Abstract

The characterization of grain boundary (GB) in atomic level is essential to understand and design the materials. It is well-known that the materials properties of GB are not same as that in bulk. Also, in the case of ceramics, the chemical composition in the vicinity of GB is different to bulk and the imperfection of bonding structure at GB core usually provides more vacancies than at bulk. In addition, GB core structure provides the faster mass transfer path, which gives high diffusion coefficient at GB. The atomic structure in the vicinity of GB plays an important role to understand the nonstoichiometry and the diffusion behavior at GB.

On the other hand, a systematic study on the atomic structures of GBs in engineering materials is difficult to perform because GB structure could not be controlled properly in polycrystalline and GB morphology changes dramatically with heat-treatment condition. Therefore, the bicrystal method has been extensively studied to characterize the atomic structure of GB in various materials. The bicrystal consists of two single crystals intentionally oriented. In addition, recent advents on the characterization technique such as Scanning Transmission Electron Microscopy (STEM) made it possible to characterize the atomic structure of GBs with the support of first principles calculation.

Especially, the atomic structure of GBs in SrTiO3 has been studied extensively because it is a cubic Perovskite structure with high symmetry and two different cations, Sr and Ti, of which the atomic columns are distinguishable in a high-angle annular dark-field (HAADF)-STEM method. In addition, SrTiO3 is one of important electroceramic materials used as capacitors and low-voltage varistor. In this material, it was reported that the electrical property such as non-linear I-V characteristics strongly depends on GB structures. Moreover, it was suggested that the electronic properties and the nonstoichiometry at GB are correlated to the morphology of the GB. Therefore, the characterization of the atomic structures of the GB and the relationships with the GB morphology are important for further understanding and finding the way to control the material's properties

Due to its importance, the atomic structures and nonstoichiometry of SrTiO3 symmetric tilt GBs have been extensively studied by combining bicrystal experiments, high resolution microscopy, and theoretical calculations. Ti excess near GB plane in Perovskite materials compared to bulk was reported in many literatures and it was believed that nonstoichiometry at GB was related to GB electronic property. However, the relationship between GB structure and nonstoichiometry was not fully understood. In Chapter 3, for understanding the chemical composition at GB in SrTiO3, defect energetics in nonstoichiometry in four model symmetric tilt GBs, [110](111)Σ3[001](210)Σ5, [001](510)(c)13A and [001](510)(C)13Bare discussed. . Examining the chemical composition with STEM-EDS methods and calculations of defect energetics in model boundaries systematically, the nonstoichiometry in the vicinity of GB is examined and discussed energetically. It is found that the change of chemical composition could be understood by the difference of defect energetics

Although a number of studies on the atomic structure of GB in SrTiO3 have been reported, most studies focused on the characterization of symmetric tilt GBs while the characterization of asymmetric tilt GBs has not been studied yet. This is due to the difficulties to make the proper model structures of the asymmetric tilt GB and the hardness to characterize the atomic structure at GB core with the conventional approaches. V. Randle reported that the microstructure could not compose of only symmetric tilt GB and the most observed boundaries were asymmetric tilt GB expect [110](111)(c)3 by observing the microstructure of Ni grains. Moreover, the impact of asymmetric tilt GBs was more effective to GB electrical properties than symmetric tilt GBs with the similar misorienetation angle in SrTiO3. Thus, the study on the asymmetric tilt GBs is necessary to apply bicrystal experiments to the engineering materials which contain a number of GBs. Modeling the asymmetric tilt GB with the help of simple geometry, the atomic structure of the asymmetric tilt GB, [001](100)//(430) is examined theoretically and experimentally in Chapter 4. Four model structures with different terminations, Sr-Sr, Sr-Ti, Ti-Sr and Ti-Ti, were considered and HAADF-STEM characterization in [001](100)//(430) bicrystal was also performed. It was found that the atomic structure of Ti-Ti termination were in good agreement with the observed structure. In addition, GB energy of [001](100)//(430) was related to the chemical potential of each element and that could be achieved in 1.0J/m2, which is almost same as the symmetric tilt GB, [001](210)(c)5 and [001](310)(c)5. Before this study, GB energies of the asymmetric tilt GB were considered as around 2.0J/m2 and these GBs were regarded as the unstable GB.

Furthermore, GB morphology in atomic level is also necessary to understand GB. It was reported that the microstructure of polycrystalline ceramics GB morphology depends on sintering condition and the material's properties also changed dramatically. However, GB morphology change of SrTiO3 in atomic level has not been studied yet. In Chapter 5, based on the calculated GB energy (in Chapter 3 and Chapter 4) and model experiments, the effect of temperature and atmosphere on GB morphology in the asymmetric tilt bicrystal is examined and discussed in the atomic in the atomic level. The asymmetric tilt [001] (100)//(430) bicrystal consists of two symmetric tilt GBs and one asymmetric tilt GB. The length and portion of each GB structure changed with heat-treatment was investigated. In order to examine the effect of temperature on GB morphology, the samples heat-treated in 1450°C, 1600°C and 1650°C air for 120hr were prepared. The experimental results is discussed with the change of anisotropy in GB energies and GB migration. Moreover, the sample heat-treated in 5% H2-95% Ar on 1450°C for 120hr were prepared to examine the effect of atmosphere. With heat-treatment in reducing atmosphere, the chemical potential of each element is also changed. The morphology change with heat-treatment could be understood by GB energetics of [001](100)//(430) Ti-Ti termination in different equilibrium conditions. This study shows the possibility to understand and predict GB morphology thermodynamically if GB energies of structures consisting GB morphology are calculated.

In SrTiO3, the electronic structure is also important to understand materials properties. Therefore, the electronic structure at each model GB was evaluated in Chapter 6. Recently, it was reported that the GB-induced unoccupied state formed and changed materials' properties in MgO GB. Similar, the extra state due to GB, which reduces band gap apparently, was examined in the model GBs, the electronic structure of each GB was examined to understand electronic properties at GB. Examining the band gap of each GB systematically, the relationship between atomic structure and electronic structure of GB is investigated. The GB-induced unoccupied states was found within bandgap. Moreover, the square of wave functions in the GB-induced level was illustrated. Interestingly, in the asymmetric tilt GB, [001](100)//(430), the localization of electrons at the specific Ti sites was calculated and it would be related to the distortion of bonding structure at GB core. The relationship between the electronic structure and the material's properties is also discussed.

Moreover, in Chapter 7, the case study for the geometric method to model the asymmetric tilt GB model was introduced. In order to confirm the geometric modeling for asymmetric tilt GB, two additional bicrystals satisfying Pell's number, [110](221)//(001) and [110](114)//(110), were prepared and these boundaries were calculated. It was found that the atomic structure of [110](221)//(001) was characterized and the newly introduced GB, [110](225)//(441), was found in [110](114)//(110) bicrystal. The geometric relationship and GB energetics in [110](114)//(110) bicrystal was discussed and the atomic structure of [110](225)//(441) were characterized. This results shows that the geometrically prepared bicrystal gives a chance to find the stable asymmetric or symmetric tilt GB structures, which are essential to extend our understanding of GB and make it possible to predict GB morphology.

In this study, the atomic structures, nonstoichiometry and GB morphology of model SrTiO3 GBs, including both symmetric and asymmetric tilt GBs, are systematically investigated by using aberration corrected (STEM) and first principles calculations to understand SrTiO3 GBs further. The atomic structures of three symmetric tilt GB structures, [110](111)(c)3, [001](210)(c)5 and [001](510)(c)13, and three asymmetric tilt GB structures, [001](100)//(430), [110](221)//(001) and [110](225)//(441) are discussed. The atomic models of asymmetric tilt GBs, which are important but not examined yet, were constructed with the help of geometric consideration, Pythagoras's triangle and Pell's number. In addition, the other important issues in understanding GB such as the chemical composition at GB and GB morphology are also discussed. Finally, in the case study, with the proposed the modeling methods for the asymmetric tilt GB, it is success to characterize the new asymmetric tilt GB, which has not been reported within author's knowledge. This indicated that the basic GB structures, which are necessary to understand GB phenomena, could be found in this approach and these GB structures make the further understanding of GB structure possible.

Based on the results presented in this thesis, a general conclusion can be given: the atomic and electronic structures of SrTiO3 GBs could be achieved with the combination of calculation and experiment with a help of the geometric consideration. Moreover, the chemical composition at GB and GB morphology, which is essential to predict GB properties, could be understood energetically.

本提出論文では、代表的な機能性酸化物のチタン酸ストロンチウム(SrTiO3)中に存在する結晶粒界に着目し、主に第一原理計算を用いることにより、粒界において形成される特異な原子配列および電子状態、また、それに起因して生じる粒界での過剰なエネルギーについて明らかにしている。本論文で研究の対象としたSrTiO3では、電気特性などの諸特性が結晶粒界に大きく影響を受けることが知られている。また、焼結体において形成される粒界の形態や特有の晶癖面等は焼結条件に大きく依存し、これに伴い原子レベルの構造や状態も様々に変化する。このような粒界における原子配列や電子状態は未だ十分には理解されておらず、本研究では特徴的な幾つかのSrTiO3粒界をとりあげ、その原子・電子構造と諸特性、焼結挙動との相関性について明らかにすることを目的としている。

本論文は、第1章の序論に始まり、第2章の具体的な計算手法および計算方法の説明、第3章から第7章では計算結果および実験結果を議論し、第8章で総括を行う8章の構成となっている。

第1章においては、本研究で対象とするSrTiO3に関する結晶構造、基本的な物性、応用等の背景、結晶粒界の幾何学的な記述方法、粒界における理論計算および実験的な観察手法等、本論文において必要とされる背景について記述されている。第2章ではSrTiO3の粒界におけるモデリングの方法について、粒界面に対して対称な構造である対称粒界と、本研究の特色である非対称粒界とに分けて詳細に記述している。また、本研究の主要な方法である密度汎関数理論を用いた第一原理計算、粒界原子配列、電子状態、粒界エネルギー、点欠陥形成エネルギーの導出法、ならびに電子顕微鏡観察の手法について記述されている。

第3章では、[110]/(111)Σ3、[001]/(310)Σ5、[001]/(510)Σ13の3種類のSrTiO3対称傾角粒界について、第一原理計算および電子顕微鏡観察を用いた原子構造解析について記述されている。また、得られた粒界原子配列から、結合欠損および局所的な歪みの分布状態の解析、粒界エネルギーとの相関性の探索を行っている。さらに粒界の各原子位置における空孔の形成エネルギーを評価し、各原子位置における配位環境や各原子の化学ポテンシャル依存性などを議論するとともに、実験的に得られた粒界における化学組成変化などについて考察している。これらの詳細な解析は、粒界の静的な原子配列の理解にとどまらず、試料作製時の温度・雰囲気条件に依存した構造・組成の変化等についての知見をも与えている。

第4章では、SrTiO3[001](100)/(430)非対称傾角粒界について、第一原理計算および高分解能電子顕微鏡観察を用いた、原子構造解析、エネルギーおよび電子状態についての検討が行われている。粒界における微視的な自由度の1つとなる終端面の組み合わせを詳細に考慮し、この非対称粒界がTi過剰組成の対称傾角粒界と同等のエネルギーを持つ安定構造を有することなどが明らかとされた。これまで非対称傾角粒界におけるエネルギーや原子配列・電子状態の解析は行われてこなかったが、今回の結果は、非対称傾角粒界がその諸特性や焼結挙動に及ぼす影響を理解する上で重要となることを示している。

第5章では、モデル試料を用いた実験を行い、観察されたSrTiO3粒界の晶癖面およびその熱処理条件による変化について検討されている。還元雰囲気で熱処理を行った試料では、主に(100)/(430)の非対称成分で構成される粒界から(210)および(310)の対称成分で構成される粒界へと構造が変化する様子が観察された。このことは、上述の第3章および第4章において得られた粒界エネルギーにより理解できる。また、粒界モフォロジーについても、このような電子状態計算から得られる粒界エネルギーから理解できることは重要な知見である。

第6章では、数種類のSrTiO3[001]対称および非対称傾角粒界において形成される電子状態の考察が行われている。電子状態は粒界性格に依存し、幾つかの粒界では非占有準位が伝導帯下端近傍に形成されることが明らかとなった。この非占有準位はTiの3d軌道によるものであり、粒界近傍の特定のTiサイトに局在している。このような粒界に局在したエネルギー準位は、粒界を横断する方向の電流-電圧特性に影響を与える可能性があることについて議論されている。

第2章~第6章で対象とした安定な粒界原子配列、粒界モフォロジー、粒界エネルギーの探索は、第7章においてさらにSrTiO3[110]傾角粒界の解析へ適用されている。このような系の適用は、SrTiO3粒界一般における構造安定化の理解に、ひいては粒界一般における構造安定化の理解につながることが期待できる。最後に第8章において論文全体が総括されている。

本論文は全体として良く構成されており、また、当該分野において十分に価値のある研究がなされているものと判断する。それぞれの理論計算、実験観察は注意深くかつ効果的に行われており、これより得られた結果についても詳細かつ合理的に議論されている。

よって本論文は博士(工学)の学位請求論文として合格と認められる。