Atomic Energy of Canada Limited. ELECTRON DIFFRACTION PATTERNS FOR H.C.P. a-zirconium

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1 Atomic Energy of Canada Limited ELECTRON DIFFRACTION PATTERNS FOR H.C.P. a-zirconium by G.J.C. Carpenter and J.F. Watters Chalk River Nuclear Laboratories Chalk River, Ontario November 1972 AECL-4355

2 ELECTRON DIFFRACTION PATTERNS FOR H.C P. a-zirconium by G. J. C. Carpenter and J. F. Watters ABSTRACT Data are presented to facilitate the identification of electron diffraction patterns from a-zirconium. Single crystal spot patterns can be conveniently indexed by comparison with a series of standard patterns produced by plotting planes of the reciprocal lattice. For detailed contrast experiments or more accurate orientation analysis, schematic Kikuchi maps are provided. Chalk River Nuclear Laboratories Chalk River, Ontario November 1972 AECL-4355

3 Motifs de diffraction électronique pour H.C.P. a-zirconium par G.J.C. Carpenter et J.F Watters Résumé Des données sont présentées pour faciliter l'identification des motifs de diffraction électronique provenant de a-zirconium. Des motifs a taches monocristallines peuvent être commodément indexés par comparaison avec une série de motifs de type standard produits par les plans de traçage du réseau réciproque. Des cartes schématiques Kikuchi sont fournies pour permettre de faire des expériences de contrastes détaillés ou des analyses d'orientation plus précises. L'Energie Atomique du Canada, Limitée Laboratoires Nucléaires de Chalk River Chalk River, Ontario Novembre 1972 AECL-4355

$INTRODUCTION Much of the value of transmission electron microscopy in materials science comes from the ability to correlate features in the image with specimen orientation and diffraction conditions.$

4 INTRODUCTION Much of the value of transmission electron microscopy in materials science comes from the ability to correlate features in the image with specimen orientation and diffraction conditions. It is therefore very useful to be able to identify diffraction patterns quickly and easily, particularly when doing contrast experiments at the microscope. The most convenient method of indexing straightforward single crystal spot patterns is by comparison with a series of standard patterns produced by plotting planes of the reciprocal lattice. In this report, the more densely populated planes for a-zirconium (h.c.p.) are presented concisely together with sufficient data for precise identification Schematic Kikuchi patterns, which are also included, are useful for doing detailed diffraction analysis. SPCT PATTERNS Since the reciprocal lattice of a h.c.p. crystal contains a large number of densely packed planes, the results are most conveniently obtained using a computer. Several programs are available for generating spot patterns(1~3). The results presented in Figure 1 were obtained using Meakin's(l) program with some modifications to allow automatic plotting. The patterns are defined using the crystal lattice zone axis which is specified as the upward normal parallel to the electron beam, using both the three- and four-index systems, [UVW] and [uvtw] respectively. In some cases <U"V'W'> is used in addition to draw attention to planes in the same family but having permutations of different indices in the 3-index system. Reciprocal lattice points are indexed using the convenient four-index notation of Okamoho and Thomas( 4 ) which represents the crystal plane (hki ) as a point hkia in reciprocal space. The indices are situated above the appropriate reflection. The scale of the patterns corresponds to a camera constant of 1.5 A.cm for a-zirconium. Patterns from other h.c.p. materials with c/a ratios near will be similar provided the corresponding camera constant is altered to take account

5 - 2 - of the different absolute values of a and c. For example, the patterns will be closely similar to those from a-titanium (c/a = 1.587) at a camera constant of 1.37 A. cm. To use these results, the unknown diffraction pattern is first tentatively identified by inspection. Its identity is then confirmed by determining: (a) the ratio of the spacing of the two spots indicated, R = a/b and (b) the angle 6 between these reciprocal lattice vectors (i.e. tho angles between the corresponding planes). In addition, the distance of these spots from the origin, r^ki^' can be used as a further check, providing the camera constant, yl, is known, using the standard relation: hkufc (hkitf) where d(hki ) is t^e interplanar spacing. Some values of c3(hki ) are listed in Table 1. Attention is drawn to the fact that some spot patterns of different indices are closely similar, for example zone axes [120] and [122]. In such cases it is difficult to distinguish between the patterns using the standard technique and it is better to tilt to a nearby zone that can be identified without ambiguity. Experience has shown that if the spot patterns are unambiguous the orientation can be obtained sufficiently accurately for most normal work provided thin areas of foil containing bend contours are avoided. KIKUCHI PATTERNS For detailed contrast experiments and accurate orientation analysis the use of Kikuchi patterns is essential. Normally, orientations close to a crystal zone axis are adopted for contrast experiments. It is therefore useful to have the more prominent Kikuchi poles plotted accurately for ease of identification. However, in order to use the Kikuchi patterns to perform systematic tilting operations over large angles, a Kikuchi map which includes a number of poles is useful. Prominent poles have therefore been constructed and joined to provide schematic diagrams showing their relationship (Figure 2)

6 3 Positions of the poles correspond roughly to their position on the stereographic projection shown in Figure 3, which indicates the relative orientations of the three maps. A, B and c. The trace of the plane (hki ) corresponds to a line midway between the Kikuchi line pair. Strictly, the intersection of a Kikuchi line with the photographic plate is a hyperbola rather than a straight line. However, with the small angular range normally recorded by the photographic plate no curvature is visible and the patterns have been drawn as such. The maps have been indexed in accordance with the observation by Maher and Eyre^5) that there is a 180 inversion with respect to tha standard stereographic projection, it should be noted that the indices of the Kikuchi lines always relate to the line below them. The maps can therefore be used to characterize crystal defects using the analytical approach of Maher and ^5) Certain features of the Kikuchi patterns that are worth noting are: (a) although the 1010 reflection appears strongly in spot patterns, it is the 2020 lines that appear strongest in the Kikuchi patterns ^, and (b) whereas forbidden reflections often appear in spot patterns through double diffraction, the corresponding Kikuchi linss are not observed (e.g. as in the case of - % ie forbidden 0001 and 1121 reflections). Readers who are unfamiliar with the uses of Kikuchi maps are referred to detailed accounts elsewhere(6~8).

7 REFERENCES 1. J.D. Meakin, Trans. Met. Soc. AIME., 245, 170 (1969). 2. CM. Sargent, Trans. Met. Soc. AIME., 242, 2365 (1968). 3. R.A. Ploc and G.H. Keech, J. Applied Crystallography, j>, 245 (1972). 4. P.R. Okamoto and G. Thomas, Phys. Stat. Sol.,.25, 81 (1968), 5. D.M. Maher and B. L. Eyre, Phil. Mag., 23., 409 (1971). 6. P.R. Okamoto, E. Levine and G. Thomas, J. Appled Physics, 3_8, 289 (1967). 7. G. Thomas, Trans. Met. Soc. AIME., 233, 1608 (1965). 8. E. Levine, W.L. Bell and G. Thomas, J. Applied Physics,.37., 2141 (1966).

8 TABLE 1 Interplanar Spacings for ot-zirconium (a = , c = ) hki o d A hkia o d A

9 [UVW] [uvtw] <U'V'W'> R, hki kvl 1 ) ^ a o Allowed reflections Forbidden reflections, often present due to double diffraction [uvw] zone axis, Miller indices [uvtw] 2one axi S/ Miller-Bravais indices <UVw'> Zone axes. Miller-indices, of same family as [uvtw] R = a>b) Camera constant, XL = 1.5 A. cm Pig. 1. Schematic Spot Diffraction Patterns for a-zirconium: (a) key to diagrams (b)-(d) spot patterns

10 [OO1][OOO1] 1.0,60, ouo_, JLx ltnn «[O11][T2T3] <111> 10]0. 1 Of 1.15,64 jjor 0111 [i2i][oni] 1.3,50 a 0 2ll][220ii ,53 j 10 )2 # 0112 [021] [2423] 1.48,70 <221 > ioio. 1 "J)2, QXJ2 # #. ' [03i][l21i]» 0 " 1 ; ,75 ^ [411][7253] 1.88,80 ' 0111., ] 11JI3 \ t [3i2][5UB] 1.82, ";: «0221 [4ii][32li] 2.31, , Toi4 O m o [023][2429] 2.88, \ ""TJ22» [313] [5148] [323"1[8719]» " 1 2.3B. V; [4O1][B443] 2311 ' v , a ,77 i 0110,\z- [4l4][32ll] IMS: «161T 942d -^ U3 [013] [1219] 2.70,80 0 ioio -» » [33:i][33ifij 1120 / : », Pig. l(b)

11 [223][2203] 1120 ' 1 10 fifi^ [441][44O1] 11.39, 6B [342][1O 111 6JI [443] [4403] 1.61, ' [4?3][32"13] [113][H29] 2.7,79 [403][8449] 3.44,81 [01O][l210] ,90 [122] [0112] 11.52,90 [120] [QUO] 1.58,90 <012> 1.82,90 [31i][5l43] 11.3, I 21T0 Q 0002" TC? o o 01J1 1 1T02. o [3?3][7529] [O32][I212] [310] [5140] 4.85,90 c 1011 f l"3" «0332 I Fig. l(c)

12 [410][7250] 6.6,90 [322][87l6] 2.27,1 [214][ioT4] 1.2,90 [332][3302] 1.11,90 000T' Mi: Olii I Q. [1O4][2TT12] 3.51,90 e [304][2114] 3.83,90 "421 ][ ] 1.38,83 [234] [781 12] 1.01, # I 4131 ^ _422l_ I 1122 U J 3 I 1212 O- [412][321'2] 1.4,82 [32l][8713] 1.23,70 [412][7256] 1.23,77 [234][U5 12] 1.14,85" o 1012 i 0112 _f 1121 <0 10, I o o [431][ ji.db. [314][5l"412] 1.14,85 [354][3304] 1.49,90 [434][527 12] 3.04, o I I 2203 o "l Fig. l(d)

13 Fig. 2 (a)-(c). Schematic Kikuchi maps for a-zirconium

14 B SCALE -5'.-I flois] [07)2] [Toil] [OTll] [55731 Pig. 2(b)

15 O 8 fm H

16 mo 1210 Tim Dim TO 10 (0002) Pig. 3 The relation of the Kikuchi maps using a sterographic projection showing Kikuchi poles, uvtw, and traces of planes, (hki ).

17 Additional copies of this document may be obtained from Scientific Document Distribution Office Atomic Energy of Canada Limited Chalk River, Ontario, Canada KOJ UO Price 50c per copy

Simulation and Analysis of Kikuchi Patterns Including Double Diffraction Effect. (SAKI3d) User s manual. X.Z. LI, Ph. D.

$Simulation and Analysis of Kikuchi Patterns Including Double Diffraction Effect. (SAKI3d) User s manual. X.Z. LI, Ph. D.$ Simulation and Analysis of Kikuchi Patterns Including Double Diffraction Effect (SAKI3d) User s manual X.Z. LI, Ph. D (May 6, 2018) Copyright 2011-2018 LANDYNE All Right Reserved 1 Contents 1. Introduction...3