Object Thickness

Consider an object of thickness t across which the incident beam travels along Oz (the thickness). Spherical waves produced at various levels z have an amplimde proportional to the FT of the atom potential F(p z) (p represents the aystallographic directions in the object plane xoy, z is the third space direction). It is convenient to average all the potentials along Oz (columnar approximation). They are replaced by l (p), the projected potential on the exit surface of the object Then, calculus is done by considering the projected potaitial as uniquely responsible for the resulting scattering. 

Above the film, the electron wave function is the incident planar wave. At the exit the transmitted wave function generates planar scattered waves. During passage, the phase changes but not the amplitude. The incident wave is refracted by the film so that a nil phase shift occurs (Fresnel half period zone) [19]. 

The columnar approximation implies that the object is thin, because the depletion of energy of the incident wave is neglected. This means that the amplitude of the incident beam Aq is kept constant, whereas only the phase is modified by the object crossing (phase object). To approach this condition, even at the exact Bragg angle, the object must be sufficiently thin to provide scattered beams that are very faint relative to the transmitted beam (yveak phase object). The resulting contrast is the object CTF (contrast transfer function). 

When the object is not thin enough, a strong scattered beam may act as a secondary incident beam. Oscillations would then be produced in the scattered amphtude this is a dynamic effect. At the hmit, the transmitted beam dis ears and the incident beam energy is entirely spent in scattering. The corresponding thickness of the object is the extinction distance. To avoid dynamic effects [18,19], the object thickness must be much smaller than the extinction distance. For gr hite [18] at 200 kV, the thickness must be smaller than 50 A to keep 90% of the incident beam in the transmitted one (40 A at 100 kV [19]) it must be inferior to 20 A to keep 95%. In the case of graphene, because it behaves as a single layer (t 5 A), it is a weak phase object. 

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For interpretation of measuring results, calibration characteristics obtained on the samples in advance is used in the above instruments. However, if number of impediment factors increases, the interpretation of the signals detected becomes more complicated in many times. This fact causes the position that the object thickness T and crack length I are not taken into consideration in the above-mentioned instruments. It is considered that measuring error in this case is not significant. 

At the same time advisability of designing the instrument taken into consideration cracks length 1 and object thickness T and of defining the instrument application sphere can be only determined after research work. 

Fig. 3 Calibration characteristics of electropotential transformer in case of object thickness (T) varying.

An operator puts initial data through K into, in particular, information of crack length, object thickness, transformer parameters. After that the device are prepared to work. 

The exposure At (GBq hours) required for an optical density 0 = log (incident light/transmitted light)) 2 at an absorber (object) thickness x (cm) using a typical industrial X-ray film and a Co y-ray source positioned at a distance of 1 m from the film can be estimated by the expressions... 

Although measurements of threshold object thickness are difficult to conduct reliably, one may take advantage of the fact that on a given system, they are simply related to the contrast-to-noise ratio (CNR) of alarge area object (sometimes called signal-difference-to-noise-ratio SDNR) as shown in (3.1). 

A reacting system has a rate constant of 0.1 s at 475 K (Arrhenius activation energy of 20 kcal/g mole) is compression-molded. The mold wall temperature is at 510 K. Polymer pre-compression temperature is 375 K. Object thickness is 0.03 m (length and width are 0.10 and 0.08 m, respectively). How long a cycle time is needed for a 90% reaction rate ... 

Because of beam hardening, the linear relationship between attenuation value and object thickness no longer applies. As a result, attenuation values towards the... 

Visualization in TEM of single BSUs [32,33] is not possible by using interference images, becanse randomization cannot be avoided due to object thickness. In a 100-A-thick object, whether edge-on or face-on, more than 10 single BSUs are thereby superimposed (see Section 1.1.3.2.1). 

Method Object thickness Width of image Maximal defects density (cm )... 

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