Schwarz surfaces

The first periodic (in one direction only) minimal surface [12] discovered in 1776 was a helicoid The surface was swept out by the horizontal line rotating at the constant rate as it moves at a constant speed up a vertical axis. The next example (periodic in two directions) was discovered in 1830 by Herman Scherk. The first triply periodic minimal surface was discovered by Herman Schwarz in 1865. The P and D Schwarz surfaces are shown in Figs. 2 and 3. The revival of interest in periodic surfaces was due to (a) the observation[13-16] that at suitable thermodynamic conditions, bilayers of lipids in water solutions form triply periodic surfaces and (b) the discovery of new triply periodic minimal... 

The SCL2 structure is composed of three different embedded periodic surfaces. The middle surface is the Schwarz minimal surface P. Similarly, the middle phase surface in GLl (Fig. 8(c)) and GL2 (Fig. 8(d)) structures is the Schoen minimal surface G. 

I. S. Barnes, S. T. Hyde, B. W. Ninham. The caesium chloride zero potential surface is not the Schwarz P-surface. J Physique Colloque 51 C7 19-24, 1990. 

Surfaces of Nanoparticles and Porous Materials, edited by James A. Schwarz and Cristian I. Contescu... 

Wang, S. G., Schwarz, W. H. E., 1996, Simulation of Nondynamical Correlation in Density Functional Calculations by the Optimized Fractional Occupation Approach Application to the Potential Energy Surfaces of 03 and... 

Hirano, S., K.S. Young, A. Kwabena and J.A. Schwarz, The high surface area activated carbon hydrogen storage system. Frontiers Sci. Ser., 7 (New Energy Systems and Conversions), 67-72, 1993. 

Another key contribution of the Schwarz group was the recognition of the dramatic influence of oxide surfaces on bulk solution pH. In a landmark 1989 paper, Noh and Schwarz [7] demonstrated the method of mass titration, in which successive additions of oxide cause stepwise shifts in solution pH. This procedure is illustrated in Figure 6.7 [7], As indicated in Figure 6.1, the protonation-deprotonation chemistry of the surface hydroxyl groups is coupled to the liquid-phase pH. In mass titration, as the mass (or more appropriately, the surface area) of oxide in solution increases, the solution pH is brought to the PZC of the oxide, at which point no driving force for proton transfer exists... 

Weiske, T. Koch, W. Schwarz, H. Experimental Evidence for the Existence of the Protonitronium Dication (H0N02+) in the Gas Phase and ab Initio Molecular Orbital Calculations of Its Potential Energy Surface. J. Am. Chem. Soc. 1993,115, 6312-6316. 

In a 5-m deep surface water body, the calculated half-lives for direct photochemical transformation at 40 °N latitude in the midsummer during midday were 5.9 and 4.2 d with and without sediment-water partitioning, respectively (Zepp and Schlotzhauer, 1979). Schwarz and Wasik (1976) reported a fluorescence quantum yield of 0.69 for pyrene in water. 

Special modified hair in the region of a scent gland can enhance its function. Such scent hairs have been termed osmetrichia (Miiller-Schwarze et ah, 1977 Fig. 3.12). They may be stiff bristles with surface chambers formed by their cuticular scales, as in the tarsal tuft of black-tailed deer (Fig. 3.12a), spoon or spatula like, as in the ventral gland of the Mongolian gerbil Meriories unguiculatus Fig. 3.12d), or a wick formed by a hollow medulla and vacuolated cortical... 

Copper is a face-centered cubic (fee) metal. Band structure calculations show the valence bands to be copper d bands and hybrid bands of sd, pd, and sp character. The hybridization is essential for the conductivity of copper, as some of the bands cross the Fermi surface and are thus only partially occupied (K. Schwarz, private communication). 

Haefke, H., Meyer, E., Howald, L., Schwarz, U., Gerth, G., and Krohn, M. (1992). Atomic surface and lattice structures of AgBr thin films. Ultramicroscopy 42-44, 290-297. 

This reaction profile also illustrates one of the other important challenges in the study of transition metal systems, namely that the metal-containing active site often has several accessible spin states. Specifically in the case of Fe(IV)=0, the triplet, quintet, and septet spin states. Consequently, the reaction can, in principle, proceed on different electronic potential energy surfaces and it is necessary to test all possibilities when exploring a reaction surface. This has been labeled two-state reactivity and has been elaborated by Shaik, Schwarz, Schroder, and co-workers (36—40). In the case of TauD, the results show that the reaction is only feasible on the quintet surface, in agreement with earlier DFT studies (11,41 —45). 

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