The Energetics of Hydrogen-Vacancy Clusters in BCC Iron
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The Energetics of Hydrogen-Vacancy Clusters in BCC Iron Erin Hayward1 and Chaitanya S. Deo1 1 Georgia Institute of Technology, Atlanta, GA 30332, U.S.A. ABSTRACT We present a general method for investigating the energetics of small impurity-vacancy clusters in crystalline materials. We use a combination of molecular dynamics and Monte Carlo methods to locate low energy configurations of the bubbles, from which the binding energies of various point defects can be determined. This method is applied to case of hydrogen bubbles in alpha-iron. Clusters with ratios of up to 10 hydrogen atoms to a vacancy are studied. We find that hydrogen does help to stabilize voids in alpha-iron, but that hydrogen is quite weakly bound to these voids. Ratios of up to approximately 4 can be supported at low temperatures. INTRODUCTION Materials, particularly those subject to irradiation, often contain impurities due to implantation, absorption, processing, or transmutation. These impurities may gather with point defects such as interstitials and vacancies to cause undesirable phenomena. When multiple vacancies cluster together, a void is formed. This void may be filled with impurity atoms, helping to stabilize it and forming a bubble. Bubbles are thought to related to such effects as embrittlement, hardening, and swelling. Small bubbles are difficult or impossible to study experimentally, but are of vital importance in understanding macroscopic phenomena. Atomistic methods can be used to gain insight into these structures. THEORY In order to calculate the energetics of a bubble accurately, its minimum energy state will ideally be known. For a cluster of m impurities and n vacancies (ImmVn), this is not a trivial task. Binding energies are on the order of 1-10 eV, so any deviation from the lowest energy configuration or contributions to energy from thermal motion will be significant. For an atomistic simulation, an appropriately sized simulation box is needed. The box must be large enough to fully encompass the bubble and avoid boundary or image effects, but be small enough to allow for reasonable processor time. Periodic boundary conditions are simple to implement and physically realistic for the simulation of a bubble in the bulk. Additionally, an appropriate interatomic potential must be specified. Initially, a vacancy is introduced into the center of the box, all atoms are minimized using some algorithm, and the energy is measured. Next, the atom with the highest potential energy is removed, and the system is again relaxed. This step is repeated until voids of the largest desired size are created, by removing the atoms with most energy. Due to symmetry, there will often be multiple atoms that meet this requirement. Void shapes will be determined by the characteristics of the interatomic potential used, but roughly spherical voids are generally expected. Void configurations of n vacancies will form the initial configurations into which impurities will be introduced.
For a void of a given size, a spherical region of an appropriate radi
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