Metals, except in a few instances, are crystalline in nature and, except for single crystals, they contain internal boundaries known as grain boundaries. When a new grain is nucleated during processing (as in solidification or annealing after cold working), the atoms within each growing grain are lined up in a specific pattern that depends upon the crystal structure of the metal or alloy. With growth, each grain will eventually impinge on others and form an interface where the atomic orientations are different.

As early as the year 1900, it was well known that most mechanical properties were improved as the size of the grains decreased. A few notable exceptions exist where a coarse grain structure is desired. Alloy composition and processing must be controlled to achieve the desired grain size. Metallographers examine polished cross sections of specimens from appropriate locations to determine the grain size.

Grain size measurement is complicated by a number of factors. First, the three-dimensional size of the grains is not constant and the sectioning plane will cut through the grains at random. Thus, on a cross-section we will observe a range of sizes, none larger than the cross section of the largest grain sampled. Grain shape also varies, particularly as a function of grain size. One of the earliest studies of grain shape was made by Lord Kelvin in 1887. He showed that the optimum space-filling grain shape, with a minimum surface area and surface tension, is a polyhedron known as a tetrakaidecahedron, which has 14 faces, 24 corners, and 36 edges. While this shape meets most grain criteria, it does not satisfy the required 120 degree dihedral angles between grains where three adjacent grains meet at an edge, unless the faces exhibit a minor amount of curvature. Another ideal grain shape, the pentagonal dodecahedron, agrees well with observations of grains, but is not a space filling shape. It has twelve five-sided faces. However, it must be recognized that we are sampling grains with a range of sizes and shapes. In most cases, the grains observed on a polished cross-sectional plane exhibit a range of sizes around a central mean and individual measurements of grain areas, diameters, or intercept lengths exhibit a normal distribution. In the vast majority of cases, we merely determine the mean value of the planar grain size, rather than the distribution. There are cases where the grain size distribution is not normal but bimodal, or "duplex." Also, our grain shapes can be distorted by processing procedures so that they are flattened and/or elongated. Different product shapes, and different processing procedures, can produce a variety of non-equiaxed grain shapes. This, of course, does influence our ability to measure the grain size.

Grain size measurement is also complicated by the different types of grains that can be present in metals, although their fundamental shapes are the same. For example, in body-centered cubic metals, such as Fe, Mo, and Cr, we have ferrite grains; in face-centered cubic metals, such as Al, Ni, Cu, and certain stainless steels, we have austenite grains. The grains exhibit the same shapes and are measured in the same way, but we must be careful in describing what kind of grains we are measuring. In the face-centered cubic metals, we may observe so-called twin boundaries within the grains (see sidebar on grain types). Aluminum alloys, however, rarely exhibit twins. When twins are present, they are ignored if we are trying to define the grain size. However, if we are trying to establish a relationship between microstructure and properties, for example, strength, we must consider twin boundaries as they influence dislocation movement, just as grain boundaries do. Hence, we must recognize the intent of the work being performed.

In heat-treated steels, it is recognized that the grain size of the product of the heat treatment, usually martensite, is not measured or cannot be measured. For low-carbon steel, the martensite forms in packets within the parent austenite grains. In high-carbon martensites, we do not observe any convenient structural shape that can be measured. In most cases, we try to measure the size of the parent austenite grains that were formed during the high temperature hold during the heat treatment. This is usually referred to as the "prior-austenite grain size" and it has been widely correlated to the properties of heat treated steels. The most difficult process here is the etching procedure needed to reveal these prior boundaries. Sometimes they cannot be revealed, particularly in low-carbon steels. In this case, it may be possible to measure the low-carbon lath martensite packet size, which is a function of the prior-austenite grain size.

Another complicating factor is the different measures of grain size. The
planimetric method, described below, yields the number of grains per square
millimeter area, N_{A}, from which we can calculate the average grain
area, A. It is common practice to take the square root of A and call this
the grain diameter, *d*, although this assumes that the cross sectional
shape of the grains is a square, which it is not. The intercept method yields
a mean intercept length, L_{3} ; its relationship to N_{A},
A, or *d *is not exceptionally well defined. A variety of planar grain
size distribution methods have also been developed to estimate the number
of grains per unit volume, N_{v}, from which the average grain volume,
V, can be calculated. The relationship between these spatial measures of
grain size and the above planar measures is also ill-defined.

It is now common to express grain sizes in terms of a simple exponential equation: (Equation 1)

**n = 2 ^{G - 1 }**

where:

n = the number of grains per square inch at 100X magnification, and

G = the ASTM grain size number.

This approach was developed and introduced in 1951 with the premiere of
ASTM standard E 91, Methods for Estimating the Average Grain Size of Non-Ferrous
Metals, Other Than Copper and Their Alloys. Although the N_{A},
*d*, or L_{3}, values had been used for many years as measures
of grain size, the G values were adopted readily due to their simplicity.
As shown in Eq. 1, we can directly relate the number of grains per unit area
to G, but the relationship between L_{3}, and G, or N_{V}
and G are not as clearly defined. This problem is one of many being addressed
by ASTM Committee E4 on Metallography.

Although Committee E-4 was formed in 1916 for the express purpose of
establishing standard magnifications for micrographs, its first standard,
E 2-17T, Methods of Preparation of Micrographs of Metals and Alloys, was
partly devoted to grain size measurement. Two basic approaches to measure
grain size were being developed at that time. In the United States in 1894,
Albert Sauveur published a "planimetric" approach, which was further developed
by Zay Jeffries with two 1916 publications. This approach measured grain
size in terms of the number of grains visible on a cross section within a
fixed area, the number per square inch at 100X, or the number per square
millimetre at 1X, N_{A}. From this value, the average cross-sectional
area of the bisected grains can be computed. This is not an average of the
maximum cross-sectional area of each grain because the sectioning plane does
not intersect each grain at its maximum width.

In Germany in 1904, Emil Heyn published an intercept approach for measuring grain size. In this method, one or more lines are superimposed over the structure at a known magnification. The true line length is divided by the number of grains intercepted by the line. This gives the average length of the line within the intercepted grains. This average intercept length will be less than the average grain diameter but the two are interrelated.

Many grain size raters expressed the need for simpler ways to estimate the grain size. In some cases, such as heat clearance, grain size measurement is required. In many cases, it is required that G be 5 or greater (i.e., "fine- grained"). Hence, if the grain size is substantially finer than this, a quick method, which may not be as precise as an actual measurement, is adequate. A comparison chart method with examples of grain sizes meets this need adequately, as long as the grain size distribution is normal. Additionally, the specimens should be etched in the same manner as depicted on the chart. If the grain size is near the specification limit, an actual measurement is preferred due to the improved precision. The first grain size comparison chart was introduced in Methods E 2 in its 1930 revision; this chart was for copper.

Note that these methods are applied on the polished surface of the specimen,
that is, on a plane that cuts through the three-dimensional grains. Thus,
these are planar rather than spatial measures of the grain size. The planimetric,
or Jeffries method, defines the grain size in terms of the number of grains
per unit area, the average grain area, or the average grain diameter, while
the Heyn intercept method defines it in terms of the average intercept length.
The comparison chart method expresses the grain size only in terms of G,
except for the copper charts, which use *d*.

Methods E 2-17T was only slightly more than three pages long and had three sections: standard magnifications, lenses, and grain size. The grain size section did not actually detail the measurement method, it merely suggested the method to apply depending on whether the grains were equiaxed (Jeffries planimetric method) or elongated (Heyn intercept method). The 1920 revision of Methods E 2 added details on performing the Jeffries planimetric measurement method. The 1930 revision of Methods E 2 witnessed the addition of Committee E-4's first standard chart, a grain size chart (ten pictures) for brass, i.e., a twinned austenitic structure with a grain contrast etch at 75X magnification. The chart was developed by a special committee formed on June 28, 1928, which consisted of: C.H. Davis, chairman (American Brass Co.); Henry S. Rawdon (U.S. Bureau of Standards); Edgar H. Dix, Jr. (Aluminum Co. of America); and Francis F. Lucas (Bell Telephone Laboratories). Types of grain structures are shown in the sidebar on grain types.

A special subcommittee to study grain characteristics of steels was formed in 1931 with Clarence J. Tobin (General Motors Research Laboratory) as chairman. They decided to adopt the McQuaid-Ehn carburizing test for evaluating the grain growth characteristics of steel, again with the aid of a comparison chart. The proposed chart method was approved as E 19-33T, Classification of Austenite Grain Size in Steels. At that time, grain size was defined in terms of the number of grains per square inch at 100X; ASTM grain size numbers were not introduced until much later. However, this chart was criticized for being inaccurate and it was eventually dropped when E 112, Test Methods for Determining the Average Grain Size, was introduced.

Oscar E. Harder took over this special subcommittee in 1936, with the idea of revising Classification E 19 and adding a non-carburizing method. The next year, Dr. Marcus A. Grossman (Carnegie-lllinois Steel Co.) took over control of this group, which became Subcommittee Vlll (Arabic numerals are now used) on Grain Size in 1938. Grossman ---famous for his work on hardenability---was chairman of Subcommittee Vlll until his death in 1952. Subcommittee Vlll formed three sections (the term task group was not used at that time), referred to as A, B, and C. Section A was chaired by Grossman and was concerned with improving Classification E 19 on austenite grain size of steels. Section B was chaired by R. Earl Penrod (Bethlehem Steel-Johnstown Plant) and was to develop a ferrite grain size rating method and chart. Section C was chaired by Carl Samans (American Optical Co., later with Standard Oil Co. of Indiana) and was to develop charts for nonferrous metals and alloys that could not be rated by the brass chart in Methods E 2. The brass grain size chart and grain size measurement information was deleted from Methods E 2 in the 1949 revision and this information was incorporated into a new standard, E 79-49T, Methods for Estimating the Average Grain Size of Wrought Copper and Copper-Base Alloys. Two pictures were added to the chart; later when it was transferred to Test Methods E 112, two more pictures were added (14 in all). Methods E 2 was discontinued in 1984 when E 883, Guide for Metallographic Photomicrography, was introduced.

Section B produced E 89-50T, Methods for Estimating the Average Ferrite Grain Size of Low-Carbon Steels, with a chart depicting a ferritic grain structure as revealed by nital etching. This was the first chart (eight pictures) to define grain size in terms of the now familiar ASTM grain size numbers (1 to 8 in this chart). Methods E 89 also marked the first detailed description of the Heyn intercept method with equations and a conversion approach to yield ASTM grain size numbers. Earlier Methods E 2 versions only gave a general description of how to do the intercept test with no interrelationship to the results from the planimetric method. Methods E 89, however, had a short life, being discontinued when Test Methods E112 was adopted.

Section C produced E 91-51T, Methods for Estimating the Average Grain Size of Non-Ferrous Metals, Other Than Copper, and Their Alloys. This consisted of two charts, one for twinned alloys, the other for non-twinned alloys; both charts had 17 pictures with grain sizes from 2 to 10. Methods E 91 also had a short life, also being discontinued when Test Methods E 112 was adopted. Neither of the charts of Methods E 91 were incorporated in Test Methods E 112.

The net result was four standards (Methods E 19, E 79, E 89, and E 91) dealing with various aspects of grain size measurement. It was recognized that all four shared many common points and it was believed that they could be combined into one overall grain size standard, hence the birth of Test Methods E 112. However, the story of ASTM and grain size measurement does not end with the adoption of Test Methods E 112 in 1961. Since then, the standard has been revised nine times and is presently now under intense scrutiny for further refinement. (webmasters note: E112 has been updated and reissued as E112-96e3)

Test Methods E 112, one of the most widely cited ASTM standards, is chiefly concerned with the measurement of grain size when the grains are equiaxed in shape, that is, non-deformed, although it does contain some information about measurement of grain size when the grains have been elongated by processing. There are other situations where Test Methods E 112 is not helpful and other standards have been developed. For example, certain alloys may not exhibit a uniform distribution of grain sizes. Instead, a bimodal distribution (see sidebar on grain size distributions for examples) may exist; several types have been observed. Two ASTM standard test methods deal with such structures. Standard E 930, Test Methods for Estimating the Largest Grain Observed in a Metallographic Section (ALA Grain Size), is used to measure the size of an unusually large grain in an otherwise uniformly fine grain size distribution, while standard E 1181, Test Methods for Characterizing Duplex Grain Sizes, is used to measure the grain size when the distribution is non-normal. With the growth of image analysis, test methods for performing measurements must be established and a new standard, E 1382, Test Methods for Determining the Average Grain Size Using Semiautomatic and Automatic Image Analysis, completed the balloting process in 1990. This standard describes a number of equivalent approaches for measuring grain size using both tablet digitizer systems and fully automatic systems.

Committee E-4's work on grain size has been followed closely by other industrial countries and the lnternational Organization for Standardization (ISO). Many countries have adopted one or more of the grain size charts of ASTM Test Methods E 112. Some countries have also developed very useful charts. For example, for rating McQuaid-Ehn carburized specimens, most U.S. raters etch the pearlitic matrix dark as depicted in Plate IV of Test Methods E 112. As the sidebar on grain structures demonstrates, it is easier to see the intergranular carbide phase if we use an etchant that darkens the grain boundary cementite. The French grain size standard, NF A04-102, contains a rating chart where the grain boundary cementite was darkened with alkaline sodium picrate. The German SEP 1510 grain size standard also contains a very useful chart. It illustrates non-twinned grains (such as ferrite grains) that are equiaxed or deformed (elongated 2 to 1 and 4 to 1) by cold working. Eq. 1 described the approach used to compute ASTM grain size numbers which, de- veloped in the United States in the late 1940s, was based on English units rather than metric units. Countries that used the metric system at that time developed an alternate equation that produces nearly identical grain size numbers: (Equation 2)

**m = 8(2 ^{Gm})**

where:

m = the number of grains per mm^{2} at 1 X, and

G_{m} = the metric grain size number.

G_{m} is slightly greater than G but the difference is negligible.
Eq. 2 is used in the Swedish (SIS 11 11 01), ltalian (UNI 3245), Russian
(GOST 5639), French (NF A04-102), and ISO (ISO 643) standards.

The German standard (SEP 15l0)also uses the metric system, but a different equation is employed : (Equation 3)

**K= 3.7 + 3.33Log(Z)**

where:

K = the photomicrograph serial number (same as G), and

Z = the number of grains per cm^{2} at 1OOX.

In this case, K equals G. Japanese standards JIS G 0551 and G 0552 also use the metric system, with a slightly different equation than Eq. 2 (but equivalent) that produces the same values as Eq. 2: (Equation 4)

**m = 2 ^{(Gm+3)}**

where m and G_{m} are defined as before.

ASTM Committee E-4 has been a world leader in the standardization of grain size measurement methods. Initially, Methods E 2 recommended the ]effries planimetric method as the preferred measurement method. This method is more difficult to apply on a production basis than the intercept method due to the need to mark off the grains as you count them to minimize counting errors. This is unnecessary with the intercept method.

With the 1974 revision of Test Methods E 112, the intercept method, as modified by Halle Abrams, became the preferred analysis technique. The three-circle intercept method, as described in Test Methods E 112 since 1974, provides a more precise estimate of the grain size in much less time than required by the planimetric method. In manual methods, it is essential to recommend the most efficient method for any measurement.

Test Methods E 112 is designed for rating the grain size of equiaxed grain structures with a normal size distribution; the standard is presently being revised to provide better instructions for rating the grain size of deformed grains. Other standards have been introduced by E-4 to handle the measurement of occasional, very large grains present in an otherwise uniform, fine grain size dispersion (E 930, Methods of Estimating the Largest Grain Observed in a Metallographic Section (ALA Grain Size)) or for rating the grain size when the size distribution is non-normal, for example, bi-modal or "duplex" (E 1181, Methods of Characterizing Duplex Grain Sizes). Committee E-4 has recently developed a grain size standard for ratings made using semiautomatic or automatic image analyzers (E 1382, Test Methods for Determining the Average Grain Size Using Semi-Automatic and Automatic lmage Analysis). No other standards writing organization has developed standards similar to Methods E 930, Methods E 1181 or Test Methods E1382.

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