Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLattice vibrations in the harmonic approximation
245
0
0.0
(
0
)
Added by
Georgii Paradezhenko
Publication date
2017
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We present some theoretical results on the lattice vibrations that are necessary for a concise derivation of the Debye-Waller factor in the harmonic approximation. First we obtain an expression for displacement of an atom in a crystal lattice from its equilibrium position. Then we show that an atomic displacement has the Gaussian distribution. Finally, we obtain the computational formula for the Debye-Waller factor in the Debye model.
rate research
Read More
The energy-spectrum of two point-like particles interacting in a 3-D isotropic Harmonic Oscillator (H.O.) trap is related to the free scattering phase-shifts $delta$ of the particles by a formula first published by Busch et al. It is here used to find an expression for the it shift rm of the energy levels, caused by the interaction, rather than the perturbed spectrum itself. In the limit of high energy (large quantum number $n$ of the H.O.) this shift is shown to be given by $-2frac{delta}{pi}$, also valid in the limit of infinite as well as zero scattering length at all H.O. energies. Numerical investigation shows that the shifts differ from the exact result of Busch et al, by less than $<frac{1}{2}%$ except for $n=0$ when it can be as large as $approx 2.5%$. This approximation for the energy-shift is well known from another exactly solvable model, namely that of two particles interacting in a spherical infinite square-well trap (or box) of radius $R$ in the limit $Rrightarrow infty$, and/or in the limit of large energy. It is in this context referred to as the it phase-shift approximation rm. It can be (and has been) used in (infinite) nuclear matter calculations to calculate the two-body effective interaction in situations where in-medium effects can be neglected. It has also been used in expressing the energy of free electrons in a metal.
Transmission electron microscopes use electrons with wavelengths of a few picometers, potentially capable of imaging individual atoms in solids at a resolution ultimately set by the intrinsic size of an atom. Unfortunately, due to imperfections in the imaging lenses and multiple scattering of electrons in the sample, the image resolution reached is 3 to 10 times worse. Here, by inversely solving the multiple scattering problem and overcoming the aberrations of the electron probe using electron ptychography to recover a linear phase response in thick samples, we demonstrate an instrumental blurring of under 20 picometers. The widths of atomic columns in the measured electrostatic potential are now no longer limited by the imaging system, but instead by the thermal fluctuations of the atoms. We also demonstrate that electron ptychography can potentially reach a sub-nanometer depth resolution and locate embedded atomic dopants in all three dimensions with only a single projection measurement.
The renormalization of electronic eigenenergies due to electron-phonon interactions (temperature dependence and zero-point motion effect) is important in many materials. We address it in the adiabatic harmonic approximation, based on first principles (e.g. Density-Functional Theory), from different points of view: directly from atomic position fluctuations or, alternatively, from Janaks theorem generalized to the case where the Helmholtz free energy, including the vibrational entropy, is used. We prove their equivalence, based on the usual form of Janaks theorem and on the dynamical equation. We then also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a first-principle context. The AHC theory relies on the rigid-ion approximation, and naturally leads to a self-energy (Fan) contribution and a Debye-Waller contribution. Such a splitting can also be done for the complete harmonic adiabatic expression, in which the rigid-ion approximation is not required. A numerical study within the Density-Functional Perturbation theory framework allows us to compare the AHC theory with frozen-phonon calculations, with or without the rigid-ion terms. For the two different numerical approaches without rigid-ion terms, the agreement is better than 7 $mu$eV in the case of diamond, which represent an agreement to 5 significant digits. The magnitude of the non rigid-ion terms in this case is also presented, distinguishing specific phonon modes contributions to different electronic eigenenergies.
The quasiparticle band structures of nonmagnetic monoxides, MO (M=Mg, Ca, Ti, and V), are calculated by the GW approximation. The band gap and the width of occupied oxygen 2p states in insulating MgO and CaO agree with experimental observation. In metallic TiO and VO, conduction bands originated from metal 3d states become narrower. Then the partial densities of transition metal e_g and t_2g states show an enhanced dip between the two. The effects of static screening and dynamical correlation are discussed in detail in comparison with the results of the Hartree-Fock approximation and the static Coulomb hole plus screened exchange approximation. The d-d Coulomb interaction is shown to be very much reduced by on-site and off-site d-electron screening in TiO and VO. The dielectric function and the energy loss spectrum are also presented and discussed in detail.
We present a study of the lattice response to the compressive and tensile biaxial stress in La0.67Sr0.33MnO3 (LSMO) and SrRuO3 (SRO) thin films grown on a variety of single crystal substrates: SrTiO3, DyScO3, NdGaO3 and (La,Sr)(Al,Ta)O3. The results show, that in thin films under misfit strain, both SRO and LSMO lattices, which in bulk form have orthorhombic (SRO) and rhombohedral (LSMO) structures, assume unit cells that are monoclinic under compressive stress and tetragonal under tensile stress. The applied stress effectively modifies the BO6 octahedra rotations, which degree and direction can be controlled by magnitude and sign of the misfit strain. Such lattice distortions change the B-O-B bond angles and therefore are expected to affect magnetic and electronic properties of the ABO3 perovskites.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
