Errors sources

A particular attention must be given to the examination of spectra, because they can be an error source. The magnetic spectrum presence is very important, because it conditions the testing sanction. Generally we proceed to an identification of the real defect nature which has lead to the formation of the spectrum... 

Theoiy related to material characteristics states that a minimum quantity of sample is predicated as that amount required to achieve a specified limit of error in the sample-taking process. Theoiy of sampling in its apphcation acknowledges sample preparation and testing as additional contributions to total error, but these error sources are placed outside consideration of sampling accuracy in theoiy of sample extraction. 

Computer simulation is an experimental science to the extent that calculated dynamic properties are subject to systematic and statistical errors. Sources of systematic error consist of size dependence, poor equilibration, non-bond interaction cutoff, etc. These should, of course, be estimated and eliminated where possible. It is also essential to obtain an estimate of the statistical significance of the results. Simulation averages are taken over runs of finite length, and this is the main cause of statistical imprecision in the mean values so obtained. 

The main error sources are noise in the wavefront sensor measurement, imperfect wavefront correction due to the finite number of actuators and bandwidth error due to the finite time required to measure and correct the wavefront error. Other errors include errors in the telescope optics which are not corrected by the AO system (e.g. high frequency vibrations, high spatial frequency errors), scintillation and non-common path errors. The latter are wavefront errors introduced in the corrected beam after light has been extracted to the wavefront sensor. Since the wavefront sensor does not sense these errors they will not be corrected. Since the non-common path errors are usually static, they can be measured off-line and taken into account in the wavefront correction. 

In most situations analysts can achieve a rapid reasonable separation of compounds using an appropriate standard CE method with generic operating conditions [877]. This eliminates or reduces dramatically the need for method development. Major instrumental error sources in CE are detection, integration and injection. General guidelines for validation of CE methods are available and similar to those of HPLC [878]. Validated CE methods often perform the same as, or better than, the corresponding HPLC methods. 

The accuracy of experimentally determined structure factors is limited by various error sources, which may be introduced by the experimental method itself or during the data reduction stage. A reduction of those errors is expected by the use of high-energy synchrotron radiation (E(/ ) > 100 keV) as primary beam source, because absorption and extinction corrections are negligible in most practical cases. 

Gross errors are generated by human mistakes or by instrumental or computational error sources. Depending on whether they are short- or longterm effects, they may have systematic or random character. Frequently, it is easy to perceive and to correct for them. They will not play any role in the following discussion. 

An even larger asymmetry in introduced by a fact we have discussed previously the physical causes of the error source under consideration preclude both the numerator... 

Eckart conditions, Renner-Teller effect, triatomic molecules, 610-615 Ehrenfest dynamics, direct molecular dynamics error sources, 403—404 Gaussian wavepacket propagation, 378-383 molecular mechanics valence bond (MMVB), 409-411... 

Ben Yaakov and Lorch [8] identified the possible error sources encountered during an alkalinity determination in brines by a Gran-type titration and determined the possible effects of these errors on the accuracy of the measured alkalinity. Special attention was paid to errors due to possible non-ideal behaviour of the glass-reference electrode pair in brine. The conclusions of the theoretical error analysis were then used to develop a titration procedure and an associated algorithm which may simplify alkalinity determination in highly saline solutions by overcoming problems due to non-ideal behaviour and instability of commercial pH electrodes. 

Given this array of error sources, how can a geochemical modeler cope with the uncertainties implicit in his calculations The best answer is probably that the modeler should begin work by integrating experimental results and field observations into the study. Having successfully explained the experimental or field data, the modeler can extrapolate to make predictions with greater confidence. 

Thirteen minerals appear supersaturated in the first block of results produced by the chemical model (Table 6.6). These results, therefore, represent an equilibrium achieved internally within the fluid but metastable with respect to mineral precipitation. It is quite common in modeling natural waters, especially when working at low temperature, to find one or more minerals listed as supersaturated. Unfortunately, the error sources in geochemical modeling are large enough that it can be difficult to determine whether or not a water is in fact supersaturated. 

In those cases where concentrations are not measured directly, the problem of calibration of the in-situ technique becomes apparent. An assurance must be made that no additional effects are registered as systematic errors. Thus, for an isothermal reaction, calorimetry as a tool for kinetic analysis, heat of mixing and/or heat of phase transfer can systematically falsify the measurement. A detailed discussion of the method and possible error sources can be found in [34]. 

For hydrogenations under normal pressure and isobaric conditions, we use a device which registers gas consumption automatically (Fig. 10.3). Possible error sources resulting from such gas consumption measurements and possibilities of their minimization will be discussed. 

This method, although being used analogously in other devices, incorporates a number of principal error sources. These result substantially from transport phenomena, vapor pressure of the solvent, gas solubility, and tempering problems. Particular points, together with possible means of their minimization, will be discussed in the following section. 

A second likely error source in the experimental determination of the appearance energy has also a kinetic origin. As shown in figure 4.4, recombination of the products A+ and B may involve an activation barrier (Etec). Therefore, even if Akin = 0, when Eiec is not negligible the measured appearance energy will be an upper limit of the true (thermodynamic) value. 

Some of these problems can be overcome with a different calorimetric design (see later discussion). Other problems, which are more dependent on the chemistry and physics of the process under study than on the instrumentation, require careful attention. Unnoticed side reactions or secondary photolysis are examples, but one of the most serious error sources in photocalorimetry is caused by the quantum yield values, particularly, as explained, when they are small. Unfortunately, many literature quantum yields are unreliable, and it is a good practice to determine n for each photocalorimetric run. Errors in

inner filter effects, that is, photon absorption by reaction products. 

Other error sources discussed for the isoperibol instrument are not a problem in Teixeira and Wadso s microcalorimeter. For instance, as shown by equations 10.15 and 10.16, the radiation wavelength does not influence the precision or the accuracy of the final A rH result. However, the precision is still affected when the reaction quantum yield is low, because the experimental error will be divided by a small value of n. On the other hand, problems like side reactions or secondary photolysis, already mentioned, that are not related to the instrumental design may also lead to large errors. 

What are the main error sources in PAC experiments One of them may result from the calibration procedure. As happens with any comparative technique, the conditions of the calibration and experiment must be exactly the same or, more realistically, as similar as possible. As mentioned before, the calibration constant depends on the design of the calorimeter (its geometry and the operational parameters of its instruments) and on the thermoelastic properties of the solution, as shown by equation 13.5. The design of the calorimeter will normally remain constant between experiments. Regarding the adiabatic expansion coefficient (/), in most cases the solutions used are very dilute, so the thermoelastic properties of the solution will barely be affected by the small amount of solute present in both the calibration and experiment. The relevant thermoelastic properties will thus be those of the solvent. There are, however, a number of important applications where higher concentrations of one or more solutes have to be used. This happens, for instance, in studies of substituted phenol compounds, where one solute is a photoreactive radical precursor and the other is the phenolic substrate [297]. To meet the time constraint imposed by the transducer, the phenolic... 

Despite the problems that can afflict experimental cyclic voltammograms, when the method for deriving standard redox potentials is used with caution it affords data that may be accurate within a few tens of mV (10 mV corresponds to about 1 kJ mol-1), as remarked by Tilset [335]. Kinetic shifts are usually the most important error source The deviation (A If) of the experimental peak potential from the reversible value can be quite large. However, it is possible to estimate AEp if the rate constant of the chemical reaction is available. For instance, in the case of a second order reaction (e.g., a radical dimerization) with a rate constant k, the value of AEV at 298.15 K is given by equation 16.24 [328,339] ... 

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