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which results are tabulated below:

Peak Index 2θ dhkl(nm) a (nm)
200 36.6 0.2455 0.4910
220 52.6 0.1740 0.4921
311 62.5 0.1486 0.4929
222 65.5 0.1425 0.4936
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3-79
3.64 The first four diffraction peaks that will occur for BCC consistent with h + k + l being even are (110),
(200), (211), and (220).
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3-80
3.65 (a) Since W has a BCC crystal structure, only those peaks for which h + k + l are even will appear.
Therefore, the first peak results by diffraction from (110) planes.
(b) For each peak, in order to calculate the interplanar spacing we must employ Equation 3.13. For the
first peak which occurs at 40.2°

d110 =
nλ
2 sin θ
= (1)(0.1542 nm)
(2) sin 40.2°
2
⎛
⎝
⎜
⎞
⎠
⎟
= 0.2244 nm

(c) Employment of Equations 3.14 and 3.3 is necessary for the computation of R for W as

R =
a 3
4
=
(dhkl)( 3) (h)2 + (k)2 + (l)2
4

=
(0.2244 nm)( 3) (1)2 + (1)2 + (0)2
4

= 0.1374 nm

Similar computations are made for the other peaks which results are tabulated below:

Peak Index 2θ dhkl(nm) R (nm)
200 58.4 0.1580 0.1369
211 73.3 0.1292 0.1370
220 87.0 0.1120 0.1371
310 100.7 0.1001 0.1371
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3-81
Noncrystalline Solids

3.66 A material in which atomic bonding is predominantly ionic in nature is less likely to form a
noncrystalline solid upon solidification than a covalent material because covalent bonds are directional whereas
ionic bonds are nondirectional; it is more difficult for the atoms in a covalent material to assume positions giving
rise to an ordered structure.
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