Major Crystallographic Directions Research Articles

Anisotropic elasticity drives negative thermal expansion in monocrystalline SnSe

Negative thermal expansion (NTE) materials have been at the center of attention for the past few decades as thermal expansion compensators in the fields of engineering, photonics, electronics, and medicine. Numerous crystalline materials exhibit NTE, wherein a combination of positive and negative linear thermal expansion coefficients results from their highly anisotropic elasticity. In this study, we selected SnSe, an anisotropic uniaxial NTE material as a model system where theoretical studies have linked its NTE along the $c$ direction to transverse phonons and to positive Gr\uneisen parameters along all crystallographic axes. However, the fundamental origin of NTE in SnSe have not been experimentally resolved. Here we performed temperature-dependent resonant ultrasound spectroscopy (between 295--773 K) on single-crystalline SnSe to experimentally measure all nine independent elastic constants (${C}_{11}, {C}_{22}, {C}_{33}, {C}_{44}, {C}_{55}, {C}_{66}, {C}_{12}, {C}_{13}, {C}_{23}$). Our data revealed a high degree of anisotropy in the temperature-dependent elastic constants with shear anisotropic factors show a contrasting pattern with increasing temperature. From this data we also deduced its material compressibility and negative Poisson's ratios in the major crystallographic directions that could explain its colossal linear thermal expansion coefficient along the $c$ direction, reaching $\ensuremath{\sim}--12\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at 773 K as reported in this study. Furthermore, we confirmed positive Gr\uneisen parameters along all the crystallographic axes and observe that SnSe behaves like a semicompressible parallelepiped with elastically coupled $a$ and $b$ axes, with the NTE being driven by the displacement of Sn atoms in the $c$ direction.

(Invited) Role of Anharmonicity on Thermoelectric Properties of Fully Dense Single-Crystalline Snse

Thermoelectric (TE) materials enable conversion of “waste” heat to electricity, leading to environmentally friendly solutions for power generation applications. The thermal-to-electrical energy conversion efficiency of a TE material is largely determined by its dimensionless figure-of-merit, ZT = S2σT/κ that consists of interrelated material properties, viz., the Seebeck coefficient (S), electrical conductivity (σ), and the thermal conductivity (κ). Recently, single-crystalline SnSe has attracted much attention due of its record high figure-of-merit ZT ≈ 2.6, [1] that was debated in subsequent reports due to the low mass density of these single crystals. [2] We performed structural, electrical, and thermal transport measurements on high-quality fully dense SnSe single crystals over a wide temperature range along the major crystallographic directions, that yielded a maximum ZT ~ 1 along one of the major crystallographic directions.[3] It is well known that phonon anharmonicity is one of the contributing factors that yields a remarkably low κ in binary SnSe. As an attempt to understand the role of phonon anharmonicity, we performed a combined temperature-dependent polarized Raman spectroscopic and heat-capacity study on fully dense single-crystalline SnSe, which revealed that the anharmonicity in SnSe is driven by soft optical modes in its bc plane. [4] This study provides a deeper understanding of the role of phonon-phonon scattering and anharmonicity leading to reported thermal transport properties of SnSe. [1] Zhao, L.-D., Lo, S.-H., Zhang, Y., Sun, H., Tan, G., Uher, C., Wolverton, C., Dravid, V. P., Kanatzidis, M. G. Ultralow Thermal Conductivity and High Thermoelectric Figure of Merit in SnSe Crystals, Nature 2014, 508 (7496), 373–377. [2] Wei, P. C., Bhattacharya, S., He, J., Neeleshwar, S., Podila, R., Chen, Y. Y., Rao, A. M., The Intrinsic Thermal Conductivity of SnSe, Nature 2016, E1–E2. [3] Wei, P.C., Bhattacharya S., Liu Y-F., Liu F., He J., Tung Y-H., Yang C-C., Hsing C-R., Nguyen D.L., Wei C-M., Chou M-Y., Lai Y-C., Hung T-L, Guan S-Y., Chang C-S., Wu H-J., Lee C-H., Li W-H., Hermann R. P., Chen Y-Y., Rao A.M., Thermoelectric figure-of-merit of fully dense single crystalline SnSe, ACS Omega, 2019, 4 (3), 5442–5450. [4] Liu F., Parajuli P., Rao R., Wei P.-C., Karunarathne A., Bhattacharya S., Podila R., He J., Maruyama B., Priyadarshan G., Gladden J. R., Chen Y.-Y., Rao A.M., Phonon Anharmonicity in single-crystalline SnSe, Phys. Rev. B 2018, 98, 224309.

Thermoelectric Figure-of-Merit of Fully Dense Single-Crystalline SnSe.

Single-crystalline SnSe has attracted much attention because of its record high figure-of-merit ZT ≈ 2.6; however, this high ZT has been associated with the low mass density of samples which leaves the intrinsic ZT of fully dense pristine SnSe in question. To this end, we prepared high-quality fully dense SnSe single crystals and performed detailed structural, electrical, and thermal transport measurements over a wide temperature range along the major crystallographic directions. Our single crystals were fully dense and of high purity as confirmed via high statistics 119Sn Mössbauer spectroscopy that revealed <0.35 at. % Sn(IV) in pristine SnSe. The temperature-dependent heat capacity (Cp) provided evidence for the displacive second-order phase transition from Pnma to Cmcm phase at Tc ≈ 800 K and a small but finite Sommerfeld coefficient γ0 which implied the presence of a finite Fermi surface. Interestingly, despite its strongly temperature-dependent band gap inferred from density functional theory calculations, SnSe behaves like a low-carrier-concentration multiband metal below 600 K, above which it exhibits a semiconducting behavior. Notably, our high-quality single-crystalline SnSe exhibits a thermoelectric figure-of-merit ZT ∼1.0, ∼0.8, and ∼0.25 at 850 K along the b, c, and a directions, respectively.

Transport properties and pinning analysis for Co-doped BaFe2As2 thin films on metal tapes

We report on the transport properties and pinning analysis of BaFe1.84Co0.16As2 (Ba122:Co) thin films on metal tapes by pulsed laser deposition. The thin films exhibit a large in-plane misorientation of 5.6°, close to that of the buffer layer SrTiO3 (5.9°). Activation energy U0(H) analysis reveals a power law relationship with field, having three different exponents at different field regions, indicative of variation from single-vortex pinning to a collective flux creep regime. The Ba122:Co coated conductors present = 20.2 K and = 19.0 K along with a self-field Jc of 1.14 MA cm−2 and an in-field Jc as high as 0.98 and 0.86 MA cm−2 up to 9 T at 4.2 K for both major crystallographic directions of the applied field, promising for high field applications. Pinning force analysis indicates a significant enhancement compared with similar Ba122:Co coated conductors. By using the anisotropic scaling approach, intrinsic pinning associated with coupling between superconducting blocks can be identified as the pinning source in the vicinity of H//ab, while for H//c random point defects are likely to play a role but correlated defects start to be active at high temperatures.

Energy dependence of He-ion-induced tungsten nanofuzz formation at non-normal incidence angles

We report measurements of He-ion-beam induced tungsten nanofuzz formation for normal and non-normal incidence angles in the energy range 218eV–10keV. At 218eV, the fuzz tendrils are fine and grow randomly away from the interface in the direction of the surface normal. Above 480eV, the fuzz tendrils become increasingly coarser, and their growth direction is in the direction of the incident beam. This change is attributed to the ion-induced displacement damage which becomes effective once the displacement damage threshold energy is exceeded, and produces additional near-surface trapping sites in those portions of the surface that are in direct line of sight of the incident beam which can nucleate He clusters and initiate bubble growth. Once the surface morphology roughens sufficiently for shadowing to occur, the subsequent fuzz growth occurs preferentially toward the incident ion beam. Molecular dynamics (MD) simulations were carried out to determine the displacement damage threshold energies in the near-surface region along the three major crystallographic directions. It was found that the tungsten bulk values are established within the first 2–4 atomic layers below the tungsten surface. SRIM simulations based on the MD energy thresholds indicate that vacancy damage production in the near-surface region quickly dominates over sputtering in near-surface lattice modification effects as the energy above the damage threshold increases.

Experimental evidence of high-frequency complete elastic bandgap in pillar-based phononic slabs

We present strong experimental evidence for the existence of a complete phononic bandgap, for Lamb waves, in the high frequency regime (i.e., 800 MHz) for a pillar-based phononic crystal (PnC) membrane with a triangular lattice of gold pillars on top. The membrane is composed of an aluminum nitride film stacked on thin molybdenum and silicon layers. Experimental characterization shows a large attenuation of at least 20 dB in the three major crystallographic directions of the PnC lattice in the frequency range of 760 MHz–820 MHz, which is in agreement with our finite element simulations of the PnC bandgap. The results of experiments are analyzed and the physics behind the attenuation in different spectral windows is explained methodically by assessing the type of Bloch modes and the in-plane symmetry of the displacement profile.

Bremsstrahlung from relativistic bare heavy ions: Nuclear and electronic contributions in amorphous and crystalline materials

A charged particle emits bremsstrahlung while traversing matter. We calculate the radiation cross section for bare heavy ions penetrating amorphous materials and single crystals at highly relativistic energies. The main component originates in scattering of the virtual photons of screened target nuclei on the projectile. It appears at, approximately, $2\ensuremath{\gamma}$ times the energy of the giant dipole resonance of the projectile, approximately 25$\ensuremath{\gamma}$ MeV for a lead nucleus ($\ensuremath{\gamma}\ensuremath{\equiv}E/M{c}^{2}$, where $E$ and $M$ denote the projectile energy and mass). The emission pertains to relatively close impacts, with impact parameters ranging to, at maximum, the screening radius of the target atoms. As a result, the main bremsstrahlung component shows channeling dips, that is, dips in yield upon variation of the incidence angle to major crystallographic directions of a single crystal. The minimum yield increases with $\ensuremath{\gamma}$ but saturates at a very low value. Incoherent interaction with single target electrons gives rise to two additional bremsstrahlung components, a modest component due to scattering of virtual photons of the electrons on the projectile and a strong low-energy component due to scattering of the virtual photons of the projectile on the electrons. The difference in radiation levels can be traced to the mass of the scatterer. Since target electrons are more widely distributed than nuclei in a crystal channel the variation of the electron component of the bremsstrahlung with incidence angle to a major crystallographic direction is less abrupt than the variation of the nuclear component. In consequence, the shape of the total bremsstrahlung spectrum changes when the crystal is tilted and the individual components may be singled out. Pair creation is also sensitive to the orientation of a crystalline material, resulting in a pronounced directional dependence of the energy loss of bare heavy ions at extreme relativistic energies.

Magnetic phase diagram of MnSi inferred from magnetization and ac susceptibility

We report simultaneous measurements of the magnetization and the ac susceptibility across the magnetic phase diagram of single-crystal MnSi. In our study we explore the importance of the excitation frequency, excitation amplitude, sample shape, and crystallographic orientation. The susceptibility, dM/dH, calculated from the magnetization, is dominated by pronounced maxima at the transition from the helical to the conical and the conical to the skyrmion lattice phase. The maxima in dM/dH are not tracked by the ac susceptibility, which in addition varies sensitively with the excitation amplitude and frequency at the transition from the conical to the skyrmion lattice phase. The same differences between dM/dH and the ac susceptibility exist for Mn1-xFexSi (x=0.04) and Fe1-xCoxSi (x=0.20). Taken together our study establishes consistently for all major crystallographic directions the existence of a single pocket of the skyrmion lattice phase in MnSi, suggestive of a universal characteristic of all B20 transition metal compounds with helimagnetic order.

Measurements of high energy loss rates of fast highly charged U ions channeled in thin silicon crystals

The results of two channeling experiments show that highly charged heavy ions at moderate velocities ($v\ensuremath{\ll}{\mathit{Zv}}_{0}$) may lose more energy in the traversal of a thin crystal when they are injected along a major crystallographic direction than when they traverse the crystal in random conditions. This is due to the fact that the large reduction of electron capture probabilities allows them to keep their high electronic charge throughout the crystal, which is not the case for projectiles traveling in random conditions. Although channeled projectiles experience reduced electron densities, their energy loss rate, that is, at first order, proportional to the square of the ions charge, is then strongly enhanced. This feature could be used as a step for decelerating highly charged ions from the high energies that are needed to produce them, and also to improve our understanding of the slowing down of very highly charged projectiles at low velocities, for which the current perturbative models are not well suited.

Displacement threshold and Frenkel pair formation energy in ionic systems

Displacement threshold energies ( E d ) and Frenkel pair formation energies ( E Fp ) are investigated in detail by molecular dynamics computer simulation for three different ionic systems with the same crystal structure, MgO, SrO and NaCl in order to see if there is a functional relationship between them. It is found that there are wide variations in the values of E d depending on the direction in which energy is imparted to a static atom in the lattice. Large values of E d are found along the major crystallographic directions and lower values elsewhere. Typically these thresholds are between 5 and 9 times bigger than the Frenkel pair formation energies E Fp with no observable dependence on mass or ion charge. The differences in the interaction potentials also means that for any given direction, there is only limited correlation between values of E d in the different systems studied and no quantifiable relationship with E Fp .

Polarization-dependent x-ray absorption spectroscopy of hexagonal and orthorhombic TbMnO3 thin films

Pure phase TbMnO3 manganite thin films with hexagonal (h-TMO) and orthorhombic (o- TMO) crystal structures were prepared by pulsed laser deposition. The distinctive orientation alignments between film and substrate obtained here have allowed us to perform the x-ray absorption near edge spectroscopy (XANES) measurements with the electric field applied along the three major crystallographic directions. The XANES results, as expected, display significantly different spectral features for the h-TMO and o-TMO films. In addition, the XANES spectra also exhibit strong polarization dependence at O K and Mn L edges for both samples.

Anisotropic electronic structure in single crystalline orthorhombic TbMnO 3 thin films

We have deposited the c-axis-oriented orthorhombic TbMnO 3 ( o-TMO) films with well-aligned in-plane orientations on NdGaO 3 (001) substrates by using pulsed laser deposition. The distinctive orientation alignments between the film and substrate allow the study of the X-ray absorption spectroscopy (XAS) with the electric field along three major crystallographic directions, respectively. Polarization-dependent XAS spectra show significant anisotropy in the electronic structure of o-TMO. The correlation between the electronic structure, the bonding anisotropy, and the magnetoelectric effect in the multiferroic materials is revealed.

Silicon‐Doped LiFePO4 Single Crystals: Growth, Conductivity Behavior, and Diffusivity

AbstractSingle crystals of silicon doped LiFePO4 with a silicon content of 1% are grown successfully by the floating zone technique and characterized by single‐crystal and powder X‐ray diffraction, secondary ion mass spectroscopy, and chemical analysis. Electron paramagnetic resonance demonstrates the presence of only Fe2+; no traces of Fe3+ are found. Impedance spectroscopy as well as step‐function polarization/depolarization (DC) measurements are carried out using the cells Ti/LiFe(Si)PO4/Ti and LiAl/LiI/LiFe(Si)PO4/LiI/LiAl. The electronic and ionic conductivities as well as the Li‐diffusivity of the sample in the major crystallographic directions ([h00], [0k0], and [00l]) are determined. Within experimental error the transport properties along the b‐ and c‐axes are found to be the same but differ significantly from the a‐axis, which exhibits lower values. Compared to undoped LiFePO4, Si‐doping leads to an increase of the ionic conductivity while the electronic conductivity decreases, which is in agreement with a donor effect. The activation energies of conductivities and diffusivities are interpreted in terms of defect chemistry and relevant Brouwer diagrams are given.

Magnetic phase transitions and ferromagnetic short-range correlations in single-crystalTb5Si2.2Ge1.8

Magnetic phase transitions in a ${\text{Tb}}_{5}{\text{Si}}_{2.2}{\text{Ge}}_{1.8}$ single crystal have been studied as a function of temperature and magnetic field. Magnetic-field dependencies of the critical temperatures are highly anisotropic for both the main magnetic ordering process occurring around 120 K and a spin reorientation transition at $\ensuremath{\sim}70\text{ }\text{K}$. Magnetic-field-induced phase transitions occur with the magnetic field applied isothermally along the $a$ and $b$ axes (but not along the $c$ axis) between 1.8 and 70 K in fields below 70 kOe. Strong anisotropic thermal irreversibility is observed in the Griffiths phase regime between 120 and 200 K with applied fields ranging from 10 to 1000 Oe. Our data (1) show that the magnetic and structural phase transitions around 120 K are narrowly decoupled; (2) uncover the anisotropy of ferromagnetic short-range order in the Griffiths phase; and (3) reveal some unusual magnetic domain effects in the long-range ordered state of the ${\text{Tb}}_{5}{\text{Si}}_{2.2}{\text{Ge}}_{1.8}$ compound. The temperature-magnetic field phase diagrams with field applied along the three major crystallographic directions have been constructed.

Aluminium-doped LiFePO4 single crystals : Part II. Ionic conductivity, diffusivity and defect model

We report on lithium ion conductivity and diffusivity along major crystallographic directions of Al-doped LiFePO4 single crystals. Impedance spectroscopy as well as galvanostatic polarization measurements have been carried out on the electronically blocking symmetric cell LiAl/LiI/LiFe(Al)PO4/LiI/LiAl. Neither ionic conductivity nor lithium diffusivity show anisotropy in the bc planes within the experimental error, but much lower values in the a-direction. Similar features were observed earlier by us for the pure single-crystal and the Si-doped single crystal. On Al-doping the ionic conductivity has increased while the electronic conductivity has decreased compared to undoped LiFePO4. Not only this donor doping effect but also the temperature dependence of ionic conductivity and of lithium-diffusivity are successfully interpreted in terms of lithium vacancies, holes and associates in the framework of a detailed defect chemical analysis. Ion-electron as well as ion-ion associates play a significant role in this system.

Porous silicon Bragg reflectors with sub-micrometer lateral dimensions

Bragg reflectors with widths down to 300 nm have been fabricated in porous silicon. This was achieved by irradiation of highly-doped p-type silicon with a focused beam of high-energy ions in a channeled alignment, in which the beam is aligned with a major crystallographic direction. The reflected colour is controllably tuned across the visible spectrum by varying the ion irradiated dose. The depth distribution of ion induced defects differs in channeled alignment compared to random beam alignment, resulting in the hole current during subsequent anodisation being more confined to narrower lateral regions, enabling different reflective wavelengths to be patterned on a sub-micron lateral scale. This work provides a means of producing high-density arrays of micron-size reflective colour pixels for uses in high-definition displays, and selectively tuning the wavelengths of porous silicon Fabry-Perot microcavities across the visible and infra-red ranges for optical communications and computing applications.

Channeling investigation of the crystalline structure ofU4O9−y

The crystallographic structure of ${\mathrm{U}}_{4}{\mathrm{O}}_{9\ensuremath{-}y}$ crystals can be described in terms of a spatial arrangement of special aggregates of oxygen atoms distributed throughout the basic fluorite framework of ${\mathrm{UO}}_{2}$. The structure of ${\mathrm{U}}_{4}{\mathrm{O}}_{9\ensuremath{-}y}$ single crystals was investigated with the ion-channeling method by recording angular scans across major crystallographic directions and along major atomic planes. Monte Carlo simulations were performed to interpret the channeling data. The presence of various anionic clusters previously proposed (such as the Willis-type 2:2:2 aggregate and Bevan-type cuboctahedral cluster), as well as more recent models involving the incorporation of extra oxygen atoms as oxo groups forming uranyl-type bonds and a structural disordering of part of the uranium sublattice, were investigated. Channeling data exhibit satisfactory agreement with both the Willis and Bevan-type aggregates. They are incompatible with the presence of a glassy part in the uranium sublattice and indicate that the presence of uranyl-type bonds is unlikely.

The interaction of relativistic particles with strong crystalline fields

Crystals present a uniquely simple environment for the investigation of strong electromagnetic fields. When energetic charged particles are incident on crystals close to major crystallographic directions, their electromagnetic interactions depend crucially on the kinematic conditions. The coherence of the crystalline field can produce very strong electric fields in the rest frame of the particle, exceeding the so-called Schwinger field or quantum critical field. In that domain, the radiation emission takes a substantial part of the electron energy and the ``formation zone'' changes character. In this review the theory appropriate to the different kinematics domains is described, concentrating on the effects occurring at extreme fields. Properties discussed include strong field synchrotron radiation, channeling radiation, bremsstrahlung, and photon interactions. Applications are given to radiation sources, bending of particle beams, and sources of polarized GeV photons.

Raman scattering and X-ray powder diffraction studies of hydrate layered perovskites: dirubidium aquapentafluoromanganate(III) and dipotassium aquapentafluoroferrate(III)

The structural and vibrational properties of above mentioned crystals were determined using X-ray powder diffraction and Raman scattering experiments. At room temperature hydrate layered perovskites: Rb 2MnF 5·H 2O and K 2FeF 5·H 2O exhibit orthorhombic—Cmcm (D 2h 17) and monoclinic—C2/c (C 2h 6) symmetry. Their structure is built up of MnF 6 or FeF 5·H 2O octahedra forming trans-linked zig–zag chains or hydrogen bonded zig–zag chains along the major crystallographic direction [0 0 1], respectively. To confirm crystal structures and to describe lattice dynamics of these compounds the vibrational normal modes (in Γ point of first Brillouin zone) were calculated on the base of the group theory analysis and compared with the spectra obtained from Raman scattering experiments. A relatively good reliability was obtained for both X-ray powder diffraction and Raman scattering.

Crystal-field analysis of the magnetic properties measured on aHo2Co15Si2single crystal

We have measured the magnetic properties of a ${\mathrm{Ho}}_{2}{\mathrm{Co}}_{15}{\mathrm{Si}}_{2}$ single crystal in the temperature range 5--350 K with magnetic fields applied on the free crystal and along three major crystallographic directions of the fixed crystal. The temperature dependence of the magnetization measured on the free crystal shows that the Ho and Co moments compensate at 35 K, and continuous plane-cone-axis spin-reorientation transitions take place in a certain temperature range above room temperature. The field dependence of the total magnetization shows strong differences when measured along the three main crystallographic directions. In particular, this is the case at low temperatures where the magnetic isotherms are indicative of field-induced magnetic phase transitions. The magnetic isotherms at high temperatures show a marked magnetization anisotropy. We have analyzed our data, especially the field-induced and temperature-induced magnetic phase transitions in terms of a two-sublattice model in which the molecular-field interaction, the crystal-field interaction, and the moment anisotropy are important ingredients. A set of crystalline-electric-field parameters as well as the Ho-Co exchange field has been determined for the ${\mathrm{Ho}}_{2}{\mathrm{Co}}_{15}{\mathrm{Si}}_{2}$ single crystal by fitting the experimental results with model calculations. The calculated magnetic behavior shows a good agreement with the experimental results in the temperature range presently studied, demonstrating the reliability of the determined parameters. It has been found that the Ho moment changes slightly in value during the spin-reorientation transition, and that there is a distinct magnetization anisotropy in the magnetic isotherms at high temperatures. These phenomena are intimately related to the marked direction dependence of the Ho moment.