I have estimated avg. domain/grain size (D) from Williamson-Hall (W-H) plot for thin foils of copper after heat treatment experiment. I have considered UDM, USDM and UDEDM model for this estimated value from XRD data.
Now I want to co-relate my estimated value of 'D' with the SEM image of Cu-foil. Can anyone suggest how to do this process? Or any other approach in context to this?
Samit Karmakar
Your apparently simple question raises a number of issues not the least that you may be comparing apples with turnips. What's the reason for comparing? What if they are similar (how close?) and what if they are different? OK, some points to ponder:
- XRD will examine many millions of domains/crystallites in as much as (say) 1 g of sample and the W-H (or other) analysis will provide an 'average' size. Now what is the form of that average - is it volume, projected area, or intensity weighted? To what shape is the 'average' related in order to provide a single number? Disc? Sphere? Is it a volume weighted surface area mean (D[3,2])? Surprisingly, it appears that scientists haven't really considered this aspect of moment means in XRD
- XRD provides a single number and doesn't provide a crystallite size distribution when we know one is present
- SEM allows us to directly examine the domain/crystallite structure. Thus, we have some idea of the shape and structure of the domains and also a qualitative view of the distribution of shapes and sizes. This is essential
- SEM provides a 2D image and the stated value for any single domain is usually referenced to 'circular equivalent' to deal with the shape issue (where there are many 'shapes' and ways to express them. See ISO9276-6)
- The average we obtain from microscopy and image analysis is usually the (projected/2D) area weighted by number of considered particles (D[2,0] - see attached)
- SEM is generally looking at small number (and therefore small masses, say ng or pg) of sample, so there are heterogeneity issues to consider. We need to sample a statistically significant number of sampled particles/domains in order to get a robust statistical value. For a 1% standard error on the mean we'd need 10000 random particles imaged and counted. For extremes in the top tail of the distribution we’d require large sample masses
So, summarizing, what averages do we compare in the case of XRD and SEM? Are we comparing like with like on the same measured sample (instead of a small fraction of the sample)? Are the measured samples representative of the whole? Is the crystallite distribution tight or broad?
Prof. Alan F Rawle ,
Sir, In point no. 4, you have mentioned "SEM provides a 2D image". .... Doesnt TEM pruduce 2D images??
Aarif Hussain Shah
A 2D image is processed for information in both TEM and SEM. Unfortunately, shape (and particles) is a 3D issue... Also many shape descriptors (e.g. aspect ratio) are ratios of linear dimensions in 2 dimensions. A confocal microscope can help but adds to the complexity. Consider slicing objects (or better still, a single object) in 2D (e.g. cubes or spheres). See attached from Claude Bragdon A Primer of Higher Space Manas Press (1913). See how different shapes need to be interpreted in 2 dimensions...
Dear Dr. Alan F Rawle, I am immensely thankful for your detailed but very easily understandable explanation to my query. I truly gained knowledge from your answer. I will read the shared technical paper of yours for better understanding.
These are two different aspects to consider and need not be co-related.
Dr. Alan F Rawle , can you please share the full text of ISO 9276-6:2008 Representation of results of particle size analysis — Part 6: Descriptive and quantitative representation of particle shape and morphology? If possible.
Samit Karmakar
Unfortunately, I can't post an ISO (or ASTM document) on this forum. You can obtain standards from your local standards authority (I believe it's the Bureau of Indian Standards (BIS) in India) or on-line with the appropriate payment. Both ISO and ASTM exist solely through sales of their standards. Copying them and circulating is unethical and piracy. These bodies would cease to exist if their standards were freely available - what would be the consequence of that? These standards are created by unpaid volunteers (such as myself) who spend long hours of (financially) unrewarded (but maybe rewarded in other ways?) time on these.
One point in my answer that I wasn't completely clear on (although it's obvious in careful examination) is that the averages from the W-H analysis may not be the same average(s) from microscopy/SEM. Are we comparing a D[3,2] (?) with a D[2,0]? Do we need to convert the form of one average to another? From reading the attachment, this difference should be immediately obvious.
And, lastly, your domains/crystallites are obviously 3 dimensional not 2. What is the 'average' shape of a domain? I always think (or feel) that it's like a grain of rice (or a nematic liquid crystal), but my intuition is often wrong. How do they pack together in 3 dimensions?
Dear Dr. Alan F Rawle , I will search on BIS website. I agree with you.
Yes, I am also considering 3D not 2D for my copper foil. Hence, while estimating in W-H analysis, USDM and UDEDM approach are much more convenient considering anisotropic approach instead of isotropic approach in UDM.
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