1、Designation: E 562 02Standard Test Method forDetermining Volume Fraction by Systematic Manual PointCount1This standard is issued under the fixed designation E 562; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last re
2、vision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) 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
3、cross section by the manual point count procedure.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
4、 automatic image analysis to determine thevolume fraction of constituents is described in Practice E 1245.1.3 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 an
5、d health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:E 3 Guide for Preparation of Metallographic Specimens2E 7 Terminology Relating to Metallography2E 407 Practice for Microetching Metals and Alloys2E 691 Practice for Co
6、nducting an Interlaboratory Study toDetermine the Precision of a Test Method3E 1245 Practice for Determining the Inclusion or SecondPhase Constituent Content of Metals by Automatic ImageAnalysis23. Terminology3.1 DefinitionsFor definitions of terms used in this prac-tice, see Terminology E 7.3.2 Def
7、initions of Terms Specific to This Standard:3.2.1 point countthe 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 fractionthe ratio, usually express
8、ed as a per-centage, 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 stereologythe methods
9、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 grida transparent sheet or eyepiece reticle witha regular pattern of lines or c
10、rosses that is superimposed overthe microstructural image for counting microstructural featuresof interest.3.2.5 volume fractionthe 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
11、count on the ithfield.PP(i) =PiPT3 100 = percentage of grid points, in theconstituent observed on the ithfield.n = number of fields counted.Pp= 1n(i 5 1nPpi! = arithmetic average of Pp(i).s = estimate of the standard deviation (s) (see (Eq3) in Section 10).1This practice is under the jurisdiction of
12、 ASTM Committee E04 on Metallog-raphy and is the direct responsibility of Subcommittee E04.14 on QuantitativeMetallography.Current edition approved April 10, 2002. Published June 10, 2002. Originallypublished as E 562 76. Last previous edition E 562 01.2Annual Book of ASTM Standards, Vol 03.01.3Annu
13、al Book of ASTM Standards, Vol 14.02.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.95 % CI = 95 % confidence interval= 6ts/=n (see Note 1).t = a multiplier related to the number of fieldsexamined and used in conjunction with thesta
14、ndard deviation of the measurements to de-termine the 95% CI.VV= volume fraction of the constituent or phaseexpressed as a percentage (see (Eq 5) in Section10).% RA = % relative accuracy, a measure of the statisticalprecision = (95 % CI/ Pp) 3 100.NOTE 1 Table 1 gives the appropriate multiplying fac
15、tors (t) for anynumber of fields measured.4. Summary of Test Method4.1 A clear 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 num
16、berof 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
17、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
18、 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).45.2 This test method has been described (4) as beingsuperior to
19、 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-dimensiona
20、l 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) a
21、re 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 1
22、00 mm 3 125 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 resu
23、lt 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
24、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
25、 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 general microstruc-ture,
26、or of the microstructure at a specified location within a lot,heat, or part.7.2 A description 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 i
27、t may have an effect upon the precisionobtained.7.4 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 m
28、etallographic, ceramographic, or other polishingprocedures, such as described in Methods E 3.4The 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 2.093
29、7 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 1.960E5620228.2 Smearing or other distortions of the phases or constitu-ents during preparation of
30、 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 MethodsE 407, should be as shallow (that is, light) as possible becausedeviations from a planar two-dimensional se
31、ction 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
32、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 m
33、agnified 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 po
34、ints in the array (PT)isanunbiased statistical estimation of the volume percent of themicrostructural constituent of interest.9.1.4 A condensed 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 inte
35、rsection 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
36、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
37、 the entire range of volume fractions. The use of 100pointgrid facilitates easy volume percent calculations. the use ofonly 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 400point grid may
38、 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
39、 a grid having asimilar pattern.Circular GridSquare GridNOTE 1The 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 1A grid size selection which gives a significant nu
40、mber 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 spentcounting and for the
41、 statistical information obtained per grid placement.E5620239.3 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 mag
42、nification 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 precisio
43、n.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 bo
44、undaryshould be counted as one half.9.4.4PPi!5Pi3 100PT(1)9.4.5 The values of PP(i)are used to calculate Ppandstandard 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 guid
45、e 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
46、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
47、 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 FieldsMake grid pos
48、itioningof each field without viewing the microstructure to eliminateany possibility 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 recommen
49、dedthat 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 data is not acceptable (see Section11).10. Calculation of the Volume Percentage Estimate and% Relative Accuracy10.1 The average percentage of grid points on the featuresof interest provides an unbiased statistical estimator for thevolume percentage within the three dimensional microstruc-ture. The value of the multiplier, t, can be found in Table 1.Thus, the averag
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