Carbide precipitation in austenitic stainless steel carburized at low temperature

Acta Materialia 55 (2007) 1895–1906 www.actamat-journals.com

Carbide precipitation in austenitic stainless steel carburized at low temperature F. Ernst *, Y. Cao 1, G.M. Michal, A.H. Heuer Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, OH 44106-7204, USA Received 16 August 2006; received in revised form 14 September 2006; accepted 14 September 2006 Available online 12 January 2007

Abstract Low-temperature gas-phase carburization can significantly improve the surface mechanical properties and corrosion resistance of austenitic stainless steel by generating a single-phase ‘‘case’’ with concentrations of interstitially dissolved carbon exceeding the equilibrium solubility limit by orders of magnitude. Upon prolonged treatment, however, carbides (mostly v, M5C2) can precipitate and degrade the properties. High-resolution and spatially resolved analytical transmission electron microscopy revealed the precise carbide–austenite orientation relationship, a highly coherent interface, and that precipitation only occurs when (i) the carbon-induced lattice expansion of the austenite has reached a level that substantially reduces volume-misfit stress and (ii) diffusional transport of nickel, chromium, and iron – enhanced by structural defects – can locally reduce the nickel concentration to the solubility limit of nickel in v-carbide.  2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Austenitic stainless steel; Fe–Cr–Ni; Surface alloying; Low-temperature gas-phase carburization; v-Carbide (M5C2, Ha¨gg)

1. Introduction In recent work [1–6], we reported that the surface mechanical properties and corrosion resistance of 316-type austenitic stainless steel (Fe–Cr–Ni alloy) can be significantly improved by a novel, conformal, low-temperature gas-phase carburization process, developed by the Swagelok Company. This process, after activating the alloy surface by removing the passivating chromium oxide scale [7], supplies carbon from a conventional carburizing atmosphere at a processing temperature Tp = 748 K for a duration sp between 26 and 38 h. As a result, carbon diffuses into the alloy to form a single-phase carbon-rich ‘‘case’’. With increasing depth z into the case, the concentration ltc X ltc C ½z smoothly decreases from its maximum X C ½0 at the nc surface to the intrinsic carbon level X C of the non-carburized alloy core. For low-temperature-carburized bulk *

Corresponding author. E-mail address: [email protected] (F. Ernst). 1 Present address: Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.

316, the case is 25 lm thick, and X-ray diffractometry and X-ray photoelectron spectrometry indicated X ltc C ½0 ¼ 0:12 [4,6]. Recent scanning Auger microprobe (SAM) measurements, based on calibration standards, even suggest X ltc C ½0 ¼ 0:14 (Avishai et al., unpublished data). This exceeds the equilibrium solubility limit of carbon by a factor of 700 at the processing temperature – and a factor 105 at room temperature. Such a ‘‘colossal’’ supersaturation with carbon is possible because Tp is high enough for interstitially dissolved carbon atoms to retain considerable mobility but low enough to limit the mobility of the metal atoms to a level at which the usual precipitation of carbon in metal carbides cannot readily occur [1–3]. Another important requirement we have identified for obtaining a colossal supersaturation with carbon is the presence of sufficient atom fractions of elements with a high affinity for carbon. In the 316L-type alloys, the main element playing this role is Cr (chromium). As long as carbon stays in solid solution, a colossal supersaturation of the austenite greatly improves the surface hardness, resistance to fatigue crack nucleation, wear resistance and corrosion resistance [1,2,4,6,8]. Precipitation

1359-6454/$30.00  2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2006.09.049

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of carbon-rich second phases, in contrast, generally degrades the properties. Therefore, the duration sp of the carburization stage of the Swagelok process is designed to maximize the uptake of carbon, while entirely retaining it in solid solution. However, on prolonged carburization or multiple application of the Swagelok process, which may be of considerable interest for increasing the case depth, metal carbides can eventually precipitate. They form in a zone below the surface in which the average carbon fraction exceeds the non-equilibrium solubility limit X C (0.12 for bulk 316L). Carbon uptake in excess of this limit correspondingly increases the volume fraction of the carbide phase and the depth of the carbide-containing zone below the surface. Previous work [5,6] revealed two different carbide modifications: M5C2 (or v phase) and M7C3 (‘‘M’’ stands for the metal atoms, i.e. Fe or alloying elements substituting Fe in its lattice sites, in appropriate proportions). The majority of the carbide particles – by far – are v phase (M5C2). Laterally, the particles are not distributed uniformly within the carbide zone. Rather, they occur in groups or ‘‘colonies’’ with virtually carbide-free austenite regions between them. Fig. 1a presents a typical conventional transmission electron microscopy (TEM) bright-field image of a v colony [6]. The particles appear with large aspect ratios, typically featuring a short dimension of 20 nm and a long dimension up to several micrometers. They contain a high density of planar faults oriented roughly orthogonal to the long axis. The v particles have the crystal structure of Fe5C2 (‘‘Ha¨gg carbide’’) [9–11] with very similar lattice parameters [5,6]. Table 2 compiles the lattice parameters of v we have determined by X-ray diffractometry (XRD) from low-temperature-carburized 316L powder [6] using the software packages Celref [12,13] and RIETAN [14,15]. The lattice parameters obtained from our measurements agree very well with those found for Fe5C2 in two other publications [16,17], also listed in Table 2. The space group is C2/c (15). Table 3 lists the atom positions as determined by Retief [16]. The unit cell contains 20 Fe and 8 carbon atoms, consistent with the stoichiometry M5C2. Fig. 2 projects the structure of Fe5C2 in [0 1 0], the direction of the symmetry axis. The v particles grow in a unique crystallographic orientation relationship (OR) with the c matrix [5]. Based on Fig. 1b, originating from a region including several carbide particles, and about 20 similar TEM selected-area diffraction (SAD) patterns, we have described this OR as [5] ð0 0 1Þv k ð1 1 1Þc ;  1 1 ½0 1 0 k ½2 v

c

ð1Þ ð2Þ

The direction (2) corresponds to the viewing direction of Fig. 1. Note that [0 1 0]v and the normal of (0 0 1)v make an angle of 90, as do ½ 2 1 1c and the normal of (1 1 1)c. The diffraction pattern of Fig. 1b is correctly oriented with respect to Fig. 1a. The streaks between the spots form-

Fig. 1. Conventional TEM of v (M5C2) needles that precipitated in a c (austenite) matrix with a colossal supersaturation of carbon (X ltc C ½0 ¼ 0:12, recorded with a 200 kV Philips CM20 transmission electron microscope). (a) Bright-field image. (b) Selected-area diffraction pattern, correctly oriented with respect to (a). The pattern constitutes a superposition of a [0 1 0] zone-axis pattern of v and a [2 1 1] zone-axis pattern of c. The white spots superimposed onto the v pattern in the lower right quadrant were obtained by simulating the [0 1 0] diffraction pattern of Fe5C2.

ing [1 0 0]-oriented rows originate from the high density of planar faults apparent in the image and identify the fault plane as (2 0 0)v. As all the carbide particles constituting the colony in Fig. 1a have the same OR with the matrix, and their long axes as well as their planar faults are parallel to each other, a unique correspondence exists between the (idealized) particle shape and the orientation of the crystal lattice therein. According to Fig. 1a, the typical particle extension in [0 0 1]v is much smaller than in [1 0 0]v. TEM

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Fig. 2. The crystal structure of Fe5 C2, the ‘‘Ha¨gg’’ carbide, shown in [0 1 0] projection. The structure belongs to the monoclinic crystal system and has the space group is C2/c (15). The shaded region corresponds to one unit cell.

images in [0 0 1]v [5,6] show that the extension in [0 1 0]v is comparable to that in [0 0 1]v, i.e. it is also much smaller than in [1 0 0]v. Accordingly, the particle shape resembles that of needles or laths, but not plates or discs. As carbides generally degrade the surface mechanical properties and corrosion resistance, it is important to identify the parameters that control X C and to gain a fundamental understanding of the micromechanism by which the carbide particles nucleate and grow – in order to develop strategies for avoiding them. In the work reported here, we have studied the atomistic structure of the v–c interface (the interface between M5C2 particles and the austenite matrix) and the spatial redistribution of atom species associated with carbide formation under the constraints of low-temperature carburization by advanced methods of TEM. 2. Experimental methods and procedures The material we investigated was a low-temperature-carburized foil of 316L-type austenitic stainless steel (ADT15) with a thickness of 38 lm and annealed at 1338 K for 1.5 h. Table 1 lists the results of a wet-chemical analysis. Carbide formation occurred after two applications of the Swagelok process, corresponding to a total carburization time sp = 44 h at Tp = 748 K. X-ray diffractograms were obtained before and after carburization with a Scintag X-1 X-ray diffractometer, utilizing Cu Ka radiation with the wavelength k = 0.154056 nm in the Bragg–Brentano (h–2h) mode [18]. From the diffractograms, we determined the peak centers hi of the reflections {1 1 1}, {2 0 0}, {2 2 0}, {3 1 1} (corresponding to i = 1, 2, 3, 4, respectively). From these data,

Table 1 Composition of the ADT15 foil (at%) C 0.16

Mn 1.61

Si 0.98

P 0.05

S 0.01

Cr 18.76

Ni 10.65

Mo 1.10

Al 0.21

N 0.24

O 0.07

Ti 0.07

Co 0.19

B 0.05

Nb 0.02

Ca 0.14

Se 0.07

Fe 65.29

Cu 0.35

we obtained best estimates ac and b for the austenite lattice parameter and the Nelson–Riley coefficient, respectively, by performing a non-linear regression analysis [19]. With this approach, ac and b are given by the values of ^ ac and ^ that minimize the sum of the square residuals between b the measured hi and their theoretical values " # kqi H½qi  ¼ arcsin ð3Þ ^ cos½H½q  cot½H½q Þ 2ð^ac þ b i i qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where qi :¼ h2i þ k 2i þ l2i and hi,ki,li are the Miller indices of the planes reflecting under hi. The relation (3) follows directly from the Bragg equation [18] and the Nelson–Riley correction [20,18]. For evaluating H[q] (an implicit func^ we developed tion) and for fitting the parameters ^ac and b, a C++ implementation of the downhill simplex algorithm [21]. To determine standard error limits for the best estimate ac, we generated 104 new data sets fh0i g, drawing random values from normal distributions centered on the theoretical H[qi] obtained from (3) with the best estimates ac and b. The standard deviation of these distributions was chosen to [19] vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u P u 1 X 2 r¼t ð4Þ ðhi  H½qi Þ P  f i¼1 where P = 4 is the number of peaks and f = 2 the number of fitting parameters (or degrees of freedom). Fitting (3) to each new data set fh0i g, we obtained histograms of the 104 ^ best values a0c and b 0 for the fitting parameters ^ ac and b, respectively. Sorting these data yielded corresponding cumulative distributions, from which we eventually determined (asymmetric) confidence intervals for ac and b at the 68% level of confidence. The symmetric ‘‘standard errors’’ indicated for the data in the following sections correspond to the largest possible deviation within the asymmetric 68% confidence interval. A corresponding procedure was applied to diffusion data from the literature to obtain pre-factors and activation energies. The v particles and the v–c interface were studied by high-resolution TEM (HRTEM), scanning TEM (STEM) with a high-angle annular dark-field (HAADF) detector,

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electron-spectroscopic imaging (ESI), and X-ray energy dispersive spectroscopy (XEDS). The instrument we employed was a Tecnai F30 S-TWIN (FEI), operating with a field-emission gun at 300 kV and providing an information resolution limit of 0.14 nm. The instrument is equipped with a HAADF detector (Model 3000, Fischione Instruments), a post-column imaging energy filter (‘‘GIF 2001’’, Gatan, retrofitted with a 2k · 2k CCD camera), and an X-ray energy-dispersive spectrometer with an Si– Li detector. Employing these attachments, we performed elemental mapping using the ‘‘three-window method’’ [22] and XEDS line scans. The latter were conducted in STEM mode, based on Z-contrast imaging with the aid of the HAADF detector. In these experiments, the full width at half intensity maximum of the electron probe was 0.5 nm, corresponding to gun lens setting # 7 and spot size # 6 in nanoprobe mode. Specimen drift was compensated by the instrument’s built-in capability of monitoring the position of a characteristic image feature. Cross-sectional specimens for TEM were prepared from the low-temperature-carburized steel foils following the method developed by Strecker et al. [23], using specially prepared specimen holders. After mechanically reducing the thickness to 80 lm and further reducing the thickness in the center to 20 lm by means of a dimple grinder (Gatan Inc.), the final thinning to electron transparency was accomplished by ion-beam milling in a precision ion polishing system (PIPS, Gatan Inc.) from both sides until perforation occurred. Prior to loading the specimen into the microscope, we cleaned the surface from adsorbants and contamination by a means of an Ar+ plasma cleaner (Fischione Model 1020). For simulating HRTEM images and diffraction patterns, as well as for generating ball models of the crystal structures of v and c, we employed the JAVA version of the EMS software package [24–26]. 3. Results 3.1. X-ray diffractometry Fig. 3 shows a Nelson–Riley plot obtained from X-ray diffractograms of the 316L-type austenitic stainless steel foil recorded before and after carburization [6]. The best estimates for the lattice parameter anc c of the non-carburized austenite and the lattice parameter altc c ½0 at the surface of the low-temperature-carburized material are anc c ¼ ð0:35931  0:00008Þ nm

ð5Þ

altc c ½0

ð6Þ

¼ ð0:368  0:002Þ nm

This corresponds to an expansion factor of 1.024 ± 0.005. Based on the empirical relationship [27–30] nc ltc altc c ½z ¼ ac þ a  X C ½z

ð7Þ

and a = 0.104 nm [30], the value (6) for altc c ½0 corresponds to [6]

Fig. 3. Nelson–Riley plot of XRD (X-ray diffractometry) data obtained from the 316L-type austenitic stainless steel foil before and after lowtemperature carburization. (After [6].)

X ltc C ½0 ¼ 0:084  0:020

ð8Þ

The increased scatter about the least-square-fit line observed for the points representing the carburized material in Fig. 3 does not reflect statistical error, but is a systematic and reproducible effect [6], which we attribute to peak shifts introduced by an increased density of stacking faults [31–33]. The peak shifts can be modeled [34,35] and the stacking fault density can be quantified by including it as a third fitting parameter in the non-linear regression analysis (Ernst, unpublished data). However, the value for altc c obtained in that way is not significantly different from the result (6) obtained by treating the peak shifts as a stochastic effect. 3.2. Conventional and high-resolution TEM Fig. 4 presents another conventional TEM bright-field image of a v colony. This image includes the thin edge at the hole of the TEM specimen. The carbide particles, one of them marked ‘‘v’’, appear with uniform gray levels, indicating that they have the same crystallographic orientation. While TEM images recorded in certain crystallographic directions reveal a high density of planar faults on planes orthogonal to the long axis of the particles (e.g. Fig. 1a), these defects do not produce much contrast under the imaging conditions of Fig. 4. The regions of carbon-supersaturated matrix (marked ‘‘c’’) also have the same crystallographic orientation (average gray level), implying that the matrix regions belong to a single c-grain and the c–v orientation relationship is constant across the entire image. Different from the carbide particles, the matrix regions exhibit distinct gray level variations on the subnanometer length scale, indicating a high density of dislocations. While part of these dislocations will have resulted from from cold work (foil rolling) prior to carburization, a significant fraction may have formed by yielding under biaxial compressive stress introduced by the (depth-dependent) lattice expansion accommodating the interstitially dissolved carbon [2].

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Fig. 4. Conventional TEM bright-field image of v (M5C2) particles embedded in c (austenite) with a colossal supersaturation of carbon ðX ltc C ½0 ¼ 0:084Þ. The upper part of the image features the amorphous edge and the hole of the TEM specimen.

Fig. 5a is an HRTEM image of the interface between a v particle (top) and the c matrix (bottom). The v–c interface resides in the lower third of the image and lies approximately horizontal and parallel to the viewing direction (‘‘edge-on’’). It can be identified with the transition between the contrast patterns in the upper and lower half of the image. Within the region included in Fig. 5a, the interface does not exhibit considerable roughness. Fig. 5b shows the interface at higher magnification. The contrast pattern observed in c – in the lower half – features two sets of equally spaced lattice fringes making an angle of 71. Accordingly, the fringes correspond to {1 1 1}c and the viewing direction corresponds to [1 1 0]c. In v, as it exhibits only one set of lattice fringes, the viewing direction does not coincide with a low-indexed zone axis. Different from what might have been expected based on (1) and (2), the lattice fringes parallel to the one set of {1 1 1}c fringes do not originate from {0 0 2}v planes. This becomes obvious by considering the misfit between the corresponding plane spacings. According to the lattice parameters of the carbide (Table 2) and the lattice parameter altc c ¼ ð0:368  0:002Þ nm of the expanded austenite dis0 2g cussed before, the spacing d f0 of the {0 0 2}v planes is v f111g 0.250 nm, while the spacing d c of {1 1 1}c planes is only (0.212 ± 0.001) nm. Taking into account that these planes make an angle of /  20 with the plane of the interface, the misfit e :¼ 1

0 2g 1 1g jd f0  d f1 j v c

0 2g 1 1g ðd f0 þ d f1 Þ v c 2

¼ ð0:17  0:01Þ

ð9Þ

between the plane spacings would require misfit dislocations with an average spacing of

Fig. 5. Atomistic structure of the v–c interface. (a) High-resolution TEM image of an interface between a v needle (top) and the supersaturated c matrix (bottom). The viewing direction corresponds to [1 1 0] in c and  ½1 2 4 in v. This image was recorded in an ultra-thin region of the TEM specimen, close to the hole (upper right). The lattice fringes that apparently reach into the hole constitute an artifact related to the high coherence of the field-emission electron gun employed for imaging. (b) Enlarged region of the interface in (a).

Table 2 Lattice parameters of v (M5C2) Parameter

Dirand and Afqir [17]

Retief [16]

a (nm) b (nm) c (nm) b a, c

1.1563 1.1588 ± 0.0002 0.4573 0.4579 ± 0.0001 0.5058 0.5059 97.7 (97.746 ± 0.002) 90 (invariant for space group C2/c)

Cao [6] 1.1552 ± 0.0002 0.45638 ± 0.00004 0.50432 ± 0.00006 (97.68 ± 0.01)

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Table 3 Crystal structure of v (M5C2) (after [16]) Space group Unique axis

C2/c (15) b

Atom positions

4 8 8 8

D¼

Fe at 4e (0.000, 0.561, 0.250) Fe at 8f (0.097, 0.078, 0.423) Fe at 8f (0.215, 0.581, 0.306) C at 8f (0.107, 0.285, 0.149)

f0 0 2g 1 1g þ d f1 Þ b 12 ðd v c   4:0 nm e sin½/e

ð10Þ

along the interface. As the field of view in Fig. 5a has a lateral extension of 16 nm, it would have to include four misfit dislocations. However, this is not the case – the image does not reveal any misfit dislocations at all. This means D > 16 nm, which according to (10) implies a misfit e < 0.04. In reality, the misfit is rather smaller, as the region adjacent to the left edge of the field of view did not feature misfit dislocations either. Actually, the dominant fringes in the v crystal in Fig. 5 originate from {0 2 1}v planes: owing to the low symmetry of the space group C2/c of the v crystal structure, the

OR (1) and (2) implies that the six crystallographically equivalent directions Æ1 1 0æc correspond to six non-equivalent crystallographic directions in v. The particular direction in which the carbide is viewed in Fig. 5 happens to be  ½1 2 4v . In this zone axis, the dominant planes are (0 2 1)v and ð0 2 1Þv . The misfit between their spacing, 2 1g 1 1g d f0 ¼ 0:208 nm, and d f1 only amounts to e = v c 0.019 ± 0.004, in agreement with the experimental observation that e < 0.004. As expected, the {0 2 1}v planes lie roughly parallel to the long axis of the particle in Fig. 5, roughly parallel to [1 0 0]v and the normal of the (1 0 0)v (fault) planes. The {0 0 1}v planes, accordingly, are parallel to a set of {1 1 1}c planes that are inclined versus the viewing direction of Fig. 5. This interpretation is confirmed by the results of HRTEM image simulations we have carried out for a viewing direction of ½1 2 4v , shown as inset in the upper right of Fig. 5, as well as several other viewing directions. 3.3. Elemental mapping Fig. 6 presents ESI data from the region in Fig. 4. Fig. 6a is a thickness map, and Fig. 6b–d shows elemental

Fig. 6. Elemental mapping of the region imaged in Fig. 4 by ESI. (a) Thickness map, obtained by evaluating electron energy loss due to interaction with plasmons. The local foil thickness is proportional to the local image intensity. (b) Carbon map, obtained with the C–K edge (284 eV). (c) Fe map, obtained with the Fe–L2,3 edge (708 eV). (d) Ni map, obtained with the Ni–L2,3 edge (855 eV).

F. Ernst et al. / Acta Materialia 55 (2007) 1895–1906

maps of carbon, Fe and Ni. Fig. 6a was obtained by evaluating the energy loss of the primary electrons caused by plasmon scattering. Although the high dislocation density in c causes some spatial fluctuations of the intensity, regions of v and c appear with basically the same average gray level – representing local foil thickness – in this image. This indicates that both phases were uniformly attacked during thin-foil preparation by Ar+ ion milling. Accordingly, intensity differences in the elemental maps of Fig. 6b–d mainly do represent local differences in composition, not artifacts caused by lateral fluctuations of the specimen thickness. In the carbon map of Fig. 6b, v appears brighter than c. This is expected because the theoretical carbon atom fraction in v, X vC ¼ 0:29, is more than three times the c carbon fraction (8). Interestingly, the v–c interfaces feature dark fringes, suggesting the existence of a carbon-depleted layer around the carbide particles. The elemental maps in Fig. 6c and d reveal the spatial distribution of Fe and Ni, respectively. In the Fe map, the intensity in the interior of v regions is somewhat higher than in c regions. Moreover, the interior of the c regions exhibits faint contrast fluctuations, presumably residual bright-field contrast originating from the high density of structural defects in c. The stron-

1901

gest contrast feature in this Fe map, however, are dark fringes, less than 5 nm wide, indicating Fe deficiency along the v–c interfaces. In the Ni map, the v regions appear significantly darker than the c regions. Accordingly, the concentration of Ni in the carbide precipitates is much less than in the austenite matrix. Moreover, fringes of high intensity decorate the v–c interfaces, indicating pronounced Ni enrichment in a shallow c layer framing the carbide particles. The bright fringes in the Ni map coincide with the dark fringes in the Fe map and the carbon-depleted regions in Fig. 6b. In conclusion, the elemental maps indicate that the v particles are substantially richer in carbon than the c matrix (as expected), have roughly the same Fe concentration, but contain a substantially lower concentration of Ni. The c side of the v–c interface, on the other hand, appears to be rich in Ni and deficient in carbon and Fe. 3.4. Z-contrast imaging and concentration line profile The micrograph in Fig. 7a originates from another region of the TEM specimen than Fig. 4. This image was recorded in the instrument’s STEM mode, employing an HAADF detector and imaging conditions yielding Z-con-

Fig. 7. Z-contrast imaging and elemental concentration profiles across a v particle. (a) STEM image of v particles embedded in supersaturated c. This image was recorded by means of an HAADF detector at a camera length suitable for obtaining atom number (‘‘Z’’)-contrast. (b) Elemental concentration– line profiles recorded by XEDS while positioning an electron probe with a diameter of 0.5 nm at 30 different, equally spaced positions along the scan P line indicated P in (a). (c) Profiles Ym[x] of the metal atoms (m = Fe, Cr, Ni) obtained by renormalizing their concentrations Xm shown in (b) to Y m =X m = m X m , implying m Y m ¼ 1.

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trast (atom-number contrast). Therefore, the image intensity level representing the c matrix gradually increases from the very thin specimen region near the hole (top right) to the relatively thick region at the bottom left. The image includes two v particles. Their interior appears darker than the c matrix, indicating a lower average atom number Z per unit volume. The v–c interface features bright fringes with an intensity higher than that of the interior of the v particles and even higher than that of the c matrix. This observation is consistent with the conclusion drawn from the elemental maps in Fig. 6: the interior of the v particles is richer in carbon than c, but carbon does not contribute much to Z-contrast. On the other hand, the interior of the v particles is depleted of Ni, which does strongly contribute to Z-contrast. The bright fringes observed at the v–c interface correspond to the accumulation of Ni observed in Fig. 6d. The XEDS concentration line profiles in Fig. 7b confirm these conclusions. The profiles were recorded along the line labeled ‘‘scan line’’ across the central v particle in Fig. 7a, successively halting the focused electron probe (B  0.5 nm) for a fixed time of 30 s at 30 individual scan points xj, equally spaced and spanning a total line length of 70 nm. The integrated Ka peak intensities of the individual elements n = C, Fe, Cr, Ni measured at each scan point were converted to atom fractions X 0n by assuming that the material exclusively consists of Fe, Ni, Cr and C, and multiplying with appropriate conversion factors kn. The concentrations Xn[xj] in Fig. 7b were obtained by multiplying the X 0n ½xj  with correction factors j[xj] compensating for the variation of integrated peak intensities due to fluctuationsP of the specimen thickness along the scan line, such P that n X n ½xj   n j½xj X 0n ½xj  ¼ 1. Conforming with the conclusions drawn from Figs. 6 and 7a,b indicates an increased carbon concentration and a reduced Ni (nickel) concentration XNi  0.03 in the v particle compared with the c matrix. As expected from the bright fringes observed at the v–c interfaces in Figs. 6d and 7a, the Ni concentration line profile features strong peaks on each side of the shaded region, indicating the position of the v particle. The Fe profile indicates similar Fe concentrations in v and c, but exhibits two dips where the Ni profile has its maxima. The Cr profile, finally, does not indicate substantially different Cr concentrations in v and c, but also exhibits two dips at the location of the maxima in the Ni profile. Comparing the position of the two maxima in the concentration line profiles of Ni with the shape of the concentration profile of carbon confirms that Ni has accumulated in the c matrix adjacent to the particle, i.e. outside of the v particle. 4. Discussion The processing temperature Tp of the Swagelok process is optimized to enable carbon diffusion into substantial case depths, while minimizing the mobility of the metal atoms (solute atoms in substitutional sites) to avoid precip-

itation of carbides. In the limit of infinite carbon mobility and complete immobilization of the metal atoms, a ‘‘paraequilibrium’’ would result in which the chemical potential lC of carbon is uniform, i.e. until rlltc C ¼ 0, whereas local variations in the chemical potentials of the metal atoms persist because they cannot be equilibrated by corresponding transport [36,37]. In such a paraequilibrium, a hypothetical carbide particle would not grow because the carbide–c interface would not experience any driving force. A related scenario is that of a ‘‘partitionless’’ transformation under full local equilibrium, also known as ‘‘quasiparaequilibrium’’ [36]. Here, in addition to rlltc C ¼ 0, the chemical potentials of the metal P atoms can change as long as the relative fractions Y m =X m = m X m of the metal atom species m = Fe, Cr, Ni remain constant – except in a narrow region on the c side of the carbide–c interface: to establish a local equilibrium, the concentration profiles of the metal atom fractions across the interface have to feature spikes reflecting the c composition required for equilibrium with the forming carbide. As the carbide phase grows, these compositional spikes have to move along with the carbide– c interface. In reality, oz lltc C < 0 as carbon diffuses inward. An ideal paraequilibrium, rlltc C ¼ 0, is neither established nor desired, as this would mean a constant carbon concentration instead of a graded concentration profile. Moreover, the metal atom fractions X vm in v differ significantly from those in c. This ‘‘partitioning’’ rules out a true paraequilibrium, quasi-paraequilibrium, and all potential intermediate scenarios between these two limiting cases (although the Ni spike we have observed in c has some resemblance with the spike expected for quasi-paraequilibrium). Interestingly, the observed carbon depletion in the matrix, as discussed with regard to Fig. 6b, is of too limited a spatial extent to account for the carbon content of the carbide particles. Apparently, the carbon accumulating in the precipitates is balanced by a corresponding carbon uptake from the gas phase. The resulting v carbide is unusual in austenitic stainless steel and differs markedly from the commonly observed carbides M7C3 and M23C6 in a number of characteristic features. Of particular interest are the particle shape and the OR with c. In the following, we explain these features as a result of the limitation Tp imposes on the mobility of the metal atoms (substitutional solutes). Under conditions of minimum metal atom mobility, an important aspect of the c ! v phase transformation is the change of the average metal atom volume X. If the metal atom volume Xv in the carbide differs from the local metal atom volume Xltc c ½z in the carburized austenite, the transformation will generate volume-misfit strain and corresponding stress, increasing the energy barrier for nucleation of v precipitates. The unit cell of v contains 20 metal atoms. With the lattice parameters of Table 2, this yields av  ðbv cv Þ av bv cv  cos½bv  90  ¼ 20 20 ¼ 0:0131 nm3

Xv ¼

ð11Þ

F. Ernst et al. / Acta Materialia 55 (2007) 1895–1906

In the face-centered cubic (fcc) lattice of c, there are four metal atoms per unit cell. According to the lattice parameters (5) and (6), low-temperature carburization increases the metal atom volume in c from Xnc c ¼

3 ðanc c Þ ¼ 0:0116 nm3 4

ð12Þ

to 3

Xltc c ½0

ðaltc c ½0Þ ¼ ¼ ð0:0125  0:0002Þ nm3 4

ð13Þ

Defining the misfit between atom volumes analogous to (9), the misfit between Xv and Xnc c amounts to +12%. The misfit between Xv and Xltc ½0, in contrast, is only +(4.7 ± 1.6)%. c Assuming linear elasticity and that v is ideally hard, the strain energy of a given nucleus increases with the square of the volume misfit [38,39], implying that replacing the atom volume (12) by (13) reduces the contribution of volume-strain energy to the nucleation energy barrier by a factor of 7. The conclusion we draw from this result is that strain energy associated with carbide precipitation significantly contributes to the magnitude of the non-equilibrium carbon solubility limit (8). As the mobility of the metal atoms is small, stress introduced by volume misfit can hardly relax by long-range transport of vacancies. This may be one reason why the v particles are not spherical but adopt a shape with a high aspect ratio, known to reduce the strain energy per unit volume of precipitate [38,39]. Another characteristic feature of the v particles is their unique OR with the c matrix. During conventional, hightemperature carburization, carbides often nucleate in grain boundaries. However, this requires long-range transport of metal atoms. The unique OR between v and c observed here, in contrast, indicates intragranular nucleation, which requires smaller transport distances of metal atoms (if any). Intragranular precipitation usually generates unique ORs by a particular mechanism of nucleation, e.g. a shear mechanism [40], or because particular ORs reduce the energy of the resulting phase boundaries, thus the energy barrier for precipitate nucleation. The OR (1) and (2) was derived from TEM SAD patterns we have obtained from about 20 different v particles [5]. However, SAD patterns are not particularly sensitive against small specimen tilts (up to 3). The high-resolution image of Fig. 5, on the other hand, indicates that one set of {1 1 1}c planes is exactly parallel to the {0 2 1}v planes. Moreover, the [1 0 0]v direction indicated in the diffraction pattern of Fig. 1b (which makes an angle of b  90 = 7.7 with g2 0 0) precisely intersects with the ð0 2  2Þc reflection. Note that the ð0 2  2Þc and (1 1 1)c reflections are split – presumably by small-angle grain boundaries in c. The [1 0 0]v direction passes through the lower one of the two ð0 2  2Þ intensity maxima. In view of these considerations, the preferred v–c OR is more accurately described by

ð0 2 1Þv kð1 1 1Þc ½1 0 0 k½0 1 1 v

c

1903

ð14Þ ð15Þ

Note that ð111Þc are close-packed planes in c and ½01 1c  is a close-packed direction. The relationship (14) and (15) is approximately – but not strictly – equivalent to (1) and (2). The misorientation of c in the OR (1) and (2) with v versus c in the OR (14) and (15) with v is 5. In fact, it can be observed in Fig. 1b that the c spots in the lower half are weaker than those in the upper half because the center of the Laue circle is not on ð2 1 1c Þ, but shifted by 5 upwards, towards the ð3 1 1Þ zone. Accordingly, the (1 1 1)c planes are approximately – but not exactly – parallel to {0 0 1}v, as observed in Fig. 1b. The remaining two out of the four different sets of {1 1 1}c planes are approximately parallel to the f301gv and {4 0 1}v planes. Further, (1) and (2) implies that the symmetry axis of v, [0 1 0]v, is parallel to ½5 2 2c rather than ½2 1 1c . This means that v has no non-trivial point symmetry element in common with c. With respect to a reference state {aviac, bvibc}, in which the first two fundamental translations of c are parallel to the corresponding translations of c, the relationship (14) and (15) is crystallographically equivalent to a 136.6 rotation of c about[0.1073, 0.9600, 0.2590]c, i.e. in good approximation 135 about [0 4 1]c. The OR (14) and (15) apparently enables a low interface energy, particularly for the extended interface sections parallel to the long axes of the particles, as the high degree of coherence observed at these interfaces implies a small density of misfit dislocations and a correspondingly small strain energy per unit area [41]. In addition to the energetic advantage, the observed coherence of the v–c interface provides a kinetic advantage over a less coherent interface, i.e. an interface containing a high density of misfit dislocations: in order to grow a carbide particle radially, the misfit dislocations would need to climb. Since this requires transport of vacancies towards or away from the dislocation cores, it will be problematic under conditions of low metal atom mobility. If the v–c interface were ideally coherent – which it is not because the misfit (9) does not completely vanish – the one-to-one correspondence of {0 1 2}v and {1 1 1}c combined with Xltc c  Xv would enable radial growth of the v precipitates merely by inward diffusion of carbon and short-distance rearrangement of metal atom positions. However, Fig. 8 shows that there is no simple correspondence between the metal atom positions in {1 1 1}c and {0 1 2}v. In v, the atom positions belonging to one {0 1 2}v plane are not even coplanar. The combination of Xltc c  Xv with a perfectly coherent v–c interface would, in principle, allow carbide formation without long-range transport of metal atoms or vacancies. However, our results show that metal atom transport does occur over significant distances (compared with interatomic spacings). To expose the spatial redistribution of the metal atoms more clearly, Fig. 7c depicts the atom fractions XP of the metalP atoms renormalized to m Y m =X m = m X m such that m Y m ¼ 1. Confirming the

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F. Ernst et al. / Acta Materialia 55 (2007) 1895–1906

austenite matrix. Apparently, v cannot incorporate more than YNi  0.05, corresponding to XNi  0.025 ± 0.005 (Fig. 7b). Accordingly, nucleation and growth of v requires transport of Ni away from v into the adjacent c matrix. As expected, c has a high solubility for Ni, and the excess Ni expelled from the carbide accumulates in the c region immediate to the v–c interface. These results resemble what Ishikawa et al. observed by atom probe studies of carbide formation 304-type stainless steel [42]. The fractions of the two other metals, Fe and Cr, are correspondingly increased. Interestingly, mainly Fe atoms – not Cr atoms – replace the expelled Ni. While YFe increases from 0.70 to 0.75, YCr only increases from 0.20 to 0.22. Considering that Cr is known to possess a higher affinity for carbon than Fe, this result is unexpected and deserves further investigation. Experimental low-temperature data for the self-diffusion coefficients Dm of Fe, Cr and Ni in austenitic stainless steel are sparse. In lieu of corresponding data for the composition of 316L-type alloys, Table 4 shows the pre-factors D0,m and activation energies Qm obtained from experimental tracer diffusion data measured for Fe–15Cr–20Ni [43]. As recommended by Klicˇa et al. [44], the parameters D0,m and Qm and their standard errors were obtained by non-linear regression analysis based on D = D0 exp[Q/kBT] – not linear regression analysis based on the linearized Arrhenius relation ln[D] = ln[D0]  (Q/kB)(1/T). (T denotes the absolute temperature and kB the Boltzmann constant.) For the parameter fitting, we employed the same method we used for the determination of lattice parameters, described in Section 2. Dm[Tp] in Table 4 indicates the best estimate for the respective diffusion coefficient at Tp. The data in columns 5 and 6 provide upper limits for Dm[Tp] with confidence levels g = 0.67 and g = 0.95, respectively, obtained by the Gauß law of error propagation under the assumption that D0 and Q vary independently. The formation of carbide particles like those observed in Fig. 7a requires a typical diffusion distance of qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dm ½T p   sp  10 nm ð16Þ for all three metal species, implying

Fig. 8. Atom positions in viewing directions and planes of v and c that are parallel according to the experimentally determined orientation relationship (14) and (15). (a) c and v in ½0 1 1c /[1 0 0]v projection, featuring parallel (1 1 1)c and (0 2 1)v planes. (b) Plan view of a (1 1 1)c layer in [1 1 1]c projection and a (0 2 1)v layer viewed in [0 5 2]v projection (the frame corresponds to the projected v unit cell). The ½0 1 1c direction is parallel to the [1 0 0]v direction.

Dm ½T p   6  1022 m2 s1

ð17Þ

The best estimates for DFe[Tp] and DCr[Tp] in Table 4 are two orders of magnitude smaller, and even on the 0.95 level of confidence the hypothesis that bulk diffusion is sufficiently rapid can be rejected. For DNi[Tp], the best estimate is four orders of magnitude too low, and even at the 0.95 level of confidence the diffusion coefficient is still three or-

results obtained by ESI, Fig. 7c indicates that the concentration of Ni in the carbide is significantly (about three times) lower than the average concentration of Ni in the Table 4 Experimentally determined tracer-diffusion data for Fe–15Cr–20Ni (after [43]) Element Fe Cr Ni

D0 (m2 s1) (4.0±0.4)

0.30 · 10 0.61 · 10(4.0±0.3) 3.08 · 10(4.0±0.2)

Q (eV) 2.80 ± 0.12 2.85 ± 0.08 3.20 ± 0.08

D[Tp] (m2 s1) 24

3.9 · 10 3.9 · 1024 8.2 · 1026

g¼0:67 Dmax ½T p  (m2 s1) 23

1.2 · 10 9.4 · 1024 1.9 · 1025

2 1 Dg¼0:95 max ½T p  (m s )

1.7 · 1023 1.3 · 1023 2.6 · 1025

F. Ernst et al. / Acta Materialia 55 (2007) 1895–1906

ders too small to account for the observed transport distance (16). This means that the observed exchange of Ni for Fe and Cr and the pile-up of Ni in front of the v carbide particles must involve non-equilibrium structural defects assisting atom transport. Most likely, these defects are: (i) excess vacancies, e.g. generated by dislocation activity related to yielding under biaxial compressive stress introduced by the dissolved carbon, and (ii) the dislocations themselves, acting as low-temperature diffusion channels. The reduction in the activation energies Qm required for compatibility with the observed transport distance (16) are 0.3eV for Fe and Cr and 0.6 eV for Ni. It seems plausible that the high dislocation density (roughly estimated to 1016 m2 from TEM images) effectively reduces the Qm by these amounts, corresponding to only 10% and 5%. Obviously, the species that diffuses most slowly in c is Ni. Correspondingly, the requirement for transporting Ni atoms away from growing carbide particles is most important for retarding the undesired precipitation of carbides during low-temperature carburization. The particularly small mobility of Ni could be another reason (in addition to strain energy reduction) why the v precipitates adopt an extremely elongated shape: it minimizes the distance over which Ni needs to be transported.

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tions that are particularly resistant against carbide precipitation – the ultimate limit to the outstanding improvement of surface mechanical properties and corrosion resistance that a colossal supersaturation with interstitial solutes can provide for austenitic stainless steel and related alloys. Acknowledgements We acknowledge financial support of the Swagelok Company, the Department of Energy/Office of Industrial Technology (DOE-OIT) under contract number DEFC36-04GO14145, the Defense Advanced Research Projects Agency (DARPA) under Contract No. HR001105-1-0055, and the Office of Naval Research (ONR) under Contract No. N00014-04-1-0269. We thank P. Williams (Swagelok) and S. Collins (Swagelok) for numerous inspiring discussions. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.actamat. 2006.09.049. References

5. Conclusion The present study has provided insight into the constraints under which v-carbide (M5C2) eventually precipitates in low-temperature-carburized austenite (316L), characterized by a non-equilibrium in which only carbon atoms possess significant mobility: (1) Carbides do not precipitate before the lattice expansion introduced by interstitially dissolved carbon has decreased the initial metal atom volume misfit between c and v to a level that substantially reduces the contribution of misfit strain energy to the nucleation barrier. (2) A special, non-trivial orientation relationship between the two crystal lattices enables a high degree of coherence across extended sections of the v–c interface. This provides energetic and kinetic advantages for carbide nucleation and growth. (3) Nucleation and growth of v particles requires Ni to diffuse out of the corresponding region and Fe and Cr to diffuse in. This is facilitated by the presence of structural defects and by the elongated shape of the v particles. Since Ni has the smallest mobility of all three metal species, the limited solubility of Ni in v constitutes an important factor retarding undesired carbide precipitation. The insights gained by the present study are important for optimizing the processing parameters of low-temperature gas-phase carburization and to design alloy composi-

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