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Article

Lattice Parameter Evolution during the β-to-α and β-to-ω Transformations of Iron- and Aluminum-Modified Ti-11Cr(at.%)

by
JoAnn Ballor
1,
Jonathan D. Poplawsky
2,
Arun Devaraj
3,
Scott Misture
4 and
Carl J. Boehlert
1,*
1
Department of Chemical Engineering and Material Science, Michigan State University, East Lansing, MI 48824, USA
2
Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA
3
Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA 99352, USA
4
Inamori School of Engineering, Alfred University, Alfred, NY 14802, USA
*
Author to whom correspondence should be addressed.
Crystals 2024, 14(2), 145; https://doi.org/10.3390/cryst14020145
Submission received: 29 December 2023 / Revised: 27 January 2024 / Accepted: 29 January 2024 / Published: 30 January 2024
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Abstract

:
β-titanium (β-Ti) alloys are useful in diverse industries because their mechanical properties can be tuned by transforming the metastable β phase into other metastable and stable phases. Relationships between lattice parameter and β-Ti alloy concentrations have been explored, but the lattice parameter evolution during β-phase transformations is not well understood. In this work, the β-Ti alloys, Ti-11Cr, Ti-11Cr-0.85Fe, Ti-11Cr-5.3Al, and Ti-11Cr-0.85Fe-5.3Al (all in at.%), underwent a 400 °C aging treatment for up to 12 h to induce the β-to-ω and β-to-α phase transformations. Phase identification and lattice parameters were measured in situ using high-temperature X-ray diffraction. Phase compositions were measured ex situ using atom probe tomography. During the phase transformations, Cr and Fe diffused from the ω and α phases into the β matrix, and the β-phase lattice parameter exhibited a corresponding decrease. The decrease in β-phase lattice parameter affected the α- and ω-phase lattice parameters. The α phase in the Fe-free alloys exhibited α-phase c/a ratios close to those of pure Ti. A larger β-phase composition change in Ti-11Cr resulted in larger ω-phase lattice parameter changes than that for Ti-11Cr-0.85Fe. This work illuminates the complex relationship between diffusion, composition, and structure for these diffusive/displacive transformations.

1. Introduction

β-Ti alloys are used in diverse industries because they can exhibit a wide range of mechanical properties through transforming the metastable body-centered cubic β phase into other metastable and stable phases, such as the metastable ω phase and the stable α phase. Due to these transformations, β-Ti alloys can exhibit high strengths that are attractive for structural applications [1]. Because of their high strength-to-weight ratios, β-Ti alloys are also a promising option for lightweighting in the automotive industry [2]. However, the relatively high cost of Ti alloys compared to steels or aluminum (Al) alloys impedes their widespread use. One way to reduce the cost of β-Ti alloys is to alloy with less expensive alloying elements, such as chromium (Cr), iron (Fe), and Al. To choose the best combination of alloying elements for achieving desired mechanical properties, a thorough understanding of how alloy composition and processing can affect the microstructure and mechanical properties is necessary.
To retain the metastable β-phase upon quenching, β-phase stabilizing elements are needed. To compare the compositions of β-Ti alloys, the molybdenum equivalency (Mo-Eq.) equation was developed, which provides the amount of Mo that could replace the elements in the alloy the provide the same β-phase stability [3]. The average atomic radii and average electron d-shell energy (Md) of the alloy compositions are also important to alloy design, as they are related to the deformation mechanisms in β-Ti alloys. Average atomic radius, average Md, and composition (through Mo-Eq.) show clear interrelationships; see Figure 1.
In addition to the relationships shown in Figure 1, the β-phase lattice parameter (aβ) is related to Mo-Eq. (as well as the average radius and Md) as aβ decreases with increasing Mo, Cr, and Fe content [4,5,6], increases with increasing Nb contents between 5 and 22 at.% [7], and remains relatively constant for Nb contents between 22 and 35 at.% [8].
These lattice parameter changes have been documented in fully β-phase microstructures, but they have not been fully explored in multiphase microstructures. β-phase alloys can be strengthened through aging due to the precipitation of the ω and α phases through a diffusive/displacive phase transformation mechanism, where the β-phase stabilizers diffuse from the ω- and α-phase precipitates into the surrounding β matrix [9,10]. This diffusion changes the β-phase Mo-Eq. during the phase transformations, and thus affects the average Md, average atomic radius, and lattice parameter of the β phase. Similarly, the α-phase lattice parameters have also been reported to change during the displacive/diffusive phase transformation during aging [11], and the changes in α- and β-phase lattice parameters with changing phase compositions have been reported in the α + β alloys Ti-6Al-4V(wt.%) [12] and Ti-6Al-6V-2Sn(wt.%) [13], but these changes are not well reported in metastable β alloys.
Diffusion is important to both β-to-α and β-to-ω transformations because they are both displacive/diffusive transformations. The metastable ω-phase composition is particularly important as its precipitation can be affected by the addition of elements such as tin and oxygen, as athermal ω-phase prefers Ti-rich compositions, and diffusion during the isothermal ω-phase transformation makes the β-to-ω transformation irreversible [14,15,16,17]. Understanding the evolution of the lattice parameters of each phase during the phase transformations is critical for understanding the lattice misfit, which can affect the growth and morphology of the transforming phases [18], the local deformation mechanisms [19,20], and the residual stress [21,22]. The ledges of the ω phase at the ω/β boundary are favorable locations for the ω-assisted α-phase transformation [23,24,25,26,27]. The ω-assisted α-phase transformation is desired due to the nanoscale α-phase that forms and the corresponding attractive mechanical properties, such as increased strength and hardness [28,29,30,31]. The lattice misfit and ω/α interfaces have been investigated using high-resolution imaging techniques, but the lattice parameters of the phases are not always reported, and these are usually evaluated ex situ (after the aging has occurred). High-temperature XRD (HTXRD) offers a unique opportunity to monitor the lattice parameter transformations in the bulk material during aging. The small size of the ω and α precipitates poses a challenge to this technique, but the potential knowledge to be gained through such in situ experiments makes it worth investigating. Similarly, these small precipitates pose a challenge to composition measurement, so atom probe tomography (APT), with its nanoscale resolution, was chosen to investigate the details of the precipitates’ compositions. As the phase diagrams for the tertiary and quaternary alloys are not yet established, this work also adds to the knowledge of the phases and the associated phase fields in these more complex alloy systems.
In this work, the evolution of the β-, α-, and ω-phase lattice parameters during the β-to-ω and β-to-α phase transformations is explored in the Ti-Cr alloy system, which undergoes the β-to-ω and β-to-α phase transformations [32,33,34]. A base alloy composition of Ti-11Cr(at.%) was chosen for this study, and the β-phase stabilizer, Fe, and the α-phase stabilizer, Al, were added to determine their effects on the phase transformations and the lattice parameters with increased aging time. In situ (HTXRD) was performed to investigate both the phase transformations and the lattice parameters of all the phases present during the 400 °C aging, and APT was used to determine the composition of each phase in each alloy. Through the combination of APT and HTXRD, the relationship between the lattice parameters and phase compositions during the β-to-ω and β-to-α phase transformations was determined for Fe- and Al-modified Ti-11Cr(at.%)

2. Materials and Methods

Ti-11Cr(at.%) (TC), Ti-11Cr-0.85Fe(at.%) (TCF), Ti-11Cr-5.3Al(at.%) (TCA), and Ti-11Cr-0.85Fe-5.3Al(at.%) (TCFA) were levitation melted in a 2 kg, 90Dx80L LEV levitation induction furnace and hot forged at approximately 1047 °C into 25 × 60 × 250 mm3 blocks, then homogenized using a 900 °C anneal for 1 h in vacuum, followed by ice-water quenching at an estimated cooling rate of 34.7 °C/s. All of these processing steps were performed at Daido Steel Company, Ltd. (Nagoya, Japan). The measured composition of each alloy was reported earlier [35]. All alloy compositions are reported in atomic percent. A 400 °C aging heat treatment was chosen to induce the ω- and α-phase transformations, as Ti-Cr alloys have formed both phases after aging at that temperature [32,33,34].
For the APT sample preparation, samples were cut from the forgings using a diamond saw. These sample were then aged at 400 °C in a vacuum followed by air quenching. TC and TCFA were aged for 0.75, 1.5, 3, 6, and 12 h, while TCF and TCA were aged for 0.75, 1.5, and 12 h. After aging, the samples were metallographically polished to a mirror finish according to [36]. APT needle specimens were extracted using the FIB-based lift-out and annular milling method described in [37]. A CAMECA local electrode atom probe (LEAP) 4000X HR system was used for all APT data collection. Pulsed-voltage mode with a 200 kHz pulse frequency, 50 K specimen temperature, pulse fraction of 0.2, and a detection rate of 0.5% was used for all the 12 h aged samples, and the 0.75 h and 1.5 h aged TC and TCFA samples. Pulsed-laser mode with a 50 pJ laser energy, 200 kHz pulse frequency, 30 K specimen temperature, and a detection rate of 0.5% was used for all the other samples.
Samples for HTXRD were cut using an electrodischarge machine and polished using 320 grit silicon carbide paper to remove any macroscopic surface defects and oxides. The final sample dimensions were approximately 17 mm × 17 mm × 1.1 mm. HTXRD was performed using a Bruker-AXS (Madison, WI, USA) D8 diffractometer with an automatic sample changer, a Vantec linear position-sensitive detector, Cu-Kα radiation, and an Anton-Paar HTK1200 furnace with ultra-high-purity nitrogen gas to prevent sample oxidation during heating. XRD peaks associated with Ti nitrides were not observed, so it is believed that nitriding did not occur. The room temperature (RT) XRD scan of the β-homogenized condition exhibited only the (101)β, (200)β, and (211)β peaks, confirming the fully β-phase microstructure. The heating rate to 400 °C was 30 °C/min. Data were collected in situ over a 2θ range of 25°–75° every 0.5 h during the 12 h aging period with a scan rate of 2°/min.
For each alloy, Rietveld analysis was performed on the HTXRD data to determine the lattice parameters of the β, α, and ω phases after each 0.5 h time step. The Rietveld refinement and lattice parameter calculations were accomplished for TCF, TCA, and TCFA using the Topas software package 5.0 (Bruker-AXS). The Rietveld lattice parameter refinement for TC was accomplished using software suite PDXL version 2 [38], and the weighted-profile residual (Rwp) for each Rietveld analysis was between 4.87% and 7.85%. For TC, only the lattice parameters were refined. For TCF, TCA, and TCFA, both the lattice parameters and the profiles were refined. Table 1 contains the crystallographic information of the phases considered for the Rietveld refinement.

3. Results

3.1. Microstructural Evolution Evaluated by In Situ High-Temperature XRD (HTXRD)

The in situ HTXRD data revealed that phase transformations occurred during the first 0.5 h at 400 °C. β-, ω-, and α-phase peaks were observed in the 0.5 h XRD profiles of TC and TCF, see Figure 2a,b. Only β- and α-phase peaks were observed in the 0.5 h XRD profiles of TCA and TCFA, see Figure 2c,d. The lack of ω-phase peaks in TCA and TCFA suggest that the Al addition promoted the formation of the α phase preferentially over the ω phase.
The HTXRD data, taken every 0.5 h during the 400 °C aging, revealed the evolution of the phase peaks in each alloy with increased aging time. Heatmap-style waterfall plots were used to reveal the peak evolutions as a function of both 2θ diffraction angle and aging time. In the two-phase TCA and TCFA, the β-phase peaks appeared to shift to larger 2θ values with increased aging time, while the α-phase peaks 2θ values remained relatively with increased aging time, see Figure 3. The β-phase peak shift were more pronounced for the higher 2θ values and for the lower aging times. No ω-phase peaks were observed in any of the TCA or TCFA profiles.
The peak overlap in the TC and TCF data made it difficult to determine the evolution of each peak with aging time. Rietveld analysis was performed to deconvolute the contributions from the β, ω, and α phases for each XRD profile. Figure 4 shows the deconvolution of the TC XRD profile after 3 h of aging at 400 °C. This deconvolution is representative of the deconvolution for each of the alloys.
Through the deconvolution of the peaks, it was possible to determine the evolution of each phase’s peaks with increased aging time in the TC and TCF data, see Figure 5a,b. Plotting the deconvoluted profiles show that the TC and TCF β-phase peaks also appear to shift to higher angles with increased aging times. The α-phase peaks remained relatively constant with increased aging time similar to that for TCA and TCFA. The ω-phase peaks also remained relatively constant throughout the 12 h aging for TC. The ω-phase peaks were not clearly visible after 7.5 h at 400 °C for TCF, suggesting that the Fe addition in TCF limits the stability of the metastable ω phase compared that for TC. Although it is possible that the ω-phase remained in small amounts in TCF past 7.5 h of aging, during the deconvolution of the TCF 8–12 h profiles, the Rietveld analysis used the ω-phase profile as a smoothing function to decrease the residual between the calculated and experimental profiles, which led to unrealistic peak locations for all three phases. Thus, the ω phase was removed from the iterative Rietveld analysis of the TCF profiles for aging times from 8 to 12 h.
The evolution of the phase peaks in each alloy suggests that aβ decreased with increasing aging time, while the α- and ω-phase lattice parameters remained approximately constant. Lattice parameters were determined as part of the Rietveld analysis, and peak overlap and peak broadness made certain profiles difficult to refine. The TCA profiles were particularly difficult to refine during the later aging times due to peak broadness. For TC and TCF the Rietveld analysis tended to reverse the ω- and α-phase peak locations due to the overlap between the β, ω, and α peaks. This reversal led to calculated lattice parameters and phase profiles that were unrealistic. When these inaccuracies occurred, the Rietveld analysis was performed again, holding the parameters corresponding to peak shape and location constant, to prevent the reversals. This generally followed the pattern of holding the ω-phase and α-phase parameters constant to refine the β phase, then holding the ω-phase and β-phase parameters constant to refine the α phase, and finally holding the β-phase and α-phase parameters constant to refine the ω phase. This process was repeated as necessary to complete the refinement. The phase volume fractions were also calculated as part of this Rietveld analysis, and they can be found in Ballor et al. [42].
The aβ values of each alloy were found to decrease with increasing aging time; see Figure 6. The aβ values of the Fe-containing and the Fe-free alloys decreased at different rates, i.e., the decrease in aβ of TC and TCA were comparable and the decrease in aβ of TCF and TCFA were comparable. The Fe addition resulted in an increased aβ for all aging times. Due somewhat to the difficulty in refining certain profiles, some data scatter exists in the calculated lattice parameters of each phase.
The ‘a’ (aα) and ‘c’ (cα) lattice parameters and the corresponding c/a ratios of the α phase were plotted as a function of aging time for each alloy, see Figure 7. The aα for TC and TCA were similar, where the decrease followed similar trends throughout the aging, and the aα for TCF and TCFA were similar for shorter aging times (it is noted that more scatter exists in the TCF data for longer aging times). The cα for each alloy were similar (taking into account the data scatter). The c/a ratios for TCF and TCFA approached approximately 1.582 and 1.580, respectively, after 12 h of aging, see Figure 7. The c/a ratio for TC approached approximately 1.588. The scatter in the TCA cα values translated into scatter in the TCA c/a ratios, making it less obvious which c/a ratio value TCA approached, but the general trend of the TCA c/a ratios appeared to be similar to that for TC. It is noted that the c/a ratio of the α phase in pure Ti is 1.587, and this is indicated with a dashed line in Figure 7 [43,44].
The ‘a’ (aω) and ‘c’ (cω) lattice parameters and the c/a ratios of the ω phase are plotted as a function of aging time for TC and TCF in Figure 8. The aω of TC decreased and the cω of TC increased with increasing aging time, which resulted in the c/a ratio of TC increasing from approximately 0.613 to approximately 0.622. The aω, cω, and c/a ratios of TCF remained relatively constant throughout the aging period, with the c/a ratio of TCF increasing slightly from approximately 0.612 to 0.613 during the 7.5 h that the ω phase was present. The lattice parameter values for TC and TF are within the range of lattice parameters reported for β-Ti and Zr alloys [45,46,47,48,49].

3.2. Phase Composition Evolution Evaluated by Atom Probe Tomography

The precipitates in each alloy were poor in the β-phase stabilizing element Cr. Therefore Cr isosurfaces were used to characterize the precipitates. Reconstructions of the TC, TCF, TCA, and TCFA samples after 0.75 h aging are shown along with their corresponding proximity histograms in Figure 9a–d. The precipitates in TCA and TCFA were considered to be the α phase since the XRD results indicated that only the β and α phases were present in those alloys. SEM and TEM images of TCA and TCFA confirmed the lenticular morphology of the α phase precipitates in the β matrix [42]. The precipitates in the APT samples of TC and TCF were identified as either α or ω based on their morphology, where the lenticular or plate-shaped precipitates were considered to be the α phase, and the more equiaxed precipitates, resembling those found in Devaraj et al. [50], were considered to be the ω phase.
The precipitates in TC and TCF consisted almost entirely of Ti after 0.75 h of aging, as the β-stabilizers Cr and Fe diffused from the precipitates into the surrounding β matrix. The α-phase precipitates in TCA and TCFA were also β-stabilizer free after 0.75 h aging, but contained higher concentrations of the α-stabilizer Al than the surrounding β matrix and lower Ti concentrations (by approximately 10%) in the α phase compared to the precipitates in TC and TCF. The datasets in Figure 9 were representative of the datasets collected for the alloys after each aging time, and the phase compositions for each aging time were calculated from the proximity histograms to determine the evolution of phase composition as a function of aging time.
The β phase decreased in Ti content and increased in Cr content for each alloy, see Figure 10a. In contrast, the compositions of the α and ω phases remained relatively constant with increasing aging time, see Figure 10b. The changes in the β-phase composition occurred because the β-phase stabilizers, Cr and Fe, diffused from the α and ω phases into the β phase during their nucleation and growth, while the α-phase stabilizer, Al, diffused into the α phase. In TCF, less Cr diffused into the β phase than in TC, achieving 15.5 at.% compared to the 27 at.% achieved in TC after 12 h of aging. It is noted that higher concentrations of the impurity element O were measured in the α phase than in the β phase for all samples. O was present in the α phase in average concentrations of 1.2 ± 0.6%, while O was present in the β phase in average concentrations of 0.2 ± 0.1% (the averages and standard deviations were taken from 18 samples). Because O is an impurity element, it was not included in the phase composition analysis as the starting O content of each sample, before the phase transformations occurred, was unknown.
The ratios of the concentration of the solute atoms Cr, Fe, and Al, in the ω and/or α phases to the concentration of these solute atoms in the β phase were calculated, see Figure 11. Most of the Cr ratios ranged between 0.01 and 0.03. TC and TCF exhibited slightly more variation in the Cr ratios than that for TCA and TCFA. The Fe ratios in TCF and TCFA were approximately 0.1. The Al ratios in TCA and TCFA were approximately 1.5 throughout the aging treatment. These ratios can be compared to the partition coefficients during solidification described by Porter and Easterling, as they represent the ratios of solute atoms in the transforming phase compared to the parent phase [51]. However, some key differences should be noted. The partition coefficient described by Porter and Easterling compares solute compositions between the solidifying phase and the liquid phase, not between solid–solid phase transformations. Also, the partition coefficient is calculated from the equilibrium phase diagram, and the ω phase does not appear on the equilibrium phase diagram of Ti-Cr alloys, making it difficult to directly compare the ratios for the ω-containing TC and TCF.

4. Discussion

4.1. The β Phase

The aβ was expected to decrease linearly as the Cr and Fe concentrations in the β phase increased because Cr and Fe have smaller atomic radii as Ti, see Table 2. Linear relationships were exhibited between aβ and Mo-Eq, aβ and average atomic radius, and aβ and average Md, see Figure 12. The changes in aβ during the phase transformations were consistent with data from fully β-phase Ti alloys. The average atomic radius and average Md decreased as Mo-Eq increased, which was expected as the Md and atomic radii values of each alloying element are smaller than those of Ti, see Table 2.
While clear relationships between Mo-Eq, average Md, and average atomic radius exist for the Ti-Mo, Ti-Fe, Ti-Nb, and Ti-Cr-Nb alloys shown in Figure 1, more universal relationships appear to exist between each of those parameters and aβ. The agreement between the literature and the current work suggest that all β-Ti alloys should follow the relationships represented in Figure 12 during the phase transformations. These relationships are important as they could affect β-phase deformation mechanisms. Md, in particular, is useful for determining whether alloys will deform via slip or twinning [53], and a changing Md could indicate a changing deformation mechanism.
The composition changes during the 400 °C aging could also affect the subsequent phase transformations. For example, a higher β-stabilizer concentration in the β matrix could favor the nucleation of new precipitates at phase boundaries over the growth of existing precipitates, which could assist in promoting the formation of nanoscale α phase at the ω/β boundary during the ω-assisted α-phase transformation. The decreasing aβ could also introduce strain at the α/β and/or ω/β boundaries, which could affect phase nucleation, growth, and morphology. The effect of aβ on the α and ω phases is discussed in detail below.

4.2. The α Phase

As the α phase nucleated and grew in each alloy, its composition remained relatively constant (see Figure 10b), but the α-phase lattice parameters showed some change (see Figure 7). Thus, the relationships between lattice parameters (aα and cα and c/a ratio) were explored. TCFA showed the only statistically significant trends (R2 values above 0.99), with aα, cα, and the c/a ratio increasing as the Cr and Fe decreased, and aα, cα, and the c/a ratio decreasing as the Al concentration increased. The c/a ratios are presented in Figure 13 and the scatter is representative of the scatter in both aα and cα. TC, TCF, and TCA did not exhibit any statistically-significant relationships (all R2 values were below 0.95). This suggests that composition does not directly influence the α-phase lattice parameters through atomic radius differences, but the composition could be facilitating α-phase lattice parameter change by changing the aβ and inducing strain at the α/β boundary. To further explore the effects of composition, the relationships between aβ and the α-phase lattice parameters were explored.
Both aα and cα decreased as aβ decreased, see Figure 14. The c/a ratios of TC and TCA both approached the c/a ratio of the α-phase in pure Ti (1.587 [43]). The c/a ratios of TCF and TCFA did not approach 1.587, instead they approached values of ~1.582 and ~1.580, respectively. This supports the idea that composition influences the α-phase lattice parameters through the changing aβ, as TC and TCA had similar aβ evolutions and TCF and TCFA had similar aβ evolutions.
This relationship is significant as the misfit between the α and β phases and the coherency strains along the ( 1 ¯ 100)α and ( 1 ¯ 1 2 ¯ )β planes, where the misfit between the α and β phases is minimized, could have been affected [54]. If the changing aβ and c/a ratio affect the misfit between the two phases, the ledges that transition the crystal from the α to the β phase could be affected. In particular, the ledges could become a more favorable location for the nucleation or growth of the α phase than the β-stabilizer-rich β-matrix, which could explain the clusters of the α phase observed in the TCFA APT sample shown in Figure 9d and in the SEM micrographs in Ballor et al. [42]. Further investigation into the misfit and coherency strain between the α and β phases as aβ and the α-phase c/a ratio change during the β-to-α transformation would be valuable.

4.3. The ω Phase

The ω-phase lattice parameters of TC and TCF were compared to Ti and Cr concentrations, and no clear relationships were found between these concentrations and the aω, cω, or the c/a ratios. The c/a ratios are presented in Figure 15 and the scatter is representative of the scatter in aω and cω.
Like that for the α phase, the ω-phase parameters changed as the β-phase β-stabilizer content increased and the aβ decreased. In TC, cω increased and aω decreased as aβ decreased. In TCF, both aω and cω decreased as aβ decreased. These changes resulted in an increased ω-phase c/a ratio for TC and an approximately constant c/a ratio for TCF, see Figure 16. This agrees with the observation that TC exhibited a greater change in the β-phase Cr concentration than that for TCF, which resulted in a greater change in the aβ for TC compared with that for TCF.
This relationship is significant because the ω phase is known to change its morphology from ellipsoidal to cuboidal as it grows. The morphology of the ω phase is affected by the difference between the radii of the alloying elements and Ti [25,50], so that the diffusion of the β-stabilizers with increased aging time would drive the ω-phase morphology to be more cuboidal. These results suggest that the morphology of the ω phase in TC changed from more ellipsoidal to more cuboidal during the aging process, while a change in the ω phase morphology in TCF may not have occurred. More broadly, these results suggest that, along with aging time, the speed at which β-stabilizers diffuse in a β-Ti alloy could affect the ω-phase morphology during aging. This should be the focus of future study, as ω-phase morphology, ω/β boundary interfacial energy, and coherency strains at the ω/β interface all affect the ω-assisted α-phase transformation [26,27,55].

5. Summary and Conclusions

Fe- and Al-modified β-Ti alloys, each containing nominally 11 at.% Cr, underwent a 400 °C aging treatment to induce the β-to-ω and β-to-α phase transformations. The ω and α phases precipitated in TC and TCF during aging, while the 5.3 at.% Al addition in TCA and TCFA inhibited ω-phase formation. During the phase transformations, the β-phase stabilizers Cr and Fe diffused from the α and ω phases into the β matrix, leaving the α and ω phases nearly β-phase stabilizer free. Ti diffused from the β-matrix into the α and ω phases, and the α-phase stabilizer Al diffused into the α phase. The β phase retained some Al while being enriched with Cr and Fe. The β-phase lattice parameter decreased with increased Cr and Fe content during the phase transformations. The relationship between lattice parameter, atomic radius, Md, and Mo-Eq was explored. As Mo-Eq increased, the β-phase lattice parameter decreased with decreasing atomic radius and Md.
The α-phase lattice parameters exhibited a relationship with the β-phase lattice parameter and thus the β-phase composition. The c/a ratios of TC and TCA approached 1.587, and the c/a ratios of TCF and TCFA approached ~1.582 and ~1.580, respectively, as the β-phase lattice parameter decreased. Similarly, the ω-phase lattice parameters exhibited a relationship with the β-phase lattice parameter and composition. TC exhibited larger composition changes, larger β-phase lattice parameter changes, and larger ω-phase lattice parameter changes than TCF. The ω-phase c/a ratio change suggests a change in ω-phase morphology during aging in TC. The smaller β-phase composition changes in TCF and an essentially constant ω-phase c/a ratio suggests no ω-phase morphology change.
The relationships between composition, β-phase lattice parameter, and the c/a ratios of the α and ω phases has implications for interfacial strain at the β/α or β/ω boundaries and the ω-assisted α-phase transformation. This work has shown that combining APT with HTXRD is a powerful means to systematically and accurately study compositional effects on lattice parameters. Overall, this work has provided important details of the interdependence of composition and the β-, α-, and ω-phase lattice parameters.

Author Contributions

Conceptualization, J.B. and C.J.B.; methodology, J.B.; formal analysis, J.B., J.D.P. and S.M.; investigation, J.B., J.D.P. and S.M.; resources, C.J.B., J.D.P., A.D. and S.M.; data curation, J.B., J.D.P. and S.M.; writing—original draft preparation, J.B.; writing—review and editing, J.B., C.J.B., A.D., J.D.P. and S.M.; visualization, J.B.; supervision, A.D. and C.J.B.; project administration, J.B. and C.J.B.; funding acquisition, C.J.B., S.M. and A.D. All authors have read and agreed to the published version of the manuscript.

Funding

This material is based in part on work supported by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists, Office of Science Graduate Student Research (SCGSR) program. The SCGSR program is administered by the Oak Ridge Institute for Science and Education for the DOE under contract number DE-SC0014664. The funding for the alloy processing, metallographic preparation, and HTXRD was supported by National Science Foundation Division of Material Research (grant No. DMR1607942) through the Metals and Metallic Nanostructures (MMN) program. A portion of the funding for this research was supported by the U.S. Department of Energy, Office of Basic Energy Science through grant No. DE-SC0001525. A.D. would like to acknowledge the funding support from the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division as a part of the Early Career Research Program FWP 76052. S.M. acknowledges support via the Inamori Professorship which supported the in situ XRD measurements and analysis.

Data Availability Statement

The data presented in this study are available on request from the corresponding author. The data are subject to an approval for release process.

Acknowledgments

The authors would like to thank Swavek Zdzieszynski of Alfred University for assistance in performing the HTXRD experiments and James Burns of Oak Ridge National Laboratory for assistance in performing APT sample preparation and running the APT experiments. The APT research was supported by the Center for Nanophase Materials Sciences (CNMS), which is a US Department of Energy, Office of Science User Facility at Oak Ridge National Laboratory and the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and environmental Research located at Pacific Northwest National Laboratory. The authors acknowledge Masahiko Ikeda of Kansai University for donating the materials studied and useful insights, Elizabeth Kautz of North Carolina State University for helpful discussions about the APT data, and Alexandra Zevalkink of Michigan State University for helpful discussions about the Rietveld analysis.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. The relationship between Mo-Eq, average atomic radius, and average electron d-shell energy (Md) for the β-Ti alloys Ti-Cr-Nb [4], Ti-Fe [5], Ti-Mo [6], and Ti-Nb [7].
Figure 1. The relationship between Mo-Eq, average atomic radius, and average electron d-shell energy (Md) for the β-Ti alloys Ti-Cr-Nb [4], Ti-Fe [5], Ti-Mo [6], and Ti-Nb [7].
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Figure 2. HTXRD intensity versus 2θ plots after 0.5 h at 400 °C showing the β-, α-, and ω-phase peaks for (a) TC and (b) TCF, and the β- and α-phase peaks for (c) TCA and (d) TCFA.
Figure 2. HTXRD intensity versus 2θ plots after 0.5 h at 400 °C showing the β-, α-, and ω-phase peaks for (a) TC and (b) TCF, and the β- and α-phase peaks for (c) TCA and (d) TCFA.
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Figure 3. The experimental profiles for (a) TCA and (b) TCFA presented as a function of aging time, where darker values indicate higher intensities. Each peak is labeled with its corresponding phase along the bottom horizontal axis.
Figure 3. The experimental profiles for (a) TCA and (b) TCFA presented as a function of aging time, where darker values indicate higher intensities. Each peak is labeled with its corresponding phase along the bottom horizontal axis.
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Figure 4. The experimental XRD profile of TC at 3 h at 400 °C containing the Rietveld-calculated profile (blue) and the individual contributions from the β (green), ω (orange), and α (pink) phases. The Rietveld-calculated profile is the sum of the individual contributions from each phase, and the residual (red) shows the difference between the experimental and the calculated profiles.
Figure 4. The experimental XRD profile of TC at 3 h at 400 °C containing the Rietveld-calculated profile (blue) and the individual contributions from the β (green), ω (orange), and α (pink) phases. The Rietveld-calculated profile is the sum of the individual contributions from each phase, and the residual (red) shows the difference between the experimental and the calculated profiles.
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Figure 5. The experimental profiles (top) and the Rietveld deconvolutions of the β (green), α (pink), and ω (orange) phases during the 400 °C HTXRD experiment for (a) TC and (b) TCF, where darker values indicate higher intensities. The ω-phase peaks, which were not visible for TCF after 7.5 h at 400 °C, were removed from the Rietveld analysis after 7.5 h. This Rietveld deconvolution has previously been presented in Ballor et al. [42].
Figure 5. The experimental profiles (top) and the Rietveld deconvolutions of the β (green), α (pink), and ω (orange) phases during the 400 °C HTXRD experiment for (a) TC and (b) TCF, where darker values indicate higher intensities. The ω-phase peaks, which were not visible for TCF after 7.5 h at 400 °C, were removed from the Rietveld analysis after 7.5 h. This Rietveld deconvolution has previously been presented in Ballor et al. [42].
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Figure 6. The aβ evolution as a function of the square root of aging time.
Figure 6. The aβ evolution as a function of the square root of aging time.
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Figure 7. The α-phase lattice parameter and c/a ratio evolution as a function of the square root of aging time for each alloy. The c/a ratio for pure Ti is marked with a dashed line [43,44].
Figure 7. The α-phase lattice parameter and c/a ratio evolution as a function of the square root of aging time for each alloy. The c/a ratio for pure Ti is marked with a dashed line [43,44].
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Figure 8. The ω-phase lattice parameter and c/a ratio evolution as a function of the square root of aging time for TC and TCF.
Figure 8. The ω-phase lattice parameter and c/a ratio evolution as a function of the square root of aging time for TC and TCF.
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Figure 9. APT tip reconstruction and the corresponding proximity histogram for (a) TC, (b) TCF, (c) TCA and (d) TCFA. All samples were aged at 400 °C for 0.75 h. The vertical line shows the 8% Cr isoconcentration surface, and the dashed lines show the APT-measured compositions of the β-homogenized material reported by Ballor et al. [35].
Figure 9. APT tip reconstruction and the corresponding proximity histogram for (a) TC, (b) TCF, (c) TCA and (d) TCFA. All samples were aged at 400 °C for 0.75 h. The vertical line shows the 8% Cr isoconcentration surface, and the dashed lines show the APT-measured compositions of the β-homogenized material reported by Ballor et al. [35].
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Figure 10. The APT measured Ti, Cr, Fe, and Al concentrations of the (a) β phase and (b) α and ω phases as a function of the square root of aging time for each alloy. Error bars indicate ±1 standard deviation. For the cases when error bars were lacking, only one measurement was taken.
Figure 10. The APT measured Ti, Cr, Fe, and Al concentrations of the (a) β phase and (b) α and ω phases as a function of the square root of aging time for each alloy. Error bars indicate ±1 standard deviation. For the cases when error bars were lacking, only one measurement was taken.
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Figure 11. The ratios of the concentration of solute elements (a) Cr, (b) Fe, and (c) Al in the α and/or ω phases to the concentration of these solute elements in the β phase for each alloy. The ratios are shown as a function of the square root of aging time.
Figure 11. The ratios of the concentration of solute elements (a) Cr, (b) Fe, and (c) Al in the α and/or ω phases to the concentration of these solute elements in the β phase for each alloy. The ratios are shown as a function of the square root of aging time.
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Figure 12. The β-phase lattice parameters (aβ values) as a function of Mo-Eq (top), average atomic radius (middle), and average Md (bottom). Data were taken from this work and work involving Ti-Cr-Nb alloys [4], Ti-Fe alloys [5], Ti-Mo alloys [6], Ti-Ta alloys [7], and Ti-Nb alloys [7].
Figure 12. The β-phase lattice parameters (aβ values) as a function of Mo-Eq (top), average atomic radius (middle), and average Md (bottom). Data were taken from this work and work involving Ti-Cr-Nb alloys [4], Ti-Fe alloys [5], Ti-Mo alloys [6], Ti-Ta alloys [7], and Ti-Nb alloys [7].
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Figure 13. The α-phase c/a ratios of all alloys as a function of composition of (a) Ti, (b) Cr, (c) Fe, or (d) Al for each alloy.
Figure 13. The α-phase c/a ratios of all alloys as a function of composition of (a) Ti, (b) Cr, (c) Fe, or (d) Al for each alloy.
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Figure 14. The α-phase lattice parameters c (top), a (middle), and c/a ratios (bottom) of TC, TCF, TCA, and TCFA as a function of aβ for each alloy. The dashed line corresponds to the c/a ratio of the α-phase in pure Ti (1.587 [43]).
Figure 14. The α-phase lattice parameters c (top), a (middle), and c/a ratios (bottom) of TC, TCF, TCA, and TCFA as a function of aβ for each alloy. The dashed line corresponds to the c/a ratio of the α-phase in pure Ti (1.587 [43]).
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Figure 15. The ω-phase c/a ratios of TC and TCF as a function of composition of (a) Ti and (b) Cr for TC and TCF.
Figure 15. The ω-phase c/a ratios of TC and TCF as a function of composition of (a) Ti and (b) Cr for TC and TCF.
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Figure 16. The ω-phase lattice parameters c (top), a (middle), and c/a ratios (bottom) for TC and TCF as a function of aβ.
Figure 16. The ω-phase lattice parameters c (top), a (middle), and c/a ratios (bottom) for TC and TCF as a function of aβ.
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Table 1. The crystallographic data of the β, α, and ω phases used for the Rietveld refinement.
Table 1. The crystallographic data of the β, α, and ω phases used for the Rietveld refinement.
Phasea (Å)b (Å)c (Å)StructureSpace GroupAtomic Positions (x,y,z)Reference
β3.21--CubicIm 3 ¯ m(229)(0,0,0) (1/2,1/2,1/2)[39]
α2.9508-4.6855Hexagonal close-packedP63/mmc(194)(0,0,0) (1/3,2/3,1/2)[40]
ω4.6-2.82HexagonalP6/mmm(191)(0,0,0) (1/3,2/3,1/2) (2/3,1/3,1/2)[41]
Table 2. The atomic radii and electron d-shell energy (Md) for Ti, Cr, Fe, and Al in bcc Ti. The atomic radii are from Callister [52] and the Md values are from Morinaga et al. [53].
Table 2. The atomic radii and electron d-shell energy (Md) for Ti, Cr, Fe, and Al in bcc Ti. The atomic radii are from Callister [52] and the Md values are from Morinaga et al. [53].
ElementAtomic Radius (Å)Md (eV)
Ti1.452.447
Cr1.251.478
Fe1.240.969
Al1.432.200
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Ballor, J.; Poplawsky, J.D.; Devaraj, A.; Misture, S.; Boehlert, C.J. Lattice Parameter Evolution during the β-to-α and β-to-ω Transformations of Iron- and Aluminum-Modified Ti-11Cr(at.%). Crystals 2024, 14, 145. https://doi.org/10.3390/cryst14020145

AMA Style

Ballor J, Poplawsky JD, Devaraj A, Misture S, Boehlert CJ. Lattice Parameter Evolution during the β-to-α and β-to-ω Transformations of Iron- and Aluminum-Modified Ti-11Cr(at.%). Crystals. 2024; 14(2):145. https://doi.org/10.3390/cryst14020145

Chicago/Turabian Style

Ballor, JoAnn, Jonathan D. Poplawsky, Arun Devaraj, Scott Misture, and Carl J. Boehlert. 2024. "Lattice Parameter Evolution during the β-to-α and β-to-ω Transformations of Iron- and Aluminum-Modified Ti-11Cr(at.%)" Crystals 14, no. 2: 145. https://doi.org/10.3390/cryst14020145

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