Temperature Dependence of the Structure of Langmuir Films of Normal-Alkanes on Liquid Mercury

The temperature dependent phase behavior of Langmuir films of n-alkanes [CH3(CH2)n−2CH3, denote Cn] on mercury was studied for chain lengths 19 ⩽ n ⩽ 22 and temperatures 15 ⩽ T ⩽ 44 °C, using surface tensiometry and surface x-ray diffraction methods. In contrast with Langmuir films on water, where molecules invariably orient roughly surface normal, alkanes on mercury are always oriented surface parallel and show no long-range in-plane order at any surface pressure. A gas and several condensed phases of single, double, and triple layers of lying-down molecules are found, depending on n and T. At high coverages, the alkanes studied here show transitions from a triple to a double to a single layer with increasing temperature. The transition temperature from a double to a single layer is found to be ∼ 5 °C, lower than the bulk rotator-to-liquid melting temperature, while the transition from a triple to a double layer is about as much below the double-to-single layer transition. Both monolayer and bulk transition temperatures show a linear increase with n with identical slopes of ∼ 4.5 °C/CH2 within the range of n values addressed here. It is suggested that the film and bulk transitions are both driven by a common cause: the proliferation of gauche defects in the chain with increasing temperature.Engineering and Applied Science

Competition between Surface Layering and Surface Phase Formation in Dilute Liquid Hg−Au Alloys

We present temperature-dependent X-ray reflectivity measurements of liquid Hg alloyed with 0.06−0.20 atom % Au. At low Au concentrations, we find temperature-dependent surface-induced layering similar to that observed in pure Hg, except that the presence of Au reduces the layering amplitude. Upon approaching the solubility limit of Au in Hg, a new surface phase forms which is 1−2 atomic diameters thick and has a density of about half that of bulk Hg. We present a surface phase diagram, summarizing the evolution of this unexpected surface structure upon varying composition and temperature. Such surface modifications may account for the variations observed in catalytic and electrochemical reactions at liquid metal surfaces upon alloying.Engineering and Applied Science

Langmuir Films of Normal-Alkanes on the Surface of Liquid Mercury

The coverage dependent phase behavior of molecular films of n-alkanes ($CH_{3}CH_{n−2}CH_3$, denote Cn) on mercury was studied for lengths 10 $\leq$ n $\leq$ 50, using surface tensiometry and surface x-ray diffraction methods. In contrast with Langmuir films on water, where roughly surface-normal molecular orientation is invariably found, alkanes on mercury are always oriented surface-parallel, and show no long-range in-plane order at any surface pressure. At a low coverage a two-dimensional gas phase is found, followed, upon increasing the coverage, by a single condensed layer (n $\leq$ 18), a sequence of single and double layers (19 $\leq$ n $\leq$ 20; n $\geq$ 26), or a sequence of single, double, and triple layers (22 $\leq$ n $\leq$ 24). The thermodynamical and structural properties of these layers, as determined from the measurements, are discussed.Engineering and Applied Science

Surface Induced Order in Liquid Metals and Binary Alloys

Measurements of the surface x-ray scattering from several pure liquid metals (Hg, Ga, and In) and from three alloys (Ga-Bi, Bi-In, and K-Na) with different heteroatomic chemical interactions in the bulk phase are reviewed. Surface-induced layering is found for each elemental liquid metal. The surface structure of the K-Na alloy resembles that of an elemental liquid metal. Bi-In displays pair formation at the surface. Surface segregation and a wetting film are found for Ga-Bi.Comment: 10 pages, 3 fig, published in Journal of Physics: Condensed Matte

Electrochemically induced reconstruction of the Au(001) surface: An x-ray scattering study

In-situ x-ray specular reflectivity and glancing incident angle x-ray diffraction measurements have been performed in the Au(001) surface in two solutions under potential control in an electrochemical cell. In both the 0.01 M HCl0{sub 4} and 0.01 M KBr solutions a ``(5 {times} 20)`` reconstruction is formed at sufficient negative potentials. The reconstruction is similar to that obtained for the clean surface in vacuum

Surface Crystallization in a Liquid AuSi Alloy

X-ray measurements reveal a crystalline monolayer at the surface of the eutectic liquid Au_{82}Si_{18}, at temperatures above the alloy's melting point. Surface-induced atomic layering, the hallmark of liquid metals, is also found below the crystalline monolayer. The layering depth, however, is threefold greater than that of all liquid metals studied to date. The crystallinity of the surface monolayer is notable, considering that AuSi does not form stable bulk crystalline phases at any concentration and temperature and that no crystalline surface phase has been detected thus far in any pure liquid metal or nondilute alloy. These results are discussed in relation to recently suggested models of amorphous alloys.Comment: 12 pages, 3 figures, published in Science (2006

Quantum codes give counterexamples to the unique pre-image conjecture of the N-representability problem

It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are "N- representable" is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle pre-image, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.Comment: 4 pages, 1 figur