Direction-dependent phase error

Each atom in the lattice acts as a scattering centre, which means that the total intensity of the diffracted beam in a given direction depends on the extent to which contributions from individual atoms are in phase. Relating the underlying structure to the observed diffraction pattern is not straightforward, but is essentially a trial-and-error search involving extensive computer-based calculations. 

As described in Section 4.6A I fTs can displi a wavelength-dependent time response. These effects can also be present in the PD measurements. In FD measurements the effects are somewhat more difficult to understand. There can be systematic errors in the phase or modulation values, and the direction of the errors is not always intuitively obvious. Fortunately, the color edicts are minor with presently used side-window dynode PMTs. and they ap-... 

The amplitudes and the phases of the diffraction data from the protein crystals are used to calculate an electron-density map of the repeating unit of the crystal. This map then has to be interpreted as a polypeptide chain with a particular amino acid sequence. The interpretation of the electron-density map is complicated by several limitations of the data. First of all, the map itself contains errors, mainly due to errors in the phase angles. In addition, the quality of the map depends on the resolution of the diffraction data, which in turn depends on how well-ordered the crystals are. This directly influences the image that can be produced. The resolution is measured in A... 

The exact amount of error introduced cannot immediately be inferred from the strength of the amplitudes of the neglected Fourier coefficients, because errors will pile up in different points in the crystal depending on the structure factors phases as well to investigate the errors, a direct comparison can be made in real space between the MaxEnt map, and a map computed from exponentiation of a resolution-truncated perfect m -map, whose Fourier coefficients are known up to any order by analysing log(<7 (x) tm (x)). 

Although SIKIE may well occur in neutral chemistry (e.g., O3 formation), gas phase ion chemistry has shown itself to be a valuable arena for exploring the phenomenon and evaluating emerging theories. For example, one theory of non-mass-dependent KIE indicated that isotopic fractionation cannot ensue directly from symmetry alone. However, such a conclusion would appear to be incorrect, because that is exactly what is happening in the several cases discussed. The error in that analysis arises in the statistical thermodynamic treatment of the reversible association reaction ... 

In the dense phase the intermolecular potential consists mainly of a two-body term to which small three-body contributions should be added. This problem is poorly documented for molecular systems, and the classic example remains that of argon where an effective two-body Lennard-Jones potential accounts fairly well for the thermodynamic data simply as a result of cancellation of errors. For vibrational energy relaxation one is not directly concerned with the whole intermolecular potential, but rather by its vibrationally dependent part. As mentioned earlier, three-body effects are not usually observable and may be masked by inadequate knowledge of the true potential. Nevertheless one can expect some simply observable solvent effects describable by changes of either the intermolecular or the vibrational potentials. 

Typically, both forms of error occur in a spectrum directly after the FT. The procedure for phase correction is essentially the same on all spectrometers. The zero-order correction is used to adjust the phase of one signal in the spectrum to pure absorption mode, as judged by eye , and the first-order correction is then used to adjust the phase of a signal far away from the first in a similar manner. Ideally, the two chosen resonances should be as far apart in the spectrum as possible to maximise the frequency-dependent effect. Experimentally, this process of phase correction involves mixing of the real and imaginary parts of the spectra produced by the FT process such that the final displayed real spectrum is in pure absorption mode whereas the usually unseen imaginary spectrum is pure dispersion. 

In the dispersed phase, only the unsteady state method is applicable. The tracer must be introduced in the form of marked drops and its concentration recorded at two positions downstream from the point where the drops were introduced. Conventional techniques proved to be too inaccurate for this purpose and special probes were therefore developed which coalesced the dispersed phase and measured the light absorption directly in the column. It was found that any attempt to withdraw drops from the column and carry out time-dependent measurements on them led to unacceptable errors. 

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