Single Crystal Orientation Research Articles

Effect of Single Crystal Orientation on Forming

Among processes involving plastic deformation, sheet metal forming requires a most accurate description of plastic anisotropy. One of the main sources of mechanical anisotropy is the intrinsic anisotropy of the constituent crystals. In this paper, we present the single-crystal yield criterion recently developed by Cazacu et al. [1] and its application to the prediction of anisotropy in uniaxial tension of strongly textured polycrystalline sheets. Namely, it is shown that using this single crystal yield criterion the Lankford coefficients exist and have finite values for all loading orientations. Moreover, the variation of both the yield stress and Lankford coefficients with the crystallographic direction can be expressed analytically. An application of this criterion to forming a cylindrical cup from a single crystal of (100) orientation is presented. Finally, we show that using this single-crystal model, one can describe well the effect of the spread around an ideal texture component on the anisotropy in uniaxial tensile properties of a polycrystal.

Probing the lattice structure of dynamically compressed and released single crystal iron through the alpha to epsilon phase transition

Experiments using broadband Laue x-ray diffraction (XRD) were used to examine the lattice structure of dynamically compressed [100]-oriented single crystal iron samples at the Dynamic Compression Sector at the Advanced Photon Source. These experiments used 1 μm thick iron single crystal samples sandwiched between a polyimide ablator and a polycarbonate window. A 100 J, 10 ns duration laser pulse incident on the polyimide ablator was used to shock compress the iron samples to initial stresses greater than 25 GPa, exceeding the ∼13 GPa alpha (body-centered-cubic or bcc structure) to epsilon (hexagonal-close-packed or hcp structure) phase transition stress. XRD measurements were performed at various times relative to the shock wave entering the iron sample: early times, <∼150 ps while the initial shock waves propagated through the iron; intermediate times, after the iron equilibrated with the ablator and window reaching a plateau stress state (12 or 17 GPa) lasting several nanoseconds; and late times, during uniaxial strain release. The early time measurements show that in <∼150 ps, the high-pressure hcp phase is relaxed with a c/a ratio of 1.61, contrary to previous laser shock experiments where a c/a ratio of 1.7 was inferred. In the plateau stress state and partially released states, XRD measurements showed that the hcp structure retained a c/a ratio of 1.61 with no observable changes in the microstructure. Upon stress release at ∼1 GPa/ns release rate, the reverse phase transition (hcp to bcc) to the original single crystal orientation (implying a transformation memory effect) was observed to reach completion somewhere between 13 and 11 GPa, indicating little stress hysteresis under rapid uniaxial strain release. A similar memory effect for the reverse hcp to bcc transformation has been previously observed under hydrostatic compression. However, the bcc/hcp orientation relationships differ somewhat between dynamic and static compression experiments, implying that the transformation pathway under uniaxial dynamic strain differs from the Burgers mechanism.

Study on the formation and competitive growth mechanism of stray grains during spiral grain selector of nickel-based single crystal superalloy

Microstructure evolution and competitive grain growth in the spiral part of a single crystal sample whose crystal orientation deviating from the axial direction was analyzed. The results showed that the appearance of stray grains in the spiral part and the elimination of the originally preferred orientation grains by the competitive growth of stray grains are the reasons for the single-crystal orientation deviation defect. It was indicated that stray grains tend to nucleate at the initial stage of crystal selection in the spiral part. The inclined temperature gradient in the spiral part promoted the development of stray grains, whose growth direction was closer to the direction of the heat flow. Stray grains maintained the competitive growth in the spiral part, and a single crystal with the orientation deviated from the expected direction of 〈001〉 is formed.

Phase heritage during replacement reactions in Ti-bearing minerals

Replacement reactions occur during metamorphism and metasomatism in response to changes in pressure, temperature and bulk rock and fluid compositions. To interpret the changes in conditions, it is necessary to understand what phases have previously been present in the rocks. During fluid-mediated replacement, the crystallography of the replacement phases is often controlled by the parent reactant phase. However, excessive fluid fluxing can also lead to extreme element mobility. Titanium is not mobile under a wide range of fluid compositions and so titanium-bearing phases present an opportunity to interpret conditions from the most extreme alteration. We map orientation relationships between titanium-bearing phases from ore deposits using EBSD and use symmetry arguments and existing relationships to show that completely consumed phases can be inferred in ore deposits. An ilmenite single crystal from Junction gold deposit is replaced by titanite, rutile and dolomite. The rutile has the following well-documented orientation relationship to the ilmenite [0001]ilmenite // rutile and < $$10{\bar{1}}0$$ > ilmenite // [001]rutile The anatase is a single crystal and shows a potential orientation relationship [0001]ilmenite = (0001)ilmenite // {211}anatase and < $$10{\bar{1}}0$$ > ilmenite // < $$0{\bar{1}}1$$ > anatase The single crystal orientation and lack of symmetrical equivalent variants suggest nucleation dominates the anatase production. Dolomite grew epitaxially on the ilmenite despite only sharing oxygen atoms suggesting the surface structure is important in dolomite nucleation. Titanite partially replaced ilmenite during metasomatism at Plutonic gold deposit. The titanite orientation is weakly related to the ilmenite orientation by the following relationship: [0001]ilmenite // titanite and { $$10{\bar{1}}0$$ }ilmenite // (001)titanite The prevalence of subgrain boundaries in the titanite suggests multiple nucleation points on an already deformed ilmenite needle leading to the formation of substructure in the absence of deformation. Existing known topotaxial replacement relationship can be used to infer completely replaced phases using the misorientation distributions of the replacement polycrystals. Orientation modelling for a cubic phase replaced by rutile in a sample from Productora tourmaline breccia complex shows misorientation distributions consistent with Rutile // cubic and Rutile // cubic Combining this with volume constraints and assuming Ti is immobile, the composition of the cubic phase is constrained as titanomagnetite with 85% ulvospinel. Complex microstructures with domanial preferred orientations can also be used to document the microstructure of replaced phases. An aggregate of rutile grains with two parts that share a common axis is interpreted as having replaced a twinned ilmenite grain. Modelling shows that the misorientation distribution for the aggregate is consistent with the above relationship replacing ilmenite with a { $$10{\bar{1}}2$$ } twin.

Two-gap time reversal symmetry breaking superconductivity in noncentrosymmetric LaNiC2

We report a $\mu$SR investigation of a non-centrosymmetric superconductor (LaNiC$_2$) in single crystal form. Compared to previous $\mu$SR studies of non-centrosymmetric superconducting polycrystalline and powder samples, the unambiguous orientation of single crystals enables a simultaneous determination of the absolute value of the magnetic penetration depth and the vortex core size from measurements that probe the magnetic field distribution in the vortex state. The magnetic field dependence of these quantities unambiguously demonstrates the presence of two nodeless superconducting energy gaps. In addition, we detect weak internal magnetic fields in the superconducting phase, confirming earlier $\mu$SR evidence for a time-reversal symmetry breaking superconducting state. Our results suggest that Cooper pairing in LaNiC$_2$ is characterized by the same interorbital equal-spin pairing model introduced to describe the pairing state in the centrosymmetric superconductor LaNiGa$_2$.

Crystal plasticity model for single crystal Ni-based superalloys: Capturing orientation and temperature dependence of flow stress

We develop a dislocation density based crystal plasticity model to capture the micromechanical behavior of γ′ strengthening nickel-based superalloys. The elasto-viscoplastic model presented here accounts for hardening behavior of both γ and γ′ which are the two phases considered in the present work. The model includes multiple strengthening mechanisms such as Orowan stress, evolving slip resistance caused by dislocation interactions, and γ′ structural contribution to initial slip resistance. Interaction between γ and γ′, a key feature of these alloys has been modelled in terms of back stress induced by dislocation pileup or looping around the large γ′ precipitates. Furthermore, anti-phase boundary (APB) shearing is considered as the dominant deformation mechanism for shearable γ′ precipitates. In addition to octahedral {111}⟨110⟩ slip, the model also accounts for cube slip systems {100}⟨110⟩ which are known to be instrumental in γ′ shearing and introducing flow stress orientation dependence. Temperature dependence of the initial slip resistance is fitted against experimental observation of anomalous yielding for two different single crystal orientations. An optimization procedure based on the minimization of the error between simulated and experimental stress strain curves, is adopted to evaluate a selected group of material parameters. Subsequently, proper working of the model is tested against an independent set of single crystal experimental data available for CMSX-4 around service temperature and MD2 at room temperature. The model also represents a strong orientation dependence of yield stress anomaly (YSA), a salient feature of Ni-based superalloys.

Hardness and Young's modulus of Al3Yb single crystal studied by nano indentation

The orientation, hardness and Young's modulus of Al3Yb single crystal were analyzed using the electron back scatter diffraction (EBSD) and nanoindentation techniques, combined with the first principles calculations. The Al3Yb single crystal of about 1 mm size could be obtained by heating hypereutectic Al-38.5 (wt%)Yb alloy to liquid state and cooling to room temperature at 60 °C/h. The results showed that the hardnesses of the Al3Yb single crystals oriented in (318), (023), (213), (112) and (122) directions varied between 5.4 ± 0.1 and 5.7 ± 0.1 GPa, and the reduced modulus were between 131.9 ± 1.6 and 140.5 ± 3.9 GPa. First principles calculations by assuming standard Yb pseudopotential with 4f electrons showed that the elastic constants of C11, C12 and C44 were 149.4, 32.94 and 66.59 GPa, respectively, and the Poisson's ratio was 0.161. Based on these calculated elastic constants and Poisson's ratio and the reduced modulus values, the Young's modulus of the Al3Yb single crystal was determined to be between 148.4 ± 2.3 and 154.9 ± 2.3 GPa for different orientations and the anisotropy coefficient (A) was 1.17 ± 0.01.

The Anisotropic Stress-Induced Diffusion and Trapping of Nitrogen in Austenitic Stainless Steel during Nitriding

Plasma nitriding of austenitic stainless steels at moderate temperatures is considered in the presented work. The anisotropic aspects of stress-induced diffusion and influence of nitrogen traps are investigated by kinetic modeling based on rate equations. The model involves diffusion of nitrogen in the presence of internal stress gradients induced by penetrating nitrogen as the next driving force of diffusion after the concentration gradient. The diffusion equation takes into account the fact that nitrogen atoms reside in interstitial sites and in trapping sites. Stress-induced diffusion has an anisotropic nature and depends on the crystalline orientation while trapping–detrapping is isotropic. The simulations are done considering the synergetic effects of both mechanisms and analyzing the properties of both processes separately. Theoretical curves are compared with experimental results taken from the literature. Good agreement between simulated and experimental results is observed, and gives the possibility to find real values of parameters needed for calculations. The nitrogen depth profile shapes, the dependences of nitrogen penetration on nitriding time and on diffusivity, are analyzed considering crystalline orientation of steel single crystal.

Integrated Wafer Scale Growth of Single Crystal Metal Films and High Quality Graphene.

We report on an approach to bring together single crystal metal catalyst preparation and graphene growth in a combined process flow using a standard cold-wall chemical vapor deposition (CVD) reactor. We employ a sandwich arrangement between a commercial polycrystalline Cu foil and c-plane sapphire wafer and show that close-spaced vacuum sublimation across the confined gap can result in an epitaxial, single-crystal Cu(111) film at high growth rate. The arrangement is scalable (we demonstrate 2″ wafer scale) and suppresses reactor contamination with Cu. While starting with an impure Cu foil, the freshly prepared Cu film is of high purity as measured by time-of-flight secondary ion mass spectrometry. We seamlessly connect the initial metallization with subsequent graphene growth via the introduction of hydrogen and gaseous carbon precursors, thereby eliminating contamination due to substrate transfer and common lengthy catalyst pretreatments. We show that the sandwich approach also enables for a Cu surface with nanometer scale roughness during graphene growth and thus results in high quality graphene similar to previously demonstrated Cu enclosure approaches. We systematically explore the parameter space and discuss the opportunities, including subsequent dry transfer, generality, and versatility of our approach particularly regarding the cost-efficient preparation of different single crystal film orientations and expansion to other material systems.

Selective excitation of two-wave structure depending on crystal orientation under shock compression

Single crystals subjected to shock compression exhibit responses with distinct two-wave structures for certain crystal orientations. However, little is known to date regarding how the shock response depends on crystal orientation, and especially why the two-wave structure depends on the crystal orientation. In this work, molecular dynamics simulations of shock compressions in copper single crystals are performed to investigate the orientation dependence of shock responses and the corresponding deformation mechanisms. Four copper single crystals with [001], [011], [012], and [123] crystal orientations along the depth direction are investigated. The [011], [012], and [123] crystal orientations of copper single crystals show distinct two-wave structures in their shock responses, while such a two-wave structure in the shock response is not seen for those orientations having a [001] crystal orientation. The potential causes are analyzed by considering the propagation velocities of both elastic and plastic waves. We develop a technique for identifying twin structures in face-centered cubic crystals and this technique can effectively identify the twin structure. The morphology of shock-induced defects (e.g., dislocations and twins) shows the significant dependence of crystal orientation and the mechanisms behind these are discussed in detail. Finally, the Johnson-Cook constitutive model describing dynamic deformations at high temperatures and high strain rates is used to analyze the relationships between the shock responses and microscopic defects. The predictions of the Johnson-Cook constitutive model are consistent with the results of the molecular dynamics simulations.

Epitaxial Aluminum Scandium Nitride Super High Frequency Acoustic Resonators

This paper demonstrates super high frequency (SHF) Lamb and surface acoustic wave resonators based on single-crystal orientation Aluminum Scandium Nitride (AlScN) thin films grown on silicon substrates by molecular beam epitaxy (MBE). We report on the experimental frequency response and electromechanical properties of 400 nm-thick crystalline AlScN acoustic resonators with up to 12% Sc/(Sc+Al) ratio. The film thickness is optimized for operation at the SHF range, targeting emerging wireless communication standards, such as 4G LTE/5G. We report on high-performance acoustic devices that take advantage of the crystallinity, and high piezoelectric properties of 400 nm-thick epitaxial AlScN films. Our work presents enhanced effective electromechanical coupling coefficients (k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) up to 5.3% and unloaded quality factors (Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> ) of ~192 at 3-10 GHz. However, fabrication challenges due to the high-stress levels of sub-micron AlScN epi-layers grown on Si substrates remain challenging and will be discussed in this paper. [2019-0231].

Comment on “Prediction of strain distribution and four, six, or eight ears depending on single-crystal orientation using a new single crystal criterion”

Comment on “Prediction of strain distribution and four, six, or eight ears depending on single-crystal orientation using a new single crystal criterion”

Simulation of a micro-milling single crystal copper process based on crystal plastic constitutive theory

The anisotropy of single crystal copper and crystal orientation have a significant effect on the micro-milling process. At present, there is no systematic and perfect theory to explain the influence of single crystal orientation on the micro-milling process. Therefore, it is urgent to conduct an in-depth study on the micro-milling process of single crystal copper. In this paper, based on the theory of crystal plasticity, considering the anisotropy of single crystal copper, the VUMAT material subroutine of single crystal copper is programmed by the Fortran language, and the crystal plastic constitution is introduced into the finite element simulation. The model of the micro-milling tool and work-piece is established and meshed. Considering the friction among the tool and the work-piece, material removal, etc., the three-dimensional finite element simulation model of single crystal copper micro-milling process is achieved by ABAQUS software. The validity of the simulation model of the micro-milling process of single crystal copper considering the single crystal plastic constitution is verified by experimental micro-milling forces. The research has explored a feasible way to predict the micro-milling force of single crystal copper, and has provided a reference for revealing the micro-milling mechanism of single crystal materials.

Economical Laue x-ray diffraction using photographic film and orientation of single crystals.

Many Laue x-ray diffraction systems using the Polaroid XR-7 Land Diffraction Cassette camera became inactive after production of the required high sensitivity Polaroid T-57 instant film ceased. This Tutorial reports on a low-cost solution using the readily available replacement film with push processing to increase the effective film speed. The use of this film in the polaroid camera is described along with film development and digitization. The orientation of single crystals with the obtained data and free software is explained. A simple method to prepare single crystals with surfaces perpendicular to a desired crystallographic orientation is described. The content of this Tutorial may prove beneficial for educational and research laboratories.

Cryo-quenched Fe–Ni–Cr alloy decorative steel single crystals II: Alloy phases, structure, hardness, tensile, tribological, magnetic and electronic properties

Abstract We have previously reported (Boatner et al., J. Alloys Compd. 691 (2017) 666–671) on the discovery, formation, processing, and application of a new decorative ternary steel. alloy and on its use in a wide range of practical applications including: custom and commercial knives, art objects, jewelry, electronics, and furniture. This decorative property results when polished single crystals of the 70 wt%Fe-15 wt%Ni-15 wt% Cr austenitic alloy are cryo-quenched into the martensitic phase resulting in the formation of a three-dimensional raised pattern of mixed austenitic/martensitic laths. These laths propagate across large dimensions of the material due to the absence of grain boundaries in the single crystal. The macroscopic optically reflective 3-D decorative pattern reproduces the structural symmetry inherent in the single-crystal orientation. This pattern results solely from the metallurgical phase properties of the ternary alloy and is completely distinct from the properties of Damascus steels or more modern so-called pattern-welded steels. Here we use X-ray diffraction, nanoindentation, hardness measurements/scratch testing, tribological measurements, and alloy resistivity and magnetization methods to obtain a more fundamental and comprehensive study of the effects of the austenitic/martensitic phase transition on the structural and physical properties of the 70 wt%Fe-15 wt%Ni-15 wt% Cr alloy. These results reveal new insight into irreversible phenomena that are associated with the inhibited phase transition on heating of the two-phase, mixed austenitic/martensitic structure that is formed subsequent to cryo-quenching the alloy crystal to 77 K.

Improved epitaxial growth of TbAs film on III–V semiconductors

In order to achieve high epitaxial quality of rocksalt TbAs, the authors studied the molecular beam epitaxy growth of TbAs films on zincblende (001) GaAs and (001) InP:Fe wafers. Despite the opposite strain condition of TbAs on these two substrates, mixed-orientation TbAs growth was observed on both substrates. However, the nucleation time and the continuing growth of the TbAs misoriented domains were influenced by the substrate type. By suppressing the growth of misoriented domains in the TbAs film, enhanced single-crystal orientation of TbAs grown on the (001) InP:Fe substrate was observed as compared to the (001) GaAs substrate. In addition, the cube-on-cube epitaxial arrangement of (001) TbAs with a thick film of up to ∼1150 nm is maintained on the (001) InP:Fe substrate but not on the (001) GaAs substrate. The improved TbAs film growth on the InP:Fe substrate exhibited enhanced optical properties when compared to that grown on the GaAs substrate, including a threefold reduction in the scattering rate. This largely improved optical property highlights the importance of increasing the epitaxial quality of TbAs films for future optoelectronic as well as other applications.

Crystallographic orientation effect on the incipient plasticity and its stochastic behavior of a sapphire single crystal by spherical nanoindentation

Relying on spherical nanoindentation, we investigated the characteristics of incipient plasticity via the first pop-in event in the four typical crystallographic orientations of a sapphire single crystal. Statistically, critical loads at the occurrences of incipient plasticity were uniformly distributed in a wide range in A-, C-, and R-planes. While in M-plane, two distinct distribution ranges of the critical loads were discernible. The displacement burst at first pop-in was approximately varied from 5 to 150 nm and strongly dependent on the crystallographic orientation. Cracking and twin deformation were revealed as deformation mechanisms under nanoindentation, whilst their type and size were varied in different orientations. The critical strengths at incipient plasticity and their statistical laws were also summarized. The crystallographic orientation effect on the yielding strength of a sapphire could be well explained from the perspective of deformation mechanisms. The Weibull modulus of stochastic distribution of yield strength was estimated and exhibited higher failure reliability under micro-contact deformation than bulk fracture in sapphire.

Dynamic behaviors of RDX single crystal under ramp compression

The dynamics of RDX single crystal under ramp wave loading is studied experimentally and numerically. The ramp wave loading experiments on RDX single crystal in the orientation of (210) and (100) within 15 GPa are carried out with the magnetic driven device CQ-4, which can provide a loading pressure waveform with a rising time of 450–600 ns. The particle velocity curves of the interface between RDX single crystal and LiF window are obtained with the photonic Doppler velocimetry (PDV). The velocity profiles show an obvious three-wave structure, indicating that the RDX undergoes physical processes such as elastic-plastic transition and α-to-&lt;i&gt;γ&lt;/i&gt; phase transition in the loading section. The stress yield limits of different crystallographic orientations of RDX single crystal show obvious difference. The onset phase transition pressures in two crystallographic orientations are the same, which is between 3.5 GPa and 4.0 GPa. The pressure range of phase transition is between initial phase transition pressure and 5 GPa. The &lt;i&gt;γ&lt;/i&gt; phase is stable from 5 GPa to 15 GPa. The Hayes multi-phase equation of state and non-equilibrium phase transition kinetic model are employed to simulate the experimental process, and the numerical results can well describe the experimental physical processes such as elastoplastic transformation and phase transformation in the loading section. The calculated results reveal that the correction of the bulk modulus with pressure is necessary under ramp wave compression.

Controlling the Growth of Stacks of Correlated Lamellar Crystals of a Block Copolymer

In the crystallization of polymers, besides monolamellar polymer crystals, stacks of correlated lamellae with a unique orientation and signatures of single crystals have often been observed. However, we still lack a generic criterion for such stacking, that is, vertical growth of polymer crystals. Here, by employing self-induced nucleation on the fold surface of a basal lamella for generating appropriate seeds, we identify experimental conditions allowing for a controlled formation of stacks of crystalline lamellae of a block copolymer. Adopting a two-step crystallization procedure, we decoupled nucleation and growth conditions of stacked lamellae and thereby favored vertical growth of polymer crystals in thin films. A sufficient reservoir of molten polymers in combination with slow lateral growth of the basal lamella is required for observing the formation of stacks of correlated lamellae. Taking this path, we were able to form stacks reaching heights of about 10 times the initial film thickness.

Orientation-Dependent Proton Relaxation of Water Molecules Trapped in Solids: Crystallites with Long-Lived Magnetization.

The longitudinal spin-lattice relaxation properties of water molecules trapped in a static powdered polycrystalline sample of barium chlorate monohydrate are investigated by means of solid-state 1H NMR spectroscopy. Different portions of the inhomogeneous Pake pattern that are associated with crystallites at different orientations with respect to the external magnetic field show either a mono- or a biexponential recovery. At high field (9.4 T), the chemical shift anisotropy is the main interaction that is responsible for the inhomogeneity of the relaxation rates. A theoretical description of rapid two-site hopping about the H-O-H bisector in the framework of Liouville space agrees very well with the experimental evidence. Numerical simulations predict a distribution of monoexponential time constants associated with individual single-crystal orientations. Overlapping signals give rise to biexponential recovery. This is confirmed experimentally by 1H NMR spectra of static single crystals.