**HP 42S/DM42/Free42: X-Ray Spectrometric Calculations**

**Introduction**

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

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

[ →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)

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=1k12l9Un9LgtrdC3139jS3SGYjNF30Qni

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

Eddie

All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.