Pulse examples

For the study of diffusion phenomena in solids it is also possible to work with potential pulses (potentiostatic pulses) or with constant current pulses (galvanostatic pulses). Examples described in the following paragraphs are based on the coulometric titration method described in Chapter 3. Weppner and Huggins reviewed these methods.In a continuous series of pulses the concentration of lithium in a sheet of aluminum is increased. The diffusion in each pulse is followed by either potential or current measurements. 

Additionally, more sophisticated pulse sequences (the procedure is called spectral editing) enable one to obtain spectra, after addition or subtraction, where only the following are present (see, for example Bouquet, 1986) ... 

Standard procedures that are used for testing of construction materials are based on square pulse actions or their various combinations. For example, small cyclic loads are used for forecast of durability and failure of materials. It is possible to apply analytical description of various types of loads as IN actions in time and frequency domains and use them as analytical deterministic models. Noise N(t) action as a rule is represented by stochastic model. 

Some of the problems often encountered during ultrasonic inspection of plane specimens are also found on cylindrical specimens. For example, problems associated with the directional characteristic of the ultrasonic transducer. Furthermore, the discontinuity influences the shape and propagation direction of a reflected pulse, causing wave mode transformation. In addition, the specimen influences the shape and amplitude of the reflected pulse by sound absorption. 

Secondly, a short pulse duration is required in order to achieve a good axial resolution, i.e. two signals close together should be detected without interference. The task can be, for example, to detect a small reflector close to the surface or back wall of the test object, as the inspection has to cover the total volume as complete as possible, including the near-surface regions. 

Another example shows a 4 MHz longitudinal wave probe WSY70-4 normally used for testing of coarse grained austenitic material. In this application a high pulse amplitude is... 

For immersion probes we also get similar improvements using piezocomposite transducers as demonstrated by the third example. In Fig. 8 we compare pulse form and frequency spectrum for a 2 MHz probe Z2K with 10 mm transducer diameter. The echo of the composite probe has 11 dB more amplitude and is clearly shorter than for the old design, also indicated by the increase in bandwidth from 45 to 76 %. 

The function h(t) to be restored is the impulse response of the medium x(t) is the transmitted pulse measured by reflection on a perfect plane reflector, for example the interface between air and water and y(t) is the observed signal. 

Another example of a teclmique for detecting absorption of laser radiation in gaseous samples is to use multiphoton ionization with mtense pulses of light. Once a molecule has been electronically excited, the excited state may absorb one or more additional photons until it is ionized. The electrons can be measured as a current generated across the cell, or can be counted individually by an electron multiplier this can be a very sensitive technique for detecting a small number of molecules excited. 

Many other pulsed NMR experiments are possible, and some are listed in the final sections. Most can be canied out using the standard equipment described above, but some require additions such as highly controllable, pulsed field gradients, shaped RF pulses for (for example) single-frequency irradiations, and the combined use of pulses at several different frequencies. 

The absolute measurement of areas is not usually usefiil, because tlie sensitivity of the spectrometer depends on factors such as temperature, pulse length, amplifier settings and the exact tuning of the coil used to detect resonance. Peak intensities are also less usefiil, because linewidths vary, and because the resonance from a given chemical type of atom will often be split into a pattern called a multiplet. However, the relative overall areas of the peaks or multiplets still obey the simple rule given above, if appropriate conditions are met. Most samples have several chemically distinct types of (for example) hydrogen atoms within the molecules under study, so that a simple inspection of the number of peaks/multiplets and of their relative areas can help to identify the molecules, even in cases where no usefid infonnation is available from shifts or couplings. 

The remarkable stability and eontrollability of NMR speetrometers penults not only the preeise aeeiimulation of FIDs over several hours, but also the aequisition of long series of speetra differing only in some stepped variable sueh as an interpulse delay. A peak at any one ehemieal shift will typieally vary in intensity as this series is traversed. All the sinusoidal eomponents of this variation with time ean then be extraeted, by Fourier transfomiation of the variations. For example, suppose that the nomial ID NMR aequisition sequenee (relaxation delay, 90° pulse, eolleet FID) is replaeed by the 2D sequenee (relaxation delay, 90° pulse, delay i -90° pulse, eolleet FID) and that x is inereased linearly from a low value to ereate the seeond dimension. The polarization transfer proeess outlined in die previous seetion will then eause the peaks of one multiplet to be modulated in intensity, at the frequeneies of any other multiplet with whieh it shares a eoupling. 

In the linear approximation there is a direct Fourier relationship between the FID and the spectrum and, in the great majority of experunents, the spectrum is produced by Fourier transfonnation of the FID. It is a tacit assumption that everything behaves in a linear fashion with, for example, imifonn excitation (or effective RF field) across the spectrum. For many cases this situation is closely approximated but distortions may occur for some of the broad lines that may be encountered in solids. The power spectrum P(v) of a pulse applied at Vq is given by a smc fiinction 18]... 

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