Question

A copper-nickel diffusion couple is annealed at 1025 C for 100 hours. The specimen is partially sectioned into sequential thin layers, each of 50 micrometers thick, located around the original Cu/Ni interface. The sections are analyzed using an electron microprobe with the following results:

Section Number	Atomic Percent Cu
1	100
2	100
3	100
4	99.5
5	99.0
6	98.3
7	97.0
8	94.5
9	90.7
10	83.4
11	70.7
12	50.0
13	27.7
14	10.4
15	2.8
16	0.6
17	0.0
18	0.0

Determine the diffusion coefficient for Cu-Ni at 1025 C using the Boltzmann-Matano method.

Answer 1

Solution: Here it is required to calculate the diffusion coefficient for Cu/Ni at the given temperature of 1025 ^oC, using Boltzmann- Matano method.

Given that the copper-ni couple is annealed for 100 hours.

taken, t = 100 hours

will convert the given t in seconds as:

Also it is given that the specimen is partially sectioned into sequential thin layers,

the thickness of each layer = x* (say) = 50 m (given)

The relation for diffusion by the Boltzmann -Matano method in the simplified form for each section is given as:

;

Here, D(wt) = diffusion for each section, in m²/s, at different atomic wt % of Cu.

C = is the atomic percent of Cu for each section

x = thickness of each section

t = time in seconds for annealing at the given temperature of 1025 ^oC.

The parameter , indicates that for the every concentration distribution in terms of atomic percent of Cu, will have a fixed value, and is given as Boltzmann parameter. the Boltzmann parameter , can be given as:

;

This suggests that every concentration in the region of inter-diffusion will move in such a way that the Boltzmann parameter , will be constant for each section.

Calculating the diffusion for section 1 as:

the thickness of each layer = x* (say) = 50 m (given)

Here 100 is the atomic percent of section 1, (given)

................................(i)

Similarly for section 2,

the thickness of each layer = x* (say) = 50 m (given)

Here 100 is the atomic percent of section 2, (given)

.................................(ii)

Similarly for section 3,

the thickness of each layer = x* (say) = 50 m (given)

Here 100 is the atomic percent of section 3, (given)

..........................(iii)

Similarly for section 4,

the thickness of each layer = x* (say) = 50 m (given)

Here 99.5 is the atomic percent of section 4, (given)

............................(iv)

Similarly for section 5,

the thickness of each layer = x* (say) = 50 m (given)

Here 99 is the atomic percent of section 5, (given)

............................(v)

..................

similarly calculating Diffusion for all the different sections given and get the value as:

............................(vi)

............................(vii)

............................(viii)

............................(ix)

............................(x)

............................(xi)

............................(xii)

............................(xiii)

............................(xiv)

............................(xv)

............................(xvi)

The value for the diffusion coefficient for 0 percent of Cu, in sections 17 and section 18 will not be calculated out.

Now adding the values of diffusion of all the sections, value (i) to value (xvi) are added, to get:

Diffusion coefficient = 2.21797 x10^-15 m²/s

we get the Total diffusion of Cu-Ni at the given temperature of 1025 ^oC, using Boltzmann- Matano method, when annealed for 100 hrs, with a section of 50 micrometer each is 2.21797 x10^-15 m²/s

...........................................................................................................................................................