Computed epitaxial monolayer structures: I. One-dimensional model: Comparison of computed and analytical results

An exact computational procedure is developed which, when applied to Frank and van der Merwe's one-dimensional dislocation model, yields the equilibrium structures of a one-dimensional atom chain with elastic interatomic forces and sinusoidal substrate potential. This forms the first part of the development of a general procedure for calculating the equilibrium structures of two-dimensional monolayers with elastic interatomic forces and substrate potentials of more complex character. The minimum energy principle is applied to distinguish the stable structures from the computed equilibrium ones. The results aie in close agreement with the analytical approximate solutions of Frank and van der Merwe. The atomic displacements and limiting misfits agree almost perfectly. The curves of lowest energy against misfit are likewise in excellent agreement for long chains. For relatively short chains, containing only few dislocations, the curves are composed of segments, one segment for each additional dislocation. The discreteness of dislocations in finite chains is also borne out in other properties. The calculations further show (i) that, for a finite chain with odd numbers of dislocations and atoms, the stable configuration is one with the central atom on a potential crest and (ii) that the cusped minima present in the interfacial energy curve of thick bicrystals disappear when complete or partial accommodation of lattice parameters is energetically possible as in thin films.     

Dependence of the specific energy of the β/α interface in the VT6 titanium alloy on the heating temperature in the interval 600–975°C

The specific energy of interphase boundaries is an important characteristic of multiphase alloys, because it determines in many respects their microstructural stability and properties during processing and exploitation. We analyze variation of the specific energy of the β/α interface in the VT6 titanium alloy at temperatures from 600 to 975°C. Analysis is based on the model of a ledge interphase boundary and the method for computation of its energy developed by van der Merwe and Shiflet [33, 34]. Calculations use the available results of measurements of the lattice parameters of phases in the indicated temperature interval and their chemical composition. In addition, we take into account the experimental data and the results of simulation of the effect of temperature and phase composition on the elastic moduli of the α and β phases in titanium alloys. It is shown that when the temperature decreases from 975 to 600°C, the specific energy of the β/α interface increases from 0.15 to 0.24 J/m². The main contribution to the interfacial energy (about 85%) comes from edge dislocations accommodating the misfit in direction [0001]_α || [110]_β. The energy associated with the accommodation of the misfit in directions \({\left[ {\bar 2110} \right]_\alpha }\left\| {{{\left[ {1\bar 11} \right]}_\beta }} \right.\) and \({\left[ {0\bar 110} \right]_\alpha }\left\| {{{\left[ {\bar 112} \right]}_\beta }} \right.\) due to the formation of “ledges” and tilt misfit dislocations is low and increases slightly upon cooling.     

The size dependence of equilibrium elastic strain in finite epitaxial islands

The equilibrium elastic strain in epitaxial islands of small size is shown to have a sawtooth dependence on island width by minimizing the systems energy as calculated from a periodic interaction potential between substrate and overgrowth. Such a sawtooth variation is consistent with Vincent's observations and idea that a given misfit between island and substrate may not be entirely accommodated by an integral number of identical misfit dislocations, and hence, the remaining misfit, which depends in part on island width, will be accommodated by residual elastic strain. The present calculations of mechanical equilibrium support these ideas and further reveal that in some cases misfit dislocations may over compensate for the misfit, thereby introducing an elastic strain of opposite sign to that normally expected. Other results of the calculations are in agreement with earlier theoretical and experimental observations.     

A one-dimensional SiGe superlattice grown by UHV epitaxy

One-dimensional SiGe superlattices with periods ranging from 100 to 800 Å have been deposited on Si substrates by periodically varying the Ge content of a mixed Si_1-x Ge _x multilayer structure fromx=0 tox=0.15. The deposition was successful, employing and UHV evaporation technique at a substrate temperature of 750°C fulfilling the four conditions: Single crystal growth, no interdiffusion, two-dimensional growth, and pseudomorphic growth. It is shown that mismatch above 8 · 10^?3 favours growth by three-dimensional nucleation. The experimentally determined spacing of misfit dislocations is compared with theoretical results obtained by van der Merwe. The pseudomorphic growth behaviour of layers thinner than a critical thickness could be confirmed.     

Role of edge dislocations in plastic relaxation of GeSi/Si(001) heterostructures: Dependence of introduction mechanisms on film thickness

It has been shown that, in the GeSi/Si(001) heterosystem at lattice parameter mismatches of ～2% and more, a small critical thickness of the introduction of dislocations leads to the implementation of the mechanism of induced nucleation of misfit dislocations. This mechanism consists in that the stress field of an already existing 60° dislocation provokes introduction of a secondary 60° dislocation with an opposite-sign screw component. As a result of the interaction of such dislocation pairs, edge misfit dislocations are formed, which do control the plastic relaxation process. This mechanism is most efficient when dislocations are introduced at the GeSi film thickness only slightly exceeding the critical thickness of the introduction of 60° dislocations, and there are threading dislocations. The dominant type of misfit dislocations (60° or edge) in the Ge-on-Si(001) system can be controlled by varying the mismatch parameter in the heteropair.     

晶体相场法模拟异质外延过程中界面形态演化与晶向倾侧

采用晶体相场模型研究了异质外延过程中失配应变与应力弛豫对外延层界面形态演化的影响, 并对由衬底倾角引起的外延层晶向倾侧进行了分析.研究结果表明: 在有一定倾角的衬底晶体上进行外延生长时,若衬底和外延层之间失配度较大 (ε>0.08),外延层中弹性畸变能会以失配位错的形式释放, 最终薄膜以稳定的流动台阶形式生长且外延层的晶向倾角与衬底倾角呈近似线性关系. 而当衬底和外延层之间失配度较小(ε<0.04)不足以形成失配位错时, 外延层中弹性畸变能会以表面能的形式释放,最终使薄膜以岛状形态生长. 在高过冷度条件下,衬底倾角和失配度较大时,衬底和外延层之间会形成由大量位错规则排列而成的小角度晶界从而显著改变外延层的生长位向.     

采用纳米晶柱阵列衬底抑制失配位错形成的分子动力学模拟研究

运用分子动力学方法对纳米晶柱阵列衬底上铝簿膜的外延生长进行了模拟研究.所采用的原子间相互作用势为嵌入原子法(EAM)多体势.模拟结果表明：采用纳米晶柱阵列衬底可以在不形成失配位错的条件下释放其上生长的外延薄膜晶体中的失配应变,有效地抑制其中失配位错的形成,获得高质量的外延薄膜晶体;这种纳米晶柱阵列的几何设计应满足两个基本条件：1) 晶柱的横截面尺寸应大于对应温度下的晶柱热失稳临界尺寸,以克服纳米结构的热失稳,模拟显示700K下铝的热失稳临界尺寸为19nm;2) 晶柱的高度与间距之比应大于076,以保证 关键词： 失配位错 分子动力学 纳米晶柱 铝     

Commensurate-incommensurate transition in adsorbed monolayers under two different experimental conditions

We consider a spreading pressure-driven transition in comparison to that induced by the chemical potential change. The differences in the energy gain and incommensurability, small in terms of the natural misfit, become significant in terms of the bulk gas pressure P. The empirical laws for the incommensurability versus the chemical potential change and for the critical pressure P_c(T) are explained by the large temperature effects in the gas phase, while the adsorbate behaviour is of the Frank-van der Merwe type in the whole studied range of temperature.     

Heterophase dislocations — An approach towards interpreting high temperature grain boundary behavior

When the conditions of full thermodynamic equilibrium are added to the conventional linear elastic theory of dislocations a hybrid concept of “heterophase” dislocations arises. As developed here, heterophase dislocation theory provides a self-consistent method for calculating the core configuration, energy, and stress-strain field which minimize the thermodynamic potential of a dislocated crystal. Simple grain boundaries in crystals near the melting point are treated as constrained arrays of heterophase misfit dislocations with a liquid-like core phase similar to, but not identical with the properties of ordinary liquid phase. Measurements of the properties and behavior of {011&#x0304;} tilt boundaries in bismuth crystals near the melting point show that the new theory accounts accurately for the energetic dependence on tilt misorientation in the range 0° to 6°, and then deviates from the observed dependence. The new theory also permits prediction of a structural transition in grain boundaries which is extremely sensitive to the density of misfit dislocations. This transition, predicted to occur in bismuth at a tilt misorientation of 15° was also confirmed by hot-stage electron microscopy.     

Modeling elasticity in crystal growth

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to time scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.     

Effect of long-range stresses on the structure of semiconductor heterosystems

The dependence between the misfit value of the interface layers f and the structural parameters of the misfit dislocations is obtained for arbitrary orientation of the interface of a semiconductor heterosystem subjected to the complete relaxation of misfit stresses. Such parameters are the distance D _i between neighboring dislocations of the ith family and projection of the edge component of the Burgers vector onto the interface (b _i ^e ). The number of families incorporated into the interface is determined by the orientation of the boundary and occurrence of the relaxation process. The role of specific cases of this expression for experimental and technological applications is discussed using the appearance of long-range shear and normal stresses in films with orientations of (001) and (111) as examples.     

Faceting transitions in crystal growth and heteroepitaxial growth in the anisotropic phase-field crystal model

We modify the anisotropic phase-field crystal model(APFC),and present a semi-implicit spectral method to numerically solve the dynamic equation of the APFC model.The process results in the acceleration of computations by orders of magnitude relative to the conventional explicit finite-difference scheme,thereby,allowing us to work on a large system and for a long time.The faceting transitions introduced by the increasing anisotropy in crystal growth are then discussed.In particular,we investigate the morphological evolution in heteroepitaxial growth of our model.A new formation mechanism of misfit dislocations caused by vacancy trapping is found.The regular array of misfit dislocations produces a small-angle grain boundary under the right conditions,and it could significantly change the growth orientation of epitaxial layers.     

Interdiffusion in two-layer Pd/Ag films III. TEM investigation of diffusion-induced grain boundary migration

Diffusion-induced grain boundary migration (DIGM) is studied by the transmission electron microscopy method in polycrystalline two-layer Pd/Ag thin films with a grain size (100–2000 nm). In addition to the typical features of DIGM known for coarse-grained bulk objects and foils, new features are found which are caused by a quite dense network of triple junctions and by misfit dislocations: fast increase of grain boundary curvature and inclination; back motion of grain boundaries owing to recrystallization forces and termination of DIGM. Homogenization resulted from diffusion-induced migration of misfit dislocations is observed in addition to DIGM.     

New “surface” criterion of melting

From the assumption that the pressure exerted on the nanocrystal surface under melting passes into the Laplace surface pressure, an expression for a relative volume within which the solid phase of the nanosystem remains stable at different pressures is derived. It is shown that such a “surface” criterion of melting slightly depends on the crystal size and external pressure and is determined solely by the interatomic potential parameters. Calculations for macrocrystals with van der Waals bonding demonstrate good agreement with experimental data for the relative crystal volume at the melting point.     

Vibrational properties of straight dislocations in bcc and fcc metals within the harmonic approximation

We calculate the vibrational spectra of straight screw and edge dislocations in several body-centered cubic (bcc) (Mo and Fe) and face-centered cubic (fcc) (Cu and Al) metals within the harmonic approximation. We take advantage of the translational symmetry of straight dislocations to efficiently calculate their phonon eigenstates in the harmonic limit. This allows us to calculate the low-temperature contribution of straight screw and edge dislocations to the heat capacity of each respective metal, and show that the dominant temperature dependence below 5 K is linear. Comparison with heat capacity measurements of heavily cold-worked Cu reveals very good agreement with our calculations. At higher temperatures, the contribution from the non-linear terms becomes significant. As a result, maxima in the straight dislocation heat capacities are observed in the temperature range from 9% to 16% of the Debye temperature. We investigate the appearance of localized and resonance peaks in the vibrational spectra induced by dislocations, and study in detail their spatial spread around the dislocation cores by projecting vibrational eigenstates onto individual atoms. We study the deviation of these atomic-level vibrational free energies from that of the perfect crystal as a function of distance to the dislocation cores, and establish that, similar to the dislocation energy, the vibrational free energy of an isolated dislocation behaves logarithmically in the long-range limit. Finally, we obtain vibrational spectra for propagating waves along the dislocation line and find that the dispersion for these waves is consistent with the notion of kink formation and motion for screw dislocations.     

Structure of epitaxial crystal interfaces

Theoretical work on the structural influences of misfit, bonding and crystal dimension in epitaxial bicrystals is reviewed. The main contents relate to the model in which the inter-action between the crystal halves is represented by a periodic force acting at the interface, the crystals are approximated by elastic continua and the structure is assumed to be governed by lowest energy principles. In this model the misfit is accommodated by sequences of misfit dislocations located at the interface and/or overall lattice strains. The degree to which one or the other mechanism dominates depends on the size and shape of the crystal in addition to the elastic and bonding properties. Realistic approximations for various special cases, e.g. monolayers, thick crystals and intermediate thicknesses, are considered. An exact solution covering the entire spectrum of interest does not exist.     

分子束外延生长GaN薄膜中的一种早期位错结构

利用高分辨电子显微术，对在GaP基体上由分子束外延生长六角GaN晶体薄膜中的晶体缺陷结构进行了研究．实验中发现了GaN薄膜外延生长过程中产生的一种典型早期刃型位错结构．此晶体缺陷位于一大块GaN晶粒内部，其外观类似于一段（1120）晶界．它由一条（1120）高能孤立晶界段及其两端的两个1/6［1120］不完全刃型位错组成．从大晶格失配材料之间分子束外延生长的机理上对这种缺陷结构的形成进行了解释． 关键词：     

Critical film properties for epitaxy

The conditions for overlayer coherency were investigated, by means of molecular dynamic simulations, for two-dimensional triangular Lennard-Jones solids. Up to a certain critical misfit, i.e. difference in the film-substrate lattice parameters, the film remains coherent and in a state of homogeneous strain parallel to the interface, in agreement with continuum calculations based on energy criteria. However, contrary to the predictions of such theories, the critical misfit quickly saturates as a function of film thickness. Further, the generation of misfit dislocations was favored by reducing the film-substrate bonding parameter but inhibited by an increase in this parameter. These factors indicate that in our overlayer-substrate system the occurrence of misfit dislocations is better described by a critical local force rather than a critical energy criterion.     

单向拉伸作用下Cu(100)扭转晶界塑性行为研究

应用分子动力学方法研究了在不同扭转角度下的Cu（100）失配晶界位错结构,以及不同位错结构对晶界强度的影响.模拟结果表明：小角度扭转晶界上将形成失配位错网,失配位错密度随着晶粒之间的失配扭转角度的增加而增加.变形过程中,位错网每个单元中均产生位错形核扩展.位错之间的塞积作用影响晶界的屈服强度：随着位错网格密度的增加,位错之间的塞积作用增强,界面的屈服强度得到提高.大角度扭转晶界将形成面缺陷,在变形中位错由晶界角点处形核扩展,此时由于面缺陷位错开动应力趋于一致,因此晶界的临界屈服强度趋于定值. 关键词： 扭转晶界 失配位错网 强化机理 分子动力学     

Atomic-scale study of precipitates (NbC and Cu-rich phase) at the twin boundary in the long time ageing austenitic stainless steel

ABSTRACT

Microstructures of Cu-rich phases and NbC precipitated phases have been studied in a long time ageing austenitic stainless steel by high resolution scanning transmission electron microscopy. The interaction difference between the twins and the second phases found to be dependent on the nature of the precipitates. The Cu-rich phases were identified to be twinned at the twin boundary. Nevertheless, the NbC precipitates not only twinned at the twin boundary but also induced the twin boundary bypass them. A particle size dependence of the generation of misfit dislocations also was detected at interface between precipitates and the austenitic matrix.