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Register a new userOxygen-covered tungsten crystal shape: time effects, equilibrium, surface energy and the edge-rounding temperature
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Added by
Andrzej Szczepkowicz
Publication date
2011
fields
Physics
and research's language is
English
Authors
Andrzej Szczepkowicz
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The equilibrium crystal shape (ECS) of oxygen-covered tungsten micricrystal is studied as a function of temperature. The specially designed ultrafast crystal quenching setup with the cooling rate of 6000 K/s allows to draw conclusions about ECS at high temperatures. The edge-rounding transition is shown to occur between 1300 K and 1430 K. The ratio of surface free energies $gamma(111)/gamma(211)$ is determined as a function of temperature.
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Equilibrium crystal shape of oxygen-covered tungsten is followed as a function of temperature using field ion microscopy. In the vicinity of the (111) region, at the temperature $970pm70$ K, the system undergoes a phase transition from a polyhedral form (sharp edges and sharp vertex) to a rounded form (sharp edges, rounded vertex).
We investigate the approach to stable and metastable equilibrium in Ising models using a cluster representation. The distribution of nucleation times is determined using the Metropolis algorithm and the corresponding $phi^{4}$ model using Langevin dynamics. We find that the nucleation rate is suppressed at early times even after global variables such as the magnetization and energy have apparently reached their time independent values. The mean number of clusters whose size is comparable to the size of the nucleating droplet becomes time independent at about the same time that the nucleation rate reaches its constant value. We also find subtle structural differences between the nucleating droplets formed before and after apparent metastable equilibrium has been established.
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In standard nucleation theory, the nucleation process is characterized by computing $DeltaOmega(V)$, the reversible work required to form a cluster of volume $V$ of the stable phase inside the metastable mother phase. However, other quantities besides the volume could play a role in the free energy of cluster formation, and this will in turn affect the nucleation barrier and the shape of the nucleus. Here we exploit our recently introduced mesoscopic theory of nucleation to compute the free energy cost of a nearly-spherical cluster of volume $V$ and a fluctuating surface area $A$, whereby the maximum of $DeltaOmega(V)$ is replaced by a saddle point in $DeltaOmega(V,A)$. Compared to the simpler theory based on volume only, the barrier height of $DeltaOmega(V,A)$ at the transition state is systematically larger by a few $k_BT$. More importantly, we show that, depending on the physical situation, the most probable shape of the nucleus may be highly non spherical, even when the surface tension and stiffness of the model are isotropic. Interestingly, these shape fluctuations do not influence or modify the standard Classical Nucleation Theory manner of extracting the interface tension from the logarithm of the nucleation rate near coexistence.
Nonperturbative expressions are derived for the angular resolved energy transfer spectra in the quantum regime of multiphonon scattering of inert gas atoms from surfaces. Application to He atom scattering from a prototype heatbath Xe/Cu(111) shows good agreement with experiments. This enables a full quantum calculation of the total energy transfer $mu$ and therefrom the much debated recovery or equilibrium temperature $T_{r}$ characteristic of zero energy transfer in gas-surface collisions in the free molecular flow regime. Classical universal character of $mu$ and $T_{r}$ is refuted.
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