Calculating the Lattice Misfit and Misfit Hardening of Ni and Ni3Al

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In summary, the lattice misfit between Ni and Ni3Al phases is 0.013. The addition of Cr to 50a/o results in a lattice misfit of 0.0119 and a decrease in misfit hardening of 0.0011.
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matt222
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Homework Statement


Ni lattice parameter a1=3.52*10^-10m, and for Ni3Al lattice pameter a2=3.525*10^-10m,

1-what is the lattice misfit between these phases?

2-if there is addition of Cr to 50a/o, the lattice parameter of lattice increased to a3= 3.525*10^-10m, what will be the change in misfit hardening ?


Homework Equations





The Attempt at a Solution


1-misfit=a2-a1/a1=0.013

2-misfit=a2-a3/a3=0.0119

i am not sure about the second answer can you help me, and is the first one is right
 
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Hello!

Your first answer is correct. The lattice misfit between these two phases is 0.013.

For the second question, the change in misfit hardening can be calculated by comparing the lattice misfit before and after the addition of Cr. The lattice misfit before the addition of Cr was 0.013, and after the addition of Cr, it became 0.0119. Therefore, the change in misfit hardening would be 0.013 - 0.0119 = 0.0011. This means that the addition of Cr reduced the lattice misfit, resulting in a decrease in the misfit hardening.

I hope this helps! Let me know if you have any further questions.
 

1. What is lattice misfit and how is it calculated?

Lattice misfit refers to the difference in lattice parameters between two materials in a crystal structure. It is calculated by taking the difference between the lattice parameters of the two materials and dividing it by the lattice parameter of the host material.

2. How does misfit affect the strength of a material?

Misfit can lead to the formation of dislocations and defects in the crystal structure, which can increase the strength of the material through a process called misfit dislocation strengthening. This is known as misfit hardening and can improve the mechanical properties of the material.

3. How is misfit hardening calculated for Ni and Ni3Al?

Misfit hardening for Ni and Ni3Al is calculated by taking the difference in lattice parameters between the two materials and multiplying it by a factor known as the misfit parameter. This parameter represents the strength of the interaction between the two materials and is determined experimentally.

4. What factors can influence the misfit and misfit hardening of Ni and Ni3Al?

The misfit and misfit hardening of Ni and Ni3Al can be influenced by factors such as temperature, composition, and crystal orientation. Changes in these factors can alter the lattice parameters and misfit parameter, thereby affecting the strength of the material.

5. How is the misfit between Ni and Ni3Al related to the formation of intermetallic compounds?

The misfit between Ni and Ni3Al can lead to the formation of intermetallic compounds in the crystal structure. These compounds can have a significant impact on the properties of the material, such as its strength and corrosion resistance. Therefore, understanding the misfit is crucial in predicting the behavior of these materials.

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