The hardness of a material is generally related to the grain size through a Hall-Petch equation (HV=Ho+Kd-1/2). So, in a nanomaterial that consists of different size how can find variation of hardness with grain size.
Do you mean that you have a bimodal/multimodal distribution of grain sizes?
Are you asking about an equation that has a parameter for the distribution in it or about what methods you would actually measure them?
If it is the measurement of the material then It depends on what scale you want to measure your hardness over. Are you interested in the overall hardness of the material, if so standard macro/micro indentation should give you the answer because these measure a number of grains at any one time. If you are looking for hardness of individual grains or micro/nanostructural features then nanoindentation may give you the answers you are looking for, but you need to consider the size of features you are looking at and the applied contact area of the indentation tip. For very small features you might need low loads and cube corner indentation, but beware of indentation size effects.
Dear Martin
Thank you for your swift respond.
Actually, I am a little confused. Some of the articles show, a correlation between hardness with grain size based on Hall-Patch method. But, It is not clear that grain size how measured in the a nano powders. For more information, please find the attachment article and look to P. 4862 as highlighted.
I would be grateful, If I get you respond.
Dear Armin
The paper available on link below may help you:
Article Nanomechanics of Hall-Petch Relationship in Nanocrystalline Materials
Dear Armin Rajabi,
The review paper by Pande & Cooper is excellent, but as far as I can see it does not contain indications about the measurement of grain size in the nanometer-range. They start their paper by stating: Nanocrystalline materials are polycrystalline materials consisting of grains in nanometer range. Apparently they assume that the grain size in the nanometer range can be defined and measured. By definition the orientation on both sides of a grain border differs randomly. Otherwise, the grains concerned would show crystallographic links like twinning or defined crystallographic relationships. The foregoing means that a reliable determination of the grain size in the nanometer range will involve electron microscopy. X-diffraction line broadening can also result from crystallite size. It is suggested that analysis of X-ray diffraction line broadening in terms of crystallite size and micro and/or macro strains could be an additional approach.
See also: Klug and Alexander: X-ray diffraction procedures
Dear Armin Rajabi,
In case the nanocrystalline alloy can be conceived as a two-phase system (see the the oxide strengthened austinitic alloy of the above indicated paper 36.pdf) misift strains may contribute to X-ray line shift and broadening and be part of the strengthening mechanism. For the case of Al alloys this was studied earlier. See attached reference, especially Section III.1 thereof: Unusual lattice parameters in two-phase systems after annealing.
https://www.researchgate.net/profile/P_Mourik/publications?pubType=thesis
https://www.researchgate.net/profile/P_Mourik/publications?pubType=thesis
Sorry for interrupting ..but am having a problem and that is ... I have developed iron based composite where in am using solid lubricant and the process followed is powder metallurgy and with the addition of solid lubricant in the base matrix I am having increase in hardness with a decrease in density.Is it possible. KIndly help me out
Dear sanjay mohan Sharma,
Assuming that your observations are correct, the statement is that it is indeed possible that your treatment yielded a hardness increase combined with a density decrease. Then, an explanation remains to be given. Do you think that a chemical reaction of the lubricant with the iron based composite is possible yielding an intermetallic contributing to an average hardness increase and an average density decrease?
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