Compatible domain structures in ferroelectric single crystals

The aim of the current study is to develop an efficient model which can predict low-energy compatible microstructures in ferroelectric bulks and film devices and their dynamic behaviour. The results are expected to assist in the interpretation of microstructure observations and provide a knowledge of the possible domain arrangements that can be used to design future materials with optimum performance.Several recent models of ferroelectric crystals assume low energy domain configurations. They are mainly based on the idea of fine phase mixtures and average compatibility, and can require intensive computation resulting in complex domain configurations which rarely occur in nature. In this research, criteria for the exact compatibility of domain structure in the form of a periodic multi-rank laminate are developed. Exactly compatible structure is expected to be energetically favourable and does not require the concept of a fine mixture to eliminate incompatibilities. The resulting method is a rapid and systematic procedure for finding exactly compatible microstructures. This is then used to explore minimum rank compatible microstructure in various crystal systems and devices. The results reveal routes in polarization and strain spaces along which microstructure can continuously evolve, including poling paths for ferro- electric single crystals. Also, the method is capable to generate all possible exactly compatible laminate configurations for given boundary conditions. It is found that simple configurations are often energetically favourable in conditions where previous approaches would predict more complex domain patterns. Laminate domain patterns in ferroelectrics are classified and corre- lated with observations of domains in single crystals, showing good agreement.The evolution of microstructures under applied mechanical and electrical loads is studied. A variational method, which minimises the overall energy of the crystal is developed. A new concept of transitional “pivot states” is introduced which allows the model to capture the feature that the microstructure in ferroelectric crystal switches between possible domain patterns that are energetically favourable, rather than assuming one particular domain pattern throughout. This model is applied to study the hysteresis responses of barium titanate (BaTiO3) single crystals subjected to a variety of loads. The results have good agreement with experimental data in the literature. The relationship between domain patterns and ferroelectric hysteresis responses is discussed.</p

Compatible domain structures in ferroelectric single crystals

The aim of the current study is to develop an efficient model which can predict low-energy compatible microstructures in ferroelectric bulks and film devices and their dynamic behaviour. The results are expected to assist in the interpretation of microstructure observations and provide a knowledge of the possible domain arrangements that can be used to design future materials with optimum performance. Several recent models of ferroelectric crystals assume low energy domain configurations. They are mainly based on the idea of fine phase mixtures and average compatibility, and can require intensive computation resulting in complex domain configurations which rarely occur in nature. In this research, criteria for the exact compatibility of domain structure in the form of a periodic multi-rank laminate are developed. Exactly compatible structure is expected to be energetically favourable and does not require the concept of a fine mixture to eliminate incompatibilities. The resulting method is a rapid and systematic procedure for finding exactly compatible microstructures. This is then used to explore minimum rank compatible microstructure in various crystal systems and devices. The results reveal routes in polarization and strain spaces along which microstructure can continuously evolve, including poling paths for ferro- electric single crystals. Also, the method is capable to generate all possible exactly compatible laminate configurations for given boundary conditions. It is found that simple configurations are often energetically favourable in conditions where previous approaches would predict more complex domain patterns. Laminate domain patterns in ferroelectrics are classified and corre- lated with observations of domains in single crystals, showing good agreement. The evolution of microstructures under applied mechanical and electrical loads is studied. A variational method, which minimises the overall energy of the crystal is developed. A new concept of transitional “pivot states” is introduced which allows the model to capture the feature that the microstructure in ferroelectric crystal switches between possible domain patterns that are energetically favourable, rather than assuming one particular domain pattern throughout. This model is applied to study the hysteresis responses of barium titanate (BaTiO3) single crystals subjected to a variety of loads. The results have good agreement with experimental data in the literature. The relationship between domain patterns and ferroelectric hysteresis responses is discussed.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Simulation of Piezoelectric Device and Ultrasonic Wave using Finite Element Analysis

本論文透過有限元素法對壓電元件進行模擬與設計分析。主要應用於三方面：壓電元件的導納模擬、距離感測器指向性模擬與醫用高功率燒灼器模擬。 在壓電元件的導納模擬方面，本論文提出一個新的方法以有限元素法來模擬壓電元件的機械能量耗損。其中機械能量耗損可藉由迭代法所求出之複數材料參數被考慮進壓電元件中。並利用QR分解法將欲求之任意形狀元件的能量耗損分析成9種基本模態。且因為這些基本模態的能量耗損因子已知，故可將其轉換成總體等效黏滯阻尼比，如此即可直接被一般的有限元素動力分析考慮進模擬系統中。本文並利用實驗與理論公式驗證此數值方法之結果，證實此方法的確可提供準確的機械能量損失因子，並模擬出相當精準的導納頻率響應曲線。 在距離感測器指向性模擬方面，本文針對感測器發波面的結構邊界條件對音波半衰角的影響進行分析。一般車用距離感測器的要求為垂直面半衰角小，水平面半衰角大的不對稱指向特性。由結果可知發波面邊界條件類似為固定端的狀況下半衰角最大；鉸支承次之；自由端半衰角最小。利用以上結果，本文將市售距離感測元件的垂直方向外殼挖洞，使發波面結構邊界條件更類似於一個自由端，由模擬結果看來，此舉可使元件指向性的不對稱約增加50%。但邊界條件過度趨近於自由端，卻會使音波能量降低，減少感測距離。為了顧及感測範圍。本文進一步透過改變洞長參數，求得最佳洞長約為0.4倍之元件直徑。 在醫用高功率燒灼器模擬方面。一般醫用燒灼器的需求為-3dB壓力值所圍的面積長寬比必須大，因此本文建製燒灼器元件之模型，瞭解其振動模態與共振頻率，再以實驗證實數值模擬的正確性。並進一步針對相同元件面積下，探討改變曲率半徑及張角對於燒灼面積的影響。由結果得知，曲率半徑愈小張角愈大會導致燒灼面積減小、長寬比增加以及壓力主峰值的提高。 本論文成功地透過有限元素法精準模擬壓電元件的能量耗損，並找出距離感測元件設計最佳解，以及預測醫療燒灼器幾何變化所造成的影響。不僅如此，研究中模擬的結果能在壓電元件實作之前，即提供一定程度的分析與預測能力。在未來研究中更可進一步探討壓電片在元件中的配置與效率間的關係，以及超音波在不同介質中傳遞的行為，拓展模擬輔助設計之功能性。In this thesis, we analyze and design the piezoelectric device by finite element simulation. The modeling and simulation have been applied in three subjects: admittance of piezoelectric device, directivity of distance sensor, and high intensity focused ultrasound( HIFU). For admittance of piezoelectric device, a methodology to model mechanical losses of piezoelectric devices by the finite element analysis is presented. Complex parts of the material constants are extracted using an iterative method. Mechanical losses of piezoelectric devices are taken into account through these complex constants. A scheme using the QR factorization is developed to decompose mechanical losses of an arbitrary-shaped device into fundamental modes. These losses are then transformed into an equivalent viscous damping ratio in a standard finite element dynamics analysis. The proposed method enables us to obtain a reliable mechanical loss factor. Numerical results demonstrate that the proposed method can predict measured admittance spectra reasonably well. For directivity of distance sensor, we analyze the effect of different boundary conditions to the half decay angle. The goal for vehicle short-range sensing is that the half decay angle in the vertical direction has to be less than that in horizontal. Our simulation reveals that the half decay angle of free end boundary condition is much less than that of simple-supported and fixed ends. With such design criterion in mind, we further improve the distance sensor device by cutting a square hole in the vertical direction to mimic the free-end boundary condition. This procedure can improve the asymmetry of directivity up to 50%. However, it shortens the detect region. Therefore, we change the length of cave and obtain an optimized value, 0.4 times of device diameter, for the directivity and detect region. The HIFU application requires the length to width ratio of -3dB focal area to reach a maximum value. To this end, we construct the HIFU simulation model to find out the relations between the modal shape and resonance frequency, and compare the numerical result with experimental measurements. Furthermore, we change geometric focal length and angle in the same active area to explore the effect of -3dB focal area. The result reveals that small geometric focal length and large angle may decrease the -3dB focal area, and increase length to width ratio and the pressure magnitude of main lobe. In conclusion, we have successfully shown the feasibility of using finite element simulation to analyze the behavior of piezoelectric devices. Through the aforementioned simulation, we can predict the energy loss of piezoelectric material and provide a guideline for design of distance sensor and HIFU.致謝 i 摘要 v Abstract vii 目錄 ix 圖目錄 xiii 表目錄 xvii 第1章 緒論 1 1-1 簡介 1 1-2 研究目的 4 1-3 論文架構 5 第2章 壓電材料行為與量測 6 2-1 壓電效應 6 2-2 壓電材料簡介 7 2-3 壓電方程式 9 2-4 複數壓電材料係數量測方法 12 2-5 壓電有限元素理論 20 2-5-1 壓電元件之有限元素理論 20 2-5-2 壓電元件模態分析 23 2-5-3 壓電元件頻率域分析 27 第3章 壓電元件導納量測與模擬 30 3-1 研究背景 30 3-2 壓電材料之能量損失因子 32 3-3 任意形狀元件之能量損失因子 35 3-4 考慮能量損失之導納模擬 41 3-4-1 具有導納解析式之標準形狀 42 3-4-2 無導納解析式之形狀 48 3-5 結果討論 51 第4章 壓電元件應用於車用超音波距離感測器 52 4-1 研究背景 52 4-2 壓電元件指向性模擬相關理論 54 4-2-1 波傳理論 55 4-2-2 有限元素應用於流體與結構之耦合計算 57 4-2-3 超音波元件指向性與半衰角 59 4-3 超音波距離感測器量測與模擬 60 4-3-1 壓電元件指向性量測實驗 60 4-3-2 距離感測器與波傳系統模型建置與模擬 61 4-3-3 量測與模擬結果驗證討論 65 4-4 壓電元件設計與指向性分析 69 4-4-1 結構邊界條件與半衰角之關係 69 4-4-2 壓電元件設計改進與模擬 72 4-4-3 元件設計討論 76 4-5 結論 79 第5章 壓電元件應用於醫用高功率燒灼器 81 5-1 研究背景 81 5-2 醫用高功率燒灼器量測與模擬 82 5-2-1 燒灼器壓力量測實驗 82 5-2-2 燒灼器壓力模擬模型建製與模擬 84 5-2-3 量測與模擬結果驗證討論 88 5-3 定表面積下曲率半徑及張角之影響討論 89 5-4 結論 95 第6章 結論 96 6-1 研究成果與貢獻 96 6-2 未來研究方向 98 參考文獻 100 附錄一 105 附錄二 109 附錄三 113 作者簡歷 11

The Analysis of Superelasticity and Microstructural Evolution in NiTi Single Crystals by Molecular Dynamics

Superelasticity in shape memory alloys is an important feature for actuators and medical devices. However, the function of the devices is typically limited by mechanical bandwidth and fatigue, which are dominated by the microstructures. Thus, in order to correlate the mechanical response and the microstructures, the microstructural evolution in NiTi single crystals under the compression, tensile, and shearing tests is simulated by molecular dynamics (MD) in the current study. Then, the martensite variant identification method, which identifies the crystal variants/phases of each lattice based on the transformation matrix, is used to post-process the MD results. The results with the detailed information of variants and phases reveal many features that have good agreement with those reported in the literature, such as X-interfaces and the transitional orthorhombic phase between the austenite and monoclinic phases. A new twin structure consisting of diamond and wedge-shaped patterns is also discovered. The macroscopic behavior, such as stress-strain curves and the total energy profile, is linked with the distribution of dislocation and twin patterns. The results suggest that the loading cases of shear and compression allow a low critical strain for the onset of martensitic transformation and a better superelasticity behavior. Therefore, the two loading cases are suitable to apply to the NiTi actuators. The current work is expected to provide insight into the mechanical responses and design guideline for NiTi shape memory alloy actuators

A Hybrid Model for Predicting Bone Healing around Dental Implants

Background: The effect of the short-term bone healing process is typically neglected in numerical models of bone remodeling for dental implants. In this study, a hybrid two-step algorithm was proposed to enable a more accurate prediction for the performance of dental implants. Methods: A mechano-regulation algorithm was firstly used to simulate the tissue differentiation around a dental implant during the short-term bone healing. Then, the result was used as the initial state of the bone remodeling model to simulate the long-term healing of the bones. The algorithm was implemented by a 3D finite element model. Results: The current hybrid model reproduced several features which were discovered in the experiments, such as stress shielding effect, high strength bone connective tissue bands, and marginal bone loss. A reasonable location of bone resorptions and the stability of the dental implant is predicted, compared with those predicted by the conventional bone remodeling model. Conclusions: The hybrid model developed here predicted bone healing processes around dental implants more accurately. It can be used to study bone healing before implantation surgery and assist in the customization of dental implants

Healing Pattern Analysis for Dental Implants Using the Mechano-Regulatory Tissue Differentiation Model

(1) Background: Our aim is to reveal the influence of the geometry designs on biophysical stimuli and healing patterns. The design guidelines for dental implants can then be provided. (2) Methods: A two-dimensional axisymmetric finite element model was developed based on mechano-regulatory algorithm. The history of tissue differentiation around eight selected implants can be predicted. The performance of the implants was evaluated by bone area (BA), bone-implant contact (BIC); (3) Results: The predicted healing patterns have very good agreement with the experimental observation. Many features observed in literature, such as soft tissues covering on the bone-implant interface; crestal bone loss; the location of bone resorption bumps, were reproduced by the model and explained by analyzing the solid and fluid biophysical stimuli and (4) Conclusions: The results suggested the suitable depth, the steeper slope of the upper flanks, and flat roots of healing chambers can improve the bone ingrowth and osseointegration. The mechanism related to solid and fluid biophysical stimuli were revealed. In addition, the model developed here is efficient, accurate and ready to extend to any geometry of dental implants. It has potential to be used as a clinical application for instant prediction/evaluation of the performance of dental implants

Failures of Cu-Cu Joints under Temperature Cycling Tests

In this study, the failure mechanisms of Cu-Cu joints under thermal cycling were investigated. Two structures of dielectrics (PBO/underfill/PBO and SiO2) were employed to seal the joints. Stress gradients induced in the joints with the different dielectrics were simulated using a finite element method (FEM) and correlated with experimental observations. We found that interfacial voids were forced to move in the direction from high stress regions to low stress ones. The locations of migrated voids varied with the dielectric structures. Under thermal cycling, such voids were likely to move forward to the regions with a small stress change. They relocated and merged with their neighboring voids to lower the interfacial energy