Lattice strain during compressive loading of AlCrFeNiTi multi-principal element alloys

Through an appropriate combination of 5 different input metal powders, an MPEA with an equimolar ratio of the base elements Al, Cr, Fe, Ni and Ti (MPEA5) as well as a composition with a reduced amount of Ti to 10 mol% (MPEA_Ti10) were generated. The chemical composition of the input metal powders as well as of the materials MPEA5 and MPEA_Ti10 is listed in Table 1. The pre-alloyed powders L718 and W722 contain minor amounts of additional elements, e.g., Co, Mo and Nb, which are introduced into the mixture alongside the main elements Al, Cr, Fe, Ni and Ti. The chemical composition of our MPEA5 is altered by changing the mixing ratio of the powders. A detailed description of the production of the samples of this study is presented in [10], and is briefly summarized in the following subsection.

A total amount of 39 g of powder per batch was placed into a 250 ml tungsten carbide milling chamber combined with tungsten carbide milling balls in a ball-to-powder mass ratio of 10:1. The milling chamber was sealed under argon atmosphere in a glove box and was then placed into a planetary ball mill of the type Pulverisette P6 (Fritsch GmbH, Idar-Oberstein, Germany). The milling speed was 400 rpm and the milling time was 2 h. For the sake of cooling the milling chamber, five minutes of milling were alternated with 20 minutes of resting. After the milling process, only the loose powder in the milling chamber was used for further processing.

Encapsulation of the mechanically alloyed powder is required for powder densification employing hot isostatic pressing. The powder (6 g) with the chemical composition MPEA5 or MPEA_Ti10 is filled and sealed in Ti tubes (grade 2, 10 mm outer diameter, 1 mm wall thickness and 100 mm length) under argon atmosphere. A pressure of 75 MPa and a temperature of 950 \(^\circ \hbox {C}\) were applied to the capsules by using a hot isostatic press (EPSI, Belgium) with high-purity argon gas as pressure medium. After maintaining this environment for 4 hours, the temperature is reduced moderately to room temperature with a maximum cooling rate of 12 K/min. For each composition, a sample for analysis by in situ synchrotron X-ray diffraction and a sample for dilatometry was prepared. The amount of mechanically alloyed powder was low, resulting in a limitation of the number of specimens that could be produced.

Compression tests were performed by using a deformation-dilatometer of type DIL 805A/D/T (TA Instruments, New Castle, USA). One test was performed for each composition. Cylindrical samples with a diameter of 4 mm and a length of 8 mm were used in these tests (Fig. 1a). The strain-controlled room temperature tests were conducted with a fixed traverse speed of 10 \(\mu \hbox {m/s}\).

Synchrotron X-ray diffraction of the samples MPEA5 and MPEA_Ti10 combined with a compression test was performed at High Energy Materials Science (HEMS) beamline run by the Helmholtz-Zentrum Geesthacht at PETRA III at DESY in Hamburg [14]. One test was performed for each composition. Cylindrical samples with a diameter of 4 mm and a length of 8 mm were fabricated via wire electrical discharge machining (WEDM) (Fig. 1a). The samples were compressed with a constant traverse speed of 7.00 \(\times \) \(10^{-4}\) mm \(\hbox {s}^{-1}\). The beam possesses a mean photon energy of 87.1 keV and a wavelength of 0.14235 Å. A PerkinElmer XRD 1622 flat panel detector was used to analyze the diffracted beam (Fig. 1b). The detector had a pixel matrix of 2048 \(\times \) 2048 and a pixel size of 200 \(\times \) 200 \(\mu \hbox {m}^{2}\). The distance between sample and detector was set to approximately 1490 mm which was calibrated with an \(\hbox {LaB}_\mathrm {6}\) powder standard.

The radial displacement of the respective diffraction peak center with consideration of an unstrained reference peak position was determined to define the lattice parameter and the lattice strain during compression of the samples [15]. For this purpose, \(10^\circ \) pie segments in loading direction (\(0^\circ \)) and perpendicular to it (\(90^\circ \)) of the two-dimensional diffraction patterns were integrated azimuthally using the software STeCa2-2.0.5RC4 (Fig. 1b, c). Three reflections per phase, which are labeled in Fig. 2, were fitted using Gaussian functions. From the position of the i-th peak, \(\mathrm {\Theta }_{{\mathrm {hkl}},i}\), the corresponding lattice plane spacing \(d_{\mathrm {hkl,}i}\) is calculated using Bragg’s law: n \(\lambda \) = 2 \(d_{\mathrm {hkl,}i}\) sin(\(\mathrm {\Theta }_{{\mathrm {hkl}},i}\)). \(\lambda \) is the wavelength of the X-ray beam (0.14235 Å) and n represents the order of the reflection. The elastic strains were calculated via \(\varepsilon _{{\mathrm {hkl}},i}\) = (\(d_{{\mathrm {hkl}},i}\) - \(d_\mathrm {hkl,0}\))/ \(d_\mathrm {hkl,0}\). Here, \(d_\mathrm {hkl,0}\) represents the respective lattice plane spacing in unloaded condition. The \(\sigma \)-\(\varepsilon _{\mathrm {hkl}}\) curves (see Figs. 3 and 4) were linearly fitted to determine the lattice-dependent elastic moduli \(E_{\mathrm {hkl}}\). Thereby, each stage (I, II, III) was linearly fitted separately and the lattice-dependent elastic moduli were calculated from \(E_{\mathrm {hkl}}\,=\,|\mathrm {\Delta }\sigma /\mathrm {\Delta }\varepsilon _{\mathrm {hkl}}|\). Further, the lattice-dependent Poisson’s ratios were determined from the lattice-dependent elastic moduli in the loading direction (\(0^\circ \)) and perpendicular to it (\(90^\circ \)) as \(\nu _{\mathrm {hkl}}\) = \(E_\mathrm {hkl,0^\circ }/E_\mathrm {hkl,90^\circ }\). Detailed analysis of single peaks was performed by using the software FullProf Suite vers. 07.2017 with the included tool WinPLOTR vers. 09.2018.

The calculation-of-phase-diagrams-method (CALPHAD) as part of the software Thermocalc along with the database TCHEA1 was used for the calculation of stable phases occurring in the alloys.

Samples for the analysis via light microscopy and electron backscatter diffraction (EBSD) were embedded in resin, ground and polished, after they have been tested via in situ synchrotron X-ray diffraction. EBSD measurements were undertaken with a Jeol JSM-7600F field emission scanning electron microscope equipped with an Oxford SYMMETRY system and AZtech software. The results were analyzed with the software Channel5 and a NIST structural database.

The macroscopic stress–strain development during the in situ synchrotron compression test of composition MPEA5 is presented in Fig. 5. In the loading range between 0 and 200 MPa different effects, e.g., settlement of the sample on a microscopic scale, results in a nonlinear curve progression. In the compressive stress range from 200 to 636 MPa, the stress increase is linearly correlated to the strain increase. There are two stress levels at which the stress–strain curve exhibits a kink. The enlarged areas in Fig. 5 at stress levels of 348 MPa resp. 463 MPa show an increment in strain. Figure 6 shows the results of dilatometric compression tests where stress is plotted over strain. The shape of the MPEA5 stress–strain curve is similar to that from the in situ synchrotron compression test. The stress–strain curve of MPEA5 obtained in the dilatometer shows three positions where an increase in strain occurs. The increments in strain at the stress levels of 350 MPa and 570 MPa are nearly at the same stress levels as the strain-increments detected in the in situ compression test of MPEA5. Due to the loading cell capability of the dilatometer application of higher compressive stresses than in the in situ synchrotron experiment (maximum applied load \(\sim \) 635 MPa) was possible. At a stress level of 790 MPa, another increment in strain is detected in the dilatometer experiment.

The reason for the increase in macroscopic strain (in some cases associated with a drop in stress) and a decrease in the elastic modulus is a phenomenon which is most likely caused by the formation of long cracks [16‐18]. This is supported by the observation that the MPEA5-samples used for the compression tests fracture during unloading after the maximum stress was applied. Since the macroscopic determination of the stress–strain curve is influenced by the entire isotropic material structure of the specimen, microstructural changes such as crack formation do not lead to any detectable change in the tangent modulus. The MPEA_Ti10 samples did not show any kinks in the stress–strain curves (Figs. 6 and 7) that would indicate the development of long cracks through the sample. Furthermore, the MPEA_Ti10 samples did not fracture into pieces during unloading at the end of the compression tests. Plastic deformation has not been observed in connection with the kinks.

A microscopic analysis of the samples after the compression tests showed cracks in both alloys (Fig. 8). While the cracks in MPEA_Ti10 developed with multiple branches (Fig. 8b), MPEA5 contains a continuous crack without branches (Fig. 8a). As branching is energetically inefficient for crack growth, crack propagation is hindered more than for continuous cracks [19‐21]. This observation correlates to the stress–strain development of the alloys. Due to the interrupted growth of cracks forming branches in MPEA_Ti10, the stress–strain curve is only little affected.

Figure 2 shows diffractograms of MPEA5 and MPEA_Ti10 obtained from samples in the absence of mechanical loads. The peaks which were used for analysis of the lattice strain during macroscopic compression of the samples are marked by the respective phase including the reflecting lattice plane. One of the detected phases is the Full Heusler-phase (H_L21-phase) whose diffraction peaks are labeled as (220), (400) and (422). Further peaks in the diffractograms indicate the presence of a body-centered cubic phase (BCC-phase). The reflecting lattice planes are (110), (200) and (211). H_L21-phase exhibits the peaks with the highest intensity, followed by peaks originating from the BCC-phase. As C14_Laves-phase is expected to be present only in small amounts, the according peaks in the diffractograms are small. The observed peaks for the C14_Laves-phase stem from the lattice planes (110), (103) and (302). The same phases observed in this work were also detected in X-ray diffraction experiments using an equimolar AlCrFeNiTi-alloy [10, 12, 22].

Thermocalc software predicts the presence of a H_L21-phase (\(\hbox {Ni}_2\hbox {AlTi}\)) and several BCC-phases (Cr-rich, Fe-rich) in MPEA5 and MPEA_Ti10 (Fig. 9). In MPEA5, C14_Laves-phase (\(\hbox {Fe}_2\hbox {Ti}\)) is predicted to be not stable at room temperature but it should be present at temperatures above 130 \(^{\circ }\hbox {C}\). In MPEA_Ti10 a small amount of C14_Laves-phase is predicted to occur at room temperature. Probably due to a non-equilibrium state of MPEA5 and MPEA_Ti10, it is possible that a small amount of C14_Laves-phase is also detected at room temperature in MPEA5. Small peaks in the diffractograms indicating C14_Laves-phase support this assumption (Fig. 2).

Microstructure phase analysis via EBSD shows the presence of C14_Laves-phase (\(\hbox {Fe}_2\hbox {Ti}\)) in both, MPEA5 and MPEA_Ti10 (Fig. 10c, d). Furthermore, BCC-phases (Fe-rich, Cr-rich) as well as H_L21-phase (Ni2AlTi) are detected. C14_Laves-phase agglomerates in areas with a maximum diameter of \(1\mu \hbox {m}\). The distribution of BCC- and H_L21-phases is much finer. Figure 10c, d shows no correlation between crack propagation and microstructural phase distribution. Moreover, inverse pole figure maps (IPF-maps) of MPEA5 and MPEA_Ti10 (Fig. 10a, b) show, that the crack propagation in both alloys in general is intercrystalline. Only MPEA5 shows regions (about \(2\mu \hbox {m}\) in size, circle in Fig. 10a) where crack propagation seems to be transcrystalline.

The analysis of lattice-dependent elastic moduli is separated into 3 regions depending on the applied macroscopic stress. As labeled in Fig. 5, stage I is defined up to the first major crack event (348 MPa), which can be detected from the stress–strain data. Stage II ranges between the first and second major crack events (348 MPa to 469 MPa). Stage III starts at a stress level of 469 MPa and ranges up to the maximum applied stress of 636 MPa. The macroscopic stress is plotted over the calculated lattice strain (see Sect. 2.5) in Fig. 3. Thereby, different phases are presented separately (a, b, c). The diagrams show results for distinct phase lattice planes and are presented for the loading direction (\(\hbox {0}^\circ \)) as well as the direction perpendicular to it (\(\hbox {90}^\circ \)).

Figure 11a shows diffraction peaks resulting from the lattice plane (220) of the H_L21-phase extracted from 4 diffractograms. The peaks represented by full lines stem from diffractograms which were taken just below the upper bound of stage I, whereas the dotted lines stem from the same peak slightly above the stress level at which stage II begins. The enlarged plot in Fig. 11b clearly shows that the gap between these two peaks just before the detected increment in strain is minimal. Also, the two peaks just after the detected increase in strain are nearly identical in position and shape. In contrast to this, the gap between the two pairs of peaks is clearly detectable. This results in distinctive increments in strain between stage I and stage II (Fig. 3). Having a look at the overall lattice-dependent elastic moduli, it is clearly visible that the value is reduced in later stages (Table 2). For example, the elastic modulus determined from lattice plane (220) of the H_L21-phase is 211.8 ± 0.7 GPa in stage I, and thereby reaches values that have been determined before in other studies (209.4 GPa [23], 193.0 GPa [24], 84.7–234.1 GPa [25, 26]). In stage II, the lattice-dependent elastic modulus is about 28 % lower and reaches 151.2 ± 1.3 GPa. A further decrease in the lattice-dependent elastic modulus of over 6 % is detected by reaching stage III (141.8 ± 1.1 GPa). This trend is shown by all lattice planes of all detected phases in the sample MPEA5. The BCC-phase shows lattice-dependent elastic moduli in stage I in the range of 232.3–301.5 GPa. These values have been confirmed before in other studies (Cr-rich BCC: 270–438 GPa [25, 26], 289.6 GPa [27]; Fe-rich BCC: 233.3–287.6 GPa [25, 26], 243.0 GPa [28]). The lattice-dependent elastic moduli of C14_Laves-phase are between 192.5 GPa and 207.2 GPa in stage I. Values close to this level have been determined in previous studies, as well (221–230 GPa [29], 179.0–265.0 GPa [25, 26]). The decrease in lattice-dependent elastic moduli with increasing stage-number is supporting the assumption of the development of long, un-branching cracks between the single stages, as cracks decrease the materials’ stiffness. Additionally, the increment in lattice strain between the stages supports the assumption of crack development, as crack development reduces the load-bearing cross section. This influences the lattice parameter.

The diagrams in Fig. 4 present the macroscopic stress plotted over the lattice strain of composition MPEA_Ti10. The curves show increases in lattice strain at constant macroscopic stress levels of 398 MPa and 636 MPa. In contrast to the increases of lattice strain in the composition MPEA5, here they do not correlate with crack development but with short stops at these loads during the test. The stops were used to perform texture measurements that revealed no noticeable change in texture in the sample. Creeping that occurs during the stops might be the reason for the increase in lattice strain. These positions were taken to divide the diagrams into 3 stages to compare the lattice-dependent elastic moduli at different stress levels. The stages are indicated in Fig. 7. Thereby, it has to be noted that the stress–strain curve progression in Fig. 7 does not give any indication of the stops in compression. Stage I is located between 167 MPa and 398 MPa. Stage II is located between 398 MPa and 636 MPa. Lastly, stage III is located between 636 MPa and the maximum applied stress of 795 MPa.

In contrast to MPEA5, MPEA_Ti10 shows only little changes of the lattice-dependent elastic moduli in the different stages (Table  3). For example, the lattice-dependent elastic modulus determined from the reflection (220) of H_L21-phase in compression direction is 225.5 ± 0.4 GPa. In stage II, the lattice-dependent elastic modulus is just 5% higher (238.0 ± 0.9 GPa). In stage III, the lattice-dependent elastic modulus is 206.7 ± 3.0 GPa (13% lower than in stage II). As the development of long, un-branching cracks is not the reason for the segmentation of the stress lattice strain curves of MPEA_Ti10, pronounced changes in lattice-dependent elastic moduli are not expected and hence are not detected.

MPEA5 shows different lattice-dependent elastic moduli depending on the reflections investigated. For example, the lattice-dependent elastic moduli, determined from H_L21 reflections (220) and (422), are significantly higher than those determined from reflection (400). This implies that the lattice deformation during compression is larger in lattice direction [400] than in the lattice directions [220] and [422]. Comparing the reflections of the BCC-phase to each other, they result in nearly similar lattice-dependent elastic moduli. Still, there is a reflection identifiable in all stages that exhibits the minimal lattice-dependent elastic modulus. These are the (211) reflection in stage I, the (200) reflection in stage II and the (110) reflection in stage III even though the lattice-dependent elastic moduli determined from the two other reflections are just negligibly higher (+9% for (200), +11% for (211)). Determination of the lattice-dependent elastic moduli from reflections of the C14_Laves-phase is less accurate than for H_L21-phase and BCC-phase due to the small intensity and lower symmetry of the diffraction peaks originating from the C14_Laves-phase. The resulting lattice-dependent elastic moduli show no significant differences in dependence of the reflection. This indicates that the elastic deformation of the C14_Laves-phase is roughly the same in all observed lattice directions as determined from the reflections (110), (103) and (302). Comparing the lattice-dependent elastic moduli of H_L21- and BCC-phases shows that in general the elastic moduli of BCC-phase are significantly higher than those of the H_L21-phase. This means that the H_L21-phase takes a larger share of the total deformation during compression than the BCC-phase.

MPEA_Ti10 shows trends similar to MPEA5 in the development of phase-specific elastic moduli in dependence of the reflecting lattice plane.

The evolution of Poisson’s ratio as a function of the stages varies depending on the phase considered. The deviation regarding Stage I for both compositions is between − 39.0 % and 22.9 % for BCC, between − 21.1 % and 32.7 % for C14_Laves and between − 1.5 % and 10.2 % for H_L21 (Tables 2, 3). Therefore, H_L21 shows the smallest deviations of the Poisson’s ratio. Further regularities or trends in the development of Poisson’s ratio have not been detected.