ASTM E562-99

Designation: E 562 – 99
Standard Test Method for
Determining Volume Fraction by Systematic Manual Point
1
Count
This standard is issued under the fixed designation E 562; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
This test method may be used to determine the volume fraction of constituents in an opaque
specimen using a polished, planar cross section by the manual point count procedure.
1. Scope 3.2.2 point fraction—the ratio, usually expressed as a per-
centage, of the point count of the phase or constituent of
1.1 This test method describes a systematic manual point
interest on the two-dimensional image of an opaque specimen
counting procedure for statistically estimating the volume
to the number of grid points, which is averaged over n fields to
fraction of an identifiable constituent or phase from sections
produce an unbiased estimate of the volume fraction of the
through the microstructure by means of a point grid.
phase or constituent.
1.2 The use of automatic image analysis to determine the
3.2.3 stereology—the methods developed to obtain informa-
volume fraction of constituents is described in Practice E 1245.
tion about the three-dimensional characteristics of microstruc-
1.3 This standard does not purport to address all of the
tures based upon measurements made on two-dimensional
safety concerns, if any, associated with its use. It is the
sections through a solid material or their projection on a
responsibility of the user of this standard to establish appro-
surface.
priate safety and health practices and determine the applica-
3.2.4 test grid—a transparent sheet or eyepiece reticle with
bility of regulatory limitations prior to use.
a regular pattern of lines or crosses that is superimposed over
2. Referenced Documents the microstructural image for counting microstructural features
of interest.
2.1 ASTM Standards:
2
3.2.5 volume fraction—the total volume of a phase or
E 3 Methods of Preparation of Metallographic Specimens
2
constituent per unit volume of specimen, generally expressed
E 7 Terminology Relating to Metallography
2
as a percentage.
E 407 Practice for Microetching Metals and Alloys
3.3 Symbols:
E 691 Practice for Conducting an Interlaboratory Study to
3
Determine the Precision of a Test Method
E 1245 Practice for Determining the Inclusion or Second
P 5 total number of points in the test grid.
T
th
Phase Constituent Content of Metals by Automatic Image
P 5 point count on the i field.
i
2
Analysis
P
P (i) 5
i
P
3 100 5 percentage of grid points, in the
P
T
3. Terminology th
constituent observed on the i field.
3.1 Definitions—For definitions of terms used in this prac-
n 5 number of fields counted.
n
¯
tice, see Terminology E 7. P 5 1
p
P ~i! 5 arithmetic average of P (i).
(
p p
3.2 Definitions of Terms Specific to This Standard:
n
i 5 1
s 5 estimate of the standard deviation (s) (see (Eq
3.2.1 point count—the total number of points in a test grid
3) in Section 10).
that fall within the microstructural feature of interest, or on the
95 % CI 5 95 % confidence limit562.0s/ n21 (see
=
feature boundary; for the latter, each test point on the boundary
Note 1).
is one half a point.
V 5 volume fraction of the constituent or phase
V
expressed as a percentage (see (Eq 5) in Section
1
This practice is under the jurisdiction of ASTM Committee E-4 on Metallog-
10).
raphy and is the direct responsibility of Subcommittee E04.14 on Quantitative
% RA 5 % relative accuracy, a measure of the statistical
Metallography.
¯
precision 5 (95 % CI/ P ) 3 100.
Current edition approved October 10, 1999. Published December 1999. Origi- p
nally published as E 562 – 76. Last previous edition E 562 – 95.
NOTE 1—The multiplier is given as 2.0 for purpose of definition. Table
2
Annual Book of ASTM Standards, Vol 03.01.
3 1 gives the appropriate multiplying factors for any number of fields
Annual Book of ASTM Standards, Vol 14.02.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
1

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E 562
TABLE 1 Prediction of the Number of Fields (n) to be Observed as a Function of the Desired Relative Accuracy and of the Estimated
Magnitude of the Volume Fraction of the Constituent
33 % Relative Accuracy 20 % Relative Accuracy 10 % Relative Accuracy
Amount of volume
Number of fields n for a grid of P 5 Number of fields n for a grid of P 5 Number of fields n for a grid of P 5
T T T
fraction, V in percent
v
16 25 49 100 16 25 49 100 16 25 49 100
points points points points points points points points points points points points
2 110 75 35 (20) 310 200 105 50 1,250 800 410 200
5 50 30 (15) (8) 125 80 40 (20) 500 320 165 80
10 (25) (15) (10) (4) 65 40 (20) (10) 250 160 85 40
20 (15) (10) (
...