# ASTM E562-11

Designation: E562 − 11Standard Test Method forDetermining Volume Fraction by Systematic Manual PointCount1This standard is issued under the fixed designation E562; 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.INTRODUCTIONThis test method may be used to determine the volume fraction of constituents in an opaquespecimen using a polished, planar cross section by the manual point count procedure. The samemeasurements can be achieved using image analysis per Practice E1245.1. Scope1.1 This test method describes a systematic manual pointcounting procedure for statistically estimating the volumefraction of an identifiable constituent or phase from sectionsthrough the microstructure by means of a point grid.1.2 The use of automatic image analysis to determine thevolume fraction of constituents is described in Practice E1245.1.3 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:2E3 Guide for Preparation of Metallographic SpecimensE7 Terminology Relating to MetallographyE407 Practice for Microetching Metals and AlloysE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE1245 Practice for Determining the Inclusion or Second-Phase Constituent Content of Metals by Automatic ImageAnalysis3. Terminology3.1 Definitions—For definitions of terms used in thispractice, see Terminology E7.3.2 Definitions of Terms Specific to This Standard:3.2.1 point count—the total number of points in a test gridthat fall within the microstructural feature of interest, or on thefeature boundary; for the latter, each test point on the boundaryis one half a point.3.2.2 point fraction—the ratio, usually expressed as apercentage, of the point count of the phase or constituent ofinterest on the two-dimensional image of an opaque specimento the number of grid points, which is averaged over n fields toproduce an unbiased estimate of the volume fraction of thephase or constituent.3.2.3 stereology—the methods developed to obtain informa-tion about the three-dimensional characteristics of microstruc-tures based upon measurements made on two-dimensionalsections through a solid material or their projection on asurface.3.2.4 test grid—a transparent sheet or eyepiece reticle witha regular pattern of lines or crosses that is superimposed overthe microstructural image for counting microstructural featuresof interest.3.2.5 volume fraction—the total volume of a phase orconstituent per unit volume of specimen, generally expressedas a percentage.3.3 Symbols:PT= total number of points in the test grid.Pi= point count on the ithfield.PP(i) =PiPT31005 percentage of grid points, in theconstituent observed on the ithfield.n = number of fields counted.1This test method is under the jurisdiction of ASTM Committee E04 onMetallography and is the direct responsibility of Subcommittee E04.14 on Quanti-tative Metallography.Current edition approved Oct. 1, 2011. Published October 2011. Originallyapproved in 1976. Last previous edition approved in 2008 as E562 – 08ε1. DOI:10.1520/E0562-11.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1P¯p=1n(i51nPp~i!5 arithmetic average of Pp(i).s = estimate of the standard deviation (σ) (see (Eq 3)in Section 10).95 % CI = 95 % confidence interval56ts/= n; see Note 1.t = a multiplier related to the number of fieldsexamined and used in conjunction with the stan-dard deviation of the measurements to determinethe 95% CI.VV= volume fraction of the constituent or phase ex-pressed as a percentage (see (Eq 5) in Section10).% RA = % relative accuracy, a measure of the statisticalprecision = (95 % CI/P¯p) × 100.NOTE 1—Table 1 gives the appropriate multiplying factors (t) for anynumber of fields measured.4. Summary of Test Method4.1 Aclear plastic test grid or eyepiece reticle with a regulararray of test points is superimposed over the image, or aprojection of the image, produced by a light microscope,scanning electron microscope, or micrograph, and the numberof test points falling within the phase or constituent of interestare counted and divided by the total number of grid pointsyielding a point fraction, usually expressed as a percentage, forthat field. The average point fraction for n measured fieldsgives an estimate of the volume fraction of the constituent.Thismethod is applicable only to bulk opaque planar sectionsviewed with reflected light or electrons.5. Significance and Use5.1 This test method is based upon the stereological prin-ciple that a grid with a number of regularly arrayed points,when systematically placed over an image of a two-dimensional section through the microstructure, can provide,after a representative number of placements on different fields,an unbiased statistical estimation of the volume fraction of anidentifiable constituent or phase (1, 2, 3).35.2 This test method has been described (4) as beingsuperior to other manual methods with regard to effort, bias,and simplicity.5.3 Any number of clearly distinguishable constituents orphases within a microstructure (or macrostructure) can becounted using the method. Thus, the method can be applied toany type of solid material from which adequate two-dimensional sections can be prepared and observed.5.4 A condensed step-by-step guide for using the method isgiven in Annex A1.6. Apparatus6.1 Test Grid, consisting of a specified number of equallyspaced points formed by the intersection of very thin lines.Twocommon types of grids (circular or square array) are shown inFig. 1.6.1.1 The test grid can be in the form of a transparent sheetthat is superimposed upon the viewing screen for the measure-ment.6.1.2 Eyepiece Reticle, may be used to superimpose a testgrid upon the image.6.2 Light Microscope, or other suitable device with aviewing screen at least 100 mm × 125 mm, preferably withgraduated x and y stage translation controls, should be used toimage the microstructure.6.3 Scanning Electron Microscope, may also be used toimage the microstructure; however, relief due to polishing orheavy etching must be minimized or bias will be introduced asa result of deviation from a true two-dimensional sectionthrough the microstructure.6.4 Micrographs, of properly prepared opaque specimens,taken with any suitable imaging device, may be used providedthe fields are selected without bias and in sufficient quantity toproperly sample the microstructure.6.4.1 The applicable point counting grid shall only beapplied once to each micrograph. Point counting measurementsshould be completed on different fields of view and, therefore,different micrographs. Repeated point count measurements onan individual micrograph is not allowed.6.4.2 The magnification of the micrograph should be as highas needed to adequately resolve the microstructure withoutresulting in adjacent grid points overlaying a single constituentfeature.7. Sample Selection7.1 Samples selected for measurement of the phase orconstituent should be representative of the generalmicrostructure, or of the microstructure at a specified locationwithin a lot, heat, or part.7.2 Adescription of the sample locations should be includedas a part of the results.7.3 Any orientation of the prepared section (that is, whetherlongitudinal or transverse) can be used. However, it should berecorded since it may have an effect upon the precisionobtained.3The boldface numbers in parentheses refer to the list of references at the end ofthis standard.TABLE 1 95 % Confidence Interval MultipliersNo. of Fields n t No. of Fields n t5 2.776 19 2.1016 2.571 20 2.0937 2.447 21 2.0868 2.365 22 2.0809 2.306 23 2.07410 2.262 24 2.06911 2.228 25 2.06412 2.201 26 2.06013 2.179 27 2.05614 2.160 28 2.05215 2.145 29 2.04816 2.131 30 2.04517 2.120 40 2.02018 2.110 60 2.000` 1.960E562 − 1127.4 If the sample microstructure contains gradients or inho-mogeneities (for example, banding) then the section shouldcontain or show the gradient or inhomogeneity.8. Sample Preparation8.1 The two-dimensional sections should be prepared usingstandard metallographic, ceramographic, or other polishingprocedures, such as described in Methods E3.8.2 Smearing or other distortions of the phases or constitu-ents during preparation of the section or sections should beminimized because they tend to introduce an unknown biasinto the statistical volume fraction estimate.8.3 Etching of the sections, as described in Test MethodsE407, should be as shallow (that is, light) as possible becausedeviations from a planar two-dimensional section will cause abias toward over estimation of the volume fraction.8.4 Stain- or coloring-type etchants are preferable to thosethat cause attack of one or more of the constituents or phases.8.5 Description of the etchant and etching procedure shouldbe included in the report.8.6 If etching is used to provide contrast or distinguishabil-ity of constituents then the volume fraction estimates should beobtained as a function of etching time to check the significanceof any bias introduced.9. Procedure9.1 Principle:9.1.1 An array of points formed by a grid of lines or curvesis superimposed upon a magnified image (that is, a field ofview) of a metallographic specimen.9.1.2 The number of points falling within the microstruc-tural constituent of interest is counted and averaged for aselected number of fields.9.1.3 This average number of points expressed as a percent-age of the total number of points in the array (PT)isanunbiased statistical estimation of the volume percent of themicrostructural constituent of interest.9.1.4 Acondensed step-by-step description of the procedureis provided in Annex A1.9.2 Grid Selection:9.2.1 The grid should consist of equally spaced pointsformed by the intersection of fine lines. Diagrams of twopossible grids, one with a circular pattern and one with a squarepattern, which are recommended for use, are shown in Fig. 1.9.2.2 Determine the number of points (that is, the grid size,PT) from a visual estimate of the area fraction occupied by theconstituent of interest. Table 2 provides guidelines for thisselection. The values in Table 2 do not correspond to theoreti-cal constraints; but, by using these values, empirical observa-tions have shown that the method is optimized for a givenprecision.9.2.2.1 The user may choose to employ a 100 point gridover the entire range of volume fractions. The use of 100–pointgrid facilitates easy volume percent calculations. the use ofCircular GridSquare GridNOTE 1—The entire 24 points can be used, or the outer 16, or the inner8 points.FIG. 1 Examples of Possible Grid Configurations That Can BeUtilizedTABLE 2 Guidelines for Grid Size SelectionANOTE 1—A grid size selection which gives a significant number offields having no grid points on the constituent of interest should beavoided.Visual Area Fraction EstimateExpressed as a PercentageGrid Size (Number of Points, PT)2to5% 1005to10% 4910 to 20 % 2520 % 16AThese guidelines represent an optimum for efficiency for the time spent countingand for the statistical information obtained per grid placement.E562 − 113only one overlay or eyepiece reticle for all volume percentdeterminations may save both time and money.9.2.2.2 For constituents present in amount of less than 2%,a 400–point grid may be used.9.2.3 Superimpose the grid, in the form of a transparency,upon a ground glass screen on which the section image isprojected.9.2.4 A grid in the form of an eyepiece reticle may also beused.9.2.5 If the constituent areas form a regular or periodicpattern on the section image, avoid the use of a grid having asimilar pattern.9.3 Magnification Selection:9.3.1 Select the magnification so that it is as high as neededto clearly resolve the microstructure without causing adjacentgrid points to fall over the same constituent feature.9.3.2 As a guideline, choose a magnification that gives anaverage constituent size that is approximately one half of thegrid spacing.9.3.3 As the magnification is increased, the field areadecreases, and the field-to-field variability increases, thusrequiring a greater number of fields to obtain the same degreeof measurement precision.9.4 Counting:9.4.1 Count and record for each field the number of pointsfalling on the constituent of interest.9.4.2 Count any points falling on the constituent boundaryas one half.9.4.3 In order to minimize bias, any point that is doubtful asto whether it is inside or outside of the constituent boundaryshould be counted as one half.9.4.4PP~i!5Pi3100PT(1)9.4.5 The values of PP(i)are used to calculate P¯pandstandard deviation, s.9.5 Selection of the Number of Fields:9.5.1 The number of fields or images to measure depends onthe desired degree of precision for the measurement. Table 3gives a guide to the number of fields or images to be countedas a function of PT, the selected relative accuracy (statisticalprecision), and the magnitude of the volume fraction.9.6 Selection of the Array of Fields:9.6.1 Use a uniformly spaced array of fields to obtain theestimated value, Pp, and the estimated standard deviation, s.9.6.2 If gradients or inhomogeneities are present, then auniform spacing of fields may introduce a bias into theestimate. If another method of field selection is used, forexample, random, then describe it in the report.9.6.3 When the microstructure shows a certain periodicityof distribution of the constituent or phase being measured, anycoincidence of the points of the grid and the structure must beavoided. This can be achieved by using either a circular grid ora square grid placed at an angle to the microstructuralperiodicity.9.7 Grid Positioning Over Fields—Make grid positioning ofeach field without viewing the microstructure to eliminate anypossibility of operator bias. This can be accomplished bymoving the x and y stage mechanism a fixed amount whileshifting to the next field without looking at the microstructure.9.8 Improving Measurement Precision—It is recommendedthat the user attempt to sample more of the microstructureeither by multiple specimens or by completely repeating themetallographic preparation on the same sample when theprecision for a single set of dat