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論文

The Precipitation and redistribution of alloying element in Zircaloy-4 cladding tube oxidized in high-temperature steam

天谷 政樹

High Temperature Corrosion of Materials, 15 Pages, 2024/00

 被引用回数:0 パーセンタイル:0.04(Metallurgy & Metallurgical Engineering)

Zirconium (Zr)-based alloys are widely used as fuel cladding material for light water reactors. Under a loss-of-coolant accident (LOCA) condition, the oxidation of fuel cladding by high-temperature steam induces the degradation of mechanical properties of the cladding and would affect the integrity of fuel rods and/or assemblies, etc., during LOCA. In this study, the distribution of the elements (zirconium, oxygen, tin, iron and chromium) in Zircaloy-4 cladding specimens oxidized in the temperature range of $$sim$$ 1350- $$sim$$ 1700 K in steam was analyzed along the radial direction of the specimens by using SEM/EPMA, and the cause of element distribution in the specimens was discussed in consideration of the morphology of precipitates in the specimens and hypothesized phase diagrams related to the elements contained in the specimens. The form of the particles precipitated and the comparison between SEM/EPMA results and hypothesized phase diagrams of Zr-Sn-O system suggested that the liquefaction of tin-rich material and/or Zr-(Fe,Cr) compounds occurred during the oxidation test. The results obtained indicate that Zircaloy-4 cladding tubes would start melting at the melting point of tin-oxide and the eutectic point of Zr-(Fe,Cr)compounds, which is much lower than the melting point of Zr, $$alpha$$-Zr(O), or zirconium oxide (ZrO$$_{2}$$).

論文

Effects of azimuthal temperature distribution and rod internal gas energy on ballooning deformation and rupture opening formation of a 17 $$times$$ 17 type PWR fuel cladding tube under LOCA-simulated burst conditions

古本 健一郎; 宇田川 豊

Journal of Nuclear Science and Technology, 60(5), p.500 - 511, 2023/05

 被引用回数:0 パーセンタイル:0.01(Nuclear Science & Technology)

In order to contribute to better modeling and evaluation of fuel fragmentation, relocation, and dispersal expected under loss of coolant accident (LOCA) conditions, LOCA-simulated cladding burst experiments were performed on as-received nonirradiated 17 $$times$$ 17 type Zircaloy-4 cladding specimens that were internally pressurized. The experiments were designed to terminate at burst occurrence to focus on ballooning and rupture opening formation and to investigate the effects of various factors. The postburst cladding hoop strain decreased with the increase in azimuthal temperature distribution (ATD) of the cladding, as found previously. The rupture opening size increased with the increase in ATD and the increase in energy of the pressurized gas stored inside the pressure boundary of the test sample system. Comparison with the existing database, which included tests on irradiated rods containing fuel pellets, suggested that formation of the rupture opening was influenced by the characteristic behavior of high burnup fuels, such as limited gas migration in the cladding tube due to fuel-cladding bonding and interaction of the ejected fuel fragments with the cladding tube.

論文

The Effect of a cyclic bending load on the bending resistance of ballooned, ruptured, and oxidized Zircaloy-4 cladding

Li, F.; 成川 隆文; 宇田川 豊

Journal of Nuclear Science and Technology, 12 Pages, 2023/00

 被引用回数:0 パーセンタイル:0.01(Nuclear Science & Technology)

The seismic resistance of fuel cladding during the long-term core cooling after loss-of-coolant accidents (LOCAs) was investigated by performing cyclic four-point bending tests (4PBTs) of up to 1000 cycles with fresh fuel cladding samples that experienced integral thermal shock test, simulating LOCA conditions, including ballooning, rupture, oxidation, and quench. 4PBTs were performed on the samples that survived the quenching process. The results showed that up to 1000 cycles and 5.8 Nm of cyclic loading moment, there was no apparent effect on the bending fracture limit of the fuel cladding under the 4PBT. The scatter of the bending fracture limit for a given equivalent cladding reacted (ECR) evaluated by the Baker-Just oxidation rate equation (BJ-ECR) is attributed to two primary factors: first, the difference between the prescribed and the actual oxidation behavior, confirmed by comparing the BJ-ECR and the ECR evaluated based on metallographic observation (M-ECR), and second, the variated shape of the rupture-opening area after the integral thermal shock test. The strength of the alpha phase-dominant zone near the rupture opening seems to contribute to the bending fracture limit.

論文

Mechanical property evaluation with nanoindentation method on Zircaloy-4 cladding tube after LOCA-simulated experiment

垣内 一雄; 山内 紹裕*; 天谷 政樹; 宇田川 豊; 北野 剛司*

Proceedings of TopFuel 2022 (Internet), p.409 - 418, 2022/10

In order to examine the influence of cladding microstructural changes upon the mechanical property of the fuel cladding under LOCA conditions in a more direct and quantitative manner, the nanoindentation method has been applied to Zircaloy-4 cladding specimens after LOCA simulated tests (about 1473 K, ECR 20%, quench at 973 K after slow cooling); results for two specimens taken from the rupture opening part and secondary hydriding part were compared. In addition to hardness and Young's modulus, the plastic work fraction that corresponds to the relative ductility was evaluated from the load-displacement curve. The plastic work fraction at the secondary hydriding part was found to be obviously lower than that at the rupture opening part and closer to that in $$alpha$$-Zr(O) layers beneath the outer surface. This result from the nanoindentation method agrees with the conventional knowledge about low ductility at the secondary hydriding part.

論文

Fracture-mechanics-based evaluation of failure limit on pre-cracked and hydrided Zircaloy-4 cladding tube under biaxial stress states

Li, F.; 三原 武; 宇田川 豊; 天谷 政樹

Journal of Nuclear Science and Technology, 57(6), p.633 - 645, 2020/06

 被引用回数:3 パーセンタイル:24.28(Nuclear Science & Technology)

To better understand the failure limit of fuel cladding during the pellet-cladding mechanical interaction (PCMI) phase of a reactivity-initiated accident (RIA), pre-cracked and hydrided cladding samples with base metal final heat-treatment status of cold worked (CW) and recrystallized (RX) were tested under biaxial stress conditions (axial to hoop strain ratios of 0 and 0.5). Displacement-controlled biaxial-expansion-due-to-compression (biaxial-EDC) tests were performed to obtain the hoop strain at failure (failure strain) of the samples. The conversion of the failure strains to J-integral at failure by finite-element analysis involving data of stress-relieved (SR) cladding specimens from our previous study revealed that the failure limit in the dimension of J-integral at failure unifies the effects of pre-crack depth. About 30 to 50 percent reduction in the J-integral at failure was observed as the strain ratio increased from 0 to 0.5 irrespective of the annealing type, pre-crack depth, and hydrogen content. the rate of fractional decreases of J-integral at failure with increase of hydrogen content are in the order of CW$$>$$SR$$>$$RX, which are essentially independent of strain ratio for the CW and SR samples. The results were incorporated into the failure prediction model of the JAEA's fuel performance code in the form of a correction factor that considers the biaxial loading effect.

論文

Effects of ballooning and rupture on the fracture resistance of Zircaloy-4 fuel cladding tube after LOCA-simulated experiments

湯村 尚典; 天谷 政樹

Annals of Nuclear Energy, 120, p.798 - 804, 2018/10

 被引用回数:6 パーセンタイル:52.79(Nuclear Science & Technology)

To investigate the relationship between the fracture resistance of a cladding tube and the amount of deformation of the cladding tube due to ballooning and rupture during a loss-of-coolant accident (LOCA), four-point-bending tests were performed using non-irradiated Zircaloy-4 cladding tubes which experienced a LOCA-simulated sequence (ballooning, rupture, high temperature oxidation and quench). According to the obtained results, it was found that the maximum bending stress of the cladding tube after the LOCA-simulated sequence, which was defined as the fracture resistance, correlated to the average thickness of prior-$$beta$$ layer in the cladding tube. Based on the average thickness of prior-$$beta$$ layer, the fracture resistance of the cladding tube with ballooning and rupture was expressed as functions of isothermal oxidation time and temperature and the maximum circumferential strain on the cladding tube.

論文

Application of Bayesian optimal experimental design to reduce parameter uncertainty in the fracture boundary of a fuel cladding tube under LOCA conditions

成川 隆文; 山口 彰*; Jang, S.*; 天谷 政樹

Proceedings of 14th International Conference on Probabilistic Safety Assessment and Management (PSAM-14) (USB Flash Drive), 10 Pages, 2018/09

The reduction of epistemic uncertainty for safety-related events that rarely occur or require high experimental costs is a key concern for researchers worldwide. In this study, we develop a new framework to effectively reduce parameter uncertainty, which is one of the epistemic uncertainties, by using the Bayesian optimal experimental design. In the experimental design, we used a decision theory that minimizes the Bayes generalization loss. For this purpose, we used the functional variance, which is a component of widely applicable information criterion, as a decision criterion for selecting informative data points. Then, we conducted a case study to apply the proposed framework to reduce the parameter uncertainty in the fracture boundary of a non-irradiated, pre-hydrided Zircaloy-4 cladding tube specimen under loss-of-coolant accident (LOCA) conditions. The results of our case study proved that the proposed framework greatly reduced the Bayes generalization loss with minimal sample size compared with the case in which experimental data were randomly obtained. Thus, the proposed framework is useful for effectively reducing the parameter uncertainty of safety-related events that rarely occur or require high experimental costs.

論文

Uncertainty quantification of fracture boundary of pre-hydrided Zircaloy-4 cladding tube under LOCA conditions

成川 隆文; 山口 彰*; Jang, S.*; 天谷 政樹

Nuclear Engineering and Design, 331, p.147 - 152, 2018/05

 被引用回数:3 パーセンタイル:30.05(Nuclear Science & Technology)

To quantify the fracture boundary uncertainty for non-irradiated, pre-hydrided Zircaloy-4 cladding tube specimens under loss-of-coolant accident conditions at a light-water reactor, data from integral thermal shock tests obtained by an earlier study are analyzed statistically and the fracture boundary is estimated in terms of probability, as follows. First, a method is proposed to obtain the specimens' fracture probability curve as a function of equivalent cladding reacted (ECR) and initial hydrogen concentration using Bayesian inference with a generalized linear model. A log-probit model is used, modified to reflect the effect of the initial hydrogen concentration on the fracture boundary and the ECR evaluation uncertainty, and scaled to improve convergence. Second, using the modified log-probit model, it is shown that the boundary representing a 5% fracture probability with 95% confidence for the pre-hydrided cladding tube sample is higher than 15% ECR, for initial hydrogen concentrations of up to 800 wppm.

論文

The Effect of azimuthal temperature distribution on the ballooning and rupture behavior of Zircaloy-4 cladding tube under transient-heating conditions

成川 隆文; 天谷 政樹

Journal of Nuclear Science and Technology, 53(11), p.1758 - 1765, 2016/11

 被引用回数:10 パーセンタイル:68.36(Nuclear Science & Technology)

In order to investigate the effect of azimuthal temperature distribution on the ballooning and rupture behavior of Zircaloy-4 (Zry-4) cladding tube, laboratory-scale experiments on non-irradiated Zry-4 cladding tube specimens were performed under transient-heating conditions which simulate loss-of-coolant-accident (LOCA) conditions by using an external heating method, and the data obtained were compared to those from a previous study where an internal heating method was used. The maximum circumferential strains ($$varepsilon$$s) of the cladding tube specimens were firstly divided by the engineering hoop stress ($$sigma$$). The divided maximum circumferential strains, ${it k}$s, of the previous study, which used the internal heating method, were then corrected based on the azimuthal temperature difference (ATD) in the cladding tube specimen. The ${it k}$s for the external heating method which was used in this study agreed fairly well with the corrected ${it k}$s obtained in the previous study which employed the internal heating method in the burst temperature range below $$sim$$1200 K. Also, the area of rupture opening tended to increase with increasing of the value which is defined as $$varepsilon$$ multiplied by $$sigma$$. From the results obtained in this study, it was suggested that $$varepsilon$$ and the size of rupture opening of a cladding tube under LOCA-simulated conditions can be estimated mainly by using $$sigma$$, $$varepsilon$$ and ATD in the cladding tube specimen, irrespective of heating methods.

報告書

Zircaloy-4の高温酸化挙動に及ぼす固体ホウ酸の影響

小宮山 大輔; 天谷 政樹

JAEA-Research 2016-013, 20 Pages, 2016/08

JAEA-Research-2016-013.pdf:6.05MB

PWRの冷却材喪失事故(LOCA)において、流路の閉塞等により燃料棒の冷却が十分に行われない場合、燃料被覆管表面に冷却材中のホウ酸が析出する可能性が考えられる。通常運転温度域では、実機での実績からホウ酸水はZircaloy-4の酸化挙動に影響を及ぼさないと考えられるが、LOCAを想定した高温域におけるホウ酸とZircaloy-4との反応に係る知見は十分に得られていない。本研究では、固体ホウ酸を載せたZircaloy-4の板材を900$$^{circ}$$Cまでの温度及び複数の雰囲気で酸化させることにより、固体ホウ酸の高温時挙動、ホウ酸とZircaloy-4との反応の有無、及びホウ酸がZircaloy-4の酸化挙動に及ぼす影響を調べた。実験結果から、高温酸化雰囲気においてZircaloy-4表面に固体ホウ酸の脱水により生成する無水ホウ酸が存在すると、この無水ホウ酸がZircaloy-4と雰囲気との接触を断つことでZircaloy-4の酸化を抑制することが示唆された。また、酸化膜付きZircaloy-4の表面に固体ホウ酸が付着し高温まで加熱された場合は、形成している酸化膜の空隙に無水ホウ酸が浸透することでその後の酸化を抑制することがうかがえた。

論文

The Effect of oxidation and crystal phase condition on the ballooning and rupture behavior of Zircaloy-4 cladding tube-under transient-heating conditions

成川 隆文; 天谷 政樹

Journal of Nuclear Science and Technology, 53(1), p.112 - 122, 2016/01

 被引用回数:7 パーセンタイル:55.03(Nuclear Science & Technology)

In order to investigate the effect of oxidation and crystal phase condition on the ballooning and rupture behaviors of cladding tube under simulated loss-of-coolant-accident (LOCA) conditions, laboratory-scale experiments were performed in which internally pressurized non-irradiated Zircaloy-4 (Zry-4) cladding specimens were heated to burst in steam and argon gas conditions. Values of the maximum circumferential strain were normalized by dividing them by engineering hoop stress at the time of rupture. The dependence of the normalized value on burst temperature and the relationship between the normalized value and the length, width and area of rupture opening were evaluated. The correlation between the normalized value and the burst temperature suggested that the fraction of the $$beta$$ phase in Zry-4 cladding specimens affected the strain in the specimens and the oxidation of specimens suppressed the amount of ballooning of the specimens. The relationship between the normalized value and the length, width and area of rupture opening indicated that the length, width and area of rupture opening depended on the crystal phase condition in Zry-4 cladding specimens irrespective of atmosphere in the case of the heating rate of $$sim$$3 K/s.

報告書

冷却材喪失事故時の被覆管延性低下に及ぼす冷却時温度履歴の影響

宇田川 豊; 永瀬 文久; 更田 豊志

JAERI-Research 2005-020, 40 Pages, 2005/09

JAERI-Research-2005-020.pdf:4.63MB

急冷開始温度及び急冷前の冷却速度がLOCA時の被覆管延性低下に及ぼす影響を調べることを目的とし、未照射PWR用17$$times$$17型ジルカロイ-4被覆管から切り出した試料を水蒸気中、1373及び1473Kで酸化し、ゆっくりと冷却(徐冷)してから急冷した。試験条件のうち、徐冷の速度を2$$sim$$7K/s、急冷開始温度を1073$$sim$$1373Kの範囲で変化させて複数の試験を行い、冷却条件の異なる試料を得た。酸化,急冷した試料に対しリング圧縮試験,ミクロ組織観察,ビッカース硬さ試験を実施した。急冷開始温度低下に伴い、金属層中に析出する$$alpha$$相の面積割合が大幅に増加し、被覆管の延性が明確に低下した。徐冷速度の減少に伴い、析出した$$alpha$$相の単位大きさ及び硬さの増大が生じたが、面積割合及び被覆管の延性はほとんど変化しなかった。析出$$alpha$$相は周りの金属層より硬く、また酸素濃度が高いことから、その延性は非常に低いと考えられる。したがって、析出$$alpha$$相の面積割合増大が、急冷開始温度低下に伴う延性低下促進の近因である。

報告書

ジルカロイ-4とMDAの機械特性に及ぼす水素吸収と中性子照射の影響(共同研究)

永瀬 文久; 菅野 光照*; 小澤 正明*; 小松 和志*; 古田 照夫*

JAERI-Research 2001-008, 61 Pages, 2001/03

JAERI-Research-2001-008.pdf:2.62MB

水素吸収及び中性子照射が軽水炉高燃焼度燃料被覆管の機械的特性に及ぼす影響に関し系統的な知見を得るために、さまざまな水素濃度を有するジルカロイ-4とMDA被覆管をJMTRにて照射し、引張試験を実施した。水素濃度範囲は10~140wtppmとした。照射量は1.1~3.6$$times$$10$$^{25}$$n/m$$^{2}$$(E>1MeV)であった。293及び633Kにおける試験により、水素濃度及び照射量に依存する機械特性の変化が調べられた。それらの変化は、ジルカロイ-4とMDAではほぼ同等であった。いずれの試験温度でも、800wtppm以上の水素濃度を有し照射された被覆管は、著しく小さな破断伸びを示すことがあった。このような破断伸びの著しい低下は、水素吸収量や照射量からは予想されない。本試験結果は、非常に高い水素濃度を有する照射被覆管において、水素吸収と照射の重畳的な影響を考慮する必要があることを示唆している。

報告書

水素添加ジルカロイ-4燃料被覆管の620Kにおける高速加圧バースト試験

永瀬 文久; 大友 隆; 上塚 寛

JAERI-Research 2000-046, 31 Pages, 2000/12

JAERI-Research-2000-046.pdf:3.72MB

RIA条件下における高燃焼度燃料棒の破損挙動を調べるために、水素を添加した被覆管に対する高速加圧バースト試験を620Kで実施した。本試験は、NSRRパルス照射時に高燃焼度燃料棒で生じる急激なPCMIを模擬するものである。水素濃度と半径方向の水素化物分布を変えた非照射Zry-4管を、最大加圧速度0.2MPa/msで加圧し破裂させた。試験の結果、被覆管は昇圧開始後400ms以内に破裂した。高燃焼度燃料被覆管を模擬し被覆管外面に水素化物を集積させた被覆管は、試験の比較的早い段階に破裂し、破裂圧力は相対的に低下した。また、水素化物集積する領域の厚さが100$$mu$$mを超える被覆管では、周方向残留ひずみは非常に小さく、1.1~2.8%であった。本試験の結果は、620Kにおいても、被覆管外面への水素化物集積が、パルス照射時の高燃焼度燃料棒の破損挙動に重要な役割を果たすことを示している。

報告書

室温における水素吸収ジルカロイ-4燃料被覆管の高速加圧バースト試験

永瀬 文久; 大友 隆; 上塚 寛

JAERI-Research 98-064, 25 Pages, 1998/11

JAERI-Research-98-064.pdf:2.17MB

高燃焼度軽水炉燃料棒のRIA条件下における破損挙動を調べるために、NSRRパルス照射時に生じるPCMIを模擬し被覆管を急速加圧できる装置を製作した。最初の実験として、室温で水素吸収Zry-4管に内圧を最大1.9MPa/msの高速で負荷するバースト試験を行った。その結果、水素吸収被覆管には、NSRR実験で見られた破損と酷似した軸方向に長い破損開口が生じた。さらに、破損挙動に及ぼす水素の影響が明瞭に観察された。円周方向の残留ひずみ量は、水素濃度が高いほど明確に低下した。また、水素化物を被覆外表面に偏析させた試料は、極めて小さなひずみ量で破裂し、破裂圧力も相対的に低かった。一方、加圧速度の及ぼす影響は比較的小さかった。NSRR実験等で見られたパルス照射時の高燃焼度燃料棒の破損が、被覆管の水素吸収と外面への水素化物偏析と深く関連していることが示された。

報告書

高温における銀とジルカロイ-4の反応性

永瀬 文久; 大友 隆; 上塚 寛; 古田 照夫

JAERI-M 92-179, 31 Pages, 1992/11

JAERI-M-92-179.pdf:2.66MB

ジビアアクシデント時におけるPWR用銀-インジウム-カドミウム制御棒合金とジルカロイの反応は、集合体溶融に大いに影響を及ぼすし、著者らはジルカロイ-4と制御棒合金の反応を調べすでに報告をした。この複雑な反応系のメカニズムを探るために、合金の主成分である銀とジルカロイ-4を、アルゴン中1273~1473Kで等温加熱しジルカロイの溶解挙動を調べた。本実験の結果と制御棒を用いた試験の結果を比較し、インジウムの寄与を考察した。反応速度は制御棒合金を用いた反応と同様に、試験温度の上昇とともに増大したが、低温側で制御棒材/ジルカロイ反応に比べて小さかった。この差は主に銀と制御棒合金の融点の差によるものと考えられる。1473Kでは2つの反応速度はほぼ同等であった。反応時間の経過に伴うジルカロイの肉厚減少はほぼ2乗則に従った。各温度での反応速度定数と見かけの活性化エネルギ580.8kJ/molを求めた。

論文

Hydrogen generation during cladding/coolant interactions under reactivity initiated accident conditions

更田 豊志; 藤城 俊夫

Proc. of the 1st JSME/ASME Joint Int. Conf. on Nuclear Engineering, p.271 - 277, 1991/00

反応度事故条件下では被覆管と水蒸気の反応によって、急激に水素が発生することが考えられる。発生した水素気泡は冷却材流動上の問題などを引き起こす可能性がある一方、事故発生直後のランアウト出力抑制に強い効果を持つことが予測される。そこで反応度事故時の水素発生挙動を調べるために、PWR型燃料棒を用いてNSRRでパルス的な中性子照射を行い、ボイド計によって水素発生量の過渡変化を測定するとともに、照射後の被覆管の酸化状態を調べることによって、総水素発生量を評価した。短時間での大量の水素発生が測定され、冷却材流動やランアウト出力抑制に大きな影響があることが明らかとなった。また総発生水素量は被覆管の欠陥状態に強く依存することがわかった。更に、LOCA条件に対して開発されたPRECIP-IIコードを用いて解析を行い、比較的緩やかな条件には同コードが適用可能であることを示した。

論文

High-temperature oxidation kinetics of Zircaloy-4 in oxygen/argon mixtures

上塚 寛; P.Hofman*

Journal of Nuclear Materials, 168, p.47 - 57, 1989/00

 被引用回数:23 パーセンタイル:89.04(Materials Science, Multidisciplinary)

被覆管試験片を用いた等温酸化試験によって、酸素/アルゴン混合気中におけるジルカロイ-4の反応速度を1173~1773Kの温度範囲で調べた。1173Kにおける酸化反応は3乗則に従った。一方、1273K以上の試験温度での反応則は2乗則であった。反応速度定数の温度依存性の不連続が1273Kと1373Kの間で認められた。この不連続はZrO$$_{2}$$反応層の結晶構造が同素変態することに起因するものであろう。酸化による重量増加、酸化膜の成長さらに酸化膜+酸素安定化$$alpha$$相の成長速度式を決定した。

論文

Zircaloy-4 oxidition behavior in steam-hydrogen and steam-argon mixtures from 1000 to 1500$$^{circ}$$C

上塚 寛; 大友 隆; 川崎 了

Severe Accidents in Nuclear Power Plants, Vol. 2, p.99 - 108, 1988/00

軽水炉の炉心損傷事故条件下の燃料被覆管の酸化挙動を明らかにするために、水蒸気/水素およびアルゴン/水蒸気混合気中でのジルカロイ-4高温酸化試験を実施した。

報告書

正方晶ZrO$$_{2}$$を含むジルカロイ酸化膜の特性; ジルカロイ-4管の酸化膜

本橋 治彦; 古田 照夫

JAERI-M 83-132, 15 Pages, 1983/08

JAERI-M-83-132.pdf:0.66MB

ジルカロイ-4管が水素・水蒸気の混合気流中、1000$$^{circ}$$Cで酸化した時に生成する層状酸化膜の特性を20$$^{circ}$$C~1300$$^{circ}$$Cの温度でX線回折法により調べた。室温におけるX線回析図形の解析から、正方晶ZrO$$_{2}$$を含む層状酸化膜中の単斜晶ZrO$$_{2}$$は340$AA$の小さな結晶子となり0.03%の大きな格子歪を持ちそして111の格子面間隔が標準物質より0.7%大きくなっていることを明らかにした。また高温X線回折から正方晶ZrO$$_{2}$$を含む層状酸化膜中の単斜晶ZrO$$_{2}$$はゆるやに相変化を起こすことがわかった。この相変化の起こる温度は正方晶ZrO$$_{2}$$を含まない酸化膜中の単斜晶ZrO$$_{2}$$の相変化温度より低くなっている。これらの事実から正方晶ZrO$$_{2}$$を含む層状酸化膜の生成は酸化膜の結晶子の微細化と大きな格子歪か生じる事と相関性があることを明らかにした。

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