Crystal Symmetry Directions Research Articles

Dynamic martensitic phase transformation in single-crystal silver microcubes

The ability to transform the crystal structure of metals in the solid state enables tailoring their physical, mechanical, electrical, thermal, and optical properties in unprecedented ways. We demonstrate a martensitic phase transformation from a face-centered-cubic (fcc) structure to a hexagonal-close-packed (hcp) structure that occurs in nanosecond timescale in initially near-defect-free single-crystal silver (Ag) microcubes impacted at supersonic velocities. Impact-induced high pressure and high strain rates in Ag microcubes cause impact orientation dependent extreme micro- and nano-structural transformations. When a microcube is impacted along the [100] crystal symmetry direction, the initial fcc structure transforms into an hcp crystal structure, while impact along the [110] direction does not produce phase transformations, suggesting the predominant role played by the stacking faults generated in the [100] impact. Molecular dynamics simulations at comparable high strain rates reveal the emergence of such stacking faults that coalesce, forming large hcp domains. The formation of hcp phase through the martensitic transformation of fcc Ag shows new potential to dramatically improve material properties of low-stacking-fault energy materials.

Dynamic Martensitic Phase Transformation in Single-Crystal Silver Microcubes

The ability to transform the crystal structure of metals in the solid state enables tailoring their physical, mechanical, electrical, thermal, and optical properties in unprecedented ways. We demonstrate a martensitic phase transformation from a face-centered-cubic (fcc) structure to a hexagonal-close-packed (hcp) structure that occurs in nanosecond timescale in initially near-defect-free single-crystal silver (Ag) microcubes impacted at supersonic velocities. Impact-induced high pressure and high strain rates in Ag microcubes cause impact orientation dependent extreme micro- and nano-structural transformations. When a microcube is impacted along the [100] crystal symmetry direction, the initial fcc structure transforms into an hcp crystal structure, while impact along the [110] direction does not produce phase transformations, suggesting the predominant role played by the stacking faults generated in the [100] impact. Molecular dynamics simulations at comparable high strain rates reveal the emergence of such stacking faults that coalesce, forming large hcp domains. The formation of hcp phase through the martensitic transformation of fcc Ag shows new potential to dramatically improve material properties of low-stacking-fault energy materials.

Uniaxial Strain Redistribution in Corrugated Graphene: Clamping, Sliding, Friction, and 2D Band Splitting.

Graphene is a promising material for strain engineering based on its excellent flexibility and elastic properties, coupled with very high electrical mobility. In order to implement strain devices, it is important to understand and control the clamping of graphene to its support. Here, we investigate the limits of the strong van der Waals interaction on friction clamping. We find that the friction of graphene on a SiO2 substrate can support a maximum local strain gradient and that higher strain gradients result in sliding and strain redistribution. Furthermore, the friction decreases with increasing strain. The system used is graphene placed over a nanoscale SiO2 grating, causing strain and local strain variations. We use a combination of atomic force microscopy and Raman scattering to determine the friction coefficient, after accounting for compression and accidental charge doping, and model the local strain variation within the laser spot size. By using uniaxial strain aligned to a high crystal symmetry direction, we also determine the 2D Raman Grüneisen parameter and deformation potential in the zigzag direction.

Nucleation and growth of primary nanostructures in SrTiO3 homoepitaxy.

SrTiO3 nanoislands on SrTiO3 (001) in a diffusion-limited growth regime were studied using in situ scanning tunneling microscopy (STM). The STM images revealed two characteristic features of nucleation stages. First, the minimum lateral size of the one-unit-cell (uc)-high SrTiO3 islands was 4 × 4 uc2. Second, one-dimensional SrTiO3 islands of a 4 uc width grew along the crystal symmetry directions. These observations suggest that 4 × 4-uc2 islands act as a minimum nucleation seed, and the addition of SrTiO3 molecular species of the same width is the primary and dominant growth process in SrTiO3 homoepitaxy. A close inspection of the surface of the substrate during the deposition process revealed possible connections between surface reconstruction and energetically favorable nucleation of SrTiO3 islands.

Equilibrium magnetization in the vicinity of the Bragg glass to vortex glass transition inV3Si

We present a study of the quasiequilibrium magnetization of single crystalline ${\mathrm{V}}_{3}\mathrm{Si}$ spheres of different pinning strength in the vicinity of Bragg glass to disordered vortex solid transition. We report a first-order-like magnetization step below the onset of the peak effect. Its occurrence is hysteretic with respect to the direction of field scan. The step is observed only for fields oriented away from the high crystal symmetry directions [110] and [100]. Accompanying the magnetization step is an abrupt reorientation of the vortex lattice towards a crystal symmetry direction. Coupling between the vortex lattice and the underlying crystal lattice is suggested as a possible mechanism for the reorientation transition.

Invariant formulation of the strain dependence of the critical temperature Tc of Nb 3Sn in a three term approximation

It has been shown previously in a full detailed analysis that the strain dependence of the critical temperature may be obtained from a general strain invariant formulation of T c in strong superconductivity. A physical model was presented in which the phonon frequency spectrum is represented through generalized elastic stiffness coefficients that include strain dependence. The primary purpose of the present work is to achieve a simplification of the analysis in order to facilitate calculation and reveal the essential physical content. The formulation in wave vector space of the equations for T c in strong superconductivity is reviewed. The method of simplification employs a succession of approximations to the effective elastic constants that enter the relation between phonon frequency and wave number. It is found that the effective elastic constants in the crystal symmetry directions may be grouped into sets having similar form, and this form includes terms in common among the sets and difference terms. The difference terms are found to be in the nature of gradients and may be eliminated to good approximation. The common terms include the strain dependence in a form identified as a deformation strain parameter. The analysis treats spherical (hydrostatic) and deformation strain dependence under longitudinal and transverse applied strain for wire and tape conductor. The analysis is applicable over a full range of applied strain, including small strains often described by a power law strain dependence, and larger strains often described by a deviatoric strain approach. A comparison is provided between the results of the full detailed analysis and the results of the approximate treatment showing the degree of agreement in the various applied strain orientations.

Elastic stiffness model for the critical temperature Tc of Nb 3Sn including strain dependence

A calculation is established for the critical temperature T c of the superconductor Nb 3Sn that includes the dependence on applied mechanical strain. The calculation employs the formalism of strong coupling phonon superconductivity, as usually given in frequency space. The directional nature of strain is included by expressing the equations of strong coupling in wave vector space. The relation between wave number and frequency is provided by the dispersion relations incorporating the effective elastic constants for the symmetry directions of the cubic crystal. An analytical formalism is established in which the elastic constants are derived in a unified way from an assumed strain energy potential function. The form of the strain energy potential is governed by the cubic symmetry. The scalar invariants of the strain tensor under the cubic symmetry group are determined as a set of basis functions for the strain energy potential. In the harmonic approximation, the relation between the strain energy function and the elastic constants determines the harmonic amplitudes of the strain potential from the measured dispersion relations. The electron–phonon coupling characteristic is approximated in a simple analytic form determined by inspection of the experimentally determined tunneling and phonon density of states. The critical temperature is calculated, through the equations of strong coupling, as a sum over the crystal symmetry directions. The anharmonic terms of the strain energy potential are introduced as the source of the strain dependence of the critical temperature. The allowed form of the anharmonic terms is again governed by cubic symmetry. The amplitudes of the anharmonic terms are determined from the strain dependence characteristics of single crystals and composite superconductors. The calculations are found to represent the observed strain dependence well with a strain energy function that contains three scalar invariants of the strain tensor, including the spherical (hydrostatic) strain invariant, and the principle parts of the second and third invariants of the deviatoric strain tensor. The formalism is applied to the analysis of composite conductors. The characteristics of the strain dependence of wire and tape geometries under longitudinal and transverse loads are related to the symmetry of the conductor and direction of applied load. Implications of conductor symmetry and constraint on the measurement of the strain dependent properties are identified.

Realignment of the flux-line lattice by a change in the symmetry of superconductivity in UPt3

In 1957, Abrikosov described how quanta of magnetic flux enter the interior of a bulk type II superconductor. It was subsequently predicted that, in an isotropic superconductor, the repulsive forces between the flux lines would cause them to order in two dimensions, forming a hexagonal lattice. Flux-line lattices with different geometry can also be found in conventional (type II) superconductors; however, the ideal hexagonal lattice structure should always occur when the magnetic field is applied along a hexagonal crystal direction. Here we report measurements of the orientation of the flux-line lattice in the heavy-fermion superconductor UPt3, for this special case. As the temperature is increased, the hexagonal lattice, which is initially aligned along the crystal symmetry directions, realigns itself with the anisotropic superconducting gap. The superconductivity in UPt3 is unusual (even compared to unconventional oxide superconductors) because the superconducting gap has a lower rotational symmetry than the crystal structure. This special feature enables our data to demonstrate clearly the link between the microscopic symmetry of the superconductivity and the mesoscopic physics of the flux-line lattice. Moreover, our observations provide a stringent test of the theoretical description of the unconventional superconductivity in UPt3.

Power Losses of a High‐Temperature Superconducting Slab in the Presence of Alternating Currents

AbstractThe power loss and its two constituent terms due to dissipated and reactive energies are developed for a system of a normal conducting wire (two wires) carrying ac current parallel to a high‐temperature type‐II superconducting infinite slab (moving slab) of arbitrary thickness. The reactive term is found to be either capacitively or inductively reactive. When the thickness of the slab tends to infinity it is found that the results will be in good agreement with the previous results. It is found that the loss along the versor of the anisotropy axis increases as λ‖ increases, moreover it is greater than the power loss along the crystal symmetry direction a. In the isotropic case a satisfactory agreement with previous results is achieved.

Acoustic microscopy measurement of elastic constants and mass density

A method is presented to determine the elastic constants and the mass density of isotropic and anisotropic solids and anisotropic thin films. The velocity and attenuation of leaky surface acoustic waves (SAWs) have been obtained for specified propagation directions from V(z) curves measured by line-focus acoustic microscopy (LFAM). The experimentally obtained velocities have been compared to velocities obtained from a measurement model for the V(z) curve which simulates the experiment. Since the measured and simulated V(z) curves have the same systemic errors, the material constants are free of such errors. For an isotropic solid, Young's modulus E, the shear modulus G and the mass density /spl rho/ have been determined from the leaky Rayleigh wave velocity and attenuation, measured by LFAM, and a longitudinal wave velocity measured by a pulse-echo transit-time technique. For a cubic-crystalline solid, the ratios of the elastic constants to the mass density (c/sub 11///spl rho/, c/sub 12///spl rho/, c/sub 44///spl rho/) have been determined from the directional variation of measured SAW velocities, using a preliminary estimate of /spl rho/. The mass density /spl rho/ has subsequently been determined by additionally using the attenuation of leaky SAWs in crystal symmetry directions. For a cubic-crystalline thin film deposited on a substrate, the elastic constants and the mass density (c/sub 11/, c/sub 12/, c/sub 44/, /spl rho/) of the film have been determined from the directional variation of the measured SAW velocities, and a comparison of the corresponding attenuation coefficient with the measured attenuation coefficient has been used to verify the results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Power Losses of a High‐Temperature Superconducting Semi‐Infinite Space

AbstractAn exact solution of the anisotropic London equation is obtained for the system of a vibrating wire carrying dc current (a non‐vibrating wire carrying ac current) parallel to a high‐temperature superconducting planar surface. Also, the distribution of the external magnetic field outside the superconductor is exactly determined. The power losses and the reactive power losses on the surface of the sample are completely determined. It is found that these losses along the versor of the anisotropy axis are increased as λ increases, moreover, they are greater than the power losses along the crystal symmetry direction a. In the isotropic case a satisfactory agreement with previous results is achieved.

Structure of an isolated vortex in an anisotropic type-II superconductor.

The Ginzburg-Landau equations with general effective-mass anisotropy are diagonalized for a general direction v of an isolated vortex core. For v not parallel to one of the three crystal axis directions, the local magnetic induction b contains components ${b}_{\ensuremath{\rho}}$ and ${b}_{\ensuremath{\varphi}}$, perpendicular to v, which vanish as ${\ensuremath{\rho}}^{2}$ away from the center of the core with coefficients that are odd in the azimuthal angle \ensuremath{\varphi}. In the London limit far from the core, ${b}_{\ensuremath{\rho}}$ and ${b}_{\ensuremath{\varphi}}$ are comparable to ${b}_{3}$=v^\ensuremath{\cdot}b, and all fall off exponentially in \ensuremath{\rho}, with two distinct exponents, each of which depends explicitly upon the azimuthal angle \ensuremath{\varphi} about v^. The presence of ${b}_{\ensuremath{\rho}}$ and ${b}_{\ensuremath{\varphi}}$ reduces the energy cost of the locking of the core into the lattice but does not remove it entirely, as the leading correction to the line energy is proportional to the parameter ${\ensuremath{\beta}}^{2}$ (rather than \ensuremath{\beta}), where \ensuremath{\beta} is the parameter introduced previously by the author. With the use of an ansatz, an exact form for the field components and reduced order parameter f in the core region is obtained. The lines of constant ${b}_{3}$ and \ensuremath{\Vert}${b}_{\ensuremath{\perp}}$\ensuremath{\Vert} in the core region are found for arbitrary effective-mass anisotropy and v^. These forms should be observable by scanning tunneling microscopy and by large-momentum-transfer neutron-scattering experiments for fields slightly greater than ${H}_{c1}$. In addition, the angular dependence of ${H}_{c1}$ should exhibit a kink, as the vortex cores prefer to lie along one of the crystal symmetry directions.

Lower critical field of an anisotropic extreme type-II superconductor.

It is shown that the procedure of Klemm and Clem (abbreviated as I) for the transformation to isotropic form of the Ginzburg-Landau free energy for a superconductor with a general effectivemass anisotropy leads to a current which is not perpendicular to the magnetic induction $\mathbf{B}$, unless $\mathbf{B}$ is in a crystal-symmetry direction. In general, the mean-field free energy is thus a function of a new parameter $\ensuremath{\beta}$, which depends upon the direction cosines of $\mathbf{B}$, as well as a function of the renormalized $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\kappa}}$ parameter of I, except at the upper critical field ${H}_{c2}$. A perturbation solution in $\ensuremath{\gamma}=\frac{\ensuremath{\beta}}{(1+\ensuremath{\beta})}$ is found to order ${\ensuremath{\gamma}}^{2}$, and the angular dependence of the lower critical field ${H}_{c1}$ is determined. The parameter $\ensuremath{\beta}$ is found to cause $\mathbf{B}$ to nearly lock on to a crystal-symmetry direction, so that as the external field angle is varied, $\mathbf{B}$ switches from near to one symmetry direction to (near to) another, yielding a kink in the angular dependence of ${H}_{c1}$ that is more pronounced than in I.

Incoherent quasielastic neutron scattering investigation of chlorine ion hopping in the fast-ion phase of strontium chloride

Energy broadening of the incoherent quasielastic neutron scattering from a single crystal of the fast-ion conductor strontium chloride at 1053K has been measured for scattering vectors along the three principal crystal symmetry directions. The data are well accounted for by either the random-jump diffusion model of Chudley and Elliott (1961) or by Wolf's encounter model. A vacancy diffusion mechanism is found to predominate in the fast-ion phase, with anion hops mainly between nearest and next-nearest neighbour regular anion sites and a mean residence time of 25-29*10-12s.

Atomic band structure effects on resonant scattering of atoms from solid surfaces

Bound state resonances related to the band structure of adsorbed atoms and their usefulness for determining the periodic components of atom-solid interaction potential are theoretically investigated. A variety of specular intensity patterns associated with bound state resonances near the Brillouin zone boundaries are exhibited. The (10) and (11̄) bound state resonances give rise to two split specular minima with the splitting depending essentially on v 10 for a fixed beam energy; however, the detailed features are dependent on other periodic components. For incidence along a crystal symmetry direction, symmetrization of basis states not only makes numerical computation very efficient, but also implies that there is only one specular minimum for a pair of bound states which are equivalent by symmetry. The (01) and (10) resonances along and near the x = y direction are presented to illustrate the symmetrization principle. The depth of one of the specular minima decreases and finally vanishes as the symmetry direction is approached. The single specular minimum corresponds to a resonance with the bound state which is a symmetric linear combination of (01) and (10) states in a potential well of v 0 + V 11. As expected, the shift in positions of specular minima caused by the periodic surface potential increases with decreasing beam energy.