Dear Ahmad,

While it is conceptually correct that the degree of etching is related to the relative energy of the grain boundary, it is not practically a very good or unambiguous way to study boundary energies. This is partly due to what Dr. Nolze pointed out about etching being an unexact, subjective process. The other factor is that the contrast we see in LOM is because of the difference between energy stored within the grain and at the grain boundary (hence 'relative'). So even for the same material, if specimens are identically etched at different annealing conditions, you may notice a difference in the visual clarity of grain boundaries. As for grains being differently coloured, this is often a consequence of these grains having different orientations. The etching behaviour of different materials is certainly different, you may not draw much inference from that.

Now coming to grain boundary energy, it is quite a complicated process experimentally. One approach applies the physics of interfaces, line tension and interfacial energy to grain boundaries (Ref[1] Chapter 3). Allied is the measurement of thermal grooves - as you are looking at etching I think this might be of interest (Ref [2], Chapers1,4). Another way is to conduct calorimetric studies of grain growth, measure the change in energy and relate it to the change in grain boundary length. This is mentioned in Ref [1] but I am not aware of published work in this area. Another method is to measure the boundary velocity of a given boundary in-situ upon heating, and determine the grain boundary mobility, which is in turn used to determine boundary energy (Ref [2]).

A fourth method, experimentally popular, is based on the CSL model. In this, low angle boundaries and CSL boundaries are assigned precise energy values based on geometry of the boundary (Ref [2], Chapter 2). The remaining high angle boundaries (non CSL) are assigned a constant common value, typically taken from previous literature on the material of interest (Ref [3]). The length of CSL boundaries and non CSL high angle boundaries is determined using EBSD, and the multiplied with the respective energy values to get an overall grain boundary energy for the microstructure studied (not for an individual boundary).

Refs:

[1] Grain boundaries in metals, D. McLean

[2] Grain boundary migration in metals, Gottstein & Shvindlerman

[3] http://pajarito.materials.cmu.edu/rollett/27750/L18-GB_props-Energy-05Apr16.pdf

You can try holographic TEM - Electron holography. However, you will need to well prepare the sample and measure carefully.

All etchants are the results of trial-error procedures mixed with long-time experience. There is no "science" behind it. It enables us to define simple models for correlations.

There are grain-boundary etchants, or color etchants. They have totally different reasons. The first attacks lattice defects, the second is very sensitive with respect to the surface orientation. I believe you could find for practically each phase an etchant which preferably attacks grain boundaries. However, as for color etching or EBSD you do not need to see the grain boundaries (which are anyway only "a few nm thick" and not that big as etched and visible by light microscopy. You can also derive them by measuring grains and simply define this object between as grain boundary. Never see but anyway derived... Regarding grain boundary energies I am not sure whether we are talking about the same thing. I guess, you define grain boundary as expression of the "energetically" effective for conductivity, mechanical deformation, corrosion etc... You don't want really calculate the energy, but you are looking for some kind of classification of boundaries which enables you the explanation of any discovered experimental result, do you? I mean, everything is explainable by the killer argument "energetic reasons". Practically, it does not tell you anything. If your calculations do not match, either the calculations are wrong, the experiment is wrong or both. Only the match of these calculations do not automatically tell you that you are right. It is comparable to the operation 2+2 and 2*2. Both give the correct result but only one formulation is correct if you use these operators with other numbers. 

Dear Ahmad,

While it is conceptually correct that the degree of etching is related to the relative energy of the grain boundary, it is not practically a very good or unambiguous way to study boundary energies. This is partly due to what Dr. Nolze pointed out about etching being an unexact, subjective process. The other factor is that the contrast we see in LOM is because of the difference between energy stored within the grain and at the grain boundary (hence 'relative'). So even for the same material, if specimens are identically etched at different annealing conditions, you may notice a difference in the visual clarity of grain boundaries. As for grains being differently coloured, this is often a consequence of these grains having different orientations. The etching behaviour of different materials is certainly different, you may not draw much inference from that.

Now coming to grain boundary energy, it is quite a complicated process experimentally. One approach applies the physics of interfaces, line tension and interfacial energy to grain boundaries (Ref[1] Chapter 3). Allied is the measurement of thermal grooves - as you are looking at etching I think this might be of interest (Ref [2], Chapers1,4). Another way is to conduct calorimetric studies of grain growth, measure the change in energy and relate it to the change in grain boundary length. This is mentioned in Ref [1] but I am not aware of published work in this area. Another method is to measure the boundary velocity of a given boundary in-situ upon heating, and determine the grain boundary mobility, which is in turn used to determine boundary energy (Ref [2]).

A fourth method, experimentally popular, is based on the CSL model. In this, low angle boundaries and CSL boundaries are assigned precise energy values based on geometry of the boundary (Ref [2], Chapter 2). The remaining high angle boundaries (non CSL) are assigned a constant common value, typically taken from previous literature on the material of interest (Ref [3]). The length of CSL boundaries and non CSL high angle boundaries is determined using EBSD, and the multiplied with the respective energy values to get an overall grain boundary energy for the microstructure studied (not for an individual boundary).

Refs:

[1] Grain boundaries in metals, D. McLean

[2] Grain boundary migration in metals, Gottstein & Shvindlerman

[3] http://pajarito.materials.cmu.edu/rollett/27750/L18-GB_props-Energy-05Apr16.pdf