Specimen function

Traditionally the performance of HRTEM is judged in terms of its ability to resolve two adjacent atom columns. Resolution is ruled by a few basic principles A position dependent image intensity g(r) is described as a convolution of the specimen function f(r) with a point spread function h(r). It is convenient to express this convolution in real space as a product in reciprocal space ... 

The observed peak shapes are best described by the so-called peak shape function (PSF), which is a convolution of three different functions instrumental broadening, Q, wavelength dispersion. A, and specimen function, E. Thus, PSF can be represented as follows ... 

In this chapter I adopt a functional orientation to our understanding chemical substance, according to which a specimen is known by those capacities that technicians try to exploit during laboratory research. Consequently, a specimen functions as both... 

So, whenever a modern spectrometer is used in chemical research, the probative powers of the instrument are united with the specimen s causal capacities. Both instrument and specimen are characterized by their tendencies to generate change. Again, an analytical instrument has powers to produce certain states that can be converted to information. The specimen functions in laboratory research as a system of dynamic properties associated with the exchange of energy. The unity of instrument and specimen is localized in the signal generator, where the specimen s causal capacities to produce phenomenon are activated by an instrument s manipulative powers. 

Once the the instramental broadening and wavelength dispersion portions of the peak width are modeled, the remainder of the peak width can be described by Ae specimen function, which relates to the sample itself. More specifically, the peak broadening due to crystalhte size and microstiain can be described mathematically. Scherrer s equation expresses peak broadening, p, as k... 

Some discontinuities may be identified by a conventional two-dimensional ultrasonic technique, from which the well-known C-scan image is the most popular. The C-scan technique is relatively easy to implement and the results from several NDE studies have been very encouraging [1]. In the case of cylindrical specimens, a circular C-scan image is convenient to show discontinuity information. The circular C-scan image shows the peak amplitude of a back-scattered pulse received in the circular array. The axial scan direction is shown as a function of transducer position in the circular array. The circular C-scan image serves also as an initial step for choosing circular B-scan profiles. The latter provides a mapping between distance to the discontinuity and transducer position in the circular array. 

The property to be predicted must be considered when choosing the method for simulating a polymer. Properties can be broadly assigned into one of two categories material properties, primarily a function of the nature of the polymer chain itself, or specimen properties, primarily due to the size, shape, and phase... 

The copolymer composition equation relates the r s to either the ratio [Eq. (7.15)] or the mole fraction [Eq. (7.18)] of the monomers in the feedstock and repeat units in the copolymer. To use this equation to evaluate rj and V2, the composition of a copolymer resulting from a feedstock of known composition must be measured. The composition of the feedstock itself must be known also, but we assume this poses no problems. The copolymer specimen must be obtained by proper sampling procedures, and purified of extraneous materials. Remember that monomers, initiators, and possibly solvents are involved in these reactions also, even though we have been focusing attention on the copolymer alone. The proportions of the two kinds of repeat unit in the copolymer is then determined by either chemical or physical methods. Elemental analysis has been the chemical method most widely used, although analysis for functional groups is also employed. 

Figure 36 is representative of creep and recovery curves for viscoelastic fluids. Such a curve is obtained when a stress is placed on the specimen and the deformation is monitored as a function of time. During the experiment the stress is removed, and the specimen, if it can, is free to recover. The slope of the linear portion of the creep curve gives the shear rate, and the viscosity is the appHed stress divided by the slope. A steep slope indicates a low viscosity, and a gradual slope a high viscosity. The recovery part of Figure 36 shows that the specimen was viscoelastic because relaxation took place and some of the strain was recovered. A purely viscous material would not have shown any recovery, as shown in Figure 16b. 

Another resonant frequency instmment is the TA Instmments dynamic mechanical analy2er (DMA). A bar-like specimen is clamped between two pivoted arms and sinusoidally oscillated at its resonant frequency with an ampHtude selected by the operator. An amount of energy equal to that dissipated by the specimen is added on each cycle to maintain a constant ampHtude. The flexural modulus, E is calculated from the resonant frequency, and the makeup energy represents a damping function, which can be related to the loss modulus, E". A newer version of this instmment, the TA Instmments 983 DMA, can also make measurements at fixed frequencies as weU as creep and stress—relaxation measurements. 

For both the tongue and Elmendorf test methods, it is important to observe the behavior of the specimen as the tear is propagated. In cases where the yams in the test direction are much stronger than the perpendicular yams, it is sometimes difficult or impossible to propagate the tear in the desired direction. In this case, a crosswise tear results. Tear resistance is primarily a function of fabric constmction. Loose, open weaves such as cheesecloth tend to resist tear, whereas tight weaves tend to tear easily. In the open weave, the concentrated force field at the point of tear is dissipated by the compliance of the fabric stmcture to accommodate the stress field, thereby distributing the force over a greater number of yams. 

Plastic deformation is commonly measured by measuring the strain as a function of time at a constant load and temperature. The data is usually plotted as strain versus time. Deformation strain can be measured under many possible loading configurations. Because of problems associated with the preparation and gripping of tensile specimens, plastic deformation data are often collected using bend and compression tests. 

Creep tests require careful temperature control. Typically, a specimen is loaded in tension or compression, usually at constant load, inside a furnace which is maintained at a constant temperature, T. The extension is measured as a function of time. Figure 17.4 shows a typical set of results from such a test. Metals, polymers and ceramics all show creep curves of this general shape. 

In Secondary Ion Mass Spectrometry (SIMS), a solid specimen, placed in a vacuum, is bombarded with a narrow beam of ions, called primary ions, that are suffi-ciendy energedc to cause ejection (sputtering) of atoms and small clusters of atoms from the bombarded region. Some of the atoms and atomic clusters are ejected as ions, called secondary ions. The secondary ions are subsequently accelerated into a mass spectrometer, where they are separated according to their mass-to-charge ratio and counted. The relative quantities of the measured secondary ions are converted to concentrations, by comparison with standards, to reveal the composition and trace impurity content of the specimen as a function of sputtering dme (depth). 

In neutron reflectivity, neutrons strike the surface of a specimen at small angles and the percentage of neutrons reflected at the corresponding angle are measured. The an jular dependence of the reflectivity is related to the variation in concentration of a labeled component as a function of distance from the surface. Typically the component of interest is labeled with deuterium to provide mass contrast against hydrogen. Use of polarized neutrons permits the determination of the variation in the magnetic moment as a function of depth. In all cases the optical transform of the concentration profiles is obtained experimentally. 

The overall function of the electron gun is to produce a source of electrons emanating from as small a spot as possible. The lenses act to demagnify this spot and focus it onto a sample. The gun itself produces electron emission from a small area and then demagnifies it initially before presenting it to the lens stack. The actual emission area might be a few pm in diameter and will be focused eventually into a spot as small as 1 or 2 nm on the specimen. 

Figure 6 Total electron yield as a function of the primary electron s energy when it arrives at the surface of the specimen.

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