1. Introduction

Grain size in materials science and metallurgy refers to the size of the individual crystalline grains within a material microstructure. It plays a crucial role in determining the materials' mechanical, physical, and even chemical properties. Grain size and its accurate measurements are fundamental aspects of materials science and engineering. The ability to control grain size allows for the customization of material properties to meet specific application requirements, thereby making it a critical factor in the design and manufacture of materials and components. Grain size measurements are an essential characteristic of microstructures, and they influence different properties of materials, starting from the mechanical properties (strength, toughness, hardness, ductility, etc.). Some key points related to grain size and its measurements are discussed below.

Mechanical properties
Grain size significantly influences a material mechanical properties. Smaller grain sizes often increase hardness and strength, while larger grain sizes show improved ductility and toughness. Engineers and materials scientists use grain size control to tailor the application-specific material properties.

Heat treatment
Grain size control is an essential aspect of the heat treatment process in metallurgy. Heat treatment processes like annealing and quenching can modify grain sizes and, consequently, the material’s mechanical properties.

Corrosion resistance
It is well known that fine-grain materials always show enhanced corrosion resistance compared to coarse-grain materials. So, in areas where corrosion resistance becomes a key parameter, grain sizes should be considered.

Fatigue resistance
It is well known that smaller grains always lead to enhanced resistance against fatigue failure, and so in areas where cyclic loading becomes a key parameter, such as aircraft components, grain size should be carefully taken into consideration for the material applied for that specific application.

Weldability
In welding applications, base material grain size becomes a critical consideration for affecting the strength and quality of welds, so grain size control plays an important role here.

Microstructure analysis
Grain size measurements play a crucial role in characterizing the microstructure of a material. Advanced characterization techniques using microscopy, including optical, scanning electron microscopy, transmission electron microscopy, and x-ray diffraction, are effectively utilized in determining the grain sizes with accuracy and precise control.

Quality control
Consistency of product and quality are always confirmed by any company or industry using grain size measurements. It helps to ensure that the material meets specific performance and standard criteria.

Research and Developments
Grain size studies and measurements are an integral part of developing newer materials with enhanced properties. Researchers use grain size controls to explore novel materials for various industries, from aerospace to electronics

2. Techniques for grain size measurements:
The importance of grain size measurement is established in the previous section. This section discusses about the various measurements techniques known, which include:

• Line Intercept Method
  
• Jefferies Method
  
• Standard ASTM Grain Size Calculations
  

2.1 Line Intercept Method
It is also known as Heyn’s method and is a simple technique used widely in materials science and engineering to estimate the average grain size of polycrystalline materials. It defines a practical way to calculate the grain size from the microstructures of the material cross-section. The brief procedure for calculating the grain size using Heyn’s intercept method is given below:

• Sample preparation
Start using the sample preparation route and create a polished sample cross-section.

• Micrograph acquisition
Capturing a good quality microstructure of the polished cross-section using the microscope

• Selection of Fields
Now, choose regions within the micrographs randomly and carefully try to choose the areas representative of the entire microstructure.

• Drawing lines
Draw lines of known length (mm) on the micrographs in a random orientation to the material's crystallographic structure.

• Counting intercepts
For each line drawn, count the number of times it intersects the boundaries between individual grains. These intercepts indicate the total number of grains intersected by the lines.

• Calculating the mean intercept length (L)

Calculate L by dividing the total length of lines drawn by the total number of intercepts counted. The formula for the same is given below:
L = (Total length of lines) / (Total number of Intercepts)

• Grain size estimation (D)

Use the mean intercept length (L) to estimate the average grain size (D) using the following equations:
D=(L/π)*(1/2)
Where:
D is the estimated grain length
L is the mean intercept length
Π is the constant value, with a value of 3.14

• Repeat and Average
Repeat the above steps to ensure statistical accuracy. Calculate the average grain size from the results obtained in different fields.

Advantages

• It is a relatively straightforward method, doesn’t require any special instruments for study, and is easily accessible to every laboratory for usage.
  
• The average grain size provided is a statistically valid estimate. Calculations were done by sampling the multiple areas within a microstructure.
  
  

Disadvantages

• Equiaxed grain size assumptions (with equal grain sizes in all directions) used during most calculations proved to reduce the formula's accuracy and the calculated results as they are not valid in many cases for different materials.
  

• The accuracy of the obtained results depends on the choice of the fields and the randomness of the line orientations.
  

• This method is more accurate for materials with more grains, and alternate methods are helpful for finer-grained materials.
  

2.2 Jeffries method
This method is known as the planimetrictric method for calculating quantitative grain size. It helps to calculate the average grain size of the metallographic specimen. It is an alternative to other grain size calculation methods primarily used with finer-grained materials. It uses a circular area for calculating the grain sizes. Some key points related to Jeffries grain size calculation methods are given below:

• Principle
The base of this method relies heavily on planimetry, which involves measuring the areas of grains within a micrograph to estimate the grain sizes.

• Sample preparation
Sectioning, mounting, grinding, polishing, and etching are some of the key sample preparation steps that need to be taken care of in this step.

• Micrograph acquisition
Capturing a good quality microstructure of the polished cross-section using the microscope

• Selection of Fields
Now, choose regions within the micrographs randomly and carefully try to choose the areas representative of the entire microstructure.

• Grain area measurements
Use a planimetry tool in each selected field to calculate the visible grains' total area. This is done by boundary tracing for each grain present within the micrograph.

• Calculating the average grain size

Use the formula given below to calculate the average grain size:
Average grain diameter (D) = (Total grain area) / (number of grains * π/4)
Total grain area: combined grain area for all measured grains within a field
Number of grains: Total grain counts within the same field.
π/4 is a constant.

• Repeat and Average

Repeat the above steps to ensure statistical accuracy. Calculate the average grain size from the results obtained in different fields.

Advantage:

• Useful for finer-grained materials
  
• Uses multiple statistical fields to provide meaningful results.
  

Disadvantages:

• Complex process- Higher and more advanced imaging tools are required for precise calculations of grain sizes using this method.
  
• Sample preparation should be very accurate to obtain accurate grain sizes.
  

2.3 ASTM grain size calculation method
The American Society for Testing and Materials (ASTM) calculation method is a standard approach for determining the grain sizes for metallic materials. This method is one of the most commonly used in materials science and metallurgy to quantify the sizes of individual grains in a polycrystalline material. ASTM has its guidelines to be followed for the calculation of grain sizes with accurate results, and the same is shown below:

• Sample preparation
Start using the sample preparation route and create a polished sample cross-section.

• Micrograph acquisition
Capturing a good quality microstructure of the polished cross-section using the microscope

• Selection of Fields
Now, choose regions within the micrographs randomly and carefully try to choose the areas representative of the entire microstructure.

• Identification of the grain boundaries
In each of the selected fields of view, identify and mark the individual grain boundaries, and this step requires distinction from one grain to another. Based on the differences in the crystallographic orientations

• Grain counting
Count the number of grains within each field of view. These counts should be made without grain overlap; each grain must be counted only once.

• Determining the ASTM grain size numbers
Use the grain counts to determine the ASTM grain size number using a table provided by ASTM. The ASTM E112 standard provides a chart that correlates the number of grains per square inch (or per square millimetre) to a specific grain size. Use the standard formula from ASTM given below for calculating the average grain size:

n=2^(N-1)

Where n is the total number of grains visible in the microstructure per square inch, it is measured at 100x magnification.

N = ASTM grain size parameter
It is also important to note that the Grain size is ~ (1/ N)

• Calculating the average grain size
Repeat the above steps several times to ensure statistical significance. Calculate the average grain size by taking the mean of the grain size numbers obtained from different fields.

Advantages:

• This method is standard, widely accepted, and ensures consistency in grain size determination across all laboratories worldwide.
  
• The average grain size provided is a statistically valid estimate, as calculations were done by sampling the multiple areas within a microstructure.
  
• This method is widely accepted for different metals and material systems.
  

Disadvantages:

• Closed pack and complex-shaped grains require some critical evaluation
  
• Extreme care should be taken during the sample preparation and etching; otherwise, grain boundaries cannot be properly revealed, which ultimately alters the grain size calculations.
  
• For extremely large and extremely fine grains, this method is not suitable for calculation.