Iain D. Boyd and Brandon Smith Department of Aerospace Engineering University of Michigan Ann Arbor, MI Molecular Dynamics Simulation of Sputtering and Pathway for Use in Thruster and Plume Analyses

Background (1) Electric propulsion (EP): –being implemented in various forms by DOD, NASA, and industry for several functions –due to lower thrust compared to chemical propulsion systems, EP thruster operation time requirements are much longer (e.g. 10,000 hours)

Background (2) EP thruster erosion: –arises from accelerated ions impacting thruster walls and causing sputtering –leads to beam divergence and performance degradation –can lead to thruster failure –enormously expensive to study experimentally

Sputter Modeling Objective: –to accurately calculate sputter yields for boron nitride under low energy xenon ion impacts Motivation: –erosion of BN channel walls is main life-limiter for Hall thrusters –no measurements of sputter yield exist for BN at Xe+ energies below 100 eV –this region of the sputter yield profile has a large influence on Hall thruster erosion

Binary collision approximation (BCA) –Monte-Carlo approach to model molecular systems –not well suited for low-energy regimes –sputter yields highly sensitive to binding energy Molecular dynamics (MD) –slower than BCA method –provides greater accuracy and more detail Modeling Approach

Boron nitride interatomic potentials –modified version of Tersoff potential proposed by Albe et al. r ij is the distance between particle i and particle j f c is a cutoff function which limits the interaction range f R is the repulsive component of the force f A is the attractive component of the force b ij incorporates bond stretching and bending terms B-N Interaction

Repulsion and attraction terms B-N Potential

Bond bending and stretching terms –Attraction term modifier –Sum over all three-body sites –Bond bending term –Bond stretching term i j k  jik r ik r ij k' k'' BN Bond Modeling

Xenon ion interatomic potential –Purely repulsive shielded Molière potential a F is the Firsov screening length, based on Bohr radius –Purely repulsive force is acceptable since van der Waals interaction of Xe with B or N is much weaker than the strength of BN covalent bonds Xe-B/N Interaction

Consider hexagonal BN: –has structure akin to graphite: hexagonal sheets –5200 boron and nitride atoms modeled as 13 10x10 hexagon sheets in a 4.3 nm x 4.2 nm x 2.5 nm box –periodic boundary conditions applied in the lateral directions –bottommost layer kept immobile to prevent translation BN Structural Model

Amorphized layer: –after a number of ion impacts, the near surface region of the BN block becomes amorphized –reduces effect of crystal orientation on sputtering –once a steady state is reached, generate sputter yield statistics beginning from this state instead of starting from initial ordered structure BN Surface Topology

Sputtering Event

Sputter Yield T w =423 K; Xe+:  =45 deg.

Reflected Xe Properties T w =423 K; Xe:  =50 eV,  =45 deg.

Pathway for Analysis Of Thruster and Plume Large computational database to be generated: –variation of xenon impact energy and angle –output of nonequilibrium probability density functions: properties of reflected xenon particles (accommodation) properties of sputtered products (B, N, BN, etc.) required for use in thruster plasma analysis simulations also needed for plume contamination assessment Validation: –measurements of differential sputter yield (Yalin, CSU) –need to characterize nonequilibrium material effects –measurements of BN plume transport (Gallimore, UM)

Plume Simulation BN Xe+