A probabilistic crystal plasticity model for modeling grain shape effects based on slip geometry

A new statistical theory is introduced that takes into account the coupling between grain size, shape and crystallographic texture during deformation of polycrystalline microstructures. A “grain size orientation distribution function” (GSODF) is used to encode the probability density of finding a grain size D along a direction (given by unit vector n) in grains with orientation g. The GSODF is sampled from the input microstructure and is represented in a finite element mesh. During elastoplastic deformation, the evolution of grain size D (in direction θ) and the orientation g is tracked by directly updating the GSODF probabilities using a Lagrangian probability update scheme. The effect of grain shape (e.g. in high aspect ratio grains) is modeled by including the apparent grain size as seen by various different active slip systems in the grain within the constitutive law for the slip system resistance. The prediction of texture and strains achieved by the statistical approach is compared to Taylor aggregate and finite element deformation analysis of a planar polycrystalline microstructure. The role of grain shape and size in determining plastic response is investigated and a new adaptive GSODF model for modeling microstructures with multimodal grain shapes is proposed.     

Simulations of faceted polycrystalline thin films: Asymptotic analysis

We have used a level set construction to simulate the growth of faceted polycrystalline thin films in 2 + 1 dimensions using the van der Drift model. The evolution of several different crystal geometries into their self-similar late-stage surfaces is described. Each simulation resulted in a columnar microstructure and growth statistics including grain diameter and area, RMS surface roughness and surface texture were collected at each time step. We describe the dependence of each of these statistical measures upon the crystal geometry.     

Thermal instability of Ni electrodeposits applied in replication of optical recording devices

Thermal evolution of the crystallographic texture and microstructure in Ni electrodeposits, with a specific application for replication of optical recording devices, was examined. As-deposited microstructure was comprised of bimodal grains with a size of 4 and 0.1 μm and the 〈100〉 fibre texture with inhomogeneous strength across the deposit thickness. The 〈100〉 texture was unstable and transformed during annealing to the 〈211〉 fibre. The texture transformation was accompanied by grain growth and deposit softening and the temperature range for rapid changes of all parameters was between 623 and 673 K. A numerical analysis of texture data was conducted to identify the type of Ni grain boundaries, which control grain growth and texture transformation. The microstructural observations suggested that the growth of grains with new orientation starts in fine-grained regions and controls the thermal stability of the entire deposit. The results are discussed in terms of the mechanism of texture transformation during annealing.     

Effect of β grain growth on variant selection and texture memory effect during α → β → α phase transformation in Ti-6 Al-4 V

In the present study, the texture evolution and the role of β grain growth on variant selection during β → α phase transformation have been investigated in Ti-6 Al-4 V with and without 0.4 wt.% yttrium addition. The aim of adding yttrium was to control β grain growth above the β transus by pinning grain boundaries with yttria. Both materials were first thermomechanically processed to generate similar starting microstructures and crystallographic textures. Subsequently, both materials were solution-heat-treated above the β transus followed by slow cooling to promote growth of the α lath structure from grain boundary α. Additional interrupted slow cooling experiments were carried out to identify the α lamellae that nucleate first from β grain boundaries. Detailed electron backscatter diffraction analysis was carried out and it was found that the β heat treatment did not generate new texture components although the intensities of the individual components changed dramatically depending on the alloy/β grain size. Variant selection was assessed by comparing measured α texture components with predicted α texture components based on the high-temperature β texture assuming equal variant selection. It was found that with increasing β grain size variant selection intensified favouring the {φ1, Φ, φ2} {90°, 30°, 0°} texture component. Interrupted cooling experiments revealed that α nucleates first on β grain boundaries that are formed by two β grains having a common (1 1 0) normal and that these α lamellae display almost exclusively a {φ1, Φ, φ2} {90°, 30°, 0°} orientation. Consequently, the dominance of this variant with increasing β grain size can be related to the relative free growth of this particular α texture component into an “empty” β grain.     

Cu掺杂对Be薄膜微结构的影响(英文)

利用离子束溅射法在硅基底上制备高纯Be薄膜并实现Cu元素的可控掺杂,利用X射线能谱、扫描电镜、X射线衍射以及透射电镜等对Cu掺杂Be薄膜进行表征分析。研究结果表明:Cu元素在Be膜内分布均一,且Cu掺杂量对Be薄膜的微观结构有显著影响。Cu掺杂能抑制Be晶粒生长,Be晶粒随着薄膜中Cu含量的增多而减小,并且尺寸分布更加均匀;Cu掺杂影响Be晶粒的生长取向,使其形成更为紧凑的薄膜结构。这些因素使得掺杂Cu的Be薄膜的表面粗糙度明显降低。     

Effects of topology on abnormal grain growth in silicon steel

This work addresses the role of grain topology on abnormal grain growth in silicon steel. The question was investigated whether the abnormal grain growth of Goss grains during secondary recrystallization can be interpreted in terms of an initial size advantage that these grains inherit from rolling and primary recrystallization. For this purpose the correlation between crystallographic orientation, size and number of next neighbors of large grains in the subsurface layer of a primary recrystallized silicon steel sheet was investigated. It was found that most of the large grains have an orientation on the η-fiber (<001> axis parallel to the rolling direction) but are not particularly close to the Goss orientation. Also, no tendency of grains to be larger the closer they are to the Goss orientation was visible. Rather it was found that the scatter of the angular deviation to the Goss orientation is similar over a large range of grain sizes and this was found to be true too if the number of next neighbors of a grain rather than its grain size was checked. One single grain, however, was found that was close to the Goss orientation and had a high number of next neighbors and might therefore act as a nucleus for secondary recrystallization. Nevertheless, grains with a similarly high number of neighbors and a large deviation to the Goss orientation were found, too. Thus, a topological reason for the Goss texture evolution could not yet be proved. However, it might be that the extreme rareness of Goss nuclei (1 out of 10⁶ grains) has prevented, up to now, from observing a true nucleus.     

Quantitative TEM analysis of 3-D grain structure in CVD-grown SiC films using double-wedge geometry

We have characterized the structure of chemical vapor deposition-grown polycrystalline cubic SiC films by quantitative transmission electron microscopy. A new double-wedge sample geometry allowed accurate statistical measurements of the grain size as a function of distance from the substrate. The data are well described by the van der Drift model of faceted film growth with a 〈1 1 1〉 texture that narrows with distance h from the substrate. It was found that the distribution of grain sizes d(h) is self-similar and the mean grain size follows a power law of the type 〈d〉 ∝ h^ν. However, the measured exponent ν = 0.68 ± 0.1 is significantly larger than that previously predicted from mean field models and computer simulations of three-dimensional film growth (ν = 0.4). This difference may be due to the polarity of SiC, its low stacking fault energy and abundant defects, or impurities. The accuracy of the experimental observations due to the new sample geometry reported here is sufficient to enable statistical tomography or provide guidelines for improved computer modeling.     

In situ observation of Si faceted dendrite growth from low-degree-of-undercooling melts

We directly observed the transition of crystal growth behavior of Si in a low undercooling region. We succeeded in observing the initiation of faceted dendrite growth from a portion of parallel twins with increasing degrees of undercooling. The critical undercooling for growing a faceted dendrite was experimentally determined to be ΔT = 10 K. We also confirmed that parallel twins associated with faceted dendrite growth were formed between grain boundaries and not at grain boundaries during melt growth. The parallel-twin formation was explained in terms of a model of twin formation on the {1 1 1} facet plane at the growth interface.     

On misorientation distribution evolution during anisotropic grain growth

In order to study the development of texture and boundary character during annealing, three-dimensional grain crystallography and crystallographically mediated grain boundary properties were incoporated into a finite temperature Monte Carlo model for grain growth. Randomly textured microstructures evolve normally, with growth exponent n=0.96. While texture remains random, the steady-state boundary misorientation distribution favors low-angle boundaries. To first order, low-angle boundaries increase by lengthening, not by proliferating. In contrast, microstructures with a strong single-component texture develop four-grain junctions and highly curved grain boundaries, which alter evolution. The boundary misorientation distribution narrows and shifts to low angles, and no steady state is observed. The accompanying decrease in mean boundary mobility causes growth to slow, resulting in a growth exponent n=0.62. The dependence of the growth exponent on average boundary mobility may explain experimental observations of exponents less than unity.     

The role of microtexture on the faceted fracture morphology in Ti–6Al–4V subjected to high-cycle fatigue

Microtextured regions (or macrozones) are commonly reported in titanium alloys and are believed to be related to fatigue life. Here, fractographic investigations are conducted on bimodal Ti–6Al–4V plate, including transmission electron microscopy to determine the mechanism of fatigue facet formation and electron backscattered diffraction to examine the underlying macrozone structures. It is found that macrozones oriented with their c-axis close to the loading direction are responsible for facet formation, and that the facets are associated with basal slip. Microtextured regions with c-axis orientations near-perpendicular to the loading direction are believed to act as barriers to faceted crack growth, based on the change in crack morphology as the crack crosses a macrozone boundary. The variant selection occurring during the transformation of the retained beta appears to favour a common orientation with the surrounding primary alpha grains, contributing to the size of the macrozones and therefore to the extent of the observed faceted regions.     

Grain morphology,texture, and microhardness gradients in aluminum diffusion-bonded to aluminum oxide

The evolution of grain morphology, crystallographic texture, and microhardness in Al bonded to Al₂O₃ is dealt with. Specimens of a bilayer Al–Al₂O₃ and symmetric trilayer Al₂O₃–Al–Al₂O₃ were produced by solid-state diffusion bonding. Metallographic examination revealed the size and shape of grains in the Al layer, and the X-ray diffraction technique was used to measure the crystallographic texture at various through-thickness and in-plane locations. The results showed the existence of gradients in grain size, grain shape, texture, and microhardness through the thickness of the Al. Away from the interface, the aluminum grains were equiaxed, with a sharp cube recrystallization texture. Near the interface elongated and slanted grains, with a rotated cube texture, were observed. The microhardness was seen to correlate with the distribution of grain size. Finite element analyses employing crystal plasticity models were carried out to simulate the polygranular flow of Al during diffusion bonding. The interface constraint imposed by the Al₂O₃ layer was found responsible for the evolution of the observed gradients in microstructure in the Al layer. The predicted grain morphology trend was also in agreement with experimental observations.     

A model of grain fragmentation based on lattice curvature

A new model is proposed that aims to capture within a single modelling frame all the main microstructural features of a severe plastic deformation process. These are: evolution of the grain size distribution, misorientation distribution, crystallographic texture and the strain-hardening of the material. The model is based on the lattice curvature that develops in all deformed grains. The basic assumption is that lattice rotation within an individual grain is impeded near the grain boundaries by the constraining effects of the neighbouring grains, which gives rise to lattice curvature. On that basis, a fragmentation scheme is developed which is integrated in the Taylor viscoplastic polycrystal model. Dislocation density evolution is traced for each grain, which includes the contribution of geometrically necessary dislocations associated with lattice curvature. The model is applied to equal-channel angular pressing. The role of texture development is shown to be an important element in the grain fragmentation process. Results of this modelling give fairly precise predictions of grain size and grain misorientation distribution. The crystallographic textures are well reproduced and the strength of the material is also reliably predicted based on the modelling of dislocation density evolution coupled with texture development.     

Faceting behavior of an asymmetric SrTiO3 Σ5 [001] tilt grain boundary close to its defaceting transition

Using high-resolution transmission electron microscopy (HRTEM), an asymmetric Σ5 [001] grain boundary in SrTiO₃ with an inclination of 2.5° away from the symmetric (310) plane was studied. A defaceting transition is observed between 1500 and 1600 °C. From 1520 to 1570 °C, the grain boundary is faceted into the symmetric (310) and asymmetric (100)//(430) planes. At 1590 °C, the grain boundary is observed to be defaceted, which implies that the defaceting occurs between 1570 and 1590 °C. The faceted structure observed between 1500 and 1590 °C is interpreted in terms of the step free energy of the asymmetric (100)//(430) facet orientation. The faceting-defaceting transition is schematically represented as the temperature evolution of the equilibrium grain shape.     

Off-axis texture in nanostructured Ti1 − xAlxN thin films

Standard θ-2θ and pole figure X-ray diffraction techniques were used to study structural properties and preferred orientation of nanostructured TiAlN thin films prepared using cathodic arc deposition. Systematic collection of reflections from lattice planes {111}, {200}, {220}, and {311} showed that the in-plane orientation of crystallites exhibits cylindrical symmetry with random distribution of crystallites, while the out-of-plane growth presents strong texture which is inclined with respect to the surface normal. This brings the crystallographic orientation of fibre texture towards high indices lattice planes (113) and (115) contrary to traditionally grown films that develop a preferred orientation following to low indices close-packed planes (111) and (200). The origin of inclined growth is discussed taking into account the role of crystallographic defects in particular twin faults that develop in the lattice of growing crystal and change the stacking sequences of atom layers.     

Recrystallization Process in Fe-Cr-Al Oxide Dispersion-Strengthened Alloy: Microstructural Evolution and Recrystallization Mechanism

Mechanically alloyed iron-base oxide dispersion-strengthened (ODS) alloys are the class of advanced materials for application in heat exchangers tubing in which creep and oxidation resistance are paramount. The yttria dispersion in such alloys improves the high-temperature creep and stress rupture life. The strength is further enhanced by the development of a coarse-grained microstructure during recrystallization. Factors controlling the evolution of this desirable microstructure are explored in this work, focusing specifically on PM 2000. The results presented in terms of orientation imaging, transmission electron microscopy, and scanning electron microscopy indicate that the recrystallization process consists of two different stages. Before the coarse grain takes place, the alloy undergoes an extended recovery process followed by abnormal grain growth. The initial microstructure consisted of subgrains (submicrometer sizes) with a strong 〈110〉∥RD fiber texture (α fiber), which are transformed into coarse grains (mm sizes) with orientations 〈112〉∥RD. The aim of this study is to describe the mechanisms involved in the intermediate stages of recrystallization process from the submicrometer grain size to the abnormal grain size.     

Texture evolution during normal and abnormal grain growth in an Al–1 wt% Mn alloy

The texture evolution during normal and abnormal grain growth in an Al–1 wt% Mn alloy was studied. Prior to deformation the amount of precipitates was enhanced by annealing at 500°C for 4 days (3.5×10⁵ s). After 80% cold rolling and recrystallization the alloy had a weak cube ({001}〈100〉) texture and a minority texture component, the A component, related to the cube texture by a Σ5 (36.9°〈100〉) orientation relationship. After limited normal grain growth both the cube and the A component were strengthened. However, both after abnormal grain growth and after extensive normal grain growth, the A component became the dominant texture component. The result is interpreted based on the assumption that Σ5 boundaries can migrate faster than other boundaries in this alloy. Possible reasons to support this hypothesis are discussed. The situation bears resemblance to abnormal grain growth in Fe–3 wt% Si alloys, where special properties are attributed to Σ9 boundaries.     

冷加工态Ti6Al4V合金的回复和再结晶行为研究

对冷拉拔变形量为60%的钛合金进行700～880℃,1～240min再结晶退火,利用金相显微镜、X射线衍射仪和透射电镜等手段分析不同状态下的组织演变、织构组成和位错组态。结果表明:冷变形后的Ti6Al4V合金经完全再结晶后α晶粒呈等轴状,β相在α相周围以条状沿α晶界析出或以小晶粒形式存在。计算表明,经60%冷变形量的钛合金再结晶激活能为107kJ/mol,较相同变形量的纯钛再结晶激活能高约50%。钛合金的再结晶分为回复、形核和晶核长大阶段,包括位错胞向亚晶转变、回复亚晶通过合并或长大形核、形核诱导高角度晶界形成而长大成新晶粒。经过冷拉拔后的丝材,存在着较强的100织构,而在再结晶过程中,沿100方向上产生的回复亚晶优先形核并长大形成新的晶粒。这导致在初始再结晶阶段,再结晶织构与冷变形织构取向一致,而在晶粒长大阶段,原先取向不利的晶粒吞并周围小晶粒长大,形成新的织构组元使原来的织构被弱化。     

Abnormal grain growth in Al–3.5Cu

Significant abnormal grain growth has been observed in an Al–3.5 wt.% Cu alloy at temperatures where the volume fraction of small CuAl₂ particles was less than about 0.01. The initial fine-grained material had a weak crystallographic texture and there was no indication that any special boundaries were involved in the abnormal growth. Island grains isolated within the abnormal grains also showed no indication of special orientation relationships with their surrounding grains. Measurements indicated that the island grains initially had a size advantage over other matrix grains. The fraction of pinning phase was much lower at abnormal grain boundaries than at boundaries in the fine-grained matrix into which they were growing. A variety of simulations were made, including attempts to model that difference in pinning phase distribution, but none of these were successful in predicting abnormal grain growth.     

Abnormal grain growth and grain boundary faceting in a model Ni-base superalloy

Normal or abnormal grain growth in a model Ni-base superalloy is observed to depend on the grain boundary structure when heat-treated in a solid solution temperature range above the solvus temperature (1150°C) of the γ′ phase. When heat-treated at 1200°C abnormal grain growth occurs and most of the grain boundaries are observed to be faceted by optical microscopy, transmission electron microscopy, and scanning electron microscopy at the intergranular fracture surface. Some of the grain boundary facet planes are expected to be singular corresponding to the cusps in the polar plot of the boundary energy against the inclination angle, and it is proposed that if these boundary segments move by a boundary step mechanism, the abnormal grain growth can occur. When heat-treated at 1300°C normal grain growth occurs, the grain boundaries are defaceted, and hence atomically rough. Normal growth is expected if the migration rate of the rough grain boundaries increases linearly with the driving force arising from the grain size difference. The correlation between the grain boundary structural transition and the growth behavior thus appears to be general in pure metals and solid solution alloys.     

Package-and wafer-level electromigration tests on Al−Cu interconnect with Ti and TiN underlayers

The effect of A1 underlayer between Ti and TiN on the electromigration (EM) lifetime of Al stack film were compared with package-level and conventional wafer-level EM tests. The higher EM resistance of the Al stacks prepared with Ti underlayer can be best explained by their better Al (111) texture and grain size distribution than those with TiN underlayer. The surface roughness of the underlayer is related to the grain size distribution and surface roughness of Al film. The conventional wafer-level EM test results showed a similar trend with respect to Ti and TiN underlayers with less accuracy than those from package-level EM test results.