Hi All,
The following equation is suggested to estimate grain size changes due to grain growth during annealing
Dn - D0n=K(t-t0)
I have seen in many papers that the n is obtained by plotting ln(D-D0) vs ln(t-t0), but isn't this wrong?? How can the equation above be rewritten as
nln(D-D0)=k(t-t0)?
This is correct only if D0 is much smaller than D, so Dn -Don ~ Dn
But, if Do is not that small compared to D, how "n" is calculated??
I would be grateful if you would clarify this issue for me.
Thanks in advance for helping.
Dear Ahmad Zafari,
We worked about this problem, few years ago, about pore migration and grain growth kinetics in uranium dioxide during long annealing times, up to 300 h. We had a big and homogenous data avalaible to fit this kind of equations, typically one used by MacEwan et Hayashi : G(t)n-G0n = k(t).tm with k=k0 exp(-Q/RT). That means there are four parameters (n, m, k0, Q) to fit the data ; so, many set of these parameters (n1, m1, k01, Q1), or (n2, m2, k02, Q2) or (,,,) are digital solutions. What you have to do is to investitage what physical mechanism(s) can be involved in the grain growth.
Please read our publication for more details here inclosed
Refer this link:https://www.upc.edu/cmem/recerca/.../grain-growth
Refer this link:www.u.arizona.edu/~deymier/deymier_group/refs/miscal5.pdf
Refer this link:https://books.google.co.in/books?isbn=3867276846
Refer this link:iopscience.iop.org/0965-0393/11/6/004
Dear Ahmad Zafari,
Some remarks:
*As far as I can see, it is impossible to rewrite original equation into nln(D-D0)=k(t-t0) without further assumptions.
*A possible way to deal with Dn - D0n=K(t-t0) is to assume that (D-Do)n
equals K(t-to).
However, some physical considerations should be available to justify the above indicated rewriting. It should be noticed that the application of the original equation also demands a physical justification.
Dear Ahmad Zafari,
We worked about this problem, few years ago, about pore migration and grain growth kinetics in uranium dioxide during long annealing times, up to 300 h. We had a big and homogenous data avalaible to fit this kind of equations, typically one used by MacEwan et Hayashi : G(t)n-G0n = k(t).tm with k=k0 exp(-Q/RT). That means there are four parameters (n, m, k0, Q) to fit the data ; so, many set of these parameters (n1, m1, k01, Q1), or (n2, m2, k02, Q2) or (,,,) are digital solutions. What you have to do is to investitage what physical mechanism(s) can be involved in the grain growth.
Please read our publication for more details here inclosed
Measure the initial grain size before the annealing treatment => problem solved.
Hello everybody.. could you do me a favor and answer my question...
I want to know the type of the mechanism of grain growth for Specified value of n.
For example, when value of n is between 2 and 2.5, what is mechanism of grain growth?
Amirhossein,
First how sure are you about the difference between 2 and 2.5? These values are obtained from curve fitting so I don't think 2 and 2.5 are much different as the difference may stem from calculation error.
In my opinion, n just shows the mobility of grain boundaries: a larger n represents slower boundary migration, as for example, solute drag effect increases n value to > 2 (e.g. 4).
Hope this helps.
Ahmad
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