Thank you very much sir. Textbooks show that growth rate is maximum near Tm, but you showed that it follows the same pattern as nucleation rate. Please explain where the difference is coming from
Growth rate depends noth on the driving force and the atomic mobility. Near Tm atomic mobility is high but te driving force is close to zero. So, the growth rate does not attain maximum close to Tm.
Sir, could you explain why Growth rate (G) is dominant at high temperature and Nucleation rate(I) is dominant at low temperature in T vs. I,G,dx/dt graph? I am not sure why Growth rate graph(G) which is biased toward Tm and Nucleation rate graph(I) is biased toward 0K. Why do those two graphs have that kind of shape?
I think nucleation rate depends on under cooling(difference in temperature between melt and cooling), as we increase under cooling temperature nucleation rate is increased....hence it is favoured at low temperature.....
@@introductiontomaterialsscience Can we give the explanation as, 1) Growth occurs by diffusion. At high temperature, diffusion is higher. So at high temperature growth rate dominates. 2) At low temperature critical radius is less. So the probablity of formation of a stable nuclie is more. So at low temperature, nucleation rate dominates. ?????????????????
@@MOLTEN1818 This seems reasonable. But then again at very high temperature, say T=Tm the growth rate becomes zero although diffusion should be extremely high. Similarly, at 0 K the critical radius is least, but nucleation rate is still zero.
Sir, why does fractional transformation was low in the beginning?? Sir is it due to less no. of nuclei in the beginning? And if so why formation of nuclei takes time???
Yes, it is low because there are less number of nuclei. Formation of nuclei requires atomic movement and probabilistic creation of critical cluster. This requires time.
Sir could you please explain why the growth rate maximum is occuring at high temperature than the max nucleation rate? Or the reason why at high temperature growth rate is dominant
@@introductiontomaterialsscience sir can i think of diffusion ( the concentration gradient) as the reason. Diffusion is dominant at high temperatures. For nucleation to take place concentration gradient is high(fully liq to first solid) so diffusion can occur even at low temperature because of this high concentration gradient.. Where as for growth process the concentration gradient is low( from liquid to already formed solid, meaning a less gradient).. So growth should relatively require more temperature due to less concentration gradient. Can this be a possible assumption or am I wrong sir?
Sir, in some books and papers, the growth rate is shown max at melting point temperature and gradually decreases with temperature and finally zero at 0K. However, you have shown growth rate to be zero at melting point temperature, gradually increases to maximum at some intermediate temperature and then decreasing back to zero at 0K temp. Sir, can you please explain the fallacy. Although, in those references, nucleation rate and overall transformation rate nature is shown similar to your video.
This is an interesting and important question. Could you please share the references of those books. I would like to have a look before giving an answer.
@@introductiontomaterialsscience Sir, kindly look into the following references. References: 1. BOOK: Material Science and Engineering An Introduction (8th Edition) by William D. Callister CHAPTER 10: Phase Transformations (Sub topic : The Kinetics of Phase Transformations FIG 10.8: (Pg353) Schematic plot showing curves for nucleation rate, growth rate, and overall transformation rate versus temperature. 2. Fig 11, Dai, T., Wheeling, R.A., Hartman-Vaeth, K. et al. Precipitation behavior and hardness response of Alloy 625 weld overlay under different aging conditions. Weld World 63, 1087-1100 (2019). doi.org/10.1007/s40194-019-00724-1
@@abhinababanerjee683 Thanks Abhinaba for raising this issue and bringing these two references to my notice. And thanks again for reminding me. I have now looked at both the references. I think both these references are considering growth rate to vary in the same manner as the diffusion rate. But this clearly has a problem. The diffusion rate continues to increase even above the transformation temperature. But certainly, there should zero growth rate above the transformation temperature. So it is not correct to think that the growth rate simply depends only on the diffusion rate. It also depends upon the driving force for the transformation, which is zero at the transformation temperature and increases below it. It is this zero of the driving force at the transformation temperature which brings the growth rate as well as the nucleation rate to zero at the transformation temperature. I hope I have clarified.
@@rajeshprasad101 Thank you Sir for your clarification. So, precisely speaking both the references are incorrect since they have incorporated only the diffusion rate parameter while plotting the growth rate graph and completely neglected the driving force parameter.
The thermodynamic analysis presented here indicates that some undercooling is essential for nucleation. At the melting point the free energies of solid and liquid phases are equal. So the driving force for nucleation is zero and no nucleation is expected.
@@rajeshprasad101 sir thank you for reply. I want to add that given free energies of both solid and liquid phase are same at melting temperature then saying that melting or solidification occurs at melting point temperature is wrong??
@@rajeshprasad101 It is true that growth rate is given in ms^-1, but at the same time if we know the radial change of volume (i.e. sphere) we can easily evaluate the volume change.
