University:
York University
Course:
CHEM 1100 | Chemistry and Materials Science for Engineers
Academic year:

2021
Views:

77

Pages:

3
Author:

Nick T.

Special Case: Non-Steady State Diffusion Copper molecules trying to diffuse into an aluminum bar. Both copper and aluminum are solids and require thermal energy to diffuse. Variables: Cs: Copper stuck at the surface of aluminum Co: Whatever copper we have in the beginning Cx: Concentration of copper at different x t: Time x: Distance from the interface Initial Conditions: At t=0, x=0, Cx=Co At t=0, x=∞, Cx=Cs Equation: (Cx - Co) / (Cs - Co) = 1 - erf(x / (2√(Dt))) Interpretation: If Cs and Co are given, the other side will be constant too. If Cs is known, x/√(Dt) is constant too. Example: Diffusion coefficient (D) = 4.8 x 10^-14 m²/s at 500°C Diffusion coefficient (D) = 5.3 x 10^-13 m²/s at 600°C Question: What is the time needed at 500°C to produce the same concentration profile as 10 hours treatment at 600°C? Equation: (x / √(D500t500)) = (x / √(D600t600)) t500 = (D600 / D500) * t600 Calculation: t500 = (5.3 x 10^-13 m²/s / 4.8 x 10^-14 m²/s) * 10 hours t500 = 110.4 hours Image Analysis Visual Elements: Handwritten text: The majority of the image is filled with handwritten text, likely representing notes or a textbook chapter. Mathematical equations: Several equations are written to solve for the diffusion coefficient at 350°C. Textual Content: Example: At 300°C, the diffusion coefficient (D) for Cu in Si is 7.8 x 10^-14 m²/s. The activation energy (Qa) is 41.5 kJ/mol. Question: What is the diffusion at 350°C? Equation: D = Do * exp(-Qa / RT)