1. a) The reason is in the used system of units:  the Susceptibility of the Gaussian system and the SI differ in pi time, despite the fact that is a dimensionless quantity: xi(Gauss) = xi(SI)/4pi = -1/4pi for ideal superconductors. b) When we say that xi is less than -1, it means that xi is smaller in modulus (absolute value) in the SI system.

2. In reality, we cannot achieve absolute zero temperature.

3. Susceptibility for real superconductors deteriorates due to the residual resistance which is in real conductors even at absolute zero temperature (see Mattissen rule). Therefore, the induction currents, which create a diamagnetic moment and is responsible for diamagnetism, be less than that required for complete quenching (compensation) of the external magnetic field.

You have also to take into account the real field which depends on the demagnetizing factor of the sample : a sphere, a disc parallel or permendicular to the applied field ... will give various "apparent" diamagnetic susceptibility values

To dr Tholence:

Dear Jean,

You're right about the necessity of taking into account the sample shape. However, the so-called “demagnetizing” field in any form of pattern in the case of a diamagnetic substance will be “magnetizing” field, i.e. directed towards the same external field. Thus, the absolute value of the sample magnetization will reach even larger values than in the absence of demagnetizing factor. The apparent value of the modulus of the susceptibility should be even higher.

Sincerely,

AM

for the superconducting volume fraction, you could try measuring a reference sample made of a "perfect superconductor" which has the same shape and size as the real sample you are measuring. 

you can then take the ZFC susceptibility of the reference sample as a hypothetical 100% of volume fraction and compare it to the magnitude of your real sample. 

With ceramics, the ac susceptibility can be large in very small fields when there are

screening currents between the superconducting grains (Josephson currents) . It becomes smaller when the applied field is larger, so that the screening is due to the currents of all the individual grains.

So, to evaluate the superconducting fraction of a ceramics sample, it is better to take an ac field as large as 1 gauss or more (not to see the screening through the contacts between grains)

Previous answers are right about demagnetizing factor, and reference to a (Pb, Sn..) spherical superconductor, for calibration.

Folks!! I think you have not yet answered all of my questions yet.

Please let me know the answers and then start correcting among yourself.

I am not able to be online everyday because of the floods out here!!

Thanks

Dinesh

Dinesh,

A perfect diamagnet would indeed have a susceptibility of -1. A superconductor is formed by the pairing of wavefunctions of electrons of complementary spin. This forms what is called a "Cooper Pair." As with all materials, the wavefunctions of the electrons (and Cooper Pairs) must transition continuously across any boundary, a surface is such a boundary. The wavefunction's derivatives must also be continuous across the boundary.

This gives rise to two interesting and related effects:

Now that we understand that the superconductor will ALWAYS have a region where it is less "good" near the surface it becomes clear that the concept of perfect diamagnetic susceptibility is a simplistic exercise that is used as a very good approximation for materials where the volume of the surface layer of the superconductor is considerably less than that of the total superconductor.

Now for the other questions:

I am afraid that, like much in the real world the answer really begins with "it depends...." For the need/non-need of a factor of 4pi and so on -- this depends on the units (cgs/mks/other)  system which you are working within. In SI (mks) units it is dimensionless however depending on whether or not it is a volumetric or mass based measurement there are factors that enter into the numerical value.

Insofar as using Field Cooled vs. Zero field cooled measurements of the susceptibility to determine the volume fraction of the sample that is superconducting the technique presumes that:

I hope that this helps.

Grover Larkins

To Alexander T. Morchenko, Grover Lamar Larkins, Jean Louis Tholence and Alma Dorantes

Dear All,

Thank you so much for all the answers, I have learnt so much from all of the conversations above I will always be grateful to you all (and of course researchgate team). 

I feel I have understood all of what have been written by you all.

Sincerely,

Dinesh Kumar

Dear Dinesh, regarding to your question for the ideal superconductor the susceptibility equal (-1) and actually it is smaller one. that is depend on the concept of London equations which states the presence of partial magnetic field penetrate a limited area of the superconductor surface. this will make creating induced surface current. this is the reason why the susceptibility is smaller than (-1). for more details you can go to the subject London equations in any text book containing a chapter in the superconductivity.           

Surface currents are exactly the same for a full Pb sphere as for an empty one.

In a ceramics sample they can give a larger susceptibility in very low fields (due to Josephson contacts between grains) than in larger ac fields where each grain has its own circulating current at the surface of the grain

Susceptibility value "-1" (SI) is performed in perfect quality samples 1 type superconductors, for example, a Pb purity relative RRR samples at least 1000. It is the full realization of the Meissner effect, ie. the total displacement of the magnetic field from the sample or, in other words, the outer appearance of the magnetic induction field directed opposite of the initial induction field inside the specimen. Meaning | chi |

Susceptibility value "-1" (SI) is performed in perfect quality samples 1 type superconductors, for example, a Pb purity relative RRR samples at least 1000. It is the full realization of the Meissner effect, ie. the total displacement of the magnetic field from the sample or, in other words, the outer appearance of the magnetic induction field directed opposite of the initial induction field inside the specimen. Meaning | chi |