MSE 170

Would you expect the surface energy to be greater than, the same, or less than the grain boundary energy?

-Greater -For grain boundaries, some atoms on one side of a boundary will bond to atoms on the other side; such is not the case for surface atoms. -fewer unsatisfied bonds along a grain boundary.

5.1 Rank the magnitudes of the diffusion coefficients from greatest to least for the following systems: N in Fe at 700˚C Cr in Fe at 700˚C N in Fe at 900˚C Cr in Fe at 900˚C

1) N in Fe at 900 2) N in Fe at 700 3) Cr in Fe at 900 4) Cr in Fe at 700 Explanation: Nitrogen is an interstitial impurity in Fe (on the basis of its atomic radius), whereas Cr is a substitutional impurity. Since interstitial diffusion occurs more rapidly than substitutional impurity diffusion, DN > DCr. Also, inasmuch as the magnitude of the diffusion coefficient increases with increasing temperature, D(900) > D(700).

3.2 What is the difference between crystal structure and crystal system?

A crystal structure is described by both the geometry of, and atomic arrangements within, the unit cell, whereas a crystal system is described only in terms of the unit cell geometry. For example, face-centered cubic and body-centered cubic are crystal structures that belong to the cubic crystal system.

3.1 What is the coordination number for the simple-cubic crystal structure? + Calculate the atomic packing factor for simple cubic.

Coordination number = 6 Each atom, located in the corner of a unit cell, has three nearest neighbors located in this unit cell and three nearest neighbors in adjacent cells. APF = 0.52

3.4 Do noncrystalline materials display the phenomenon of allotropy (or polymorphism)? Why or why not?

Noncrystalline materials do not display the phenomenon of allotropy; since a noncrystalline material does not have a defined crystal structure, it cannot have more than one crystal structure, which is the definition of allotropy.

4.2 Explain why complete solid solubility may occur for substitutional solid solutions but not for interstitial solid solutions.

One requirement for the formation of a solid solution is that solute atoms fit into the crystal lattice without introducing significant lattice distortions -substitutional atoms completely replace -interstitial cause lattice distortions

3.3 For cubic crystals, as values of the planar indices h, k, and l increase, does the distance between adjacent and parallel planes (i.e., the interplanar spacing) increase or decrease? Why?

The interplanar spacing between adjacent and parallel planes decreases as the values of h, k, and l increase. As values of the planar indices increase, the magnitude of the denominator in Equation 3.22 increases, with the result that the interplanar spacing (dhkl) decreases.

4.1 Is it possible for three or more elements to form a solid solution?

Yes, it is possible for three or more elements to form a solid solution. For three or more elements, the same criteria apply as for two elements, as stipulated by the Hume-Rothery rules.

does the grain size number G increase or decrease with the decrease in the grain size?

increases

4.3 The surface energy of a single crystal depends on crystallographic orientation. Does this surface energy increase or decrease with an increase in planar density? Why?

surface energy decreases with an increase in planar density (more satisfied bonds, more atoms)