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Submitted on 1 Jan 1984
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ELECTRON DIFFRACTION ANALYSIS
M. Whitehead, V. Balmer
To cite this version:
M. Whitehead, V. Balmer. ELECTRON DIFFRACTION ANALYSIS. Journal de Physique Colloques, 1984, 45 (C2), pp.C2-239-C2-242. �10.1051/jphyscol:1984253�. �jpa-00223966�
JOURNAL DE PHYSIQUE
Colloque C2, supplkment au n02, Tome 45, fgvrier 1984 page C2-239
ELECTRON DIFFRACTION ANALYSIS
M.E. Whitehead and V. Balmer
EDAX INTERNATIONAL, Inc., P.O. Box 235, Prairie V i e w , I L 60069, U.S.A.
R6sum6 - On a d6velopp6 un programme qui permet le stockage pra- tique et prEcis, sur ordinateur, de diagrammes de diffraction Blec- tronique. On utilise une table 5 numgriser et le programme d6ter- mine automatiquement l'axe d e zone.
Abstract - A program has been developed which allows convenient and accurate computer storage of electron diffraction spot patterns via a digitising pad, with subsequent zone axis evaluation.
Method - Conventional characterisation of diffraction spot patterns can be a tedious and m o n s u m i n g exersise. 1 he program developed uses conventional techniques, and aids the user in the diffraction analysis without making decisions which should be l e f t t o his judgement. l h u s , the spot positions on a diffraction pattern (photographic film) a r e inputed via a digitising pad, rapidly and accurately. With knowledge of the camera constant of the electron microscope, the d-spacing and inter-vector angles a r e automatically determined and displayed.
The stored pattern can then be plotted and by inspection two low order spots chosen (X and 1 ) whose indicies (as yet undetermined) when vectorially added give indicies for a third chosen spot (Z):
? h a t is, the three spots X, Y and Z a r e chosen such that, together with the zero spot, they form a parallelogram.
7 he system then searches a list of interplanar spacings of a given structure for the 5 nearest d-spacings t o each of the 3 chosen vectors. After a decision has been made which determines the appropriate d-spacings match for each vector, a consistent s e t of indicies is determined from the multiplicity of indicies associated with each spot (relationship 1). If none exists then the initial choice of matching d-spacing was incorrect for that system.
Once the specific indicies of X, Y and Z have been determined, the zone axis (A) is readily given by the cross product of any 2 of t h e 3 determined reciprocal vectors OX, OY, OZ.
That is
A check of the validity of this zone value is then output a s a comparison of the angles measured between the chosen experimental vectors and those angles calculated using the determined indicies.
A final definitive check t o the accuracy of the determination is made by indexing and generating all the other spots by simple vector additions and plotting these over the experimentally acquired spots t o determine the degree of match by visual inspection. The zone axis can then be approximately equated with the beam direction.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984253
C2-240 JOURNAL RE PHYSIQUE
ZIRCONIA 31-AUG-B3 09148: 47
NO. 05971
11 25KeV _ 31 Mm. A n q .
File: DKl: ZIRCl3. DFP 31 -AUG-83
M09 : 1.61 10; 33: 30
R o t : D
I 1
Fig. l a - Negative of diffraction pattern
Fig. l b - Plot of diffraction pattern after digitisation.
Example - The indexing procedure is rapid and possesses 4 criteria of 'goodness1. They a r e (i) t h e p a c i n g match (ii) the existence or not of a possible zone axis (iii) the angular matching and (iv) the f i t between experimental spots and those generated from the determined zone axis.
A simple example is chosen t o illustrate the procedure. A spot pattern from zirconia (high temperature form), digitised and plotted, is shewn in Figure 1. The d-spacings and inter- vector angles determined a r e shewn in Figure 2.
A separate routine is used to generate a list on file of interplanar spacings (for allowed reflections) possessed by face centered cubic zirconia. l h i s routine can be applied t o any of the crystal systems desired. The first part of this list is shewn in Figure 3, clearly indicating the multiplicity factor for each set of planes.
? h e final analysis shewn in Figure 2, after choosing X, Y and Z vectors, illustrating a satisfactory evaluation of a possible zone axis, and consistent fitting of the parameters.
C2-241
Fig. 2 - List of the determined d-spacings and angles with zone axis evaluation.
OLD PATTERN: ZIRCONIA No. 05971 31-AUG-83 125.0 KEV 09:48:47 31.00 MM.ANG
SPOT D- ANGLE RECIPR.
NUMBER SPACING WRT-X SPACING (ANG) (DEG) (MM)
# 21 2.92 212.6 10.6 X(#22) Y(#14) Z{#15)
# 29 2.90 102.5 10.7
X# 22 2.90 32.8 10.7 DATA 2.90 2.90 2.46 Y# 14 2.90 283.0 10.7 DPIT1 2.927 2.927 2.535
# 28 2.52 157.0 12.3 DFIT2 2.535 2.535 2.927 Z# 15 2.46 337.1 12.6 DFIT3 1.793 1.793 1.793
# 2 1.77 247.8 17.5 DFIT4 1.529 1.529 1.529
# 1 1.76 68.0 17.6 DFIT5 1.464 1.464 1.464
# 10 1.50 312.5 20.7
# 33 1.50 132.6 20.7 X/Y Y/Z Z/X
# 27 1.48 183.0 21.0
# 16 1.48 3.3 21.0 DATA 1.000 1.179 0.848
# 34 1.46 102.5 21.3. 1:1:1 1.000 1.155 0.866
# 9 1.44 281.8 21.5
# 20 1.44 212.1 21.6 <X0Z <ZOY
# 23 1.42 32.5 21.8
# 3 1.24 158.3 24.9 DATA 55.7 54.1
# 4 1.23 338.1 25.2 AFIT 54.7 54.7
# 35 1.14 80.9 27.1
# 13 1.14 234.0 27.2
# 30 1.13 54.2 27.5 VECTOR X = ( 1 1 1 )
# 38 1.02 122.6 30.4 VECTOR Y = ( 1 1 1 )
# 5 1.02 302.8 30.5 VECTOR Z = ( 2 0 0 )
# 17 1.01 13.6 30.7
# 26 1.01 193.2 30.6
# 37 0.96 142.2 32.3 ZONE AXIS = ( 0 1 1 ) OF ZR02
# 6 0.95 322.9 32.5
# 11 0.95 353.8 32.6
# 19 0.95 212.0 32.7
# 32 0.95 173.8 32.6
# 24 0.95 32.4 32.8
# 36 0.83 157.9 37.5
# 7 0.82 338.5 37.7
# 31 0.82 48.3 38.0
# 18 0.75 18.5 41.6
# 12 0.74 3.8 42.0
# 25 0.70 32.8 44.0
# 8 0.70 327.2 44.6
# 39 0.69 146.8 44.8
C2-242 JOURNAL DE PHYSIQUE
Fig. 3 - List of interplanar spacings for face centered cubic zirconia.
****** CRYSTAL PARAMETERS ******
#1 CRYSTAL = ZIRCONIA LABEL
#2 CRYSTAL = CUBIC SYSTEM
#3 LATTICE = FACE-CENTERED SYMMETRY
#4 TRANSL.
SYMMETRY
#5 CELL A = 5.070 ANGSTROM DIMENS. B = 5.070 "
C = 5.070 "
#6 CELL <A = 90.00 DEGREES ANGLES <B = 90.00
<C = 90.00 "
#7 VECTOR H = 5 RANGE K = 5 L = 5 H K L D-SPACING
1 1 1 2.927 1 1 1 3 3 1.163 7 33 1 1 1 2.927 1 2 3 1 3 1.163 7 34 1 1 1 2.927 1 3 3 1 3 1.163 7 35 1 1 1 2.927 1 4 3 3 1 1.163 7 36 1 3 3 1.163 7 37 2 0 0 2 . 5 3 5 2 5 3 3 1 1.163 7 38 0 0 2 2 . 5 3 5 2 6 3 1 3 1.163 7 39 0 2 0 2 . 5 3 5 2 7 3 1 3 1.163 7 40 3 3 1 1.163 7 41 2 0 2 1.793 3 8 1 3 3 1.163 7 42 0 2 2 1.793 3 9 3 3 1 1.163 7 43 2 0 2 1.793 3 10 1 3 3 1.163 7 44 2 2 0 1.793 3 11
0 2 2 1.793 3 12 0 2 4 1.134 8 45 2 2 0 1.793 3 13 0 2 4 1.134 8 46 2 4 0 1.134 8 47 1 1 3 1.529 4 14 2 0 4 1.134 8 48 1 1 3 1.529 4 15 4 2 0 1.134 8 49 2 4 0 1.134 8 50 1 1 3 1.529 4 16 0 4 2 1.134 8 51 1 3 1 1.529 4 17 4 2 0 1.134 8 52 1 1 3 1.529 4 18 0 4 2 1.134 8 53 3 1 1 1.529 4 19 2 0 4 1.134 8 54 3 1 1 1.529 4 20 4 0 2 1.134 8 55 1 3 1 1.529 4 21 4 0 2 1.134 8 56 3 1 1 1.529 4 22
1 3 1 1.529 4 23 2 4 2 1.035 9 57 3 1 1 1.529 4 24 2 4 2 1.035 9 58 1 3 1 1.529 4 25 2 2 4 1.035 9 59 4 2 2 1.035 9 60 2 2 2 1.464 5 26 2 4 2 1.035 9 61 2 2 2 1.464 5 27 4 2 2 1.035 9 62 2 2 2 1.464 5 28 2 2 4 1.035 9 63 2 2 2 1.464 5 29 4 2 2 1.035 9 ' 64
2 2 4 1.035 9 65 4 0 0 1.268 6 30 2 2 4 1.035 9 66 0 0 4 1.268 6 31 4 2 2 1.035 9 67 0 4 0 1.268 6 32 2 4 2 1.035 9 68
