Lorentz–Lorenz Coefficient of Ethane

Abstract

The index of refraction of ethane at 6328 Å has been measured in the density range 0.02 to 0.36 g/cm3(1 to 200 amagats). The coefficient in the Lorentz–Lorenz expression [Formula: see text] is constant to within 0.5% for the temperature and density range studied. The coefficient [Formula: see text] increases with density reaching a maximum near the critical density and decreases with density for densities larger than the critical density. The critical density has been measured in the same experiment and is 0.2062 ± 0.0003 g/cm3.

Structures of small metal clusters. I. Low temperature behavior

“…The surface free energy is quite dependent on the definition of surface area of small clusters. 9 Here, we rotate randomly the cluster and project it on a plane. We then draw tangent lines to opposite sides of the structure.…”

“…(5b), the surface free energy is given by r=rco +cn-1/3 • (9) Equation (9) can be also derived by the Tolman classical thermodynamic model by recognizing that the Gibbs thermodynamic dividing surface between the cluster and the surrounding vapor does not necessarily coincide with the physical surface of the cluster. 4O Here, roo is the surface free energy of an infinite planar surface of Ni and the constant c incorporates a factor which locates the Gibbs thermodynamic boundary with respect to the physical surface of clusters.…”

“…Table I summarizes the main conclusions found for the structures and energetics of small metal clusters at low temperatures for both the U and the EA potentials with parameters fitted to Ni. For n = [2][3][4][5][6][7][9][10][11][12][13][14][15]19, clusters have the same structure but for other sizes, clusters have different structures. For both potentials, PIC structures are the most stable for sufficiently small cluster sizes (with the exception of n = 6 for both potentials and n = 8 for the EA potential).…”

“…3,4,8-1O In particular, the n = 13 and n = 55 atom fcc cuboctahedra transform to MacKay IC. 8 ,9,11 Atoms tend to form fivefold rings rather than sixfold configurations as in crystalline material. Au clusters can also exhibit non-fcc structure under possibly nonequilibrium conditions [distorted dodecahedron, hexagonal closed packed structure (hcp) ] 12 and Si clusters can have pentagonal and square faces rather than diamond symmetry.…”

“…For small clusters, bulk atoms have only a few shells of neighbors filled and their properties are expected to be different from properties of bulk atoms in infinite extent crystals. Similarly, eightfold and Panel (a) shows the average coordination number of U and EA clusters versus size, An abrupt transition to lower coordination number occurs from n = 30to n = 3lforU clusters, EA clusters lie on a lowercoordination branch for n>17 (\\ith the exception of n = 19), Panel (b) shows the surface free energy versus size for both potentials, Solid lines are fits to theTolman model, Eq,(9), and dashed lines connect the points, The horizontal dashed lines indicate values of rlOO for unrelaxed(Ioo) infinite sur· face for the U potential (top line) and the EA potential (bottom line), Panel (c) shows the dispersion versus size for both potentials. Some EA clusters have more surface atoms than U clusters.…”