Counting time

The counting times required for measurement range between a few seconds and several minutes per element, depending on specimen characteristics and the desired precision. 

The counting time for one pixel, and the number of pixels, determine the measurement time for one image. For low concentrations of the elements of interest the Pois-... 

Figure 2. XRD pattern of an EMD sample (Chemetals). The diffractogram is taken with a Bruker AXS D5005 diffractometer using CuKa radiation and a scintillation counter. The step width is 0.02° with a constant counting time of 10 s / step.

To evaluate the counting times obtained on unknown samples, it is obviously desirable to find a function of t/.t that is simply related to the sulfur content, IIV A similar problem was solved in Section 3.8 in eonneetion with the determination of chlorine in a chlorinated polymer. The present problem is different enough to warrant translating the treatment of Hughes and Wilezewski into our language. 

Added NaOH (normality) Number of Determinations Rt (ratio of counting times) Sa (standard deviation)... 

NC samples were irradiated for 3 min and TNT and HMX for 1 min at a 14 MeV neutron flux of approx 108n/cmasec, Simultaneous counting was performed by means of a matched dual 7.6x7.6cm flat Nal crystal detector assembly in conjunction with a Kaman Nuclear programmed timer system for automatic sample transfer, A one-min count time was usually sufficient to exceed 10 counts. The signal from each de-... 

Usually, lg of propint is irradiated for 0.5 to 2 min depending on the flux level. Decay time is 45 sec. Counting time is 5 min for 28Al under the 1.78 MeV peak. Because of its higher initial activity, 27Mg (from Al activation) is counted 20—40 min after irradiation. The authors estimate an overall relative error of 5% for the... 

Seed germination bioassay of root exudates. Bioassay results are presented as a 23 week mean for each germination count time (Table III, IV, V, VI). Means were separated by LSD after data normalization by the inverse sine transformation. 

We shall present, in the following sections, two complementary measurement strategies which allow the value of this variance to be minimised. The first concerns the technique by which the measuring time is divided between the two polarisation states, and the second minimises the variance by determining an optimal division of the counting times. 

With the new VME/UNIX control system on the polarised hot-neutron normal-beam diffractometer D3 at ILL, each measurement cycle for both peak and background intensities lasts 2 s, and the (+)/(-) counting-time fractions are defined with a 1 MHz clock. There are two detector scalers and two monitor scalers ((+) and (-) states). In Table 1, we compare the flipping ratio measured for the strong 200 and the weak 600 Bragg peak reflections of a CoFe sample. As expected, the standard deviation cr (if) is improved in the case of the strong reflection (16%). 

We present here the theory behind the method, which has been used on D3 for some 20 years, to achieve such optimisation. Because (+) and (-) peak count rates and peak/background ratios may differ strongly from one reflection to another and are not known a priori, the measurement is divided into a number of steps of duration T. A first flipping ratio measurement is made in predefined conditions (4+, 4-> 4+, 4-). Then, after calculating the counting-time proportions which minimise the variance of the flipping ratio, the time already spent is subtracted and the measurement is made again with times chosen to achieve these optimised proportions. The process of calculation and measurement is repeated in each step. 

To determine the expressions for the optimised counting times, we write the expressions (10) and (11) in terms of count-rates and times (count rates are constant quantities for each Bragg reflection). We assume that the incident neutron flux is constant during a flipping ratio measurement, and that no dead-time correction is needed. In these conditions, we have the relations ... 

Minimising this expression subject to the constraint tp+ + tp + 4+ + 4- = T using the Lagrange multipliers, one obtains the optimal counting-time proportions ... 

Figure 3. Time variation of c(R)/R (dashed lines) and of the relative improvement (full line) for the 600 reflection. Starting with bad counting-time proportions, die improvement is more than 17%.

The only problem with this method is observed for weak reflections where (+)/(-) count-rates are similar (i.e. R 1). The (+)/(-) optimised counting-time proportions must be 50%/50%, but with low count-rates, we have observed that the lack of precision may lead to proportions which are not optimum (e.g. 47%/53%). The same behaviour has been observed for peak to background proportions. In fact, when measuring a flipping ratio in many steps, we observe oscillations of the time proportions which slow the decrease of the standard deviation. Of course, these time variations have no sense, and one should calculate the variances of the optimised counting-times (Equations (16)) to avoid such spurious fluctuations ... 

X-ray diffraction was done using a Siemens D-500 diffractometer utilizing CuKa radiation (1.406 A). The data were collected as step scans, with a step size of 0.05° 29 and a count time of 2 s/step between 10° and 80° 29. 

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