Theoretical diffraction patterns corresponding to some simple types of molecular arrangement in liquids

Short range order in anomalous liquid metals

“…where k B is the Boltzmann constant, T is an absolute temperature, K is the compressibility of the liquid metal and V is its molar volume [26]. c Thermal is the thermal velocity of the atoms at the given temperature and c is the sound velocity.…”

“…Generalizing this result to a series of spherical shells, Prins and Petersen [26] suggested that a model for the liquid may be obtained by choosing…”

“…An alternative approach to analyze the liquid structure is to represent the short range order (SRO) of the liquid in terms of an underlying crystal lattice structure, i.e., within the quasi-crystalline model (QCM) [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. In this model, the liquid structure is characterized by: (i) a crystal lattice symmetry which may or may not be identical with that of the underlying solid; (ii) lattice parameters; (iii) thermal broadening of the nearest neighbor distances and (iv) a length scale associated with the persistence of SRO in the liquid.…”

Structural change in silicon from undercooled liquid state to crystalline state during crystallization

“…here,ã u is the vector connecting the nearest site in the unit cell,b v is the reciprocal lattice vector scaled 2p, V is the unit cell volume and D is the Prins parameter [16], which indicates the thermal fluctuation of an atom in the liquid state. In the present analysis, we assume the modified b-tin structure in order to fit the calculated S(Q) by the RSE method to that of the experimental results.…”

Evolution of short range order in Ar: Liquid to glass and solid transitions–A computational study

“…25 An alternative method to analyze liquid structure is based on correlating the short range order (SRO) of the liquid with a reference crystalline lattice, known as the quasi-crystalline (QCM) approach. This approach dates back to the early 20th century and several variants have been proposed over the years which are simple and possibly provide physical insight as proposed by Prins and Petersen 26 and emphasized by Frenkel. 27 The QCM has been recently shown to successfully reproduce the RDF of simple elemental liquids such as Ar and Cu 28 as well anomalous elemental liquids of columns IV and V 29,30 respectively and is commonly applied to identify the "structural" order in liquids, e.g., Ref.…”