Introduction

Texture changes during phase transformations in metals are of longstanding interest, particularly a commonly observed memory effect, when the metal is heated, transforms to a new structure and returns to the original structure upon cooling. This implies a crystallographic relationship between parent and product phases, as well as variant selection, during the forward and reverse phase transformations occurring during heating and cooling. The relationships have been studied extensively in diffusionless transformations such as in martensitic steels.[1] Transmission electron microscopy revealed details on intergrowths between martensite and austenite,[2–4] and the preferred structural relationships have been modeled with molecular dynamics calculations.[5,6] Currently, there is much interest in epitaxial relations in thin films of martensitic systems.[7] While much of this work concentrates on local features, the microscopic processes are also expressed in macroscopic bulk properties such as crystal orientation distributions.

There is an extensive literature on textures in steel (e.g., reviews[8–12]), including effects of phase transformations.[13–15] Yet not much direct experimental information about the high-temperature γ-phase (fcc) texture exists. The reason is because quantitative in-situ texture measurements above 950 °C have been very difficult to achieve. Recently, new methods have become available for such investigations, such as synchrotron X-ray and time-of-flight (TOF) neutron diffraction with vacuum furnaces. The incentive behind this investigation was to test the capabilities of the new TOF diffractometer high-pressure preferred orientation (HIPPO) at Los Alamos Neutron Science Center (LANSCE), and a common metal such as iron was a good example. The results of the study are interesting enough to warrant reporting.

The review of Ray et al.[12] on phase transformations in steel and their effect on texture still provides most of the background, and the reader is referred to it for any details on previous work. Based on single-crystal studies and orientation relationships in precipitates, three orientation relationships between low-temperature bcc and high-temperature fcc structures have been proposed.[16] The first suggestion was by Bain and Dunkirk,[17] {001} <100>  (bcc) → {001} <110>  <fcc> , which produces three crystallographically equivalent variants for each parent orientation. Later Kurdjumov–Sachs (KS)[18] introduced a {110} <111>  (bcc) → {111} <110>  <fcc> relationship (Figure 1). In this case, there are 24 variants. Nishiyama–Wassermann (NW)[20,21] proposed the {110} <001>  (bcc) → {111} <01–1>  <fcc> correspondence with 12 equivalent variants (this is equivalent to {110} <1–10>  (bcc) → {111} <2–1–1>  <fcc> , and in the literature, one finds both descriptions). The relationships rely on structural similarities; e.g., <111>  is the direction in the bcc structure in which atoms are densely arranged and <110>  is the corresponding direction in the fcc structure. As the pole figure in Figure 1 demonstrates, the orientation patterns for all three relationships are similar, with more or less dispersion. The crystallographic transformation from fcc to bcc can be achieved by an intracrystalline shear (diffusionless). However, the transition may also involve nucleation and growth of new grains in structurally favorable orientations, e.g., according to coincidence lattice criteria.[22]

Fig. 1
figure 1

(001) pole figure displaying the crystallographic relationships for the bcc → fcc transformation according to the KS ({111}γ//{110}α <110> γ// <111>α), NW ({111}γ//{110}α <112> γ// <110> α), Bain ({001}γ//{001}α <110> γ// <010> α), and Pitsch ({100} γ// {011}α <011> γ// <111> α) relationships. The fcc parent crystal is in standard setting with [100] to the bottom, [010] right, and [001] center (hexagonal symbols). The insert displays the precise distribution of the product orientations for the aforementioned correspondences around the [001] γ pole.[19]

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Experimental

The sample used in this study is a sheet of ultra-low-carbon (ULC) steel (with 19 ppm C, 24 ppm N, 10 ppm S, 10 ppm P, 0.080 wt pct Mn, 0.005 wt pct Ti, and 0.023 wt pct Al), which was industrially cast and rough rolled. The material was hot rolled to a thickness of 20 mm on a laboratory mill with a finish rolling temperature of 930 °C, i.e., well above the estimated Ar3 temperature. After hot rolling, the sheet was further cold rolled with a reduction of 95 pct to a final thickness of 1.0 mm. A pure composition was chosen to avoid any second-phase precipitates during heating that could obscure the texture pattern. For the neutron diffraction study, the 1-mm-thick sheet was cut into 10 × 10 mm squares that were assembled into a cube, keeping orientations parallel. The cube was enclosed in a sheet of vanadium with no coherent scattering with neutrons.

The texture measurements were performed on the TOF neutron diffractometer HIPPO. This diffractometer is equipped with a large number of detector panels positioned at different angles, and each detector views differently oriented lattice planes. Detectors are arranged on four rings (banks) at different diffraction angles θ. Details of the instrument and general procedures for texture analysis have been described.[23] For the present study, only the 150 deg bank (8 detectors), the 90 deg bank (10 detectors), and the 40 deg bank (12 detectors) were used. The incident beam size was 12 × 12 mm.

The sample was mounted on a rod in a vacuum furnace with vanadium heating elements. Vanadium has the advantage that it does not produce coherent scattering. It should be noted that this furnace was never rigorously calibrated, and there is some uncertainty about absolute temperatures at the sample. In fact, in a first cycle, it was discovered that the wrong thermocouple was used in the furnace, and this erroneous cycle below the transition temperature has modified the texture and induced recrystallization. During each data collection, the sample was rotated around the furnace axis (perpendicular to the incident neutron beam and corresponding to the rolling direction RD) into four positions to increase pole figure coverage. At each position, the data collection time was 10 minutes, resulting in a total time for a temperature interval of about 60 minutes (including time for heating/cooling, data readout, and rotation). Figure 2 shows the temperature profile during the second heating cycle and indicates where pole figure measurements took place. As one can see, heating and cooling are rather sluggish, particularly at low temperatures. Also, as is commonly the case with spallation sources, neutron production is often interrupted and thus the actual time for data collection may be much longer than the effective counting time.

Fig. 2
figure 2

Temperature profile during the neutron diffraction texture measurements at LANSCE. The heavy line is actual temperature, and the thin line is programmed temperature. The time is in hours and minutes. The arrows indicate the data sets illustrated in this article.

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The neutron diffraction spectra were analyzed with the Rietveld method implemented in the program package MAUD.[24] The procedure is analogous to that described for texture analysis of a sample of experimentally deformed limestone.[23] First, instrument parameters were refined, including background and scale factors, and then crystallographic parameters and microstructure and finally all parameters with texture. The input data are 4 × 30 = 120 spectra, which were refined simultaneously. Examples for a 150 deg detector are shown in Figure 3 for 900 °C (bcc, top) and 950 °C (fcc, bottom). At both temperatures, there is only a single phase present.

Fig. 3
figure 3

Typical TOF diffraction spectra collected with a 150 deg detector at 900 °C (bcc) and 950 °C (fcc). The square root of intensities that are normalized with incident spectrum, d-spacing scale in Ångstrom. Note the poor counting statistics for large d-spacings.

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The orientation distribution (ODF) was obtained in a separate refinement cycle, using le Bail factors extracted by the Rietveld procedure as input and determining the texture with the tomographic algorithm WIMV,[25] in a special version (EWIMV) that allows data to be entered at arbitrary pole figure positions. For EWIMV, we chose an ODF resolution of 7.5 deg and a projection tube radius of 15 deg, compatible with actual instrument resolution.[26] The ODF was exported from MAUD and further processed with Beartex [27] to first smooth the distribution with a 7.5 deg Gauss filter to eliminate stochastic effects, to rotate the ODF to bring it into a standard setting, and to calculate pole figures for representation.

Results

As described in Section II, neutron diffraction spectra were used to obtain the orientation distributions for ULC steel at various temperatures. We show the φ2 = 45 deg sections of the ODF (Bunge convention, φ1, Φ, φ2) (Figure 4) and 110 and 111 pole figures to visualize the main textural features (Figure 5). Orientation distributions in standard ASCII format are available for anyone who wants to further investigate these textures. Bulk textural properties such as ODF maximum and minimum, as well as texture strength (F2[28]), are listed in Table I.

Fig. 4
figure 4

φ2 = 45 deg sections of ODF of ULC iron (Bunge convention): (a) before heat treatment (cold-rolling texture) and (b) through (e) textures measured in situ at temperature during the second heating cycle (recrystallization and transformation textures); (a) room temperature, (b) 400 °C, (c) 800 °C, (d) 950 °C (fcc), and (e) 400 °C. (f) Some important texture components.

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Fig. 5
figure 5

Pole figures recalculated from the ODF for ULC iron, measured in situ at different temperatures. Equal area projection, linear contours.

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Table 1. Statistical information about textures. Model data are in italics. (MRD: multiples of a random distribution; and f2 texture index)
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The starting material is a typical steel rolling texture with strong concentrations at α-fiber components {112} <110> , {111} <110> , and {001} <110>  (Figure 4(a)). After the first heating cycle, the material recrystallizes, which produces an equiaxed ferrite grain structure with an average grain size of 21 μm. The texture changes accordingly, which is revealed by the attenuated rolling components, and instead an intense γ-fiber component {111} <123>  develops (Figure 4(b)). This texture does not change much during the second heating cycle, except for the phase transformation (Figures 4(c) and (e)). This pattern is typical of a steel annealing texture exhibiting the well-known memory of the preceding recrystallization texture being present in the microstructure after α-γ-α transformation.[8,11,29,30] The final microstructure obtained after forward and reverse transformation with large equiaxed grains (>100 μm) is also consistent with the occurrence of texture memory.

In the pole figures, changes are also apparent. The starting material has a 111 maximum in the normal direction and a 110 maximum in the rolling direction (Figure 5(a)). These maxima all disappear during recrystallization and instead a strong 111 maximum in the normal direction develops (Figures 5(b) and (c)). There is not much change in texture upon heating to 800 °C and even 900 °C (not shown). Above 900 °C, the phase transformation initiates, and at 950 °C, it is complete and only fcc is present in the diffraction pattern (Figure 3, bottom).

A qualitative description of orientation changes during the phase transformation reveals that the 110 fcc pole figure is similar to the 111 bcc pole figure, and the 111 fcc pole figure is similar to the 110 bcc pole figure. Upon cooling to 400 °C, the material reverts completely to bcc and the pole figures are similar to those of the starting material, though there is a less pronounced 111 maximum in the normal direction (Figure 5(e)).

Looking at ODF texture strengths F2, we find that they are similar between 400 °C and 800 °C and very strong (3.3 to 3.6). They decrease already significantly during the first phase transformation (2.7) and more substantially during the cooling phase transformation (2.2).

Discussion

To our knowledge, these are the first quantitative in-situ texture determinations of fcc ULC steel, after transformation from bcc at 950 °C, thus providing data to evaluate changes in the bulk texture during both the heating and the cooling phase transformations. Previously, the high-temperature texture had to be mainly implied from indirect microstructural evidence or by orientations of precipitates that formed at high temperature, such as martensitic intergrowths[3,31] or Widmanstätten structures.[32] In this study, we are dealing with a homogeneous polycrystalline phase, at low and high temperature.

In order to understand the observed texture patterns, orientation changes are modeled with the KS, NW, and Bain relationships. The orientation of the fcc variants is shown in Figure 1, where it is assumed that the bcc crystal is in a standard orientation ([100] bottom, [010] right, and [001] center, hexagonal symbols). For modeling, the ODFs are discretized into a population of 5000 randomly oriented grains, and each grain is assigned a weight according to its volume fraction in the texture. In a next step, the 24 (KS), 12 (NW), and 3 (Bain) symmetrically equivalent product variants are determined, first to the prograde bcc-fcc transformation (using the 800 °C texture as a start) and then to the retrograde fcc-bcc transformation (using the 950 °C texture as a start). The resulting orientations (120,000 for KS, 60,000 for NW, and 15,000 for Bain) were then again converted to a continuous ODF by first placing them in 5 deg × 5 deg × 5 deg ODF cells and subsequently smoothing with a 7.5 filter to eliminate stochastic effects. With this, ODF pole figures were calculated and are shown in Figure 6 for fcc and Figure 7 for bcc. No (orthorhombic) sample symmetry was imposed in the present calculations, because it is assumed that minute deviations from the perfect sample symmetry may give additional information on the crystal correspondence between parent and product orientations.

Fig. 6
figure 6

Pole figures for fcc iron, based on application of all variants of KS, NW, and Bain relationships to 5000 orientations of the bcc rolling texture before transformation (800 °C in Fig. 6). Equal area projection, linear contours.

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Fig. 7
figure 7

Pole figures for bcc iron, based on application of all variants of KS, NW, and Bain relationships to 5000 orientations of the fcc transformation texture (950 °C in Fig. 6). Equal area projection, linear contours.

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For all three models, the patterns show a striking resemblance with those that are actually observed, reproducing all important features, including the reduced 111 maximum in the normal direction when the fcc texture transforms to bcc again during cooling. The KS produces weaker textures than NW and Bain, consistent with the larger dispersion of orientations, given the two- and eightfold multiplicity of the NW and Bain orientation relations, respectively (Figure 1). The three distributions are similar, and, based on bulk textures, it is not possible to discriminate between the models because of the smoothing inherently associated with the inversion procedure of measured pole figures. Electron microscopy has revealed that in many samples, both NW and KS orientation relationships are observed, whereas the precise Bain correspondence is virtually absent from experimental data records.[3,31,33]

The main difference between experiments and models lies in the texture strength: simulated textures are much weaker than experimental ones (lower F2 and higher ODF minimum). Looking at the texture strength data (Table I), the variant selection obviously plays a role. The experimental value of the F2 texture strength drops from 3.6 to 2.7 (25 pct reduction) during the forward α-γ transformation and further to 2.2 (19 pct) during the reverse γ-α transformation. The model calculations predict a much larger reduction in strength: from 3.6 to 1.45 (60 pct) and from 2.7 to 1.35 (50 pct) for the forward and reverse transformations, respectively (averaging KS and NW simulations and excluding the Bain correspondence because of lack of experimental relevance[33]). This indicates that there is an active variant selection during both the forward and reverse transformations. This is different from the data presented by Brückner and Gottstein,[34] who observed a much more pronounced variant selection during the back transformation than during the forward transformation.

For variant selection in steel, there are different models.[35,36] Humbert et al.[37] suggest that macroscopic sample dimensions control the selection. Wittridge and Jonas[38] attribute it to the deformation microstructure, Bate and Hutchinson[39] think that elastic interaction is the cause, whereas Brückner and Gottstein[34] also consider the crystallographic compatibility at grain boundaries and triple junctions in addition to the aforementioned phenomena. We will not go into a discussion of these details but wanted to present the in-situ textural data that can provide data for a more quantitative analysis of the actual processes. On the basis of the present data, though, it seems highly improbable that the variant selection is controlled by a particular feature of the initial structure prior to transformation, such as the presence of a dislocation substructure as required by the model of Jonas et al.[40] The data rather seem to indicate that variant selection is an intricate feature of the γ-α transformation, which is compatible with the features of the models based on elastic interaction and accommodation of the transformation eigenstrains.

Conclusions

With the availability of in-situ texture measurements at high temperature by neutron diffraction, it has become possible to quantitatively investigate changes during phase transformations in polycrystalline aggregates. These experimental data provide a basis for developing models to understand crystallographic relationships, variant selection rules, and texture memory details, many of which are still enigmatic. With this example, it is shown that in the α-γ-α transformation occurring in a recrystallized sample of ULC steel, variant selection plays a role during both the prograde and retrograde transformation.