Anisotropy Of Single Crystals Research Articles

Magnetization, magnetic anisotropy and magnetocaloric effect of the Tb0.2Gd0.8 single crystal in high magnetic fields up to 14 T in region of a phase transition

The Tb0.2Gd0.8 single crystal magnetization, magnetic anisotropy and adiabatic temperature change ΔT dependencies on magnetic field and temperature have been studied in high magnetic fields (up to 14 T). In this work, we analyze experimental data within the framework of thermodynamic Landau theory for second order magnetic phase transitions to describe the relationship between the magnetization, adiabatic temperature change ΔT and magnetic field in the region of a phase transition. Moreover, it is proved that the Landau-Ginzburg equations are applicable in the case of high magnetic fields. Furthermore it is discovered that the adiabatic temperature change is proportional to the magnetic field with the relation ΔT ∼ (μ0H)2/5 in the region of high magnetic fields.

Growth of anisotropic single crystals of a random copolymer, poly[(R)-3-hydroxybutyrate-co-(R)-3-hydroxyhexanoate] driven by cooperative –CH···O H-bonding

Single crystals of a random copolymer, Poly[(R)-3-hydroxybutyrate-co-(R)-3-hydroxyhexanoate] (PHBHx), with a relatively high (R)-3-hydroxyhexanoate (3HHx) content of 3.9 mol% were grown from dilute solutions over a wide range of crystallization temperatures (Tc) from −20 °C to 75 °C. Unlike Poly[(R)-3-hydroxybutyrate-co-(R)-3-hydroxyvalerate] (PHBV) which allows the 3-hydroxyvalerate (3HV) to be included into PHB lattice, 3HHx is excluded from the lattice as a non-crystallizable molecular defect. Remarkably, however, even at such a high defect content, all the samples (except for Tc = −20 °C) formed well-developed needle-shaped single crystals, with a crystal morphology similar to that found for crystals of the homopolymer PHB. A very characteristic anisotropic lateral growth habit is observed, with the growth rate along the a axis being much higher than that along the b axis. This anisotropic growth pattern was significantly enhanced at Tc = 20 °C, wherein the unit cell packing velocity along the a direction is approximately 55 times faster than that along the b direction. This thermal dependent anisotropy was attributed to an unusual cooperative hydrogen bond-like network formed by methyl hydrogen and a neighboring carbonyl oxygen in the α crystal of PHB. Another manifestation of this H-bonding network can be seen in unusually thin crystal lamellae at −20 °C, with only ∼6 repeat units per stem, suggesting a superior stability of crystal structure. Interestingly, at this temperature, although 3HHx still cannot be accommodated along the a direction (the H-bonding direction), it could be included along the b direction, indicated by the observation of lattice expansion along the b direction. Also at Tc = −20 °C, we found that 3HHx began to show some impact on the crystalline morphology, indicated by the development of a twisted lamellar texture. This effect was believed to arise from the release of stress induced by a congested fold surface dominated by non-crystalline 3HHx and 3HB units.

Magnetic Anisotropy in Single Crystals: A Review

Empirical relationships between magnetic fabrics and deformation have long served as a fast and efficient way to interpret rock textures. Understanding the single crystal magnetic properties of all minerals that contribute to the magnetic anisotropy of a rock, allows for more reliable and quantitative texture interpretation. Integrating information of single crystal properties with a determination whether or not mineral and magnetic fabrics are parallel may yield additional information about the texture type. Models based on textures and single crystal anisotropies help assess how the individual minerals in a rock contribute to the rock’s anisotropy, and how the individual anisotropy contributions interfere with each other. For this, accurate and reliable single crystal data need to be available. This review paper discusses magnetic anisotropy in single crystals of the most common rock-forming minerals, silicates and carbonates, in relation to their mineralogy and chemical composition. The most important ferromagnetic minerals and their anisotropy are also discussed. This compilation and summary will hopefully lead to a deeper understanding of the sources of magnetic anisotropy in rocks, and improve the interpretation of magnetic fabrics in future structural and tectonic studies.

Identification of elastic-plastic and phase transition characteristics for relaxor ferroelectric PMN-PT anisotropic single crystals using nanoindentation technique

ABSTRACTAs one kind of important ferroelectric ceramics, relaxor ferroelectric PMN-PT single crystals have triggered a revolution in electromechanical devices owing to their giant piezoelectric properties and ultra-high electromechanical coupling factors. The present study focused on the mechanical responses of [100]- and [110]-oriented poled PMN-PT ferroelectric single crystals under an indenter loading. The hardness and Young’s modulus with different crystallographic orientations of the crystals were measured by using the continuous stiffness measurement (CSM) with nanoindentation technique. Using a spherical indenter pressured at different indentation depths, the typical quasi-static nanoindentation tests with displacement-controlled mode were performed on the PMN-PT single crystal samples. Load–displacement curves of indentations were recorded to reveal the yielding or inelasticity behaviour in [100]- and [110]-oriented PMN-PT through a pop-in event. It was further verified by the stress–strain curves evaluated from the corresponding load–displacement curves, to show the similar characteristic on the elastic–inelastic transition. When a Berkovich indenter was employed for mechanical response testing, another pop-in event was observed at a smaller indentation depth compared to the one for elastic–inelastic transition, which may indicate a pressure-induced phase transition from rhombohedral (R) to tetragonal (T) of the PMN-PT single crystals.

Giant optical anisotropy in a quasi-one-dimensional crystal

Optical anisotropy is a fundamental building block for linear and nonlinear optical components such as polarizers, wave plates, and phase-matching elements1–4. In solid homogeneous materials, the strongest optical anisotropy is found in crystals such as calcite and rutile5,6. Attempts to enhance anisotropic light–matter interaction often rely on artificial anisotropic micro/nanostructures (form birefringence)7–11. Here, we demonstrate rationally designed, giant optical anisotropy in single crystals of barium titanium sulfide (BaTiS3). This material shows an unprecedented, broadband birefringence of up to 0.76 in the mid- to long-wave infrared, as well as a large dichroism window with absorption edges at 1.6 μm and 4.5 μm for light with polarization along two crystallographic axes on an easily accessible cleavage plane. The unusually large anisotropy is a result of the quasi-one-dimensional structure, combined with rational selection of the constituent ions to maximize the polarizability difference along different axes.

Application of a polarized modulation technique in supramolecular science: chiroptical measurements of optically anisotropic systems

The chirality of a supramolecular assembly provides particularly valuable information because the bonding nature of noncovalent interactions, such as electrostatic interactions, π effects, van der Waals forces, and hydrophobic effects, makes the development of supramolecular assemblies an attractive and useful approach in chiral induction, chiral amplification, and chirality transfer. However, chiroptical measurements of optically anisotropic samples cannot be generally achieved with modern chiroptical spectrophotometric methods such as circular dichroism (CD) or circular birefringence (CB) and circularly polarized luminescence (CPL) that are based on polarization modulation techniques because of the coupling effect of the nonideal optics and the electronics with strong macroscopic anisotropies, that is, nonchiral signals related to linearly polarized phenomena. These artifact signals are often much stronger than the chiroptical signals. Only CD and CPL spectrophotometers developed in 2001 and 2016, respectively, and integrated into a Stokes–Mueller matrix analysis for optically anisotropic samples are capable of obtaining accurate chirality measurements of samples with macroscopic anisotropies. Therefore, these spectrophotometers enable chiral investigations of optically anisotropic samples, for example, single crystals, supramolecular assemblies, gels, films, membranes, polymers, and liquid crystals. This focus review presents a short and elementary discussion of the chiroptical measurement techniques for optically anisotropic samples in supramolecular science and signal interpretation in polarization spectroscopy.

Universal doping evolution of the superconducting gap anisotropy in single crystals of electron-doped Ba(Fe1−xRhx)2As2 from London penetration depth measurements

Doping evolution of the superconducting gap anisotropy was studied in single crystals of 4d-electron doped Ba(Fe1−xRhx)2As2 using tunnel diode resonator measurements of the temperature variation of the London penetration depth . Single crystals with doping levels representative of an underdoped regime x = 0.039 ( K), close to optimal doping x = 0.057 ( K) and overdoped x = 0.079 ( K) and x = 0.131( K) were studied. Superconducting energy gap anisotropy was characterized by the exponent, n, by fitting the data to the power-law, . The exponent n varies non-monotonically with x, increasing to a maximum n = 2.5 for x = 0.079 and rapidly decreasing towards overdoped compositions to 1.6 for x = 0.131. This behavior is qualitatively similar to the doping evolution of the superconducting gap anisotropy in other iron pnictides, including hole-doped (Ba,K)Fe2As2 and 3d-electron-doped Ba(Fe,Co)2As2 superconductors, finding a full gap near optimal doping and strong anisotropy toward the ends of the superconducting dome in the T-x phase diagram. The normalized superfluid density in an optimally Rh-doped sample is almost identical to the temperature-dependence in the optimally doped Ba(Fe,Co)2As2 samples. Our study supports the universal superconducting gap variation with doping and pairing at least in iron based superconductors of the BaFe2As2 family.

Uncertainty bounds on ultrasonic phase velocities for polycrystalline media

Most theoretical work related to the study of the effective properties of polycrystals assume infinite media with randomly oriented grains. Therefore, the bulk material has absolute isotropy. However, real samples always include a finite number of grains such that the inspection volume will have some associated anisotropy. Hence, bounds on the bulk properties can be expected for a given measurement. In this work, the effect of the number of grains on this anisotropy variation is studied using Dream.3D software. The effective elastic modulus tensor is derived using Voigt, Reuss, and self-consistent techniques with 1700 microstructures comprised of equiaxed cubic grains in 17 different volumes. The bond transformation is utilized to quantify the standard deviation of the average elastic modulus. The standard deviations of several materials are shown to be inversely proportional to the square root of the number of grains. Based on the single-crystal anisotropy, a master curve is derived which relates modulus anisotropy to the number of grains. In addition, Christoffel equation is used to study the relevant phase velocities. With appropriate normalization, a similar master curve is derived. Such results will have important impacts on ultrasonic models associated with metals. [Research supported by AFRL under prime contract FA8650-15-D-5231.]

Interpreting magnetic fabrics in amphibole-bearing rocks

If amphibole is a major constituent in a rock, its magnetic fabric can be largely controlled by the crystallographic preferred orientation of amphibole. This study describes the (para)magnetic anisotropy in two amphibolites, both containing ca. 70% hornblende with rather strong crystallographic preferred orientation. Both amphibolites display a significant and well-defined anisotropy of magnetic susceptibility, with the minimum susceptibility approximately normal to foliation. However, in one amphibolite, the maximum susceptibility is parallel to the lineation, whereas in the other it is not. This seemingly inconsistent observation can be explained by the intrinsic susceptibility anisotropy of single crystals of hornblende, and their texture in the rocks. Numerical models show how the principal susceptibility axes relate to macroscopic foliation and lineation for point and fiber textures. This study underlines the potential of using magnetic anisotropy to obtain information about mineral fabrics in mafic rocks. At the same time, it highlights the necessity for taking into account single crystal properties of the mineral(s) responsible for the anisotropy and their crystallographic preferred orientation when interpreting magnetic fabrics.

Elasto-viscoplastic self consistent modeling of the ambient temperature plastic behavior of periclase deformed up to 5.4 GPa

Anisotropy has a crucial effect on the mechanical response of polycrystalline materials. Polycrystal anisotropy is a consequence of single crystal anisotropy and texture (crystallographic preferred orientation) development, which can result from plastic deformation by dislocation glide. The plastic behavior of polycrystals is different under varying hydrostatic pressure conditions, and understanding the effect of hydrostatic pressure on plasticity is of general interest. Moreover, in the case of geological materials, it is useful for understanding material behavior in the deep earth and for the interpretation of seismic data. Periclase is a good material to test because of its simple and stable crystal structure (B1), and it is of interest to geosciences, as (Mg,Fe)O is the second most abundant phase in Earth's lower mantle. In this study, a polycrystalline sintered sample of periclase is deformed at ∼5.4 GPa and ambient temperature, to a total strain of 37% at average strain rates of 2.26 × 10−5/s and 4.30 × 10−5/s. Lattice strains and textures in the polycrystalline sample are recorded using in-situ synchrotron x-ray diffraction and are modeled with Elasto-Viscoplastic Self Consistent (EVPSC) methods. Parameters such as critical resolved shear stress (CRSS) for the various slip systems, strain hardening, initial grain shape, and the strength of the grain–neighborhood interaction are tested in order to optimize the simulation. At the beginning of deformation, a transient maximum occurs in lattice strains, then lattice strains relax to a “steady-state” value, which, we believe, corresponds to the true flow strength of periclase. The “steady state” CRSS of the 11011¯0 slip system is 1.2 GPa, while modeling the transient maximum requires a CRSS of 2.2 GPa. Interpretation of the overall experimental data via modeling indicates dominant 11011¯0 slip with initial strain softening, followed by strain hardening. This approach illustrates the utility of combining EVPSC and experimental data to understand deformation of materials at high pressures.

Novel superhard nanopolycrystalline materials synthesized by direct conversion sintering under high pressure and high temperature

Abstract

Ultrasonic study of elastic anisotropy of unidirectional Rochelle salt single crystals grown using the Sankaranarayanan-Ramasamy method

Sodium potassium tartrate tetrahydrate-NaKC4H4O6·4H2O known as Rochelle salt is a well-known ferroelectric. This paper deals with the following topics: (i) the Sankaranarayanan-Ramasamy method of growth of a parallelepiped-shaped single crystal of Rochelle salt having the (100), (010) and (001) planes mutually perpendicular to each other, (ii) evaluation of the second-order elastic stiffness constants C11, C22, C33, C44, C55 and C66 using the parallelepiped-shaped single-crystal sample of Rochelle salt, (iii) growth of large [011]-, [101]- and [110]-oriented cylindrical-shaped single crystals of Rochelle salt from appropriately prepared seeds using the same method, (iv) determination of elastic constants C23, C13 and C12 using the [011]-, [101]- and [110]-oriented single-crystal samples of Rochelle salt, respectively, and (v) calculations of elastic compliance constants S11, S22, S33, S44, S55, S66, S12, S23and S13, Young’s modulus E, bulk modulus K, Poisson’s ratio υ, linear compressibility β1, β2 and β3 along the three principal directions and volume compressibility β of the crystal.

Magnetic anisotropy and spin-flop transition of NiWO4 single crystals

NiWO4 exhibits a spin chain structure built by magnetic Ni2+ ions, which may be considered as a one dimensional S=1 system. In this work, large-sized single crystals of NiWO4 were successfully synthesized by a flux method and the crystal quality was confirmed by X-ray diffraction. Magnetic properties of obtained single crystals were studied by means of magnetic susceptibility and high field magnetization along crystallographic axes. The results demonstrate that NiWO4 is highly magnetic anisotropic and possesses a three-dimensional long range ordering below 60K, where a spin flop transition can be observed at 17.5T in applied magnetic fields along the magnetic easy axis (c-axis).

Doping-driven structural distortion in the bilayer iridate (Sr1−xLax)3Ir2O7

Neutron single crystal diffraction and rotational anisotropy optical second harmonic generation data are presented resolving the nature of the structural distortion realized in electron-doped (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$ with $x=0.035$ and $x=0.071$. Once electrons are introduced into the bilayer spin-orbit assisted Mott insulator Sr$_3$Ir$_2$O$_7$, previous studies have identified the appearance of a low temperature structural distortion and have suggested the presence of a competing electronic instability in the phase diagram of this material. Our measurements resolve a lowering of the structural symmetry from monoclinic $C2/c$ to monoclinic $P2_1/c$ and the creation of two unique Ir sites within the chemical unit cell as the lattice distorts below a critical temperature $T_S$. Details regarding the modifications to oxygen octahedral rotations and tilting through the transition are discussed as well as the evolution of the low temperature distorted lattice as a function of carrier substitution.

How magnesium accommodates local deformation incompatibility: A high-resolution digital image correlation study

The plastic deformation of single crystal magnesium is strongly anisotropic. This gives rise to deformation incompatibilities between grains during polycrystalline deformation, which are thought to limit ductility and formability. Wrought polycrystalline magnesium alloys are far from brittle, especially in uniaxial tension, implying that these incompatibilities can be accommodated to some extent, although it is not clear how. We have used high-resolution digital image correlation (HRDIC), supported by electron backscatter diffraction (EBSD), to study quantitatively and at the microstructural scale the accommodation of deformation incompatibility in an AZ31 magnesium alloy. Using a new gold remodelling procedure that improves the spatial resolution to 44 nm, we quantified the deformation heterogeneity after a small stretch in uniaxial tension. Our results confirm that polycrystalline deformation is very heterogeneous, with local axial true strains at grain boundaries 32 times higher than the applied average strain of 0.027, and 18 times higher at slip bands within grains. The local and macroscopic deformation gradients are very different in character as well as magnitude. The resultant deformation incompatibility is accommodated primarily by gradients in basal slip and the activation of difficult slip in “hard” grains, giving rise to grain breakup, with a smaller contribution by enhanced grain boundary shear and twinning. These results support the idea that a homogeneous distribution of “hard” and “soft” grains can prevent the development of strain localization and, therefore, that controlling texture and microtexture is a powerful way of enhancing the formability of magnesium alloys without reducing their single crystal plastic anisotropy.

Effect of temperature and doping with Cu on the reflectance spectra of PbSb2Te4 crystals

For the anisotropic PbSb2Te4 single crystal, the effect of temperature and doping with Cu on the reflectance spectrum R(ν) is studied for reflection from a cleavage plane orthogonal to the trigonal axis C3. It is found that the spectrum is complex in structure and exhibits a sharp increase in the reflectance in the far-infrared region and two minima in the mid-infrared region. It is shown that the experimentally observed feature of the reflectance spectra can be quantitatively described in the context of the Drude–Lorentz theory, with the dielectric function that takes into account the contributions of hole plasma oscillations and two optical lattice vibrations at different frequencies. The static conductivity estimated from optical data is in good agreement with the results of electrical measurements of the dc conductivity.

An anisotropic distribution dislocation loop model for simulation of nanoindentation of single crystals

An anisotropic distribution dislocation loop model is proposed for simulation of nanoindentation of single crystals based on the recently available solution of the elastic displacement and stress fields due to a polygonal dislocation within an anisotropic homogeneous half-space (Chu et al., 2012). The present investigation is a direct extension of the approach established by Mura et al. (1989), and its recent application to triangular dislocation loop model (Muraishi, 2013), which is only capable of describing the indentation processes of isotropic materials, thus ruling out the possibility of characterizing the nanoindentation of elastically anisotropic single crystals. By following the procedure of Mura et al. (1989), we adopt square and triangular prismatic dislocation loops (PDLs) as building blocks with Burgers vectors normal to the free surface to simulate the Vickers and Berkovich indentation, respectively. However, we place all the prismatic dislocation loops within a semi-ellipsoidal volume rather than a semi-spherical region as adopted by Mura et al. (1989) after analyzing the existing simulation results based on dislocation density formulation (Huang et al., 2000). The nanoindentation is performed in [001] and [111] crystallographic directions employing Vickers and Berkovich indenters, respectively, and different magnitude of pile-up, sink-in and spring-back is observed in different directions, clearly demonstrating the effects of elastic anisotropy of the indented single crystals on nanoindentation, hence a further improvement of the original model of Mura et al. (1989).

Hill–Mandel condition and bounds on lower symmetry elastic crystals

Despite advances in contemporary micromechanics, there is a void in the literature on a versatile method for estimating the effective properties of polycrystals comprising of highly anisotropic single crystals belonging to lower symmetry class. Basing on variational principles in elasticity and the Hill–Mandel homogenization condition, we propose a versatile methodology to fill this void. It is demonstrated that the bounds obtained using the Hill–Mandel condition are tighter than the Voigt and Reuss [1,2] bounds, the Hashin–Shtrikman [3] bounds as well as a recently proposed self-consistent estimate by Kube and Arguelles [4] even for polycrystals with highly anisotropic single crystals.

Critical investigation of calculation methods for the elastic velocities in anisotropic ice polycrystals

Abstract. Crystallographic texture (or fabric) evolution with depth along ice cores can be evaluated using borehole sonic logging measurements. These measurements provide the velocities of elastic waves that depend on the ice polycrystal anisotropy, and they can further be related to the ice texture. To do so, elastic velocities need to be inverted from a modeling approach that relate elastic velocities to ice texture. So far, two different approaches can be found. A classical model is based on the effective medium theory; the velocities are derived from elastic wave propagation in a homogeneous medium characterized by an average elasticity tensor. Alternatively, a velocity averaging approach was used in the glaciology community that averages the velocities from a given population of single crystals with different orientations. In this paper, we show that the velocity averaging method is erroneous in the present context. This is demonstrated for the case of waves propagating along the clustering direction of a highly textured polycrystal, characterized by crystallographic c axes oriented along a single maximum (cluster). In this case, two different shear wave velocities are obtained while a unique velocity is theoretically expected. While making use of this velocity averaging method, reference work by Bennett (1968) does not end with such an unphysical result. We show that this is due to the use of erroneous expressions for the shear wave velocities in a single crystal, as the starting point of the averaging process. Because of the weak elastic anisotropy of ice single crystal, the inversion of the measured velocities requires accurate modeling approaches. We demonstrate here that the inversion method based on the effective medium theory provides physically based results and should therefore be favored.

Synthesis, structural, X-ray photoelectron spectroscopy (XPS) studies and IR induced anisotropy of Tl4HgI6 single crystals

In the present work, we report on the synthesis and structural properties including X-ray protoelectron spectroscopy (XPS) analysis of Tl4HgI6 crystals that were grown by Bridgman-Stockbarger method up to 80 mm in length and 18 mm in diameter. The existence of the ternary compound Tl4HgI6 that melts incongruently at 641 K was confirmed. Phase equilibria and structural properties for the TlI–HgI2 system were investigated by differential thermal analysis (DTA) and X-ray diffraction (XRD) methods. X-ray photoelectron spectra were measured for both pristine and Ar+ ion-bombarded Tl4HgI6 single crystal surfaces. The data reveal that the Tl4HgI6 single crystal is sensitive with respect to Ar+ ion-bombardment as 3.0 keV Ar+ irradiation over 5 min at an ion current density 14 μA/cm2 induces changes to the elemental stoichiometry of the Tl4HgI6 surface, leading to a decrease of the mercury content in the topmost surface layers. X-ray photoelectron spectroscopy (XPS) measurements indicate very low hygroscopic nature of the Tl4HgI6 single crystal surface. The IR coherent bicolor laser treatment at wavelengths 10.6/5.3 μm has shown an occurrence of anisotropy at wavelengths 1540 nm of Er:glass laser. This may open the applications of Tl4HgI6 as a material for IR laser triggering.