From the following data for the depth of oxidation of Ni metal particles in Al_2

Question

From the following data for the depth of oxidation of Ni metal particles in Al_2O_3 by exposure of the surface to dry air or water, Explain why the data is plotted as x^2 versus time. What is the oxidation depth in microns after exposure for 20 hours to dry air oxidation at 1250C versus 1300C? Why would the oxidation depth depend on temperature? The reaction steps include adsorption of oxygen on the surface, diffusion of oxygen along grain boundaries to the interior of the sample, and oxidation of Ni particles at the grain boundaries. If the slowest step is diffusion along grain boundaries, what equation would you use to model diffusion at 1300C after 20 hours this assuming the sample is 1 cm thick?

Explanation / Answer

a) x^2 (m^2) here refers to depth of oxidation of Ni in alumina by exposure to dry air,water.

According to fick’s second law ,concentration of diffused particle changes as per the equation,

Cx-Co/Cs-Co=1-erf(x/2(Dt)^1/2)

Cx=concentration of O2 at depth x,

Co=concentration of O2 at time,t=0 and depth 0</= x </= infinity

Cs=constant concentration at x=0

For a concentration C of O2,

Cx-Co/Cs-Co=1-erf(x/2(Dt)^1/2)=constant

Or, Squaring both sides, x^2/Dt=constant , D=diffusion coefficient.,t=time

X^2 vs t can be plotted.

b)from graph At T=1250 C,

x^2/t=slope =(6.0-2.0)*10^-9 m2/(3.5-1.75)*10^5 s=2.3*10^-14 m^2/s

at t=20 hr=20*3600s=72000s

X^2=const*t=2.3*10^-14 m^2/s * 72000s=8.2*10^-11 m^2/s=0.82*10^-10 m^2

X=sqrt(0.82*10^-10 m^2)=9.0*10^-6 m=9.0 micron

from graph at T=1300 C

x^2/t=slope =(7.25-5.5)*10^-9 m2/(5.25-5)*10^4 s=7*10^-13 m^/s

at t=20 hr=20*3600s=72000s

x^2= const*t=7*10^-13 m^/s*72000s=5.0*10^-8 m^2/s=50.0*10^-9 m^2/s

x=7.0*10^-6 =70*10^-6=7 micron

difference=9.0 micron-7.0 micron=2 micron

c)D=Do exp(-Qd/RT) where D= diffusion coefficient is a function of temperature.Higher the temperature more is the diffusion as the particles strikes the surface with higher energy.

d) to fick’s second law ,concentration of diffused particle changes as per the equation,

Cx-Co/Cs-Co=1-erf(x/2(Dt)^1/2)

Cx=concentration of O2 at depth x,

Co=concentration of O2 at time,t=0 and depth 0</= x </= infinity

Cs=constant concentration at x=0

For a concentration C of O2,

Cx-Co/Cs-Co=1-erf(x/2(Dt)^1/2)=constant

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