Microscopic information from

Interlude 4.2 Getting Microscopic Information from Macroscopic Observations The Inverse Problem When one thinks of equilibrium statistical mechanics, what usually comes to mind is its classical mission, namely, predicting macroscopic structure and properties from microscopic, pairwise interaction forces. However, more often than not, we are faced with a need to deduce information on the (conservative) pair interaction forces [equivalently, the pair potential observed macroscopic properties. The information thus obtained can then be used to predict other properties of interest. The problem of extracting microscopic information from macroscopic observations is known as the inverse problem. 

In spite of the already high, and continuously increasing, power of ab initio methods, there are situations which remain much too complex to be modeled with them. These situations (e.g., the vibrational modes of, or the adsorption-energy distribution on, highly dispersed systems, like powders or colloids) can often be described quite accurately on experimental grounds but are of difficult theoretical description. Because the experimental data (e.g., the specific heat as a function of temperature or the adsorption isotherm) can be written in terms of unknown microscopic quantities (like the vibrational density of states or the adsorption-energy distribution, in the above examples), one can try to extract the inaccessible microscopic information from the accessible macroscopic data. This generates a kind of ab fine problem. 

It is therefore quite natural to put the following question Whither the future of controlling quantum phenomena in the broad context (Rabitz et al. 2000). Even today, one can expect with confidence that these new concepts will lead to the extraction and deciphering of microscopic information from coherent molecular dynamics. This will be an important qualitative jump from the preceding period of studying and... 

One more significant aspect of modem microscopy is the quantitative interpretation of the images in terms of the microstmcture of the object. Although most microscopes include or can be combined with powerful image processing systems, the interpretation of the contrast is still the main problem. On the other hand, reliable micromorpbological information could be easily obtained from a set of thin flat cross sections which reveal only density information, from which case accurate two- and three-dimensional numerical parameters of the internal microstmcture could be calculated. 

Considering existing microscopical techniques, one can find that non-destmctive information from the internal stmcture of an object in natural conditions can be obtained by transmission X-ray microscopy. Combination of X-ray transmission technique with tomographical reconstmction allows getting three-dimensional information about the internal microstmcture [1-3]. In this case any internal area can be reconstmcted as a set of flat cross sections which can be used to analyze the two- and three-dimensional morphological parameters [4]. For X-ray methods the contrast in the images is a mixed combination of density and compositional information. In some cases the compositional information can be separated from the density information [5]. Recently there has been a... 

The moving invariant manifolds determine the reactivity or nonreactivity of an individual trajectory under the influence of a specific noise sequence. They thus provide the most detailed microscopic information on the reaction dynamics that one can possibly possess. In practice, though, one is more often interested in macroscopic quantities that are obtained by averaging over the noise. To illustrate that such quantities can easily be derived from the microscopic information encoded in the TS trajectory, we calculate the probability for a trajectory starting at a point (q, v) in the space-fixed phase space to end up on the product side of the... 

The frequencies of absorption bands present gives diagnostic information on the nature of functional groups in materials as well as information from any observed frequency shifts on aspects such as hydrogen bonding and crystallinity. In many cases, spectra can be recorded non-destructively using either reflection or transmission procedures. IR spectra of small samples can also be obtained through microscopes (IR microspectrometry). Chalmers and Dent [8] discuss the theory and practice of IR spectroscopy in their book on industrial analysis with vibrational spectroscopy. Standard spectra of additives for polymeric materials include the major collection by Hummel and Scholl [9]. 

Much of the microscopic information that has been obtained about defect complexes that include hydrogen has come from IR absorption and Raman techniques. For example, simply assigning a vibrational feature for a hydrogen-shallow impurity complex shows directly that the passivation of the impurity is due to complex formation and not compensation alone, either by a level associated with a possibly isolated H atom or by lattice damage introduced by the hydrogenation process. The vibrational band provides a fingerprint for an H-related complex, which allows its chemical reactions or thermal stability to be studied. Further, the vibrational characteristics provide a benchmark for theory many groups now routinely calculate vibrational frequencies for the structures they have determined. 

The good agreement between electrochemical and UHV data, documented in Figure 4, is a very important result, because it proves for the first time that the microscopic information which one obtains with surface science techniques in the simulation studies is indeed very relevant to interfacial electrochemistry. As an example of such microscopic information, Figure 5 shows a structural model of the inner layer for bromide specific adsorption at a halide coverage of 0.25 on Ag 110 which has been deduced from thermal desorption and low energy electron diffraction measurements /12/. Qualitatively similar models have been obtained for H2O / Br / Cu( 110) /18/and also for H2O/CI /Ag 110. ... 

The origins of analytical electron microscopy go back only about 15 years when the first x-ray spectra were obtained from submicron diameter areas of thin specimens in an electron microscope [1]. Characterization of catalyst materials using AEM is even more recent[2,3] but is currently a very active research area in several industrial and academic laboratories. The primary advantage of this technique for catalyst research is that it is the only technique that can yield chemical and structural information from individual submicron catalyst particles. 

The macroscopic properties of a material are related intimately to the interactions between its constituent particles, be they atoms, ions, molecules, or colloids suspended in a solvent. Such relationships are fairly well understood for cases where the particles are present in low concentration and interparticle interactions occur primarily in isolated clusters (pairs, triplets, etc.). For example, the pressure of a low-density vapor can be accurately described by the virial expansion,1 whereas its transport coefficients can be estimated from kinetic theory.2,3 On the other hand, using microscopic information to predict the properties, and in particular the dynamics, of condensed phases such as liquids and solids remains a far more challenging task. In these states... 

Local composition is very useful supplementary information that can be obtained in many of the transmission electron microscopes (TEM). The two main methods to measure local composition are electron energy loss spectrometry (EELS), which is a topic of a separate paper in this volume (Mayer 2004) and x-ray emission spectrometry, which is named EDS or EDX after the energy dispersive spectrometer, because this type of x-ray detection became ubiquitous in the TEM. Present paper introduces this latter method, which measures the X-rays produced by the fast electrons of the TEM, bombarding the sample, to determine the local composition. As an independent topic, information content and usage of the popular X-ray powder dififaction database is also introduced here. Combination of information from these two sources results in an efficient phase identification. Identification of known phases is contrasted to solving unknown stmctures, the latter being the topic of the largest fiaction of this school. 

---