<html>
<head>
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
</head>
<body>
<div class="moz-cite-prefix">On 6/23/20 8:36 PM, wrote:<br>
</div>
<blockquote type="cite"
cite="mid:522385259af84031b167496d56ea740a@BN3PR01MB1969.prod.exchangelabs.com">
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
Dr. Pounds,
<div> How did you get the radius for the BCC and the FCC
questions? I haven’t been able to figure it out. </div>
<div><br>
</div>
<div>Thanks</div>
<div><br>
</div>
<br>
</blockquote>
<p><br>
</p>
<p>So the trick here is determining the length of the diagonal. In
the case of the FCC lattice we would use the Pythogorean theorem.</p>
<p><img alt="$d^2=a^2+b^2$" style="vertical-align: middle;"
src="cid:part1.FAB1ED74.E9D42F23@mercer.edu"> <br>
</p>
<p>remember that in this problem a and b are "1", so the length of
the diagonal is</p>
<p><img alt="$d=\sqrt{1^2+1^2}=\sqrt{2}$" style="vertical-align:
middle;" src="cid:part2.D4DBE8AF.80220CD4@mercer.edu"></p>
<p>The diagonal is composed of 4 radii, <br>
</p>
<p><img alt="$4r = \sqrt{2}$" style="vertical-align: middle;"
src="cid:part3.3E1DCFA0.0D896110@mercer.edu"> or</p>
<p><img alt="$r=\frac{\sqrt{2}}{4}$" style="vertical-align: middle;"
src="cid:part4.7A45D15F.9A7567B5@mercer.edu"></p>
<p><br>
</p>
<p>In the case of the BCC packing the diagonal goes through the
CENTER of the cube and we have to extend the Pythagorean theorem
to 3D.</p>
<p><img alt="$d^2=a^2+b^2+c^2$" style="vertical-align: middle;"
src="cid:part5.454A83A6.E5384BE8@mercer.edu"></p>
<p>a,b, and c are all one so...</p>
<p><img alt="$d=\sqrt{1^2+1^2+1^2}=\sqrt{3}$" style="vertical-align:
middle;" src="cid:part6.90AB95B4.6AD68A7C@mercer.edu"></p>
<p>The diagonal is composed of 4 radii, <br>
</p>
<p><img alt="$4r = \sqrt{3}$" style="vertical-align: middle;"
src="cid:part7.2FA1917C.34287401@mercer.edu"> or</p>
<p><img alt="$r=\frac{\sqrt{3}}{4}$" style="vertical-align: middle;"
src="cid:part8.6BE0AA84.4B0E321B@mercer.edu"></p>
<p><br>
</p>
<p>Does that help?</p>
<p><br>
</p>
<p><br>
</p>
<pre class="moz-signature" cols="72">--
Andrew J. Pounds, Ph.D. (<a class="moz-txt-link-abbreviated" href="mailto:pounds_aj@mercer.edu">pounds_aj@mercer.edu</a>)
Professor of Chemistry and Computer Science
Director of the Computational Science Program
Mercer University, Macon, GA 31207 (478) 301-5627
</pre>
</body>
</html>