Some Difficulties Encountered with Rule

Even with the assurance that quantum mechanics has firm underpinnings in experimental observations, students learning this subject for the first time often encounter difficulty. Therefore, it is useful to again examine some of the model problems for which the Schrodinger equation can be exactly solved and to learn how the above rules apply to such concrete examples. 

The layer-type structures and chemical nature of the constituents of the bismuth and thallium-based cuprate superconductors - notably the lone-pair stereochemistry of Bis+, variable valence of copper, and considerable exchange among some of the cation sites - combine to make structural non-ideality, nonstoichiometry, and phase intergrowth the rule rather that the exception in these families of materials. These features, as well as the probable metastability of the phases (and possibly all high-temperature oxide superconductors), also contribute to the difficulties typically encountered in preparing single-phase samples with reproducible properties and compositions. 

Historically, two periods occurred for the determination of the number of hydrate water molecules per guest molecule. In the first century (1778-1900) after the discovery of hydrates, the hydration number was determined directly. That is, the amounts of hydrated water and guest molecules were each measured via various methods. The encountered experimental difficulties stemmed from two facts (1) the water phase could not be completely converted to hydrate without some occlusion and (2) the reproducible measurement of the inclusion of guest molecules was hindered by hydrate metastability. As a result, the hydrate numbers differed widely for each substance, with a general reduction in the ratio of water molecules per guest molecule as the methods became refined with time. After an extensive review of experiments of the period, Villard (1895) proposed Villard s Rule to summarize the work of that first century of hydrate research ... 

As a rule, microwave attenuators introduce phase shift as well as attenuation. An exception is the type of attenuation known as rotary vane , which has negligible phase shift. Some attenuator manufacturers have achieved fairly constant phase shift for microwave coaxial structures. Often the level set attenuator in the reference arm is of lower quality with large phase shift, but the operator encounters little difficulty because the reference level is seldom changed. The reader can appreciate the frustration that would occur if for every change in the main attenuator setting an accompanying phase shift were to occur. 

Since this text is intended for readers previously unfamiliar with infrared spectroscopy in general and especially with such theoretical aspects as are presented in this chapter, some general remarks concerning the limitations of theoretical calculations may be in order. Let us consider specifically the problem of determining the structure of a molecule by means of infrared and Raman spectroscopy. It must be pointed out that the structure cannot always be unambiguously assigned, even if experimental conditions are ideal. When experimental conditions are such that vapor state spectra cannot be obtained, further difficulties are encountered in assigning the structure and/or the vibrations of the molecule. For example, selection rules which indicate that an U2 vibration may not be infrared active may break down in the liquid and/or solid state. 

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