Grain Growth Equation: Solving for d & t at 500K

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In summary, a question is raised regarding the units used in a calculation involving the growth of grains in a nanocrystalline material. The temperature, time, and material constant are specified, but it is unclear whether the grain diameters should be given in meters or nanometers. A calculation using meters results in a questionable answer, while using nanometers does not produce a numerical result. Assistance is requested in clarifying the correct units to use.
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thephysicsman
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Homework Statement



In a nanocrystalline material the grains grow from d0 = 5nm to d = 10nm over a period of t = 1h. The temperature is 500K and the material constant is k0 = 1/s.

Homework Equations



http://en.wikipedia.org/wiki/Grain_growth#Ideal_grain_growth

The Attempt at a Solution



This should be quite simple, but I don't know if the diameters should be gived in SI units (meters) or nanometers. Since the material constant is 1/s, I assume the time should be given in seconds.

I tried using meters, and ended up with Q = 188 kJ/mol
 
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, which I doubt is right. With nanometers, the answer is not even a number. Any help would be greatly appreciated!
 

1. What is the Grain Growth Equation?

The Grain Growth Equation is a mathematical formula that describes the change in grain size over time in a material. It takes into account factors such as temperature, time, and initial grain size to determine the final grain size.

2. How do you solve for d and t at 500K?

To solve for d (final grain size) and t (time) at 500K, you would need to use the Grain Growth Equation and input the known values for temperature, initial grain size, and other relevant parameters. You can then solve for d and t using algebraic manipulation or computer software.

3. What is the significance of 500K in the Grain Growth Equation?

500K is the temperature at which the Grain Growth Equation is being applied. This temperature is a critical factor in determining the final grain size, as it affects the rate of grain growth and the activation energy of the process.

4. Can the Grain Growth Equation be applied to any material?

Yes, the Grain Growth Equation can be applied to any material with a microstructure that is undergoing grain growth. However, the specific parameters and constants used in the equation may vary depending on the material being studied.

5. What are some limitations of the Grain Growth Equation?

The Grain Growth Equation is based on certain assumptions, such as the material being homogenous and isotropic, and may not accurately predict grain growth in all situations. It also does not take into account other factors that may affect grain growth, such as impurities or external stresses.

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