Title                  :TOTCS
Keywords               :Sputtering,Defects,Displacement Damage,EELS,XEDS,HVEM
Computer               :DEC VAX 11/785
Operating System       :VAX/VMS
Programming Language   :VAX Fortran V4.0
Hardware Requirements  :None
Author(s)              :Charles R. Bradley
Correspondence Address :Argonne Nat. Lab, Electron Microscopy Center,  Bldg  212
                       :Materials Science Division, Argonne, Illinois 60439, USA
Description            :Outline/Description and the purpose of the code.

Version:
	2.0

Purpose:
	Compute the total Mott cross-section for a range of accelerating
	voltages running up to 1500KV.	The calculation method of
	Doggett and Spencer is used and results agree with O. S. Oen's
	implementation of that calculation to within 0.5%. The program
	requires as input Z - the atomic number, A - the atomic mass,
	and Ed the assumed displacement energy. Preliminary results
	of this study are to be published in:

	Proceedings of the Workshop on Analytical Electron Microscopy
	San Francisco Press, Fall 1987


References: 
	McKinley & Feshbach
	Phys Rev 74,1759(1948)

	Feshbach
	Phys Rev 88,295(1952)

	Doggett & Spencer
	Phys Rev 103,1597(1956)

	O. S. Oen
	CROSS-SECTIONS FOR ATOMIC DISPLACEMENTS
	IN SOLIDS BY FAST ELECTRONS
	ORNL Report # TM-4897,(1973)

	T. J. I'A Bromwich
	AN INTRODUCTION TO THE THEORY OF
	INFINITE SERIES, 2nd ed.
	Macmillan 1955

	Francis Scheid
	NUMERICAL ANALYSIS
	Schaum's Outline Series
	McGraw Hill Book Co. 1968

	Abromowitz and Stegun
	HANDBOOK OF MATHEMATICAL FUNCTIONS
	Dover, New York 1972

	James W. Corbett
	ELECTRON RADIATION DAMAGE IN SEMICONDUCTORS AND METALS
	in: Solid State Physics Advances in Research and Applications
	Supplement 7, Ed. Frederick Seitz and David Turnbull
	Academic Press, New York 1966

Compilation Procedure: 
	Using VAX-Fortran compiler
	1. Rename file to TOTCS.FOR
	2. At DCL prompt type FORTRAN/EXTEND/NOF77 TOTCS
	
Linking Procedure: 
	At DCL prompt type LINK TOTCS

Input/Output:
	UNIT 1	input	(to be assigned)
	UNIT 2	output	(to be assigned)

Test Data: 
	This routine is designed to read input from a data file
	with the format (3F10.3).

Input file format:
	Z,A,Es
	(EOF)
	where;	Z = atomic number
		A = atomic mass(amu)
		Es = Displacement/sputtering energy(eV).  The energy required
	to produce the defect or sputter an atom from the surface.
	The atom is bound by an isotropic square well of depth Es.

example:
	13.000,26.980,3.420
	(EOF)

General Comments: 
	To run the program it is convienient to create a DCL command
	file which assigns fortran device 1 to the input file and
	device 2 to an output file.
  
	$ASSIGN filename.INP  FOR001
	$ASSIGN filename.OUT  FOR002
	$RUN TOTCS

	Since the program takes a substantial amount of CPU time the
	program is usually submitted to a batch queue.  This can be done
	in VAX/VMS by typing:

	submit/noprint/notify <fn>

	where <fn> is the above command file's name.


	VAX/VMS CPU time is approximately 30 seconds for each point calculated.
	The number of points varies since the threshold is a function of the
	atomic mass, and Z.  For the example here 1 hr 35 min 56.61 sec
	of CPU time was used.

	Subroutines and function subprograms required are included in the
	listing.  Amoung those included are:
		D which returns coefficients in the legendre
		  expansions which express the cross-section.
		EULER which preforms an euler transformation of an
		  alternating series and returns the sum of the series.
		LGDRE which returns legendre polynomials.
		LNGAM which returns the complex value of the log of
		  a gamma function with complex arguments
		SIGMR which returns the ratio of the Mott cross-section
		  to the Rutherford Cross-section.
		QATRGL a 16-point Gauss-Legendre numerical quadrature routine

Sample Output: 
	The following is output generated by the above sample input
	which corresponds to Al with an assumed Es=3.420 eV.

 Atomic number of target =       13.
   Atomic mass of target =    26.980
       Sputtering Energy =     3.420
  Threshold Energy (KeV) =    40.436
  
 Accelerating	Cross-Section	Cascade CS
 Voltage(KV)	(Barns/atom)	(Barns/atom)
  
     40.436	     0.000	     0.000
     41.000	    22.380	    22.380
     42.000	    59.264	    59.264
     43.000	    92.871	    92.871
     44.000	   123.530	   123.530
     45.000	   151.533	   151.533
     46.000	   177.140	   177.140
     47.000	   200.578	   200.578
     48.000	   222.052	   222.052
     49.000	   241.743	   241.743
     50.000	   259.813	   259.813
     55.000	   330.434	   330.434
     60.000	   377.058	   377.058
     65.000	   407.918	   407.918
     70.000	   428.164	   428.164
     75.000	   441.128	   441.128
     80.000	   449.016	   449.143
     85.000	   453.328	   454.798
     90.000	   455.099	   458.956
     95.000	   455.058	   461.966
    100.000	   453.724	   464.089
    110.000	   448.570	   466.425
    120.000	   441.574	   467.070
    130.000	   433.788	   466.693
    140.000	   425.790	   465.713
    150.000	   417.901	   464.395
    160.000	   410.290	   462.909
    170.000	   403.045	   461.366
    180.000	   396.203	   459.837
    190.000	   389.773	   458.368
    200.000	   383.746	   456.988
    210.000	   378.107	   455.714
    220.000	   372.833	   454.556
    230.000	   367.901	   453.517
    240.000	   363.288	   452.599
    250.000	   358.970	   451.799
    260.000	   354.926	   451.114
    270.000	   351.133	   450.541
    280.000	   347.573	   450.074
    290.000	   344.228	   449.708
    300.000	   341.082	   449.438
    310.000	   338.120	   449.259
    320.000	   335.327	   449.165
    330.000	   332.692	   449.152
    340.000	   330.202	   449.215
    350.000	   327.847	   449.350
    360.000	   325.618	   449.551
    370.000	   323.505	   449.815
    380.000	   321.501	   450.138
    390.000	   319.598	   450.517
    400.000	   317.790	   450.947
    450.000	   309.961	   453.772
    500.000	   303.738	   457.487
    550.000	   298.703	   461.847
    600.000	   294.563	   466.672
    650.000	   291.114	   471.828
    700.000	   288.205	   477.219
    750.000	   285.726	   482.769
    800.000	   283.592	   488.422
    850.000	   281.742	   494.137
    900.000	   280.124	   499.880
    950.000	   278.700	   505.626
   1000.000	   277.438	   511.356
   1050.000	   276.314	   517.054
   1100.000	   275.307	   522.709
   1150.000	   274.401	   528.313
   1200.000	   273.580	   533.857
   1250.000	   272.836	   539.338
   1300.000	   272.156	   544.751
   1350.000	   271.534	   550.095
   1400.000	   270.963	   555.366
   1450.000	   270.437	   560.565
   1500.000	   269.951	   565.691