Quantity Calibration

Similar to mass calibration, quantity calibration can be done internally or externally by using appropriate calibration compounds. The calibration curve covers the intensity range corresponding to the intensities of analyte peaks. In order to obtain the highest accuracy, the calibrants used in quantity calibration should have similar atomic composition, molecular structure, and mass as analytes. This requirement is because ionization efficiency depends on molecular structure, and detection efficiency is mass-dependent. In fact, ion detectors rely on secondary electrons produced by the impact of primary ions with detector surfaces, including microchannel plates, electron multipliers, and many others. 

The most reliable way to perform quantity calibration is to label the compound of interest with a heavy isotope, and use such an isotope-labeled compound as a calibration reference. Because the molecular weight as well as physical and chemical properties of such isotope-labeled compounds are very similar to those of the analyte, the ionization and detection efficiency of the mass spectrometer for analytes and the calibrants are almost the same. An important example of quantitative measurement with isotope-labeled compounds is isotope-coded aflhnity tags (ICATs) in quantitative proteomics (see also Chapter 8). 

Dynamic range describes the ratio of the highest to lowest intensity feature in a mass spectrum. The lowest intensity feature needs to provide meaningful information on an ion, such as with the S/N ratio 3. Dynamic range is an important factor when mass spectrometers are used to analyze samples with large concentration differences for example, when one of the sample molecules has an abundance several thousand times lower than others. Dynamic range is distinct from detection limit of a mass spectrometer because detection limit concerns the smallest detectable sample quantity without considering the interference of other species. 

In principle, the dynamic range can be increased 10-fold by accumulating 10 mass spectra to yield the final spectrum. 

---

One that does not have an exact relationship between the temperature and measured quantity calibration is required. 

In Chapter 14, Roux and Temprado have provided a detailed survey of the many facets of thermochemistry, including the history of the subject, methods of measurement of thermodynamic quantities, calibration of instruments, estimation of accuracy and the application of correction factors. Reference materials are discussed and data bases of thermodynamic properties are described, including an introduction to computation thermochemistry. The chapter concludes with some examples of the solving of thermochemical problems. 

The accurate and absolute measurement of the distance, D, between the surfaces is central to the SFA teclmique. In a typical experiment, the SFA controls the base position, z, of the spring and simultaneously measures D, while the spring constant, k, is a known quantity. Ideally, the simple relationship A F(D) = IcA (D-z ) applies. Since surface forces are of limited range, one can set F(D = go) = 0 to obtain an absolute scale for the force. Furthennore, SF(D = cc)/8D 0 so that one can readily obtain a calibration of the distance control at large distances relying on an accurate measurement of D. Therefore, D and F are obtained at high accuracy to yield F(D), the so-called force versus distance cur >e. 

With most non-isothemial calorimeters, it is necessary to relate the temperature rise to the quantity of energy released in the process by determining the calorimeter constant, which is the amount of energy required to increase the temperature of the calorimeter by one degree. This value can be detemiined by electrical calibration using a resistance heater or by measurements on well-defined reference materials [1], For example, in bomb calorimetry, the calorimeter constant is often detemiined from the temperature rise that occurs when a known mass of a highly pure standard sample of, for example, benzoic acid is burnt in oxygen. 

The term on the left-hand side is a constant and depends only on the constituent values provided by the reference laboratory and does not depend in any way upon the calibration. The two terms on the right-hand side of the equation show how this constant value is apportioned between the two quantities that are themselves summations, and are referred to as the sum of squares due to regression and the sum of squares due to error. The latter will be the smallest possible value that it can possibly be for the given data. 

The U.S. Environmental Protection Agency publishes sets of Series Methods that describe procedures for detecting and estimating the quantity of environmentally hazardous substances. There are strict requirements for accuracy, reproducibility, and for calibration of mass spectrometers. 

The accuracy in RBS results is -3% for areal densities and better than 1% for stoichiometric ratios. This high accuracy is obtained only when all relevant quantities are measured or evaluated carefully. Pitfalls which often prevent RBS from achieving its full accuracy are described elsewhere [3.129]. Calibration can be achieved by measuring standards obtained by either implanting into or depositing on a light element (silicon) a known amount of a much heavier element (e.g. Ta or Sb). 

Such data can provide a calibration curve and allow the constants (E) and F ) in equation (20) to be determined. The value of the molecular weight of an unknown solute can then be obtained from its (H) value by reading the value directly from the curve or by calculation using the predetermined constants (E) and (F ) in equation (20). It should be pointed out that an error of up to 30% may not appear to be very useful but, in fact, such precision can be extremely valuable in the preliminary examination of many biochemical substances where only very small quantities of material are available. It is also an ideal method for molecular weight determination before more accurate, labor-intensive and time-consuming methods are considered. 

For MPN determination, sterile pipettes calibrated in 0.1-ml increments are used. Other equipment includes sterile screw-top dilution bottles containing 99 ml of water and a rack containing six sets of five lactose broth fermentation tubes. A sterile pipette is used to transfer 1.0-ml portions of the sample into each of five fermentation tubes. This is followed by dispensing 0.1 ml into a second set of five. For the next higher dilution (the third), only 0.01 ml of sample water is required. This small quantity is very difficult to pipette accurately, so 1.0 ml of sample is placed in a dilution bottle containing 99 ml of sterile water and mixed. The 1.0-ml portions containing 0.01 ml of the surface water sample are then pipetted into the third set of five tubes. The fourth set receives 0.1 ml from this same dilution bottle. The process is then carried one more step by transferring 1.0 ml from the first dilution bottle into 99 ml of water in the second for another hundredfold dilution. Portions from this dilution bottle are pipetted into the fifth and sixth tube sets. After incubation (48 h at 35 C), the tubes are examined for gas production and the number of positive reactions for each of the serial dilutions is recorded. 

The bias error is a quantity that gives the total systematic error of a measuring instrument under defined conditions. As mentioned earlier, the bias should be minimized by calibration. The repeatability error consists of the confidence limits of a single measurement under certain conditions. The mac-curacy or error of indication is the total error of the instrument, including the... 

From the calibration point of view, manometers can be divided into two groups. The first, fluid manometers, are fundamental instruments, where the indication of the measured quantity is based on a simple physical factor the hydrostatic pressure of a fluid column. In principle, such instruments do not require calibration. In practice they do, due to contamination of the manometer itself or the manometer fluid and different modifications from the basic principle, like the tilting of the manometer tube, which cause errors in the measurement result. The stability of high-quality fluid manometers is very good, and they tend to maintain their metrological properties for a long period. 

Fig. 53 Fluorescence scan of femtogram quantities of 2,1,3-naphthoselenodiazole (A) and associated calibration curve (B).

The above procedure may be adapted to the determination of molybdenum in steel. Dissolve a 1.00 g sample of the steel (accurately weighed) in 5 mL of 1 1 hydrochloric acid and 15 mL of 70 per cent perchloric acid. Heat the solution until dense fumes are evolved and then for 6-7 minutes longer. Cool, add 20 mL of water, and warm to dissolve all salts. Dilute the resulting cooled solution to volume in a 1 L flask. Pipette 10.0 mL of the diluted solution into a 50 mL separatory funnel, add 3 mL of the tin(II) chloride solution, and continue as detailed above. Measure the absorbance of the extract at 465 rnn with a spectrophotometer, and compare this value with that obtained with known amounts of molybdenum. Use the calibration curve prepared with equal amounts of iron and varying quantities of molybdenum. If preferred, a mixture of 3-methylbutanol and carbon tetrachloride, which is heavier than water, can be used as extractant. 

The absorbance and the percentage transmission of an approximately 0.1M potassium nitrate solution is measured over the wavelength range 240-360 nm at 5 nm intervals and at smaller intervals in the vicinity of the maxima or minima. Manual spectrophotometers are calibrated to read both absorbance and percentage transmission on the dial settings, whilst the automatic recording double beam spectrophotometers usually use chart paper printed with both scales. The linear conversion chart, Fig. 17.18, is useful for visualising the relationship between these two quantities. 

To obtain a calibration curve for benzoic acid, six discs should be prepared using potassium bromide containing 0.1 per cent potassium thiocyanate as described in Section 19.8 and increasing quantities of pure benzoic acid using the following quantities ... 

To obtain the calibration standards, take aliquots ranging from 50 /xL to 300 juL As, from the working standard solution, using an Eppendorf micropipette. Add the appropriate microlitre quantities to the reaction vessel of the vapour generation system, together with 10 mL of hydrochloric acid (AM), delivered from a calibrated dispenser. 

Taking advantage of the associative property of matrix multiplication, we can compute the quantity [KTK] KT at calibration time. 

Notice that we can pre-calculate the quantity VcT A at calibration time. Let s call the result Fcal. Equation [63] becomes... 

The state of research on the two classes of acetylenic compounds described in this article, the cyclo[ ]carbons and tetraethynylethene derivatives, differs drastically. The synthesis of bulk quantities of a cyclocarbon remains a fascinating challenge in view of the expected instability of these compounds. These compounds would represent a fourth allotropic form of carbon, in addition to diamond, graphite, and the fullerenes. The full spectral characterization of macroscopic quantities of cyclo-C should provide a unique experimental calibration for the power of theoretical predictions dealing with the electronic and structural properties of conjugated n-chromophores of substantial size and number of heavy atoms. We believe that access to bulk cyclocarbon quantities will eventually be accomplished by controlled thermal or photochemical cycloreversion reactions of structurally defined, stable precursor molecules similar to those described in this review. 

It is important to avoid saturation of the signal during pulse width calibration. The Bloch equations predict that a delay of 5 1] will be required for complete restoration to the equilibrium state. It is therefore advisable to determine the 1] values an approximate determination may be made quickly by using the inversion-recovery sequence (see next paragraph). The protons of the sample on which the pulse widths are being determined should have relaxation times of less than a second, to avoid unnecessary delays in pulse width calibration. If the sample has protons with longer relaxation times, then it may be advisable to add a small quantity of a relaxation reagent, such as Cr(acac) or Gkl(FOD)3, to induce the nuclei to relax more quickly. 

Two factors determine the intensity of the scattered beam the scattering cross section for the incident ion-target atom combination and the neutralization probability of the ion in its interaction with the solid. It is the latter quantity that makes LEIS surface sensitive 1 keV He ions have a neutralization probability of about 99 % on passing through one layer of substrate atoms. Hence, the majority of ions that reach the detector must have scattered off the outermost layer. At present, there is no simple theory to adequately describe the scattering cross section and the neutralization probability. However, satisfactory calibration procedures by use of reference samples exist. The fact that LEIS provides quantitative information on the... 

---