Structural materiaL 3 Calculate the vacancy concentration in

Structural materiaL

3) Calculate the vacancy concentration in aluminum at 40%, 65%, and 85% of TMP=1811 K. Gvf = 1.08 eV, and k = 8.62 x 10-5 eV/K. Calculate ln (nv/N) and 1/T, and plot on a linear scale (hint: should be a straight line).

4) Determine the largest size of an interstitial hole in FCC Co. RFe = 0.126 nm. Would a B atom sit in an interstitial or substitutional site (rC = 0.082 nm)?

5) If the distance between equivalent planes in a material is 2 angstroms (.2nm) what is the longest x-ray wavelength that can diffract at a 20 degree angle? Assume the incident beam shines into the crystal at a 20 degree angle to the planes and the diffracted beam exits at a 20 degree angle as well.

Solution

dont know 2 and 5

From this diagram, it is obvious that each octahedral site is generated by two set of equilateral triangles whose apexes point in opposite directions. We may also note that there is only one octahedral site for every sphere. This means that the number of octahedral site are half as many as there are tetrahedral sites. The size of an octahedral hole is larger than a tetrahedral hole which in turn is larger than a trigonal hole. But once again the size of an octahedral site will vary with the size of the spheres. The size of each empty space is fixed relative to the size of the spheres. The radius of the small sphere that may occupy the site can be calculated by simple geometry. For example, it may be shown that the radius of small sphere which can fit into a trigonal site is 0.155 times the radius of large close packed spheres.

Proof:

Let r_c and r_a the radii of the cation and anion, respectively.

In an equilateral triangle ABC

AD=r_aand AE=r_a+r_c

cos ( EAD) = AD / AE