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