Using the Bloch Simulator

The use of variable spin system parameters and the visualization of magnetization vectors using the Bloch simulator module require additional commands to be implemented in the NMR-SIM pulse programs that do not appear in the standard BRUKER pulse programs. The increment or decrement of a spin system parameter is triggered by a command line in the pulse program. The Bloch simulator module uses the increment of the virtual chemical shift to generate the offset dependence of a pulse. 

The following Check its will use the Bloch simulator module of NMR-SIM to study and analyse a number of different shaped pulses. Time Evolution, the Excitation Profile and the Rf field profile simulation are illustrated using a 90° Gaussian pulse while an adiabatic CHIRP pulse is used for the Waveform analysis. 

This chapter is organized in 6 sections. Section 2 describes the geometry of (CBED). Section 3 covers the theory of electron diffraction and the principles for simulation using the Bloch wave method. Section 4 introduces the experimental aspect of quantitative CBED including diffraction intensity recording and quantification and the refinement technique for extracting crystal stmctural information. Application examples and conclusions are given in section 5 and 6. 

Fig. 4 shows an example of simulated CBED pattern using the Bloch wave method described here for Si [111] zone axis and electron accelerating voltage of 100 kV. The simulation includes 160 beams in both ZOLZ and HOLZ. Standard numerical routine was used to diagonalize a complex general matrix (for a list of routines freely available for this purpose, see [23]). The whole computation on a modem PC only takes a few minutes. 

Figure 4. A simulated CBED pattern for Si[l 11] zone axis at 100 kV using the Bloch wave...

To verify the syimnetry and identify the sensitivity of CBED to CO syimnetry, dynamic simulations using the Bloch wave method were examined to see the difference between the two models. The atomic positions within the unit cells for the two models from RadaeUi etal. are very close to each other. To avoid the possible pseudo-symmetry generated in the Bi-stripe model, dynamic simulations from the CO stmctures described by the Wigner-crystal model and Bistripe model are calculated and compared for the thickness of 300 nm in Figure 15(d) and (e). The difference between the two simulations is that the G-M lines exist in four (303) reflections and 2n +, 0, 0) reflections simulated by the Wigner-crystal model, as they are in the experimental CBED patterns, but do not show up in four (303) reflections simulated by the Bi-stripe model. 

Meakin and Jesson (48) used the Bloch equations in part of their work on the computer simulation of multiple-pulse experiments. They find that this approach is efficient for the effect upon the magnetization vector of any sequence of pulses and delays in weakly coupled spin systems. However, relaxation processes and tightly coupled spin systems cannot be dealt with satisfactorily in this way and require the use of the density matrix. 

In all the books in the series Spectroscopic Techniques An Interactive Course the emphasis is on the interactive method of learning and this volume follows the same approach. The remaining chapters in this book all have a similar format, a short written introduction and number of Check its for the reader to complete. Before each Check it is a short introduction which may include the discussion of new concepts or the advantage or disadvantage of a particular pulse sequence etc. The Check its are then used to illustrate the points being discussed either by displaying the processed data in ID WIN-NMR or 2D WIN-NMR or in the case of the Bloch simulator in a spherical or other display modes. 

The Bloch Simulator is based on the BLOCH equations, named after Felix Bloch, one of the pioneers of NMR. The underlying mathematical approach used by Bloch to understand the phenomenon of the resonance experiment was based upon the concept of... 

The Bloch Simulator is used primarily to calculate and visualize the basie effects of different types of pulses and small pulse sequence fragments using a purely elassical macroscopic magnetization approach. To simplify the calculations the simulator ignores the relaxation processes that formed part of the original Bloch equations. There are three main applications for the Bloch simulator ... 

The Bloch simulator is started using the pull-down menu command Utilities Bloch module... The main display window is shown in Fig. 4.23. The different representation modes are available from the corresponding commands of the Calculate pull-down menu opening particular dialog boxes. The FilelCopy to clipboard function offers the possibility to transfer the current graphical representation in the main display window to the Windows clipboard and then into other Windows programs. 

Using the file ch4321.cfg open the Bloch Simulator (UtilitiesIBIoch module...) and in the Calculate Setup... 

Because the Bloch simulator is based on a classical approach rather than a quantum mechanical approach to the NMR phenomena its use in analysing pulse sequence fragments is somewhat restricted. Nevertheless, as will be illustrated in the next three examples, in spite of these restrictions the Bloch simulator is a very powerful aid in visualizing what is happening in a pulse sequence fragment and consequently is an extremely valuable teaching and research tool. 

The most common application for composite pulses is the substitution of 180° heteronuclear pulses, which are very sensitive to off-resonance effects and rf field inhomogenity, as the element of cpd and pulsed spinlock sequences. In Check its 5.3.2.1 and 5.3.2.2 the advantages of a 90° composite pulses are illustrated using the Parameter Optimizer routine and Bloch Simulator module. The use of the Bloch simulator to study a composite 180° pulse, the 90°xl80°y90°x sequence, has been discussed in section 4.3.4. 

P. Meakin and J. P. Jesson, "Computer simulation of multipulse and Fourier transform NMR experiments. I. Simulations using the Bloch equations", J. Magn. Resonance 10, 290-315 (1973). 

Could you use the Bloch wave sums in Equation 5.13 to simulate a hexagonal (wurtzite) semiconductor and distinguish the result from the corresponding cubic (zincblende) calculation Explain why or why not. 

In NMR-SIM the simulation of an NMR experiment is based on the density matrix approach with relaxation phenomena implemented using a simple model based on the Bloch equations. Spectrometer related difficulties such as magnetic field inhomogenity, acoustic ringing, radiation damping or statistical noise cannot be calculated using the present approach. Similarly neither can some spin system effects such as cross-relaxation and spin diffusion can be simulated. 

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