Search

Finding the possible stopping sites for muons inside a crystalline sample is a key problem of muon spectroscopy. In a previous study, we suggested a computational approach to this problem when dealing with muonium, the pseudoatom formed by a positive muon that has captured an electron, using density functional theory software in combination with a random structure searching approach that relies on a Poisson sphere distribution. In this work, we test this methodology further by applying it to muonium in three organic molecular crystal model systems: durene, bithiophene, and tetracyanoquinodimethane. Using the same sets of random structures, we compare the performance of density functional theory software CASTEP and the much faster lower level approximation of Density Functional Tight Binding provided by DFTB+ combined with the use of the 3ob-3-1 parameter set. We show the benefits and limitations of such an approach, and we propose the use of DFTB+ as a viable alternative to more cumbersome simulations for routine site-finding in organic materials. Finally, we introduce the Muon Spectroscopy Computational Project software suite, a library of Python tools meant to make these methods standardized and easy to use.

Molecular dynamics simulation starting from a lamellar crystal model of a single polyethylene chain is performed to investigate the lamellar reorganization during heating at the molecular level. It is shown that three stages are involved in the process of the reorganization: at temperatures 300 K 500 K the lamella starts to melt and becomes a random coil in the end. Particularly, the thickening process is investigated in our simulations. It is found that the lamellar thickening occurs in discrete steps and is driven mainly by the van der Waal attraction between the chain segments. There are two mechanisms for the lamellar thickening. At lower temperature the thickening occurs by the sliding diffusion of adjacent chain segments, while at higher temperature the recrystallization after the partial melting of thinner stems leads to the thickening.

A one-dimensional crystal model is constructed with a complex periodic potential. A wave function solution for the crystal model is derived without relying on Bloch functions. The new wave function solution of this model is shown to correspond to the solution for the probability amplitude of a two-level system. The energy discriminant is evaluated using an analytic formula derived from the probability amplitude solution, and based on an expansion parameter related to the energy and potential amplitude. From the wave function energy discriminant the crystal band structure is derived and related to standard energy bands and gaps. It is also shown that several of the properties of the two-level system apply to the one-dimensional crystal model. The two-level system solution which evolves in time is shown to manifest as a spatial configuration of the one-dimensional crystal model. The sensitivity of the wave function probability density is interpreted in the context of the new solution. The spatial configurat...

As part of a series of studies on energy transfer processes between optical centers in condensed matter, an analysis is made of the problem of a crystalline system made up by a majority of regular optical centers and small amounts of defective optical centers. Within the conceptual framework of the crystal model, analytic equations are derived that allow a direct connection between the microscopic study of the interaction and kinetic type equations to describe the relaxation dynamics from excited states. As an example, Ln3+ ions in elpasolite type lattices are used, showing the biexponential character of the decay curves. These results can be used in the study of relaxation from excited states in crystals with heterogeneities due to crystallographic defects, trace impurities, or slightly distorted optical centers.

The study of energy transfer processes between optical centers in crystalline cubic materials is reexamined within the conceptual framework of the crystal model. The initial assumption of modest transfer rates is relaxed, thereby correcting the master equation of the crystal model and making it possible to explain the nonexponential behavior of the radiation decay curves from excited states. This study shows that such experimental trends are the result of a purely statistical effect related to the fluctuation in the population of optically active ions in a crystal lattice. The corrected crystal model does not need to invoke migration of excitation processes to explain the fast exponential decay observed in crystals with a high concentration of optical centers.

A general study of energy transfer processes in organized condensed matter is presented. Considering the nature of these media, i.e., the periodic properties of the lattice, a theoretical microscopic model is worked out for the general case. It takes full advantage of the translational periodicities in the crystalline phase, using the real discrete distribution of ions in the lattice. A general master equation is obtained and, for the sake of completeness, a particular case is analyzed for the dipole–dipole nonradiative mechanism for energy transfer processes in the elpasolite lattices where the Ln3+ impurities are in cubic sites.

We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and used to analyse colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.

The ability of the classical nucleation theory (CNT) and atomistic nucleation theory (ANT) to predict the stationary nucleation rate J of single-component crystals and crystalline monolayers is verified with the aid of numerical and computer simulation data obtained in the scope of the Kossel crystal model. It is found that in both cases CNT significantly overestimates J because it does not account for the work needed to attach an atom to the periphery of the two-dimensional nucleus or to form such a nucleus on the surface of the three-dimensional one. In contrast, ANT is successful in providing a good quantitative description of J, especially for high enough effective binding energy between nearest-neighbor atoms in the crystal and in capturing the existence of extended, nearly linear portions in the dependence of ln J on the supersaturation s when the values of both s and the binding energy are sufficiently great. However, the ANT prediction about broken linear ln J versus s dependence is not confirmed by the numerical and simulation results presented. General formulas for the nucleation work, the nucleus size, and the nucleation rate are proposed which are applicable to nucleation of single-component crystals and crystalline monolayers in vapors, solutions, or melts and which correct the respective CNT formulas. The proposed J(s) formula provides a good description of the numerical and simulation data and can justifiably be used up to the supersaturation at which the nucleus becomes monomer. When experimental data for the J(s) dependence are available and the nucleus specific edge and surface energies are unknown parameters, the proposed J(s) formula can be employed for estimation of these energies even if the nucleus is constituted of a few atoms only.

Consider a fast nonrelativistic, positively charged particle (ion) traversing a crystal, assumed to be simple cubic and monatomic for simplicity. Let the Cartesian coordinates X1,X2,X3 be parallel to the crystal axes, and ηi be the initial value of the component of the particle’s momentum vector along Xi. If ∣η3∣ is sufficiently large compared to ∣η1∣,∣η2∣, then (under mild technical assumptions) the ion’s motion is well approximated for a long time by a solution of the equations of motion (EOM) of the axial-continuum Hamiltonian H¯, obtained from the ion’s nonrelativistic Hamiltonian H by replacing the potential V(X1,X2,X3), describing its interaction with the atoms of the crystal, by its average V¯(X1,X2) over X3. Furthermore, if ∣η2∣,∣η3∣ are sufficiently large compared with ∣η1∣,∣η2∣, respectively, then to a good approximation its motion is given, again for a long time, by a solution of the EOM of the planar continuum Hamiltonian H, obtained from H¯ by replacing V¯(X1,X2) by its average V(X1) over X...

An extended discussion is given of a crystal model showing successive ``rotational'' or orientational transitions. This model consists of an array of classical rotators with next‐neighbor coupling, the potential energy of coupling being E(θij)=AP1(cosθij)+BP2(cosθij), where θij is the angle between the molecular axes of symmetry. It is treated by both the internal field approximation (Bragg‐Williams approximation) and Chang's modification of Bethe's method. The internal field approximation is applied in two ways, the first involving use of consistency relations, the second involving calculations of the thermodynamic potentials. The consistency relations are shown to be equivalent to the condition that the free energy be stationary, but not necessarily a minimum, with respect to variation of the orientational distribution of the molecules. Depending on the relative values of A and B, the model shows a single second‐order transition, a single first‐order transition, two first‐order transitions, or a second‐...

The effect of the internal vibrations of monomers (or molecules) on the electronic absorption spectra of aggregates with either helical or three dimensional translational symmetry is considered using molecular exciton theory. In this treatment the single‐particle excitations (vibronic excitons) are coupled to all those two‐particle manifolds in which vibronic and ground vibrational excitons occupy different lattice sites. This allows for collective coupling among single‐particle levels overlapped by two‐particle continua. The main approximations invoked are (a) the crude Born—Oppenheimer approximation to factorize the wavefunctions of isolated monomers, (b) neglect of electron exchange between monomer wavefunctions (tight binding), and (c) the neglect of any mixing of different electronic states by intermonomer forces. Wave sums of exciton resonance interactions are eliminated in favor of a density of sums function. To test the range of coupling strengths for which the theory is valid calculations are performed for a one‐dimensional polymer model with only nearest‐neighbor interactions and a three‐dimensional crystal model with a simple density function. For intermediate coupling the influence of three‐ and higher‐particle states becomes important and these states are included in the energy calculations by an extended fraction type of technique. Other calculations explore the effect of (a) a change in the vibrational frequency of the monomer after electronic excitation, (b) changes in the energy of the optical k=0 levels with direction of the exciting radiation, and (c) changes in the transition intensity of the isolated monomer.

A modified Frenkel—Kontorova dislocation model, with a piecewise linear substrate potential, is extended to two dimensions to describe the entire slip plane of the dislocation with one kink. Accurate solutions are found, with the aid of several analytic techniques and a digital computer, for the static configuration under applied stress. The kink Peierls stress σk P, the kink width w, and the kink energy F, are determined for a range of values of γ, the perfect crystal shear strength. σk P is found to be very sensitive to γ, and to have maxima of the order of 10−6 to 10−5, in units of the shear modulus. w and E are less sensitive to γ; w ranges from ∼4 to ∼30 lattice parameters, while E varies from several hundred to several thousand degrees Kelvin for typical crystal parameters.