Surface diffusion of H on Ni(100): Interpretation of the transition temperature (original) (raw)
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Quantum diffusion of hydrogen and deuterium on nickel (100)
Surface Science, 1998
The diffusion constants of hydrogen and deuterium at low temperature are calculated using the surrogate Hamiltonian method and an embedded atom potential. A comparison with previous experimental and theoretical results is made. A crossover to temperature-independent tunneling occurs at 69 K for hydrogen and at 46 K for deuterium. An inverse isotope effect at intermediate temperatures is found, consistent with experiment. Deviations are found at low temperature where a large isotope effect is calculated.
Hydrogen transport in nickel (111)
Physical Review B, 1997
The intricate dynamics of hydrogen on a nickel ͑111͒ surface is investigated. The purpose is to understand the unique recombination reaction of subsurface with surface hydrogen on the nickel host. The analysis is based on the embedded diatomics in molecules many-body potential surface. This potential enables a consistent evaluation of different hydrogen pathways in the nickel host. It is found that the pathway to subsurfacesurface hydrogen recombination involves crossing a potential-energy barrier. Due to the light mass of the hydrogen the primary reaction route at low temperature occurs via tunneling. A critical evaluation of tunneling dynamics in a many-body environment has been carried out, based on a fully quantum description. The activated transport of subsurface hydrogen to a surface site, the resurfacing event, has been studied in detail. It is shown that the tunneling dynamics is dominated by correlated motion of the hydrogen and the nickel hosts. A fully correlated quantum-dynamical description in a multimode environment was constructed and employed. The ''surrogate Hamiltonian method'' represents the nickel host effect on the hydrogen dynamics as that of a set of two-level systems. The spectral density, which is the input of the theory is obtained via classical molecular-dynamics simulations. The analysis then shows that the environment can both promote and hinder the tunneling rate by orders of magnitude. Specifically for hydrogen in the nickel host, the net effect is suppression of tunneling compared to a frozen lattice approximation. The added effect of nonadiabatic interactions with the electron-hole pairs on the hydrogen tunneling rate was studied by an appropriate ''surrogate Hamiltonian'' with the result of a small suppression depending on the electron density of nickel. The resurfacing rates together with surface recombination rates and relaxation rates were incorporated in a kinetic model describing thermal-desorption spectra. Conditions for a thermal-programmed-desorption peak which manifest the subsurface-surface hydrogen recombination were found.
The Journal of Chemical Physics, 2001
Recent experiments by Lauhon and Ho using scanning tunneling microscopy ͑STM͒ observed the direct hopping of H and D on Cu͑001͒ as a function of temperature. They found nearly temperature independent tunneling for H below 60 K, but could not detect the tunneling threshold for D ͑it is at least 1000 times lower than for H͒. The availability of such direct and accurate measurements provides the opportunity for validating the level of theory required to predict the diffusion of adsorbates on surfaces. Thus, we carried out density functional theory ͑DFT͒ using the generalized gradient approximation ͑GGA-II͒ on periodic slabs. The calculated tunneling rate of 4.74 ϫ10 Ϫ4 s Ϫ1 for H is in close agreement with the experimental value of 4.4ϫ10 Ϫ4 s Ϫ1 . We predict 4.66ϫ10 Ϫ9 s Ϫ1 for the tunneling rate of D ͑one hop every 83 months!͒. Between 60 and 80 K, the calculated thermally activated diffusion rate of H is 10 12.88 exp(Ϫ0.181 eV/kT͒ s Ϫ1 in close agreement with the STM value: 10 12.9Ϯ0.3 exp(Ϫ0.197 eV/kT). For deuterium, between 50 and 80 K, the calculated rate is 10 12.70 exp(Ϫ0.175 eV/kT͒ s Ϫ1 in close agreement with the STM value: 10 12.7Ϯ0.2 exp(Ϫ0.194 eV/kT͒ s Ϫ1 . These results validate that such first principles theory can be used to predict the diffusion ͑including tunneling͒ for adsorbates on surfaces, providing important data needed to unravel surface processes in catalysis and crystal growth.
Temperature-Dependent Diffusion Coefficients from ab initio Computations: Hydrogen in Nickel
2006
The temperature-dependent diffusion coefficients of interstitial hydrogen, deuterium, and tritium in nickel are computed using transition state theory. The coefficient of thermal expansion, the enthalpy and entropy of activation, and the pre-exponential factor of the diffusion coefficient are obtained from ab initio total energy and phonon calculations including the vibrations of all atoms. Numerical results reveal that diffusion between octahedral interstitial sites occurs along an indirect path via the metastable tetrahedral site and that both the migration enthalpy and entropy are strongly temperature dependent. However, the migration enthalpy and entropy are coupled so that the diffusion coefficient is well described by a constant activation energy, i.e., D = D 0 exp͓−Q / ͑RT͔͒, with Q = 45.72, 44.09, and 43.04 kJ/ mol and D 0 = 3.84ϫ 10 −6 , 2.40ϫ 10 −6 , 1.77 ϫ 10 −6 m 2 s −1 for H, D, and T, respectively. The diffusion of deuterium and tritium is computed to be slower than that of hydrogen only at temperatures above 400 K. At lower temperatures, the order is reversed in excellent agreement with experiment. The present approach is applicable to atoms of any mass as it includes the full coupling between the vibrational modes of the diffusing atom with the host lattice.
Diffusion of small Cu islands on the Ni(111) surface: A self-learning kinetic Monte Carlo study
Surface Science, 2017
We elucidate the diffusion kinetics of a heteroepitaxial system consisting of twodimensional small (1-8 atoms) Cu islands on the Ni(111) surface at (100-600) K using the Self-Learning Kinetic Monte Carlo (SLKMC-II) method. Study of the statics of the system shows that compact Cu N (3≤N≤8) clusters made up of triangular units on fcc occupancy sites are the energetically most stable structures of those clusters. Interestingly, we find a correlation between the height of the activation energy barrier and the location of the transition state (TS). The activation-energy barriers (of processes for Cu islands on the Ni(111) surface are in general smaller than those of their counterpart Ni islands on the same surface. We find this difference to correlate with the relative strength of the lateral interaction of the island atoms in the two systems. While our database consists of hundreds of possible processes, we identify and discuss the energetics of those that are the most dominant, or are rate-limiting, or most contributory to the diffusion of the islands. Since the energy barriers of single-and multi-atom processes that convert compact island shapes into non-compact ones (owing to a significantly smaller barrier for their reverse processes) are larger than that for the collective (concerted) motion of the island, the later dominate in the system kinetics-except for the cases of the dimer, pentamer and octamer. Short-jump involving one atom, long jump dimer-shearing, and long-jump corner shearing (via a single-atom) are, respectively, the dominating processes in the diffusion of the dimer, pentamer and octamer. Furthermore single-atom corner-rounding and edge-shearing are, respectively, the rate limiting processes for the pentamer and the octamer. Comparison of the energetics of selected processes and lateral interactions obtained from semi-empirical interatomic potentials with those from density functional theory show minor quantitative differences and overall qualitative agreement.
Stability of adsorbed states and site-conversion kinetics: CO on Ni(100)
Physical Review B, 1994
The site conversion of adsorbed CO between the terminal site and the bridged site on Ni(100) was studied by means of infrared reflection absorption spectroscopy (IRAS). The temperature dependence of the relative occupation for two sites was measured from 80 to 266 K in detail, where the binding-energy difference was determined to be 11 meV. The driving force for the predominant occupation of the terminal site at higher temperature is ascribed to the vibrational entropy of the low-energy degeneratehindered translational mode of the terminal CO. The kinetics of approaching the equilibrium was studied by time-resolved IRAS combined with a pulsed gas dose. Following a rapid dose, CO molecules are initially adsorbed at the terminal site and the bridged site with the a priori ratio of 1:2, indicating that gas-phase CO molecules are directly trapped by the potential minima initially, are thermalized, and migrate on the surface to approach the equilibrium occupation ratio. The microscopic hopping rate from the terminal site to the bridged site was estimated to be 0.02 s and that from the bridged site to the terminal site was estimated to be 0.005 s at 83 K. A random-walk model assuming the microscopic hopping rates gives a self-diffusion coefficient of 3. 1X10 ' cm s ' at 83 K, which is in good agreement with the previously reported macroscopic results. Thus, the elementary step of surface diffusion is ascribed to the hopping between the terminal site and the bridged site. The difference between the estimated barrier by assuming a harmonic potential and the activation energy for diffusion suggests the presence of anharmonicity in the potential between the terminal site and the bridged site.
Physical Review B, 2013
We have examined the self-diffusion of small 2D Ni islands (consisting of up to 10 atoms) on the Ni(111) surface using a self-learning kinetic Monte Carlo (SLKMC-II) method with an improved pattern-recognition scheme that allows inclusion of both fcc and hcp sites in the simulations. Activation energy barriers for the identified diffusion processes were calculated on the fly using a semiempirical interaction potential based on the embedded-atom method. Although a variety of concerted, multiatom, and single-atom processes were automatically revealed in our simulations, we found that, in the temperature range of 300 K-700 K, these small islands diffuse primarily via concerted motion. Single-atom processes play an important role in ensuring that diffusion is random for islands containing 5 or more atoms, while multiatom processes (shearing and reptation) come into play for noncompact islands. The effective activation energy barriers obtained from the Arrhenius plot of the diffusion coefficients showed an increase with the size of the island, although there were interesting deviations from linear dependence. Several other processes also contributing to diffusion of islands were identified.
Finite temperature quantum distribution of hydrogen adsorbate on nickel (001) surface
Surface Science, 2006
Finite temperature quantum behavior of hydrogen and deuterium adsorbates on Ni(0 0 1) surface has been simulated using path-integral Monte Carlo technique. The adsorbate-surface interaction is described by the many-body alloy potential form, fitted to the adsorption parameters from DFT calculations. This allows consideration of substrate atom dynamics. Temperatures 100 K and 300 K have been considered and contribution of the thermal motion of Ni surface atoms is analyzed.
Theory of Surface Diffusion: Crossover from Classical to Quantum Regime
Physical Review Letters, 1994
A theory is developed for adatom diffusion on surfaces, employing the memory function formalism. The diffusion constant is expressed in terms of static correlation functions which are computed via Monte Carlo path integrations. Our theory is valid at all temperatures in the high friction limit and indicates a sharp crossover from the classical Arrhenius regime at high temperatures to the quantum tunneling regime at low temperatures. Comparisons with experimental data are presented for the H/Ni(100) system.
A simulation study of the chemisorption dynamics of molecular hydrogen on the Ni(111) surface
Surface Science, 1996
The dissociative chemisorption of an H 2 beam on the Ni(lll) surface was simulated by running quasi classical trajectories, using for the molecule-surface interaction a LEPS potential built from ab initio results available for the H atom interacting with Ni clusters. The adsorption of H 2 is an activated process, with barrier of 200 meV in the entrance channel, followed by a non-dissociative chemisorpfion well in the exit channel which is separated by a narrow saddle point region from the well of adsorbed H atoms. In the rigid surface approximation, the dependence of the dissociative chemisorption probability, Pa, on the H 2 collision energy, Eco 1, is described by an S-shaped curve. When the nickel atoms of the impact region of H 2 at the surface are allowed to move (generalized Langevin equations in the ghost atoms formulation were used), Pa increases with Eco I along a smooth curve comparable to that observed in molecular beam experiments. The results of a study of the influence on Pa of the H 2 internal and translational energies, of the surface temperature, of the beam incident angle and of the surface corrugation are presented and discussed.