Interplay of superconductivity and magnetism in strong coupling

A model is introduced describing the interplay between superconductivity and spin-ordering. It is characterized by on-site repulsive electron-electron interactions, causing antiferromagnetism, and nearest-neighbor attractive interactions, giving rise to d-wave superconductivity. Due to a special choice for the lattice, this model has a strong-coupling limit where the superconductivity can be described by a bosonic theory, similar to the strongly coupled negative U Hubbard model. This limit is analyzed in the present paper. A rich mean-field phase diagram is found and the leading quantum corrections to the mean-field results are calculated. The first-order line between the antiferromagnetic- and the superconducting phase is found to terminate at a tricritical point, where two second-order lines originate. At these lines, the system undergoes a transition to- and from a phase exhibiting both antiferromagnetic order and superconductivity. At finite temperatures above the spin-disordering line, quantum-critical behavior is found. For specific values of the model parameters, it is possible to obtain SO(5) symmetry involving the spin- and the phase-sector at the tricritical point. Although this symmetry is explicitly broken by the projection to the lower Hubbard band, it survives on the mean-field level, and modes related to a spontaneously broken SO(5) symmetry are present on the level of the random phase approximation in the superconducting phase.Comment: 16 pages Revtex, 5 figure

Multiparadigm modeling of dynamical crack propagation in silicon using a reactive force field

We report a study of dynamic cracking in a silicon single crystal in which the ReaxFF reactive force field is used for several thousand atoms near the crack tip, while more than 100 000 atoms are described with a nonreactive force field. ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. Our results reproduce experimental observations of fracture in silicon including changes in crack dynamics for different crack orientations

Quantization of Crack Speeds in Dynamic Fracture of Silicon: Multiparadigm ReaxFF Modeling

We report a study of dynamic cracking in a silicon single crystal in which the ReaxFF reactive force field is used for about 3,000 atoms near the crack tip while the other 100,000 atoms of the model system are described with a simple nonreactive force field. The ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. This model has been successfully used to study crack dynamics in silicon, capable of reproducing key experimental results such as orientation dependence of crack dynamics (Buehler et al., Phys. Rev. Lett. 2006). In this article, we focus on crack speeds as a function of loading and crack propagation mechanisms. We find that the steady state crack speed does not increase continuously with applied load, but instead jumps to a finite value immediately after the critical load, followed by a regime of slow increase. Our results quantitatively reproduce experimental observations of crack speeds during fracture in silicon along the (111) planes, confirming the existence of lattice trapping effects. We observe similar effects in the (110) crack direction

Threshold Crack Speed Controls Dynamical Fracture of Silicon Single Crystals

Fracture experiments of single silicon crystals reveal that after the critical fracture load is reached, the crack speed jumps from zero to [approximate]2 km/sec, indicating that crack motion at lower speeds is forbidden. This contradicts classical continuum fracture theories predicting a continuously increasing crack speed with increasing load. Here we show that this threshold crack speed may be due to a localized phase transformation of the silicon lattice from 6-membered rings to a 5–7 double ring at the crack tip

Modeling the sorption dynamics of NaH using a reactive force field

We have parametrized a reactive force field for NaH, ReaxFFNaH, against a training set of ab initio derived data. To ascertain that ReaxFFNaH is properly parametrized, a comparison between ab initio heats of formation of small representative NaH clusters with ReaxFFNaH was done. The results and trend of ReaxFFNaH are found to be consistent with ab initio values. Further validation includes comparing the equations of state of condensed phases of Na and NaH as calculated from ab initio and ReaxFFNaH. There is a good match between the two results, showing that ReaxFFNaH is correctly parametrized by the ab initio training set. ReaxFFNaH has been used to study the dynamics of hydrogen desorption in NaH particles. We find that ReaxFFNaH properly describes the surface molecular hydrogen charge transfer during the abstraction process. Results on heat of desorption versus cluster size shows that there is a strong dependence on the heat of desorption on the particle size, which implies that nanostructuring enhances desorption process. To gain more insight into the structural transformations of NaH during thermal decomposition, we performed a heating run in a molecular dynamics simulation. These runs exhibit a series of drops in potential energy, associated with cluster fragmentation and desorption of molecular hydrogen. This is consistent with experimental evidence that NaH dissociates at its melting point into smaller fragments

Predictions of melting, crystallization, and local atomic arrangements of aluminum clusters using a reactive force field

A parametrized reactive force field model for aluminum ReaxFFAl has been developed based on density functional theory (DFT) data. A comparison has been made between DFT and ReaxFFAl outputs to ascertain whether ReaxFFAl is properly parametrized and to check if the output of the latter has correlation with DFT results. Further checks include comparing the equations of state of condensed phases of Al as calculated from DFT and ReaxFFAl. There is a good match between the two results, again showing that ReaxFFAl is correctly parametrized as per the DFT input. Simulated annealing has been performed on aluminum clusters Aln using ReaxFFAl to find the stable isomers of the clusters. A plot of stability function versus cluster size shows the existence of highly stable clusters (magic clusters). Quantum mechanically these magic clusters arise due to the complete filling of the orbital shells. However, since force fields do not care about electrons but work on the assumption of validity of Born–Oppenheimer approximation, the magic clusters are therefore correlated with high structural symmetry. There is a rapid decline in surface energy contribution due to the triangulated nature of the surface atoms leading to higher coordination number. The bulk binding energy is computed to be 76.8 kcal/mol. This gives confidence in the suitability of ReaxFF for studying and understanding the underlying dynamics in aluminum clusters. In the quantification of the growth of cluster it is seen that as the size of the clusters increase there is preference for the coexistence of fcc/hcp orders at the expense of simple icosahedral ordering, although there is some contribution from distorted icosahedral ordering. It is found that even for aluminum clusters with 512 atoms distorted icosahedral ordering exists. For clusters with N≥256 atoms fcc ordering dominates, which implies that at this point we are already on the threshold of bulklike bonding

Parametrization of a reactive force field for aluminum hydride

A reactive force field, REAXFF, for aluminum hydride has been developed based on density functional theory (DFT) derived data. REAXFF_(AlH_3) is used to study the dynamics governing hydrogen desorption in AlH_3. During the abstraction process of surface molecular hydrogen charge transfer is found to be well described by REAXFF_(AlH_3). Results on heat of desorption versus cluster size show that there is a strong dependence of the heat of desorption on the particle size, which implies that nanostructuring enhances desorption process. In the gas phase, it was observed that small alane clusters agglomerated into a bigger cluster. After agglomeration molecular hydrogen was desorbed from the structure. This thermodynamically driven spontaneous agglomeration followed by desorption of molecular hydrogen provides a mechanism on how mobile alane clusters can facilitate the mass transport of aluminum atoms during the thermal decomposition of NaAlH_4