Determining the Burgers vectors and elastic strain energies of interface dislocation arrays using anisotropic elasticity theory

A formalism for describing interface dislocation arrays linking the Frank–Bilby equation and anisotropic elasticity theory under the condition of vanishing far-field stresses is developed. The present approach enables the determination of a unique reference state for interface misfit dislocations, within which the Burgers vectors of individual dislocations are defined and allows for the unequal partitioning of elastic fields between neighboring crystals. The elastic strain energies of interface dislocation arrays are computed using solutions for short-range elastic fields. Examples of applications to simple interfaces are given, namely symmetric tilt and twist grain boundaries, as well as a pure misfit heterophase interface.     

A crystallographic model of fcc/bcc martensitic nucleation and growth

A crystallographic model of face-centered cubic/body-centered cubic martensitic nucleation and growth has been developed in which the glissile martensitic interface is described in terms of discrete transformation and misfit dislocations within the framework of the Frank–Bilby equation. In the present model heterogeneous nucleation of a martensitic embryo occurs spontaneously by dissociation of an existing perfect dislocation under certain conditions, such as the catalysis on grain boundaries. Autocatalytic dislocation is proposed to be responsible for embryo growth, then nucleation and subsequent growth of a single embryo can be regarded as an autocatalytic process. As a natural result the crystallographic features of grown martensite are consistent with the phenomenological theory of martensite crystallography. Martensitic nucleation in this model agrees with many experimental observations.     

Recent progress in thin film epitaxy across the misfit scale (2011 Acta Gold Medal Paper)

This paper discusses recent progress in thin film epitaxy across the misfit scale through the paradigm of domain matching epitaxy (DME). This epitaxy across the misfit scale is critical for integrating multifunctionality on a chip and creating smart structures for next-generation solid-state devices. There are three sources of strains that are cumulative at the growth temperature, and the relaxation process starts during the growth process. Upon cooling, unrelaxed lattice, thermal and defect strains give rise to net residual strains. In large misfit (ε ? 10%) systems, where lattice misfit strain is predominant, it can be relaxed completely, and then only thermal and defect strains remain upon cooling. In low misfit systems, all three sources contribute to the residual strain upon cooling, as result of incomplete lattice relaxation. The predominant strain relaxation mechanism in thin films is by nucleation of dislocations at the free surface, as the nucleation energy in the bulk is considerably higher. At the free surface, the activation barrier for dislocation nucleation is considerably lower at the steps. Since the step formation energy is lower under a compressive stress compared with tensile stress, it reduces nucleation energy under compressive stress and lowers the critical thickness compared with tensile stresses in thin films. Once the dislocation nucleates, it propagates or glides to the interface to relieve the strain. However, if lattice frictional stress in the film is high, most dislocations may not reach the interface, depending upon the growth temperature and rate. Thus, these two key steps, dislocation nucleation and propagation, play a critical role in the thin film relaxation process. Once the dislocations reach the interface, the atomic structure of the dislocation at the heterointerfaces determines its electronic properties, specifically trapping and recombination characteristics. It is found that the atomic structure of the dislocation is determined by the interplay between strain and chemical free energies. Thus, the dislocations (representing missing or extra planes) play a critical role in the relaxation of thin film heterostructures. This paper focuses on epitaxy across the misfit scale, based upon matching of integral multiples of lattice planes. If the misfit falls between the integral multiples, it is accommodated by the principle of domain variation, where domains alternate to accommodate the misfit. Details of epitaxy from low misfit (～4%) in Ge/Si) to large misfit (～22%) in TiN/Si are shown. In III-nitride/sapphire and II-oxide/sapphire systems, this paper deals with polar orientations, where misfit is uniform in the basal plane, and non-polar orientations, where misfit varies over an order of magnitude in the film plane. It is shown that the DME paradigm is key to the integration of thin film heterostructures across the misfit scale and other complex systems such as vanadium oxide and PZT systems on Si(1 0 0) substrates for the integration of functionalities on a computer chip. Finally, it is shown that the formation of epitaxial and self-assembled nanodots on Si(1 0 0) provides a critical advance, with tremendous implications for information and data storage and related nanomagnetics applications.     

Behavior of Vacancies and Interstitials at Semicoherent Interfaces

Using atomistic simulations on a model semicoherent interface, we show that the formation, migration, and clustering of vacancies and interstitials at semicoherent interfaces depend on the structure of the misfit dislocation network of the interface. Interfacial point defects trap at misfit dislocation intersections and migrate from one intersection to another along misfit dislocations by a multistage process. Interfacial point defect clusters are thermodynamically less stable than individual defects and the largest cluster size depends on the spacing between misfit dislocation intersections. Our results show that the behavior of interfacial point defects is intimately connected to interface structure.     

Configuration and interaction of misfit dislocations in si1-xgex/si(001) epilayer heterostructures grown by gas-source mbe

Transmission electron microscopy has been employed to investigate dislocation configurations and interactions m Si_1-xGe_x/Si(001) epilayer heterostructures grown by Gas-Source MBE Thick Si_1-xGe_x/Si(001) epilayers had 3-dimensional configuration of misfit dislocations in the entire structure The main arrays of misfit dislocations at each single Si_1-xGe_x/Si(001) interface were along the two <110> directions, being 60° type in character Three-way dislocation configuration, resulting from the interaction between dislocations, was observed at the interface Observation of <001> oriented dislocations having striation lines was new in low misfit (1<%) Si_1-xGe_x/Si(001) epilayer heterostructures     

马氏体相变晶体学的简易矢量分析方法

基于界面错配可以通过一组缺陷松弛的假设, 发展了一种简易矢量分析法来计算界面包含一组缺陷的系统的相变晶体学. 通过该方法可以方便地求解惯习面的取向. 本文运用该方法求解了fcc/bcc系统中经典马氏体表象理论对应的相变晶体学, 所有计算结果与文献报道完全一致. 并根据矢量分析方法求解了满足上述假设条件惯习面取向的一般表达式. 这一结果对系统地研究fcc/bcc中无理取向的惯习面提供了简便的分析工具.     

Mechanism of induced nucleation of misfit dislocations in the Ge-on-Si(0 0 1) system and its role in the formation of the core structure of edge misfit dislocations

Ge-on-Si(0 0 1) films are grown by molecular beam epitaxy via a three-step epitaxial growth method (Ge/Ge seed/GeSi buffer/Si(0 0 1)). The dislocation structure of the Ge/GeSi buffer interface is studied by high-resolution electron microscopy. Misfit dislocations on the interface are edge dislocations and are aligned regularly with a period of 9–10 nm. A variety of atomic structures of the dislocation core is observed, known in the literature as dissociated or asymmetric Lomer edge dislocations. The assumption that atomic structures of various degrees of complexity are intermediate states in the formation of a perfect edge misfit dislocation in the course of plastic relaxation of a stressed film is justified. A model is proposed which explains the intermediate states in terms of statistical variation of the nucleation site of the complementary 60° dislocation which forms, together with the primary dislocation, a Lomer dislocation at the interface.     

Microstructures and strength of nanoscale Cu–Ag multilayers

Cu–Ag multilayers were found to have lower peak hardness than Cu–Ni in spite of lower misfit dislocation spacing that is expected to increase the resistance of interfaces to glide dislocation transmission. This is attributed to misfit dislocation core spreading in the interface plane in Cu–Ag.     

Dislocation dynamics simulations of dislocation interactions and stresses in thin films

The dislocation interactions that stop threading dislocations (threads) during relaxation at increasing applied strains in single-crystal thin films are investigated using large-scale three-dimensional dislocation dynamics simulations. Threads were observed to stop via interactions with both threads and misfit dislocations (misfits). Both types of interactions were shown to depend on stress inhomogeneity. Low-stress regions enabled threads to stop in weak thread–misfit interactions even at high average film stresses. Threads were also concentrated in low-stress regions, which facilitated their interaction with other threads. Threads accumulated in thread–thread interactions, and stopped only temporarily in thread–misfit interactions. The mean free path for dislocation motion is shown to be accurately predicted from details of the inhomogeneous stress state arising from the applied strain and the misfit structure. These behaviors are analyzed to present a more complete picture of film strength, strain hardening and relaxation.     

Critical misfit of epitaxial growth metallic thin films

The critical misfit of epitaxial growth metallic thin films fc was thermodynamically considered. It is found that there exists a competition between the energy of the misfit dislocation of film and non-coherent interface energy of film-substrate. Equilibrium between these energies was present at a critical atomic misfit ft. When the atomic misfit is larger than the critical value, epitaxial growth does not occur. The critical misfit of the epitaxial growth thin films can be predicted. The results show that fe is proportional to the non-coherent interface energy of the film-substrate, and inversely proportional to the elastic modulus and the thickness of the film.     

On the measure of dislocation densities from diffraction line profiles: A comparison with discrete dislocation methods

In this work the accuracy and range of applicability of peak broadening models, from which dislocation densities can be extracted, is studied. For that purpose dislocation microstructures are generated via a discrete dislocation dynamics method and the internal elastic strains within the simulated volume are calculated. Diffraction peaks are generated from the simulations and a whole pattern line profile analysis method based on the Wilkens model is used to quantify the dislocation densities associated with the simulated microstructures. The work is applied to the case of face-centered cubic crystals deforming in coplanar slip. The accuracy of the analytical models is quantified by considering realistic three-dimensional microstructures containing curved dislocations with a specified distribution. The dependence and sensitivity of the analytical models upon dislocation density and long-range order are investigated. It was found that, provided the distribution of dislocations is rather homogeneous, line profile analysis provides fairly accurate predictions of the dislocation density.     

Near-coincidence-sites modeling of the edge facet dislocation structures of α precipitates in a Ti–7.26 wt.% Cr alloy

While much attention has been paid to the orientations and structures of the habit planes of various precipitates, the orientations and structures of the edge facets are less well understood. This work presents a new approach to the interpretation of edge facets. The orientations and dislocation structures of the edge facets of α precipitates in a β matrix in a Ti–7.26 wt.% Cr alloy were investigated with a near-coincidence-sites (NCS) model combined with the analysis of Moiré planes based on the O-lattice theory. The distribution of NCS clusters exhibits two orders of modulated periodicities, which can be defined by the approximate intersections between several sets of Moiré planes. Two possible edge facets are suggested, based on the NCS distribution. Based on the misfit analysis, the dislocation structures in the edge facets were calculated. The calculated orientations and dislocation structures of the edge facets are consistent with the experimental observations.     

B2结构的铝-镝金属间化合物位错性质的研究

采用截断近似法,研究了B2结构的铝-镝(B2-Al Dy)金属间化合物{110}面的位错性质。结果表明,伯格斯矢量为<110>方向的螺位错、刃位错和混合位错的芯宽度都要比<100>方向窄。它们相应的不稳定层错能存在γus<110>大于γus<001>的关系,可见,不稳定层错能是影响具有B2结构的金属间化合物位错性质的重要因素之一。B2-Al Dy滑移系为<111>{110}的位错,除了位错角为54.7°的位错以外,其他位错角的弹性应变能都要大于失配能,而且在相同周期内看,它们的相位总是相反;位错角为54.7°的位错,失配能比弹性应变能大,而且两者在相同周期内同相位。总体来说,B2-Al Dy的{110}面上<100>、<110>和<111>方向的位错,随着位错角的减小(<111>方向的54.7°的位错角除外),总能量以及相应的应力都依次增大。     

界面精细结构与界面反应产物结构

界面的原子结构特征对材料的性能有很重要的影响.本文介绍用选区电子衍射及高分辨电子显微术研究半导体超晶格、金属多层膜、陶瓷和复合材料相界面的精细结构及界面反应产物结构的结果.对两相之间的取向关系,界面的台阶、小面和粗糙度,界面的原子键合,界面的共格性,错配位错的性质及界面附近弹性应变松弛度,界面附近缺陷结构,电子束辐照或制备工艺条件引起的界面固态化学反应动力学和反应机制以及界面反应产物结构进行了分析和讨论。     

Growth and dislocation distribution of single Si1-xGex/Si(001) epilayer structures grown by gas source molecular beam epitaxy

The degree of strain relaxation via a formation of misfit dislocation has been calculated in single Si_1-xGe_x/Si (001) epilayers grown at 640°C, by gas-source molecular beam epitaxy. The scale of strain relief via misfit dislocation was below 22% for Ge content x≤0.15. However, in the case of growth temperature of 550°C. the degree of strain relaxation in 270 nra single epilayer structures was 9% via misfit dislocation formation with negligible relaxation by surface undulation. As growth temperature decreased from 640°C to 550°C with higher Ge content (x=0.22), the mode of strain relaxation appears to have changed from one of misfit dislocation and surface undulation mechanism to that of predominant misfit dislocation formation.     

Strain relaxation and it’s mechanism of single Si1-xGex/Si epilayer structures grown on Si(00l) substrate

The degree of strain relaxation via a formation of misfit dislocation has been calculated in single Si_1-xGe_x/Si (001) epilayers grown at 640°C, by gas-source molecular beam epitaxy. The scale of strain relief via misfit dislocation was below 22% for Ge content x≤0.15. However, in the case of growth temperature of 550°C. the degree of strain relaxation in 270 nra single epilayer structures was 9% via misfit dislocation formation with negligible relaxation by surface undulation. As growth temperature decreased from 640°C to 550°C with higher Ge content (x=0.22), the mode of strain relaxation appears to have changed from one of misfit dislocation and surface undulation mechanism to that of predominant misfit dislocation formation.     

Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin films

Dislocation dynamics near a free surface and in heteroepitaxial thin films are simulated using an extended version of the nanoscale Phase Field Microelasticity model of dislocations [Acta Mater. 49 (2001) 1847]. The model automatically takes into account the effect of image forces on dislocation motions. In particular, the operations of Frank–Read sources in epitaxial films grown on infinitely thick and relatively thin substrates are investigated. The simulation reveals different misfit dislocation behaviors at the interface. Its implication on the interface susceptibility to crack nucleation is discussed.     

Qualitative data for precision, closed-die forging via “line-averaged” residual plastic-strains

Plastic-strains are widely used in predicting the formation of defects during the forging process. Simulation correlations normally involve measured grain-distortions and physically observed cracks, voids or folds. However, direct correlation with plastic-strain is not done because of the lack of internal plastic-strain measurements. This paper presents some “line-averaged” plastic-strains measured after a precision closed-die (PCD), isothermal forging and hence are termed “residual”. Line-average refers to the fact that two of the “pointwise” strains (ε_rr and ε_zz) are obtained by averaging over some finite length. Internal displacements were measured using initially vertical arrays of tracer particles (IVATP) at discrete radial locations. The deformed IVATP permit a continuous measurement of three strains ε_rr ε_θθ and ε_zr at discrete radial locations if ε_zz is assumed constant per IVATP. A measure-of-error for this assumption is the relative volume-change and some values are presented. The history of Von Mises's effective strain is presented via strain-contours and strain-surfaces as a function of reductions-in-height of the work piece. These contours and strain-surfaces provide insight into the complex plastic-strain behavior that can occur during PCD forging. Also, these histories are useful for qualitative comparisons with plastic-strains predicted by simulation programs.     

Molecular Dynamics Simulation of the Evolution of Interfacial Dislocation Network and Stress Distribution of a Ni-Based SingleCrystal Superalloy

The evolution of misfit dislocation network at γ/γ' phase interfaces and the stress distribution characteristics of Ni-based single-crystal superalloys under different temperatures of 0,100 and 300 K are studied by molecular dynamics(MD) simulation.It was found that a closed three-dimensional misfit dislocation network appears on the γ/γ' phase interfaces,and the shape of the dislocation network is independent of the lattice mismatch.Under the influence of the temperature,the dislocation network gradually becomes irregular,all[110]dislocations in the y matrix phase emit and partly cut into the γ′ phase with the increase in temperature.The dislocation evolution is related to the local stress field,a peak stress occurs at γ/γ' phase interface,and with the increase in temperature and relaxation times,the stress in the γ phase gradually increases,the number of dislocations in the y phase increases and cuts into γ' phase from the interfaces where dislocation network is damaged.The results provide important information for understanding the temperature dependence of the dislocation evolution and mechanical properties of Ni-based single-crystal superalloys.     

O点阵模型及其在界面位错计算中的应用

介绍了描述O点阵特征的基本参量：主O点陈基矢，主O点阵面和O胞壁的定义和计算公式，提供了一般界面上周期位错结构的矩阵方法和计算特殊界面位错结构的简易矢量方法：还分析了O点阵描述界面位错的条件和局限，讨论了一般界面和大错配界面上位错结构的计算。