Incident neutrons Q 2

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1 Q 1 Slit Incident neutrons Collimator Q 2 Collimator TD Detector Bank #1-90 o LD Detector Bank #2 +90 o Supplementary Figure 1. Schematic illustration of the in situ neutron diffraction experimental setup on VULCAN (top view, not to scale). The red-square represents the sampling volume. The -90 and +90 detector banks record diffraction from the grains whose lattice plane-normals are parallel to Q 1 and Q 2, respectively. The tensile specimen (light blue rectangular) is positioned at 45 from the incident beam such that Bank1 probes the strain component along the loading direction (LD) while Bank 2 detects the strain component in the transversal direction (TD) simultaneously. 1

2 Induction coil Grip Grip Supplementary Figure 2. In situ neutron diffraction of tensile loading of a NFA specimen at 800 C. The red dashed-square indicates where the incident neutron beam shines. Numbers 1-4 denote the four thermocouples spot-weld on the specimen. 2

3 Supplementary Figure 3. The true stress-strain curve showing the cyclic tensile loading/unloading at RT of the NFA during in situ neutron diffraction measurements. Supplementary Figure 4. Comparison of the true stress-strain curves for the NFA and 416 SS obtained in tension at RT during in situ neutron diffraction measurements. 3

4 Supplementary Figure 5. The fundamental crystallographic triangle for the body-centered cubic structure, showing the triangular cells chosen for the barycentric interpolation. (a) (b) (c) (d) Supplementary Figure 6. Inverse pole figures (IPFs) of 416 SS in the LD and TD before (a, b) and after (c, d) tensile loading. 4

5 (a) (b) (c) (d) Supplementary Figure 7. Inverse pole figures (IPFs) of a NFA sample in LD and TD before (a, b) and after (c, d) tensile loading at RT. 5

6 416SS 416SS (a) (b) (c) (d) Supplementary Figure 8. Stress factors determined from in situ tensile loading at RT for 416 SS (a, b) and NFA (c, d) with respect to the LD and TD directions. 6

7 LD, 400 C TD, 400 C (a) (b) LD, 600 C TD, 600 C (c) (d) LD, 750 C TD, 750 C (e) (f) Supplementary Figure 9. Stress factors (in units of TPa -1 ) determined from in situ loading of the NFA at 400 C (a, b), 600 C (c, d) and 750 C (e, f) with respect to the LD and TD directions, respectively. 7

8 (a) (b) Supplementary Figure 10. The stress factors with respect to the LD direction at different temperatures. (a) Scattered symbols represent the experimental data corresponding to (from left to right) <001>, <013>, <012> and the average of <112> and <123>; solid lines denote the best-fit results. (b) Comparison between the stress factors corresponding to <011> and <112> directions indicative of stress partition (symbols experimental, lines model). 8

9 Temperature ( C) Supplementary Figure 11. In situ neutron diffraction patterns of a 14YWT sample during cooling from 1300 C. The right panel contains the range of d -spacing around the bcc(110) peak and the left panel around the bcc(211) peak. As shown in the figure, the diffraction peaks of the fcc phase are observed in-between 810 C and 910 C. The hightemperature diffraction experiment was conducted at Intense Pulsed Neutron Source, Argonne National Laboratory, using the GPPD powder diffractometer. 9

10 Supplementary Note 1: In situ neutron diffraction measurements 1.1 Sample preparation The 14YWT NFA, together with a reference sample made from the 416 stainless steel (416 SS) were tested on the VULCAN diffractometer by in situ tensile loadings at a broad range of temperatures. The NFA was mechanically alloyed from pre-alloyed Fe-Cr-W-Ti alloy powder and Y 2 O 3 powder, yielding a nominal composition of Fe-14Cr-0.16W-0.4Ti-0.14Y-0.4O (at.%). The mechanical alloying was followed by canning in an evacuated mild steel jacket and hot extrusion at 850 C. The hot-extruded ingot was then annealed for 1 h at 1000 C. An annealed 416 stainless steel, with a nominal composition of Fe-13Cr-1Mn-0.5Si (wt.%), was used as a reference for the studied NFA. 1.2 In situ time-of-flight (TOF) neutron diffraction measurements In situ time-of-flight (TOF) neutron diffraction experiments were performed on VULCAN, the Engineering Materials Diffractometer at the Spallation Neutron Source, Oak Ridge National Laboratory (ORNL). The top view schematic of the experimental setup is shown in Supplementary Figure 1. A MTS (Materials Testing System) loadframe is placed in the beam area on the sample stage together with an induction heater attached (see Supplementary Figure 2). In each experiment, a threaded, cylindrical 2.90-mm-diameter dogbone-shaped NFA specimen with the gauge length of 20.6 mm was mounted into the grips of the loadframe. The tensile axis was oriented at 45 relative to the incident neutron beam, and uniaxially deformed under tension. The macroscopic engineering strains for the RT measurements were recorded by a mechanical extensometer. In situ monitoring by neutron diffraction was performed during tensile loading at RT and 400 C, 600 C, 750 C, and 800 C, respectively. Four fine-gauge K-type thermocouples were spot weld onto each specimen to control and monitor the temperatures at locations near the specimen center and the two ends. A uniform temperature zone of 10 mm in the center of each specimen (i.e., in-between the No.2 and No.3 thermocouples) was insured by fine-tuning the induction heater prior to mechanical loading. The sampling volume probed by the neutron beam (red rectangular in Supplementary Figure 2), had a temperature gradient of less than 3 C and was the hottest part of the specimen. This configuration provided in situ structural evolution of the NFA under tensile loading at elevated temperatures. 10

11 True stresses and true strains during plastic deformation at high temperatures were evaluated from measured engineering stresses, together with engineering strains estimated from relative cross-head displacements after a linear correction. In other words, where is the engineering strain, is the cross-head displacement relative to the sample gauge length, and are constants. and were determined by matching the slope of the true stress vs. engineering strain curve with that of the stress vs. <110> lattice-strain curve during each of two unloading cycles, one in the middle and the other at the end of plastic deformation. In this approach, we consider that elastic properties keep unchanged during plastic deformation. It should be noted that the true stress and true strain thus evaluated follow a simple power law relation, as observed in the flow curve of many metals. On the other hand, strains in the elastic regime were evaluated by imposing the macroscopic Young s modulus being equal to the slope of the stress vs. <110> lattice-strain curve for each elevated temperature, as has been experimentally observed for room temperature. It is also noted that the hydraulically-driven load frame is slightly less stiff than the sample at RT, but turn to be increasingly stiffer than the sample at elevated temperatures. At VULCAN, diffraction patterns are collected by an energy dispersive method at fixed scattering angles, i.e., the time interval between the neutron pulse generation and the detection moment, time-of-flight (TOF), is essentially proportional to the neutron wavelength,. Thus, each diffraction pattern is collected simultaneously over a large range of wavelengths, in this case, from 0.5 Å to 2.5 Å in d-spacing. The sample is located far away from the neutron source (~42 m) and, therefore, a good reciprocal space resolution is ensured. The sampling volume was defined by the incident beam slits (i.e., 5 mm wide and 3 mm high) and the radial collimators located between the specimen and the detector banks restricting the field of view to 5 mm along the neutron beam path. Diffraction patterns were recorded by the two detector banks (namely, B1 and B2) positioned at diffraction angles of +/-90. As such, B1 and B2 collected diffraction from the lattice planes parallel and perpendicular to the loading direction, and denoted LD (loading direction) and TD (transverse direction), respectively. Each bank includes three wavelength- Shifting-fiber Scintillator Detectors (SSD) position sensitive detectors [1]. The detector horizontal spatial resolution of 5 mm matches the effective sample size and provides a horizontal angular resolution of 0.2 for a detector pixel. The total angular coverage of a detector encompasses with pixels. A cross-correlation calibration procedure performed 11

12 using the diffraction patterns generated in each detector pixel by a diamond powder sample generates the TOF shifts look-up table, and allows reducing the set of patterns recorded on individual pixels to a unique diffraction pattern corresponding to the nominal scattering angle defined by the detector center. Following this procedure, referred as time focusing, the total pattern essentially preserves the angular resolution of a pixel pattern. The TOF neutron diffraction data were collected continuously during the mechanical loading at various temperatures, with the chopper running at 30 Hz. The central wavelength and the bandwidth were λ = 2 Å, and = 2.88 Å, respectively. The instrument calibrations and data normalizations were performed with a V rod, and Si powder and/or diamond powder loaded in vanadium can, measured in the same conditions as the studied samples. 1.3 Neutron diffraction data reduction and analysis Under the time event data acquisition at SNS, each detected neutron is recorded with a timestamp from a master time clock allowing a versatile and accurate post-experiment data binning. Moreover, neutron time event data can be easily synchronized with the mechanical loading data during a continuous loading test. The recorded neutron data were reduced with a dedicated software, VDRIVE [2], and then sliced and binned into histograms corresponding to small temporal intervals that were synchronized with the loading parameters (e.g., force, displacement, temperature, etc.). Two time intervals were used for chopping the data: 2 min and 10 min. Single peak-fitting implemented in the SMARTSWare program [3] and VDRIVE was used to extract from the diffraction patterns the peak information including peak position (dspacing), full-width-at-half-maximum (FWHM), and integrated intensity for each recorded hkl reflection. 1.4 Mechanical behaviors of the NFA The in situ tensile loading of the NFA was performed at RT and temperatures of 400 C, 600 C, 750 C, and 800 C. In order to obtain sufficient data points with good counting statistics, a low strain rate of s -1 was used. Typically, a few loading-unloading cycles were conducted for each experiment (see Supplementary Figure 3) in order to measure elastic constants. For instance, a RT loading experienced initially loading under stress control up to a stress level below the yield strength, and proceeding under strain-control to a few percent of 12

13 plastic strain, followed by unloading under stress control; this procedure was then followed by the subsequent cycles. The elastic and plastic regimes were analyzed in correlation with the diffraction response to characterize the orientation-dependent anisotropy. The observed stressstrain curves during in situ neutron measurements for both NFA and 416 SS, as shown in Supplementary Figure 4. Supplementary Note 2: Crystallographic texture For crystallographic texture characterizations, integrated peak intensities obtained from the single peak-fitting scheme were used to generate inverse-pole figures (IPFs) for the asreceived 416 SS and NFA and for their tensile specimens during and/or after loading at various temperatures. For a crystal with cubic symmetry, the fundamental triangle with the corners at <001>, <011>, and <111> is used to represent the preferred grain orientations through IPFs. The distribution of selected directions (<114>, <112>, <123>, <013>, <012> and <332>) characteristic of the BCC structure is shown in Supplementary Figure 5. This network of points determines 8 triangular cells, i.e., 8 spherical triangles. Inside each spherical triangular cell, the texture index is calculated by barycentric interpolation. According to this approach, the value of a function, F, in a point, P, located inside the triangle with the vertices A i, can be approximated as follows:. (1) In this equation, the area S i, corresponds to the triangle opposite to the vertex A i, and the area, S 0, refers to the whole triangle. However, the basic pole distribution is inhomogeneous and the measured values correspond to IPF integration over a certain area around the nominal direction. To evaluate the instrument coverage for each basic direction and to determine the correlation between their detection probabilities, we applied the quasi-monte Carlo (QMC) approach. The QMC method is used to generate evenly distributed networks of points in a multidimensional space. Similar to the Monte Carlo (MC) method, the integral of a multi-dimensional function reduces to the average of the function values calculated in a finite number of points. We used the method proposed by Halton [4] to generate low-discrepancy sequences. A 3D network of 1023 QMC distributed points was generated to simulate a random distribution of grain 13

14 orientations. As the single crystal orientation, characterized by an Eulerian rotation matrix, is known, it is possible to calculate which of the selected diffraction spots will be detected in each of the detector banks in the VULCAN arrangement (axial and/or transverse). The statistics of diffraction spots allows calculating the weighting factors for the basic crystallographic directions, i, and further estimate the basic texture parameters,, from experimental data:. (2) In Eq. (2), I j represents the integrated intensity of a diffraction line j, and is normalized by the reference intensity,, which is measured (or calculated) from a reference sample with randomly oriented grains. Beside the weighting factors, i, the QMC calculations provide the correlation factors, f i (m j ), defined as the probability to record the diffraction spot m j in the transverse-direction detector bank when the diffraction spot n i is recorded in the longitudinal direction for a random texture. These coefficients can be used to link the IPFs of LD and TD, if the texture is transversally isotropic (see Ref. [5] for details). The generation of the IPFs is based on the quasi-monte Carlo (QMC) method as described in [4], which has been extended here for the BCC structure. The integrated intensity for a particular hkl peak is proportional to the volume fraction of the same family of grains whose plane normal [hkl] is lying along the diffraction vector and thus contained in the solid angle delimited by the detector acceptance. This integrated intensity, after normalized to the corresponding peak intensity obtained from a powdered sample, is a direct measure of the preferential orientation. For the cubic symmetry, <001>, <011> and <111> that constitute the fundamental crystallographic orientation triangle (see Supplementary Figure 5), together with other 6 peaks including <114>, <112>, <123>, <013>, <012> and <332> were taken, allowing for a fairly good coverage for an IPF. The barycentric interpolation inside each spherical triangular cell was used to generate the IPFs with a balanced coverage. As the corresponding pole distribution of the 9 chosen peaks is not homogeneous, a quasi-monte Carlo approach based on random-start Halton sequences was applied to evaluate the instrument coverage for each hkl direction, and to determine the correlation between their detection probabilities (see Ref. [4] for details). The IPFs have been generated for LD and TD, respectively, which contain necessary features to describe the crystallographic texture evolution during tensile loading at RT and HT. 14

15 For 416 SS and NFA, nine diffraction peaks were chosen to represent the IPFs: 110, 200, 211, 310, 222, 321, 411, 420, and 332. However, it should be noted that the diffraction patterns of the NFA samples had less than the necessary 9 distinct peaks: 332 is indeed missing from the LD patterns (Detector Bank 1) and 222 is diminishing for temperatures over 600 C, so is 420 in the TD patterns. Nevertheless, the preferential grain orientations in the 416 SS samples before and after tensile deformation are represented in Supplementary Figure 6. It can be seen from the IPFs in the LD that the texture index was close to a random distribution before mechanical loading at RT, while a characteristic [011]//LD fiber texture developed during tensile deformation though the degree of preferential orientation is relatively small. In contrast, the IPFs of the NFA sample show a strong initial [011]//LD fiber texture which had moderate change due to tensile loading at RT (see Supplementary Figure 7). Supplementary Note 3: Stress factors The stress factor for each <hkl> was experimentally determined by the slope of a linear fit to the <hkl> lattice strain as a function of the applied true stress during initial loading below the yield stress. This procedure was also applied to the subsequent unloading/loading cycles. As the plastic deformation had little influence on the elastic stress factors, the final experimental values were obtained by averaging the measured slopes for all loading/unloading cycles. The results can be represented over the inverse pole figure grids. However, due to the preferred grain orientations, the stress factors of <111>//LD and <233>//LD could not be determined accurately. The LD inverse stress pole figures are thus restricted to a part of the fundamental triangle. The data obtained for 416 SS and the NFA at RT are compared in Supplementary Figure 8. The 416 SS reference sample shows a regular pattern across the triangle for both LD and TD, characteristic of a random texture for which the stress factors depend on ( ) only. This indicates, for example, that the stress factors of <011>, <123> and <112> should be equal in both LD and TD maps. Both maps for 416 SS follow this rule, whereas the NFA sample shows a completely different pattern. The high temperature data are shown in Supplementary Figure 9, exhibiting similar patterns but with widely different absolute values. This means that the stress distribution inside the fundamental triangle is controlled by the sample texture, which is independent on the sample temperature. 15

16 The modeling of stress factors reported in the present work makes use of the IPFs data. The list of basic fibers considered in the model coincides with the crystallographic directions used as a basis for the IPF representation. As a result, the volume fractions, w i, are simply calculated as: w i = t i i. Although the stress factor values for the <111> and <332> directions are not known, the contribution of these two crystallographic fibers is estimated to be less than 1% for the NFA specimens. This is well below the statistical error of our experiment. On the other hand, for the 416 SS sample, the contribution of the <111> and <332> directions, i.e., ~14%, is important and the corresponding stress factors were included in the analysis. The values of elastic constants for 416 SS resulting from our analysis are close (within 5% standard deviation) to the experimental values reported on pure Fe [6] and the theoretical values calculated for Fe 0.9 Cr 0.1 [7]. The average values of the longitudinal stress factors measured at different temperatures are presented in Supplementary Figure 10, and compared with the results of modeling based on single-crystal elastic constants. 16

17 Supplementary References 1. Crow M. L., Hodges J. P. & Cooper R. G., Nucl. Instr. Meth. Phys. Res. A 529, 287 (2004) 2. An, K. VDRIVE - Data Reduction and Interactive Visualization Software for Event Mode Neutron Diffraction. Oak Ridge National Laboratory Report ORNL-TM (2012). 3. Clausen, B. SMARTSWare. Los Alamos National Laboratory Report LAUR (2003). 4. Halton, J. H. On efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numerische Mathematik 2, (1960). 5. Stoica G. M., Stoica, A. D., An K, Ma D & Wang XL. Extracting Grain-Orientation Dependent Data from In-Situ Time-of-Flight Neutron Diffraction I. Inverse Pole Figures. Submitted to J. Appl. Cryst. 6. Dever, D. J. Temperature dependence of elastic constants in iron single crystals: relationship to spin order and diffusion anomalies. J. Appl. Phys.43, 3293 (1972). 7. Zhang H. L., Al-Zoubi N., Johansson B. & Vitos L. Alloying effect on the elastic parameters of ferromagnetic and paramagnetic Fe from first-principles theory. J. Appl. Phys.110, (2011). 17