Intermetallic superconductors have been attracted much attention and investigated for a long time. Fig.1 shows the changes of T_c in intermetallic superconductors. T_c in intermetallic superconductors is much lower than that in copper oxide superconductors. But it is easier to process like metal. Therefore earnest studies are performed for actual application. (On the other hand, copper oxide superconductors are ceramics. Copper oxide superconductors are poor in malleability and ductility. Therefore the copper oxide superconductors have difficulty in processing). Without intermetallic superconductors, superconducting theory like BCS theory could not be established. Moreover, recent discovery of MgB₂, high T_c intemetallic superconductor, enhances the research in this field.

BCS Theory and Precept for Investigation

T_c determinant equation by BCS and the McMillan equation suggests the increase of T_c !!

Basic mechanism of superconductivity was elucidated by the BCS theory published in 1957 and we could know what kind of point of view we should search from. BCS theory describes T_c determinant equation like equation(1). This equation could describe many of superconductors of an early date. However, A15 type superconductors, which were discovered by Matthias couldn’t be described by this equation. Because the equation(1) is obtained that electron interaction V is approximated as V<<1. Because of the considerable V, it couldn’t describe. Therefore it is McMillan equation (equation(3)) that suggested. This equation describe that it put the effect of the considerable V and N(0) into λ. We could describe superconductors that have higher T_c by this.  First, equation(1)and(3) say that it is necessary for heightening T_c to raise lattice vibration frequency (Debye frequency) ω_D. In addition, we could know that it is necessary to raise the density of states around Fermi energy N(0) and V (McMillan equation includes this in λ). But there is no way to measure the value V, so V is not the effective precept of investigation. And it is difficult if we really measure two other parameters. However, Tc is surely high with a light element of mass (By equation(2)) to be high Debye frequency when we take notice of the movement of the discovered superconductors by today, and the compound that has the higher density of states around Fermi energy has higher T_c in A15 type superconductors. Though it is accountable for the compounds that we presented here, it does not apply to all superconductors. For example, copper oxide superconductors that having high T_c does not correspond with almost things that we presented here. However, making consideration that superconductors in intermetallic compounds are good agreement, it’s not necessarily appropriate to suggest that the condition for high T_c from the BCS theory is pointless. It can become precept of investigation.

The Light element is advantageous for T_c !?

From the BCS theory, the high Debye frequency and the elements that mass is light are advantage for T_c. The element which having light mass is called light element, there is not a rule in particular, but from hydrogen to calcium on a periodic table correspond to a light element. The element taking lattice vibration ionizes in crystals. The electron-lattice interaction that forms cooper pairs is the interaction between ions forming this lattice and conduction electrons. If ions are heavy ( Fig.3(a) ), the electrons which came over within this lattice is strongly attracted. And because the mass is heavy, this lattice takes time to return to original form this time. However, if ions are light ( Fig.3(b) ), the lattice warps moderately. And because the mass is light, the lattice doesn’t take time to return to original form much. Therefore the light elements can form cooper pairs in the case of the heavy elements at the interval that is shorter and early. It is caused by such a thing that light elements are advantageous.  In this way the light element has advantage for superconductivity at a glance, when we try to watch in real system, beryllium (Be) is T_c = 0.03 K though Debye frequency is big. And lead (Pb) is T_c = 7.19 K, that has the low Debye frequency, there is the part which it is hard to have advantage for superconductivity unconditionally. However MgB₂, which has the best T_c in the intermetallic compound, is suggested that big lattice vibration caused by boron contributes to superconductivity expression greatly. Even if I think from this, the materials including light elements might have the superconductors having higher T_c.

The high density of states around Fermi level is advantageous for T_c !?

B.T.Matthias who comes up to find many superconductors propounded that the intermetallic superconductors have correlation between T_c and mean electric charge value. This is called Matthias rule. Later, it was known as rules of thumb that can hold true of a lot of transition metal superconductors well, but this allows for the effect that heighten the density of states around Fermi level, that BCS theory suggested that the effect is advantage for T_c. In normal conducting states, it is filled by electrons below Fermi surface and no electron exists above Fermi surface like Fig.5. In superconducting states, electrons result Bose-Einstein condensation below the Fermi level. Basically, all electrons which can form Cooper pairs is only the electrons that exist around Fermi surface. By BCS theory, it is assumed that it is advantage for it realizing high T_c to make N(0) large, but this increases the electrons that it can be superconducting electrons, and many electrons relate to expressing superconductors.The way of like this, making N(0) large, is helpful to investigating a new superconductor from existing superconductors like Matthias. NaCl-type(B1-compounds) and A15-type analogous superconductors are discovered by this idea. By similar method, an analogous material that has higher Tc might be discovered. ・    Crystal Structures of Superconductors in Intermetallic Compound Superconductors in intermetallic compound have been discovered more than 1000 type. And, there is the superconductor that plays an active part in an aspect of application because the history of superconducting search is long. Here, we show a characteristic of the crystal structure mainly on the material that updated T_c in that.

Crystal Structures of Superconductors in Intermetallic Compound

NaCl-type(B1-type) superconductors

In the history of superconductivity, this NaCl-type(B1-type) compounds are the first superconductor that is over 10K. Mainly, it is a combination of transition metal (Ti,Zr,Hf,V,Nb,Mo,W) and carbon(C) or nitrogen(N). NbN has the highest T_c=17.7K in these compounds.  In these superconducting compounds, TMN(transition metal nitride) compounds become higher in the case of all TMC(transition metal carbide) compounds. That is interpreted that it is the consequence of the effect of which changing the C atom to N atom increase the density of states around Fermi level. In Mo, MoC indicated T_c=13K which was high T_c for those days, therefore the compound in MoN was expected room temperature superconductor. Unfortunately, MoN is difficult to compose it by a single-phase, hasn’t been reported superconductivity with high temperature expected, lower than NbN, in the superconductors confirmed superconductivity. And NbN_1-xC_x indicates superconductivity at 17.7K that exceed it more a little than NbN. Triggered by discovery of a superconductor of this system, superconducting search in intermetallic compound became active, too.

A15-type superconductors

A15-type superconductors are the first materials that exceed 20K. In 1954 the first superconductor in A15-type superconductors appeared then it was studied for power by a study group of Matthias, and many superconductors were discovered in a relation material. In this system, Nb₃Ge indicates the highest T_c=23.5K (However this is thin film).   A15-type superconductors have the composition ratio of A₃B and take crystal structure such as Fig.7. Almost site A is transition metal and site B is Ge or Sn.   The superconductor makes use of the comparatively high T_c and the metal property that it is easy to treat, and it is studied power with an aspect of application with Nb-Ti alloys. Nb₃Sn has been studied as a coil of a superconducting electromagnet. A15-type superconducting coil is used for in the MRI (Magnetic Resonance Imaging) that there is in hospitals. A15-type superconductors show the power as SQUID (Superconducting QUantum Interference Device) device in MPMS (Magnetic Property Measurement System) when we measure physical property of our composed sample.

A₃C₆₀ (A: Alkali metal) superconductors

It is a superconductor of C₆₀ (Fullerene) that was discovered when a copper oxide superconductor has begun to come into the limelight. Fullerene attracted 60 C and took a soccer ball type. From the past, that this structure was possible was expected, but many studies did it from interest of the structure when really discovered. It is the superconductor that T_c is comparatively high of Fullerene in itself T_c = 17 K, but alkali metal having the biggest ion radius in a simple substance element and C form A₃C₆₀. Though alkali metal do not show superconductivity, a point to show superconductivity by forming huge C₆₀ crystal as ions is interest. The superconductor having the best T_c in this system is T_c = 33 K of RbCs₂C₆₀ (At high pressure, Cs₃C₆₀ shows superconductivity in T_c = 40 K).   For a material comprising carbon, there are graphite, diamond and carbon nanotube other than fullerene. Recently, superconductivity develops with the diamond that doped hole, and it is the system that can enliven something and the world of a superconductivity study. Room temperature superconductor may be discovered in a carbon compound sometime soon.

Borocarbide superconductors YPd₂B₂C, YNi₂B₂C

In 1994, when was lively by prevalence of copper oxide superconducors, these borocarbide superconductors YPd₂B₂C (T_c = 23 K) and YNi₂B₂C (T_c = 15.6 K) were reported by Cava and Takagi. The crystal structure is shown in Fig.8, it can make of a kind of layer structure which consisting of YC layer and Ni₂B₂ layer (Electrical conductivity looks like three-dimensional). It is YPd₂B₂C that T_c is high, but composition of a single-phase sample can be difficult, and now it is YNi₂B₂C mainly that is studied. It is thought that a 3d electron of transition metal: Ni is caused by comparatively high T_c from calculations of density of states with this superconductor. In addition, it was suggested that it was conventional BCS superconductor by a result of tunneling spectroscopy. However, shape of superconducting energy gap to be different from BCS superconductor is suggested and, from an experiment of recent thermal conductivity, attracts attention.   In system of YNi₂B₂C, superconductivity is reported in the system that it substituted for Y site in rare-earth element too. Resulting of having substituted it for a Y site in a rare-earth element, it becomes the system that superconductivity competes with magnetism that works to originally disturb a superconducting state. Therefore the interesting superconducting transition called reentrant type superconductor (superconducting state fails once and returns to superconductivity again) is observed in RENi₂B₂C (RE: Ho, Er, Tm) system.

Layered nitride superconductors

It is a superconductor of the serial halogen nitride that what was reported in 1998 is called layered nitride. It shows superconductivity at T_c = 25.5 K in Li_xHfNCl which only one showing the highest T_c in this system showed in Fig.10.   As a characteristic of this material, because Li is intercalated between Cl - Cl for a characteristic of this material, superconductivity appeared. Original material HfNCl forms bi-honeycomb structure, which is layer structure that is comprised of HfN layer and the Cl layer. In addition, it is a big characteristic that a Cl - Cl interval consists of Van der Waals binding having weak binding power. It is famous for Graphite, but it can insert the other element with having kept crystal structure between such layer and can give a change of physical properties more. By intercalating Li into Li_xHfNCl, the electrons were doped in HfN layer and Li_xHfNCl have reached superconductivity.   In this system, a lot of superconductors of a relation material are found. In ZrNCl discovered for the same time period when HfNCl was discovered, superconductivity is confirmed electrons dope by intercalation and hole dope of ZrNCl_1-x which was pulled Cl element. In addition, in the material which is intercalated organic compounds between the Cl and Cl layer, superconductivity of 20 K grade is confirmed.   Layered niteride superconductors are more developing stage and discovery of materials having higher T_c is expected.

Boride superconductors MgB₂

It is superconductor of boride MgB₂ that was reported with an opening scene of a play of the 21st century. It was paid attention very much by having shown T_c equal to copper oxide superconductors of T_c = 39 K. In addition, because of the light weight, the inexpensive materials' cost, and possibility of reduction in cost by a processing process, when it compare this material with a copper oxide superconductors, this materials are gathered interest from the side of application as superconducting wires by can have merits.

Now, the development of the MgB₂ wire is being performed in Japan, America and Europe, and it is an aspect like development competition variously exactly as to the MRI with 20K the substitution of the device and before material (Nb-Ti and Nb3Sn) under liquid helium cooling.  As for the crystal structure of MgB₂, it is it with strong structure of 2 dimensions characteristics that B layer comprising Mg layer comprising triangle lattices and honeycomb lattice did laminating in turn in a c axis direction like Fig.10. On this account the result that strongly reflected dimension characteristics in a material property of MgB₂ is observed.  After discovery of this superconductor, an intermetallic compound came into the limelight again, and a superconductor search of boride and carbide of relation thrived. As a result, various superconductors were discovered, but the superconductor, which is beyond T_c of MgB₂, is not discovered in a relation material.

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