As pointed out by careful viewers, see below, the maximum solubility of C in Fe is only 2.1 wt%. (sometimes taken to be 2 wt%) My mistake. :-(. The corresponding atom % is then only about 9% rather than 16% mentioned in the video. This makes the argument that maximum solubility is much more limited than the geometrical maximum of 50% even stronger.
I would like a better explanation of Hume-Rothery’s rules for interstitial solid solutions. I know there are electronegativity and valency and crystal-structure and “other” factors in addition to atomic-size factors in determining how soluble a solid solute is in a solid solvent especially if one of them is a metal. I am especially interested in the “other” and the valency. This lecture is the best explanation I’ve found so far, and the only one to which the lecturer answers questions.
Hume-Rothery rules are applicable only to a substitutional solid solution. The rules are conditions under which one can have complete solid solubility or, in other words, no solid solubility limit. This is never possible in interstitial solid solution. Because if we fill all the interstitial sites we reach the solubility limit. But in substitutional solid solution, it may be possible to replace all the solute atoms by solvent atoms. Still, it is not always possible, the Hume-Rothery rules specify when it is likely. I am not sure whether I have been able to answer your question. Please do ask back.
Rajesh Prasad lectures on Materials Science If I look on Wikipedia for Hume-Rothery rules I see two sets; one for substitutional solutions and one for interstitial solutions. The ones for interstititial solutions don’t make sense. But there may be rules for predicting whether an interstitial solution of one metal in another is likely; and it seems likely Hume-Rothery would have worked them out. And it seems likely Wikipedia would have partly screwed them up, or relied on sources which had screwed them up. Do you know of good rules for interstitial solid solutions? Can you look at Wikipedia’s article on Hume-Rothery and correct those rules? Nothing I can find with Google, or following Wikipedia’s bibliographical footnotes, is an improvement. My sister is a science teacher; I asked her and she said she didn’t know. I’m impressed with how understandable your lecture is; so I thought, if there’s someone who can do for interstitial solutions what Hume-Rothery did for substitutional solutions, and make me understand, it might be you. .... Thanks for asking me to reply to your reply!
@@tomhchappell Thanks for bringing this to my notice. I agree with you that the rules of interstitial solution does not make sense. In fact the original question of Hume-Rothery itself does not make sense for interstitial solution. I say this because the originally Hume-Rothery tried to figure out the conditions for complete solid solubility, that is the absence of any solubility limit. This condition simply is unattainable in interstitial solid solution simply because once all the interstitial sites are filled one cannot accommodate any more. In reality, the solubility limit is much below this geometrical limit. I think the Wikipedia author is getting the size factor of 59% from the fact that maximum size to fit in an octahedral void in CCP or HCP is 41%. (0.414 R). But many interstitials, like C in Fe have much larger radius. So when they go to the interstitial site they cause a lot of strain and this is what limits the solubility to a value much below the geometrical limit.
Introduction to Materials Science and Engineering Thank you sir! I calculated some void sizes. 1-(sqrt(3)/2) = 13.4% for triangular void Sqrt(3/2)-1 = 22.47% for tetrahedral void Sqrt(2)-1 = 41.42% for octahedral void (or square void) Sqrt(3)-1 = 73.21% for cubic void (maybe only if solvent is polonium? needs a basic cubic or simple cubic structure) If the solvent’s crystal structure is simple cubic, couldn’t the interstitial solution be equimolar? Couldn’t its share in the solution rise to 50at% if its atoms fit into the cubic voids? ....... For metallic glasses (which aren’t crystals, so though they’re solid solutions, they’re not substitutional nor interstitial because there’s no lattice), the size-ratio of cubert(0.5) = 79.37% seems important. Cube roots instead of square roots. Another difference; if the smaller atoms are SMALLER than the 79.37% size of the largest atoms, we apparently get better glass-forming ability out of the alloy if another metal whose atoms are intermediate in size is introduced. Do glass-forming alloys do better when equal volumes of the components are used, rather than equal numbers of atoms or equal masses? Do you have a lecture on metallic glasses I should watch? Thank you again!
If carbon size is larger than void size,it may introduce compressive and tensile effect ? how it affect the cell size ? can we use other atom in void ie lesser than carbon ? how does it effect the properties?
May I know which of the 4 rules in the Hume-Rothery rules have a higher priority? Eg: I got 2 rules (atomic size and electronegativity) which satisfy but the other 2 (crystal structure and valency) doesnt.
The structure rule is of the highest priority. If the crystal structure is not the same then one simply cannot get complete solid solubility even if the other rules are satisfied.
sir, I had a question. for a substitutional solid solution, I got the point of its unlimited solubility. but here are all of the atoms are not the same by radius then why not their produce strain?
An Octahedral void is larger than a tetrahedral void. But C is larger than the octahedral void. So if it goes to tetrahedral void it will create larger strain than if ir goes to the ctahedral void.
Sir, Hume rothery rules are applicable only to substitution solid solution or it is applicable to both substitution solid solution and interstitial solid solution
This is indeed an interesting question. The substitution we are talking about is not a physical process but a mental one. Ni is FCC and so is Cu. So if you mentally substitute Cu atoms one by one by Ni atoms you will end up with FCC Ni. If you think of it as a physical process then you will not get pure Ni. Cu atoms have to be somewhere in the system,.
You have asked an interesting question. If you apply Hume-Rothery rules we find that they satisfy all the rules. But they still do not for complete solid solution. This is an example of failure of the rules to predict the actual situation. It highlights the fact that it is just a rule-of-thumb and not a fundamental rule which is always expected to be true.
These are the rough rules of thumb. In this particular case, the two radii are not very different. So I just casually took Delta r/ rNi. If we take Delta r/r_Cu we get 2.3% which is not very different. If the two radii are significantly different then one can take the mean radius in the denominator.
As pointed out by careful viewers, see below, the maximum solubility of C in Fe is only 2.1 wt%. (sometimes taken to be 2 wt%) My mistake. :-(. The corresponding atom % is then only about 9% rather than 16% mentioned in the video. This makes the argument that maximum solubility is much more limited than the geometrical maximum of 50% even stronger.
In steel maximum soluility 2.1
in cast iron 6.7
In gray cast iron higher than 6.7 upto 9%
Your Honesty is admirable sir :)
at 12:6 how u get 50wt%c in Fe.
plz tell
@@missionbeingmech9550 1 C+1Fe=2atoms. atom%C=(No. C/Total no)x100=(1/2)X100=50%
Please tell about geometrical limit
I would like a better explanation of Hume-Rothery’s rules for interstitial solid solutions. I know there are electronegativity and valency and crystal-structure and “other” factors in addition to atomic-size factors in determining how soluble a solid solute is in a solid solvent especially if one of them is a metal. I am especially interested in the “other” and the valency.
This lecture is the best explanation I’ve found so far, and the only one to which the lecturer answers questions.
Hume-Rothery rules are applicable only to a substitutional solid solution. The rules are conditions under which one can have complete solid solubility or, in other words, no solid solubility limit. This is never possible in interstitial solid solution. Because if we fill all the interstitial sites we reach the solubility limit. But in substitutional solid solution, it may be possible to replace all the solute atoms by solvent atoms. Still, it is not always possible, the Hume-Rothery rules specify when it is likely. I am not sure whether I have been able to answer your question. Please do ask back.
Rajesh Prasad lectures on Materials Science If I look on Wikipedia for Hume-Rothery rules I see two sets; one for substitutional solutions and one for interstitial solutions.
The ones for interstititial solutions don’t make sense.
But there may be rules for predicting whether an interstitial solution of one metal in another is likely; and it seems likely Hume-Rothery would have worked them out.
And it seems likely Wikipedia would have partly screwed them up, or relied on sources which had screwed them up.
Do you know of good rules for interstitial solid solutions?
Can you look at Wikipedia’s article on Hume-Rothery and correct those rules?
Nothing I can find with Google, or following Wikipedia’s bibliographical footnotes, is an improvement.
My sister is a science teacher; I asked her and she said she didn’t know.
I’m impressed with how understandable your lecture is; so I thought, if there’s someone who can do for interstitial solutions what Hume-Rothery did for substitutional solutions, and make me understand, it might be you.
....
Thanks for asking me to reply to your reply!
@@tomhchappell Thanks for bringing this to my notice.
I agree with you that the rules of interstitial solution does not make sense. In fact the original question of Hume-Rothery itself does not make sense for interstitial solution. I say this because the originally Hume-Rothery tried to figure out the conditions for complete solid solubility, that is the absence of any solubility limit. This condition simply is unattainable in interstitial solid solution simply because once all the interstitial sites are filled one cannot accommodate any more. In reality, the solubility limit is much below this geometrical limit.
I think the Wikipedia author is getting the size factor of 59% from the fact that maximum size to fit in an octahedral void in CCP or HCP is 41%. (0.414 R). But many interstitials, like C in Fe have much larger radius. So when they go to the interstitial site they cause a lot of strain and this is what limits the solubility to a value much below the geometrical limit.
Introduction to Materials Science and Engineering
Thank you sir!
I calculated some void sizes.
1-(sqrt(3)/2) = 13.4% for triangular void
Sqrt(3/2)-1 = 22.47% for tetrahedral void
Sqrt(2)-1 = 41.42% for octahedral void (or square void)
Sqrt(3)-1 = 73.21% for cubic void
(maybe only if solvent is polonium? needs a basic cubic or simple cubic structure)
If the solvent’s crystal structure is simple cubic, couldn’t the interstitial solution be equimolar?
Couldn’t its share in the solution rise to 50at% if its atoms fit into the cubic voids?
.......
For metallic glasses (which aren’t crystals, so though they’re solid solutions, they’re not substitutional nor interstitial because there’s no lattice), the size-ratio of cubert(0.5) = 79.37% seems important. Cube roots instead of square roots.
Another difference; if the smaller atoms are SMALLER than the 79.37% size of the largest atoms, we apparently get better glass-forming ability out of the alloy if another metal whose atoms are intermediate in size is introduced.
Do glass-forming alloys do better when equal volumes of the components are used, rather than equal numbers of atoms or equal masses?
Do you have a lecture on metallic glasses I should watch?
Thank you again!
Great explanation sir .....🙏🙏🙏😊😊😊 thanks for making this vedio sir 🤗🤗
best explanation on hume rothery rules
Thank you sir for such a great explanation 😊
Am doing Amie by following ur videos I scored good marks sir thanks alot
Hello,i have few questions about AMIE .. could you please help me?
If carbon size is larger than void size,it may introduce compressive and tensile effect ? how it affect the cell size ? can we use other atom in void ie lesser than carbon ? how does it effect the properties?
29:50 Sir, shouldn't the valencies be same(& not 'close')?
Great explaination thanks!
May I know which of the 4 rules in the Hume-Rothery rules have a higher priority?
Eg: I got 2 rules (atomic size and electronegativity) which satisfy but the other 2 (crystal structure and valency) doesnt.
The structure rule is of the highest priority. If the crystal structure is not the same then one simply cannot get complete solid solubility even if the other rules are satisfied.
@@rajeshprasadlectures Thank you very much
👍👍👍👍
carbon maximum solubility in iron is 2%
Thanks for pointing this out. You are right. the maximum solubility of C in Fe is only 2 wt%.. My mistake. :-(
sir, I had a question.
for a substitutional solid solution, I got the point of its unlimited solubility.
but here are all of the atoms are not the same by radius then why not their produce strain?
Unequal sized atoms in a substitutional solid solution do producr strain.
SIR WHY CARBON ATOM OCCUPY OCTAHEDRAL VOIDS, NOT TETRAHEDRAL IN FCC UNIT CELL?
An Octahedral void is larger than a tetrahedral void. But C is larger than the octahedral void. So if it goes to tetrahedral void it will create larger strain than if ir goes to the ctahedral void.
Sir, Hume rothery rules are applicable only to substitution solid solution or it is applicable to both substitution solid solution and interstitial solid solution
Only to substitutional solid solution.
Sir To where Copper atom went after the Nickel atom fully substituted.
This is indeed an interesting question. The substitution we are talking about is not a physical process but a mental one. Ni is FCC and so is Cu. So if you mentally substitute Cu atoms one by one by Ni atoms you will end up with FCC Ni. If you think of it as a physical process then you will not get pure Ni. Cu atoms have to be somewhere in the system,.
25.03 .. Cubic closed pack zinc?can it really exist?
Not cubic close-packed. HCP: Hexagonal close-packed.
No, CCP zinc cant exist, that's why complete solid solubility is not possible in this case.
Sir, are hume-rothery rules applicable only for substitutional solid solutions?
Yes.
Thank you very much, Sir. It's a great explanation, but a have some doubts. Can you explain why Al-Ni does not present an extensive solid solution?
You have asked an interesting question. If you apply Hume-Rothery rules we find that they satisfy all the rules. But they still do not for complete solid solution. This is an example of failure of the rules to predict the actual situation. It highlights the fact that it is just a rule-of-thumb and not a fundamental rule which is always expected to be true.
@@rajeshprasadlectures Thank you very much Sir.
Pardon me sir,The max solubility of carbon in gamma iron is 2.1%
Thanks for pointing this out. You are right. the maximum solubility of C in gamma Fe is only 2.1 wt%.. My mistake. :-(
@@introductiontomaterialsscience your honesty is really appreciable sir,
Thank u so much sir
Ha saruuuu
At 29:00 why ∆r/rNi? why not ∆r/rCu?
These are the rough rules of thumb. In this particular case, the two radii are not very different. So I just casually took Delta r/ rNi. If we take Delta r/r_Cu we get 2.3% which is not very different. If the two radii are significantly different then one can take the mean radius in the denominator.
@@rajeshprasadlectures thank you sir😊
save your time.... watch it at 1.5X ... best explanation of hume rothery rule though
Ya i watched it at 1.5x