ISO 9276-5:2005

Overview - ISO 9276-5:2005 (Representation of results of particle size analysis)

ISO 9276-5:2005 defines methods of calculation for particle size analyses that follow a logarithmic normal probability distribution (log‑normal). The standard provides the mathematical background and presentation conventions needed to represent and verify cumulative particle size distributions (number, length, area, volume/mass) so that calculations based on distribution functions can be unequivocally checked. It explains the design of logarithmic‑normal probability graph paper and gives formulas for moments, median and average diameters, and volume‑specific surface area (Sauter diameter).

Key topics and technical requirements

• Logarithmic normal probability function - definition of the dimensionless variable z (logarithm of particle size scaled by median and standard deviation) and use of cumulative normal probability Q*(z).
• Graphical presentation - design and interpretation of logarithmic‑normal probability graph paper (or equivalent software plots) that render cumulative distributions as straight lines.
• Moments and averages - calculation of complete kth moments and conversion to average particle sizes across dimensionalities (number, length, area, volume).
• Median and geometric relationships - formulas linking median diameters for different dimensionalities; demonstration that number/length/area/volume cumulative lines are parallel and horizontally shifted.
• Geometric standard deviation and special points - use of characteristic cumulative values (e.g., ~16% and ~84%) to compute standard deviation and distribution spread.
• Volume‑specific surface area (Sauter diameter) - method to compute surface‑area‑weighted metrics from log‑normal parameters.
• Normalization and verification - prescriptions so that cumulative fractions sum to unity and numerical checks can be performed.

Practical applications and users

ISO 9276-5 is essential for practitioners who need standardized, verifiable particle size reporting and interconversion:

• Analytical laboratories performing granulometry (laser diffraction, sedimentation, microscopy)
• Material scientists & researchers in pharmaceuticals, cement, ceramics, mining, aerosols, soils
• Process and quality engineers who monitor particle distributions for product performance or process control
• Instrument manufacturers & software developers that implement plotting tools and calculation routines for particle size distributions
• Standards bodies & accreditation labs verifying data presentation and calculation accuracy

Benefits include consistent representation of cumulative distributions, straightforward conversion between number/area/volume statistics, and a robust basis for automated software checks.

Related standards

• ISO 9276‑1 - Graphical representation of particle size analysis results
• ISO 9276‑2:2001 - Calculation of average particle sizes/diameters and moments
• Other parts in the ISO 9276 series (e.g., fitting models, shape characterization) expand complementary practices for particle characterization.

Keywords: ISO 9276-5:2005, logarithmic normal probability distribution, particle size analysis, cumulative particle size distribution, log‑normal, median diameter, geometric standard deviation, Sauter diameter, probability graph paper.