JPH11329112A - Oxide superconducting multi-core wire rod - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an oxide superconducting multi-core wire rod which can meet the performance of high proof strength, a high n value, and high critical current density, and which is useful as a material for a superconducting magnet for a MNR device. SOLUTION: This wire rod is constituted by embedding a group of wire rods formed by bundling plural Ag wire rods in which oxide superconducting filaments are embedded, in a sheath material made of an Ag alloy. Here, the value represented by the equation, R value = (the sum total of cross-sectional areas of metal portions in the Ag wire rods and the Ag alloy sheath material)/(the sum total of cross-sectional areas of the oxide superconducting filaments) is set at 0.9-2.5.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a multifilamentary oxide superconducting wire which has a multicore cross-sectional structure, exhibits a high critical current density, and is useful as a constituent material of a superconducting magnet.

[0002]

2. Description of the Related Art Since rare earth element-alkaline earth element-copper oxide ceramics have attracted attention as oxide superconductors, superconducting phenomena have been studied for a number of composite oxides. For example, Bi-based oxides include a low-Tc phase having a superconducting transition temperature (hereinafter, referred to as “Tc”) of about 80K and a high-Tc phase having a superconducting transition temperature of about 110K.
When the molar ratio of i, Sr, Ca, and Cu is approximately 2: 2: 1: 2 (Bi-2212 type), a low Tc phase is obtained, and when the molar ratio is approximately 2: 2: 2: 3 (Bi-2223 type, However, Bi is partially substituted by Pb), which is known to have a high Tc phase, and any of them is considered promising as a substance showing a good Tc value.

[0003] Oxide superconductors are expected to be used in various applications because of their high Tc and higher upper critical magnetic field as compared with conventional metal-based superconductors. In particular, the Bi-based oxide is expected to have an upper critical magnetic field of 100 T or more at 4.2 K, and a Nb ₃ Sn wire, which is a typical metal-based superconducting wire for a high magnetic field, is at a practical level (10 ⁴ A). / Cm ² ), it is reported that a high current density of 10 ⁵ A / cm ² can be obtained even in a high magnetic field of 21 T or more where it is difficult to flow the current density. For these reasons, oxide superconductors are considered to be applied to superconducting magnets that generate a higher magnetic field than conventional metal-based superconducting magnets, and research and development for them are being actively conducted.

[0004] Specific examples of applications of oxide superconductors include, for example, nuclear magnetic resonance (NM) which plays a very important role in determining the molecular structure of complex protein macromolecules.
R) analyzers. In this NMR apparatus, as the magnetic field increases, the amount of information increases, so that a more detailed molecular structure can be determined, and the time required for measurement can be shortened. Therefore, by using a Bi-based oxide superconducting wire, the production of a superconducting magnet for NMR with higher performance can be expected.

In order to generate a strong magnetic field with a compact superconducting magnet, it is necessary to keep the overall critical current density (overall Jc) obtained by dividing the critical current of the wire rod by the total cross-sectional area at a high value. It is said that if the critical current density (overall Jc) is 100 A / mm ² or more in the magnetic field used, it is at a practical level. In the case of a superconducting magnet for NMR, high magnetic field stability is required in addition to the value of the generated magnetic field itself. In order to secure the temporal stability, a commercially available metal-based superconducting magnet for NMR is operated in a permanent current mode. Permanent current mode means that current is supplied from an external current up to a predetermined current,
Thereafter, the mode is a mode in which the current is continuously supplied to the superconducting coil with the power supply turned off. When the superconducting magnet is operated in the permanent current mode, it is necessary to increase the n value of the wire.

Here, the above-mentioned n value is a value corresponding to a gradient when the energizing current density and the generated magnetic field are each logarithmically slotted, and reflects the longitudinal uniformity of the current distribution in the wire. That is, the cross-sectional structure of the wire, particularly the oxide core (hereinafter, referred to as
The n value increases as the shape of the "oxide superconducting filament" becomes more uniform in the longitudinal direction, which advantageously acts on the persistent current mode. For example, when the oxide superconducting filament is non-uniform in the longitudinal direction, even if the critical current of the oxide superconducting filament is higher than the current flowing through the oxide superconducting filament in one cross section, the critical current in another cross section is higher. When the current is lower than the current, a shunt occurs from the oxide filament to another oxide superconducting filament having a margin for the critical current. then,
Since current flows through the normal conducting portion to generate electric resistance and attenuate the current flowing in the coil, it becomes difficult to operate in the permanent current mode.

The higher the value of n is, the more advantageous the permanent current mode is. For example, in a 1 GHz class NMR superconducting magnet being developed by the National Institute for Science and Technology, the borehole of a metallic superconducting coil is used. In an oxide superconducting magnet proposed to be mounted inside, an n value of 10 or more is required.

When a large current flows in a strong magnetic field, a strong electromagnetic force acts on the superconducting wire.
In order to overcome such electromagnetic force, it is necessary to provide the wire with sufficient mechanical strength. For example, in the oxide superconducting magnet proposed to be mounted in the bore of the metal-based superconducting coil with a 1 GHz class superconducting magnet for NMR, it is expected that a stress of about 160 MPa is always applied. A necessary condition is to have the above proof stress.

[0009]

Generally, the development of oxide superconductors is based on the ratio of width to thickness (aspect ratio) of the cross section of a wire.
Is mainly performed with a tape wire having a diameter of about 10 or more. Since this tape wire is constituted by embedding a plurality of oxide superconducting filaments in a sheath material made of pure Ag, the 0.2% proof stress at 4.2K is 50M.
It is about Pa, which is far below 160 MPa described above. In addition, when processing into a tape shape, the cross section is formed by rolling a round wire with a circular cross section, at this time, the cross-sectional shape of the internal oxide superconducting filament also changes from circular to flat,
Since the diameter in the longitudinal direction generally reaches 100 μm or more,
The shape is disturbed, and adjacent oxide superconducting filaments are joined. And as a result, n
There is also a problem that the value decreases.

In order to solve such problems, for example, Japanese Patent Application Laid-Open No. 9-259660 proposes a technique in which a ribbon-shaped oxide superconducting filament is arranged concentrically inside a round wire. However, in this wire, although the cross section of the wire itself remains circular, since the oxide superconducting filament is in a ribbon shape, it is inevitable that the oxide superconducting filaments are joined to each other, and the n value of the wire decreases. Is not resolved. Also, with this technology,
By adopting a structure in which the Ag alloy sheath material covers the oxide superconducting filament, the proof stress increases compared to the case of pure Ag sheath material, but the added element in the Ag alloy causes a chemical reaction with the oxide superconducting filament. This causes characteristic deterioration.

Under such a background, the present inventors further developed a structure in which a bundle of wire rods composed of a structure in which a pure Ag sheath material was disposed around an oxide superconducting filament was surrounded by Ag.
An oxide superconducting wire having a double sheath structure, which is covered with an alloy sheath material, has been proposed [Journal of the Japan Institute of Metals, Vol. 61, No. 9 (1997), p842]. This technology uses Ag
High strength with alloy sheath material and pure Ag
By arranging the sheath material around the oxide superconducting filament, it is possible to prevent the characteristic deterioration caused by the reaction of the additive element in the outer Ag alloy sheath material with the oxide superconducting filament. And while achieving high strength by adopting such a structure,
Critical current density equivalent to using pure Ag sheath material alone
Jc was obtained. However, even with this technique, the overall critical current density (overall Jc)
Remained at a small value, and the critical current density in a strong magnetic field of 23 T was about 20 A / mm ² . Such a problem also occurs in the technique of Japanese Patent Application Laid-Open No. 9-259660.

The present invention has been made to solve the above-mentioned technical problems of the conventional oxide superconducting multifilamentary wire, and its object is to provide a high yield strength, a high n value, and a high critical current. An object of the present invention is to provide an oxide superconducting multifilamentary wire which can satisfy all properties of density and is useful as a material of a superconducting magnet for an NMR apparatus.

[0013]

SUMMARY OF THE INVENTION The present invention, which has achieved the above-mentioned object, refers to an oxide superconducting multi-layer in which a plurality of Ag wires each having an oxide superconducting filament embedded therein are bundled in an Ag alloy sheath material. An oxide superconducting multi-core wire having a gist in the point that the R value represented by the following formula (1) is 0.9 to 2.5. R value = (sum of cross-sectional areas of metal in Ag wire and Ag alloy sheath material) / (sum of cross-sectional areas of oxide superconducting filament) (1)

It is preferable that the oxide superconducting multifilamentary wire of the present invention has the following requirements (1) to (3). (1) Assuming that the maximum diameter of each oxide superconducting filament in an arbitrary cross-sectional view is D, the average value _Dav of D is 0.
It is 8 to 30 μm. (2) When attention is paid to each oxide superconducting filament in an arbitrary cross-sectional view, when the distance between the superconducting filaments and a plurality of adjacent oxide superconducting filaments, which is the closest relationship, is d, the average of the d is given. Value d _av is 0.24-3
8 μm. (3) The ratio (D _av / d _av ) of the average value D _av to d _av is 0.
8 to 3.3.

[0015]

BEST MODE FOR CARRYING OUT THE INVENTION The present inventors have found that the conventional oxide superconducting wire has an overall critical current density (over).
All Jc) was examined from various angles about the cause. As a result, the fact that the ratio (Ag ratio) of the total sum of the cross-sections of the Ag alloy and Ag to the total cross-sectional area of the oxide superconducting filament is large is the cause of the decrease in the overall critical current density (overall Jc). Ascertained. That is, in the technology proposed by the present inventors earlier,
The Ag ratio is set to 5 to 6 because the strength is emphasized. If the Ag ratio is increased in this way, the critical current density (overall Jc) becomes smaller. In the technique of Japanese Unexamined Patent Application Publication No. 9-259660, nothing is disclosed about the Ag ratio, but it is considered that the value is as high as 8 or more when judged from the figures of the examples.

The inventors of the present invention have made a structure based on the previously proposed oxide superconducting multifilamentary wire, that is, a wire group in which a plurality of Ag wires each having an oxide superconducting filament embedded therein are bundled into an Ag alloy sheath material. In the configuration of the buried oxide superconducting multifilamentary wire, the sum of the cross-sectional areas of the Ag wire and the Ag alloy sheath material with respect to the sum of the cross-sectional areas of the oxide superconducting filaments (hereinafter, abbreviated as “S _o ”) Hereinafter, this is abbreviated as “S _Ag ”) (S _Ag / S _Ag ).
_{When o} ) is an R value, it has been found that the above object can be achieved satisfactorily if the R value is set so as to be in the range of 0.9 to 2.5, and the present invention has been completed.

According to the present invention, as described above, a wire group in which a plurality of Ag wires in which an oxide superconducting filament is embedded is bundled,
It is based on a configuration embedded in an Ag alloy sheath material, and by using such an Ag alloy sheath material, the proof stress of the entire wire can be improved. In order to exert such an effect, a predetermined strength is required for the Ag alloy sheath material, and as an additive component for imparting such characteristics, an element such as Mg, Ni, Sb or the like, Oxides and the like are mentioned, and one or more of these may be added. Further, it is preferable that these additives are contained in an amount of 0.1% by mass or more. However, if they are contained in too much, the hardness of the sheath material is increased and uniform processing becomes difficult. It is preferably set to 0% or less. The Ag alloy sheath material used in the present invention basically consists of Al and unavoidable impurities other than the above-mentioned additional components (Mg, Ni, Sb or oxides thereof). Elements such as Mn and Zr that form a solid solution without forming an intermetallic compound can be added in a small amount.

As the R value [ratio (S _Ag / S _o )] increases, the proof stress of the wire tends to increase. However, if this value is increased too much, the oxide superconducting multi-core as described above. The critical current density (overall Jc) of the wire is rather reduced. The inventors of the present invention have examined the optimum range of the R value. When the R value is set to 2.5 or less, the critical current density (overall Jc) can be maintained at a high level. The proof stress was also secured.

Regarding the n-value, if the maximum diameter D of each oxide superconducting filament in an arbitrary cross-sectional view is constant, the oxide superconducting filament is not deformed during the wire processing even if the R value changes. Since the stress received from the surroundings does not change, the degree of disorder of the oxide superconductor filament does not change much. Therefore, even if the R value changes, n
The value shows a substantially constant value. However, it is very sensitive to the maximum diameter D of each oxide superconducting filament. From these viewpoints, the present inventors set the average value D _av of the maximum diameter D of the oxide superconducting filament to 0.8 to 30 μm.
It has also been found that the control can be performed so that the n value can be dramatically improved. Here, the maximum diameter D of the oxide superconducting filament is the diameter of the longest part of the cross-sectional shape of each oxide superconducting filament in an arbitrary cross-sectional view, and the maximum diameter D is defined by the oxide superconducting filament. This is because the cross-sectional shape is not necessarily a perfect circle, and the change in the maximum diameter D reflects the n value best.

On the other hand, from the point of defining the maximum diameter D, when attention is paid to each oxide superconducting filament in an arbitrary cross-sectional view, the minimum value of the distance between the superconducting filament and a plurality of adjacent oxide superconducting filaments is determined. It is considered that the distance d between the two is also an important factor that affects the n value. From such a viewpoint, in the oxide superconducting multi-core wire of the present invention, the average value d _av of the d is 0.24 to 38 μm.
It is preferred that

In the present invention, it is also useful to balance the average values D _av and d _av . That is, when the ratio of the average values D _av and d _av (D _av / d _av ) is viewed as a parameter, the R value [ratio (S _Ag / S _o )] and the oxide superconducting filament diameter are constant. _{If av} / _dav is too small, the ratio of the Ag alloy responsible for the proof stress will decrease, and the proof stress will be extremely reduced. On the other hand, if D _av / d _av is too large, bonding of the oxide superconductor filaments occurs during the processing of the wire, and in this case, the n value also decreases. From such a viewpoint, it is effective to control D _av / d _av in the range of 0.8 to 3.3, and by satisfying these requirements, a high yield strength, a high n value, and a high critical current density (overall Jc) can be obtained. Can be maintained higher.

The oxide superconductor of the present invention is:
Bi ₂ Sr ₂ CaCu ₂ O _x (Bi
(Bi, Pb) ₂ Sr ₂ Ca
_{2 Cu 3 O x (Bi-} 2223 type) may be used other oxide superconductor such as it is, of course, the same effect even by adopting such a configuration is achieved.

Hereinafter, the present invention will be described in more detail with reference to Examples. However, the following Examples are not intended to limit the present invention, and any modifications that are made without departing from the spirit of the present invention will be described. It is within the technical scope of the invention.

[0024]

EXAMPLES Comparative Example 1 Bi ₂ was placed in an Ag pipe having a thickness of 2 mm and a purity of 99.9%.
A calcined powder having a composition of Sr ₂ CaCu ₂ O _x was filled, and hexagonal wire drawing was performed. Cut after wire drawing 19
Ag alloy (Ag-0.05% by mass Mg)
Was set inside and the billet was assembled. After that, it was subjected to hydrostatic extrusion, and was further drawn by drawing to be processed into a 19-core round drawn. The R value of the obtained wire was 3.1, and the average value D _av of the maximum diameter D in each oxide superconducting filament cross section was 58 μm. Also D
_av / _dav was 0.65.

A sample having a length of 1000 mm
One of the cut pieces is wound around a test coil having a diameter of 30 m, and is partially melted in an oxygen-containing atmosphere at a temperature of 860 to 910 ° C., and then cooled at a cooling rate of 1 to 5 ° C./hour. The baked powder is crystallized to form Bi-221.
A type 2 oxide superconductor was used. FIG. 1 schematically shows a cross-sectional structure of the manufactured wire.

Regarding the obtained wire, 4.2K, 23T
The critical current density (overall Jc) was measured by gradually reducing the critical current at the wire cross section, and a value of 25 A / mm ² was obtained. In addition, a value of 7.8 was obtained as the n value when an electric field reference of 0.1 to 1.0 μV / cm was used.
Thus, the critical current density (overall Jc) and the n value remained at low values.

3. heat-treat the other one under the same conditions;
When a tensile test was performed at 2K, a value of 115 MPa was obtained as 0.2% proof stress. This value is 1 GH as described above.
It is less than the design stress of 160 MPa of an oxide superconducting magnet proposed to be mounted in the bore of a metal-based superconducting coil with a z-class superconducting magnet for NMR.

Example 1 The value of D _av / d _av was changed while keeping the average value D _av of the maximum diameter D of each oxide superconducting filament constant (10 μm).
Using a cylindrical Ag alloy (Ag-0.1% by mass Mg), a hydrostatic extrusion and drawing were performed in the same manner as in Comparative Example 1 to produce 55-core round wires having different R values. FIG. 2 schematically shows a cross-sectional structure of the prepared wire.

Then, a sample was cut out from each wire in the same manner as in Comparative Example 1 and subjected to the same heat treatment as described above to obtain an oxide superconducting multi-core wire. The critical current density (overall Jc), n value, and 0.2% proof stress of each of the obtained wires were determined in the same manner as described above.

The effect of the R value on the critical current density (overall Jc) and 0.2% proof stress is shown in FIG.
When the ratio is 9 or more, the proof stress rapidly increases, and this ratio is set to 2.
The critical current density (overall
Jc) can be significantly improved. Note that the n value does not depend much on the R value,
And high values were obtained. From these facts, by controlling the R value to 0.9 to 2.5, 110 A / m
critical current density (overall Jc) of m ² or more, n of 18 or more
It can be seen that a value of 0.2% and a yield strength of 160 MPa or more can be obtained. Each of these values exceeds the value of Comparative Example 1 described above.

Example 2 Various 55-core round wires having different average values D _av of oxide superconducting filament diameters were prepared by changing the wire diameter while keeping the R value constant at 1.9. Other conditions at this time were the same as those in Example 1. Then, a sample was cut out from each wire in the same manner as in Comparative Example 1, and the same heat treatment as above was performed to obtain an oxide superconductor. For each of the obtained wires, the critical current density (overall Jc), the n value, and the 0.
The 2% proof stress was determined in the same manner as above.

The diameter of the oxide superconducting filament (average value)
D_av) Gives the critical current density (overall Jc) and n value
FIG. 4 shows the effect_avIs 0.8 μm or more and the n value is
While increasing rapidly, this D_avTo 30 μm or less
This can significantly improve the critical current density (overall Jc).
You can see that For 0.2% proof stress, D_avIn
Although it does not depend on the margin, all are as high as 190 to 210 MPa.
1GHz class NMR oxide superconductivity
Exceeding 160MPa, the design stress of body magnet
Was. From these facts, the oxide superconducting filament
Diameter (mean value D _av) Is controlled to 0.8 to 30 μm
100A / mm^Two Critical current density (over
all Jc), n value of 12 or more and 190 MPa or more
It can be seen that 0.2% proof stress can be obtained. And these
Each value exceeds the value of Comparative Example 1 described above.
You.

Example 3 Oxide superconducting material filament diameter (average value D _av ) and R
By keeping the value constant at 100 μm and 1.9, respectively, by changing the thickness of the pure Ag pipe when filling the calcined powder having the composition of Bi ₂ Sr ₂ CaCu ₂ O _x , D _av / Various 55-core round wires having different d _av were produced. Other conditions at this time were the same as those in Example 1. A sample was cut out from each wire in the same manner as in Comparative Example 1 and subjected to the same heat treatment as described above to obtain an oxide superconducting multi-core wire. The critical current density (overall Jc), n value, and 0.2% proof stress of each of the obtained wires were determined in the same manner as described above.

D_av/ D_avGives n value and 0.2% proof stress
FIG. 5 shows the effect of_av/ D _avIs over 0.8
The 0.2% proof stress rapidly increased, and this D_av/ D_avTo
N value can be significantly improved by keeping it at 3.3 or less.
I understand. For the critical current density (overall Jc),
D_av/ D_avNot much, but both are 160-1
70A / mm^Two And higher values were obtained than in the comparative example. This
From these, D_av/ D_avIn the range of 0.8 to 3.3
By controlling, 160 A / mm^Two Critical charge above
Flow density (overall Jc), n value greater than 19 and 200M
It can be seen that a 0.2% proof stress of Pa or more can be obtained. Soshi
All of these values surpass the values of Comparative Example 1 above.
Things.

Example 4 Bi ₂ was placed in a 2 mm-thick 99.9% pure Ag pipe.
A calcined powder having a composition of Sr ₂ CaCu ₂ O _x was filled, and hexagonal wire drawing was performed. 55 cut after wire drawing
The bundle was set and set in a cylindrical Ag alloy (Ag-0.5 mass% Ni) to assemble a billet. While maintaining the average value D _av of the maximum diameter D of the oxide superconducting filament at a constant value (10 μm), the value of D _av / d _av was changed. Various different 55-core round wires were produced.

A sample was cut out from each wire in the same manner as in Comparative Example 1 and subjected to a heat treatment to prepare various oxide superconducting multi-core wires.
The critical current density (overall Jc) at 23 T, the n value and 0.2% and the proof stress were measured. As a result, FIG.
A similar tendency was observed. That is, the R value is 0.9 to
By controlling in the range of 2.5, 110 A / mm
Critical current density of ² or more (overall Jc), n of 18 or more
Value and a 0.2% proof stress of 160 MPa or more. Also, the critical current density (overall J
The values of c) and n do not change much, but the minimum value for the 0.2% proof stress increased from about 125 MPa to about 160 MPa.

Example 5 Bi ₂ mm thick Ag pipe having a purity of 99.9% was placed in a Bi ₂ pipe.
A calcined powder having a composition of Sr ₂ CaCu ₂ O _x was filled, and hexagonal wire drawing was performed. 55 cut after wire drawing
The bundle was set and set in a cylindrical Ag alloy (Ag-0.3% by mass Sb) to assemble a billet. While maintaining the average value D _av of the maximum diameter D of the oxide superconducting filament at a constant value (10 μm), the value of D _av / d _av was changed. Various different 55-core round wires were produced.

A sample was cut out from each wire in the same manner as in Comparative Example 1 and subjected to a heat treatment to prepare various oxide superconducting multi-core wires.
The critical current density (overall Jc) at 23 T, the n value and 0.2% and the proof stress were measured. As a result, FIG.
A similar tendency was observed. That is, the R value is 0.9 to
By controlling in the range of 2.5, 110 A / mm
Critical current density of ² or more (overall Jc), n of 18 or more
Value and a 0.2% proof stress of 200 MPa or more. Also, the critical current density (overall J
The values of c) and n do not change much, but the minimum value for 0.2% proof stress increased from about 160 MPa to about 200 MPa.

[0039]

The present invention is configured as described above, and an oxide superconducting multifilamentary wire having all the required characteristics of high yield strength, high n value and high critical current density in a well-balanced manner can be realized. Therefore, if the oxide superconducting multifilamentary wire of the present invention is used, in a high-performance superconducting magnet that requires a persistent current mode operation in a strong magnetic field as typified by a superconducting magnet for an NMR apparatus, the conventional superconducting magnet is used. It can be expected to produce a superconducting magnet which is more excellent, and it is extremely advantageous in other superconducting applied technologies.

[Brief description of the drawings]

FIG. 1 is a diagram schematically showing a cross-sectional structure of a wire manufactured in Comparative Example 1.

FIG. 2 is a diagram schematically illustrating a cross-sectional structure of a wire manufactured in Example 1.

FIG. 3 is a graph showing the relationship between R value and critical current density (overall Jc).
4 is a graph showing the effect on 2% proof stress.

FIG. 4 is a graph showing the influence of the average value D _{av of the} oxide superconducting material filament diameter on the critical current density (overall Jc) and the n value.

FIG. 5 is a graph showing the effect of D _av / d _av on the n value and 0.2% proof stress.

Claims (4)

[Claims] 1. A method in which an oxide superconducting filament is embedded.
In an oxide superconducting multifilamentary wire in which a wire group in which a plurality of g wires are bundled is embedded in an Ag alloy sheath material, an R value represented by the following formula (1) is 0.9 to 2.5. Oxide superconducting multi-core wire. R value = (sum of cross-sectional areas of metal in Ag wire and Ag alloy sheath material) / (sum of cross-sectional areas of oxide superconducting filament) (1) 2. Assuming that the maximum diameter of each oxide superconducting filament in an arbitrary sectional view is D, an average value D of the D
The oxide superconducting multicore wire according to claim 1, wherein _av is 0.8 to 30 µm. 3. Attention is paid to each oxide superconducting filament in an arbitrary cross-sectional view. When the distance between the superconducting filament and a plurality of adjacent oxide superconducting filaments is the closest, the distance is defined as d. Average value d _av is 0.
The multi-filamentary oxide superconducting wire according to claim 1, which has a thickness of 24 to 38 μm. 4. The oxide superconductor according to claim 1, wherein a ratio (D _av / d _av ) of the average value D _{av of the} second aspect to the average value d _av of the third aspect is 0.8 to 3.3. Multi-core wire.