Influence of directional strength-to-stiffness on the elastic–plastic transition of fcc polycrystals under uniaxial tensile loading

Crystal-based finite element simulations have been conducted on virtual face-centered cubic polycrystals under uniaxial tensile loading to study the influence of single crystal elastic anisotropy on the elastic–plastic transition behavior exhibited by the lattice strains. The lattice strain response is examined for different sets of crystals corresponding to different crystallographic fibers. The lattice strain response observed in the elastic–plastic transition is related to crystals associated with different crystallographic fibers yielding on average at different levels of the macroscopic stress. The lattice strain behavior is determined by a combination of the elastic and plastic anisotropies of the single crystals, which is quantified using the directional strength-to-stiffness ratio. The directional strength-to-stiffness ratio for a single crystal and a crystallographic fiber are introduced and they are used to explain the deviation of the lattice strains from linear behavior in the elastic–plastic transition leading up to fully developed plasticity.     

What is a crystal to the new chemical crystallographer,after that first,automated structure analysis?

This educational review postulates the importance of maintaining an adequate level of crystallographic education among structure-dependent scientists whose interests are not primarily in crystallography, at a time when automation and validation have made it possible to obtain high-quality structure analyses in many cases with a minimum of crystallographic background. The topics addressed are intended to form a second round of crystallographic education for a novice user whose first round involved hands-on experience with structure solution and an introduction to elementary concepts. The specific topics, chosen for their relevance as basic knowledge and their lack of emphasis in many formal treatments, are (1) crystallographic reference frames and the utility of the reciprocal cell in geometrical calculations; (2) the relationship between the two concepts that constitute our model of the crystal, namely the unit cell and the lattice; (3) the manner in which an atom is represented in concept and in practice; (4) the importance of interleaved symmetry elements required by the presence of additional symmetry on a lattice; (5) the harnessing of the natural properties of the crystalline state for the potential manipulation of properties of synthetic crystals; and (6) useful terminology for navigating a crystal structure.     

Total scattering and the pair distribution function in crystallography

The importance of total scattering and its Fourier transform, the pair distribution function, in crystallography was understood soon after it was shown that crystals diffract X-rays. However for the next fifty years or so other techniques based more firmly on the crystal lattice came to the fore and total scattering measurements were largely the domain of those studying liquid and amorphous structure. In the late 1980s it was ‘rediscovered’ as a way to uncover disorder within crystal structures and since then the combination of improved instrumentation and analysis has led to a resurgence of the total scattering method. This review sets out this journey, highlighting both the early origins and – more importantly – the ways that total scattering and pair distribution functions are routinely used within crystallography today.     

Crystal structure and magnetic properties of ZnV2O4

We present structural and magnetic data on ZnV₂O₄ single crystals. Single crystal X-ray diffraction shows the measured crystals to be of very high quality, especially with respect to atomic order. The measured magnetic susceptibility resembles to that of a spin glass system, surprising for a translational invariant structure. The results are discussed in the framework of disorder in a magnetically frustrated lattice.     

Contribution of Diffusion Processes to Structure Formation in Intense Cold Plastic Deformation of Metals

The problems of distribution of the chemical potential of vacancies in a crystal with a cellular dislocation structure, the evolution of the properties of the lattice and its imperfections in the process of plastic flow, the contribution of diffusion to the motion of lattice dislocations, and their annihilation and transformation into grain boundary dislocations are considered. An analysis of the phenomena that occur inside and in the walls of dislocation cells in the formation of large-angle boundaries shows that intense cold plastic deformation activates the diffusion mass transfer.     

Orientation stability in equal channel angular extrusion. Part I: Face-centered cubic and body-centered cubic materials

Stability of crystallographic orientations is a key aspect in the characterization and understanding of texture evolution during plastic deformation. In this study, a rate-dependent crystal plasticity model was applied to investigate orientation stability during equal channel angular extrusion (ECAE) of face-centered cubic (fcc) and body-centered cubic (bcc) crystals. The stability of experimentally observed ideal orientations was examined according to lattice rotation fields computed at and around the orientations. It is shown that these ideal orientations are meta-stable under rate-sensitive conditions, and their stability generally increases with the decrease of strain rate sensitivity. The results also reveal a well-preserved duality in the lattice rotation and orientation stability between the two types of crystal structure. The stability results simulated at low strain rate sensitivities agree well with the experimental observations in one-pass ECAE of Al and Cu single crystals. In Part II of the paper, this analysis is extended to hexagonal materials.     

Deformation and creep modeling in polycrystalline Ti–6Al alloys

This paper develops an experimentally validated computational model for titanium alloys accounting for plastic anisotropy and time-dependent plasticity for analyzing creep and dwell phenomena. A time-dependent crystal plasticity formulation is developed for hcp crystalline structure, with the inclusion of microstructural crystallographic orientation distribution. A multi-variable optimization method is developed to calibrate crystal plasticity parameters from experimental results of single crystals of α-Ti–6Al. Statistically equivalent orientation distributions of orientation imaging microscopy data are used in constructing the polycrystalline aggregate model. The model is used to study global and local response of the polycrystalline model for constant strain rate, creep, dwell and cyclic tests. Effects of stress localization and load shedding with orientation mismatch are also studied for potential crack initiation.     

Crystallography using an X-ray free-electron laser

An X-ray free-electron laser (XFEL) produces short pulses (10–50 fs) of intense (mJ μm^?2 at 120 Hz) X-rays, with high transverse coherence. Such pulses open novel spectroscopic and scattering methods for static and time-resolved studies of matter, and many are based on X-ray crystallography. With serial femtosecond crystallography, the XFEL allows high-resolution structural determination on sub-micron protein crystals. Although the XFEL pulse is destructive, its short duration ensures that effectively undamaged material is probed. Coherent scattering features provide information on the physical crystal form and may assist in determining the crystallographic phase. By introducing synchronized optical laser pulses, one can perform ‘pump-probe’ measurements of dynamic properties, on the sub-picosecond timescale. These include photo-initiated structural modifications in biomolecules, photo-excited lattice vibrations and photo-driven structural phase transitions. As with synchrotron radiation, the XFEL wavelength can be tuned to atomic resonances, allowing time-resolved resonant-diffraction measurements, which are particularly sensitive to selected order parameters (lattice, charge, spin, and orbital) in magnetic or correlated electron materials. Finally, it is anticipated that the special properties of XFEL pulses will allow entirely new types of X-ray scattering measurements, such as ptychographic crystallography on 2D bio-crystals, correlation-function determination of nanoparticle geometry and nonlinear crystallographic mixing of optical and X-ray pulses.     

Evidence for a monoclinic incommensurate superstructure in modulated martensite

Structural modulation of martensitic phases is regarded as a prerequisite for magnetically or electrically induced reversible strains in shape-memory alloys. Controversy surrounds the crystal structure of modulated martensite. Here, we explore this critical issue through combined spatially resolved microstructural and crystallographic characterizations of a polycrystalline Ni₅₃Mn₂₂Ga₂₅ alloy, by comparing the high-resolution Kikuchi patterns with those predicted according to various hypotheses—7M(IC) or nanotwin combination structure—on the modulated martensite. Detailed analysis has demonstrated that the modulated martensite plates may possess a monoclinic incommensurate superstructure, other than the nanotwinned tetragonal non-modulated structure. Such an incommensurate superstructure can generate a more favorable plate interface configuration for field-driven twinning/detwinning, capable of producing large reversible actuation strain. Moreover, the thermodynamically metastable modulated martensite may transform into the non-modulated martensite by further local lattice distortion, which would degrade the magnetic shape-memory effect. By taking into account the microstructure–property correlation, the ambiguity concerning the modulated martensitic structure could be clarified, which is essential to the understanding of the stability of modulated martensitic phases and their functionality as shape-memory materials.     

A comparison of the phenomenological theory of martensitic transformations with a model based on interfacial defects

Structural models of martensitic interfaces are those where the habit plane (HP) is comprised of coherent terraces reticulated by arrays of interfacial defects. Such interfaces are shown explicitly to exhibit no long-range displacements and to move in a glissile manner by lateral motion of disconnections along the interface. We quantify predictions of HP and orientation relationship (OR) between the parent and product crystals for such models in terms of a reference lattice in an approach called a topological model (TM). These crystallographic quantities for the TM are compared with those of the phenomenological theory of martensite crystallography (PTMC). For the case of transformations resembling α to β in Ti, but where lattice invariant deformation is suppressed, the two models agree when the interplanar spacings of the terraces in the two crystals are the same. However, although the OR’s according to the two approaches are very similar, the predicted HP’s differ systematically when the terrace plane spacings are varied. The differences arise because the PTMC interfaces are unrelaxed configurations that are invariant planes of the geometrical shape transformation, whereas TM interfaces are physically invariant planes as a transformation progresses.     

Orientation dependence of nanoindentation pile-up patterns and of nanoindentation microtextures in copper single crystals

We present a study about the dependence of nanoindentation pile-up patterns and of microtextures on the crystallographic orientation using high purity copper single crystals. Experiments were conducted on a Hysitron nanoindentation setup using a conical indenter in order to avoid symmetries others than those of the crystal structure. Orientation measurements were conducted using a high resolution electron back-scatter diffraction technique for the automated acquisition of texture mappings around the indents. Simulations were carried out by means of a 3D elastic–viscoplastic crystal plasticity finite element method which takes full account of crystallographic slip and orientation changes during indentation. The experiments as well as the simulations show that the pile-up patterns on the surfaces of (0 0 1)-, (0 1 1)- and (1 1 1)-oriented single crystals have four-, two-, and sixfold symmetry, respectively. The different pile-up patterns can be explained in terms of the strong crystallographic anisotropy of the out-of-plane displacements around the indents. Pronounced accumulation of material entailing characteristic pile-up patterns occurs along the intersection vectors between the primary crystallographic slip planes and the indented surface planes.     

Theoretical study of interstitial atoms distribution in the bulk and at the surface of crystal. Surface segregation

A theoretical investigation of diffusion, distribution and thermally activated redistribution of impurity interstitial atoms C (hydrogen, carbon) about the volume and surface both of crystalline films and massive crystals AB has been carried out. These crystals have bcc lattice and various types of free facets. The dependence of hydrogen and carbon filling of the surface and volume interstitial sites upon the films’ temperature and composition have been studied. Changing the temperature or pressure leads to the redistribution of C atoms in the system. The thermally activated processes of C atom redistribution among the volumetric and surface film interstices in AB alloy are investigated. The formulae for the equilibrium concentrations of interstitial atoms and the rate or relaxation time of interstitial atoms redistribution in dependence on concentrations of A, B alloy components, on long range order in A, B atoms distribution at the sites of crystal lattice, on temperature, on interaction energies of atomic pairs AC, BC are determined.     

An insight into the role of the grain boundary in plastic deformation by means of a bicrystalline pillar compression test and atomistic simulation

A combination of experimental and molecular dynamics (MD) simulations is used to investigate the interaction of dislocations with a selected grain boundary (GB) in bicrystalline pillars (BCPs) with component crystals oriented for single slip and multiple slip. As a reference, single-crystalline pillars with the same orientations are also tested and compared with the BCPs. Orientations identical to the experiments are used to generate models in MD simulations. Further, electron backscatter diffraction (EBSD) measurements on the cross-section of the pillars are performed to investigate the crystal lattice rotation in correlation with the excess dislocation density. A clear change in mechanical behavior of the BCP was observed when the size of the component crystals reduced below 1 μm. The EBSD analyses of these small BCPs showed an increase in the misorientation in the vicinity of the GB. MD simulation provided atomistic insights into the dislocation nucleation process and the BCPs’ interaction with the GB. On the basis of these observations, it is concluded that in BCPs smaller than 1 μm the dislocation–GB interaction plays a more crucial role than the dislocation–dislocation interaction.     

On coherency-induced ordering in substitutional alloys—I. Analytical

As pointed out by Linus Pauling in his classic work on the relationship between crystal packing and ionic radius ratio, a difference in atomic size can be accommodated more readily by an ordered structure than by a disordered one. Because of mathematical complexity, however, very few works have been reported for substitutional alloys. In this work, coherency-induced ordering in substitutional alloys is examined through a simple model based on a two-dimensional square lattice. Within the assumption of nearest-neighbor interactions on a square lattice, both modified Bragg–Williams and Onsager approaches show that coherency strain arising due to atomic mismatch can exert profound effects on order–disorder transitions in substitutional alloys. If the alloy system is elastically homogeneous and Vegard's law is obeyed, the order–disorder transition is of a second-order kinetics. If the atomic mismatches significantly deviate from Vegard's law, however, the transition may become a first-order kinetics, as the configurational free energy surface is composed of double wells. At the transition of a first-order kinetics, the lattice parameter can either increase or decrease upon heating, i.e. the lattice parameter of an ordered state can be less or greater than that of a disordered state. The results of Onsager's approach are independently confirmed with those of the Discrete Atom Method, a Monte Carlo technique predicated upon the combination of statistical mechanics and linear elasticity.     

CYCLIC DEFORMATION OF FACE CENTERED CUBIC CRYSTALS AND ITS DISLOCATION INTERACTION MODEL——Ⅱ.DISLOCATION INTERACTION MODEL OF CYCLIC DEFORMATION

A dislocation interaction model has been proposed for cyclic deformation of fcc crystals.Ac-cording to this model,cyclic stress-strain responses and saturation dislocation structures of acrystal are associated with the modes and intensities of dislocation interactions between slipsystems active in the crystal; and,hence,may be predicted by the location of its tensile axis inthe crystallographic triangle.This model has successfully explained the different behaviours ofdouble-slip crystals and multi-slip behaviours of some crystals with orientations usually con-sidered as single-slip ones.     

FCC晶体中晶体取向对孔洞长大和聚合的影响

通过编制率相关有限元用户子程序，采用包含一个和两个球形孔洞的单胞探求了FCC晶体中晶体取向对孔洞长大和聚合的影响。计算结果表明：晶体取向对孔洞长大的影响较大，孔洞的形状和长大方向与晶体取向密切相关：由于变形不均匀，孔洞在晶界处产生尖角，易形成裂纹。由于约束较少，孔洞周围和两孔洞间的区域塑性变形较大，晶体的转动和滑移主要集中在孔洞周围以及两孔洞间的区域。     

Crystallography and the liquid crystal phase: a new approach to structural studies on a thermo-tropic smectic Schiff base

In spite of the apparent contradiction between ‘liquid crystals’ (LC, materials exhibiting some degree of disorder) and ‘crystallography’ (a paradigmatic ordered kingdom), X-ray diffraction (XRD) studies make a substantial contribution to the field of LC. Focusing this review on smectic (Sm, lamellar) LC, we first describe how extremely careful XRD studies performed on mono-domain samples in the LC phase helped to elucidate the molecular structure of ordered Sm phases. Then, we describe selected examples in which single-crystal (SC) XRD on the solid-state phase of the mesogens provided information about their supra-molecular organization in the Sm phase. Finally, we present a different approach to this problem in the case of a thermo-tropic Schiff base (SB) which undergoes crystal???LC???isotropic liquid phase transformations. By combined SC and variable-temperature powder XRD, we show that the SB LC is a hexatic smectic B phase that derives from the crystal phase by relatively small topological changes promoted by the set-in of thermal rotational disorder around the long SB molecular axis.     

A centennial: Evolution in the understanding of chemical ordering in metallic crystals

Many important metallic alloys are characterised by the chemical ordering of their atomic component elements. Examples are beta brass (βCuZn – one of the components of common brass), many of the gold-base alloys used in dentistry, Nickel–Titanium shape memory alloys with superelastic properties (great stretchability, as used for orthodontic wires) and Nickel–Aluminium gamma-prime phase which strengthens superalloys for high-temperature turbines. The figure shown below (Fig. 1) represents such an ordered arrangement of two atomic species (could be copper and gold, or nickel and aluminium) on a face centred cubic lattice. The disordered lattice would have the yellow and blue atoms randomly distributed.While such important materials, the realisation that these crystals are chemically ordered (in contrast to chemically-disordered alloys, such as alpha brass (αCuZn), steels, aluminium alloys, and most other metallic alloys) is a relatively new understanding, being just now one century old. It had been understood for a long time before that crystals contained spatially-ordered atoms, but not that there was chemical order hidden inside. It was only with the development of methods of diffraction of x-rays by crystals that it became possible to recognise and quantify such chemical order.