Experimental Phase Equilibria and Isopleth Section of 8Nb-TiAl Alloys

: The 8Nb isopleth section of a Ti-Al-Nb system is experimentally determined based on thermal analysis and thermodynamic calculation methods to obtain the phase transformation and equilibrium relations required for material design and fabrication. The phase transus and relations for the 8Nb-TiAl system show some deviations from the calculated thermodynamic results. The ordered β o phase transforms from the disordered β / α phases at 1200–1400 ◦ C over a large Al concentration range, and this transformation is considered to be an intermediate type between the ﬁrst- and second-order phase transitions. Moreover, the β o phases are retained at the ambient temperature in the 8Nb-TiAl microstructures. The ω o phase transforms from the highly ordered β o phase, rather than from α 2 or β o with a low degree of atom ordering B2 (LOB2) structure, with Al concentration of 32–43 at% at approximately 850 ◦ C. From the experimental detection, the transition of the ω o phase from the β o phase is considered to be a further ordering process.


Introduction
In the past decade, TiAl-based alloys have been considered promising candidates for high-temperature materials in aerospace and automotive applications because of their excellent properties of low density, high specific yield strength and stiffness, and favorable oxidation resistance and creep properties up to high temperatures [1][2][3]. TiAl alloys containing high amounts of Nb, based on the γ-TiAl and α 2 -Ti 3 Al intermetallic, exhibit excellent high-temperature strength and oxidation resistance [4] and have attracted significant attention [3,5]. Advanced materials based on the Ti-Al-Nb alloys can be used at temperatures above 800 • C [6]. As reported by Appel et al. [3] and Erdely et al. [7], both the hot-workability and the ductility can be effectively promoted by the β phase [5,8], which provides a sufficient number of independent slip systems to act as a ductile constituent in the final microstructure [9,10]. Moreover, the solid-state transformation pathway and the microstructure of TiAl-based alloys can be manipulated through β/β o phases [3,7,11]. According to reports by Cheng et al. [12], Kobayashi et al. [13], and Takeyama et al. [14], a multitude of solid-state transformations and resulting microstructural morphologies can be achieved by stabilizing the β phase [3].
The phase diagram and phase equilibria of the Ti-Al-Nb system play important roles in material design and fabrication, especially in the manipulation of the solid-state transformation pathway and microstructure [5,15,16]. Phase transition behaviors can be precisely detected by some thermal detection methods, such as differential scanning calorimetry In this work, the 8Nb isopleth section, as well as the phase equilibria, of the Ti-Al-Nb system is experimentally determined by DSC, scanning electron microscopy (SEM), and X-ray diffraction (XRD). The samples were annealed sufficiently in high vacuum and then slowly cooled to achieve the equilibrium state as far as possible. However, considering the difficulty of achieving thermodynamic equilibrium in practice, the experimental phase equilibria may have some deviations from thermodynamic equilibria. This work aims to establish the experimental isopleth and phase equilibria of the 8Nb-Ti-Al system, which have the treating conditions closer to the actual production, to obtain the phase transformation and equilibrium relationships required for material design and fabrication.

Materials and Methods
Eighteen ternary 8Nb-TiAl alloy buttons were prepared by non-consumable arc melting (with a tungsten electrode) from high-purity initial components (Ti, Al, Nb: 99.99 wt%) using a water-cooled copper hearth in an ultra-high-purity argon atmosphere. Only those samples with less than 1.0 wt% weight losses were adopted for further analysis. Each button (with a mass of approximately 30 g) was melted, turned over, and re-melted five times to ensure homogeneity. The diffusion annealing was performed in high vacuum at 1400 • C for 20 h to equilibrate and coarsen the phase. The samples were then slowly cooled to 50 • C in the furnace (cooling rate:~1.0 • C/min). Thermodynamic equilibrium calculations were performed by the Calculation Phase Diagrams (CALPHAD) method using the commercial software Pandat ® (v2017.1, Compu Them, Middleton, WI USA) [48], following the thermodynamic description from Witusiewicz's investigation [25]. The phase structures were detected by XRD (D8 Advance, Bruker, Bremen, Germany) using powder samples, prepared in a metallic miller, and operated at 40 kV and 40 mA with Cu Kα. For the morphology analysis, sample sizes of 8 mm × 8 mm × 8 mm were cut from the centers of the buttons with an electron discharge cutting machine (New Sparkie, Shaoxing, China), and the samples were then polished following standard mechanical polishing procedures. The microstructures of the annealed samples were obtained by SEM in back-scattered electron (BSE) mode (JSM-6380, JEOL, Musashino, Japan), operated at 20 kV and at a working distance of 10 mm. The compositions in the samples were analyzed by the optical emission spectrometer (OES, Q4 TASMAN 130, Bruker, Bremen, Germany).
The solid-state transformation temperatures were determined by DSC (404C, NET-ZSCH, Selb, Germany) with an Al 2 O 3 crucible. Discs of 4 mm diameter and 3 mm thickness (150-180 mg), which produced sufficient signals in the argon atmosphere, were machined from the centers of the buttons. Temperature calibrations for the equipment were conducted by melting high-purity Cu, Al, Ag, and Ni at scan rates of 5 and 10 • C/min to determine the correction equation. In this work, the heating rate for all test samples (excluding the calibration samples) was 10 • C/min, using a covered Al 2 O 3 crucible with a maximum temperature of 1450 • C, and within a dynamic Ar atmosphere with a flow rate of 30 mL/min. To account for the influence of the containers, the DSC signals of the empty crucibles were subtracted from the detected traces. As a standard comparison sample, thermal data were acquired from sapphire, using the same parameters as those applied to the 8Nb-TiAl samples, to determine the specific heat capacity (C p ) by Equation (1).
In this work, to improve the accuracy and uniformity of the data acquisition process, a new method was developed for determining and calibrating the onset transformation temperatures for the different cooling/heating rates in DSC detection. The first derivatives of the DSC traces (DDSC) were employed to determine the transformation temperatures. The temperature difference, ∆T = 38 • C, was adopted to calibrate the dynamic transformation temperatures. Full details are given in Supplementary Materials.

Phase Evolution
The chemical compositions of the 8Nb-TiAl alloys (S01-S18) determined by OES, with the nominal compositions, are presented in Table 2. The specific reflections of certain phases-α 2 (202), γ(002)/(200), O(310), and β o (200)/ω o (202)-were selected to describe the phase evolution, as shown in Figure 1. The reflection in S01-S12 at approximately 38.5 • was much stronger than the reflection at 40.8 • , showing the overlap of the diffraction peaks with the β o phase. For this β o phase, the (110)/(220) reflections of the disordered β structure were preserved, whereas the (200)/(211) reflections were suppressed, indicating a LOB2 structure, as shown in Figure 1b,c. However, as shown by the XRD pattern of Sample S06-S12, the reflection at approximately 39.3 • was considered to indicate overlapping of the β o and ω o phases, as shown in Figure 1c. The β o phase was fully depressed in S14-S18, as shown in Figure 1d. Check out the Supplementary Materials for more details. shown in Figure 2c. The presence of the O phase could be identified by the (310) reflection in the Al-lean S01-S05 samples, as shown in Figure 2b, and the ωo and βo phases were identified in Samples S06-S12, as shown in Figures 1b and 2d. The fraction of βo+ωo phases increased dramatically in Samples S06-S09, then decreased in S10-S13. In the Al-rich S13-S18 samples, only two phases formed: α2 and γ.   The evolution of the fraction of each phase in the samples can be roughly evaluated by the reflection peak height, where unstacked reflections should be selected first.  Figure 1. The fraction of the α 2 phase increased with increased Al content in Samples S01-S10, then decreased with continuing Al increases in Samples S11-S18, as shown in Figure 2a. The fraction of γ phase was small in Samples S01-S10, and then the γ phase fraction increased continuously as the Al content increased in Samples S11-S18, as shown in Figure 2c. The presence of the O phase could be identified by the (310) reflection in the Al-lean S01-S05 samples, as shown in Figure 2b, and the ω o and β o phases were identified in Samples S06-S12, as shown in Figures 1b and 2d. The fraction of β o +ω o phases increased dramatically in Samples S06-S09, then decreased in S10-S13. In the Al-rich S13-S18 samples, only two phases formed: α 2 and γ.

Morphology
As shown in Figure 3a,b, the morphologies of Samples S01-S05 (18.4-29.4 at% Al) comprised coarse α2 laths and O phase (dark regions); flaky α2 particles in the low order βo matrix; interwoven βo structures (bright regions). The βo phase mainly appeared along the α2 grain boundaries and only a small volume fraction of the βo phase was present within the α2 laths. As Al increased in Samples S01-S05, the fraction of α2 increased while the O and βo phases decreased, as observed by the morphology analysis. The presence of ωo in Samples S06-S12 was identified by XRD, as shown in Figure 1, whereas this phase was not observed in the microstructure, as shown in Figures 3 and 4. For Samples S06-S09, the morphology mainly consisted of the coarse α2 laths and interwoven βo+ωo structures, as shown in Figure 3c,d. The βo phase was mainly located along colony boundaries and only a small volume fraction was present within the colonies [5]. The morphologies of Samples S10-S12 consisted of lamellar colonies, (α2+γ)L, and interwoven βo+ωo structures, as shown in Figure 3e,f. Isolated γ equiaxed grains were found on the boundaries of α2 and βo, as shown in Figures 3 and 4. The morphologies of Samples S13-S17 were fully lamellar, as shown in Figure 4a-d. The size of the lamellar colonies and the interlamellar spacing in these samples increased greatly. Figure 4c,d show that both the proeutectoid α2 and the γ were largely situated along boundaries, at the triple lines of (α2+γ)L, and around the βo grains. However, the presence of βo and γ was extremely restrained as the Al content increased to 44.6 at.%, as shown in Figure 4c

Morphology
As shown in Figure 3a,b, the morphologies of Samples S01-S05 (18.4-29.4 at% Al) comprised coarse α 2 laths and O phase (dark regions); flaky α 2 particles in the low order β o matrix; interwoven β o structures (bright regions). The β o phase mainly appeared along the α 2 grain boundaries and only a small volume fraction of the β o phase was present within the α 2 laths. As Al increased in Samples S01-S05, the fraction of α 2 increased while the O and β o phases decreased, as observed by the morphology analysis. The presence of ω o in Samples S06-S12 was identified by XRD, as shown in Figure 1, whereas this phase was not observed in the microstructure, as shown in Figures 3 and 4. For Samples S06-S09, the morphology mainly consisted of the coarse α 2 laths and interwoven β o +ω o structures, as shown in Figure 3c,d. The β o phase was mainly located along colony boundaries and only a small volume fraction was present within the colonies [5]. The morphologies of Samples S10-S12 consisted of lamellar colonies, (α 2 +γ) L , and interwoven β o +ω o structures, as shown in Figure 3e,f. Isolated γ equiaxed grains were found on the boundaries of α 2 and β o , as shown in Figures 3 and 4. The morphologies of Samples S13-S17 were fully lamellar, as shown in Figure 4a-d. The size of the lamellar colonies and the interlamellar spacing in these samples increased greatly. Figure 4c,d show that both the proeutectoid α 2 and the γ were largely situated along boundaries, at the triple lines of (α 2 +γ) L , and around the β o grains. However, the presence of β o and γ was extremely restrained as the Al content increased to 44.6 at.%, as shown in Figure 4c,d. The morphology of Sample S18 consisted of coarse γ laths and interwoven eutectoid α 2 +γ microstructures, as shown in Figure 4e,f. of α2 and βo, as shown in Figures 3 and 4. The morphologies of Samples S13-S17 were fully lamellar, as shown in Figure 4a-d. The size of the lamellar colonies and the interlamellar spacing in these samples increased greatly. Figure 4c,d show that both the proeutectoid α2 and the γ were largely situated along boundaries, at the triple lines of (α2+γ)L, and around the βo grains. However, the presence of βo and γ was extremely restrained as the Al content increased to 44.6 at.%, as shown in Figure 4c,d. The morphology of Sample S18 consisted of coarse γ laths and interwoven eutectoid α2+γ microstructures, as shown in Figure    Microstructures (from SEM-BSE) of Samples (a,b) S13, (c,d) S15, and (e,f) S18.

Thermal Analysis
The phase transformation temperatures of 8Nb-TiAl alloys during experimental continuous heating were determined by thermal analysis. The phase transitions were simultaneously determined by DSC and Cp data, with the calculated Cp for comparison. Figure  5 shows the thermodynamically calculated Cp data and experimentally determined DSC and Cp data for the selected samples. The abrupt changes in the calculated Cp, shown by the narrow peaks in Figure 5a, correspond to the formation of an ordered βo phase from α/β; the order-disorder transitions of β ↔ βo and the eutectoid reaction of α ↔ βo + γ can also be determined from the experimental Cp data, as shown in Figure 5b,c. However, as shown in Figure 5c, there is a particularly broad peak at approximately 900 °C in the experimental Cp curve, indicating an additional ordering transition in Samples S06-S12, which was considered to be the βo ↔ ωo transition. For Samples S15-S18, no β ↔ βo transition was found at elevated temperatures, as shown in Figure 5d. Based on the DSC, SEM, and XRD analyses, the phase transitions in 8Nb-TiAl alloys were determined, as shown in Figure 5b    Microstructures (from SEM-BSE) of Samples (a,b) S13, (c,d) S15, and (e,f) S18.

Thermal Analysis
The phase transformation temperatures of 8Nb-TiAl alloys during experimental continuous heating were determined by thermal analysis. The phase transitions were simultaneously determined by DSC and Cp data, with the calculated Cp for comparison. Figure  5 shows the thermodynamically calculated Cp data and experimentally determined DSC and Cp data for the selected samples. The abrupt changes in the calculated Cp, shown by the narrow peaks in Figure 5a, correspond to the formation of an ordered βo phase from α/β; the order-disorder transitions of β ↔ βo and the eutectoid reaction of α ↔ βo + γ can also be determined from the experimental Cp data, as shown in Figure 5b,c. However, as shown in Figure 5c, there is a particularly broad peak at approximately 900 °C in the experimental Cp curve, indicating an additional ordering transition in Samples S06-S12, which was considered to be the βo ↔ ωo transition. For Samples S15-S18, no β ↔ βo transition was found at elevated temperatures, as shown in Figure 5d. Based on the DSC, SEM, and XRD analyses, the phase transitions in 8Nb-TiAl alloys were determined, as shown in Figure 5b

Thermal Analysis
The phase transformation temperatures of 8Nb-TiAl alloys during experimental continuous heating were determined by thermal analysis. The phase transitions were simultaneously determined by DSC and C p data, with the calculated C p for comparison. Figure 5 shows the thermodynamically calculated C p data and experimentally determined DSC and C p data for the selected samples. The abrupt changes in the calculated C p , shown by the narrow peaks in Figure 5a, correspond to the formation of an ordered β o phase from α/β; the order-disorder transitions of β ↔ β o and the eutectoid reaction of α ↔ β o + γ can also be determined from the experimental C p data, as shown in Figure 5b,c. However, as shown in Figure 5c, there is a particularly broad peak at approximately 900 • C in the experimental C p curve, indicating an additional ordering transition in Samples S06-S12, which was considered to be the β o ↔ ω o transition. For Samples S15-S18, no β ↔ β o transition was found at elevated temperatures, as shown in Figure 5d. Based on the DSC, SEM, and XRD analyses, the phase transitions in 8Nb-TiAl alloys were determined, as shown in Figure 5b-d, where the phase regions and isopleth sections are schematically identified in the DSC/C p curves.

Isopleth
Based on this work's thermal analyses, the experimental 8Nb-TiAl isopleth section was deduced and compared with a thermodynamic isopleth, as shown in Figure 6. More details about the transformation temperatures determined by DSC detection in this work and by the literatures are provided in supplementary materials. The experimental transus between phase transitions was approximated by a three-order polynomial with a leastsquares solution, as shown in Figure 6. The experimental isopleth showed some differences from the thermodynamic calculations.

Isopleth
Based on this work's thermal analyses, the experimental 8Nb-TiAl isopleth section was deduced and compared with a thermodynamic isopleth, as shown in Figure 6. More details about the transformation temperatures determined by DSC detection in this work and by the literatures are provided in Supplementary Materials. The experimental transus between phase transitions was approximated by a three-order polynomial with a leastsquares solution, as shown in Figure 6. The experimental isopleth showed some differences from the thermodynamic calculations.
The βo ↔ ωo transition temperatures in Ti-45Al-10Nb have been determined to be approximately 780 °C with a slow cooling process (10 °C/min), and approximately 850-870 °C with a heating process (10 °C/min) [20,50]. In addition, during a slow furnace cooling process, the βo ↔ ωo transition temperature in Ti-42Al-8.5Nb has been detected at 928 °C by in-situ HEXRD and DSC with a heating rate of 20 °C/min [17]. These experimental results are in good agreement with the transus determined in this work. In contrast, at the The β o ↔ ω o transition temperatures in Ti-45Al-10Nb have been determined to be approximately 780 • C with a slow cooling process (10 • C/min), and approximately 850-870 • C with a heating process (10 • C/min) [20,50]. In addition, during a slow furnace cooling process, the β o ↔ ω o transition temperature in Ti-42Al-8.5Nb has been detected at 928 • C by in-situ HEXRD and DSC with a heating rate of 20 • C/min [17]. These experimental results are in good agreement with the transus determined in this work. In contrast, at the temperatures near 800 • C, the α 2 ↔ ω o transition has been seen to occur in only a few minutes with applied stress, although the transition took several hundred hours without applied stress [51]. Moreover, the β o ↔ ω o transition is promoted by the addition of a β/β o -stabilizing element, such as Nb or Mo [20,25,52,53]. The α 2 ↔ ω o transition has been observed to be restrained by the addition of an α 2 -stabilizing element, such as C [51].
In the 8Nb-TiAl system, the β ↔ β o transition occurred over a large range of Al concentrations, as shown in Figure 6. The transitions of samples with Al ranges of 18.4-43.2 at% at 1200-1400 • C, indicated by the #1 transus line in Figure 6, exhibited higher transformation temperatures than those calculated, which increased as the Al concentration became lower than 33.5 at%, with a maximum transformation temperature of 1380 • C at 32 at% Al, while the transition temperature decreased over the range of 33.5-42.5 at% Al and disappeared entirely as the Al concentration increased above 44.0 at% Al.
For alloys with 18-36 at% Al, following the β ↔ β o transus, there was a hightemperature phase transition, determined as the ordered α 2 phase transformation from β o phases (the #2 and #3 transus lines in the isopleth), as shown in Figure 6. The preliminary α 2 phase formed the coarsening laths among the β o phase, and the subsequent α 2 phase forms the flaky particles in the β o matrix, as shown in Figure 1.
For alloys with 18-30 at% Al, the formation of the O phase was determined by XRD, although not observed in the microstructures because of the small amount of the phase fraction in the alloy matrix, as shown in Figure 1. The fraction of O phase in the samples decreased and the α 2 phase increased as the Al concentration increased, as shown in Figure 2c,d. The O phase can be formed in a large temperature range between 800-1000 • C in Ti-Al-Nb ternary alloys [54,55], with two different pathways in the Ti-Al-Nb ternary system-α 2 ↔ O and β o ↔ O-depending on the composition and treatment process [17,56]. One pathway occurs in the α 2 phase in low-Nb-containing TiAl alloys (≤12.5 at% Nb), and the other pathway occurs in the β o phase in high-Nb-containing alloys (~25 at% Nb) [17,56,57]. The transformation of the O phase from the β o phase is considered to occur through a martensitic transition [57]. Therefore, in this work, the transus line in the range of 18-30 at% Al at approximately 850 • C in the 8Nb-TiAl system was confirmed to be the α 2 ↔ O transition, in agreement with the thermodynamic calculation.
For alloys with 32-36 at% Al, there was an extra γ precipitation from α 2 , forming the ultrafine lamellar structure. As the Al concentration increased above 36 at%, the lamellar structure mainly formed through eutectoid reactions at 1150-1200 • C, with α ↔ β o + γ and β o ↔ α 2 +γ, forming the lamellar colonies as shown in Figures 3, 4 and 6. Therefore, as mentioned in the thermal analysis, the experimental phase transformation behaviors within α-containing regions were in good agreement with the thermodynamic calculations, as shown in Figure 5a,b,d, indicating that the influence of experimental conditions on these regions is small. The dominant activity under these conditions is suggested to be the main attribution.
For alloys with Al concentrations lower than 30 at% (Samples S01-S05) or greater than 43 at% (Samples S14-S18), there were no β o (LOB2 structure) and ω o phases found at the ambient temperature, as indicated by XRD and SEM detections, while for Al concentrations in the range of 32-42 at% (Samples S06-S12), the ω o phase and highly ordered β o phase were detected simultaneously. As a result, the ω o phase was preferentially formed in the highly ordered β o phase.
The experimental phase equilibrium relations and transformation pathways of the 8Nb-TiAl alloys deviated significantly from the thermodynamic calculations, as shown in Figure 6. These deviations may have been associated with the treatment conditions, such as the heating/cooling rates, and/or insufficiencies in the thermodynamic database for high-Nb-containing TiAl systems [5,11,58]. Because of the actual preparation process, the experimental isopleth showed metastable phase behavior, such as the formation of ω o from the retained β o , rather than from α 2 as expected by the thermodynamic equilibrium behavior.

β o Transformation
The β ↔ β o transition temperatures and ordering procedure were in agreement with the studies of Clemens et al. [5] and Schmoelzer et al. [11], and were strongly affected by the compositions, as in [11,25]. The transition temperature differences between the experimental and calculation results may also have been related to the ordering of the β phase [59]. Crystallographic analysis has shown that the structure of the ordered β o phase contains two sublattices: one occupied by Al (B site) and the other occupied by Ti atoms (A site). The two sublattices are randomly occupied with all species in the disordered β phase. As previously reported [60], Nb atoms should replace the Ti atoms in the structure. However, Leonard et al. [61] suggested that the site occupancy of Nb depends on the composition. The atomic occupancy and lattice parameter are slightly changed during the β ↔ β o order-disorder transition.
The phase transition type is evidently reliant on the order of the isobaric-isothermal potential derivative (free Gibbs energy) [62], which exhibits an abrupt change at the transition position. In the first-order phase transitions (first derivatives), determined by the heat release or endothermic peaks in the DSC curve, there are abrupt changes in the specific volume and entropy. In the second-order phase transitions, such as order-disorder transitions, there are continuous changes in the specific volume and entropy, with no transition heat shown in the DSC curve, although there are abrupt changes in the second derivatives of the isobaric-isothermal potential, such as in the specific heat capacity, thermal expansion coefficient, and isothermal compressibility [62].
In this work, the ordered β o phase formed from disordered β/α phases as the temperature decreased from the elevated temperatures. As mentioned in reference to the calculated C p patterns, shown in Figure 5a, there was one narrow peak in Sample S03, indicating the order-disorder β ↔ β o transition, and there were two narrow peaks in Samples S06-S15, corresponding to two types of order-disorder transitions, β ↔ β o and α ↔ β o + γ. The thermal analysis unambiguously detected the transformations of β o from β/α, as shown in Figure 5b,d; these transformations are commonly considered second-order phase transitions. However, in addition to the peaks found in the C p patterns, endothermic peaks were also detected in the DSC patterns for β ↔ β o and α ↔ β o + γ transitions, as shown in Figure 5b,d, indicating that the order-disorder transitions, β ↔ β o and α ↔ β o + γ, in the 8Nb-TiAl system should be defined as an intermediate transition type, between the firstand second-order phase transitions.

ω o Transformation
The transformation of β o phase to ω o phase in Nb-containing TiAl alloys at 700-900 • C has been frequently observed [20,[63][64][65]. The ω o phase has been found to be transformed within the β o matrix by homogeneous nucleation, or on the boundaries of β o /γ phases by heterogeneous nucleation, of particles with nano-or micro-scale sizes during continuous heating/cooling processes [17,20,51,65]. The formation of ω o phase is associated closely with the treatment process [51,66] and the chemical composition [20], and Nb has been suggested to act as the ω o stabilization element [67].
As shown in Figure 5c, there was an endothermic peak and an abrupt change in the DSC and C p patterns, respectively, indicating that, to some extent, the β o ↔ ω o transition was an ordering process. As mentioned by Stark et al. [20], the β o phase exhibits a crystallographic orientation with the ω o phase: {111}β o {0001}ω o or 110 β o 1120 ω o . According to this relationship, Figure 7 shows the atomic configuration of the ω o phase with the Wyckoff positions and site occupancies, as well as the atom distribution in β o phase as seen along its three-fold axis. During the β o →ω o transformation, the four stacking atomic layers in the β o phase, Layers 1-4 in Figure 7a, merge into double layers in the ω o phase, Layers 1-2 in Figure 7b. Furthermore, the site occupancy preference also changed, such that the Nb atoms moved into the 2a site, whereas the Ti and Al atoms move almost into the 2c and 2d sites, as shown in Figure 7. The lattice of the ω o phase is slightly compressed along the 111 β o / 0001 ω o direction, whereas it stretches significantly along the 1120 ω o direction [20]. seen along its three-fold axis. During the βo→ωo transformation, the four stacking atomic layers in the βo phase, Layers 1-4 in Figure 7a, merge into double layers in the ωo phase, Layers 1-2 in Figure 7b. Furthermore, the site occupancy preference also changed, such that the Nb atoms moved into the 2a site, whereas the Ti and Al atoms move almost into the 2c and 2d sites, as shown in Figure 7. The lattice of the ωo phase is slightly compressed along the 〈111〉β /〈0001〉ω direction, whereas it stretches significantly along the 〈1120〉ω direction [20].  [20] are given at bottom.

Conclusions
(1) The isopleth section of the 8Nb-TiAl system (with 18-48 at% Al) was determined experimentally by DSC, SEM, and XRD methods, and compared with thermodynamic calculations (from CALPHAD). The experimental isopleth showed some deviations from the calculations, especially for βo containing regions.
(2) The ordered βo phase transformed from the disordered β phase in the range of 18.4-43.2 at% Al at 1200-1400 °C. The βo phase also transformed through a eutectoid transition, α ↔ βo + γ, from the α phase. The transition type of β ↔ βo was considered to be an intermediate type between the first-and second-order phase transitions. In particular, the βo phases were retained at the ambient temperature in the 8Nb-TiAl alloys under experimental conditions.
(3) The ordered ωo phase transformed experimentally from the highly ordered βo phase rather than from the α2 phase or the βo phase with a LOB2 structure. The experimentally detected ωo formation occurred within 32-43 at% Al concentrations at approximately 850 °C, having a smaller composition range and higher transforming temperature than the calculated thermodynamic transition. The formation of the ωo phase from the βo phase was considered to be a further ordering process.
Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Figure S1: DSC and DDSC traces for samples that are closed to invariant points. Table S1: Onset phase transformation temperatures detected by thermal analysis. Table S2: DSC/DTA data for detecting the phase transition temperatures in the Ti-Al-Nb samples from the literatures.   [20] are given at bottom.

Conclusions
(1) The isopleth section of the 8Nb-TiAl system (with 18-48 at% Al) was determined experimentally by DSC, SEM, and XRD methods, and compared with thermodynamic calculations (from CALPHAD). The experimental isopleth showed some deviations from the calculations, especially for β o containing regions.
(2) The ordered β o phase transformed from the disordered β phase in the range of 18.4-43.2 at% Al at 1200-1400 • C. The β o phase also transformed through a eutectoid transition, α ↔ β o + γ, from the α phase. The transition type of β ↔ β o was considered to be an intermediate type between the first-and second-order phase transitions. In particular, the β o phases were retained at the ambient temperature in the 8Nb-TiAl alloys under experimental conditions.
(3) The ordered ω o phase transformed experimentally from the highly ordered β o phase rather than from the α 2 phase or the β o phase with a LOB2 structure. The experimentally detected ω o formation occurred within 32-43 at% Al concentrations at approximately 850 • C, having a smaller composition range and higher transforming temperature than the calculated thermodynamic transition. The formation of the ω o phase from the β o phase was considered to be a further ordering process.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/met11081229/s1, Figure S1: DSC and DDSC traces for samples that are closed to invariant points. Table S1: Onset phase transformation temperatures detected by thermal analysis. Table S2: DSC/DTA data for detecting the phase transition temperatures in the Ti-Al-Nb samples from the literatures. Table S3: Experimental transition temperatures in the Ti-Al-Nb samples summarized by Witusiewicz et al. Figure S2: individual XRD pattern of S01-S18 with phase structural information.  Data Availability Statement: Data presented in this article is available on request from the corresponding author.