Structure and phase composition studies of partially stabilized zirconia

Zirconia single crystals doped with 2.8, 3.2, 3.7, and 4.0 mol % of Y₂O₃ have been studied. The phase composition and structure have been studied by X-ray diffraction analysis and transmission electron microscopy. It has been established that all investigated samples has two ZrO₂ tetragonal phases with tetragonality c/a = 1.006–1.007 and c/a = 1.014–1.015 independent of the stabilizing impurity content. The former phase is not transformed, whereas the latter is transformed into a monoclinic one. In all cases the samples have a developed twin structure. Twinning hierarchy is observed: there are first-, second-, third-order, etc., twins, each of them containing the next-order twins inside them. Elastic stress relaxation occurs by twinning rather than by generation of dislocations. The stabilizing impurity content affects the structure nonmonotonically; the minimum dimensions of the twin lamellas refer to the Y₂O₃ concentration of 3.2 mol %.     

Statistical analyses of deformation twinning in magnesium

To extract quantitative and meaningful relationships between material microstructure and deformation twinning in magnesium, we conduct a statistical analysis on large data sets generated by electron backscattering diffraction (EBSD). The analyses show that not all grains of similar orientation and grain size form twins, and twinning does not occur exclusively in grains with high twin Schmid factors or in the relatively large grains of the sample. The number of twins per twinned grain increases with grain area, but twin thickness and the fraction of grains with at least one visible twin are independent of grain area. On the other hand, an analysis of twin pairs joined at a boundary indicates that grain boundary misorientation angle strongly influences twin nucleation and growth. These results question the use of deterministic rules for twin nucleation and Hall–Petch laws for size effects on twinning. Instead, they encourage an examination of the defect structures of grain boundaries and their role in twin nucleation and growth.     

Molecular dynamics simulation of twinning in devitrite,Na2Ca3Si6O16

Reports of Type II twins are quite rare for most crystal structures. When they do occur, they are usually one of a number of possible twinning modes observed in a particular material. However, for the triclinic phase devitrite, Na₂Ca₃Si₆O₁₆, which nucleates from commercial soda?lime?silica float glass subjected to suitable heat treatments, the only reported twinning mode to date is a Type II twinning mode. In this study, this Type II twinning mode is first examined by molecular dynamics simulation to determine the lowest energy configuration of perfect twin boundaries for the twin mode. This is then compared with the lowest energy configurations of perfect twin boundaries found for six possible Type I twinning modes for devitrite for which the formal deformation twinning shear is less than 0.6. The most favourable twin plane configuration for the Type II twinning crystallography is shown to produce reasonably low twin boundary energies and sensible predictions for the optimum locations of the twin plane, K ₁, and the [1?0?0] rotation axis, η ₁, about which the 180° Type II twinning operation takes place. By comparison, all the Type I twinning modes were found to have very energetically unstable atomic configurations, and for each of these twinning modes, the lowest energy configurations found all led to high effective K ₁ twin boundary energies relative to perfect crystal. These results therefore provide a rationale for the experimental observation of the particular Type II twinning mode seen in devitrite.     

Characterization of twinning in electrodeposited Ni–Mn alloys

Twinning is ubiquitous in electroplated metals. Here, we identify and discuss unique aspects of twinning found in electrodeposited Ni–Mn alloys. Previous reports concluded that the twin boundaries effectively refine the grain size, which enhances mechanical strength. Quantitative measurements from transmission electron microscopy (TEM) images show that the relative boundary length in the as-plated microstructure primarily comprises twin interfaces. Detailed TEM characterization reveals a range of length scales associated with twinning beginning with colonies (～1000?nm) down to the width of individual twins, which is typically <50?nm. We also consider the connection between the crystallographic texture of the electrodeposit and the orientation of the twin planes with respect to the plating direction. The Ni–Mn alloy deposits in this work possess a {110}-fiber texture. While twinning can occur on {111} planes either perpendicular or oblique to the plating direction in {110}-oriented grains, plan-view TEM images show that twins form primarily on those planes parallel to the plating direction. Therefore, grains enclosed by twins and multiply twinned particles are produced. Another important consequence of a high twin density is the formation of large numbers of twin-related junctions. We measure an area density of twin junctions that is comparable to the density of dislocations in a heavily cold-worked metal.     

Atomic-scale mapping of twins and relevant defective structures in Al20Cu2Mn3 decagonal approximant

Twins or multiple twins occur frequently in the orthorhombic Al₂₀Cu₂Mn₃ approximant of decagonal quasi crystal (DQC). Due to the specific structural units, the twins in the Al₂₀Cu₂Mn₃ approximant usually exhibit the glide-reflection characteristics. Using aberration-corrected transmission electron microscope at the atomic scale, we have observed not only glide-reflection twins but also simple mirror-reflection twins in the Al₂₀Cu₂Mn₃ approximant. The two twinning modes are found to coexist in the present sample. These twins exhibit variant configurations at the twin boundaries where the tessellations of local subunits are imaged at an atomic scale. At the twin boundaries, diversified tiles such as star-like (S), bowtie-shaped and boat-shaped (B) are observed. The diversified tiles stacking with various manners allow the coexistence of the DQC and the approximant. Furthermore, the variants of B and S tiles are also found.     

Molecular dynamics simulation of the formation of twin boundaries during agglomeration of nanoparticles

The processes controlling early stages of agglomeration of nanoparticles have been investigated by the molecular dynamics method. It has been established that the formation of boundaries with twin misorientation is the main mechanism of structural relaxation during primary agglomeration of nanoparticles. It has been shown that an increase in the temperature leads to an increase in the number of twin boundaries and that their mutual arrangement depends on the misorientation of the nanoparticles. In the case where twin boundaries are noncoplanar, structure relaxation results in the formation of pentagonal twin boundaries. The role of twinning in the formation of interfaces upon compaction of nanoparticles has been discussed.     

A study of mechanical twinning inα-solid solutions of the system Cu-Ge

Electron and optical microscopy have been used to study the structure and distribution of mechanical twins in polycrystalline Cu-Ge alloys containing up to 9.5 at.% Ge which had been deformed at room temperature. The probability of twinning occurring increases continuously with rise in concentration of the alloy up to the solubility limit. A reduction in the grain size of a polycrystalline aggregate impedes the development of twinning. It is shown that the twins have an imperfect structure even in the initial stage of growth.     

Electronic properties of PbS(111) twin boundaries and twinning superlattices

We have studied the electronic properties of single twin boundaries and twinning superlattices in lead sulfide. The results are compared against those obtained previously for such structures based on diamond/zincblende type materials, and substantial differences are noted. It is found that lead sulfide twinning superlattices can have significantly wider or narrower band gaps than the homogeneous material, depending on whether the twin interface is occupied by anion or cation atoms.     

Effect of Al and Cd impurities on the bauschinger effect during the twinning of a zinc crystal

A quantitative study has been made of the Bauschinger effect at various twin boundaries in crystals of pure zinc and of zinc containing Al and Cd impurities. In the pure zinc, the Bauschinger effect is strongest at stretched twin boundaries, while in Zn + Al and Zn + Cd crystals the effect is much weaker at twin boundaries and is approximately the same at different types of boundaries. The stress is a stronger than linear function of the displacement of twin boundaries in the impure crystals for both forward and reverse loading, because of an increase in the friction force acting on the twinning dislocations during motion along the shear plane. An increase in the Al content from 0.1% to 0.3% (by weight), which leads to the appearance of a finely dispersed precipitate, has essentially no affect on the magnitude of the Bauschinger effect.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 59–63, December, 1969.     

Asymmetrical twin boundaries and highly dense antiphase domains in BaNb0.3Ti0.7O3 thin films

Asymmetrical twin boundaries and highly dense antiphase domains were identified by means of transmission electron microscopy in a perovskite-based BaNb_0.3Ti_0.7O₃ thin film grown by laser molecular beam epitaxy on a SrTiO₃ (001) substrate. The microstructural characteristics of the BaNb_0.3Ti_0.7O₃ film were clarified in terms of lamellar {111} twins and antiphase domains, the domain boundaries of which are 1/2?110? stacking faults. It is proposed that the intersections of (111) twinning with the antiphase domain boundaries result in the asymmetrical twin boundaries.     

Point defect interactions with crystal interfaces

The structures of a small closed system of grain boundaries and the interactions of vacancies with these boundaries has been investigated using computer simulation techniques based on empirical interatomic potentials. The boundaries chosen are the {;111}; and {;112}; twins in both body centred cubic and face centred cubic metals, the potentials used being matched to the physical properties of iron and copper. Two stable structures arise for the {;112};_bcc twin so that effectively five boundaries have been studied. The structures and energies of these are extremely varied, the {;112};_fcc twin in particular being very broad. This influences the binding of vacancies to the boundaries and the migration of vacancies along the boundaries. Near the {;111};_bcc twin a split-vacancy consisting of a divacancy and an interstitial is the most stable configuration. This has a very high binding energy and an exceptionally high migration energy. Near the other boundaries the vacancy migration energies are less than in the bulk. The implications of the results are discussed.     

The incorporation of slip dislocations in twins

The conditions for the incorporation of slip dislocations either propagating into a twin or engulfed by a growing twin are studied from the geometrical point of view. The resulting dislocation formed in a twin is independent of the mechanism of the incorporation. Under suitable conditions no stacking faults are formed at the twin boundary. The decomposition of twinning dislocations forming the noncoherent twin boundary is described using complementary partial twinning dislocations. The theory is formulated for both type I and II twins. Compound twins are also briefly treated in the discussion. Using the tensor notation all the formulae are given in the form valid for all crystal structures.The author is greatly indebted to Mr. J. Koík for many helpful comments.     

Effect of dislocation distribution in twin boundaries on the nucleation of microcracks at the twin tip

The effect of dislocation distribution in the boundaries of an arrested twin on the nucleation of microcracks at its tip is investigated. The twin is simulated by a double step pileup (cluster) of twinning dislocations located in adjacent slip planes. The equilibrium equations for dislocations are solved numerically. Clusters with different total numbers of dislocations and with different ratios of the numbers of dislocations at the upper and lower twin boundaries are considered. The formation of microcracks as a result of coalescence of head dislocations according to the force and thermally activated mechanisms is analyzed. The equilibrium configurations of a single twin boundary and of the twin are calculated. It is found that the condition for microcrack formation at the twin tip considerably depends on the ratio of the numbers of dislocations in twin boundaries. In the limit, this condition coincides with the condition of crack formation at the tip of a single twin boundary with the same total number of dislocations. It is shown that thermally activated formation of a microrack corresponds to lower values of the critical stress.     

Energy of a wedge-shaped nanotwin calculated in terms of a dislocation mesoscopic model

The total energy of a wedge-shaped micro- and nanotwin is calculated in terms of a dislocation mesoscopic model. The total energy of the twin is represented as a sum of the elastic energy, energy of interaction between twinning dislocations, and stacking-fault energy of partial dislocations of the wedge-shaped twin. It is found that the evolution of the twin is controlled by the energy of interaction between twinning dislocations: in the case of a microtwin, it is five orders of magnitude higher than the elastic energy and six orders of magnitude higher than the stacking-fault energy. In the case of a nanotwin with the number of twinning dislocations at the twin boundary less than 20, all the three energies listed above are of the same order of magnitude. Therefore, all the components of the total energy contribute to the origination of a wedge-shaped twin. As the length of the twin increases with its width and the number of twinning dislocations at twin boundaries fixed, the total energy modulo grows although the density of twinning dislocations at twin boundaries decreases. This indicates that long-range stress fields due to twinning dislocations play an important part in the evolution of a wedge-shaped twin.     

Magnetoplastic effect in twinning of bismuth crystals under a concentrated load

Twinning of bismuth crystals under a concentrated load is found to be partly suppressed by a constant magnetic field. The main mechanisms of the influence of a constant homogeneous magnetic field on the twinning of bismuth single crystals subjected to long-term concentrated loading is studied. It is revealed that the length and the number of wedge twins at an indentation decrease in the magnetic field. This suggests a decrease in the mobility of partial twinning dislocations and in the intensity of the nucleation of wedge twin interlayers in a constant magnetic field. Application of the magnetic field increases the width of twins at the mouth. No anisotropy of the magnetoplastic effect is observed upon twinning.     

Effect of initial orientation on twinning in commercially pure titanium

Abstract

The effect of initial orientation on twinning micro-mechanisms during tensile deformation of commercially pure titanium has been studied using micro focus X-ray diffraction and electron back scatter diffraction (EBSD) in a scanning electron microscope. Three orientations A, B and C obtained from a rolled and annealed block of commercially pure titanium were deformed in uniaxial tension till failure and the tested specimens were characterised with regard to bulk texture, microstructure and crystal orientation mapping using EBSD. Orientation B along the transverse direction in ND-TD plane exhibits higher strength and lower strain hardening compared to orientations A and C along the rolling direction in TD-RD and ND-RD plane, respectively. This is attributed to different texture of sample B compared to samples A and C leading to dissimilar twinning micro-mechanisms and characteristic variation in nature of twinning. It is observed that limited twin nucleation and prominent lateral growth plays a dominant role in orientation B while multiple twin nucleation with significant non-Schmid behaviour is dominant for the other two orientations. It is proposed from this study that conventional factors associated with twin formation like Schmid factor play a main role in twin nucleation and propagation, however, growth or lateral thickening of the twins is explained by elastic stiffness variation across twins and their parent grains.     

Anisotropy and twinning in cubic zinc sulfide crystals

The structure of zinc sulfide single crystals grown from the vapor has been studied by a unique combination of X-ray crystallography and thermal conductivity measurements. Weissenberg patterns reveal the face centered cubic structure with rotational twinning in the [111] direction, which could be ascribed to two overlapping lattices. These could be explained by normal stacking faults or by inverted twins. A strong anisotropy in thermal conductivity was measured and interpreted as favoring the inverted twin model.     

Structure and mechanical properties of crystals of partially stabilized zirconia after thermal treatment

The phase composition and morphology of the twin structure of the Y₂O₃-stabilized zirconia crystals (from 2.8 to 4.0 mol %) after the thermal treatment at 1600°C have been investigated by X-ray diffractometry and transmission electron microscopy. It is shown that as the concentration of the stabilizing Y₂O₃ impurity increases, the character of the twin structure changes, and the amount of the untransformed phase t′ increases. The dependence of the hardness and crack resistance of the crystals of partially stabilized zirconia on the Y₂O₃ concentration and the indenter orientation is investigated using the microindentation method. The sample with the lowest concentration of the stabilizing Y₂O₃ impurity turned out the most crack resistant. This can be explained by a high content of tetragonal phase t in it, which provides the transformation strengthening mechanism of the material, and by a more multilevel character of twinning.     

A new classification of twinning in crystals

A comprehensive and informative classification of twinning in crystals is proposed. It is based on the nature of the twin mapping operation. If the mapping operation is a symmetry element of a certain prototype space group (in Aizu's sense), the twin is called an “Aim twin”. Otherwise it is called a “Bollmann twin”. Aim twins are essentially transformation twins. They may be further divided into ferroic twins and translation twins. Ferroic twins, in turn, can be of two types: ferroelastic or F-twins (e.g. the 90° twins of BaTiO₃), and nonferroelastic-ferroic or N-twins (e.g. the Dauphiné twins of quartz). The antiphase domains in Cu₃Au are a typical example of translation twins (T-twins). The three types of Aim twins (F, N and T) have distinctive macroscopic physical properties. Bollmann twins are divided into two main categories: C-twins and M-twins, where C stands for coincidence lattice and M for miscellaneous. C-twins are further categorized into two types, depending on the “total” or “partial” nature of the coincidence sublattice. M-twins can be of three types, depending on the dimensionality of the dichromatic pattern being 0, 1 or 2. Illustrative examples are discussed. A compact and informative twin symbol is introduced.     

In situ TEM study of mechanical behaviour of twinned nanoparticles

There is strong interest in studying changes in mechanical properties with reducing grain size. The rational is that consequent dislocation glide cannot be sustained, resulting in an increase in material strength. However, this comes with the cost of a reduction in ductility. It has been shown that coherent twin boundaries in nanostructured Cu improve the ductility to 14% [Lu et al., Science 324 (2009) p. 349]. In this paper, we report for the first time the compression of individual nanoparticles using an in situ force probing holder in the transmission electron microscope. Four types of nanoparticles were tested, three with twin boundaries (decahedra, icosahedra and a single twin) and one free of defects (octahedral). Our results indicate the yield strength of the twinned nanoparticles is between 0.5 and 2.0 GPa. The total malleability for the twinned particles range from 80 to 100%. In addition, experimental results were reproduced by MD simulations of the compression phenomena and suggest that the outstanding mechanical properties are related with partial dislocation multiplication at twin boundaries.