How to measure the amount of shear fracture in an impact test (ASTM A370 )

8.1 The ratio of diffusion rate of silver in silicon at 1350°C to that at 1100°C was found to be 8 in a doping process. Calculate the activation energy Q for silver diffusion in silicon.

 

8.2 The diffusion rate of A in B was studied at 500°C and 850°C. It was found that, for the same diffusion time, the depths of penetration x1 and x2 in the two experiments were in the ratio of 1 : 4. Calculate the activation energy for diffusion of A in B.

 

8.3 Amorphous selenium used as a semiconductor material exhibits unusual diffusion characteristics. The following is a set of experimental data for self-diffusion in amorphous selenium. Calculate D0 and Q and comment on your results. T, °C D, m2 s–1 35 7.7 10–16 40 2.4 10–15 46 3.2 10–14 56 3.2 10–13

 

8.4 At 900°C, what is the time required to carburize a steel with an initial composition of 0.2% carbon to 1% carbon at a depth of 0.2 mm? Assume a constant surface concentration of 1.4% carbon due to the carburizing atmosphere.

 

8.5 A 1.2% carbon steel is getting decarburized in an atmosphere of 0.0% carbon. After some time t, plot (i) c(x) curve near the surface of the steel, and (ii) J(x) curve below the above curve, using the same x-axis.

 

8.6 A diffusion couple of 95% Cu-5% Zn and pure copper is annealed at 900°C for 50 hr. The zinc concentration at a depth of 2 mm inside the copper bar was found to be 0.3% after the anneal. Determine the diffusion coefficient of zinc in copper.

 

8.7 In a steel, during carburization at 937°C, 0.6% carbon is found at a depth of 0.2 mm after 1 hr. Find the time required to achieve the same concentration at the same depth, if carburization is done at 1047°C.

 

8.8 Compare the diffusivities of hydrogen, nitrogen, and nickel in iron at 300 K and explain the difference between the three values.

 

8.9 Compute the rate at which a vacancy jumps in copper at 20°C. The activation barrier for the jump is 100 kJ mol–l.

 

8.10 An Al-4% Cu alloy is heated to 550°C during heat treatment and quenched to room temperature. Immediately after quench, the diffusion rate of Problems 197 copper (which proceeds by a vacancy mechanism) was found to be 107 times faster than what would be expected from the listed diffusion data. What fraction of vacancies in equilibrium at 550°C is retained at room temperature by the rapid quenching? The enthalpy of motion of vacancy in this alloy is 50 kJ mol–1.

 

8.11 How will the diffusivity of NaCl change, when it is doped with (i) KCl, and (ii) CaCl2? Explain.

 

8.12 Determine the ratio of cross-sectional area available for diffusion along the surface and through the lattice, when the two diffusion rates are equal at room temperature. Assume D0 to be the same for both the processes. Qsurface = 100 kJ mol–l and Qlattice = 150 kJ mol–l.

 

8.13 Find the grain size of a polycrystalline solid for the same amount of material to be transported through (i) the grain and (ii) the grain boundary at 500°C. Assume that the grains are cube shaped and the grain boundaries are 5 Å thick. For lattice diffusion: D0 = 0.7 10–4 m2 s–1 Q = 188 kJ mol–l For grain boundary diffusion: D0 = 0.09 10–4 m2 s–1 Q = 90 kJ mol–l

 

8.15 From the data in Table 8.2, calculate the diffusion coefficient of carbon in ferrite ( ) and austenite ( ) at 900°C. Explain the difference in the values on the basis of the two crystal structures.

 

8.14 Make a plot of the activation energy Q for diffusion of different species as a function of the melting point of the species. Comment on your result.

 

8.16 In a diffusion anneal, to what level should the initial temperature of 900°C be increased to double the depth of penetration? D0 = 0.4 m2 s–1 and Q = 100 kJ mol–l.

 

8.17 An amount Q of a dopant is deposited on the surface of a silicon substrate. During a subsequent anneal without the dopant in the atmosphere, the concentration c of the dopant as a function of depth x and time t is given by c = (Q/ 􀀀DT ) exp [–x2/(4Dt)] Show that this is a solution of Fick’s Second Law, when D is independent of concentration.

 

8.18 A steel containing 0.002% N is to be nitrided to yield a nitrogen content of 0.12% at depth of 4 mm from the surface. The nitriding atmosphere is equivalent to a surface concentration of 0.35% N. How long is to be the nitriding process? The steel is BCC ( ) at the nitriding temperature of 700°C.

 

From the Fe–Fe3C phase diagram, for a 0.2% C steel, name the phases and their fractions at equilibrium at the following temperatures: (i) just above 1493°C, (ii) just below 1493°C, (iii) just above 725°C, and (iv) just below 725°C.