Reliable powder sampling constitutes the first step of most powder characterization and processing procedures. The goal of powder sampling is to collect a small amount of powder from the bulk quantity, such that this smaller fraction best represents the physical and chemical characteristics of the entire bulk. Thus, the samples necessarily need to be representative of the bulk. The consequences of incorrect and/or non-representative sampling can be significant and result in poor characterization, systems/process failure, large fraction of defective parts, high rejection rates, and customer dissatisfaction. It is critical to spend the required amount of time, effort and resources in developing sampling procedures that are robust and reliable. It is just as important to recognize that a sampling procedure that works well for one material system may perform inadequately for another material system. The sampling procedure should be developed or adapted considering the following issues:

(a) quantity of powder from which samples are being obtained,

(b) amount of sample required,

(c) powder characteristics, including but not limited to flow characteristics of the powder, shape of the powder particles, size of the powder particles, tendency to segregate, surface chemistry that may cause the powder to be hygroscopic, etc.,

(d) mechanical strength of the powders, i.e., are the particles friable and thus, likely to fracture during transport or during sampling, 

(e) mode by which powders are transported,

(f) possibility of powder contamination, and acceptable limits of contamination,

(g) duration of time needed to conduct the sampling procedure (this factor requires careful consideration, as sampling procedures can be cumbersome and time-consuming; the desire to save time and money should be balanced with the need for a high level of certainty about the representative nature of the samples), and

(h) skill and knowledge of operators conducting the sampling process.

If a representative measurement of a particle size distribution is to be made, the total number of particles analysed must be representative of the powder as a whole. The process of collecting a sample should not induce segregation nor should it be taken from only part of a volume of powder which is itself segregated. If the powder is part of a continuous process then multiple samples should be taken to assess any time-based variation. A powder sample taken from a large batch must be representative of the batch, but this sample must then be split into a set of smaller sub samples for individual measurements to be taken.

It is also important to note that the entire quantity of the sample powder should pass through the device used for sampling. Sampling procedures can be supplemented by the use of established and proven mathematical techniques. Such techniques of "statistical sampling" require the inspection of only a fraction of the bulk and thus greatly reduce the amount of time and effort spent in sampling. They also provide the advantage of calculating the level of certainty of detecting mistakes, upon applying a particular level of inspection.

A typical example of the need for sampling is illustrated where a process engineer may be asked to measure the particle size distribution (PSD) of a powder before and after processing operations. A starting batch of 500 kg (bulk) of powder may be contained in several bags, but the test specimen required for analysis is only 2 g. The issue to be addressed would be what sampling processes can be developed or followed to derive from the 500 kg lot test samples of 2 g, such that these samples are representative of the larger lot? Considering the issues mentioned above, it may be decided that powder samples would have to be withdrawn from different regions of different bags (seemingly contradictory to the first golden rule, the application of which would be impractical here), blended to homogenize the powders, and then reduced into smaller sub-samples. Using a randomization technique, some of these sub-samples would be selected, blended again and checked for homogeneity. Using an iterative process of random sub-sample selection and blending, the quantity of the sub-sample lot would finally be reduced to the desired amount. This process, though time consuming, would best ensure the development of a representative sub-sample.

As powder batches can vary from a few grams to several tons, there are various devices and techniques that have been developed to aid in representative sampling of powders. The design of these incorporate the "golden rules" to the greatest possible extent. Together with statistical sampling procedures, these can provide a high degree of reliability and homogeneity in the samples produced. Some of these techniques are fairly independent of the operator, while others are strongly influenced by human factors. It is thus necessary to develop and implement practices and controls in these procedures that document and track any error or variation that may be introduced by human factors.

Even without segregation, sampling and sub-sampling will introduce variation in results as a consequence of random variations which can be predicted statistically from the number of particles sampled relative to the actual distribution width; the larger the sample and/or the narrower the distribution width, the smaller this statistical variation will be. ISO 14488 in conjunction with ISO 9276:2 describes methods of calculation of this statistical variation, or fundamental error. For example it shows a 1% coefficient of variation for the d₉₀ fraction would be expected from a homogeneous sample of ≈ 0.02 g for a 30 μm median particle size of density 1000 kg m^-3 with a distribution width ratio (d₉₀ : d₁₀) of 10.

Sources of error during a particle size measurement include: 

• Sampling; extracting a representative portion for analysis 

• Sample preparation; dispersion 

• Instrument settings and operator skill; many choices infl uence results 

• Instrument induced; no instrument is perfect 

The list of error sources above are listed in rough order of magnitude, depending on the material. There is a tradeoff between sampling and sample preparation, as shown in Figure 1.

Figure 1: Error sources

The cross over point where sampling (sample extraction) becomes the critical component in additional error to the measurement process is sample dependent, but is typically assumed to be between 50 and 100 μm. Sampling also becomes more important as the breadth of the distribution increases.

On top of this uncertainty will be the errors arising from segregation in the bulk or segregation during the process of sub-sampling. These must be estimated from repeat measurements, from which a standard deviation, and hence confidence limits, can be calculated for the size measurement of interest. In practice 30 or more samples will give a good estimate of the true standard deviation.

Possible methods of sampling and sub-sampling, and their likely impact on the reproducibility of the results measured from the samples, are clearly summarised in the NIST Guide. According to the ‘Golden Rule of Sampling’:

• A powder should be sampled when in motion

• The whole sample stream should be taken over many short time increments, rather than part of the stream being taken for the whole of the time.

Allen and Khan compared the relative standard deviation of commonly used sub sampling techniques and found that wherever possible a spinning riffler should be used. These data are presented in Table 1.

Table 1: Comparison of sampling techniques

This effect is clearly seen in Figure 2 where data were generated as part of this work to compare the effect of tumbling and riffling.

Figure 2: The coefficient of variation found for tumbled and riffled samples

In the initial round robin carried out on 10 μm silica, manual methods of sub-sampling were used by 17 of the 24 respondents whose methods of sampling were sufficiently clearly described. The silica sample was supplied as a 20 g lot occupying about 50% of the sample bottle. The sample was not free flowing. The manual methods described generally involved use of a spatula to take smaller samples from the bottle, mostly after the bottle had been rolled, shaken or rotated end-over-end. Only one laboratory reported cone and quartering and four laboratories reported the use of a rotary riffler.

In almost any case, testing every single particle in your sample is not going to be a feasible option. Instead, you should make every effort to have the most accurate representative sample possible. 

When you are working with a large sample size, the best way to start accurately breaking down that sample is to use the coning and quartering method.

How to Break Down a Sample with Coning and Quartering: 

1. Pour your material onto a clean flat surface. Once you do this it will naturally result in a “cone” shape.

2. Using a large shovel or another suitable tool, turn the entire sample over at least 3 times and form the entire sample into a conical pile

3. Flatten the material to have a circle uniform in thickness. (Typically done with a shovel.)

4. Cut the pile into 4 identical quarters

5. Remove two opposite corners

coning and quartering of sample

Many laboratories in the round robins reported multiple measurements, although others reported only single values averaged from multiple measurements. Rarely was information given on whether the multiple measurements were derived from several sub samples, or from multiple measurements made on a single sub sample which had been dispersed sufficiently in the feed system to allow what is effectively sampling of the sub sample.

Sampling is an integral and important component to the overall strategy of generating accurate, reproducible, and meaningful particle size distribution results. Th e diff erence between poor and proper results can easily be attributed to poor sampling if not approached with care and understanding. Powders must be mixed, riffl ed, and handled as discussed in this document in order to minimize errors. Remember that errors in the sampling/analysis procedures impact fi nal product specifi cations and therefore can have signifi cant economic impact on particulate based products.