Structure re nement of L2 1 Cu±Zn±Al austenite, using dynamical electron diffraction data

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1 PERGAMON Solid State Communications 116 (2000) 273±277 Structure re nement of L2 1 Cu±Zn±Al austenite, using dynamical electron diffraction data C. Satto a, J. Jansen b, C. Lexcellent c, D. Schryvers a, * a Electron Microscopy for Materials Research (EMAT), University of Antwerp, RUCA, Groenenborgerlaan 171, B-2020 Antwerp, Belgium b National Centre for HREM, Laboratory of Materials Science, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands c Laboratoire MeÂcanique AppliqueÂe Raymond Chaleat, Universite de Franche Comte, 24 chemin de l'eâpitaphe, Besancon, France Received 8 July 2000; accepted 19 July 2000 by D.E. Van Dyck Abstract The occupancies of the different atomic species in the L2 1 austenitic phase of the Cu 66.9 Zn 23.7 Al 9.4 alloy have been determined by electron diffraction using the multi-slice least-squares method taking dynamical scattering into account. The 4a site (0, 0, 0) is occupied by aluminium and zinc, while the 4b site (1/2, 1/2, 1/2) is occupied by zinc and copper, in both cases in a random fashion. q 2000 Published by Elsevier Science Ltd. Keywords: A. Metals; C. Scanning and transmission electron microscopy; C. Crystal structure and symmetry PACS: Rq; Dk 1. Introduction Cu-rich Cu±Zn±Al is known to exhibit a cubic-to-monoclinic martensitic transformation for a large range of compositions, even extending to the binary Cu±Zn and Cu±Al extremes of this ternary system. In an extensive search for the optimal composition with respect to shape memory performance, Zanzotto and Pitteri analysed existing literature data to match theoretical surfaces obtained from nonlinear elasticity theory [1,2]. Although numerous investigations on this ternary system have been published in the past, only few of these have actually determined the materials composition as well as the deformation parameters of the transformation. Both items need to be known in order to properly t the current theoretical curves. In order to improve the numerical treatment of the optimisation, new data on selected compositions thus have to be added. For this purpose, ve new samples have been prepared and investigated so far. In order to obtain correct data on the lattice parameters, thermal history of the material should be properly known. Indeed, depending on the composition and annealing processes, the austenite structure will be disordered bcc, ordered B2 or ordered L2 1. As the martensitic transformation is purely displacive, this immediately implies a different martensite structure, even with the same stacking sequence of the closed packed planes. B2 austenite transforms into a 6M stacking whereas the L2 1 austenite yields an 18R structure. Although the numerical treatment mentioned above only uses the lattice parameters of austenite and martensite and not the internal distribution of atoms in the unit cell, a thorough understanding of the actual ordering and its relation with the thermal history is important in view * Corresponding author. Tel.: ; fax: address: schryver@ruca.ua.ac.be (D. Schryvers). Fig. 1. Schematic representation of two possible occupation con gurations for the L2 1 structure, further referred to as models I and II /00/$ - see front matter q 2000 Published by Elsevier Science Ltd. PII: S (00)

2 274 C. Satto et al. / Solid State Communications 116 (2000) 273±277 Table 1 Atomic positions and occupancies for the L2 1 structure in the model I con guration Atoms x y z Occupancy Cul 1/4 1/4 1/4 1 Znl 1/2 1/2 1/ Cu2 1/2 1/2 1/ A Zn The intensities of these re ections are then compared with dynamical simulations using a multi-slice algorithm and a possible unit cell as starting con guration. Different parameters in this cell can then be optimised by a least-squares procedure in order to improve the match between the model and the experimental data, much in the same way as is done in X-ray data analysis. This procedure is currently referred to as the multi-slice least-squares (MSLS) method. Finally, the optimised results from different contents of the unit cell are compared. Table 2 Atomic positions and occupancies for the L2 1 structure in the model II con guration Atoms x y z Occupancy Cul 1/4 1/4 1/4 1 Znl 1/2 1/2 1/ Cu2 1/2 1/2 1/ A Cu of potential applications. Moreover, changes in ordering can also alter the actual lattice parameters of a basic lattice. In this investigation the atomic occupancy of the different lattice sites in a sample with nominal composition Cu 66.9 Zn 23.7 Al 9.4 is obtained using a new quantitative tool in dynamical electron diffraction. Parallel beam electron diffraction patterns are obtained from nanoscale regions of the sample at different thicknesses and zone axes. These patterns are captured on CCD ensuring a linear response from faint ordering re ections to strong Bragg re ections. 2. Experimental conditions Bulk Cu 66.9 Zn 23.7 Al 9.4 samples were prepared by melting the metals in the proper ratio. The alloy was then annealed for 20 min at 8508C and quenched in boiling water to obtain the austenitic phase. The resulting cell parameters were determined by conventional X-ray diffractometry, using CuKa radiation. Three millimetre samples are then machined and thinned to electron transparency by electropolishing at 08C, using a solution of 230 ml of orthophosphoric acid, 250 ml of ethanol, 50 ml of propanol, 500 ml of distilled water and 5 g of urea. The electron diffraction patterns were obtained in a 300 kev Ultratwin CM30 instrument equipped with a FEG electron source and captured on a CCD camera at the end of a Gatan GIF attachment. The probe size had a diameter of approximately 50 nm, allowing for the approximation of a constant thickness within the probed area. The size of the beam is essentially limited by the need for a parallel beam yielding well-focussed diffraction beams. Computer controlled lateral beam shifts up to 250 nm in Fig. 2. L2 1 diffraction patterns for the: (a) [110], and (b) [100] zone axes, as recorded on CCD.

3 C. Satto et al. / Solid State Communications 116 (2000) 273± different directions are used to obtain several patterns with the same crystallographic zone but with slight variations in average thickness and local orientation. Sets of about 20 patterns taken along different zones and from different areas were nally combined in the optimisation procedure. 3. Used methods For the re nement of the structures from electron diffraction data MSLS [3] was used. The re nement is based on minimising the following R-value: R I ˆX {I m obs 2 I m calc } 2 = X {I m obs } 2 m m It should be noted that this R-value is based on intensities and that all re ections have the same weight. The use of intensities is in accordance with the current trend in X-ray crystallography to base R-values rather on intensities than on structure factors, F. By performing a full dynamic calculation with the Multi-Slice algorithm [4] for the I m (calc), MSLS gives more accurate results than can be obtained with kinematical programs. The parameters to be re ned, besides the ones which are usual in single-crystal X-ray diffraction (i.e. atomic coordinates, Debye±Waller factors, occupancies) are, crystal properties like crystal tilt, absorption and crystal thickness. These added parameters are a bonus for using a full dynamical calculation. An additional advantage of dynamical scattering is the fact that the relative contribution of an atom is not only determined by its atomic weight and occupancy (like with X-rays), but also by the thickness of the crystal. By selecting a good set of data with different thicknesses, it is possible to have all atomic types contributing with the same weight to the resulting set of re ections. Still, the present MSLS re nement procedure suffers from the same problem as its X-ray equivalent: Debye±Waller factors and occupancies are more or less dependent parameters. Therefore, as in this work, re ning Debye±Waller factors and occupancies simultaneously imposes the use of tight constraints on the parameters. parameter. For the current material, this parameter was determined by X-ray diffraction measurements as (4) nm. The re ection conditions observed in the X-ray and electron diffraction data are in agreement with the Fm 3m 255 space group, already determined by several authors [5]. Concerning the L2 1 structure, in view of previous ground state structure calculations [6] which conclude on the 1/4 1/4 1/4 (8c) sites being occupied only by copper atoms, two structural models are possible and shown in Fig Results and discussion The B2 structure has a CsCl type ordering of the bcc lattice. In stoichiometric binary systems the atomic distribution is clear, whereas off-stoichiometric systems will accommodate the difference by anti-site occupations or the introduction of vacancies. Also ternary systems can still be ordered in the B2 structure by combining different atomic species on one given sublattice. Alternatively, a DO 3 or L2 1 superstructure cell, which consists of a double cell parameter in all three cubic directions thus incorporating eight bcc units in total, could attribute one or more sublattices to a selected atomic species. The latter of course depends on composition and so will also the unit cell lattice Fig. 3. (a) Dependency on thickness of the intensity ( 10 5, in log scale) of the 022, 002 and 024 re ections in the [100] zone axis (same plot for both models). (b,c) Dependency on thickness of superstructure re ections in the [110] zone axis, for models I and II, respectively. For clarity, 2113, 2331 and 2333 intensities are multiplied by 10.

4 276 C. Satto et al. / Solid State Communications 116 (2000) 273±277 The rst model consists of a partial and random occupancy of the 4a (0 0 0) site by aluminium and zinc atoms whereas in the second model, this site is randomly shared by aluminium and copper atoms. In accordance with the nominal alloy composition, the occupancies of each site are described in Tables 1 and 2, for model I and model II, respectively. Among the different diffraction patterns recorded along the [100] and [110] orientations, ten data sets were selected based on the degree of overlap re ections, the information content and the thickness. Examples of these two zone axes are shown in Fig. 2. The hkl all odd re ections, only appearing in the [110] zone, are superstructure re ections characteristic of the L2 1 order. The diffuse intensity along [011] directions observed in the [100] zone is due to both static and dynamic uctuations [7] and is not taken into account in the present treatment. In Fig. 3a, the dependency on thickness of the main re ections found in the [100] zone is shown, as calculated by the multi-slice algorithm, using Mac Tempas software. This evolution is roughly the same for both models. Concerning the superstructure re ections observed in the [110] orientation, the intensity evolution versus the thickness is clearly different for both models, as shown in Fig. 3b and c. In order to increase the accuracy of the re nement, diffraction patterns with different thicknesses in the range of 4±20 nm were recorded. The MSLS re nement was started on model II by introducing the atoms as described in Table 2. First the image scale factor as well as the crystal misorientation and the thickness for each data set were re ned. Ten data sets were then selected and all subsequent re nements were done simultaneously on those sets. After this, a re nement of the isotropic temperature Debye±Waller factor B was performed, introducing the constraint of the same B value for atoms on the same crystallographic site. The resulting B values are given in Table 3. Here it is worth mentioning that the Debye±Waller factor for the 4a (0 0 0) site is quite small and close to zero. The second step consists of a simultaneous re nement of the Debye±Waller factor and the occupancy, the result listed in Table 3. The occupancies were constrained in order to obtain 4a and 4b sites fully occupied by Al/Cu and Zn/Cu, respectively, in other words, no vacancies are allowed. This re nement does not change the close to zero value of B for Al1 and Cu3 but drastically changes the occupancy of the 4b (1/2 1/2 1/2) site, resulting in a signi cant different value. Data for each electron diffraction set separately are reported in Table 5. The same re nement sequence was then performed for model I. The result is given in Table 4 from which it is clear that the Debye±Waller factors reveal expected values and the occupancies do not change signi cantly in comparison with the nominal composition. At this stage, it appears interesting to compare the occupancy of the 4b (1/2 1/2 1/2) site, in the re nement of the model II with the starting conditions for model I given in Table 1. On one hand, it is clear that the occupancies as Table 3 Isotropic temperature factor and occupancies determined by MSLS re nement for model II: overall R-value ˆ 2.3% (data sets: ve [100] and ve [110]; thickness: 4±30 nm; no. of re ections: 283 signi cant re ections) Atoms x y z Only B re ned Both B and occupancies re ned Occ B Occ B Cu1 1/4 1/4 1/ (3) (3) Zn1 1/2 1/2 1/ (3) 0.36(5) 0.7(3) Cu2 1/2 1/2 1/ (3) 0.62(5) 0.73) A (9) 0.39(2) 0.07(8) Cu (9) 0.61(2) 0.07(8) Table 4 Isotropic temperature factor and occupancies determined by MSLS re nement for model I: overall R-value ˆ 2.3% (data sets, thickness; no. of re ections, see Table 3) Atoms x y z Only B re ned Both B and occupancies re ned Occ B Occ B Cu1 1/4 1/4 1/ (4) (4) Zn1 1/2 1/2 1/ (2) 0.37(4) 0.65(16) Cu2 1/2 1/2 1/ (2) 0.63(4) 0.65(16) A (14) 0.33(2) 0.22(13) Zn (14) 0.67(2) 0.22(13)

5 C. Satto et al. / Solid State Communications 116 (2000) 273± Table 5 Data on the electron diffraction sets used for the structure re nement. Reliability factor for each data set and for model I (MI) and model II (MII) Zone axis Thickness (nm) Crystal misorientation (centre of Laue circle) No. of re ections R-value (%) h k l MII MI [100] 9.20(2) (5) 0.02(4) [100] 14.40(6) (4) (6) [100] 7.80(4) 2 0.9(1) 0.15(5) [100] 9.90(4) (4) 0.12(4) [100] 18.80(5) (7) 0.23(7) [110] 4.00(6) 1.7(2) 2 1.7(2) 2 0.2(1) [110] 17.1(1) 0.66(3) (3) (3) [110] 17.2(2) 0.67(3) (3) (3) [110] 5.50(7) 0.6(1) 2 0.6(1) 2 1.5(4) [110] 6.10(6) 0.4(1) 2 0.4(1) 2 1.3(3) re ned for model II converge to values comparable with the model I ones. On the other hand, the value of B equal to 0.07 for atoms on the 4a (0 0 0) site could be an indication of a wrong element distribution. Both the re nements (with models I and II) give the same value for the reliability factor R. This is due to the fact that, in the case of model II, occupancies and isotropic thermal parameters compensate one another. It can thus be concluded that the atomic distribution given in model I yields the best t with the experimental diffraction data and is thus retained as the nal con guration. The nally obtained composition for model IisCu 65.7(1.0) Zn 26.1(1.0) Al 8.2(0.5). This result is consistent with the previous work based on neutron diffraction data [8]. These authors conclude on the same atomic distribution for different but related nominal compositions Cu 62.6 Zn 14.5 Al 16.8 and Cu 66.6 Zn 18.9 Al Of course, the possibility of obtaining a nanometer sized probe in the electron microscope offers the means for very local and non-averaged data and thus results. This, together with the fact that vacancies were excluded, can explain the difference between the nominal and re ned compositions. 5. Conclusion annealed for 20 min at 8508C is given by our model I, i.e. copper and zinc on the 4b (1/2 1/2 1/2) sites while aluminium and zinc are sharing the 4a (0 0 0) site. To our knowledge, this result is the rst MSLS structural re nement on a metallic compound in which the structure factors of the atoms involved are relatively close. References [1] M. Pitteri, G. Zanzotto, Acta Mater. 46 (1997) 225. [2] D. Soligo, G. Zanzotto, M. Pitteri, Acta Mater. 47 (1999) [3] J. Jansen, D. Tang, H.W. Zandbergen, H. Schenk, Acta Cryst. A 54 (1998) 91. [4] J.M. Cowley, A.F. Moodie, Acta Cryst. 10 (1957) 609. [5] S. Chakravorty, C.M. Wayman, Acta Metall. 25 (1977) 989. [6] M. Ahlers, Prog. Mater. Sci. 30 (1986) 135. [7] G. Van Tendeloo, M. Chandrasekaran, F.C. Lovey, Proceedings of the International Conference on Martensitic TRansformation, 1986, p [8] A. Planes, L.I. ManÄosa, E. Vives, J. Rodrigues-Carvajal, M. Morin, G. GueÂnin, J.L. Macqueron, J. Phys. Condens. Matter 4 (1992) 553. The L2 1 atomic structure of a Cu 66.9 Zn 23.7 Al 9.4 alloy