Reporting particle size and particle size distribution information is as critical a component as designing and conducting the experiments that generate this information. The main consideration while reporting size and size distribution data is to ensure that all pertinent information is presented, such that the experiments conducted to generate this information can be reproduced when necessary. This feature is of particular interest for comparing and communicating the particle size and size distribution data between different laboratories or between suppliers and customers. Thus, effective communication of size and size distribution data requires that pertinent information be provided in the most efficient manner.

At present, there are over 400 commercially available particle size analysis instruments. These instruments are based on a wide range of physical principles, and thus the information generated from these instruments tends to be of varied nature. Some instruments report size results as diameters, while some as surface area or projected area. The nature of the physical principle used may bias the results depending on the technique and parameters (mass, number, surface area, etc.) used for data representation. For example, results from instruments based on the principle of gravitational sedimentation tend to be more accurate when reporting particle size distribution on a mass basis than surface area. Similarly, results from instruments using the electrozone sensing principle tend to be more representative when represented on a number basis than mass basis. Particle size and size distribution data can be presented in varied forms (i.e., by a single number representing a particular feature of the distribution, in a tabular manner and/or graphically). Each representation has its own distinct advantages and shortcomings, and the choice of the representation to be used should be made judiciously. Various texts discuss these strengths and shortcomings, and also, the means to convert from one method of representation to another.

As of November 1999, there are two implemented standards that are pertinent to reporting particle size data. The ASTM E1617-973, Standard Practice for Reporting Particle Size Characterization Data, was originally published as El 6 17-94 and refers to means for reporting particle size measurement data. The ISO standard, ISO 9276-1:1998, on Representation of Results of Particle Size Analysis - Part 1 : Graphical Representation is the second standard that is recommended for the reporting of particle size data. Other pertinent ISO draft standards in various stages of implementation are:

• ISO/DIS 9276-2 Representation of Results of Particle Size Analysis - Part 2: Calculation of average particle sizes/diameters and moments from particle size distributions;

• ISO/CD 9276-3 Representation of Results of Particle Size Analysis - Part 3: Calculation of means and moments of particle size distributions;

• ISO/DIS 9276-4 Representation of Results of Particle Size Analysis - Part 4: Characterization of a classification process;

• ISO/WD 9276-5 Representation of Results of Particle Size Analysis - Part 5: Validation of calculations relating to particle size analyses using the logarithmic normal probability distribution.

Standard ASTM E1 61 7-97

The ASTM E 16 17-97 standard is designed to promote the use of a standard reporting technique to help reduce inconsistencies that arise when attempting to compare particle size measurement data obtained from different measurement techniques and instruments. This standard requires that all pertinent information relating to the material being analyzed, the instrument being used for analysis, the methodology used for generating data, and the statistical approaches for evaluating the data be categorized into three levels. The nature of the report then dictates what levels need to be reported. The exchanging of analysis results between two laboratories for the purpose of comparison may thus require reporting all pertinent details, while the reporting of size data from a raw materials supplier to a customer might not require the same level of detail, depending upon the application.

Level I reporting gives fundamental information about the material being analyzed. This is of a general nature and includes details such as the material type, sample source and sample lot number pertaining to material identification. With respect to size analysis, this level of reporting requires information about the basic measurement principle of the instrument used for analysis (physical principle such as sedimentation, laser light scattering or optical analysis). Information about size data needs to be defined by a "minimum reporting of size parameters," where the parameters being reported are a set of mutually agreed upon parameters between the supplier of the information and the party receiving the information. This level of information also requires that any bias in data arising due to the sensing technique used by the instrument be indicated by a suitable choice of diameter. By requiring the reporting of the physical bases for the reported parameters (e.g., number, volume or surface area distribution) this standard can help minimize errors that may arise during data interpretation. A final requirement at this level of reporting is the range of size measurement.

Level II reporting conveys in greater detail the information presented in Level I reporting. In addition to the information required for Level I, Level II requires that the instrument used for particle size analysis be explicitly identified, together with the appropriate software version, where applicable. In terms of instrumentation, this level of reporting needs a description of the  experimental parameters under which the instrument was used. The basis by which calculations are performed by the instrument (where available from the manufacturer) needs to be reported together with any additional calculations conducted on the particle size data. The report also requires quantification of some basic sample statistics, including the standard deviation, number of degrees of freedom and confidence interval, and the calculations by which this statistical information is generated. The technique used for sample preparation also needs to be described in detail for this level of size reporting.

Level III reporting requires the greatest detail about both instrument parameters and sample parameters. Level III encompasses all of the information required in Level I and Level II reports together with information and description of calibration and operations conducted on the instrument, where these operations are either non-standard operations or are not specifically asked for. The operating procedures followed while conducting the size analysis need to be mentioned; if any of these procedures are designated standardized techniques, then appropriate standard designations need to be mentioned. This level of reporting also requires, if available, a statement of precision and bias of the particle size measurement data.

Thus, this standard method of size data reporting requires the users to spell out all pertinent information that may be required for comparison of particle size data from one instrument with that from another. This technique of data repoting also has significant advantages in record-keeping and tracking, when size and distribution data need to be referred to at a later date. Depending upon the application of the powder size and distribution data, the level of detail at which these data are represented can be defined by the user.

An important procedure not spelled out in this standard is the mention of the sampling technique used to create the sample for analysis. As sampling procedures vary depending upon the size of the initial batch, the nature of the material, the mode by which the batch is transported, and the nature of the technique and instrument being used for analysis, it is imperative that the technique and any instruments used for sampling be defined.

Standard ISO 9276-1: 1998

This standard concentrates on issues pertaining to the graphical representation of particle size analysis data, particularly as represented in the form of histograms, density distributions and cumulative distributions. The distributions in questions apply not only to powders, but also to droplets and/or gas bubbles, over any size range. The standard further recommends a standard nomenclature to be followed to generate density and cumulative distributions from the measured raw data. The reference to density in this case is not to the physical property of a material, but to the fractional distribution.

An important issue highlighted in this standard is the common use of the symbols "x" and "d" to represent the particle size. While using the term "x," the standard also states that the term "d" can be used for the same purpose. The standard defines a nomenclature to distinguish between density distributions and cumulative distributions on different bases, by the use of the term q _(bases) (x) to define the density distribution and the term Q _(bases) (x) to define the cumulative distribution. The various bases used in this standard are number, length, surface or projected area and volume/mass. Recognizing that there is no single definition of particle size, this standard defines particle size as "the diameter of a sphere having the same physical properties; this is known as equivalent spherical diameter." The standard also defines the measures as either cumulative measures or density measures, either of which can be derived from the other by suitable integration of differentiation operations over the appropriate size range. As size distributions are often spread out over a very wide size range, the use of linear abscissa for representing the size range may not be practical. This standard defines equations to be used for representing cumulative and density distributions on a logarithmic abscissa.

Particle size and size distribution data can be represented in either a tabular or graphical form. The choice of representation used can be dependent on what information is being expressed and the applications to which this information will be used. Very often, both tabular and graphical representations are used to convey this information, allowing the end-user to transform the data to enable conversions or comparisons with data from other sources. However, care should be taken when attempting transformation from one form of distribution to another form, due to errors associated with the assumption of a constant shape factor throughout the distribution, which is not often the case with real materials. Both forms of representation are closely related as information displayed in one form is derived from the other.

At a very basic level, tabular representations typically convey a series of size ranges and the corresponding quantity of powder observed in that size range. Thus, the size range can be the size difference between two adjacent sieves, and the corresponding quantity would be the mass of powder on each of the  sieve. In case of analysis by laser light scattering, the size range may be the differences in sizes corresponding to the positions of consecutive detector elements, and the associated sample quantity would be the volume of sample giving rise to the signal incident on that element. Allen and Reed give suitable examples of the organization of data in typical tabular representations.

Table 1 shows a typical representation of size and size distribution data that would be obtained from sieve analysis. This information provides enough raw data to conduct some basic statistical analysis and obtain information about the size distribution, such as mean, median and standard deviation. This information however, reveals very little about the shape of the distribution which can be obtained from plotting these results.

Table 1: Size Data Obtained by Sieve Analysis of Glass Beads During Development of a NIST Size Standard (total mass sampled = 85.70 g)

Graphical representation of size and size distribution results can be obtained either as differential distribution or cumulative distribution of the size parameter, as a function of the size. When plotting distribution data, the plots are often drawn as histograms, with the frequency of occurrence as the ordinate and the size or size range over which this frequency is observed as the abscissa. The greatest drawback of this representation arises from the finite width of the abscissa. If the size range chosen is too wide, then slight variations in the size distribution will not be observed and the histogram will not have adequate resolution. More common representations involve plotting the size distribution data as differential distribution curves and cumulative distribution curves.

The reporting of particle size and particle size distribution data can be done in various forms and techniques. The first factor to be considered is the property that is being used to characterize the particle size and size distribution. One should be aware of the errors and bias associated with measurement instruments and techniques when attempting to characterize a particular property. Similarly, conversion from distributions representing a particular property to that representing another property should be conducted with extreme care and, if possible, avoided all together. In attempting such transformations, the aspect ratio of the particles should be considered and their influence on the transformation factored in. The technique used for reporting size data should preferably address the shape and extent of distribution and some representative characteristic such as median size or moment of distribution.

While reporting of the measured data satisfies one aspect of size reporting, a comprehensive report would necessarily require reporting of various aspects of sampling, sample preparation, instrumental parameters used and any additional statistical analysis. While often cumbersome and superfluous, this additional information would enable testing for reproducibility by other testing facilities or personnel and would also provide a basis for the development of good laboratory practices for an organization.