## Sampling of Powders

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. Frequently it is not possible to mix the powder and a sampling campaign has to be prepared in order to obtain representative samples.

In order to establish homogeneity it is necessary to examine samples taken from the bulk, either at random or according to some predetermined pattern. If homogeneity is established, a single sample is representative of the bulk. The definition of homogeneity requires specification of the portions or sample sizes between which the variability is sufficiently small to be neglected.

The total sampling error is made up of errors due to the primary sampling, errors in 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.

Two types of sampling errors are possible. Errors due to segregation of the bulk depend on the previous history of the powder and can be minimized by suitable mixing and building up a sample from a large number of increments.

Statistical errors 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. This is the only sampling error that cannot be suppressed and occurs in ideal sampling. It can be estimated beforehand and reduced by increasing the sample size.

Samples are withdrawn from a population in order to estimate a certain characteristic of that population and to establish confidence limits for that characteristic.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 meet preset criteria, or 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, 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 subdivided. The stages in reducing from bulk to measurement samples are bulk or process stream (10"kg), gross sample (>kg), laboratory sample (<kg), test sample (g), and measurement sample (mg).

The gross sample can be one of a series of spot samples, which have been extracted in order to determine the variability of the bulk or process stream with location or time, or it can be made up of subsamples to be representative of the bulk as a whole. Historically the bulk sample has been obtained manually, but automatic inline sampling is becoming more common.

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 subdivide it into test samples.

The test sample may be used in its entirety or further subdivided to form measurement and reference samples.

Powders may be classified as free-flowing or cohesive powders. Free-flowing powders tend to segregate during handling and storage, so spot samples are rarely representative. Cohesive powders tend to retain their characteristics during handling, so that if they are segregated during manufacture or packaging they will tend to remain segregated.

For these reasons it is recommended that, wherever possible, the golden rules of sampling should be followed:

• A powder should always be sampled when in motion.

• The whole of the stream of powder should be taken for many short increments of time, in preference to part of the stream being taken for the whole of the time.

Observance of these rules, coupled with an understanding of the manner in which segregation takes place, leads to the best sampling procedure. Any method that does not follow these rules should be regarded as a second-best method likely to lead to errors. Finally, the need or care and skill in abstracting samples cannot be overemphasized. There are a very large number of possible systems from which a gross sample has to be extracted, so it is impossible to lay down instructions that will address all situations. Essentially, the solution depends on whether the powder is stationary or moving and whether it is cohesive or free-flowing.

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