER 4 PRB 60 0163-1829/99/604/24418/$15.00 2441 ©1999 The American Physical Society