Designation: E826 − 14Standard Practice forTesting Homogeneity of a Metal Lot or Batch in Solid Formby Spark Atomic Emission Spectrometry1This standard is issued under the fixed designation E826; 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 This practice is suitable for testing the homogeneity of ametal lot or batch (L/B) in solid form by spark atomic emissionspectrometry (Spark-AES). It is compliant with ISO Guide35—Certification of Reference Materials: General and Statis-tical Principles. It is primarily intended for use in the devel-opment of reference materials but may be used in any otherapplication where a L/B is to be tested for homogeneity. It isdesigned to provide a combined study of within-unit andbetween-unit homogeneity of such a L/B.1.2 This practice is designed primarily to test for elementalhomogeneity of a metal L/B by Spark-AES. However, it can beadapted for use with other instrumental techniques such asX-ray fluorescence spectrometry (XRF) or atomic absorptionspectrometry (AAS).NOTE 1—This practice is not limited to elemental analysis or tech-niques. This practice can be applied to any property that can be measured,for example, the property of hardness as measured by the Rockwelltechnique.1.3 The criteria for acceptance of the test specimens must bepreviously determined. That is, the maximum acceptable levelof heterogeneity must be determined on the basis of theintended use of the L/B.1.4 It is assumed that the analyst is trained in Spark-AEStechniques including the specimen preparation proceduresneeded to make specimens ready for measurements. It isfurther assumed that the analyst is versed in and has access tocomputer-based data capture and analysis. The methodology ofthis practice is best utilized in a computer based spreadsheet.1.5 This practice can be applied to one or more elements ina specimen provided the signal-to-background ratio is not alimiting factor.1.6 This practice includes methods to correct for systematicdrift of the instrument with time. (Warning—If drift occurs,erroneous conclusions will be obtained from the data analysis.)1.7 This practice also includes methods to refine estimatesof composition and uncertainty through the use of a typestandard or multiple calibrants.1.8 It further provides a means of reducing a nonhomoge-neous set to a homogeneous subset.1.9 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:2E135 Terminology Relating to Analytical Chemistry forMetals, Ores, and Related MaterialsE177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE178 Practice for Dealing With Outlying ObservationsE634 Practice for Sampling of Zinc and Zinc Alloys bySpark Atomic Emission SpectrometryE716 Practices for Sampling and Sample Preparation ofAluminum and Aluminum Alloys for Determination ofChemical Composition by Spectrochemical AnalysisE1329 Practice for Verification and Use of Control Charts inSpectrochemical AnalysisE1601 Practice for Conducting an Interlaboratory Study toEvaluate the Performance of an Analytical MethodE1806 Practice for Sampling Steel and Iron for Determina-tion of Chemical Composition2.2 ISO Standard:3ISO Guide 35 Certification of Reference Materials: Generaland Statistical Principles1This practice is under the jurisdiction of ASTM Committee E01 on AnalyticalChemistry for Metals, Ores, and Related Materials and is the direct responsibility ofSubcommittee E01.22 on Laboratory Quality.Current edition approved April 1, 2014. Published June 2014. Originallyapproved in 1981. Last previous edition approved in 2013 as E826 – 08 (2013).DOI: 10.1520/E0826-14.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3Available from International Organization for Standardization (ISO), 1, ch. dela Voie-Creuse, Case postale 56, CH-1211, Geneva 20, Switzerland, http://www.iso.ch.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13. Terminology3.1 Definitions—For definitions of terms used in thispractice, refer to Terminology E135, and Practices E177, E178,E1329, and E1806.3.2 Definitions of Terms Specific to This Standard:3.2.1 ANOVA (analysis of variance)—a statistical means ofpartitioning the variance of a data set into contributing com-ponents.3.2.2 batch—a set of specimens to be tested forhomogeneity, often a subset of a lot.3.2.3 between-unit homogeneity—homogeneity with respectto the various specimens in the candidate L/B (see Section 8).3.2.4 drift—a gradual, systematic change in instrumentreadings with time.3.2.5 fair (fairness)—the assurance for a participant in aproficiency test program that all of the material from which theparticipants’ test materials are taken is sufficiently homoge-neous so that any results later identified as outliers should notbe attributed to any significant test item variability.3.2.6 homogeneity—as defined in this practice, statisticallyacceptable differences between means in the test.3.2.7 solid form—specimens are in a form equivalent to thatdescribed in 6.4.4 of Practice E1806.3.2.8 type standard—as defined in this practice, calibrantsimilar in composition to the candidate for homogeneitytesting.3.2.9 unit—specimen to be tested, referred to as a disk,regardless of the actual shape.3.2.10 within-unit homogeneity—homogeneity with respectto an individual specimen (see Section 8).4. Summary of Practice4.1 This practice, which is based on statistical methods(1-8),4consists of stepwise instructions for testing the homo-geneity of a candidate L/B. The candidate specimens areselected as described in Section 10, and then measured bySpark-AES (Section 11). The resultant data are corrected forinstrumental drift, if desired (see Sections 13–15), and thentabulated (see Tables 2, X1.3, and X1.4) to facilitate thestatistical calculations that are performed according to Section12.4.2 The homogeneity of the L/B is determined from theresults of the data analysis consisting of a one-way analysis ofvariance (ANOVA).4.3 This practice requires that repeated measurements onthe same position or specimen (P/S) have sufficient precision(that is, repeatability) through appropriate selection of instru-mental parameters so that any significant difference within orbetween positions or specimens can be detected with confi-dence. This is best done through the use of drift management:standardization, control charts (Practice E1329),normalization, and drift monitoring.4.4 This practice requires that there be an absence ofoutliers in the data (Practice E178). (Warning—The use ofPractice E178 dealing with outliers should be done withextreme care to ensure that values are not discarded that maybe valid for the analysis.)4.5 Variability introduced by sample preparation may influ-ence the findings of this practice.5. Significance and Use5.1 The purpose of this practice is to evaluate the homoge-neity of a lot of material selected as a candidate for develop-ment as a reference material or certified reference material, orfor a L/B selected for some other purpose (see Appendix X1 –Appendix X4 for examples).5.2 This practice is applicable to the testing of samplestaken at various stages during production. For example, con-tinuous cast materials, ingots, rolled bars, wire, etc., could besampled at various stages during the production process andtested.6. Summary of the Test Method6.1 General—This practice is based on J. W. Tukey’s HSD(honestly significant difference) procedure for pairwise com-parisons among means (8). It uses the ANOVA technique topartition the variation into contributing components, theneliminates contributions from sources other than heterogeneityand random processes. The model used is:xij5 µ1βi1τj1εij(1)where:xij= the result of the ith burn on the jth P/S,µ = the “true” mean of the population of all possible burnresults,βi= the variation in the ith burn due to the measurementprocess,τj= the variation in the jth P/S due to heterogeneity, andεij= the variation due to random or randomized processes.6.1.1 The data are then arranged inabbytmatrix (where bis the number of burns per P/S and t is the number of positionsor specimens) and rowwise statistics taken. These statisticsallow the estimation and elimination of the variation due to themeasurement process, leaving only the contributions fromheterogeneity and random processes. The maximum contribu-tion of random error is estimated and a critical value (w)determined. If the difference between any two pairs of meansis less than the critical value, then the set of positions orspecimens is considered homogeneous. In practice, the “ best”difference is between the maximum and the minimum. If wecall this value T, then if T is less than or equal to w, the set isconsidered homogeneous at the selected level of confidence(usually 95 % or 99 %). If T is greater than w, then the set isconsidered heterogeneous.6.2 Multiple Determinations—The reason for taking mul-tiple determinations on each P/S is to obtain a gage of thevariation associated with the measurement process and thematerial being tested.4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.E826 − 1426.3 Randomized Testing—Randomizing the measurementsequences randomizes any systematic error(s) not accountedfor with instrument, process, and drift controls.NOTE 2—It is possible to extend this to any population that can be putin this form. This means that this technique can be applied to lab datagenerated by an interlaboratory study. Currently, interlaboratory studies,even with the aid of h and k statistics (Practice E1601), only allow theadministrator to request corrections or perhaps eliminate certain databased on judgement calls. The application of this approach would allowthe option of systematic elimination through the use of an acceptedstatistical method.7. Lot or Batch Forms7.1 Lots or batches may be cast or wrought.7.1.1 Acast material lot is generally presented in the form ofingot(s) or linked pieces.7.1.2 A wrought material lot is generally presented in theform of bar stock.7.2 Lots or batches may be contiguous, piecewise, or acombination.7.2.1 A contiguous lot might be a single ingot or bar.7.2.2 A piecewise lot might be a set of pieces having beencut from bar(s), ingot(s), or linked piece casting(s). In this lastcase, even if the pieces have not been separated, it can beconsidered a piecewise lot since they are already defined.7.2.3 A combined lot would be a set of contiguous portionssuch as a set of bars from a single heat.7.3 Regardless of shape, individual specimens must bedimensionally compatible with common analytical methods.7.3.1 Most solid form techniques require a specimen to haveat least one flat analytical face.7.3.2 If the shape of a specimen is too irregular, it will betoo difficult to “clamp” to Spark-AES spark stand.7.3.3 The preferred form is cylindrical, but any form thatsatisfies the above criteria is acceptable.7.3.4 Typical forms are round, elliptical, rectangular, orhexagonal disks, truncated cones, etc.7.3.5 Spark-AES requires a specimen to be at least 6 mmthick to minimize heating effects.NOTE 3—When considering the use of cast material, the analyst mustconsider the possibility that microscopic cast structures may causeproblems with the measurement technique. It is best to use a castingtechnique that will produce “well behaved” specimens such as chillcasting.8. The Sampling Model8.1 General—The proposed sampling system is based oncylindrical geometry. That is, most lots or batches testedpresent themselves in some variant of cylindrical geometry.Round bar stock is fairly obvious. But even square, rectangular,hexagonal, or other such geometries work under this approach.8.1.1 Consider the cylinder displayed in Fig. 1. The cylinderis sitting on a flat plane. For convenience, suppose the planeFIG. 1E826 − 143corresponds to zero height. Further, suppose the axis of thecylinder defines the origin of an XYZ coordinate system. Thez axis corresponds to the cylinder axis. The x and y axes can beoriented as one chooses. Let the x axis correspond to an angleof zero degrees. Then, every point in the cylinder can bedescribed by its height from the plane (H ≥ Z), its distancefrom the central axis (R), and its angle with respect to the x axis(Θ).8.1.2 Given the cylindrical geometry described in 8.1.1(Fig. 1), homogeneity can be defined in axial, radial, andcircumferential terms. Axial homogeneity refers to the unifor-mity of the material from one end to another. Radial homoge-neity refers to the uniformity of the material from the centeroutward. Circumferential homogeneity refers to the uniformityof the material around a concentric circle.8.1.3 At any level (Z) the latter two are measured byselecting a number of positions on the analytical face of eachsample to be so characterized.The number and position of eachis a rationalization between the size and shape of the analyticalface and the size of Spark-AES burn spot. A sufficient numberof spots are chosen to represent a reasonable sampling of thesurface. Although the sample is resurfaced between samplingsand material is removed for any one test piece, this resurfacingis not to be considered a change in Z.8.1.4 Two common forms encountered are demonstrated inFigs. 2 and 3. A rationalization of sample size versus spot sizedictates a seven-position strategy for round samples in therange of 25 mm to 50 mm in diameter and a nine-positionstrategy for square samples in the range of 25 mm to 50 mmacross. For the round geometry, circumferential homogeneity iscovered with Positions 1–6. Comparisons of these to Position7 covers radial homogeneity. For the square geometry, circum-ferential homogeneity is covered with Positions 1–8. Compari-sons of these to Position 9 covers radial homogeneity.8.1.5 Each position is sampled four times. The positions aresequenced randomly. A typical sequence would be a1,a2, . ai,. anwhere aiis the ith randomly chosen position and n is thetotal number of positions. Four such sequences are run. Theresultant data are derandomized and presented as a 4 × nmatrix. The resultant matrix is processed in accordance withSection 12.8.1.6 If this process is applied at any level (Z), then theentire solid can be characterized.8.2 Within-Unit Homogeneity (R, Θ)—