Appl. Phys. A 74 [Suppl.], S1446–S1448 (2002) / Digital Object Identifier (DOI) 10.1007/s003390201742
Applied Physics A Materials Science & Processing
Neutron-, X-ray- and electron-diffraction measurements for the determination of γ/γ lattice misfit in Ni-base superalloys R. Gilles1,∗ , D. Mukherji2 , D.M. Többens3 , P. Strunz3,4 , B. Barbier5 , J. Rösler2 , H. Fuess1 1 Technische Universität Darmstadt, Petersenstr. 23, 64287 Darmstadt, Germany 2 Technische Universität Braunschweig, Langer Kamp 8, 38106 Braunschweig, Germany 3 Hahn-Meitner-Institut Berlin, Glienicker Str. 100, 14109 Berlin, Germany 4 Nuclear Physics Institute, 25068 Rez near Prague, Czech Republic 5 Mineralogisches Institut, Poppelsdorfer Schloss, 53115 Bonn, Germany
Received: 11 July 2001/Accepted: 12 March 2002 – Springer-Verlag 2002
Abstract. In this contribution, measurements of γ/γ lattice misfit in Ni-base superalloys will be presented. Misfit values are very important due to their influence on the precipitate morphology and stability. High-resolution diffraction instruments using neutron, X-ray and electron radiation are complementary and suited for the determination of the lattice parameters of the two phases. PACS: 87.64.Bx; 61.12.Ld; 68.47.De Single crystal Ni-base superalloys, used in gas turbine blade applications, are precipitation hardened by ordered Ni3 Al based intermetallic phase (γ ), which are coherent with the matrix phase (γ ). Both γ ( fcc) and γ (primitive, L12 structure) phases have cubic crystal structure with only a small difference in their unit cell size, giving rise to a lattice misfit. The shape, configuration and orientation of γ precipitates are determined, in part, by the coherency strain arising from this lattice mismatch between the two phases [1]. The evolution of precipitate morphology at high temperatures under the application of an uniaxial load (a phenomenon known as rafting) is also very much dependent on the precipitate-matrix misfit value (δ) and its sign, positive or negative [2]. The misfit δ is a −aγ defined as: δ = 0.5(aγ +aγ ) , where a is the unit cell size of the γ
unconstraint γ and γ lattices, respectively. δ is positive when the γ unit cell is larger than that of γ phase. A large number of studies have been devoted to finding suitable techniques for measuring γ/γ lattice misfit accurately [3–5]. Lattice parameter measurements in single phase crystalline solids can be easily and accurately done by using diffraction techniques, e.g. X-ray or neutron diffraction (XRD or ND) or convergent beam electron diffraction (CBED) using a transmission electron microscope (TEM). The lattice parameter values of γ and γ phases determined by XRD or ND are global average values over the relatively large gauge volume. Further, due to the coherency between γ precipitates and the γ matrix, ∗ Corresponding
author. (Fax: +49-89/289-14666, E-mail:
[email protected])
the lattice is in fact distorted near the γ/γ interface [6]. These distortions involve both dilation and contraction of the crystal as well as angular distortions of the lattice [7]. It is not very clear how these distortions exactly affect the misfit measurement by various methods. But they certainly lead to a peak broadening in XRD and ND diffraction patterns. Some attempts have been made in the past to take some of these distortions into account during peak-deconvolution in X-ray and neutron diffraction [8]. A major difference in the CBED technique, as compared to XRD or ND, is the small size of gauge volume and the resulting high spatial resolution (< 10 nm), which allows accurate determination of lattice parameter of individual γ precipitates and in the channel between precipitates. All three methods discussed above, measure the lattice parameter of γ and γ phases in a constrained condition in the microstructure. A polycrystalline Ni-superalloy was used for present study. However, the results are comparable to a similar single crystal system [3–5]. 1 Experimental A Re-rich experimental Ni-superalloy based on Ni-Al-Ta-Re system (designated Re31) was selected for the experiment. The details of the alloy are reported elsewhere [9]. The alloy was solution heat treated (1280 ◦ C/1 h+1300 ◦ C/2 h+ 1320 ◦ C/24 h/ArQ) and aged (1100 ◦ C/4 h/slow cool to 850 ◦ C + 850 ◦ C/24 h/AC) to obtain uniformly distributed cuboidal γ precipitates of average size 370 nm cube edge length. No secondary γ precipitates are present in the γ channels after this heat treatment. Neutron measurements were carried out using the high resolution powder diffractometer E9 [10] at the HMI in Berlin. This instrument operates in transmission mode. ND allows large samples volume to be examined (10 × 105 mm3 were used in this experiment). The X-ray measurements were done using a Siemens D 5000 powder [11] diffractometer (BraggBrentano geometry) with CuKα1 radiation (∆2θ = 0.02◦ , t = 12 sec/step). The beam illuminates an area of around 0.4 mm × 10 mm depending on the incidence angle. As X-ray diffraction is very sensitive to surface effects (e.g. to
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small cracks or surface scratches) due to the lower penetration of the incident beam, different positions on the sample surface were tested for measurements to find a homogeneous part of the sample. In CBED technique [12], the high order zone (HOLZ line pattern present in the transmitted electron beam < 10 µm in diameter) is analysed to determine the lattice parameters of γ and γ in the crystal. The HOLZ line positions in the pattern are sensitive to the changes in the lattice parameter of the crystal and the pattern symmetry reflects the symmetry of the crystal structure itself. By comparing the experimental HOLZ line pattern with computer simulated patterns of known crystals, e.g. with the ratios x of some line lengths (ab/bc), one can determine the lattice constants accurately [12]. 2 Results and discussion A neutron diffraction pattern from the polycrystalline sample is shown in Fig. 1. The pattern, when indexed referring to a cubic crystal, exhibits the contribution of two similar fcc phases for (111), (200), (220), (311) and (222). Even though the fundamental reflections ( fcc) are clearly separated it is not simple to assign the reflections to the two phases γ and γ as the precipitate volume fraction in Re31 is about 56%, i.e. nearly equal to that of the matrix γ phase. The zero point in the 2θ scale was refined (together with all other (hkl) reflections except the reflection marked (100) in Fig. 1 using the method of peak shape proposed by Finger et al. [13] and assuming that two fcc phases are present. The zero point was shifted in such a way that all reflections have optimal matching. After fixing the zero point position, the γ peaks are assigned to ones matching better with the (100) peak as expected due to the superlattice reflections from the cubic primitive structure of γ . The neutron diffraction results (Table 1) show that the lattice parameter of γ (0.35550 nm) is smaller than that of γ (0.35732 nm). The XRD pattern obtained from Re31 alloy shows peak splitting (Fig. 2). The very weak (100) superlattice reflection from the ordered γ allows a more definite identification of the other reflections (Table 2). Table 2 lists the d-spacing (dmeas.) corresponding to the different peaks at the measured 2θ positions. The d-calc. values correspond to the d-spacing of different reflections calculated referring to the d-meas. value of the (100) reflection. The deviation (∆d) resulting
Fig. 2. X-ray diffraction (λ = 0.154056 nm)
of
Re31
alloy
with
CuKα1
Table 1. Results of γ and γ d-values measurements by neutron diffraction method a 2θmeas
29.242 51.598 51.974 60.374 60.894 90.571 91.238 113.159 113.400 121.067 122.073 a b
dmeas (nm)a
dcalc (nm)b
∆d = dmeas − dcalc
(hkl)
phase
0.35585 0.20639 0.20500 0.17864 0.17726 0.12640 0.12568 0.10762 0.10747 0.10317 0.10267
0.35585 0.20545 0.20545 0.17793 0.17793 0.12581 0.12581 0.10729 0.10729 0.10273 0.10273
0 0.00094 –0.00045 0.00072 –0.00067 0.00059 –0.00013 0.00033 0.00018 0.00045 –0.00006
100 111 111 200 200 220 220 311 311 222 222
γ γ γ γ γ γ γ γ γ γ γ
zero point cor Calculated referring to the measured d-value of (100) reflection
Table 2. Results of γ and γ d-values measurements by X-ray diffraction a 2θmeas
dmeas (nm)a
dcalc (nm)b
∆d = dmeas − dcalc
(hkl)
phase
25.022 43.825 44.113 50.801 51.146 75.051 75.563 90.485 91.677 96.203 97.199
0.35559 0.20641 0.20513 0.17958 0.17845 0.12646 0.12573 0.10848 0.10738 0.10349 0.10269
0.35559 0.20530 0.20530 0.17780 0.17780 0.12572 0.12572 0.10721 0.10721 0.10265 0.10265
0 0.00111 –0.00017 0.00178 0.00065 0.00074 0.00001 0.00127 0.00017 0.00084 0.00004
100 111 111 200 200 220 220 311 311 222 222
γ γ γ γ γ γ γ γ γ γ γ
a b
Fig. 1. Neutron diffraction pattern of Re31 alloy λ = 0.1797 nm
pattern
zero point cor Calculated referring to the measured d-value of (100) reflection
from d-meas. and d-calc. is systematically larger for that individual peak, out of each double-peak, which appears at lower angle. Thus for all five split peaks, the ones with the higher angle (smaller d-value) match clearly better with the γ phase. On the basis of this analysis, the γ lattice parameter (0.35588 nm) is smaller than the one of γ phase (0.35853 nm) in the Re31 alloy.
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The difference in misfit values between X-ray (−0.74%) and neutron measurements (−0.51%) are partly due to the different procedures adopted for the evaluation of the two diffractograms. The X-ray peaks have a complicated profile. Nevertheless a standard peak search routine (i.e. the peak maximum of each reflection) was used to find the peak position. The high resolution of the diffractometer allowed this analysis method and attempts using a special profile fit gave no significant change in the peak positions. However, in the case of neutron data the peak profile is of a more simple shape and not strongly influenced by the sample. The lower resolution of the ND detector, seen in the weaker splitting of paired reflections, (see Fig. 1) however, do not allow determination of peak positions. Therefore, to find a more precise value of the peak positions and to assign the (100) peak to the γ phase a profile fitting following the procedure of Finger et al. [13] was adopted. The results make it obvious that a zero point correction also needs to be included. The XRD results, even though more accurate than the ND results, are also additionally influenced by peak broadening (γ size effects and changes in lattice constants due to coherency strains etc.). Results of measurements by CBED are listed in Table 3 and give γ and γ lattice parameters as 0.35756 nm and 0.35812 nm, respectively. Due to limited space in this paper, details of the analysis can not be presented and will be reported elsewhere. The misfit values estimated from XRD, ND and CBED are (–)0.74%, (–)0.51% and (–)0.16%, respectively. The difference in misfit values between X-ray and neutron measurements are small. The volume probed by XRD and ND methods are large (typically containing 3 × 107 and 4 × 1012γ particles, respectively). These methods thus give only an average value of the lattice constants of both phases. On the other hand, the misfit value determined by CBED results from a volume containing one individual γ precipitate and the surrounding γ matrix and it shows a larger difference from XRD and ND values. Since measurement accuracy for CBED technique is similar to XRD, such difference can be explained only on the basis that the measuremnts are on a very local scale.
Table 3. Results of γ and γ lattice parameter measurements by CBED phase
Measured Ratio x x = ab/bc
Lattice Parameter a (nm)
γ
0.609
γ
0.551
0.35756 (aγ = 0.0031x 2 + 0.0102x + 0.3525) 0.35812 (aγ = 0.00265x 2 + 0.0105x + 0.35314)
a calculated from measured ratio x in experimental HOLZ patterns [12] and using the calibration function generated through simulation of HOLZ patterns for Ni3 Al and Ni-13.7Re alloy crystals of different lattice sizes
Acknowledgements. Financial support of the HMI (BENSC) to one of the authors, R. Gilles, is gratefully acknowledged. We would also like to thank H. Schneider and B. Krimmer for assistance in the neutron scattering experiments.
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