Fault Vector Research Articles

Analysis of Dislocation Behavior in Low Dislocation Density, PVT-Grown, Four-Inch Silicon Carbide Single Crystals

AbstractSynchrotron White Beam X-ray Topography studies are presented of dislocation behavior and interactions in a new generation of one hundred millimeter diameter, 4H-SiC wafers grown using Physical Vapor Transport (PVT) under specially designed low stress conditions. Such low stress growth conditions have, for example enabled reductions of basal plane dislocation (BPD) densities by two or three orders of magnitude compared to previous levels down to just a few hundred per square centimeter. This provides a unique opportunity to discern details of dislocation behavior which were previously precluded due to complications of image overlap at higher densities. Among the phenomena observed in these studies is the deflection of threading dislocations onto the basal plane producing various stacking fault configurations. Analysis of the contrast from these faults enables determination of their fault vectors which, in turn, provides insight into their possible formation mechanisms.

Fuzzy Diagnosis of Tapping Process Fault

Based on analyzing the problem of tap worn and broken in the tapping process, the faults in tapping process are classified into four types: tap worn, chips jamming, uneven hardness of material and the tapping process failure; According to the fuzzy theory, this paper describes the torque characteristic of the four types of faults, ascertains the characteristic vector of fault, presents the weight matrix among faults, puts forward the judgment method of system faults and establishes the fuzzy fault diagnosis system in tapping process. The experimental study shows that the fuzzy diagnosis method can effectively identify the four types of faults in tapping process and guard against tap broken.

Research on fault location technology based on BP neural network in DWDM optical network

BP neural network is introduced to the fault location field of DWDM optical network in this paper. The alarm characteristics of the optical network equipments are discussed, and alarm vector and fault vector diagrams are generated by analyzing some typical instances. A 17 × 14 × 18 BP neural network structure is constructed and trained by using MATLAB. By comparing the training performances, the best training algorithm of fault location among the three training algorithms is chosen. Numerical simulation results indicate that the sum squared error (SSE) of fault location is less than 0.01, and the processing time is less than 100 ms. This method not only well deals with the missing alarms or false alarms, but also improves the fault location accuracy and real-time ability.

Phase‐Transformation‐Induced Twinning in Orthorhombic BaCeO3

Phase‐transformation‐induced twinning in orthorhombic barium cerate (BaCeO3) has been analyzed using transmission electron microscopy. Reflection twins with boundaries lying in {110) and {112) are generated by loss of point group symmetry elements during solid‐state phase transition along the sequence of Pm3m→R3c→o1‐Ibmm→o2‐Pbnm when pressureless‐sintered samples were cooled from 1400°C to room temperature. Fault vectors R=ɛ〈110] and ɛ〈021], in which displacements are not related in a simple way to the lattice translation, are determined for the twin boundaries exhibiting δ‐fringe patterns. The high‐ and low‐symmetry phases, rhombohedral and orthorhombic, are not related by group–subgroup symmetry, and the transformation is discontinuous and first order in nature, where twin relationships in the low‐symmetry phase are forbidden by the Landau theory. However, the transformation twins observed experimentally are consistent with those predicted directly from assuming a non‐disruption condition between transition phases, where the new structure is described in the frame of the old one geometrically. Such a phase transition can be continuous and diffusionless if it occurs via second order to and from a metastable intermediate phase, which is a shared common space group of the high‐ and low‐symmetry phases. Accordingly, two possible intermediate phases of the minimal common supergroup cubic Pm3m (No. 221) and of the maximal common subgroup monoclinic C2/c (No. 15) for the two end phases are identified.

Defect structures in B12As2 epitaxial layers grown on (0001) 6H-SiC

A detailed analysis of the microstructure in B12As2 epitaxial layers grown by chemical-vapor deposition on (0001) 6H-SiC substrates is presented. Synchrotron white beam x-ray topography enabled macroscopic characterization of the substrate/epilayer ensembles and revealed the presence of a quite homogeneous solid solution of twin and matrix epilayer domains forming a submicron mosaic structure. The basic epitaxial relationship was found to be (0001)B12As2⟨112¯0⟩B12As2∥(0001)6H-SiC⟨112¯0⟩6H-SiC and the twin relationship comprised a 180° (or equivalently 60°) rotation about [0001]B12As2 in agreement with previous reports. Cross-sectional high resolution transmission electron microscopy revealed the presence of a ∼200 nm thick disordered transition layer which was shown to be created by the coalescence of a mosaic of translationally and rotationally variant domains nucleated at various types of nucleation sites available on the (0001) 6H-SiC surface. In this transition layer, competition between the growth of the various domains is mediated in part by the energy of the boundaries created between them as they coalesce. Boundaries between translationally variant domains are shown to have unfavorable bonding configurations and hence high-energy. These high-energy boundaries can be eliminated during mutual overgrowth by the generation of a 1/3[0001]B12As2 Frank partial dislocation which effectively eliminates the translational variants. This leads to an overall improvement in film quality beyond thicknesses of ∼200 nm as the translational variants grow out leaving only the twin variants. (0003) twin boundaries in the regions beyond 200 nm are shown to possess fault vectors such as 1/6[11¯00]B12As2, which are shown to originate from the mutual shift between the nucleation sites of the respective domains.

LMI-based sensor fault diagnosis for nonlinear Lipschitz systems

The problem of sensor fault diagnosis in the class of nonlinear Lipschitz systems is considered. A dynamic observer structure is used with the objective to make the residual converge to the faults vector achieving detection and estimation at the same time. It is shown that, unlike the classical constant gain structure, this objective is achievable by minimizing the faults effect on the estimation error of the dynamic observer. The use of appropriate weightings to solve the design problem in a standard convex optimization framework is also demonstrated. An LMI design procedure solvable using commercially available software is presented.

Nonlinear biological batch process monitoring and fault identification based on kernel fisher discriminant analysis

A novel nonlinear biological batch process monitoring and fault identification approach based on kernel Fisher discriminant analysis (kernel FDA) is proposed. This method has a powerful ability to deal with nonlinear data and does not need to predict the future observations of variables. So it is more sensitive to fault detection. In order to improve the monitoring performance, variable trajectories of the batch processes are separated into several blocks. Then data in the original space is mapped into high-dimensional feature space via nonlinear kernel function and the optimal kernel Fisher feature vector and discriminant vector are extracted to perform process monitoring and fault identification. The key to the proposed approach is to calculate the distance of block data which are projected to the optimal kernel Fisher discriminant vector between new batch and reference batch. Through comparing distance with the predefined threshold, it can be considered whether the batch is normal or abnormal. Similar degree between the present discriminant vector and the optimal discriminant vector of fault in historical data set is used to perform fault diagnosis. The proposed method is applied to the process of fed-batch penicillin fermentation simulator benchmark and shows that it can effectively capture nonlinear relationships among process variables and is more efficient than MPCA approach.

Quantitative fault estimation for a class of non-linear systems

This paper develops a methodology for actuator fault diagnostics and quantitative estimation of fault signals in a class of non-linear systems. The class of non-linear systems considered is one in which the non-linearity is an incremental quadratic type of non-linearity that includes Lipschitz, positive real and sector non-linear functions. The methodology provides for both state estimation and fault vector estimation. An LMI procedure can be utilized for explicit computation of the observer gains. The procedure developed can also be specialized to linear time invariant systems. Compared to previous results for LTI systems, the procedure developed herein does not require the LTI system to be minimum phase. The use of the developed methodology is demonstrated through two illustrative examples of real world physical applications.

Detection and diagnosis for sensor fault in HVAC systems

Principal component analysis (PCA) is presented to detect single sensor faults in heating, ventilation and air conditioning (HVAC) systems. Three PCA models, based on energy balance and air side and water side flow pressure balances, respectively, are set up to detect whether there is any abnormality occurring in the systems. With any fault discovered, a joint angle plot, which compares the new fault vector with known ones in the library, can be used to isolate the faulty sensor indeed. As pre-diagnosis, some expert rules are used to improve the diagnosing process. With the strategy of joint angle plot combined with expert rules, the single sensor fault can be timely isolated on line.

Phase‐Transformation‐Induced Anti‐Phase Boundary Domains in Barium Cerate Perovskite

Anti‐phase boundary (APB) domains resulting from the orthorhombic (o1, Ibmm (No. 74)) to orthorhombic (o2, Pbnm (No. 62)) phase transformation at ∼290°C in pressureless‐sintered barium cerate (BaCeO3) ceramics have been investigated by transmission electron microscopy and large‐angle convergent beam electron diffraction (LACBED). APB exhibiting symmetric π‐fringe patterns in both bright‐field and dark‐field images, lying in {011) with the fault vector R=1/2〈111〉, were determined adopting the invisibility criteria of 2πg·R=0 or 2nπ. The curved boundaries due to symmetry change can be related to the low symmetry phase by a pure translation upon phase transition. The displacement vector, R, relating the domains is the translational symmetry element from the origin to the lattice point that was lost upon transition. The formation of such domains induced by the o1→o2 phase transition is discussed in terms of change in the Bravais lattice and loss of lattice point upon the transition. The identification has also confirmed the existence of a higher symmetry orthorhombic o1 phase along the transition sequence of R3c→Ibmm→Pbnm. The increased spatial frequency of APB domains is attributed to A‐site ordering due to vacancies created by BaO loss and/or disordering of the B‐site substitutional defects generated extrinsically when doped with either a Y3+‐acceptor or a Nb5+‐donor.

Dislocation‐Containing Planar Faults in Metastably Retained Hexagonal Barium Titanate

Planar faults, designated F1–F6 and Fa, with intermixed dislocations in metastably retained hexagonal‐BaTiO3 ceramics, were found and analyzed by transmission electron microscopy. Only faults with one, two, and four extra c‐layers parallel to the basal plane have been identified. Fault vectors RF1=RFa=1/6[0221], RF2=RF3=1/3[0111], RF4=1/3[0112], and RF′1=RF5= RF6=RF′a=1/6[0221] were determined adopting the 2πg·R=0 (or 2nπ) criteria in combination with high‐resolution imaging. Further, the embedded dislocations were half‐partials with Burgers vectors b=1/3〈1010〉 determined by the g·b=0 effective invisibility criteria in conjunction with the eligible fault vectors. A rotation by 60° about the c‐axis was found between fault segments with RF1=1/6[0221] and RF′1=1/6[2021] located on either side of a partial. Basal dislocations with bB=1/3〈1210〉 have dissociated into two prism‐plane Shockley half‐partials with bPr=1/3〈1100〉 by glide in the fault plane (0002) according to 1/3〈1210〉→1/3〈1100〉+1/3〈0110〉. The fault segment F′1 encompassed by two half‐partials is an extrinsic complex stacking fault.

A method for fault detection and isolation in the integrated navigation system for UAV

In this paper, a method for real-time fault detection and isolation is presented, which has been tested successfully for unmanned aerial vehicles. In this method, two parity vectors are constructed to achieve the fault detection and isolation. In addition, the maximum likelihood estimate is used to estimate and correct the fault vector. Simulation results show that not only can the faulty system be detected accurately in time by this method, but also the fault can be repaired efficiently. Thus, the fault tolerance of the integrated system is improved remarkably by this method.

Phase‐Transformation‐Induced Twinning in Orthorhombic LaGaO3: {121} and [010] Twins

Pressureless‐sintered lanthanum gallate (LaGaO3) ceramics have been analyzed using X‐ray diffractometry (XRD) and scanning electron and transmission electron microscopy (SEM and TEM). Twins are induced by solid‐state phase transformation upon cooling from rhombohedral to orthorhombic (o, Pnma) symmetry at ∼145°C. Two types of transformation twins have been identified, and they co‐exist in some of the grains. The {121} twins are generated by loss of the mirror plane symmetry upon phase transformation. The twin planes are on {121} about which the two crystal parts are related by a mirror operation. The fact that twins are of reflection type is also confirmed by a tilting experiment in the microscope. The other, often termed the ‐type rotation, is a rotation twin induced by loss of fourfold rotation axes upon phase transition. The spot splitting of 2φ≈0.22° because of the orthorhombic obliquity (φ) is evidenced from the corresponding electron diffraction patterns (SADPs) where triplet reflection spots are clearly identified. The {121} twin domain boundaries exhibit δ‐fringes. The fault vector across twin boundaries R=ɛ is determined by applying the invisibility criteria of 2πg·R=0, or 2nπ. Such a translation is not related in a simple way to the structure of LaGaO3, and the length of the fault vector is not a fractional of the lattice displacement vector.

Intersecting basal plane and prismatic stacking fault structures and their formation mechanisms in GaN

A systematic study of intersecting planar boundary structures observed in a GaN epifilm grown on a vicinal 6H-SiC substrate (offcut towards [12¯10]) with an AlN buffer is presented. These structures are shown to comprise stacking faults that fold back and forth from the basal plane [I1 basal plane stacking faults (BSFs)] to the prismatic plane [prismatic stacking faults (PSFs)]. The PSFs, with fault vector 12⟨101¯1⟩ nucleate at steps on the substrate surface as a consequence of the different stacking sequences exposed on either side of the step. Once nucleated, PSFs intersecting the vertical step risers in the AlN buffer and eventually in the GaN film are replicated during the predominantly step-flow growth and propagate into the growing crystal. As a consequence of the different growth rates experienced on either side of the intersection of a PSF with a vertical step riser, the PSF may be redirected onto an equivalent {112¯0} plane, leaving an I1 BSF between the bottom of the redirected section of PSF and the top of that portion of the original PSF which was below the terrace. This leads to the formation of folded PSF/BSF fault structures which exhibit various configurations. Such folded stacking fault configurations form walls which enclose domains of different stacking sequence. Stair-rod dislocations (SRDs) are observed to form at the intersections of these various faults and the Burgers vectors of some of these are discussed. In some cases, reconstruction of these SRDs occurs through the formation of partner dislocations which serve to minimize the energy associated with the lattice disconnections located at the cores of the SRDs.

Properties of intergrowths and partial dislocations in mercury‐based HTSC oxides

AbstractIntergrowths, stacking faults and dislocations have been investigated by transmission electron microscopy in (Hg, Re)Ba2Ca2Cu3O8+δ and HgBa2CaCu2O6+δ bulk superconductors. The stacking fault vectors and the Burgers vectors of partial edge dislocations associated with the nucleation or the annihilation of [Ca–CuO2] bilayers in the unit cells of both compounds are derived by different methods. We discuss the influence of uniaxial stresses on intergrowth propagation and also mechanisms yielding strain relaxation around intergrowths. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation

In this note, the problem of observer design for linear descriptor systems with faults and unknown inputs is considered. First, it is considered that the fault vector function f is s~ times piecewise continuously differentiable. If the s~th time derivative of f is null, then s~ integral actions are included into a Luenberger observer, which is designed such that it estimates simultaneously the state, the fault, and its finite derivatives face to unknown inputs. Second, when the fault is not time piecewise continuously differentiable but bounded (like actuator noise) or s~th time derivative of fault is not null but bounded too, a high gain observer is derived to attenuate the fault impact in estimation errors. The considered faults may be unbounded, may not be determinist, and faults and unknown inputs may affect the state dynamic and plant outputs. Sufficient conditions for the existence of such observer are given. Results are illustrated with a differential algebraic power system.

Planar defects in metastably retained hexagonal BaTiO3 ceramics: α-type extended stacking faults

Planar faults are analysed in hexagonal barium titanate (h-BaTiO3) (polytype 6H). This present paper is restricted to widely extended faults. Nanosize (approximately 120 nm) stoichiometric tetragonal BaTiO3 powder hot pressed at 1300°C for 2 h under a pressure of about 25.8 MPa contains the h-BaTiO3 phase that is metastably retained at room temperature. Planar defects have been characterized by transmission electron microscopy. The fault vectors and and and and have been determined by application of the invisibility criterion, and the shear component along the prismatic directions has been confirmed by high-resolution imaging. It is suggested that oxygen vacancies generated during hot pressing in the reducing atmosphere of the graphite-die assembly facilitate the metastable retention of the h-BaTiO3 phase. The stacking faults in the hexagonal matrix are identified as (pseudo)cubic lamellae intergrown with h-BaTiO3.

π‐Rotation Faults in Hexagonal BaTiO3

Planar defects in the metastably retained h‐BaTiO3 exhibiting α‐fringe pattern have been characterized via transmission electron microscopy (TEM). The eligible fault vectors were determined by adopting the invisibility criteria of 2πg·R = 0 or 2nπ augmented by high‐resolution imaging. Three stacking faults, F1, F2, and F3, of the extrinsic nature have been fully analyzed. The eligible fault vectors for faults F1 and F3 contained a basal component respectively of ⅓[0001] and ⅙[0001] and a common prismatic component of ⅓〈10[1‐macr]0〉. However, only three of the 〈10[1‐macr]0〉 vectors are the eligible prismatic component for the fault vectors RF1=⅓[0[1‐macr]11], ⅓[10[1‐macr]1], and ⅓[[1‐macr]101], and RF3=⅙[02[2‐macr]1], ⅙[2[2‐macr]01], and ⅙[[2‐macr]021] that have fulfilled the invisibility criteria. On the other hand, all fault vectors RF21=⅙〈[4‐macr]223〉 for fault F2, containing six vectors of the 〈[2‐macr]110〉 family, is eligible. Unlike the faults of πRF=⅙〈[2‐macr]203〉 found in the D019 intermetallics of Ni3Sn and Co3W, neither fault F1 nor F3 is the π‐rotation type. Fault F2, however, is a π‐rotation fault since a 60°‐rotation clockwise about [0001] has produced another eligible fault vector.

Morphology, crystallography and defects of the intermetallic -phase precipitated in a duplex ( + ) stainless steel

The ferritic matrix in the Fe-22Cr-5Ni-3Mo-0.03C ferritic-austenic duplex stainless steel undergoes a variety of decomposition processes when aged in the temperature range 650–750°C. These processes involve the precipitation of the austenite and of the σ and χ Frank-Kasper phases. The intermetallic χ-phase is found at both the grains boundaries (homo and heterophase interfaces) and inside the ferritic grains where it adopts an unexpected hexagonal shape. At the early stage of its precipitation, it nucleates at the δ/γ and δ/σheterophase interfaces and then grows by expanding exclusively in the ferritic matrix. This study is basically focused on this intermetallic χ-phase. The crystal structure and the chemical composition are respectively studied by electron diffraction and energy dispersive X-ray spectroscopy. The χ-phase exhibits rational orientation relationships with the austenite and the σ-phase with which it is in contact and an invariably cube-on-cube orientation relationship with the ferritic matrix into which it grows. Based on the orientation relationship, the morphology and the number of variants of this χ-phase are understood in terms of the group theory. The planar defects present in a large density in the χ-phase, are roughly parallel to {0 1 1}χ//{0 1 1}δ. The fault vectors are determined as: \(\frac{1}{3}\)〈110〉χ and \(\frac{1}{4}\)〈111〉χ, the latter corresponding for a bcc structure to a π phase shift, the defects can be simply described as π boundaries. Based on the obtained results, a structural proximity between the χ-phase and a super-cell derived from the ferritic matrix has been brought to light. This super-cell is described as a stacking of corrugated and planar layers obeying the following parallelism {0 1 1}χ//{0 1 1}δ. Indeed this super-cell approach provides an interpretation for several microstructural features such as the χ/δ interface plane, the planar defects in the χ-phase and their related fault vectors.

Reply to "Comment on `A Vertical Exposure of the 1999 Surface Rupture of the Chelungpu Fault at Wufeng, Western Taiwan: Structural and Paleoseismic Implications for an Active Thrust Fault,' by Jian-Cheng Lee, Yue-Gau Chen, Kerry Sieh, Karl Mueller, Wen-Shan Chen, Hao-Tsu Chu, Yu-Chang Chan, Charles Rubin, and Robert Yeats," by Yuan-Hsi Lee, Shih-Ting Lu, Tung-Sheng Shih, and Wei-Yu Wu

We welcome Y. H. Lee et al.'s interest in our article (Lee et al., 2001). We thank them for their comment, which provides a further opportunity for discussing the quantification of the slip amounts including horizontal and vertical components and the fault geometry for an earthquake thrust scarp in Wufeng, western Taiwan, during the 1999 M 7.6 earthquake. In their comment, Y. H. Lee et al. used restoration of deformed concrete fence across the 1999 scarp to estimate the slip vector of the main fault. The estimated slip amount, especially the horizontal component, is different (significantly less) from our results presented in the 2001 BSSA article. They then applied an “area-balance” technique to compare their results with ours. They showed that their area-balance method favored their estimates including the slip amounts and the fault dip angle. They concluded that their estimated slip amounts are more reasonable than ours. The fundamental questions in this issue, in our opinions, include the actual amounts of deformation (slip) and the associated deformation processes, as well as the limitation and uncertainty of the applied techniques on an earthquake-formed thrust scarp. Hereafter we attempt to answer these questions and clarify the related problems.