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Sputtering, Impact threshold energy
In this example we estimate the fraction of oxygen atoms in the atmosphere at 350 km altitude that have sufficient energy to induce sputtering on Ag and Al. Assume a Maxwellian distribution of oxygen. In order for sputtering to occur, the impact energy must exceed a threshold which is proportional to the binding energy of a surface atom to its neighbors Assume the binding energy U of a surface atom is 48 eV for Ag and 3.4 eV for Al.
clc;clear all; % Given: % Atomic Mass M_Al = 26.98; %[amu] M_Ag = 107.87; %[amu] M_O = 16; %[amu] amu = 1.66053892e-27; %[kg] ev = 1.60217657e-19; %[J] mu = 398600; %Standard gravitational parameter [km^3s-2] kb = 1.3806488e-23; %[JK-1] Boltzmann constant Re = 6378; %Earth Radius[km] Alt = 350; %[km] T = 900; %[K] % Binding energy U of a surface atom U_Al = 3.4; U_Ag = 48;
Because M_O/M_Al > 0.3 for impacting O of mass mi on a target Al atom of mass mt the energy threshold Eth to induce sputtering is
E_th_Al = 8 *U_Al*(M_O/M_Al)^0.4;
fprintf('Energy threshold of oxygen atoms to induce sputtering on Al Eth = %4.2f eV\n',E_th_Al);
Energy threshold of oxygen atoms to induce sputtering on Al Eth = 22.07 eV
Because M_O/M_Ag <= 0.3 for impacting O of mass mi on a target Ag atom of mass mt the energy threshold Eth to induce sputtering is
gamma= 4*M_O*M_Ag/(M_O+M_Ag)^2; E_th_Ag = U_Ag/gamma/(1 - gamma); fprintf('Energy threshold of oxygen atoms to induce sputtering on Ag Eth = %4.2f eV\n',E_th_Ag); % In order to sputtering to occur, the impacting atom need to have a 1D % velocity such that V_Al = (2*E_th_Al*ev/(M_O*amu))^0.5/1000; %[km/s] V_Ag = (2*E_th_Ag*ev/(M_O*amu))^0.5/1000; %[km/s] % Spacecraft velocity around Earth V_sc = (mu/(Re + Alt))^0.5; % Minimum impact velocity relative to spacecraft V_Alr = V_Al - V_sc %[km/s] V_Agr = V_Ag - V_sc
Energy threshold of oxygen atoms to induce sputtering on Ag Eth = 193.94 eV V_Alr = 8.6179 V_Agr = 40.6672
Fraction of O that will induce sputtering on Al belongs to an interval [f_min, f_max]
x = (M_O*amu/(kb*T))^0.5*V_Alr*1000;
f_min = 1/(2*pi)^0.5*exp(-x^2/2)*(1/x - 1/x^3);
f_max = 1/(2*pi)^0.5*exp(-x^2/2)*1/x;
fprintf('%4.3d < Oxygen fraction that will induce sputtering on Al < %4.3d \n',f_min, f_max)
1.036e-036 < Oxygen fraction that will induce sputtering on Al < 1.042e-036
Fraction of O that will induce sputtering on Ag belongs to an interval [f_min, f_max]
x = (M_O*amu/(kb*T))^0.5*V_Agr*1000;
f_min = 1/(2*pi)^0.5*exp(-x^2/2)*(1/x - 1/x^3);
f_max = 1/(2*pi)^0.5*exp(-x^2/2)*1/x ;
fprintf('%4.3d < Oxygen fraction that will induce sputtering on Ag < %4.3d \n',f_min, f_max)
000 < Oxygen fraction that will induce sputtering on Ag < 000