Anisotropic compression

Figure 3.19 Anisotropically compressed 2D hep Meads overlayer in presence of significant Me-S misfit, (do,Me-do,s)/doS > 0, forming a row-matching superstructure with moir6 pattern S(100)-c(6x2) MeMoiri.

In this equation. A and /i are the 2D Lame coefficients, is the area of Meads in an undistorted 2D Meads overlayer, and Ad/do = (do - d)/do denotes the relative compression of the adlayer where do and d are the atomic nearest-neighbor distances in the uncompressed and compressed overlayer, respectively. Equation (3.23) can be regarded as a first approximation for a hexagonal close-packed (hep) Meads overlayer with a 2D hep lattice. However, it is a very rough approximation for more expanded overlayer structures such as quadratic or rectangular superlattices and cannot be used for anisotropically compressed and strained Meads overlayers. 

Figure 3.31 In situ STM images with differently orientated domains (a) and (b) of an anisotropically compressed 2D hep PT>ads overlayer showing a superstructure with moir6 pattern (cf. Fig. 3.19) in the system Ag(100)/5 x lO M Pb(C104)2 + lO M HCIO4 at T = 298 K [3.87]. (a) = 80 mV,...

In order to explain the moird structure, one can consider the following two cases (i) isotropic compression or (ii) anisotropic compression of the Pb overlayer. 

In situ STM images with lateral atomic resolution were recently observed for Pb UPD on Au(lOO) [3.187, 3.300], The bare and unreconstructed Au(lOO) substrate was imaged at low For high AE. An expanded Au(100)-2c(->/2 x 3- /2 ) R 45° Pb overlayer structure was observed at medium F or AE. Similar to the system Ag(100)/Pb an Au(100)-c(2 X 6) moire superstructure was found at high For low AE, indicating an anisotropically compressed hep Pb overlayer. Obviously, a phase transition from an expanded Pb overlayer to a compressed hep structure has to be taken into consideration. 

In both molecular dynamics and lattice dynamics, the effect of pressure, essential if one is to obtain accurate predictions of phenomena such as phase transitions and anisotropic compression, can be modelled by allowing constant stress, variable geometry cells. 

Fig. 1. Schematic representation of pressure effects in proteins connected with a nonzero volume change, (a) Pressure effect on a single conformation represents a highly anisotropic compression, (b) Shift of any equilibrium in a population of conformers of proteins towards a more compact state.

In our film balance the layer is compressed anisotrop-ically, i.e. only in one direction the simulation, however, allowed us to investigate isotropic compression too. If we let the systems reach local equilibrium between two compression steps, we did not find significant differences either in the structures or in the isotherms between isotropic and anisotropic compressions. However, if the systems were compressed much faster (we did not let them reach local equilibrium, i.e. nii/H22 was significantly greater than 1 during the anisotropic compression), the A value of the anisotropically compressed system was found to be greater. This implies that the relaxation time of the monolayer is greater if it is compressed in an anisotropic manner. In Fig. 5, it was already demonstrated that monodisperse particles form a domain structure. In this context nii/H22 > 1 indicates that the domains are ordered in a rhombohedral lattice, as was visualized by Aveyard et al. [43]. 

More rigorous consideration suggests that this is not correct and that there is an anisotropic compressibility in the strained state. Gee s experimental result that the internal energy contribution is negligible, based on measurements of the change in stress with temperature at constant length, is therefore capable of another interpretation, which leads to the conclusion that the internal energy contribution may not be zero. 

Moreover, it is worth noting that the chosen width for one region may not be optimal for other regions. This is particularly important with those CVs that present an anisotropic compression of phase space (see below in Section Adaptive Gaussians for a discussion of this issue and a possible solution). 

Figure 1 2.2 Films that have Failed under Anisotropic Tensile Stress (Top SEM) and Under Anisotropic Compression (Bottom Optical Microscopy Light on Top of Blister is a Reflection)...

---