To: C. K. Beck
From: A. C. Menius, Jr.
Subject: Effect of Proposed Al Liners in Vicinity of Reactor

In the present design 4" I.D. Al liners 1/8" thick are to traverse the
reflector and reach the reactor vessel. There will be in all ten of these.
In the reflector near the surface of the reactor there will be considerable
contamination of the graphite due to this Al which will result in an increase in
the amount of U235 needed for criticality as well as a distention of the flux in
that region.

If we consider a six inch section around the reactor 6" high and assume
a homogeneous mixture, the following data is obtained (See Calculations):
For graphite [sigma] = 0.00036
For graphite and Al [sigma] = 0.00095

This means that the diffusion length L is

=950
L [~=] 31 cm.

Calculations:

• Volume of Al = 10([pi]10.16)(.32)(15) = 1530cm³
• Mass = 1530(2.4) = 3670 gms

• Volume of region	= [pi](r1² - r2²) 15 cm	=
  	= [pi](30² - 15²) 15	= [pi]15(900-225)
  		= [pi]15(675)
  		= 47.2(675) = 31800 cm³

• 

• 	0.115	= (0.222) 0.115x1023
  		= 0.0258x1023
  	Ncc	= 2.6x1021

• [sigma] = 2.6x1021 • 0.23x10-24
• [sigma]al = 0.59x10-3 = 0.00059
• For graphite, assume no change in density,
• • [sigma]c = 0.00036