Theoretical study of the diffusion of lithium in crystalline and amorphous silicon

Abstract

143Modern ideas about the mechanisms of diffusion in crystals and liquids were formed in the 1960s, mainly owing to computer simulation by the molecular dynamics and Monte Carlo methods. The problem of diffusion mechanisms in amorphous media is much more complicated than that in crystals and has not yet been completely solved. In particular, this refers to the diffusion of particles in systems that form a low mobile frame and are coupled either by strong cova lent bonds (as in amorphous silicon) or by strong Cou lomb interaction (as in silica). The methods of the the oretical analysis of the diffusion processes in these sys tems have been elaborated insufficiently (see [1]). In contrast to the case of diffusion in crystalline media with low potential barriers (V barrier ≈ (1-10)kT) for hopping of particles, when the molecular dynamics method can be applied, the hopping frequency of atoms through barriers becomes extremely low in structures with high potential barriers (the rare event problem). Therefore, these systems, particularly in the amorphous state, cannot be studied directly by the molecular dynamics method. To speed up the simula tion of the processes of activation hopping for these cases, an activation-relaxation technique (ART) was elaborated recently. It makes it possible to simulate the structure and activation processes in amorphous com pounds (see [2,3]). This method is based on the calcu lation of the transition states (saddle points) of the sys tem (activation) at arbitrarily chosen vectors of motion of atoms by means of the calculation of the forces acting on atoms, and also motion in the direc tion to the nearest saddle point. Atoms arbitrarily relaxed (relaxation) from the transition states to the nearest energy minima defining the amorphous state. The further development of this approach was the uni fication of the kinetic Monte Carlo algorithm and the ART method (the kinetic activation-relaxation tech nique (k ART)), which accelerates the convergence of this algorithm (see [4]). When the method of acceler ated dynamics is developed, it is necessary to mention also the recently elaborated bias potential method [5], the hyperdynamics method [6], and the temperature accelerated dynamics method [7]. The WootenWiner-Weaire algorithm [8], which is based on the random rearrangements of the nearest atoms, is also used to simulate the amorphous structure. It leads to the change in the number and directions of the chem ical bonds between the nearest environment of atoms and the subsequent relaxation of the structure by numerical annealing. The result of the simulation of silicon and germanium by this method showed good coincidence with the experiment for the radial distri bution function of atoms [8]. Unfortunately, all these methods have been applied exclusively to systems that are described either by the simplified embedded atom model or by empirically selected potentials with the The effect of the lattice deformation on potential barriers for the motion of a lithium atom in crystalline sili con has ...

Entanglement of multiphoton two-mode polarization Fock states and of their superpositions

“…In particular, its trace becomes different from one in contrast to the density matrix (5). Also it does not provide a correct transition to the so called coherence matrix of biphoton qutrits [18]. Indeed, the most general polarization biphoton state is qutrit, the sate vector of which is…”

“…In the case of polarization modes the single-photon wave functions in these products are ψ H (σ i ) = δ σi, H and ψ V (σ j ) = δ σj , V . In the matrix representation ψ H (σ i ) = 1 0 i and ψ V (σ j ) = 0 1 j [18]. Note that sometimes it's possible to meet in literature mentions about particle-or mode-entanglement and about differences or similarities between them.…”

“…So, the procedure of crossing out repeated columns and rows can not be considered as mathematically correct. To make it correct, one has to make first the unitary transformation of the matrix (5) [18], after which all elements in one of rows and one of columns in the 4 × 4 matrix turn zero. For the matrix (5) the required unitary transformation has the form…”

Ab initio and empirical modeling of lithium atoms penetration into silicon

“…In this process, the change in volume causes large mechanical stresses and, consequently, a break-up of the crystal [8][9][10][11]. In addition to this, silicon has a low diffusion coefficient for lithium ions [12,13]. These limitations impede application of bulk silicon in modern Li-ion batteries.…”

Cs diffusion in SiC high-energy grain boundaries

“…The high fraction of HEGBs allow them to provide a percolating path for FPs transportation, and HEGBs are one of two GB types that are present in a high enough concentration to form a percolating path (the other GB type is ∑3-GB) 18 . Also, it is often found that disordered (amorphous) materials, which are structurally similar to HEGBs 19,20 , provide a faster transportation pathway for extrinsic defects compared to crystalline materials [21][22][23] . Furthermore, our recent study has suggested that Ag diffusion via HEGB is the dominant path for diffusion in unirradiated SiC 24 .…”