A common hardening process is called carburizing. The metal is exposed to carbon
ID: 3550561 • Letter: A
Question
A common hardening process is called carburizing. The metal is exposed to carbon, which diffuses into the metal, making it harder. This is a very slow process at low temperatures, but it can be accelerated by heating the metal. The diffusivity is a measure of how fast diffusion occurs and can be modeled as
D=D_(0)exp((-Q)/(RT))
Where
D : Diffusivity, cm2/s
D0: Diffusion coefficient, cm2/s
Q : activation energy J/mol
R : ideal gas constant 8.314 J/mol K
T : temperature, K.
The values of D0 and Q for material A and B are:
Type of metal
D0
Q (J/mol K)
A
0.0062
80000
B
0.23
148000
Create a plot of diffusivity versus inverse temperature (1/T), using the data provided. Try the rectangular, semilog and log-log plots to represent results. Let the temperature to vary from room temperature (25 C) to 1200C.
Type of metal
D0
Q (J/mol K)
A
0.0062
80000
B
0.23
148000
Explanation / Answer
D0=[0.0062,0.23];
Q=[8e+4,148e+3];
R=8.314;
T=linspace(25,1200,1000);
figure(1)
title('for material A,diffusivity vs inverse temperature');
D=D0(1)*exp(-Q(1)./(R*T));
plot(1./T,D);
xlabel('inverse temeprature')
ylabel('diffusivity')
figure(2)
title('for material B,diffusivity vs inverse temperature');
D=D0(2)*exp(-Q(2)./(R*T));
plot(1./T,D);
xlabel('inverse temeprature')
ylabel('diffusivity')
figure(3)
title('for material A,diffusivity vs inverse temperature');
D=D0(1)*exp(-Q(1)./(R*T));
semilogx(1./T,D);
xlabel('inverse temeprature')
ylabel('diffusivity')
figure(4)
title('for material B,diffusivity vs inverse temperature');
D=D0(2)*exp(-Q(2)./(R*T));
semilogx(1./T,D);
xlabel('inverse temeprature')
figure(5)
title('for material A,diffusivity vs inverse temperature');
D=D0(1)*exp(-Q(1)./(R*T));
loglog(1./T,D);
xlabel('inverse temeprature')
ylabel('diffusivity')
figure(6)
title('for material B,diffusivity vs inverse temperature');
D=D0(2)*exp(-Q(2)./(R*T));
loglog(1./T,D);
xlabel('inverse temeprature')
ylabel('diffusivity')
ylabel('diffusivity')
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