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The morphology of secondary-hardening carbides in a martensitic steel at the peak hardness by 3DFIM
ARTICLE IN PRESS Ultramicroscopy 109 (2009) 518–523
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The morphology of secondary-hardening carbides in a martensitic steel at the peak hardness by 3DFIM J. Akre´ a,, F. Danoix a, H. Leitner b, P. Auger a a
Groupe de Physique des Mate´riaux, UMR CNRS 6634, Institut des Mate´riaux de Rouen, UFR Sciences et Techniques Avenue de l’Universite´-B.P. 12, 76801 Saint Etienne du Rouvray CEDEX, France ¨t Leoben, A-8700 Leoben, Austria Department of Physical Metallurgy and Materials Testing, Montanuniversita
b
a r t i c l e in f o
PACS: 61.82.Bg 61.46.+w 61.16.Fk Keywords: Secondary-hardening steel M2C Three-dimensional field ion microscopy Atom-probe tomography
a b s t r a c t The morphology and composition of secondary-hardening M2C carbides in a complex steel under nonisothermal tempering condition has been investigated with three-dimensional field ion microscopy and atom-probe tomography. The technical set-up and the condition of investigations have been developed. We will reveal for the first time, a virtually non-biased image of the so-called secondary-hardening microstructure, consisting in a very fine dispersion of nanometer-sized needles, idiomorphs and blocky carbides. Needles precipitate with a large number density at the maximum hardness peak. We have found out that this mixture of shape could be explained by the onset of coarsening, but the role of local factors have been evidenced: variation of composition among the carbides and even local strain effects due to the precipitation of a second phase can play a role in changing the growth conditions. & 2008 Published by Elsevier B.V.
1. Introduction Secondary-hardening martensitic steels are high performance steels used for cutting and hot-work applications. Their microstructure consists in a fine dispersion of so-called ‘secondaryhardening’ nanoscale carbides principally vanadium, molybdenum, tungsten, and chromium carbides. Their typical size at secondary hardness peak varies in the range of a few to tens of nanometers. The investigation of such a microstructure and its evolution upon tempering, particularly the resistance to coarsening is of great metallurgical importance considering their applications. Since its invention by Mu¨ller [1], the field ion microscope (FIM) has been widely used for metallurgical investigations, and is the preferred microscopy technique for the study of the early stages of precipitation in metals [2]. In the FIM, field ionisation of gas atoms occurs on a positively polarised metal surface and resulting ions are projected on a microchannel plate assembly for position detection. The resulting image is a projection of the near-spherical atom surface of the specimen, close to a stereographic projection [3]. In the late 1960s, Mu¨ller [4] invented the atom-probe (APFIM), enabling the chemical analysis of the atoms observed in the FIM. Set-up of a position-sensitive detector coupled with time-of-flight chemical analysis allowed the realisation of atom-probe tomography (APT) [5,6].
Corresponding author. Tel.: +33 2 32955181.
E-mail address: [email protected] (J. Akre´). 0304-3991/$ - see front matter & 2008 Published by Elsevier B.V. doi:10.1016/j.ultramic.2008.11.010
But, the field ion microscope can be used as a threedimensional microscope by the method of tomography upon field evaporation. This technique allows 3D reconstruction of the microstructure using a series of surface micrographs. The applicability of this technique is wide: void reconstruction in irradiated materials [7] or precipitate shape reconstruction [8]. A similar technique has been used by Miller [9] for the reconstruction of spinodally decomposed FeCr alloy. Recently, it has been demonstrated that lattice reconstructions could be achieved [10]. This technique have been useful in characterizing carbides morphology in an industrial steel, since the size of investigated volumes, larger than APT, correspond well to the typical size of the phase. The FIM and 3DFIM as well are particularly well suited for carbide morphology study, as they give a sharp bright phase contrast due to the large difference in evaporation field between the carbides and the matrix. Even when the carbides have a very small size, like during the nucleation events, they remain visible, whereas APT volume reconstructions suffered from drastic ‘local magnification effects’, giving a blurry vision of carbides interfaces. These effects are present for 3DFIM, but they only change the volume of precipitates, making them larger. Previous investigations [11,12] on this industrial steel, focused on the characterization of such carbides have pointed out the relevance of applying complementary global and local techniques such as SANS, TEM, DSC, and APT to finely characterize the precipitation behaviour. The present paper is thus a further contribution to this field focusing on the determination of morphologies in three dimensions and in direct space. M2C carbides are metastable carbides formed in Mo, Cr, V
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secondary-hardening steels. When they precipitate in Fe–Mo–C, they are described as a needle-shaped hexagonal close packed phase growing along /11 0S direction, with Pitsch–Schrader orientation relationship:
Cr addition leads to plate-like carbides, somewhat elongated in a preferred direction. Although M2C is a metastable carbide, this orientation relationship provides a good match between ferrite and carbides and then helps to stabilize the formation of these carbides. Thus, M2C has a higher driving force than more stable phases like M6C or M23C6, over a wide range of intermediate temperature. But the surface energy change rapidly with the orientation of precipitates with the matrix. This is the reason why these carbides grow preferentially in a direction, making them elongated in shape. The preferred shape of M2C carbides is thus a long needle. But, Davies and Ralph [13] observed that in Fe–Mo–C alloy, for small precipitate sizes, needles coexisted with spheres. They derived the explanation with an analysis based on three factors influencing the shape of precipitates: composition, surface energy (or surface tension), and strain energy [14]. But in the samples investigated here, there are two additional factors influencing on the microstructure: the anisothermal tempering and, the precipitation of B2-NiAl phase that are specific to our alloy system and tempering conditions.
2. Material, thermal treatment and specimen preparation The material of the present investigation is a X32Cr–Mo–V 3-3-3 secondary-hardening martensitic steel additionally alloyed with Ni and Al, containing typical compositions in major alloying elements given in Table 1. Rods of material have been subjected to the following thermal treatment: samples were first homogenised in the austenitic domain at 1123 K and then, quenched in oil to obtain massive lath martensite. The tempering treatment consisted of applying a continuous heating (20 K/min) followed by a rapid quench in a nitrogen flow to ‘‘freeze’’ the microstructure. The ageing conditions of the investigated specimen will thus be referred as the maximum temperature reached by the specimen just before the quench. The different ageing conditions have been characterized by microhardness measurements, enabling the detection of the secondary hardness peak temperature, as shown in Fig. 1. The maximum hardness is observed for the specimen aged up to 883 K. This paper will thus focus on the microstructure of this particular condition. The rods were finally cut into small parallelepipeds for electropolishing to obtain field evaporation specimens, i.e. a very sharp needle with a radius of curvature of less than 100 nm, using standard electropolishing solutions for steels, see e.g. [15].
3. Experimental Investigations have been carried out in a conventional FIM chamber using Ne and H2 mixture as imaging gas with a Table 1 Composition in major alloying elements of the investigated steel.
at% wt%
Fe
C
Cr
Mo
V
Ni
Al
Bal. Bal.
1.40 0.32
2.60 2.50
1.40 2.50
0.30 0.30
6.00 6.50
5.00 2.50
750 700 Hardness (HV)
ð0 1 1Þkð0 0 0 1ÞM2 C ½1 0 0k½1 1 2 0M2 C
519
650 600 550 500 450 400 200
400
600 800 Temperature ( K)
1000
1200
Fig. 1. Hardness evolution during thermal treatment.
pressure of 5 10–5 mbar, the tip being maintained at a temperature of 90–100 K and positively polarised at voltages ranging from 3 to 17 kV, depending mainly on the specimen radius of curvature. We have carried out chemical analyses with an EcoTAP [16], equipped with an advanced delay line position-sensitive detector [17]. FIM micrographs can be indexed thanks to conventional stereographic projections so that the main crystallographic directions can be deduced from the geometrical arrangement of poles, and on symmetry considerations. This procedure allows the determination of the orientation of the crystallographic grain situated at the tip apex. As the material has been cut from bulk rods with no particular texture, any grain orientation at the tip apex is possible. The specimen radius of curvature is deduced from ledge separation of plane stacking, the so-called Dreschler method [18]. Assuming that the tip radius of curvature is homogeneous, distances on the surface can be deduced approximately from the magnification. In order to distinguish the carbides from the surrounding matrix, we take advantage of the large difference in evaporation fields between carbides and martensite. Indeed, during field evaporation, due to their higher evaporation field, M2C carbides tend to protrude on the surface resulting in a local area of higher field, forming the blur areas visible on the FIM micrographs of the Fig. 2. To enhance the contrast between the matrix and the precipitates, the temperature has been raised to 80–100 K during the recording of evaporation sequences. The consequence is that the carbides appear brighter than the matrix, thus allowing easy thresholding by pixel light intensities (Fig. 3). For martensitic steels, obtaining a convenient lateral resolution may be a delicate issue; indeed, the pole contrast of the martensite matrix is poor: highly packed poles such as {11 0} and {2 0 0} can barely be seen. To improve the resolution in the matrix, a certain amount of dihydrogen (less than 5 10–7 mbar partial pressure) has been introduced in the experiment chamber together with Ne. That way, the resolution is much better [19], as can be seen in Fig. 2(b) and, matrix poles and carbides can be imaged altogether. The technique of 3DFIM consists of the stacking of images recorded during the continuous field evaporation of a specimen at DC voltage. The voltage is continuously increased to maintain a constant evaporation rate. The evaporation film has been recorded on a CCD camera with a 25 images-by-second frame rate and a
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´ et al. / Ultramicroscopy 109 (2009) 518–523 J. Akre
Fig. 2. Left: 923 K tempered specimen imaged with Ne (5 10–5 mbar) at 10 kV, the (11 0) pole is hardly visible. Right: same thermal treatment, but imaged in a mixture of Ne (5 10–5 mbar) and H2 (2 10–7 mbar) at 12 kV. The rise in contrast in the matrix is evident but deteriorates the second phase contrast (both pictures are at best image voltage) (circled: a dislocation emerges in the (0 11) pole).
Fig. 3. 2D cross-section of a 3D reconstruction after the smoothing procedure. Evaporation proceeds from the top to the bottom of the figure. Carbides appear bright.
40 ms exposure time. The shutter aperture has been adjusted to obtain a sufficient contrast without saturation of the CCD sensor. The three-dimensional reconstructions shown here, result from the stacking of evaporation sequence images where grey level pixels have been converted to a colored look-up table. In the raw stacking, the explored depth depends on the number of images recorded by the camera, i.e. on parameters such as the recording mode, integration time, diaphragm aperture, etc. But, as these parameters have been fixed and the evaporation has been maintained to a constant rate, the depth is proportional to the analysed length. The calibration of the evaporated depth has been determined as follows: the lateral lengthscale (nm/pixel) is deduced from the radius of curvature measured on the 2D image in presence of dihydrogen as explained previously and, the number of evaporated planes in a given direction (planes of {11 0}, {2 0 0} or {11 2} type are the most convenient) gives the evaporated depth. These reconstructions have been done without surface curvature corrections, thus for precipitates far from each other, the angle relations are not conserved by the stacking procedure. But, it is well known that field ion emission specimen surfaces show facets corresponding roughly to the dense planes. We have thus restricted our reconstructed volumes close to the major poles. The volume limit of the phases is inferred by thresholding voxels light intensities, high intensities correspond to carbides, whereas low intensities correspond to the matrix. The data are additionally resampled, to obtain a constant resolution in the three directions. The (x,y) resolution has been set unchanged, while the z resolution has been reduced to match approximately the (x,y) resolution. This procedure has two advantages: the memory size of the dataset is reduced and the matrix contrast appears much more uniform.
Fig. 4. Volume reconstruction of evaporation sequences. At the peak hardness, different morphologies of carbides can be seen: (a) stacked disk-shaped carbides; (b) group of small idiomorphs; (c) blocky carbides around lath boundaries; (d) lath carbides surrounded by small idiomorphs in a volume as big as 10 10 10 nm3 (Fig. 5(b)).
Indeed, it is common with highly alloyed materials that substitutional or interstitial preferentially retained alloying atoms appear as bright spots on the specimen surface; they should not be taken as a carbide extremity. Hopefully, as these features have a very small depth extension even compared to carbides nuclei consisting in a dozen of atoms, they can be distinguished from precipitates when the stacking procedure and depth calibration is completed. To eliminate those bright imaging spots, we have used a slight smoothing while resampling the data, where the mask of the filter is computed only in the direction of evaporation (Our z-direction, letting (x,y) be the position on the detector). By using a linear filter (triangle filter), the intensity of little ‘z extension’ features merges with the surrounding, because they are covered by the mask of the filter, whereas bigger features remains, although their limits become a little blur, smooth. Another limitation of using this filter is that, when two objects are very close to each other, they can merge. To avoid this issue, it is necessary to make sure that the size of the filter’s mask (in pixels) is less than half the smallest interplanar distance. The reconstructions give useful information about the carbides at the peak hardness. Fig. 3 provides information on the extent of carbides in the direction parallel to the axis of the specimen, i.e. in the direction of evaporation; and, Fig. 4 is a result of the threedimensional reconstructions on two different samples ((a), (b) and (c) come from the same sample, whereas (d) is a different sample, with the same tempering conditions).
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4. Results 4.1. 3DFIM results We can see that elongated but rather thick carbides, resembling small laths rather than needles are present (Fig. 4(a) and (d)). These carbides are about 10–15 nm in length, 2–5 nm in width, and 2 nm thick. Different orientations of the carbides can be seen, but in general neighbouring carbides share the same orientation. The reconstruction procedure is, however, not suitable to determine accurately the direction of the big axis of the lath carbides. But the carbides of Fig. 4(a), have their broad face lying perpendicular to the direction of analysis that has been chosen around a (11 0) pole. Thus, (11 0) is likely to be their habit plane, or matching plane with martensite. In Fig. 4(a), we have emphasized a superstructure formed by the stacking of many plate-like carbides. This kind of superstructure is very frequent in the analysed samples. The comparison between Fig. 4(a) and (d) reveals that the superstructure of Fig. 4(a) is formed of bigger, broader and thicker carbides than these of Fig. 4(d). Their bigger size suggests that they were formed prior to these of Fig. 4(d). APT analysis has revealed that intra-lath elongated carbides have a composition typical of equilibrium coherent M2C carbides (see Fig. 5). Besides anisotropic, elongated lath carbides, small globular carbides are also visible in Fig. 4. The small globular carbides have rather large size dispersion, but are rarely bigger than 2 nm in diameter. They could be found dispersed around the lath carbides (Fig. 4(d) arrowed) or grouped. Another type of globular carbides, differing from the latter by their size and their localisation: they are bigger (up to 6 nm.) and commonly isolated from other types of carbides. Fig. 4(c) shows such carbide, referred as ‘‘blocky’’ regarding its irregular shape, situated in the precipitate-free zone of grain-boundary allotriomorph carbides, presented in the next section.
Besides these two morphologies, lath boundary allotriomorphs can be observed since the inter-lath spacing in this type of martensite is a few hundreds of nanometers. On average, at least one lath boundary is intercepted during a 3DFIM typical analysis. The plate-like allotriomorphs ‘carpet’ the grain boundaries at stages where the microstructure coarsen partly, but as expected from heterogeneous nucleation theory, they retain a certain individuality, forming columnar structures flattened at each extremities (not shown here). They are of the M2C type. 4.2. APT results As either 3DFIM or APT are unable to give information on the phase crystallographic structure, the nature of carbides has to be inferred from chemical analysis. This analysis is based on the alloying amount of carbon and iron in the precipitates and on the strong carbide former element balance: Cr, Mo, and V (See Fig. 5). However, the concentration of carbides is altered by the local magnification effect [20]. To estimate the actual concentration of solute elements, a correction procedure has been applied [21]. The limits of carbides are assessed by considering the regions of low iron atoms density. Assuming that the iron content within the limit of the carbides is the actual iron content of the precipitates, solute atoms displaced by trajectory aberrations are then replaced inside these limits to obtain the corrected alloying element concentration. APT analysis reveals that the spheroidal carbides contain slightly lower carbon and higher iron amounts, and a balance of Cr, Mo and V, with more chromium than molybdenum, but with slightly higher molybdenum content than lath carbides. The comparison of composition between lath carbides and spheroid carbides are shown in Table 2. The low level of carbon in the spheroidal carbides might suggest that different types of carbides precipitate, i.e. M23C6 (20 at% C). But according to Grujicic and Olson [22] and Olson et al. [23] calculations, such levels of
1 nm.
1 nm.
100
100
90 80
80
Concentration (at%)
Concentration (at%)
90 70 60 50
C Cr Mo Fe V
40 30 20
70 60 C Cr Mo Fe V
50 40 30 20 10
10 0
521
3
3.5
4
4.5 5 5.5 Analysed depth (nm.)
6
6.5
7
0
2
3
4 5 Analysed depth (nm.)
6
7
Fig. 5. Top-left: 3D atom-probe volume (3 3 9 nm3) intercepting intra-lath M2C carbide. Top-right: (2 2 10 nm3) a blocky carbide. Bottom-left: concentration profile associated to the elongated carbide. The core carbon concentration level is 33 at%. Bottom-right: concentration profile through the blocky carbide represented above, the iron content is over-estimated due to local magnification (see Table 2 for corrected composition).
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Table 2 Concentration of carbides depending of their morphology measured with the ECOTAP. Type
C (at%)
Fe (at%)
Cr (at%)
Mo (at%)
V (at%)
Intra-lath elongated Blocky idiomorphs
32.670.5 20.470.7
1.670.5 8.370.7
39.970.4 41.670.6
19.470.2 24.570.3
6.670.4 5.070.6
Concentration has been corrected from local magnification effect.
elements can be found for coherent M2C in the first stages of precipitation. Moreover, thermodynamical calculations have revealed that M6C (15–18 at% C) and M23C6 although stable at 883 K, form only after long time ageing. The conclusive argument allowing ruling out the formation of M23C6 or M6C is that they are not found in the subsequent tempering conditions (i.e. at 923 and 973 K). Instead, globular carbides are found, still having a composition typical of M2C carbides (around 33 at% C). As it is very unlikely that the thermodynamically stable carbides M6C or M23C6 dissolve with increasing temperature and tempering time, we conclude that small globular carbides are M2C or M2C nuclei. This conclusion determines that all the investigated carbides at peak hardness are M2C, and differ only in concentration. The slight difference in concentration can be due to several reasons, which will be tentatively explained in relation with their morphology in the discussion section.
becomes the dominant growth factor. Anyhow, a varying amount of coarsening is always found during the whole precipitation process. In this regime, large precipitates grow at the expense of smaller ones that dissolve rapidly. The small spheroidal carbides dispersed among the comparatively large needles may originate from that mechanism. Their spheroidal shape is due to the fact that the sphere gives an optimal surface to volume ratio locally minimizing the pressure due to the capillarity. For subsequent ageing, no other such small spheroids can be found in the immediate vicinity of lath carbides. But, another explanation more related to strain effects, involving the composition changes measured by APT can be proposed. The small spheroidal carbides could be the carbides that nucleate with a composition resulting in a bigger molar volume that is not optimal for coherent growth, i.e. with more molybdenum and less chromium. These carbides grow slower and are prone to dissolve. For the reason that they have a bigger molar volume, they can be incoherent and spheroidal in shape. In other words, the chemical driving force tends to form carbides of varying composition, but, only those within a certain range of composition may grow enough to reach a consequent size. The smallest carbides can either dissolve, due to coarsening (Ostwald ripening), or being locked and grow very slowly, thus showing coarsening resistance. Note that this other explanation is not contradictory with the preceding, and includes the composition changes discussed previously.
5.3. Thermal history 5. Discussion 5.1. Composition The APT analysis revealed that, in this industrial steel, the change in composition of M2C carbides did not influence their structure. In this steel, it appears that the smallest carbides always contain more iron and less carbon. But it also appears that in the early stages, the growth of carbides with a lesser molar volume (i.e. enriched in chromium) is favoured, as long as coherent equilibrium is thermodynamically favoured [24]. The little spheroids with their slightly higher molybdenum content could be some latent germs that are prone to dissolve or, stable precipitates but with incoherent interfaces, i.e. with limited possibilities of growing rapidly compared to the precipitates with a lesser molar volume. But the complex structure of their interface and their closed-packed bonding, makes them also somewhat resistant to coarsening. That could be the reason why in more advanced stages we find spheroidal carbides together with coarse elongated carbides.
The materials have been submitted to a continuous temperature increase of 20 K/min. Investigations have revealed that the precipitation of carbides occurred before 883K, at 823K. At 823K carbides nucleate heterogeneously on dislocations. The resulting microstructure is ‘‘islands’’ of carbides located on and around dislocations, but the repartition of carbides is far from homogeneous. As these carbides are stable, they grow to a weighty size with increasing temperature, i.e. of diffusivity of carbide formers atoms. Around 873–883K, homogeneous nucleation occurs. This second nucleation event is responsible for the fast nucleation and growth of a lot of laths carbides, but they are smaller in size than the previous ones, and their spatial repartition is homogeneous. This second nucleation effect is made possible by an increase of chemical driving force due to cementite dissolution completion [12]. We thus expect that the big carbides forming superstructures are the carbides that nucleate on dislocations, and smaller laths are newly formed growing phase.
5.4. B2-NiAl precipitation 5.2. Surface energy–strain energy The surface energy influences the growth of a semi-coherent second phase as it varies with the relative orientation of the two crystals with minimal values perpendicular to the matching plane (habit plane). Surface energy is responsible for the cusp-related morphologies (discs) [25]. However, misfit strain effect makes the incoherent extremities grow more rapidly: that is essentially the reason for needle or lath morphologies. For the same reasons, the sphere is the equilibrium shape of completely incoherent precipitates. The large predominance of broad needles or small laths is in good agreement with this statement. As surface energy and strain energy are related, they cannot be treated separately. According to the analysis of Davies and Ralph [13], the occurrence of spheroid carbides reveals that in the material, coarsening
We have found that idiomorph small carbides closely grouped without any bigger carbide in the immediate vicinity. The occurrence of these carbide clusters cannot be explained by Ostwald ripening, but as follows: in this experimental steel, B2NiAl is precipitated as a second phase. This phase consists in small spherical B2-ordered precipitates fully coherent with the ferrite matrix. The precipitation of this phase makes the ferrite locally harder and can thus impinge the growth of M2C carbides, thus, only small globular carbides can grow when the local number density of B2-NiAl precipitates is rather high. Again, their globular shape can be explained by their small volume. These are carbides locked in their initial stage, because the transfer of matter is slowed down by the ordered precipitates. They are expected to dissolve slowly with further tempering, when B2-NiAl precipitates coarsen.
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6. Conclusions We have investigated the morphology of carbides at the peak secondary-hardening microstructure of a martensitic steel, and demonstrated that at the maximum hardness peak under nonisothermal tempering a mixture of precipitate morphologies was observed:
Needles or laths, with size ranging from 10 to 15 nm, nucleated on dislocations.
Small spheroids, with a size less than 2 nm, mainly resulting
from the dissolution of the previous ones, due to coarsening and/or the nucleation of incoherent germs. Blunt blocky shaped carbides with a size of about 5 nm.
All these carbides, are expected to be of the same type, i.e. of the M2C type. Acknowledgements The author gratefully acknowledge S.D. Erlach for the microhardness measurements, the Austrian Kplus competence center program for financial support, the French-Austrian exchange program Amadeus and Bo¨hler Edelstahl GmbH. References [1] E.W. Mu¨ller, Zeitschrift fu¨r Physik 131 (1) (1951) 136–142. [2] H. Wendt, Decomposition of Alloys: The Early Stages, Pergamon Press, pp. 133–138. [3] D.G. Brandon, Journal of Scientific Instrumentation 41 (1964) 373. [4] E.W. Mu¨ller, J.A. Panitz, S.B. McLane, Review of Scientific Instrumentation 10 (1968) 177.
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[5] A. Cerezo, T.J. Godfrey, G.D.W. Smith, Review of Scientific Instrumentation 39 (1988) 862. [6] D. Blavette, A. Bostel, J.M. Sarrau, B. Deconihout, A. Menand, Nature 363 (1993) 432–434. [7] C.-Y. Wei, M.I. Current, D.N. Seidman, Philosophical Magazine 23 (1981) 1045. [8] A. Hildon, P.R. Howell, A. Youle, R.J. Taunt, T.F. Page, B. Ralph, Journal of Microscopy 99 (1973) 41–56. [9] A. Cerezo, M.G. Hetherington, J.M. Hyde, M.K. Miller, G.D.W. Smith, J.S. Underkoffler, Surface Science 266 (1992) 471–480. [10] F. Vurpillot, M. Gilbert, B. Deconihout, Surface and Interface Analysis 39 (2007) 273–277. [11] M. Bischof, S. Erlach, P. Staron, H. Leitner, C. Scheu, H. Clemens, Zeitschrift fur Metallkunde 96 (9) (2005) 1074–1080. [12] H. Leitner, M. Bischof, H. Clemens, S. Erlach, B. Sonderegger, E. Kozescnhik, J. Svoboda, F.D. Fisher, Advanced Engineering Materials 8 (11) (2006) 1066–1077. [13] D.M. Davies, B. Ralph, Journal of the Iron and Steel Institute (1972) 262–266. [14] J.W. Christian, The Theory of Phase Transformation in Metals and Alloys, Pergamon Press, 1965. [15] M.K. Miller, Atom Probe Tomography, Analysis at the Atomic Level, Springer. [16] E. Be´mont, A. Bostel, M. Bouet, G. Da Costa, S. Chambreland, B. Deconihout, K. Hono, Ultramicroscopy 95 (1–4) (2003) 231–238. [17] G. Da Costa, F. Vurpillot, A. Bostel, M. Bouet, B. Deconihout, Review of Scientific Instruments 76 (2005) 013304. [18] M. Dreschler, P. Wolf, in: Proceedings of the Fourth International Conference on Electron Microscopy, Springer, Berlin, 1958, pp. 1–835. [19] E.W. Mu¨ller, in: J.J. Hren, S. Ranganathan (Ed.), Field Ion Microscopy, Plenum Press, New York, 1968, pp. 88–101. [20] F. Vurpillot, A. Bostel, D. Blavette, Applied Physics Letters 76 (2000) 3127–3129. [21] F. De Geuser, Ph.D. Thesis, Interpre´tation et traitement des donne´es de la sonde atomique tomographique: Application a` la pre´cipitation dans les Al-Mg-Si, Rouen, 2005. [22] M. Grujicic, G.B. Olson, Calphad 12 (1988) 405–414. [23] G.B. Olson, T. Kinkus, J. Montgomery, Surface Science 246 (1991) 238–245. [24] J. Akre´, Ph.D. Thesis, Caracte´risation a` la sonde atomique tomographique de se´quences de pre´cipitation dans un acier expe´rimental, Universite´ de Rouen, 2008. [25] D.A. Porter, K.E. Easterling, Phase Transformations in Metals and Alloys, second ed, Taylor & Francis, 2004.
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The morphology of secondary-hardening carbides in a martensitic steel at the peak hardness by 3DFIM J. Akre´ a,, F. Danoix a, H. Leitner b, P. Auger a a
Groupe de Physique des Mate´riaux, UMR CNRS 6634, Institut des Mate´riaux de Rouen, UFR Sciences et Techniques Avenue de l’Universite´-B.P. 12, 76801 Saint Etienne du Rouvray CEDEX, France ¨t Leoben, A-8700 Leoben, Austria Department of Physical Metallurgy and Materials Testing, Montanuniversita
b
a r t i c l e in f o
PACS: 61.82.Bg 61.46.+w 61.16.Fk Keywords: Secondary-hardening steel M2C Three-dimensional field ion microscopy Atom-probe tomography
a b s t r a c t The morphology and composition of secondary-hardening M2C carbides in a complex steel under nonisothermal tempering condition has been investigated with three-dimensional field ion microscopy and atom-probe tomography. The technical set-up and the condition of investigations have been developed. We will reveal for the first time, a virtually non-biased image of the so-called secondary-hardening microstructure, consisting in a very fine dispersion of nanometer-sized needles, idiomorphs and blocky carbides. Needles precipitate with a large number density at the maximum hardness peak. We have found out that this mixture of shape could be explained by the onset of coarsening, but the role of local factors have been evidenced: variation of composition among the carbides and even local strain effects due to the precipitation of a second phase can play a role in changing the growth conditions. & 2008 Published by Elsevier B.V.
1. Introduction Secondary-hardening martensitic steels are high performance steels used for cutting and hot-work applications. Their microstructure consists in a fine dispersion of so-called ‘secondaryhardening’ nanoscale carbides principally vanadium, molybdenum, tungsten, and chromium carbides. Their typical size at secondary hardness peak varies in the range of a few to tens of nanometers. The investigation of such a microstructure and its evolution upon tempering, particularly the resistance to coarsening is of great metallurgical importance considering their applications. Since its invention by Mu¨ller [1], the field ion microscope (FIM) has been widely used for metallurgical investigations, and is the preferred microscopy technique for the study of the early stages of precipitation in metals [2]. In the FIM, field ionisation of gas atoms occurs on a positively polarised metal surface and resulting ions are projected on a microchannel plate assembly for position detection. The resulting image is a projection of the near-spherical atom surface of the specimen, close to a stereographic projection [3]. In the late 1960s, Mu¨ller [4] invented the atom-probe (APFIM), enabling the chemical analysis of the atoms observed in the FIM. Set-up of a position-sensitive detector coupled with time-of-flight chemical analysis allowed the realisation of atom-probe tomography (APT) [5,6].
Corresponding author. Tel.: +33 2 32955181.
E-mail address: [email protected] (J. Akre´). 0304-3991/$ - see front matter & 2008 Published by Elsevier B.V. doi:10.1016/j.ultramic.2008.11.010
But, the field ion microscope can be used as a threedimensional microscope by the method of tomography upon field evaporation. This technique allows 3D reconstruction of the microstructure using a series of surface micrographs. The applicability of this technique is wide: void reconstruction in irradiated materials [7] or precipitate shape reconstruction [8]. A similar technique has been used by Miller [9] for the reconstruction of spinodally decomposed FeCr alloy. Recently, it has been demonstrated that lattice reconstructions could be achieved [10]. This technique have been useful in characterizing carbides morphology in an industrial steel, since the size of investigated volumes, larger than APT, correspond well to the typical size of the phase. The FIM and 3DFIM as well are particularly well suited for carbide morphology study, as they give a sharp bright phase contrast due to the large difference in evaporation field between the carbides and the matrix. Even when the carbides have a very small size, like during the nucleation events, they remain visible, whereas APT volume reconstructions suffered from drastic ‘local magnification effects’, giving a blurry vision of carbides interfaces. These effects are present for 3DFIM, but they only change the volume of precipitates, making them larger. Previous investigations [11,12] on this industrial steel, focused on the characterization of such carbides have pointed out the relevance of applying complementary global and local techniques such as SANS, TEM, DSC, and APT to finely characterize the precipitation behaviour. The present paper is thus a further contribution to this field focusing on the determination of morphologies in three dimensions and in direct space. M2C carbides are metastable carbides formed in Mo, Cr, V
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secondary-hardening steels. When they precipitate in Fe–Mo–C, they are described as a needle-shaped hexagonal close packed phase growing along /11 0S direction, with Pitsch–Schrader orientation relationship:
Cr addition leads to plate-like carbides, somewhat elongated in a preferred direction. Although M2C is a metastable carbide, this orientation relationship provides a good match between ferrite and carbides and then helps to stabilize the formation of these carbides. Thus, M2C has a higher driving force than more stable phases like M6C or M23C6, over a wide range of intermediate temperature. But the surface energy change rapidly with the orientation of precipitates with the matrix. This is the reason why these carbides grow preferentially in a direction, making them elongated in shape. The preferred shape of M2C carbides is thus a long needle. But, Davies and Ralph [13] observed that in Fe–Mo–C alloy, for small precipitate sizes, needles coexisted with spheres. They derived the explanation with an analysis based on three factors influencing the shape of precipitates: composition, surface energy (or surface tension), and strain energy [14]. But in the samples investigated here, there are two additional factors influencing on the microstructure: the anisothermal tempering and, the precipitation of B2-NiAl phase that are specific to our alloy system and tempering conditions.
2. Material, thermal treatment and specimen preparation The material of the present investigation is a X32Cr–Mo–V 3-3-3 secondary-hardening martensitic steel additionally alloyed with Ni and Al, containing typical compositions in major alloying elements given in Table 1. Rods of material have been subjected to the following thermal treatment: samples were first homogenised in the austenitic domain at 1123 K and then, quenched in oil to obtain massive lath martensite. The tempering treatment consisted of applying a continuous heating (20 K/min) followed by a rapid quench in a nitrogen flow to ‘‘freeze’’ the microstructure. The ageing conditions of the investigated specimen will thus be referred as the maximum temperature reached by the specimen just before the quench. The different ageing conditions have been characterized by microhardness measurements, enabling the detection of the secondary hardness peak temperature, as shown in Fig. 1. The maximum hardness is observed for the specimen aged up to 883 K. This paper will thus focus on the microstructure of this particular condition. The rods were finally cut into small parallelepipeds for electropolishing to obtain field evaporation specimens, i.e. a very sharp needle with a radius of curvature of less than 100 nm, using standard electropolishing solutions for steels, see e.g. [15].
3. Experimental Investigations have been carried out in a conventional FIM chamber using Ne and H2 mixture as imaging gas with a Table 1 Composition in major alloying elements of the investigated steel.
at% wt%
Fe
C
Cr
Mo
V
Ni
Al
Bal. Bal.
1.40 0.32
2.60 2.50
1.40 2.50
0.30 0.30
6.00 6.50
5.00 2.50
750 700 Hardness (HV)
ð0 1 1Þkð0 0 0 1ÞM2 C ½1 0 0k½1 1 2 0M2 C
519
650 600 550 500 450 400 200
400
600 800 Temperature ( K)
1000
1200
Fig. 1. Hardness evolution during thermal treatment.
pressure of 5 10–5 mbar, the tip being maintained at a temperature of 90–100 K and positively polarised at voltages ranging from 3 to 17 kV, depending mainly on the specimen radius of curvature. We have carried out chemical analyses with an EcoTAP [16], equipped with an advanced delay line position-sensitive detector [17]. FIM micrographs can be indexed thanks to conventional stereographic projections so that the main crystallographic directions can be deduced from the geometrical arrangement of poles, and on symmetry considerations. This procedure allows the determination of the orientation of the crystallographic grain situated at the tip apex. As the material has been cut from bulk rods with no particular texture, any grain orientation at the tip apex is possible. The specimen radius of curvature is deduced from ledge separation of plane stacking, the so-called Dreschler method [18]. Assuming that the tip radius of curvature is homogeneous, distances on the surface can be deduced approximately from the magnification. In order to distinguish the carbides from the surrounding matrix, we take advantage of the large difference in evaporation fields between carbides and martensite. Indeed, during field evaporation, due to their higher evaporation field, M2C carbides tend to protrude on the surface resulting in a local area of higher field, forming the blur areas visible on the FIM micrographs of the Fig. 2. To enhance the contrast between the matrix and the precipitates, the temperature has been raised to 80–100 K during the recording of evaporation sequences. The consequence is that the carbides appear brighter than the matrix, thus allowing easy thresholding by pixel light intensities (Fig. 3). For martensitic steels, obtaining a convenient lateral resolution may be a delicate issue; indeed, the pole contrast of the martensite matrix is poor: highly packed poles such as {11 0} and {2 0 0} can barely be seen. To improve the resolution in the matrix, a certain amount of dihydrogen (less than 5 10–7 mbar partial pressure) has been introduced in the experiment chamber together with Ne. That way, the resolution is much better [19], as can be seen in Fig. 2(b) and, matrix poles and carbides can be imaged altogether. The technique of 3DFIM consists of the stacking of images recorded during the continuous field evaporation of a specimen at DC voltage. The voltage is continuously increased to maintain a constant evaporation rate. The evaporation film has been recorded on a CCD camera with a 25 images-by-second frame rate and a
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Fig. 2. Left: 923 K tempered specimen imaged with Ne (5 10–5 mbar) at 10 kV, the (11 0) pole is hardly visible. Right: same thermal treatment, but imaged in a mixture of Ne (5 10–5 mbar) and H2 (2 10–7 mbar) at 12 kV. The rise in contrast in the matrix is evident but deteriorates the second phase contrast (both pictures are at best image voltage) (circled: a dislocation emerges in the (0 11) pole).
Fig. 3. 2D cross-section of a 3D reconstruction after the smoothing procedure. Evaporation proceeds from the top to the bottom of the figure. Carbides appear bright.
40 ms exposure time. The shutter aperture has been adjusted to obtain a sufficient contrast without saturation of the CCD sensor. The three-dimensional reconstructions shown here, result from the stacking of evaporation sequence images where grey level pixels have been converted to a colored look-up table. In the raw stacking, the explored depth depends on the number of images recorded by the camera, i.e. on parameters such as the recording mode, integration time, diaphragm aperture, etc. But, as these parameters have been fixed and the evaporation has been maintained to a constant rate, the depth is proportional to the analysed length. The calibration of the evaporated depth has been determined as follows: the lateral lengthscale (nm/pixel) is deduced from the radius of curvature measured on the 2D image in presence of dihydrogen as explained previously and, the number of evaporated planes in a given direction (planes of {11 0}, {2 0 0} or {11 2} type are the most convenient) gives the evaporated depth. These reconstructions have been done without surface curvature corrections, thus for precipitates far from each other, the angle relations are not conserved by the stacking procedure. But, it is well known that field ion emission specimen surfaces show facets corresponding roughly to the dense planes. We have thus restricted our reconstructed volumes close to the major poles. The volume limit of the phases is inferred by thresholding voxels light intensities, high intensities correspond to carbides, whereas low intensities correspond to the matrix. The data are additionally resampled, to obtain a constant resolution in the three directions. The (x,y) resolution has been set unchanged, while the z resolution has been reduced to match approximately the (x,y) resolution. This procedure has two advantages: the memory size of the dataset is reduced and the matrix contrast appears much more uniform.
Fig. 4. Volume reconstruction of evaporation sequences. At the peak hardness, different morphologies of carbides can be seen: (a) stacked disk-shaped carbides; (b) group of small idiomorphs; (c) blocky carbides around lath boundaries; (d) lath carbides surrounded by small idiomorphs in a volume as big as 10 10 10 nm3 (Fig. 5(b)).
Indeed, it is common with highly alloyed materials that substitutional or interstitial preferentially retained alloying atoms appear as bright spots on the specimen surface; they should not be taken as a carbide extremity. Hopefully, as these features have a very small depth extension even compared to carbides nuclei consisting in a dozen of atoms, they can be distinguished from precipitates when the stacking procedure and depth calibration is completed. To eliminate those bright imaging spots, we have used a slight smoothing while resampling the data, where the mask of the filter is computed only in the direction of evaporation (Our z-direction, letting (x,y) be the position on the detector). By using a linear filter (triangle filter), the intensity of little ‘z extension’ features merges with the surrounding, because they are covered by the mask of the filter, whereas bigger features remains, although their limits become a little blur, smooth. Another limitation of using this filter is that, when two objects are very close to each other, they can merge. To avoid this issue, it is necessary to make sure that the size of the filter’s mask (in pixels) is less than half the smallest interplanar distance. The reconstructions give useful information about the carbides at the peak hardness. Fig. 3 provides information on the extent of carbides in the direction parallel to the axis of the specimen, i.e. in the direction of evaporation; and, Fig. 4 is a result of the threedimensional reconstructions on two different samples ((a), (b) and (c) come from the same sample, whereas (d) is a different sample, with the same tempering conditions).
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4. Results 4.1. 3DFIM results We can see that elongated but rather thick carbides, resembling small laths rather than needles are present (Fig. 4(a) and (d)). These carbides are about 10–15 nm in length, 2–5 nm in width, and 2 nm thick. Different orientations of the carbides can be seen, but in general neighbouring carbides share the same orientation. The reconstruction procedure is, however, not suitable to determine accurately the direction of the big axis of the lath carbides. But the carbides of Fig. 4(a), have their broad face lying perpendicular to the direction of analysis that has been chosen around a (11 0) pole. Thus, (11 0) is likely to be their habit plane, or matching plane with martensite. In Fig. 4(a), we have emphasized a superstructure formed by the stacking of many plate-like carbides. This kind of superstructure is very frequent in the analysed samples. The comparison between Fig. 4(a) and (d) reveals that the superstructure of Fig. 4(a) is formed of bigger, broader and thicker carbides than these of Fig. 4(d). Their bigger size suggests that they were formed prior to these of Fig. 4(d). APT analysis has revealed that intra-lath elongated carbides have a composition typical of equilibrium coherent M2C carbides (see Fig. 5). Besides anisotropic, elongated lath carbides, small globular carbides are also visible in Fig. 4. The small globular carbides have rather large size dispersion, but are rarely bigger than 2 nm in diameter. They could be found dispersed around the lath carbides (Fig. 4(d) arrowed) or grouped. Another type of globular carbides, differing from the latter by their size and their localisation: they are bigger (up to 6 nm.) and commonly isolated from other types of carbides. Fig. 4(c) shows such carbide, referred as ‘‘blocky’’ regarding its irregular shape, situated in the precipitate-free zone of grain-boundary allotriomorph carbides, presented in the next section.
Besides these two morphologies, lath boundary allotriomorphs can be observed since the inter-lath spacing in this type of martensite is a few hundreds of nanometers. On average, at least one lath boundary is intercepted during a 3DFIM typical analysis. The plate-like allotriomorphs ‘carpet’ the grain boundaries at stages where the microstructure coarsen partly, but as expected from heterogeneous nucleation theory, they retain a certain individuality, forming columnar structures flattened at each extremities (not shown here). They are of the M2C type. 4.2. APT results As either 3DFIM or APT are unable to give information on the phase crystallographic structure, the nature of carbides has to be inferred from chemical analysis. This analysis is based on the alloying amount of carbon and iron in the precipitates and on the strong carbide former element balance: Cr, Mo, and V (See Fig. 5). However, the concentration of carbides is altered by the local magnification effect [20]. To estimate the actual concentration of solute elements, a correction procedure has been applied [21]. The limits of carbides are assessed by considering the regions of low iron atoms density. Assuming that the iron content within the limit of the carbides is the actual iron content of the precipitates, solute atoms displaced by trajectory aberrations are then replaced inside these limits to obtain the corrected alloying element concentration. APT analysis reveals that the spheroidal carbides contain slightly lower carbon and higher iron amounts, and a balance of Cr, Mo and V, with more chromium than molybdenum, but with slightly higher molybdenum content than lath carbides. The comparison of composition between lath carbides and spheroid carbides are shown in Table 2. The low level of carbon in the spheroidal carbides might suggest that different types of carbides precipitate, i.e. M23C6 (20 at% C). But according to Grujicic and Olson [22] and Olson et al. [23] calculations, such levels of
1 nm.
1 nm.
100
100
90 80
80
Concentration (at%)
Concentration (at%)
90 70 60 50
C Cr Mo Fe V
40 30 20
70 60 C Cr Mo Fe V
50 40 30 20 10
10 0
521
3
3.5
4
4.5 5 5.5 Analysed depth (nm.)
6
6.5
7
0
2
3
4 5 Analysed depth (nm.)
6
7
Fig. 5. Top-left: 3D atom-probe volume (3 3 9 nm3) intercepting intra-lath M2C carbide. Top-right: (2 2 10 nm3) a blocky carbide. Bottom-left: concentration profile associated to the elongated carbide. The core carbon concentration level is 33 at%. Bottom-right: concentration profile through the blocky carbide represented above, the iron content is over-estimated due to local magnification (see Table 2 for corrected composition).
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Table 2 Concentration of carbides depending of their morphology measured with the ECOTAP. Type
C (at%)
Fe (at%)
Cr (at%)
Mo (at%)
V (at%)
Intra-lath elongated Blocky idiomorphs
32.670.5 20.470.7
1.670.5 8.370.7
39.970.4 41.670.6
19.470.2 24.570.3
6.670.4 5.070.6
Concentration has been corrected from local magnification effect.
elements can be found for coherent M2C in the first stages of precipitation. Moreover, thermodynamical calculations have revealed that M6C (15–18 at% C) and M23C6 although stable at 883 K, form only after long time ageing. The conclusive argument allowing ruling out the formation of M23C6 or M6C is that they are not found in the subsequent tempering conditions (i.e. at 923 and 973 K). Instead, globular carbides are found, still having a composition typical of M2C carbides (around 33 at% C). As it is very unlikely that the thermodynamically stable carbides M6C or M23C6 dissolve with increasing temperature and tempering time, we conclude that small globular carbides are M2C or M2C nuclei. This conclusion determines that all the investigated carbides at peak hardness are M2C, and differ only in concentration. The slight difference in concentration can be due to several reasons, which will be tentatively explained in relation with their morphology in the discussion section.
becomes the dominant growth factor. Anyhow, a varying amount of coarsening is always found during the whole precipitation process. In this regime, large precipitates grow at the expense of smaller ones that dissolve rapidly. The small spheroidal carbides dispersed among the comparatively large needles may originate from that mechanism. Their spheroidal shape is due to the fact that the sphere gives an optimal surface to volume ratio locally minimizing the pressure due to the capillarity. For subsequent ageing, no other such small spheroids can be found in the immediate vicinity of lath carbides. But, another explanation more related to strain effects, involving the composition changes measured by APT can be proposed. The small spheroidal carbides could be the carbides that nucleate with a composition resulting in a bigger molar volume that is not optimal for coherent growth, i.e. with more molybdenum and less chromium. These carbides grow slower and are prone to dissolve. For the reason that they have a bigger molar volume, they can be incoherent and spheroidal in shape. In other words, the chemical driving force tends to form carbides of varying composition, but, only those within a certain range of composition may grow enough to reach a consequent size. The smallest carbides can either dissolve, due to coarsening (Ostwald ripening), or being locked and grow very slowly, thus showing coarsening resistance. Note that this other explanation is not contradictory with the preceding, and includes the composition changes discussed previously.
5.3. Thermal history 5. Discussion 5.1. Composition The APT analysis revealed that, in this industrial steel, the change in composition of M2C carbides did not influence their structure. In this steel, it appears that the smallest carbides always contain more iron and less carbon. But it also appears that in the early stages, the growth of carbides with a lesser molar volume (i.e. enriched in chromium) is favoured, as long as coherent equilibrium is thermodynamically favoured [24]. The little spheroids with their slightly higher molybdenum content could be some latent germs that are prone to dissolve or, stable precipitates but with incoherent interfaces, i.e. with limited possibilities of growing rapidly compared to the precipitates with a lesser molar volume. But the complex structure of their interface and their closed-packed bonding, makes them also somewhat resistant to coarsening. That could be the reason why in more advanced stages we find spheroidal carbides together with coarse elongated carbides.
The materials have been submitted to a continuous temperature increase of 20 K/min. Investigations have revealed that the precipitation of carbides occurred before 883K, at 823K. At 823K carbides nucleate heterogeneously on dislocations. The resulting microstructure is ‘‘islands’’ of carbides located on and around dislocations, but the repartition of carbides is far from homogeneous. As these carbides are stable, they grow to a weighty size with increasing temperature, i.e. of diffusivity of carbide formers atoms. Around 873–883K, homogeneous nucleation occurs. This second nucleation event is responsible for the fast nucleation and growth of a lot of laths carbides, but they are smaller in size than the previous ones, and their spatial repartition is homogeneous. This second nucleation effect is made possible by an increase of chemical driving force due to cementite dissolution completion [12]. We thus expect that the big carbides forming superstructures are the carbides that nucleate on dislocations, and smaller laths are newly formed growing phase.
5.4. B2-NiAl precipitation 5.2. Surface energy–strain energy The surface energy influences the growth of a semi-coherent second phase as it varies with the relative orientation of the two crystals with minimal values perpendicular to the matching plane (habit plane). Surface energy is responsible for the cusp-related morphologies (discs) [25]. However, misfit strain effect makes the incoherent extremities grow more rapidly: that is essentially the reason for needle or lath morphologies. For the same reasons, the sphere is the equilibrium shape of completely incoherent precipitates. The large predominance of broad needles or small laths is in good agreement with this statement. As surface energy and strain energy are related, they cannot be treated separately. According to the analysis of Davies and Ralph [13], the occurrence of spheroid carbides reveals that in the material, coarsening
We have found that idiomorph small carbides closely grouped without any bigger carbide in the immediate vicinity. The occurrence of these carbide clusters cannot be explained by Ostwald ripening, but as follows: in this experimental steel, B2NiAl is precipitated as a second phase. This phase consists in small spherical B2-ordered precipitates fully coherent with the ferrite matrix. The precipitation of this phase makes the ferrite locally harder and can thus impinge the growth of M2C carbides, thus, only small globular carbides can grow when the local number density of B2-NiAl precipitates is rather high. Again, their globular shape can be explained by their small volume. These are carbides locked in their initial stage, because the transfer of matter is slowed down by the ordered precipitates. They are expected to dissolve slowly with further tempering, when B2-NiAl precipitates coarsen.
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6. Conclusions We have investigated the morphology of carbides at the peak secondary-hardening microstructure of a martensitic steel, and demonstrated that at the maximum hardness peak under nonisothermal tempering a mixture of precipitate morphologies was observed:
Needles or laths, with size ranging from 10 to 15 nm, nucleated on dislocations.
Small spheroids, with a size less than 2 nm, mainly resulting
from the dissolution of the previous ones, due to coarsening and/or the nucleation of incoherent germs. Blunt blocky shaped carbides with a size of about 5 nm.
All these carbides, are expected to be of the same type, i.e. of the M2C type. Acknowledgements The author gratefully acknowledge S.D. Erlach for the microhardness measurements, the Austrian Kplus competence center program for financial support, the French-Austrian exchange program Amadeus and Bo¨hler Edelstahl GmbH. References [1] E.W. Mu¨ller, Zeitschrift fu¨r Physik 131 (1) (1951) 136–142. [2] H. Wendt, Decomposition of Alloys: The Early Stages, Pergamon Press, pp. 133–138. [3] D.G. Brandon, Journal of Scientific Instrumentation 41 (1964) 373. [4] E.W. Mu¨ller, J.A. Panitz, S.B. McLane, Review of Scientific Instrumentation 10 (1968) 177.
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