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Powder sampling 1.1 Introduction There are many instances where estimates of population characteristics have to be made from an examination of a small fraction of that population and these instances are by no means confined to the field of powder technology. Regrettably, there are many workers in this field who still believe that sample selection procedure is unimportant. This results in the analyst being presented with hastily taken biased samples on which a great deal of energy is devoted to get precise results which do not reflect the characteristics of the bulk powder. Non-representative sampling results in incorrect analyses, process failure, unacceptable products and customer dissatisfaction. It is essential that the samples selected for measurement should be representative of the bulk in particle size distribution and the relative fractions of their various constituents, irrespective of whether a physical or chemical assay is to be carried out, since these characteristics are frequently inter-dependent. The magnitude of the problem may be realized when one considers that the characteristics of many tons of material may be assumed on the basis of analyses carried out on gram, or even milligram, measurement samples so the chances of carrying out the measurement on a non-representative sample are considerable. Two case studies illustrate problems that may arise. In case 1 a binary mixture of fine and coarse granules was blended to a satisfactory end-point. The blend was next emptied into a bucket elevator and thence to a hopper through a central feed point. The material was then fed, in 60 kg lots, to an extruder to produce an unacceptable finished product. The process started with a mixing operation followed by a segregating operation in the hopper. The central region (core) of the hopper contents was rich in fines and the outer regions rich in coarse, hence the initial feeds to the extruder contained an excess of fines whereas later feeds contained an excess of coarse. Since a bimodal mixture such Powder sampling and particle size determination as this has a high tendency to segregate it is better to weigh-feed the two streams concurrently into the extruder: This also has the advantage of eliminating process steps resulting in lower operating costs and a less expensive plant. The second case was a tabletting operation where a well- mixed fine powder was emptied into a core-flow hopper in such a way that segregation occurred. The resulting tablets were well outside specification. The solution was to replace the hopper with a properly designed mass-flow hopper. The total sampling error is made up of errors due to the primary sampling, subsequent sample dividing and errors in the analysis itself Sampling is said to be accurate when it is free from bias, that is, the error of sampling is a random variable about the true mean. Sampling is precise when the error variation is small irrespective of whether the mean is the true mean or not. The ultimate that may be obtained by representative sampling may be called the perfect sample; the difference between this sample and the bulk may be ascribed wholly to the expected difference on a statistical basis. Errors in particle size analysis may be due to: \u2022 instrument limitations; \u2022 improper procedure e.g. inadequate dispersion, particle fracture during handling; \u2022 operator errors e.g. improper instrument set-up or poor calibration; \u2022 incorrect sampling. Two types of sampling errors are possible [1] \u2022 Errors due to segregation of the bulk; this depends upon the previous history of the powder and can be minimized by suitable mixing and building up the sample from a large number of increments. \u2022 Statistical errors that cannot be prevented. Even for an ideal random mixture the quantitative distribution in samples of a given magnitude is not constant but is subject to random fluctuations. It is the only sampling error, which cannot be suppressed and occurs in ideal sampling. It can be estimated beforehand and reduced by increasing the sample size. 1.2 Sample selection Samples are withdrawn from a population in order to estimate certain characteristic of that population and to establish confidence limits for that Powder sampling 3 characteristic. The characteristic may be particle size, composition or quality; a measure of the spread of the distribution may also be required. The objective may be to set up limits between which the quality of a final product is acceptable, to decide whether the characteristics of a given lot meets preset criteria, or it may be to estimate the variability within a lot or between lots. If the material comes in containers, or can be viewed as discrete units, the objective may be to estimate the number of units outside of specification. The value of the estimate is largely dependent on the sampling technique adopted. It is of little value, and could impart false information, if it is biased or imprecise. It is usually impossible to measure the size distribution of a bulk powder and so it is necessary to carry out measurements on a sample extracted from the bulk. This sample is itself frequently too large and has to be further sub-divided. The probability of obtaining a sample that perfectly represents the parent distribution is remote. If several samples are taken their characteristics will vary and, if these samples are representative, the expected variation can be estimated from statistical analysis. However, the sampling equipment will introduce a further variation, which may be taken as a measure of sampler efficiency. Imposed on this there may also be operator bias. The stages, in reducing from bulk to measurement samples may be conveniently divided into the five stages illustrated below: bulk or process stream (10" kg) gross sample (>kg) laboratory sample (<kg) test sample (g) measurement sample (mg) The gross sample is either one of a series of spot samples that have been extracted in order to determine the variability of the bulk or process stream with location or time or it is made up of sub-samples to be representative of the bulk as a whole. In some cases the gross sample is too large to send to the laboratory and has to be reduced in quantity. This reduction needs to be carried out in such a way that the laboratory sample is fully representative of the gross sample. When this reduction is unnecessary the gross sample is also the laboratory sample. The laboratory sample may be required for a number of tests, so it is sometimes necessary to further sub-divide it into test samples. Finally, the test sample may be used in its entirety or further sub- divided to form the measurement sample. 4 Powder sampling and particle size determination The object of sampling is to gain knowledge of the characteristics of the whole from measurements impracticable to apply to the whole; bias at any of the reduction stages adversely affects the final analysis. Problems arise due to inhomogeneities in the parent distribution. If the bulk powder is homogeneous, or can be mixed prior to sampling in order to generate a homogeneous powder, sampling problems do not arise. In order to establish homogeneity it is necessary to examine samples taken from the bulk, either at random or according to some pre-determined pattern. If homogeneity is established a single sample is representative of the bulk. The definition of homogeneity requires specification of the portion or sample size between which the variability is sufficiently small to be neglected. Temporal or spatial variability of inhomogeneous powders may be random, i.e. there is no discernible pattern and it is impossible to predict the value at any one point from knowledge of the value at any other point. In this case it is necessary to examine a number of samples in order to establish a mean and a standard deviation [2]. Non-random