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BCS theory (1 Viewer)
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tommykins
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回复: BCS theory
These pairs are formed when one electron distort the positively charges ions in the lattice to move inwards towards the electron. This creates a region of increased positive charge density. Due to the elasticity of the lattice, the region propagates throughout the lattice as a wave. The second electron passing through the lattice is attracted to this moving region, and is “swept” along by the lattice wave created by the first electron, essentially “pairing” up into Cooper pairs. This is called electron-lattice-electron interaction.
BCS theory was developed in 1957 by John Bardeen, Leon Cooper, and John Schrieffer in order to explain why superconductivity occurs. BCS theory describes the formation of electron pairs, or Cooper pairs, moving through the crystal lattice unimpeded and bypassing the obstacles in the crystal lattice which were responsible for electrical resistance. Bardeen, Cooper, and Schrieffer knew electrons normally repel each other and decided there must be some overwhelming attractive force between electrons of a Cooper pair. This attractive force was suggested to be phonons; packets of sound energy also acting as force particles. The process that occurs between Cooper pairs and the crystal lattice is called the electron-lattice-electron interaction.
Essentially, Cooper pairs form when one electron passes through a lattice and as a result distorts the lattice of positively charged ions inwards towards the electron, creating a region of increased positive charge density. This electron is said to release a phonon into the lattice to pull the lattice closer. Due to the elasticity of the lattice, this region is propagates through the lattice as a wave. The phonon is then retrieved by the second electron which is attracted into this moving region of increased positive charge density, and the second electron is effectively swept along by the lattice wave created by the first electron. The second electron pairs-up with the first electron and also transfers the retrieved phonon to the leading electron to be reused to distort another section of the lattice. Thus by pairing off two by two, the electrons pass smoothly through the lattice without losing energy.
Hence BCS theory explains superconductivity and the absence of electrical resistance (below the critical temperature) through Cooper pairs and electron-lattice-electron interaction.
The lone electron also gains passage but if I remember correctly, the pair produces a bigger positive charge density, allowing electrons to flow through more easily -> less resistance.
These are from my notes, haven't been able to learn it completely yet. Please point out if theres any mistakes.
These pairs are formed when one electron distort the positively charges ions in the lattice to move inwards towards the electron. This creates a region of increased positive charge density. Due to the elasticity of the lattice, the region propagates throughout the lattice as a wave. The second electron passing through the lattice is attracted to this moving region, and is “swept” along by the lattice wave created by the first electron, essentially “pairing” up into Cooper pairs. This is called electron-lattice-electron interaction.
BCS theory was developed in 1957 by John Bardeen, Leon Cooper, and John Schrieffer in order to explain why superconductivity occurs. BCS theory describes the formation of electron pairs, or Cooper pairs, moving through the crystal lattice unimpeded and bypassing the obstacles in the crystal lattice which were responsible for electrical resistance. Bardeen, Cooper, and Schrieffer knew electrons normally repel each other and decided there must be some overwhelming attractive force between electrons of a Cooper pair. This attractive force was suggested to be phonons; packets of sound energy also acting as force particles. The process that occurs between Cooper pairs and the crystal lattice is called the electron-lattice-electron interaction.
Essentially, Cooper pairs form when one electron passes through a lattice and as a result distorts the lattice of positively charged ions inwards towards the electron, creating a region of increased positive charge density. This electron is said to release a phonon into the lattice to pull the lattice closer. Due to the elasticity of the lattice, this region is propagates through the lattice as a wave. The phonon is then retrieved by the second electron which is attracted into this moving region of increased positive charge density, and the second electron is effectively swept along by the lattice wave created by the first electron. The second electron pairs-up with the first electron and also transfers the retrieved phonon to the leading electron to be reused to distort another section of the lattice. Thus by pairing off two by two, the electrons pass smoothly through the lattice without losing energy.
Hence BCS theory explains superconductivity and the absence of electrical resistance (below the critical temperature) through Cooper pairs and electron-lattice-electron interaction.
The lone electron also gains passage but if I remember correctly, the pair produces a bigger positive charge density, allowing electrons to flow through more easily -> less resistance.
These are from my notes, haven't been able to learn it completely yet. Please point out if theres any mistakes.
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Forbidden.
Banned
When I looked up this information in my Physics for Scientists and Engineers textbook its explanation is similar to the HSC's explanation except it has some mention about Coulomb forces (electrostatic forces) which aren't in the syllabus.
I don't complete understand.
From what I gather.
The lattice shifts so there is like a tunnel if you like, that accelerates the electrns due to the positive charge.
I also assume the 0 resistance is due to the stronge electric field of these cations guiding the electrons through?
So how does the cooper pair come into it?
If the cooper pair merely allows more electrons, it would merely mean more current would be allowed through and not explain the zero resistance at all.
Further clarification is needed:/
From what I gather.
The lattice shifts so there is like a tunnel if you like, that accelerates the electrns due to the positive charge.
I also assume the 0 resistance is due to the stronge electric field of these cations guiding the electrons through?
So how does the cooper pair come into it?
If the cooper pair merely allows more electrons, it would merely mean more current would be allowed through and not explain the zero resistance at all.
Further clarification is needed:/
tommykins
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回复: Re: BCS theory
Alright - at superconductivity state (or approaching it)
An electron moves along the lattice let o be the electron(s)
o---------------o---------------------o--------------------o------------>o
the superconductivity can be explained by the electron moving through, disrupting the lattice by creating a phonon (positive charge density area) which is "left behind" by an electron as it travels through the lattice, let ~ be the phonon area.
~~o-----------~~o------------------~~o----------------~~~o------------~~~~>o
the electron behind it is attracted to this phonon space, pairing the electrons up. so it then becomes -
~~oo~~---------~~oo~~----------~~~oo~~~-----------~~~~oo~~>
as more pairs are established, they leave a bigger trail of phonons which then attract other electrons to keep flowing without any resistance.
sorry if it's confusing, best way i could think of putting it.
Alright - at superconductivity state (or approaching it)
An electron moves along the lattice let o be the electron(s)
o---------------o---------------------o--------------------o------------>o
the superconductivity can be explained by the electron moving through, disrupting the lattice by creating a phonon (positive charge density area) which is "left behind" by an electron as it travels through the lattice, let ~ be the phonon area.
~~o-----------~~o------------------~~o----------------~~~o------------~~~~>o
the electron behind it is attracted to this phonon space, pairing the electrons up. so it then becomes -
~~oo~~---------~~oo~~----------~~~oo~~~-----------~~~~oo~~>
as more pairs are established, they leave a bigger trail of phonons which then attract other electrons to keep flowing without any resistance.
sorry if it's confusing, best way i could think of putting it.
Although we haven’t covered this yet in class in detail, my current understanding is that superconductivity arises from the "binding energy" inherent in each Cooper pair. Since the pairs possess a minimum threshold energy to be disturbed or separated, the thermal "knocks" from the lattice around them may be weak enough (corresponding to a 'cool' state) to leave their passage undisturbed -- hence the zero resistance.
Hope that's correct/helps.
Hope that's correct/helps.
darkchild69
Nanotechnologist
This is the worst thing in the physics syllabus.
All the text books are so wrong! Particularly with the concept of a cooper "pair"
Crappy thing is... the people writing and marking the HSC questions know no better and if you answered the question with the REAL answer you would not get the marks...
All the text books are so wrong! Particularly with the concept of a cooper "pair"
Crappy thing is... the people writing and marking the HSC questions know no better and if you answered the question with the REAL answer you would not get the marks...
Pwnage101
Moderator
yeh i was readin bout this at university level - dont actual cooper pairs travel in opposite directions (our current understanding)?darkchild69 said:
wogblogger
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...deBrogulies wave model maybe?
like after first electron enters and creates a positively charged area which attracts a second electron then each electrons 'spin' acts in phase so as to combine?
not sure,, maybe its kinda like when you have currents travelling in the same direction in two wires which causes them to be attracted ( but here its electrons and in opp. directrions(their spin)?)
or am i dreaming?
like after first electron enters and creates a positively charged area which attracts a second electron then each electrons 'spin' acts in phase so as to combine?
not sure,, maybe its kinda like when you have currents travelling in the same direction in two wires which causes them to be attracted ( but here its electrons and in opp. directrions(their spin)?)
or am i dreaming?
Jase
Member
The post by tommykins is a pretty good explanation already.
Electrons in a cooper pair do not 'travel' in opposite directions. Maybe you were reffering to two electrons having opposite 'spins'. As wogblogger said, the spins of the two electrons can combine so that the overall spin on the pair is different. All this talk about spin, phase and waves can only be interpreted by the quantum mechanical models and are WAY beyond the scope of the HSC. There really is no simple explanation in this model.
However, in the simpler HSC model.. as originially proposed by Leon Cooper, the two electrons travel in the same direction but are separated by quite some distance (at the atomic scale). They are only kept together by the positive ions in the lattice, as explained by tommykins.
While this simplified explanation is far from the complete quantum description of superconductivity, it is sufficient to explain most properties of low temperature superconductors.
Electrons in a cooper pair do not 'travel' in opposite directions. Maybe you were reffering to two electrons having opposite 'spins'. As wogblogger said, the spins of the two electrons can combine so that the overall spin on the pair is different. All this talk about spin, phase and waves can only be interpreted by the quantum mechanical models and are WAY beyond the scope of the HSC. There really is no simple explanation in this model.
However, in the simpler HSC model.. as originially proposed by Leon Cooper, the two electrons travel in the same direction but are separated by quite some distance (at the atomic scale). They are only kept together by the positive ions in the lattice, as explained by tommykins.
While this simplified explanation is far from the complete quantum description of superconductivity, it is sufficient to explain most properties of low temperature superconductors.
Pwnage101
Moderator
maybe i'm wrongJase said:
but the science co-ordinator at my skool went to an inservice thing at sydney uni and got some sheets they gave him, which he forwarded to us, which apaprently contains what the latest understanding of cooper pairs are - they say that contrary to many textbooks, cooper pairs of electrons do infact travel in opposite directions and the inetratction (the pairs) are constantly being formed, broken and reformed
I might be wrong....
here are some good links i found:
http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/coop.html
this is also a great page to read (just taht page):
http://books.google.com.au/books?id=VOo9LAogcKMC&pg=PA226&lpg=PA226&dq=cooper+pairs+opposite+direction&source=web&ots=tDKx_V17YV&sig=I2Z_VCInywVgftHN4ICANuQs5Wo&hl=en&sa=X&oi=book_result&resnum=2&ct=result
- published by cambridge university press
i dunno...
Jase
Member
That's probably a correct interpretation actually. Perhaps I would be wrong to say that they move in precisely the same direction.. but all in all it is simply a very very simplifed visual model. What textbooks are trying to do is to explain something complex at the level of a high school student.
Technically It doesn't really matter how you interpret which way the electrons as single particles move. What's important is that the net result of many many pairs of electrons interacting through the lattice vibrations allow the net movement of charge (current) to flow unimpeded and thus face zero resistance.
Technically It doesn't really matter how you interpret which way the electrons as single particles move. What's important is that the net result of many many pairs of electrons interacting through the lattice vibrations allow the net movement of charge (current) to flow unimpeded and thus face zero resistance.
Darrow
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The best things Ive found with Ideas to implementation is just to shut up and accept that we are learning from a text book
And that the HSC is basically a test where no matter how correct we are, they have a little marking guideline saying what should be right.
So,
Coopers pairs, Positive Holes ugh!
And that the HSC is basically a test where no matter how correct we are, they have a little marking guideline saying what should be right.
So,
Coopers pairs, Positive Holes ugh!
darkchild69
Nanotechnologist
Exactly right!Pwnage101 said:
Hahaha.. I went to that same inservice, lol... Should've seen the look on some of the Physics teachers faces and some of the "but that's not what is in the textbook" replies from some of the teachers, lmao.. Golden.Pwnage101 said:
TEXTBOOK != BIBLE
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The best way to handle the examiner is to quote the coauthor of BCS and author of Cooper pairing Leon Cooper.darkchild69 said:
He wrote in his review article 2 years after the BCS article, that at T<>0 BCS theory can't explain zero resistance and Meissner effect
))So be easy
))His review article:
"Adv. Phys. 8, number 29, 1-44, 1959"
Pwnage101
Moderator
lol nice to see my co-ordinator is not a skeptic and actually told us what he learnt on the day, albeit a little confusingdarkchild69 said:
syriangabsta
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Man this is so nerdy, what has this world come to...why cant we just live in the bush and hunt food and eat it