Surface topographical mapping

As was noted above, STM images are often strongly dependent both on Fbias and on the type of feature being imaged at the surface. As a result, the image is often not a simple topographical map of the surface features. Consider, for example, a surface having an adsorbed atom with an excess of... 

The surfaces defined by (j> = constant, where is the scalar field, and resembling contour lines on a topographic map, may be called isotimic surfaces. In potential theory they are referred to as equipotentials in heat conduction they are isothermals, etc. They form a family of non-intersecting surfaces. The gradient of the scalar field measures the rapidity with which the field changes as a function of position. The most rapid change occurs along a family of lines normal to the isotimic surfaces. 

Probe microscopes are characterized by two common features. On the one hand, a sharp, tiny probe gets very close to the sample and feels the surface by monitoring some kind of interaction between the probe and the surface, which is very sensitive to distance. On the other hand, the sample is scanned in a raster fashion with near atomic accuracy, and the variation in the interaction is translated into a topographic map of the surface. 

On crystal faces bounding a polyhedral crystal, step patterns resembling the contour lines on a topographic map or striations in one direction are observable depending on the nature of the face. These show the process of crystal growth or dissolution at an atomic level, and are referred to as the surface morphology or surface microtopography. 

Fig. 1.8 Topographic map of the surface of an altered archaeological glass obtained by AFM...

To measure the site energy distribution or other surface properties of powders by measuring heats of immersion as a function of the amount of preadsorbed wetting liquid. Heats of immersion of the partly covered surfaces reveal the site energy distributions. For acid sites on cracking catalysts, for example, adsorbates of different basicity can be used to develop a topographical map of the surface activity. 

The terrestrial drainage basin for each lake was digitized from 1 24,000 U. S. Geological Survey topographical maps. The reported values (which exclude lake surface area) represent the average of two estimates, one that includes and one that excludes small wetlands with internal drainage and areas where watershed boundaries were uncertain. 

Conceptually, predecessors of the scanning force microscope are the surface force apparatus (SFA) [73,74] and the stylus profilometer [75,76]. The SFA enables measurement of normal and friction forces between molecularly smooth surfaces as small as 1 nN as a function of distance with a resolution of 0.1 nm. In addition to the local force measurement, the profilometer provides a topographic map of the surface by scanning the surface with a sharp probe. However, the profilometer is not suitable for structure characterisation because of the large radius of the tip (about 1 pm) and the low sensitivity of the force sensor (in the range of 1(T2 to 1(T5 N). 

For example, an Nd YAG laser was used by the Near Earth Asteroid Rendezvous (NEAR) spacecraft in 2000 to map the surface of the asteroid Eros. Light beams sent out by the laser measured with a high degree of accuracy the elevation of various parts of the asteroid, providing one of the best topographical maps of an asteroid surface ever obtained. 

Areas of high topographic relief can be identified from topographic maps of the ground surface and from images produced by remote sensing techniques. 

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