没有用清晰的语言写，节约时间，以后的专栏也都以速记为主。

一般测量得到的超导零场冷和场冷信号都长这样，下面那根线是零场冷的，上面那根是场冷。

进入超导态后，再加场（ZFC, Zero Field Cooling)；和在正常态下加场，再进入超导（FC, Field Cooling)。这两种的抗磁信号不一致，说明样品不完全是超导体，而是有杂质的。

要注意这里加的外场，小于超导临界磁场，对于typeII的超导体，小于下临界场，所以超导体如果进入超导态的话，一定是迈斯纳态，而不是混合态。

看下面随手画的简图，FC信号是覆盖SC composition2的，但是转变温度却只反映SC而屏蔽了SC composition2。

屏蔽百分比（Shielding fraction）-->零场冷（ZFC）

迈斯纳百分比（Meissner fraction）-->场冷（FC）

Question

How do we measure Miessner fraction and Shielding fraction for superconductors?

I have attached a schematic can anyone please tell me if I am right?

一些回答如下：

All Answers (4)

Grover Lamar Larkins

Florida International University

Dinesh,

What you are describing is a magnetization measurement result. The demagnetizing factor depends upon the shape of the sample in a strong manner. I suggest that you do the measurement on a reproducible and controlled shape of sample and then measure the demagnetization of the unknown and compare it with that of a known superconductor taken well below Tc using the same sample shape and apparatus.

This will give you a better feel than attempting to do things in this manner as ZFC and FC are subject to the consideration of just how far from Hc1 you are and is the material a type II or type I material (I include weakly linked heterogenous grain boundary connected materials as type II, this is not strictly correct but behaviorly similar enough).

One other concern is the sample size -- it must be significantly larger than the penetration depth.....

Hope this helps,

Grover Larkins

Cite

1 Recommendation

O. F. de Lima

University of Campinas

Dear Dinesh,

I agree with the observations of G. Larkins, about the relevance of demagnetizing factor, measuring down to temperatures well below Tc and having sample size much larger then the penetration depth.  However, a good estimate of Meissner fraction can also be made using the usual type of magnetization measurements (ZFC and FC), paying attention to the following:  1) Use a smallest possible value of applied field (e.g. H ~ 5 or 10 Oe), this will ensure staying below Hc1 at  T << Tc;  2) Take measurements down to temperatures well below Tc, ensuring that a full Meissner state is reached. A good indication for that is to get a practically horizontal line of M vs. T in this region. The ordinate value of this line can be associated with 100% shielding for ZFC measurement and with the Meissner fraction for FC measurement (as shown in your sketch);  3) To minimize errors due to demagnetizing factor try to use samples having their length parallel to H at least three times larger than to the other transversal dimensions.

Cite

1 Recommendation

Grover Lamar Larkins

Florida International University

Dear Dinesh,

O.F. de Lima is correct, I would only add that the sample thickness must be at least 10 times the penetration depth.

Of course, if the sample is unknown, the FC/ZFC method is of limited utility as the penetration depth and, whether or not, it is a heterogenously connected set of weak links is also unknown as is Hc1. For very thin samples (small in any dimension in relationship with the penetration depth IN THAT DIMENSION's direction)  Hc1 becomes depressed and may actually go to zero, despite the field strength used to measure it. That is always worth noting when dealing with very small sample volumes with uncertain (and for the High Tc materials, LARGE) penetration depths. The penetration depth for Nb is 39nm and for YBCO it is 150nm in the ab plane and 800nm in the c direction. Note the difference; if your sample size was nbased on the Nb penetration depth you would be totally out of luck using that assumption in a mixed YBCO impure sample to get the SC volume.....

All the best,

Grover

Cite

Jean Louis Tholence

French National Centre for Scientific Research

The Meissner effect is obtained by coolig in a dc field as small as possible.

It is 100% for very good superconductors (type 1 without defect, or type 2 without pinning). In fact, the field can be trapped by defects during the cooling, which results into a reduced meissner effect.

The shielding effect,is measured after zero field cooling, and applying a very small field (<Hc1). It's larger (or equal) to the Meissner effect, since the  shielding currents are the most effective. In a ceramics of HTSC, the shielding effect can be 100% (in very small ac fields) and the Meissner effect 0 (all the flux is trapped during cooling)!