ASTM_E_2578_-_07_2012.pdf

Designation:E257807(Reapproved 2012)Standard Practice forCalculation of Mean Sizes/Diameters and StandardDeviations of Particle Size Distributions1This standard is issued under the fixed designation E2578;the number immediately following the designation indicates the year oforiginal adoption or,in the case of revision,the year of last revision.A number in parentheses indicates the year of last reapproval.Asuperscript epsilon()indicates an editorial change since the last revision or reapproval.1.Scope1.1 The purpose of this practice is to present procedures forcalculating mean sizes and standard deviations of size distri-butions given as histogram data(see Practice E1617).Theparticle size is assumed to be the diameter of an equivalentsphere,forexample,equivalent(area/surface/volume/perimeter)diameter.1.2 The mean sizes/diameters are defined according to theMoment-Ratio(M-R)definition system.2,3,41.3 The values stated in SI units are to be regarded asstandard.No other units of measurement are included in thisstandard.1.4 This standard does not purport to address all of thesafety concerns,if any,associated with its use.It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2.Referenced Documents2.1 ASTM Standards:5E1617 Practice for Reporting Particle Size CharacterizationData3.Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 diameter distribution,nthe distribution by diameterof particles as a function of their size.3.1.2 equivalent diameter,ndiameter of a circle or spherewhich behaves like the observed particle relative to or deducedfrom a chosen property.3.1.3 geometric standard deviation,nexponential of thestandard deviation of the distribution of log-transformed par-ticle sizes.3.1.4 histogram,na diagram of rectangular bars propor-tional in area to the frequency of particles within the particlesize intervals of the bars.3.1.5 lognormal distribution,na distribution of particlesize,whose logarithm has a normal distribution;the left tail ofa lognormal distribution has a steep slope on a linear size scale,whereas the right tail decreases gradually.3.1.6 mean particle size/diameter,nsize or diameter of ahypothetical particle such that a population of particles havingthat size/diameter has,for a purpose involved,properties whichare equal to those of a population of particles with differentsizes/diameters and having that size/diameter as a meansize/diameter.3.1.7 moment of a distribution,na moment is the meanvalue of a power of the particle sizes(the 3rd moment isproportional to the mean volume of the particles).3.1.8 normal distribution,na distribution which is alsoknown as Gaussian distribution and as bell-shaped curvebecause the graph of its probability density resembles a bell.3.1.9 number distribution,nthe distribution by number ofparticles as a function of their size.3.1.10 order of mean diameter,nthe sum of the subscriptsp and q of the mean diameterDp,q.3.1.11 particle,na discrete piece of matter.3.1.12 particle diameter/size,nsome consistent measureof the spatial extent of a particle(see equivalent diameter).3.1.13 particle size distribution,na description of the sizeand frequency of particles in a population.3.1.14 population,na set of particles concerning whichstatistical inferences are to be drawn,based on a representativesample taken from the population.1This practice is under the jurisdiction of ASTM Committee E56 on Nanotech-nology and is the direct responsibility of Subcommittee E56.02 on Physical andChemical Characterization.Current edition approved May 1,2012.Published May 2012.Originallyapproved in 2007.Last previous edition approved in 2007 as E2578 07.DOI:10.1520/E2578-07R12.2Alderliesten,M.,“Mean Particle Diameters.Part I:Evaluation of DefinitionSystems,”Particle and Particle Systems Characterization,Vol 7,1990,pp.233241.3Alderliesten,M.,“Mean Particle Diameters.From Statistical Definition toPhysical Understanding,”Journal of Biopharmaceutical Statistics,Vol 15,2005,pp.295325.4Mugele,R.A.,and Evans,H.D.,“Droplet Size Distribution in Sprays,”Journalof Industrial and Engineering Chemistry,Vol 43,1951,pp.13171324.5For referenced ASTM standards,visit the ASTM website,www.astm.org,orcontact ASTM Customer Service at serviceastm.org.For Annual Book of ASTMStandards volume information,refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United States1 3.1.15 sample,na part of a population of particles.3.1.16 standard deviation,nmost widely used measure ofthe width of a frequency distribution.3.1.17 surface distribution,nthe distribution by surfacearea of particles as a function of their size.3.1.18 variance,na measure of spread around the mean;square of the standard deviation.3.1.19 volume distribution,nthe distribution by volume ofparticles as a function