(42S) X-Ray Spectrometric Calculations

[Eddie W. Shore]

Introduction

The program XRAY contains a menu of several calulations involving flat crystal spectronomers, which include:

[ >EW ]: Energy wavelength conversion, where E * λ = 12.39852. E = energy and λ = wagelengtgh

[ →N ]: Store n, where n is the nth crystal. You can calculate for any crystal and have any number of crystals for this program.

[ANGLE]: Calculates the double diffraction angle, in degrees, of any crystal given n, E, and λ by using the Bragg Equation:

θ = 2 * asin( (12.39852 * n) / (E * d) )

where d = the spacing of the crystal planes

You will be prompted for E and d each time.

[E KEV]: Uses the Bragg Equation to calculate energy (E), given n, d, and θ. You will be prompted for d and θ each time.

[ENRGY]: Calculates the energy resolving power (δ) at an X-ray given its line energy (E), double refraction angle (θ), and angular divergence of the collimator (δ)).

ENERGY = (E * 1000 * δ° * π / 180) / tan θ

Enter δ in degrees.


HP 42S/DM42/Free42 Program: XRAY

This program is based on the HP 11C/HP 15C program as published by Török (see source)

Code:

00 { 241-Byte Prgm }
01▸LBL "XRAY"
02 DEG
03▸LBL 00
04 ">EW"
05 KEY 1 GTO 01
06 "→N"
07 KEY 2 GTO 02
08 "ANGLE"
09 KEY 3 GTO 03
10 "E KEV"
11 KEY 4 GTO 04
12 "ENRGY"
13 KEY 5 GTO 05
14 "EXIT"
15 KEY 6 GTO 06
16 MENU
17▸LBL 07
18 STOP
19 GTO 07
20▸LBL 01
21 EXITALL
22 1/X
23 12.39852
24 ×
25 STOP
26 GTO 00
27▸LBL 02
28 EXITALL
29 STO 01
30 GTO 00
31▸LBL 03
32 EXITALL
33 12.39852
34 RCL× 01
35 "E?"
36 PROMPT
37 ÷
38 "2d?"
39 PROMPT
40 ÷
41 ASIN
42 2
43 ×
44 "DBL ANGLE="
45 AVIEW
46 STOP
47 GTO 00
48▸LBL 04
49 EXITALL
50 12.39852
51 RCL× 01
52 "2d?"
53 PROMPT
54 ÷
55 "DBL ANGLE?"
56 PROMPT
57 2
58 ÷
59 SIN
60 1/X
61 ×
62 "E="
63 AVIEW
64 STOP
65 GTO 00
66▸LBL 05
67 EXITALL
68 "DBL ANGLE?"
69 PROMPT
70 2
71 ÷
72 TAN
73 1/X
74 "DELTA?"
75 PROMPT
76 →RAD
77 ×
78 "E?"
79 PROMPT
80 ×
81 1ᴇ3
82 ×
83 "ENERGY="
84 AVIEW
85 STOP
86 GTO 00
87▸LBL 06
88 CLMENU
89 EXITALL
90 .END.

You can download this program here: https://drive.google.com/open?id=1k12l9U...GYjNF30Qni

Note N is stored in Register R01. Every other memory register can be used.

Example

For a two-crystal spectrometer with properties:

Crystal 1 (n = 1): 6.285 Å (angstrom) (d)
Crystal 2 (n = 2): 7.285 Å

Angular divergence: 0.31° (δ)

An M_α wave with wavelength 3.415 Å enters the system. Find the energy of this M_α wave and the double refraction angle for each crystal. Also was the energy-resolving power of each of the crystals.

[ XEQ ] (XRAY)

3.415 ( >EN ) Result: E = 3.63061 keV (store this in R00)
[STO] 00

1st Crystal

[ R/S ]
1 ( →N ) (ANGL)
"E?" [RCL] 00 [R/S]
"2d?" 6.285 [R/S]

Result: DBL ANGLE = 65.82494

(ENRGY)
"DBL ANGLE?" [ R/S ] (since θ is still on the X stack)
"DELTA?" 0.31 [STO] 02 [R/S]
"E?" [RCL] 00 [R/S]

Result: ENERGY= 30.34969 eV

2nd Crystal

[ R/S ]
2 ( →N ) (ANGL)
"E?" [RCL] 00 [R/S]
"2d?" 7.285 [R/S]

Result: DBL ANGLE = 139.28586

(ENRGY)
"DBL ANGLE?" [ R/S ] (since θ is still on the X stack)
"DELTA?" [RCL] 02 [R/S]
"E?" [RCL] 00 [R/S]

Result: ENERGY= 7.28859eV

Source:

Török, I. (1990), Line identification and other simple wavelength‐dispersive x‐ray spectrometric calculations using a pocket calculator. X‐Ray Spectrom., 19: 159-161. doi:10.1002/xrs.1300190314

Blog post: http://edspi31415.blogspot.com/2020/06/h...etric.html