WS No$1$: Diffusion The steady$-$state diffusion flux through a metal plate is $5\mathrm{.}4{10}^{-10}k\frac{g}{m^2}.$s at a temperature

of $727C$ and when the concentration gradient is $-350k\frac{g}{m^4}.$ Calculate the diffusion flux

at $1027C$ for the same concentration gradient and assuming an activation energy for

diffusion of $125K\frac{J}{m}ol.$

A sheet of steel $1\mathrm{.}5$ mm thick has nitrogen atmospheres on both sides at $1200C$ and is

permitted to achieve a steady$-$state diffusion condition. The diffusion coefficient for

nitrogen in steel at this temperature is $6{10}^{-11}\frac{m^2}{s},$ and the diffusion flux is found to be

$1\mathrm{.}2{10}^{-7}kg{m}^2.s.$ Also, it is known that the concentration of nitrogen in the steel at the

high$-$pressure surface is $4k\frac{g}{m^3}.$ How far into the sheet from this high$-$pressure side will

the concentration be is $2k\frac{g}{m^3}?$ Assume a linear concentration profile.

The purification of hydrogen gas by diffusion through a palladium sheet is performed.

Compute the number of kilograms of hydrogen that pass per hour through a $5$ mm thick

sheet of palladium having an area of $0\mathrm{.}2m^2$ at $500C.$ Assume a diffusion coefficient of

$1{10}^{-8}\frac{m^2}{s},$ that the concentrations at the high$-$ and low$-$pressure sides of the plate are

$2\mathrm{.}4$ and $0\mathrm{.}6$ kg of hydrogen per cubic meter of palladium, and that steady$-$state conditions

have been attained.

A sheet of BCC iron $1$ mm thick was exposed to a carburizing gas atmosphere on one

side and a decarburizing atmosphere on the other side at $725C.$ After having reached

steady state, the iron was quickly cooled to room temperature. The carbon concentrations

at the two surfaces of the sheet were determined to be $0\mathrm{.}012$ and $0\mathrm{.}0075wt\%.$ Compute

the diffusion coefficient if the diffusion flux is $1\mathrm{.}4{10}^{-1}k\frac{g}{m^2}.s.$ The densities of carbon and

iron are respectively $2\mathrm{.}25\frac{g}{c}\frac{m^3}{?}$ and $7\mathrm{.}87\frac{g}{c}{m}^3.$

Determine the carburizing time necessary to achieve a carbon concentration of $0\mathrm{.}45wt\%$

at a position $2$ mm into an iron$-$carbon alloy that initially contains $0\mathrm{.}2wt\%C.$ The surface

concentration is to be maintained at $1\mathrm{.}3wt\%C,$ and the treatment is to be conducted at

$1000C.$ Use the diffusion data for $-Fe$ from the table.

For a steel alloy it has been determined that a carburizing heat treatment of $10$ hrs

duration will raise the carbon concentration to $0\mathrm{.}45wt\%$ at a point $2\mathrm{.}5$ mm from the

surface. Estimate the time necessary to achieve the same concentration at a $5$ mm

position for an identical steel and at the same carburizing temperature.

Calculate the values of the diffusion coefficients for the interdiffusion of carbon in both $-$

iron $($BCC$)$ and $-$iron $($FCC$)$ at $900C.$ Which is greater? Justify your answer.

At which temperature will the diffusion coefficient for the diffusion of copper in nickel have

a value of $6\mathrm{.}5{10}^{-17}\frac{m^2}{s}.$