JP2010157496A - New solid electrolyte nanoporous material and method of manufacturing the same - Google Patents

New solid electrolyte nanoporous material and method of manufacturing the same Download PDF

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JP2010157496A
JP2010157496A JP2009272378A JP2009272378A JP2010157496A JP 2010157496 A JP2010157496 A JP 2010157496A JP 2009272378 A JP2009272378 A JP 2009272378A JP 2009272378 A JP2009272378 A JP 2009272378A JP 2010157496 A JP2010157496 A JP 2010157496A
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solid electrolyte
ysz
closed pores
porosity
nanopore material
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JP5486277B2 (en
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Masashi Goto
万佐司 後藤
Naohito Yamada
直仁 山田
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NGK Insulators Ltd
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Abstract

<P>PROBLEM TO BE SOLVED: To provide a solid electrolyte nanoporous material high in ion conductivity. <P>SOLUTION: YSZ is mixed with 10 wt.% of polymethyl methacrylate particles in an average particle size of 150 nm by using water as a solvent in a planetary pot mill for three minutes. After dried, the mixture is formed into a green compact by uniaxial press molding and CIP. The green compact is calcined under a nitrogen atmosphere at 1,400°C, to form a sintered compact of YSZ having nano closed pores. When a porosity of the sintered compact is measured by Archimedes' method, the porosity is 10 wt.%. In succession, the closed pores of 100-200 nm in pore diameter are observed in the microstructure observation of a cross-section of the sintered compact. An ionic conductivity of the sintered compact is increased by a factor of about 1.5 comparing to a sintered compact of YSZ not having closed pores. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

本発明は、新規な固体電解質ナノポア材料及びその製法に関する。   The present invention relates to a novel solid electrolyte nanopore material and a method for producing the same.

近年、ナノ材料すなわちナノサイズの閉気孔が多数存在するバルク体の研究開発が行われつつある。例えば、非特許文献1には、EB−PVD法により成膜されるセラミックスコーティング層は柱状粒子により構成され、その内部にナノポアが形成されることが開示されている。こうしたナノポアは、セラミックス膜の低熱伝導特性に大きく影響するといわれている。また、非特許文献1には、ナノポアが形成されたセラミックス膜の断面観察及び平面観察を透過型電子顕微鏡(TEM)により行った例なども開示されている。   In recent years, research and development of nanomaterials, that is, bulk bodies in which a large number of nano-sized closed pores are present are being conducted. For example, Non-Patent Document 1 discloses that a ceramic coating layer formed by an EB-PVD method is composed of columnar particles, and nanopores are formed therein. Such nanopores are said to greatly affect the low thermal conductivity characteristics of ceramic films. Non-Patent Document 1 also discloses an example in which cross-sectional observation and planar observation of a ceramic film on which nanopores are formed are performed using a transmission electron microscope (TEM).

“電子ビーム(EB−PVD)法により形成されたジルコニア膜の微細構造”、[online]、JFCC(財団法人ファインセラミックスセンター)、[平成20年11月12日検索]、インターネット<URL:http://www.jfcc.or.jp/23_develop_2/09res_04a.html>“Microstructure of zirconia film formed by electron beam (EB-PVD) method”, [online], JFCC (Fine Ceramics Center), [November 12, 2008 search], Internet <URL: http: //www.jfcc.or.jp/23_develop_2/09res_04a.html>

しかしながら、本発明者の知るかぎり、これまで研究開発されてきたナノポア材料の中には、固体電解質として好適なものは報告されていない。   However, as far as the inventor knows, no nanopore material that has been researched and developed so far has been reported as a solid electrolyte.

本発明は、このような課題に鑑みなされたものであり、イオン伝導度の高い固体電解質ナノポア材料を提供することを主目的とする。   This invention is made | formed in view of such a subject, and it aims at providing the solid electrolyte nanopore material with high ion conductivity.

上述した目的を達成するために、本発明者らは、イットリア安定化ジルコニア(YSZ)にナノサイズの有機物微粒子を添加して混合し、成形してから不活性雰囲気下、又は空気雰囲気下で焼成することにより得られたナノポア材料が、高いイオン伝導度を持つことを見いだし、本発明を完成するに至った。   In order to achieve the above-described object, the present inventors added yttria-stabilized zirconia (YSZ) with nano-sized organic fine particles, mixed, molded, and then fired in an inert atmosphere or an air atmosphere. The nanopore material obtained by doing so was found to have high ionic conductivity, and the present invention was completed.

即ち、本発明の固体電解質ナノポア材料は、固体電解質に気孔径1μm以下の閉気孔が多数導入された構造を持つものである。   That is, the solid electrolyte nanopore material of the present invention has a structure in which a large number of closed pores having a pore diameter of 1 μm or less are introduced into the solid electrolyte.

また、本発明の固体電解質ナノポア材料の製法は、固体電解質の粉末に平均粒径1μm以下の有機物微粒子を添加して混合し、成形してから不活性雰囲気下、又は空気雰囲気下で焼成することによりナノポア材料を得るものである。   In addition, the method for producing the solid electrolyte nanopore material of the present invention is to add organic fine particles having an average particle size of 1 μm or less to the solid electrolyte powder, mix and form, and then fire in an inert atmosphere or an air atmosphere. Thus, a nanopore material is obtained.

本発明の固体電解質ナノポア材料は、閉気孔を有さない同成分の固体電解質の焼結体に比べて、イオン伝導度が高い。その理由は定かではないが、以下のように推察される。すなわち、東大・山口らは、ナノイオニクスの研究において、ヘテロ界面を利用した高速イオン移動現象を報告している。また、そのような高速イオン移動現象がみられる理由として、ヘテロ界面の空間電荷層でキャリア数が増加することや界面歪みによって格子が変形してキャリア移動度が向上することを挙げている。一方、山梨大・和田らは、チタン酸バリウムのナノ粒子の表面が正方晶から立方晶に変化すると報告している。そのような理由として、固体表面では長距離クーロン力が固体内部側からしか期待できないため、固体表面の構造が変化したことを報告している。また、本発明の固体電解質ナノポア材料の閉気孔の内周面をTEM観察すると、閉気孔の表面には結晶格子の歪んだ層が存在した。以上のような報告や実験結果を踏まえて考えると、今回の固体電解質ナノポア材料の閉気孔の内周表面付近でも、構造が変化した層が現れ、その層と内部の層との界面歪みによって格子が変形してキャリア移動度が向上している可能性がある。そして、その結果、イオン伝導度が向上したと推察される。構造が変化した層は、閉気孔の気孔径が小さく気孔率が大きいほど増えると推察されるため、気孔径を200nmより更に小さくすることにより更にイオン伝導度を増大できる。   The solid electrolyte nanopore material of the present invention has higher ionic conductivity than a sintered body of the same solid electrolyte having no closed pores. The reason is not clear, but it is presumed as follows. In other words, the University of Tokyo and Yamaguchi et al. Reported high-speed ion transfer phenomena using heterointerfaces in nanoionics research. In addition, the reason why such a fast ion transfer phenomenon is observed is that the number of carriers in the space charge layer at the heterointerface increases and the lattice is deformed due to interface distortion, thereby improving the carrier mobility. On the other hand, Yamanashi Univ., Wada et al. Reported that the surface of barium titanate nanoparticles changed from tetragonal to cubic. For this reason, it has been reported that the structure of the solid surface has changed since a long-range Coulomb force can be expected only from the inside of the solid surface. Further, when the inner peripheral surface of the closed pores of the solid electrolyte nanopore material of the present invention was observed with a TEM, a layer having a distorted crystal lattice was present on the surface of the closed pores. Considering the above reports and experimental results, a layer with a changed structure appears near the inner peripheral surface of the closed pores of the solid electrolyte nanopore material, and the lattice distortion occurs due to the interface strain between the layer and the inner layer. May be deformed to improve carrier mobility. And as a result, it is guessed that the ionic conductivity improved. Since the layer whose structure has changed is presumed to increase as the pore diameter of the closed pores is small and the porosity is large, the ionic conductivity can be further increased by making the pore diameter smaller than 200 nm.

気孔径と気孔率−粒内イオン伝導度のグラフを示す。The graph of a pore diameter and a porosity-intragranular ion conductivity is shown.

本発明の固体電解質ナノポア材料は、固体電解質に気孔径1μm以下の閉気孔が多数導入された構造を持つものである。   The solid electrolyte nanopore material of the present invention has a structure in which a large number of closed pores having a pore diameter of 1 μm or less are introduced into the solid electrolyte.

ここで、固体電解質のうち酸素イオン固体電解質としては、例えば、イットリア安定化ジルコニア電解質(YSZ)、スカンジア安定化ジルコニア電解質(ScSZ)、セリア系電解質(SDC、GDC)、ランタンガレート系電解質(LSGM)などが挙げられるが、このうちYSZが好ましい。   Here, among the solid electrolytes, examples of the oxygen ion solid electrolyte include yttria stabilized zirconia electrolyte (YSZ), scandia stabilized zirconia electrolyte (ScSZ), ceria based electrolyte (SDC, GDC), and lanthanum gallate based electrolyte (LSGM). Of these, YSZ is preferred.

YSZのイットリア添加量としては、3〜10mol%がより好ましい。イットリア添加量が3mol%未満もしくは10mol%以上ではイオン伝導度が低くなるため好ましくない。   The amount of yttria added to yttria is more preferably 3 to 10 mol%. If the amount of yttria added is less than 3 mol% or 10 mol% or more, the ionic conductivity is lowered, which is not preferable.

閉気孔の気孔径は1μm以下であることが好ましく、200nm以下であることがより好ましい。気孔径が小さいほど構造の変化した層が増え、イオン伝導度が高くなるからである。なお、気孔径は100nm以上であることが閉気孔を安定に形成できるため好ましい。   The pore diameter of the closed pores is preferably 1 μm or less, and more preferably 200 nm or less. This is because the smaller the pore diameter, the more layers whose structure has changed, and the higher the ionic conductivity. Note that the pore diameter is preferably 100 nm or more because closed pores can be stably formed.

閉気孔の気孔率は30〜60%であることが好ましい。こうした固体電解質ナノポア材料のイオン伝導度は閉気孔の気孔率にも依存して変化するが、気孔率が増えると構造が変化した層が増え、イオン伝導度が高くなるが、イオン伝導に寄与しない空孔部分も増えるために、気孔率が30〜60%で、イオン伝導度は最大値に近い値をとるためである。   The porosity of the closed pores is preferably 30 to 60%. The ionic conductivity of these solid electrolyte nanopore materials changes depending on the porosity of the closed pores, but as the porosity increases, the number of layers whose structure has changed increases and the ionic conductivity increases, but it does not contribute to ionic conduction. This is because the number of pores increases, the porosity is 30 to 60%, and the ionic conductivity is close to the maximum value.

本発明の固体電解質ナノポア材料の製法は、固体電解質の粉末に平均粒径1μm以下の有機物微粒子を添加して混合し、成形してから不活性雰囲気下、又は空気雰囲気下で焼成することによりナノポア材料を得るものである。   The method for producing a solid electrolyte nanopore material according to the present invention is obtained by adding organic fine particles having an average particle size of 1 μm or less to a solid electrolyte powder, mixing, molding, and firing in an inert atmosphere or an air atmosphere. Get material.

この製法によれば、固体電解質に気孔径1μm以下の閉気孔が多数導入された構造を持つ固体電解質ナノポア材料を容易に製造することができる。   According to this production method, a solid electrolyte nanopore material having a structure in which a large number of closed pores having a pore diameter of 1 μm or less are introduced into the solid electrolyte can be easily produced.

ここで、有機物微粒子としては、ポリメタクリル酸エステル微粒子、ポリアクリル酸エステル微粒子、メラミン微粒子などが挙げられる。有機物微粒子の添加量は、全体に対して5〜15wt%が好ましい。固体電解質に有機物微粒子を添加して混合する場合、溶媒(例えば水)中で湿式混合してもよい。湿式混合を行う際は、ポットミル、トロンメル、アトリッションミルなどの混合粉砕機を使用してもよい。また、湿式混合の代わりに乾式混合してもよい。混合粉末をペレット化するには、加圧成形を採用するのが一般的であり、特に一軸プレス成形を採用するのが好ましい。成形圧力は、100MPa以上とすることが好ましいが、保型が可能であれば、特に限定されない。ペレットを焼成するときの雰囲気は特に限定されないが、例えば不活性雰囲気や空気雰囲気などが挙げられる。不活性雰囲気としては、例えば、窒素雰囲気やアルゴン雰囲気、ヘリウム雰囲気などが挙げられる。焼成温度は、固体電解質の組成に応じて適宜設定すればよく、例えばYSZであれば1350〜1450℃に設定すればよい。   Here, examples of the organic fine particles include polymethacrylate fine particles, polyacrylic ester fine particles, and melamine fine particles. The addition amount of the organic fine particles is preferably 5 to 15 wt% with respect to the whole. When the organic fine particles are added to and mixed with the solid electrolyte, wet mixing may be performed in a solvent (for example, water). When performing wet mixing, a mixing and grinding machine such as a pot mill, a trommel, an attrition mill, or the like may be used. Further, dry mixing may be performed instead of wet mixing. In order to pelletize the mixed powder, pressure molding is generally employed, and uniaxial press molding is particularly preferably employed. The molding pressure is preferably 100 MPa or more, but is not particularly limited as long as the shape can be retained. Although the atmosphere at the time of baking a pellet is not specifically limited, For example, an inert atmosphere, an air atmosphere, etc. are mentioned. Examples of the inert atmosphere include a nitrogen atmosphere, an argon atmosphere, and a helium atmosphere. The firing temperature may be appropriately set according to the composition of the solid electrolyte. For example, in the case of YSZ, the firing temperature may be set to 1350 to 1450 ° C.

[実施例1]
8YSZ(8%Y23,92%ZrO2、東ソー製、TZ−8Y)に、平均粒径150nmのポリメタクリル酸メチル微粒子(綜研化学製,MP)を10wt%添加して、溶媒を水として遊星ポットミルにて3分間混合した。混合物を乾燥後、一軸プレス成形(100MPa)およびCIP(5t/cm2)により圧粉体とし、その圧粉体を1400℃にて窒素雰囲気下で焼成し、ナノ閉気孔を有する8YSZの焼結体を得た。この実施例1の焼結体の気孔率をアルキメデス法(JIS R 1634準拠)で測定したところ、気孔率は10wt%であった。また、実施例1の焼結体の断面の微構造観察を電界放射型走査型電子顕微鏡(ZEIS製,ULTRA55)にて行ったところ、気孔径100〜200nm(平均気孔径150nm)の閉気孔が観察された。
[Example 1]
To 8YSZ (8% Y 2 O 3 , 92% ZrO 2 , manufactured by Tosoh Corporation, TZ-8Y), 10 wt% of polymethyl methacrylate fine particles (manufactured by Soken Chemical Co., Ltd., MP) having an average particle diameter of 150 nm are added, and the solvent is water. And mixed for 3 minutes in a planetary pot mill. After the mixture is dried, it is made into a green compact by uniaxial press molding (100 MPa) and CIP (5 t / cm 2 ), and the green compact is fired at 1400 ° C. in a nitrogen atmosphere to sinter 8YSZ having nano-closed pores. Got the body. When the porosity of the sintered body of Example 1 was measured by the Archimedes method (based on JIS R 1634), the porosity was 10 wt%. Further, when the microstructure of the cross section of the sintered body of Example 1 was observed with a field emission scanning electron microscope (manufactured by ZEIS, ULTRA55), closed pores having a pore diameter of 100 to 200 nm (average pore diameter of 150 nm) were found. Observed.

[比較例1]
ポリメタクリル酸メチル微粒子を入れず、他は実施例1と同じ条件で、8YSZの焼結体を得た。
[Comparative Example 1]
An 8YSZ sintered body was obtained under the same conditions as in Example 1 except that no polymethyl methacrylate fine particles were added.

[イオン伝導度の比較]
実施例1の焼結体と、比較例1の焼結体のコールコールプロットを、開閉式管状炉(いすゞ製作所製,EPKPO−14)、インピーダンスアナライザ(AUTOLAB製,PGSTAT30)を用いて測定した。測定したコールコールプロット結果より、粒内抵抗と粒界抵抗を分離し、粒内抵抗より粒内のイオン伝導度を算出した。その結果、大気雰囲気下1000℃における比較例1の焼結体の粒内イオン伝導度は0.16Scm-1であったのに対して、同条件における実施例1の焼結体の粒内イオン伝導度は、0.24Scm-1であった。よって、実施例1の方が比較例1に比べ約1.5倍イオン伝導度が高かった。なお、実施例1で窒素雰囲気の代わりに空気雰囲気やアルゴン雰囲気で焼成を行ったところ、実施例1と同等の結果が得られた。
[Comparison of ionic conductivity]
The Cole-Cole plots of the sintered body of Example 1 and the sintered body of Comparative Example 1 were measured using an open / close tubular furnace (manufactured by Isuzu Seisakusho, EPKPO-14) and an impedance analyzer (manufactured by AUTOLAB, PGSTAT30). From the measured Cole-Cole plot results, the intragranular resistance and the grain boundary resistance were separated, and the ionic conductivity within the grain was calculated from the intragranular resistance. As a result, the intragranular ionic conductivity of the sintered body of Comparative Example 1 at 1000 ° C. in an air atmosphere was 0.16 Scm −1 , whereas the intragranular ions of the sintered body of Example 1 under the same conditions. The conductivity was 0.24 Scm- 1 . Therefore, the ionic conductivity of Example 1 was about 1.5 times higher than that of Comparative Example 1. In Example 1, firing was performed in an air atmosphere or an argon atmosphere instead of the nitrogen atmosphere, and the same results as in Example 1 were obtained.

[実施例2]
実施例1の実験を、ポリメタクリル酸メチル微粒子の粒径及び添加量を変えて実施した。具体的には、ポリメタクリル酸メチル微粒子として、平均粒径が100nm,200nm,1μmのものを用いた。ここでいう平均粒径とは、微粒子をSEM観察し、ランダムに選択した10個の微粒子の直径の総和を10で除した算術平均値である。また、各平均粒径ごとに、添加量を10wt%,30wt%,50wt%,70wt%に設定して実験を行った。その結果、ポリメタクリル酸メチル微粒子の平均粒径が大きいほど、焼結体に形成される閉気孔は大きくなった。具体的には、平均粒径が100nm,200nm,1μmの場合、実施例1と同様にして求めた平均気孔径はそれぞれ100nm,200nm,1μmであった。また、ポリメタクリル酸メチル微粒子の添加量が増えるほど、焼結体の気孔率は高くなった。具体的には、添加量を10wt%,30wt%,50wt%,70wt%とした場合、実施例1と同様にして求めた気孔率はそれぞれ10%,30%,50%,70%であった。但し、平均粒径100nmの場合には、添加量50wt%のときの気孔率は40%となった。
[Example 2]
The experiment of Example 1 was carried out by changing the particle diameter and addition amount of the polymethyl methacrylate fine particles. Specifically, polymethyl methacrylate fine particles having average particle diameters of 100 nm, 200 nm, and 1 μm were used. Here, the average particle diameter is an arithmetic average value obtained by dividing the sum of the diameters of 10 fine particles randomly selected by 10 by observing the fine particles with an SEM. For each average particle size, the amount of addition was set to 10 wt%, 30 wt%, 50 wt%, and 70 wt%, and experiments were performed. As a result, the larger the average particle diameter of the polymethyl methacrylate fine particles, the larger the closed pores formed in the sintered body. Specifically, when the average particle diameter was 100 nm, 200 nm, and 1 μm, the average pore diameters obtained in the same manner as in Example 1 were 100 nm, 200 nm, and 1 μm, respectively. Moreover, the porosity of the sintered body increased as the amount of polymethyl methacrylate fine particles added increased. Specifically, when the addition amount was 10 wt%, 30 wt%, 50 wt%, and 70 wt%, the porosity determined in the same manner as in Example 1 was 10%, 30%, 50%, and 70%, respectively. . However, when the average particle size was 100 nm, the porosity was 40% when the addition amount was 50 wt%.

[気孔径,気孔率−粒内イオン伝導度特性]
実施例1と実施例2の焼結体について、気孔径と気孔率に対する粒内イオン伝導度との関係を図1に示した。図1から明らかなように、同じ気孔率の場合、気孔径が小さいほど粒内イオン伝導度は高かった。また、気孔径が1μmの焼結体では、気孔率が増加するにつれて粒内イオン伝導度は減少した。一方、気孔径が200nm以下の焼結体では、気孔率が高くなるのに伴い粒内イオン伝導度は増加し、気孔率約40〜50%で粒内イオン伝導度は最大となった。しかしながら、気孔率を50%以上とすると粒内イオン伝導度は減少した。図1から、気孔径が200nm以下の焼結体では、気孔率30〜60%で粒内イオン伝導度は非常に大きな値になることがわかる。気孔径約100nm,気孔率約40%の時に粒内イオン伝導度は最大で0.55Scm-1であり、比較例1の焼結体の粒内イオン伝導度に比べ約3倍粒内イオン伝導度が高かった。
[Pore diameter, porosity-intragranular ionic conductivity characteristics]
For the sintered bodies of Example 1 and Example 2, the relationship between the pore diameter and the intragranular ion conductivity with respect to the porosity is shown in FIG. As is clear from FIG. 1, in the case of the same porosity, the intragranular ion conductivity was higher as the pore diameter was smaller. In the sintered body having a pore diameter of 1 μm, the intragranular ionic conductivity decreased as the porosity increased. On the other hand, in the sintered body having a pore diameter of 200 nm or less, the intragranular ionic conductivity increased as the porosity increased, and the intragranular ionic conductivity was maximized at a porosity of about 40 to 50%. However, the intragranular ionic conductivity decreased when the porosity was 50% or more. As can be seen from FIG. 1, in the sintered body having a pore diameter of 200 nm or less, the intragranular ion conductivity is very large at a porosity of 30 to 60%. When the pore diameter is about 100 nm and the porosity is about 40%, the intragranular ion conductivity is 0.55 Scm -1 at the maximum, and the intragranular ion conductivity of the sintered body of Comparative Example 1 is about three times that of the sintered body. The degree was high.

実施例1の焼結体の閉気孔の内周面をTEM(透過型電子顕微鏡)にて観察したところ、YSZの結晶格子が歪んだ層が存在した。   When the inner peripheral surface of the closed pores of the sintered body of Example 1 was observed with a TEM (transmission electron microscope), a layer in which the crystal lattice of YSZ was distorted was present.

Claims (8)

固体電解質に気孔径1μm以下の閉気孔が多数導入された構造を持つ、
固体電解質ナノポア材料。
Having a structure in which a large number of closed pores having a pore diameter of 1 μm or less are introduced into the solid electrolyte,
Solid electrolyte nanopore material.
前記固体電解質は、イットリア安定化ジルコニア(YSZ)である、
請求項1に記載の固体電解質ナノポア材料。
The solid electrolyte is yttria stabilized zirconia (YSZ),
The solid electrolyte nanopore material according to claim 1.
前記YSZは、イットリア添加量が3〜10mol%である、
請求項1又は2に記載の固体電解質ナノポア材料。
The YSZ has a yttria addition amount of 3 to 10 mol%.
The solid electrolyte nanopore material according to claim 1 or 2.
前記閉気孔の内周面に、結晶格子の歪んだ層が存在する、
請求項1〜3のいずれか1項に記載の固体電解質ナノポア材料。
A strained layer of crystal lattice exists on the inner peripheral surface of the closed pores.
The solid electrolyte nanopore material according to any one of claims 1 to 3.
前記閉気孔の気孔径が200nm以下、気孔率が30〜60%である、
請求項1〜4のいずれか1項に記載の固体電解質ナノポア材料。
The closed pores have a pore diameter of 200 nm or less and a porosity of 30 to 60%.
The solid electrolyte nanopore material according to any one of claims 1 to 4.
固体電解質の粉末に平均粒径1μm以下の有機物微粒子を添加して混合し、成形してから不活性雰囲気下、又は空気雰囲気下で焼成することによりナノポア材料を得る、
固体電解質ナノポア材料の製法。
Organic fine particles having an average particle size of 1 μm or less are added to a solid electrolyte powder, mixed, molded, and then fired in an inert atmosphere or an air atmosphere to obtain a nanopore material.
Manufacturing method of solid electrolyte nanopore material.
前記固体電解質は、イットリア安定化ジルコニア(YSZ)である、
請求項6に記載の固体電解質ナノポア材料の製法。
The solid electrolyte is yttria stabilized zirconia (YSZ),
The manufacturing method of the solid electrolyte nanopore material of Claim 6.
前記YSZは、イットリア添加量が3〜10mol%である、
請求項6又は7に記載の固体電解質ナノポア材料の製法。
The YSZ has a yttria addition amount of 3 to 10 mol%.
The manufacturing method of the solid electrolyte nanopore material of Claim 6 or 7.
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