Common Orientation Relationships Research Articles

Stereographic Projection of Theoretical Orientation Relationships Between Crystals of Any Types in Phase Transformation and Precipitation

AbstractStereographic projection is a classic technology to represent the angular relationships of lattice planes and directions. In some cases, it is necessary to project arbitrary lattice planes or directions of a crystal onto an arbitrary lattice plane of another crystal, e.g., when representing orientation relationships (ORs) in phase transformation or precipitation. Commercial EBSD (electron backscatter diffraction) software cannot illustrate theoretical orientation relationships based purely on the parallelism conditions. This work presents a generalized and unified formulation for stereographic projection of any lattice planes or directions onto any lattice planes of any crystals in the 32 point groups, which is utilized to represent the theoretical orientation relationships between any crystal types. Examples are given to illustrate the correlations of common orientation relationships in both cubic and hexagonal crystals. A procedure is also established to color code and simultaneously project all low‐index Miller/Bravais planes or directions of a crystal onto an arbitrary lattice plane of the same crystal, which can be utilized to visualize the crystal symmetry and determine the standard stereographic triangle (SST). All these illustrations are realized in a computer program written in C++ using the OpenGL graphic libraries.

Fatigue crack growth behavior of diffusion-bonded heterogeneous titanium alloy laminate

The fatigue crack propagation behavior of diffusion-bonded heterogeneous TA2/Ti55/TA2 laminate was investigated. Face centered cubic δ phase precipitates in TA2 during diffusion bonding process. The adjacent δ grains have a common {110} pole. The common orientation relationship between α and δ grains is {112¯0}HCP//{110}FCC. Strength improvement and secondary cracks due to δ phase play key roles to reduce fatigue crack growth rate in TA2. The fatigue crack growth rate decreases sharply in Ti55 interlayer owing to its high strength and abundant α/β interfaces.

Distinct difference between peri-eutectic and eutectic growth in ternary Fe-Ni-Ti alloy

Peri-eutectic transition L+δ-Fe→γ-Fe(Ni)+Fe2Ti in ternary Fe66.5Ni17.6Ti15.9 alloy was investigated using directional solidification technique. We found that the primary phase and the peri‑eutectic in the solid region had a common orientation relationship, while the eutectic in the mushy zone had multiple orientation relationships. This firstly provided the evidence for the different growth mechanisms of peri-eutectic and eutectic, and secondly clarified that the peri‑eutectic nucleated from the primary phase and grew cooperatively. These orientation relationships related with interface structure and solidification kinetics. The peri‑eutectic had complicated interface structure characterized by a quaternary junction and grew under near equilibrium, whereas the eutectic had fewer interfaces and formed during quenching. Besides, the primary δ-Fe phase transformed to the lamellar α-Fe phase with different orientations after peri‑eutectic transition. This work is helpful for further understanding the peri‑eutectic transition as well as the connection between growth mechanism and crystallographic orientation in ternary alloys.

New orientations between β′2 phase and α matrix in a Mg-Zn-Mn alloy processed by high strain rate rolling

Strengthening precipitates in a Mg-Zn-Mn alloy, processed by high strain rate rolling, have been characterized by transmission electron microscopy. Precipitations involve a few (0001)α plates and spherical precipitates. All the precipitates have a hexagonal structure of MgZn2 and can be defined as β′2 phase. The (0001)α plates and a portion of the spherical precipitates have a common orientation relationship of [2¯110]β2'//[011¯0]α, (0001)β2'//(0001)α and (011¯0)β2'//(2¯110)α to α-Mg matrix. New orientation relationships (for example, [2¯110]β2'//[011¯0]α and (011¯5)β2'∼//(2¯110)α) between the spherical precipitates and α-Mg matrix were firstly observed, and the formation mechanism was systematically discussed.

Orientation relationships of Au5Sn/Au interfaces and formation sequence of Au5Sn and AuSn at the Au/Sn interface

The orientation relationships and interfaces between ζ′-Au5Sn and Au have been studied by transmission electron microscopy. Epitaxial Au thin films were grown on the single-crystal NaCl surfaces and Sn was evaporated to form ζ′-Au5Sn. Results showed that on both the (1¯11)Au and (001)Au surfaces the (0001)ζ′ plane is the common interface surface with a common orientation relationship of (1¯100)ζ′//(110)Au, which has a small misfit of 1.9%. The Au atoms have good matches across both interfaces.That δ-AuSn forms before ζ′-Au5Sn in the solid-state Au/Sn interfacial reactions was discussed by heterogeneous nucleation theory. Both phases have good orientation relationships to Au and therefore low interfacial energies. Analysis of the interfaces indicated that the ζ′-Au5Sn/Au interfacial energies should be less than δ-AuSn/Au, which favors the nucleation of ζ′-Au5Sn. However, the energy of formation of δ-AuSn is much larger, about 2.3 times, than that of ζ′-Au5Sn by data from references. Therefore δ-AuSn forms before ζ′-Au5Sn.

Orientation Studies of α-Al(Fe,Mn)Si Dispersoids in 3xxx Al Alloys

Dispersoids are important in 3xxx Al alloys, influencing mechanical properties, texture and recrystallization. In this work α-Al (Fe,Mn)Si dispersoids have been studied after low temperature homogenisation. The common orientation relationship between dispersoids and Al matrix has been reported in earlier studies. Here a systematic study on the orientation relationship and its exceptions is presented. It is found that most of the dispersoids follow the common orientation relationship, [1-1 1] α //[1-1 1]Al , (5-2 -7 ) α //(0 1 1)Al . Here the dispersoids are semi coherent with the Aluminum matrix. Different morphologies and habit planes are possible. Deviations from the most commonly observed orientation relationships are presented and discussed, to underline the complexity of the phase and its relation to the matrix.

Au–ZnO hybrid nanoflowers, nanomultipods and nanopyramids: one-pot reaction synthesis and photocatalytic properties

The preparation of noble metal-semiconductor hybrid nanocrystals with controlled morphologies has received intensive interest in recent years. In this study, facile one-pot reactions have been developed for the synthesis of Au-ZnO hybrid nanocrystals with different interesting morphologies, including petal-like and urchin-like nanoflowers, nanomultipods and nanopyramids. In the synthesis strategy, oleylamine-containing solution serves as the reaction medium, and the in situ generated Au seeds play an important role in the subsequently induced growth of ZnO nanocrystals. With the aid of several surfactants, hybrid nanocrystals with different morphologies that have considerable influences on their optical and photocatalytic activities are readily achieved. Through high-resolution transmission electron microscopy measurements, an observed common orientation relationship between ZnO and Au is that ZnO nanocrystals prefer to grow with their polar {001} facets on the {111} facets of Au nanocrystals, and well-defined interfaces are evident. Surface plasmon resonance bands of Au with different positions are observed in the UV-vis spectra, and the UV and visible emissions of ZnO are found to be dramatically reduced. Finally, the as-prepared Au-ZnO nanocrystals exhibit excellent photocatalytic activity for the photodegradation of rhodamine B compared with pure ZnO nanocrystals. The Au-ZnO hybrid nanopyramids show the highest catalytic efficiency, which is correlated with the exposed crystal facets, crystallinity and the formation of hybrid nanostructures. The as-prepared Au-ZnO hybrid nanocrystals are expected to find diverse potential applications in the fields such as photocatalysis, solar energy conversion, sensing and biological detection.

Electron microscopy studies of lutetium doped erbium silicide (Er0.9Lu0.1)5Si4

Abstract Examination of bulk microstructures of lutetium doped erbium silicide (Er0.9Lu0.1)5Si4 (space group: Pnma) using scanning and transmission electron microscopy (SEM, TEM) reveals the existence of thin plates of a hexagonal phase (space group: P63/mcm) where the stoichiometric ratio in moles between the rare earths and Si is 5 to 3, i. e the 5:3 phase. The orientation relationship between the matrix and the plates was determined as [010]m ≈ ∥[-1010]p. This observation adds credence to the assumption that all linear features noted in alloys of the rare-earth intermetallic family R5(SixGe1-x)4 are of the stoichiometric ratio 5:3 and possess a common orientation relationship with the parent 5:4 alloys.

Orientation relationships, interfaces, and microstructure of η-Cu 6Sn 5 formed in the early-stage reaction between Cu and molten Sn

A very thin η-Cu 6Sn 5 layer has been formed by dipping thin Cu foil into molten Sn at 240 °C for 1 s and quenching in ice water. After removing electrolytically the Sn on the surface, the η-Cu 6Sn 5 grains on the Sn side are shown to have a worm-type shape 0.3–0.5 μm wide and up to 2 μm long. Transmission electron microscopy (TEM) analysis shows that the η-Cu 6Sn 5 grains on the Cu side can be as small as 5 nm, indicating that the η-Cu 6Sn 5 /Cu interface is the nucleation side. The orientation relationships between η-Cu 6Sn 5 and Cu are determined by TEM. The η-Cu 6Sn 5 (112̅0) surface is the interface with both the Cu (001) and (1̅11) surfaces, and a common orientation relationship of (0001) η//(110) Cu is present on both interfaces. The match of atoms between η-Cu 6Sn 5 and Cu on the interfaces is analyzed.

Grain Scale Assessment of Variant Selection in a Thermomechanically Processed TRIP Steel

Orientations of both the α and γ phases in a multi-phase commercial steel were measured by means of electron backscatter diffraction (EBSD) techniques. Using the average orientation of each austenite grain as the reference frame, the orientation relationships between the two lattices were compared with the common orientation relationships (i.e. the Kurdjumov-Sachs and Nishiyama-Wassermann) in Rodrigues-Frank space. The occurrence of variant selection in individual austenite grains was examined using a recent dislocation-based model. This model considers the role of the slip systems that were active during prior deformation, as well as those of in-plane reactions, cross-slip and the partial dislocations that are linked to specific variants. It also unites the competing K-S and N-W relationships through the dissociation of perfect dislocations. Reasonably good agreement was observed between the predictions and the observations. Possible explanations for some of the discrepancies are also presented.

Interfaces of bismuth with Al–Cu–Fe icosahedral quasicrystal

In a transmission electron microscopy study, it is shown that bismuth makes a better lattice match with an icosahedral quasilattice than with a crystalline lattice. A common orientation relationship is [0001]‖2f (two-fold axis), ‖5f (five-fold plane), in which a match of prominent planes and axes occurs. The match in the reciprocal-space and lattice images indicate epitaxy at the interfaces. In a variant of this orientation relationship, [0001]‖2f, ‖5f, where and five-fold are the closest-packed planes in bismuth and the icosahedral phase, respectively.

Crystallogeometric analysis of the orientation relationship between austenite, Widmanstätten carbides, and martensite in carbon steels

The common orientation relationships (OR) between austenite, Widmanstatten carbides (WC), and martensite have been studied as a function of the type of the WC/austenite OR (Pitsch, Thompson, or Sleeswyk OR). It has been established that only two of twelve possible OR versions, which are close to the known Bagaryatskii OR, are realized between the WC and martensite upon the martensitic transformation and are observed experimentally. The causes for the realization of these two versions observed upon the experimental investigation of high-carbon steels are discussed with allowance for the specific crystallographic features of the WC/austenite interphase interface structure.

Differential role of nanoscaled oxide dispersoids (Y2O3 vs Al2O3) in the high-temperature structural stability of NiCr alloys

The effect of nanoscaled dispersoids in contributing to the high-temperature stability of nanograined NiCr alloys has been studied. Nanoscale yttria dispersoids were far more effective in contributing to the retention of a fine-grained microstructure in NiCr alloys (via the electron beam-physical vapor deposition (EB-PVD) route) as compared to the alumina particles. The fine yttria particles (<20 nm) shared a common orientation relationship with the matrix and exerted a Zener pinning force to inhibit rapid grain growth at elevated temperatures. Coarsening of yttria took place by diffusion of the metallic species through the NiCr matrix and was marginal compared to the alumina particles, which underwent a hierarchy of phase transformations (γ(spinel)→δ→α) as an outcome of coarsening. Phase selection at the nanoscale has been examined on the basis of free energies of formation of the metastable vs stable phases at the respective size ranges. The main factor responsible for the differential role of coarsening between the two types of dispersoids has been attributed to their relative free energies of formation, at these elevated temperatures.

Simulation of electron diffraction patterns of alloys with oriented precipitates

A computer program has been developed to simulate the complicated electron diffraction patterns of alloys consisting of an underlying matrix phase in which are embedded various crystallographically oriented precipitates. These precipitates consist of different variants each with a specific orientation relationship to the underlying matrix. The program is designed to calculate the number of possible variants and the specific orientation of each variant using a general orientation relationship input by the user, usually in the form of an axis–angle pair or two parallel directions or planes. The program then plots the superimposed diffraction pattern of the matrix and all variants for a given zone axis of the matrix using the calculated orientation relationships of the variants. The crystal symmetries of the matrix and the precipitate phases are employed for the former, the Ewald-sphere concept for the latter. The program is also equipped with the option of displaying the indices and relative intensities of the screen-displayed diffraction spots. Necessary symmetry, atomic scattering and structural data required for the computations are incorporated into the program in the form of data files. The program developed has been tested for various common orientation relationships, e.g. b.c.c. and f.c.c. twins, Bain, Kurdjumov-Sachs and ω, and some of the simulation results, in the form of variant transformation matrices and diffraction patterns, are presented.

Twinning in monoclinic beta-phase plutonium

Twinning has been investigated in body-centered monoclinic beta-phase plutonium by Transmission Electron Microscopy (TEM). A triode sputtering System was used to produce single-phase thick films of room temperature stabilized beta-phase metal. General examination of the microstructure revealed a very fine grain size (~100 nm) and the presence of twins. As expected in a fine grained metal, the dislocation density was low. Morphologically the twins appeared much like annealing twins observed in many melais and alloys, however, the formation of twins may have been due to deformation, growth or transformation processes. The definitive mode of formation has not been established, although classical deformation twinning theory was used to interpret the crystallography of the observed twins. Close inspection of the twins using microdiffraction revealed the individual parent/twin orientations. Crystallographic analysis of the electron diffraction patterns showed that Type II twinning appears to predominate, with a common orientation relationship between parent and twins described as a two-fold rotation axis about the [110] shear direction (η 1). Further work is in progress to theoretically predict the complete twinning Systems for beta-phase plutonium.

Thin‐Film Reactions

AbstractA new method for studying the formation of nickel‐aluminate spinel during the reaction between nickel oxide and alumina has been developed in which a thin‐film substrate of alumina is exposed to nickel oxide at elevated temperatures. Single crystal or twinned particles of spinel then grow in either near‐ or exact‐topotactic alignment along the edges of the thin‐film substrate. The spinel also grows on and into the surface of the substrate, but the deviation from exact topotaxy then tends to be larger. The expected topotactic relationship between the spinel and the alumina substrate is such that the (0001) plane of the alumina is parallel or near parallel to the {111} planes of the spinel with 〈1100〉 parallel to 〈110〉. However, a second common orientation relationship is also found where a {1120} plane of the alumina is parallel or nearly parallel to a {111} plane of the spinel; 〈1100〉 is again parallel to 〈110〉. First‐order twin boundaries in the spinel particles which have grown on the edge of the thin alumina substrate are found to be common just as they are in bulk‐reacted samples. A change in the orientation of the spinel with respect to the alumina substrate as a result of reannealing has been directly observed. The morphology of the various types of spinel particles is discussed briefly.