Calibration, generally

In many detectors the internal counting efficiency depends on the energy of the radiation. This must also be taken into account, if sources containing other radionuclides are used for calibration. Generally, calibration curves = f E) are deter-... 

This chapter is devoted to numerical integration, and more specifically to the integration of rate expressions encountered in chemical kinetics. For simple cases, integration yields closed-form rate equations, while more complex reaction mechanisms can often be solved only by numerical means. Here we first use some simple reactions to develop and calibrate general numerical integration schemes that are readily applicable to a spreadsheet. We then illustrate several non-trivial applications, including catalytic reactions and the Lotka oscillator. 

Standardization matches the concept of calibration generally used in analytical chemistry. The number of radionuclides produced per unit time by irradiation of an infinitesimally thin target is determined by the balance of the increase due to nuclear reactions and the decrease due to radioactive decay ... 

Obviously, the bulk composition of these solid standards should ideally be as similar as possible to that of the samples of interest, because the ablation yield, the transport efficiency of the particles produced, and the generation of the signals in the ICPMS instrument will most probably be influenced by the physicochemical characteristics of the matrix. Unfortunately, perfectly matrix-matched standards are not often available, with the possible exception of the analysis of glass and, particularly, of metals, for which a large number of reference materials are accessible. Some research papers on coins and metallic artifacts have used commercially available reference materials for calibration, generally with satisfactory results [26,39,48,49,63,64,72,73]. 

The procedures for setting up a mass balance and for mass calibration of the Coulter Counter technique are identical. A weighed amount of sample of known density is suspended in a known volume of electrolyte, a known portion of which is analysed. From these data the total volume of particles in the analysed volume of electrolyte can be calculated and compared with the measured volume of particles. For a mass (or volume) balance this measured volume of particles is calculated by means of a prior calibration, generally with an appropriate latex standard. For mass calibration, on the other-hand the ratio of measured and calculated particle volume is used to correct the prior calibration constant. The following equations can be derived ... 

Primary standard A unit (e.g. ieak rate, resistivity, iength, composition), the value of which has been established by an accepted authority (e.g. NIST in the US) and against which other units are calibrated. Generally, the primary standard must be periodically recalibrated by the authority. See also Secondary standard. 

The general list of factors influencing the uncertainty in the gross rock volume included the shape of structure, dip of flanks, position of bounding faults, position of internal faults, and depth of fluid contacts (in this case the OWC). In the above example, the owe is penetrated by two wells, and the dip of the structure can be determined from the measurements made in the wells which in turn will allow calibration of fhe 3D seismic. 

Once the distortion parameters are calibrated, undistorted images are used to estimate the projection parameters. The. sample under investigation is recorded together with a calibration body. Although a 3D calibration body in general provides higher accuracy, a planar calibration body is used, because it is much easier to handle. To overcome... 

Equatiou B1.5.44 indicates that if we know -. /i and we may infer infonnation about the third-order orientational moments ( T.., Tjj, Since calibration of absolute magnitudes is difficult, we are generally concerned with a comparison of the relative magnitudes of the appropriate molecular (a ) and macroscopic (... 

The n-fold procedure (n > 2) produces an n-dimensional hyperplane in n -b 1 space. Lest this seem unnecessarily abstract, we may regard the n x n slope matrix as the matrix establishing a calibration srrrface from which we may determine n unknowns Xi by making n independent measurements y . As a final generalization, it should be noted that the calibration surface need not be planar. It might, for example, be a curwed sruface that can be represented by a family of quadratic equations. 

The comparatively inexpensive long-scale thermometer, widely used by students, is usually calibrated for complete immersion of the mercury column in the vapour or liquid. As generally employed for boiling point or melting point determinations, the entire column is neither surrounded by the vapour nor completely immersed in the liquid. The part of the mercury column exposed to the cooler air of the laboratory is obviously not expanded as much as the bulk of the mercury and hence the reading will be lower than the true temperature. The error thus introduced is not appreciable up to about 100°, but it may amount to 3-5° at 200° and 6-10° at 250°. The error due to the column of mercury exposed above the heating bath can be corrected by adding a stem correction, calculated by the formula ... 

Understanding the distribution allows us to calculate the expected values of random variables that are normally and independently distributed. In least squares multiple regression, or in calibration work in general, there is a basic assumption that the error in the response variable is random and normally distributed, with a variance that follows a ) distribution. 

Sensitivity For a coulometric method of analysis, the calibration sensitivity is equivalent to tiF in equation 11.25. In general, coulometric methods in which the analyte s oxidation or reduction involves a larger value of n show a greater sensitivity. 

Good measurement practices (GMPs) describe operations specific to a technique. In general, GMPs provide instructions for maintaining, calibrating, and using the equipment and instrumentation that form the basis for a specific technique. For example, a GMP for a titration describes how to calibrate a buret (if nec-... 

Other techniques for mass measurement are available, but they are not as popular as those outlined above. These other methods include mass measurements on a standard substance to calibrate the instrument. The standard is then withdrawn, and the unknown is let into the instrument to obtain a new spectrum that is compared with that of the standard. It is assumed that there are no instrumental variations during this changeover. Generally, this technique is less reliable than when the standard and unknown are in the instrument together. Fourier-transform techniques are used with ion cyclotron mass spectrometers and give excellent mass accuracy at lower mass but not at higher. 

Scales are sensitive to force appHed in one direction only, eg, a scale with a horizontal platform is sensitive to forces appHed perpendicular to the platform. Scales should be leveled before calibration and whenever they are moved portable scales generally have a bubble level to facilitate leveling. 

The equations and methods for determining viscosity vary greatly with the type of instmment, but in many cases calculations may be greatly simplified by calibration of the viscometer with a standard fluid, the viscosity of which is known for the conditions involved. General procedures for calibration measurement are given in ASTM D2196. The constant thus obtained is used with stress and shear rate terms to determine viscosity by equation 25, where the stress term may be torque, load, or deflection, and the shear rate may be in rpm, revolutions per second (rps), or s F... 

Various methods can be used to analy2e succinic acid and succinic anhydride, depending on the characteristics of the material. Methods generally used to control specifications of pure products include acidimetric titration for total acidity or purity comparison with Pt—Co standard calibrated solutions for color oxidation with potassium permanganate for unsaturated compounds subtracting from the total acidity the anhydride content measured by titration with morpholine for content of free acid in the anhydride atomic absorption or plasma spectroscopy for metals titration with AgNO or BaCl2 for chlorides and sulfates, respectively and comparison of the color of the sulfide solution of the metals with that of a solution with a known Pb content for heavy metals. 

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