Twinning In Single Crystals Research Articles

Evolution of partial dislocation slip–mediated deformation twins in single crystals: a discrete dislocation plasticity model and an analytical approach

Deformation twinning is an essential plastic deformation mechanism that realizes the trade–off between strength and ductility. Twins nucleate and grow by the coordinated slip of partial dislocations on consecutive {111}–type slip planes. The route of twin growth is responsible for the evolution of twin morphology, which affects the non–coplanar dislocation slips by adjusting the twinning–associated mean free path. Incorporating such twinning mechanisms is critical for the accurate modelling and simulation of deformation behavior. In this study, a discrete dislocation plasticity (DDP) model was developed by integrating the source introduction methods and source activation criteria of Shockley partial dislocation. In the model, two twin nucleation mechanisms, i.e., the internal source and surface source, were considered concurrently, and the additional effect of stacking fault energy on the motion of partial dislocations was introduced. The evolution of partial dislocation slip–mediated deformation twins in micron–sized pillars of twinning–induced plasticity steel under uniaxial compression was investigated. The predicted twin morphologies and stress–strain curves from DDP simulation both agreed well with the experimental results, highlighting the inherent characteristics of partial–dislocation–based twinning behavior. The simulation results showed that the formation of nanometer–sized sharp twin tips was caused by the strong interaction between the front and rear dislocations on adjacent slip planes. In addition, a novel analytical model verified with the DDP simulation was proposed by considering the kinetics of the newly formed twin embryos. The competition between new twin activation and near–twin merging in determining the evolution of twin thickness was analyzed using the analytical model. The dependence of flow stress and twin morphology on the density and distribution of internal sources was demonstrated by considering the new twinning route. This research thus advances the understanding of partial dislocation slip–mediated twinning mechanisms.

Orientation and temperature dependence of a planar slip and twinning in single crystals of Al0.3CoCrFeNi high-entropy alloy

This paper repots the effect of crystal orientation and test temperature on the tensile deformation behaviour, the type of dislocation structure (planar or cellular) and the deformation mechanism (slip and twinning) in single crystals of the fcc Al0.3CoCrFeNi (at%) high-entropy alloy. It was shown that, in the temperature range 77–573 K, the tensile deformation behaviour at 0.1% < ε < 15% along [001], [1¯11] and [011] orientations is related to the slip, at which a planar structure with dislocation pile-ups develops in the wide temperature range of 77–423 K. The planarity of the dislocation structure is determined by the strong effect of solid-solution hardening via Al atoms, since the effective radius of Al atoms exceeds the effective radii of the other elements included in the composition of the Al0.3CoCrFeNi alloy, and existence of short-range order. In slip deformation, the strain hardening coefficient in the linear stage of hardening, i.e., ΘII(T)/G(T), depends on the crystal orientation and the test temperature. In the [011]-oriented single crystals where the slip deformation develops predominantly in one system, ΘII(T)/G(T) has small values and it increases with an increasing number of active slip systems in the [1¯11]- and [001]-oriented single crystals. Twinning was detected at 77 K in the [1¯11]- and [011]-oriented single crystals after 15% and 20%, respectively. Deformation twinning in the [1¯11]- and [011]-oriented single crystals leads to an increase in ΘII(T)/G(T) and determines more complex deformation stages in the σ–ε curve in the [011]-oriented single crystals compared with the development of slip deformation at high test temperatures.

Twinning in [001]-oriented single crystals of CoCrFeMnNi high-entropy alloy at tensile deformation

This paper presents research about the tensile deformation behaviour and deformation mechanisms (slip and twinning) in single crystals of the equiatomic Co20Cr20Fe20Mn20Ni20 (at%) high-entropy alloy (HEA) oriented along the [001] direction in the temperature range T = 77–573K. Classical studies on single crystals of pure metals and their substitution alloys with the face-centered cubic (FCC) structure, with a low stacking fault energy, have shown that deformation twinning in single crystals oriented along the [001] direction does not develop at tensile deformation. In the present paper, extrinsic stacking faults and deformation twinning in the [001]-oriented single crystals of the equiatomic Co20Cr20Fe20Mn20Ni20 HEA were detected under tensile loading at the temperature of liquid nitrogen after a strain of 5%. The critical resolved shear stress for twinning was determined as τcrtw =210 ± 10MPa. Deformation twinning in the [001]-oriented single crystals leads to an increase in the strain hardening coefficient in comparison with the slip deformation in these crystals at T > 77K.

Complex Structural Behavior of BiMn7O12 Quadruple Perovskite.

Structural properties of a quadruple perovskite BiMn7O12 were investigated by laboratory and synchrotron X-ray powder diffraction between 10 and 650 K, single-crystal X-ray diffraction at room temperature, differential scanning calorimetry (DSC), second-harmonic generation, and first-principles calculations. Three structural transitions were found. Above T1 = 608 K, BiMn7O12 crystallizes in a parent cubic structure with space group Im3̅. Between 460 and 608 K, BiMn7O12 adopts a monoclinic symmetry with pseudo-orthorhombic metrics (denoted as I2/m(o)), and orbital order appears below T1. Below T2 = 460 K, BiMn7O12 is likely to exhibit a transition to space group Im. Finally, below about T3 = 290 K, a triclinic distortion takes place to space group P1. Structural analyses of BiMn7O12 are very challenging because of severe twinning in single crystals and anisotropic broadening and diffuse scattering in powder. First-principles calculations confirm that noncentrosymmetric structures are more stable than centrosymmetric ones. The energy difference between the Im and P1 models is very small, and this fact can explain why the Im to P1 transition is very gradual, and there are no DSC anomalies associated with this transition. The structural behavior of BiMn7O12 is in striking contrast with that of LaMn7O12 and could be caused by effects of the Bi3+ lone electron pair.

Phase-field analysis of fracture-induced twinning in single crystals

Deformation twinning at the tip of a straight crack or notch is analyzed using a phase-field method that seeks equilibrium twin morphologies via direct minimization of a free energy functional. For isotropic solids, the tendency to twin under mode I or mode II loading is found to depend weakly on Poisson’s ratio and elastic nonlinearity and strongly on surface energy and twinning shear (i.e. eigenstrain). Depending on the coherent twin boundary energy, anisotropy of surface energy is important for mode I loading but less so for mode II. Model predictions for several single crystals are in agreement with experimental observations. Calcite demonstrates a preference for mode I cleavage crack extension over crack tip twinning. Magnesium shows a likelihood for tensile twinning from a pre-existing crack on the basal plane. In sapphire, a preference for rhombohedral twins over basal twins is apparent, with the latter thinner in shape than the former.

Deformation twinning in single crystals of a D0 19 compound with an off-stoichiometric composition (Ti–36.5at.%Al)

The characteristics of deformation twinning in single crystals of a D0 19 compound Ti 3Al with off-stoichiometric composition (Ti–36.5at.%Al) have been studied in detail by trace analysis and transmission electron microscopy. Deformation twinning is operative only at high temperatures above 1000 °C when the compression axis is parallel to and close to the hexagonal c-axis. All observed deformation twins are assigned to be of the type II and the twinning elements are determined as: K 1 : ‘ { 2 ¯ 12 10 ¯ 3 } ’ , K 2 : { 2 0 2 ¯ 1 ¯ } , η 1 : 〈 5 1 ¯ 4 ¯ 6 ¯ 〉 , η 2 : ‘ 〈 1 ¯ 3 2 ¯ 2 〉 ’ , s = 0.346 . The critical resolved shear stress for the ‘ { 2 ¯ 12 10 ¯ 3 } ’ twin is estimated to be about 50 MPa at 1000 °C and it gradually decreases with increasing temperature. The possible atom movements by the deformation twinning are described and the reasons why twinning of this type occurs only under a limited condition (i.e., off-stoichiometric compositions, high temperatures and compression axis being close to the c-axis) are discussed in the light of the atom movements by the deformation twinning.

Mechanism of deformation and crystal lattice reorientation in strain localization bands and deformation twins of the B2 phase of titanium nickelide

Optical metallography and transmission electron microscopy were used to investigate the formation and microstructure of strain localization bands and deformation twins in single crystals of a TiNi alloy deformed by rolling. On the basis of these investigations, with the use of the theory of martensitic transformations based on the concept of cooperative thermal vibrations of coherent objects (close-packed planes) in crystals, a new mechanism of twinning in these alloys is suggested, namely, through the forward plus reverse (B2 → B19 → B2) martensitic transformations with the reverse transformation developing via an alternative transformation system. It is shown that using this mechanism one can describe on the same grounds the twinning in the crystal lattice of the B2 phase with twin planes of different ({1 1 2}, {1 1 3}, and {3 3 2}) Miller indices and the formation of strain localization bands with low-angle misorientations.

Investigation of the Mechanical Twinning of Antimony Single Crystals by Nanoindentation

The twinning of antimony single crystals in nanoindentation has been investigated. The role of twinning in the formation of the impression of the Berkovich pyramid on the surface (111) of antimony single crystals has been established. A new method of investigation of the mechanical twinning of single crystals has been developed. For the first time, the duration of the process of twinning has been determined experimentally by a direct technique.

Effect of irradiation by boron ions on the character of realization of twinning and slip under prolonged (more than 60 sec) loading of single crystals of bismuth

The twinning of single crystals of bismuth irradiated by boron ions with an energy of 25 keV and a dose of 1017 ion/cm2, in the case of prolonged (more than 60 sec) loading of a crystal is studied. It is found that prolonged exposure of a crystal to a concentrated load promotes a decrease in the number of twins in the concentrator of external stresses. An increase of temperature up to 400 K stimulates the process of slip in the realization of plastic deformation of a crystal.

Microstructure and texture of rolled {112}〈111〉 copper single crystals

High purity copper crystals with the orientation {112}〈111〉 were rolled at room temperature and at 77 K. At room temperature deformation twins were observed metallographically after 46% reduction and twin orientations could be detected in pole figures soon after. In crystals rolled at 77 K twinning was profuse and was readily detected metallographically and in the texture at reductions <20%. Previous reports of deformation twinning in single crystals of copper and materials of lower stacking fault energy are summarized. It is shown that there is good agreement between textures and metallographic studies and that the onset of twinning can be related to orientation by means of the ratio of the resolved shear stresses for twinning and slip and to the stacking fault energy and the deformation temperature.

Effect of a dislocation forest on the bauschinger effect during the twinning of zinc single crystals

A study was made of the effect of a dislocation in the {{11¯22}} 〈11¯23〉 system (pyramidal slip) on the characteristics of the Bauschinger effect during the twinning of single crystals of zinc and of the alloy Zn + 0.6% Cu. The dislocation forest retards the backward motion of the twinning dislocations, leading to the effect.

Deformation Twin in Single Crystals of a 3% Vanadium-Iron Alloy

Observations were made on deformation twins in single crystals of a 3% vanadium-iron alloy which were deformed in compression along the [1̄10] direction at -195°C. In most twin bands, a narrow but straight line (`midrib') is seen to run along the longitudinal direction. Electron microscope observations show that the thickness of such a `midrib' is less than 100 Å and also, near the midrib, a considerably high density of dislocations is located. The midrib runs straight without being disturbed by sub-boundaries, where twin bands are always constricted. Besides such `constrictions', `indentations' are frequently observed in a twin band, which are interpreted as regions left untwinned locally in the growth process of thickness because of the presence of isolated obstacles. These observations may suggest that a deformation twin is formed by the following two processes. A very thin twin plate less than 100 Å in thickness is first formed dynamically, and then the thickness of the twin increases with increasing stress, forming constrictions or indentations at the place of obstacles such as sub-boundaries, pre-cipitates, or pre-existing dislocations.

On mechanical twinning in single crystals of vanadium

Single crystals of vanadium have been deformed. in_compression along the [111] direction at 77°K. The specimens deformed initially by twinning on the (121)[111] and the (211)[111]-twin systems; but, twinning on the (121)[111] system was usually preferred after about 6 % strain. If specimens which had been prestrained to 10 % compression were aged for 15 min at 100°C and re-strained at 77°K deformation continued by twinning, but at a stress 20 percent lower than the final stress attained during the prestrain treatment. On ageing at 100°C for longer times, this stress difference decreases in magnitude until after 3 hr ageing at 100°C re-straining at 77°K produces a true stress-strain curve which is a continuation of that obtained during the prestraining treatment.The change in stress after short ageing times at 100°C is explained by the relaxation of long-range stresses built up during prestraining at 77°K. The gradual decrease in the stress difference is explained in terms of gradual pinning of the incoherent twin boundaries by diffusing impurity atoms.

The electron microscopy of deformation twinning

The incidence of deformation twinning in single crystals of f.c.c. Cu plus Al alloys has been studied by transmission electron microscopy. All the alloys have been found to twin under suitable conditions although in alloys with low stacking fault energy twinning is not associated with a plastic instability. In these alloys the growth of the twins can be followed from single stacking faults so that the dislocation reaction leading to the nucleation of twins may be studied experimentally.

The formation of mechanical twins

Measurements have been made of the stress required to cause the appearance of twins in single crystals of cadmium, both in tension and in compression. The results are consistent with the view that, if a twin nucleus is present, the shear stress in the twinning plane which is needed to cause it to grow is independent of the normal stress across the twinning plane.

Effect of Surface Films on the Twinning of Metal Crystals

IN a recent communication, Gilman1 reports that an electrodeposited layer of copper raises the stress necessary to cause twinning in single crystals of zinc. This result is in accord with a series of observations, to be published shortly, by Dr. S. M. Gumbrell and myself, on the effect of surface condition on the twinning behaviour of cadmium crystals.

Slip and Twinning in Single Crystals of Mercury

IN 1935 Prof. E. N. da C. Andrade and Mr. P. J. Hutchings described1 the results of interesting experiments on the deformation of single crystals of mercury, and it is concluded that in a mercury crystal the rhombohedral faces are the glide planes—as (it was stated) would be expected from the fact that these are the planes of closest packing. Of many measurements that had been made of the intersection angles between glide and twinning plane traces, three sets in particular were considered to furnish strong confirmation of the above conclusion.

Slip and Twinning in Single Crystals of Mercury

MR. FISHER is, I expect, right when he points out that the {111} planes are the most closely packed in a mercury single crystal, although I have not the time to check the work. The experiments to which he refers were carried out some years ago, and all notes referring to them were destroyed with my laboratory. Whether he is right in his surmise that the {111} planes may be the glide planes I cannot say. The only way of settling the question satisfactorily is by the X-ray method. I always intended to get the attribution checked in this way, but at the time when the work was done an X-ray set suitable for this purpose had not been installed, as it was later. We were discussing the X-ray determination in my laboratory shortly before the War broke out.