Simulation Study On Nucleation And Growth Of Hydrogen Crystal

Today, the energy problem has become one of the important constraint factors for the country’s economic growth and the society’s long-term development strategy targets. Thermonuclear fusion with deuterium(D) and tritium(T) of hydrogen isotopes is considered to be the most effective way to solve the human energy problem, and the inertial confinement fusion(ICF) is expected to generate electricity by fusion power plant in the near future. The frozen target of hydrogen isotopes molecule crystals(hydrogen crystals for short), as the ICF core device, its surface smooth degree and uniformity are critical to the behaviors of the target in the fusion reaction. Therefore, it is very important to fully understand the growth mechanism of hydrogen molecule(H2) crystals and the various properties, especially the effect of the surface structures of cladding materials on the nucleation and growth of hydrogen molecule crystals. Beryllium(Be) and copper(Cu) are the representatives of the meal cladding materials of frozen targets. The properties of defects in hydrogen crystals, the adsorption and dissociation of H2 on Be(0001) and Cu(111) surfaces have been investigated by the VASP code based on the first-principles method. Then the interaction of H2 molecules has been fitted by the molecular method. The nucleation and growth mechanism of H2 crystals on the Be(0001) surface have been studied by the developed interactions of H2 and the potentials of the Be-H2 interactions in references. The main results are as follows:1. The formation energies and the stable structures of vacancy and self-interstitial defects in hydrogen crystals were investigated using ab initio calculations based on density functional theory. The results show that the formation energy of a vacancy is dependent on molecule orientation in disordered hexagonal close-packed(hcp) H2 crystals, but independent of molecular orientation in face-centered cubic-Pa3 H2. For self-interstitial defects, H2 molecules generally prefer to occupy the basal octahedral sites, and the formation energy of an interstitial H2 depends sensitively on the volume of interstitial sites, and also on near spatial distributions of molecular axes of H2 molecules in hcp H2 crystals. In some cases, the strong force field introduced by an interstitial H2 might induce the rotation of molecular axes and greatly reduce the formation energy of the interstitial H2. However, interstitial H2 molecules prefer to occupy the octahedral sites in Pa3 hydrogen crystals, and the formation energies of interstitial H2 are slightly affected by their molecular axes, which mean that the molecular axes of interstitial H2 have weaker influence on their stabilities in Pa3 than in hcp structure.2. The climbing image nudged elastic band(CI-NEB) method was used to analyze the migration behaviors of single vacancies and interstitial H2 in hcp and Pa3 H2 crystals. Five different migration paths of a vacancy between two nearest neighbor sites were calculated in disordered hcp H2 crystals. The results show that the functions of the migration energies as relative path distance for the five paths are similar, and the average migration barrier energy is about 13.5 meV. A few vacancy migration paths were also investigated in Pa3 H2 crystals. It was found that the vacancy migration in Pa3 H2 crystals is identical and the barrier energy of a vacancy is about 19 meV. For the migration behaviors of an interstitial H2, the O-T-O and O-O jumps are possibilities in Pa3 H2 crystals, and the rotation of molecular axes enhances the migration barrier energy. In disordered hcp H2 crystals, the BO1-BT-BO2 jump on the basal plane is more favorable for interstitial diffusion. However, the migration energy barrier of an interstitial H2 is larger than a vacancy in both hcp and Pa3 H2 crystals.3. The interactions of hydrogen molecules and Be(0001) surfaces have been studied by using density functional theory based first-principles calculations. The parallel and vertical configurations of H2 at four high symmetry positions(bri、fcc、hcp、top) on Be(0001) surface were discussed in detail and the results show that H2 adsorption on the Be(0001) surface is a weak physisorption and hydrogen atom adsorption is a strong chemisorption. The dissociation or not of H2 depends mainly on the initial distance from H2 to the surface(hH)) and the distributions of molecular axes of H2. The critical dissociation distance of vertical H2 adsorption(~0.6-0.8?) is found to be shorter than that of parallel H2 adsorption(~1.2-1.5?) on perfect Be(0001) surface. Interestingly, the parallel H2 adsorption along the [1120] direction on perfect Be(0001) surface is found to be stable without dissociation as hH from 0 to 4.0 ?. The dissociation barriers and the dissociated configurations of H2 depend on the initial H2 configurations and adsorption sites.4. Considering that the surface may actually be imperfect, the adsorption and dissociation behaviors of H2 on the vacancy-defective Be(0001) surface was investigated in this work. The results show that the vacancies destroyed the high symmetry of the surfaces and do have a notable effect on the behavior of H2 adsorption. The adsorption energies and the parameters of stable H2 structures have been changed somewhat, especially the H2 molecules axes rotate significantly except for the vertical adsorption at top sites. At the same time,the vacancy on the Be(0001) surface enhanced the interaction of H2 and the Be(0001) surface. The H2 dissociation energy barrier decreases significantly, which promotes the H2 dissociation. In addition, the favorable adsorption orientation of H2 was explored initially by putting four vertical H2 on 3×3-Be(0001) supercell unit surface. It was found that the H2 molecules tend to occupy the high symmetry position close to the surface at first when a large number of hydrogen molecules are adsorbed on Be(0001) surface, then grow up vertically on the surface.5. The adsorption and dissociation of hydrogen molecules on the Cu(111) surface have been studied by using DFT calculations. The H2 molecules of vertical adsorption on Cu(111) are not dissociated for the initial hH of 0.3-4.0 ?, and the undissociated H2 are physically adsorbed on the Cu(111) surface. When H2 molecules are adsorbed on Cu(111) surface in parallel, the dissociation of H2 depends mainly on the initial hH and the initial H2 configurations. The critical distance of H2 dissociation at bri sites is 1.35 ? for parallel adsorption along the ]112[ direction and 0.65-0.86 ? for other cases. Some H2 were dissociated into two hydrogen atoms, which occupy hcp or fcc sites and form three stable chemisorption structures on the Cu(111) surface(i.e. hcp+hcp、fcc+fcc、hcp+fcc). The dissociation barriers are different for the different initial adsorption structures. The dissociation barrier at top is the highest for parallel adsorption along the ]101[ direction, then fcc and hcp. But the order of the dissociation barriers is fcc, hcp, and bri from high to low for parallel adsorption along the ]112[ direction. Finally, the interactions of H2 and the vacancy-defective Cu(111) surface were investigated and we found that the influence of vacancy defects for the Cu(111) surface is similar to that of Be(0001) surface.6. Based on the analysis of the existed interaction potentials between isotropic hydrogen molecules, the energy formula of isotropic H2-H2 interactions have been developed by revising isotropic hydrogen intermolecular interactions. The corresponding parameters were fitted using the least square method and molecular dynamics methods. The revised interaction energy formula provides good descriptions for the pressure and the elastic modulus as a function of the volume of fcc and hcp hydrogen crystals at the temperature of 0 K, which are well consistent with the experimental values and the calculation values of quantum mechanics. The present zero-pressure molar volume and the cohesive energy per molecule in H2 crystals were found to be close to the experimental results. In addition, the formation energy of defects in H2 crystals were tested in two structures of H2 crystals and compared with the DFT calculation.7. The hydrogen molecules behaviors under different H2 concentrations and substrate temperatures on Be(0001) surface have been simulated using the present potentials and the interaction potentials of Be-H system in the literature. The influences of the substrate temperature and H2 concentration on the nucleation and growth of hydrogen crystals were analyzed. The results show that the hydrogen molecules start to form the crystal nucleus on Be(0001) surface with the increase of simulation time. Especially, with the number of hydrogen molecules increasing to 300, the hydrogen grains of hcp structure were obviously observed under the 0.5K of substrate temperature. It is consistent with the experiment results: hydrogen molecules grow in the directions perpendicular to the C-axis(i.e. parallel to the Be surface), then grow along the C-axis. The simulation results show that the nucleation and growth of hydrogen crystals are probably sensitive to the concentrations and gravity of hydrogen molecules, as well as substrate temperatures.