Lattice parameter evolution during heating of Ti-45Al-7.5Nb-0.25/0.5C alloys under atmospheric and high pressures

23 Lattice strain evolution during deformation processing of Ti-Al alloys at high 24 temperature is important in terms of its microstructural evolution and microstructural 25 stability. It is shown here that careful evaluation of lattice parameters is critical for the 26


INTRODUCTION 41
Titanium aluminides are attractive candidate materials for applications in the 42 automotive industry, and more importantly for applications at high temperature in 43 aerospace industries, mainly due to their low density and excellent mechanical 44 properties [1][2][3]. A new route for the processing of titanium aluminide components 45 under high pressure has been proposed [4], for example, by utilizing a 0.8 GN forging 46 press to manufacture large aerospace products [5] or a new 0.54 GN die-forging press 47 visit data from two in-situ heating experiments, to compare (i) a high-energy 75 synchrotron radiation study on Ti-45Al-7.5Nb-0.5C under atmospheric pressure [16] 76 with (ii) an energy-dispersive synchrotron X-ray diffraction experiment on Ti-45Al-77 7.5Nb-0.25C under high pressure at 9.6 GPa [13]. 78 Figure 1(a) shows a section through the Ti-Al binary phase diagram [18], while a 79 section through a Ti-Al-7.5 at. % Nb alloy, proposed by Chladil et al. [19] is shown in 80 Figure 1(b). The alloy used in the present study is schematically shown by the 81 vertical line at 45 at. % Al. It is important to note that this section through the phase 82 diagram applies to atmospheric pressure and to the knowledge of the authors, the 83 extent to which pressure changes the pertaining phase equilibria has not been 84 determined as yet. 85 86 Figure 1. (a) Binary phase diagram of Ti-Al [18]; (b) Section through a proposed phase diagram of the 87 Ti-Al-Nb alloy system for an alloy containing 7.5 at. % Nb [19].

89
Since we study a Ti-Al-Nb-C alloy under conditions of severe-plastic deformation and 90 high temperature, it is important to identify the most critical parameters that 91 determine microstructural evolution and stability. One important variable is lattice 92 parameter evolution, since for example, a change in the c/a ratio of the α-lattice has a 93 determining influence on the pertaining slip and twinning deformation mechanisms. 94 Moreover, changes in the lattice parameter impact on orientation relationships and 95 have an influence on interphase stress development. In addition, the mechanism and 96 morphology of phase transformations need to be taken into account since they play an 97 important role in achieving microstructural stability. 98 Although the lattice parameter evolution plays a pivotal role in assessing the high-99 temperature behavior of titanium-aluminides, as argued above, only little information 100 has been traced to date, with the notable exception of the in-situ studies early by Shull 101 et al. [20], then by Yeoh et al. [21] and more recently that of Liss et al. [13]. 102 The very early work of Shull et. al in 1990 reports on the first in-situ investigation of 103 titanium aluminides at high temperature, focusing on the experimental determination 104 of phase fields, while lattice parameter evolution is traced. In 2007, Yeoh et al. [21] 105 reported the changes occurring in the c/a ratio of the lattice parameters in a Ti-45Al-106 7.5Nb-0.5C alloy during heating at atmospheric pressure. She suggested that as far as 107 X-ray analyses are concerned, a simplification should be made by assuming that the 108 α 2 -(ordered) and the α-phase (disordered) be regarded as a single phase since X-rays 109 cannot clearly distinguish between an ordered and disordered structure. 110 Liss et al. [13] recently conducted an in-situ X-ray diffraction experiment on a Ti-111 45Al-7.5Nb-0.25C alloy under high hydrostatic pressure. They studied the phase 112 evolution of a Ti-45Al-7.5Nb-0.25C alloy as a function of time under high pressure 113 and high temperature within a synchrotron X-ray source (SPring-8 beamline BL04B1, 114 run number M1472). The in-situ diffactograms are displayed in Figure 2 which have 115 been analyzed by the Rietveld method using MAUD (Material Analysis Using 116 Diffraction software [22,23]) for the evolution of phase fractions as a function of 117 temperature, shown in Figure 3. Also shown are the phase fractions determined by 118 Yeoh et al. [21] in a roughly similar alloy Ti-45Al-7.5Nb-0.5C, but under standard 119 atmospheric conditions. The two alloys have been manufactured under identical 120 conditions and the two in-situ experiments were conducted under normal atmospheric 121 and high pressure respectively. However, it is important to note that carbon can have a 122 significant influence on phase evolution in these alloys and for this reason care need 123 to be taken in comparing the alloys containing 0.25 at. % C and 0.5 at. % C 124 respectively. For example, the eutectoid temperature, T eu , is increased by 20 K from 125 1453 K to 1473 K, but the respective -solvus, T ,solv , 1565 K and 1566 K respectively 126 [24] remains essentially constant. Notwithstanding these differences, the two alloys 127 can be compared with respect to their respective pressure-induced behaviors. The fcc-128 based, ordered -phase of L1 0 structure, co-exists with an hcp-based, ordered α 2 -phase 129 of D0 19 structure at room temperature. Upon heating, the α 2 -phase undergoes an 130 inverse eutectoid order-disorder transition to form a fully disordered hexagonal α-131 phase at T eu . The fraction of the -phase decreases upon heating and finally transforms 132 fully into the disordered α-phase at T ,solv . Salient features when the Ti-45Al-7.5Nb-133 0.25C alloy is heated under a pressure of 9.6 GPa, are the appearance of the bcc β-134 phase in an (α+ α 2 + β + γ) field and the dissolution of  phase at T ,solv to form 135 (α + β). 136 Figure 2. Measured diffraction patterns of a Ti-45Al-7.5Nb-0.25C alloy obtained under high pressure 138 (9.6 GPa). Temperature tags are shown on the left and serial numbers on the right [13]. The first three 139 patterns at 310 K were taken at pressures of 0, 3.2 and 9.6 GPa, respectively (based on [13] Figure 3. Phase evolution in a Ti-45Al-7.5Nb-0.25C alloy at a pressure of 9.6 GPa (continuous lines) 145 (based on [13] under CC-BY license) compared with observations at standard atmospheric pressure 146 (dotted lines) for a Ti-45Al-7.5Nb-0.5C alloy, replotted from Yeoh et al. [21].

148
Liss et al. [13] analyzed the lattice strain development in the Ti-45Al-7.5Nb-0.25C 149 alloy at 310 K at three pressures, up to 9.6 GPa (series numbers 2, 4 and 7 in Figure  150 2). They calculated the changes in lattice parameter of the γ-and α 2 /α-phases as a 151 function of pressure at this temperature [13] and argued that at room temperature, the 152 volume response to pressure is accommodated by the phase transformation γ → α 2 , 153 rather than by volumetric strain. They further determined some crystallographic 154 aspects, specifically lattice strain and atomic order, at room temperature, but did not 155 determine lattice strain evolution during heating at high pressure, which is subject of 156 the current project. It is the dearth of information of this parameter, critical to 157 processing at high temperature and pressure, which prompted the present 158 investigation. 159 The overarching aim of the present work was the re-visit of the experimental data of 160 both experiments [13,27] in order to compare the behavior of the selected alloys 161 under atmospheric and high pressure respectively. 162 The specific aims were: 163  to determine the lattice parameter evolution as a function of temperature at 164 atmospheric pressure in the Ti-45Al-7.5Nb-0.5C alloy. 165  to determine lattice parameter evolution as a function of temperature under high 166 hydrostatic pressure in the Ti-45Al-7.5Nb-0.25C alloy. 167 It will be shown below that the experimentally determined lattice parameter 168 evolutions occur in response to thermal expansion, alloy element segregation, order 169 parameter and pressure. The specific trends and values will be decomposed based on 170 an understanding of strain evolution with reference to the reported phase diagram at 171 atmospheric pressure, before interpreting the evolution in the unknown system under 172 high pressure. These new insights are opening new pathways to better understand 173 structural transformations in the experimentally confined system. Such understanding 174 is an essential element in optimizing the intended production techniques of titanium-175 aluminides since microstructural stability plays an important role in determining 176 processing parameters. 177 178

EXPERIMENTS 179
Lattice strain evolutions were calculated from the raw data of two earlier experiments: 180  Yeoh et al. [21] conducted in-situ high-energy X-ray diffraction studies under 181 proposal number MA-77 at the ID15B beamline at the ESRF in Grenoble using a 182 two-dimensional detector. They ramped up a Ti-45Al-7.5Nb-0.5C alloy from 183 room temperature to 1375 K at a rate of 5 K/min before ramping down to a rate of 184 2 K/min. Once a temperature of 1675 K was reached, it was maintained for 5 185 minutes before cooling down to room temperature at a rate of 5 K/min. All details 186 of the experiment have been described by Yeoh et al. [21]. 187  Liss et al. [13] conducted in-situ X-ray diffraction studies at the BL04B1 188 beamline at the modern synchrotron source SPring-8 [25,26] and a detailed 189 account of the experimental procedures is to be found in their paper [13]. Because Lake Oswego, OR, USA) was then used to calculate the lattice strains and to perform 206 curve fitting. 207 11 The two titanium-aluminides of nominal chemical composition Ti-45Al-7.5Nb-208 0.25/0.5C used in the present study were produced by a powder metallurgical 209 processing technique. Powder was manufactured by a plasma-melting induction-210 guiding atomization technique and consolidated by hot-isostatic pressing for 2 h at a 211 pressure of 200 MPa and a temperature of 1553 K [27]. Both alloys were 212 characterized by Chladil et al. [4,24] and the resulting microstructure at room 213 temperature consists of a globular γ-phase and lamellar (α 2 + γ) two-phase colonies 214 [4]. 215 While the experimental settings are described in the references, we like to raise an 216 error estimate at this point, particularly to validate the later described lattice parameter 217 fluctuations and features of the present manuscript. While the atmospheric pressure 218 data in angle-dispersive setting appear as smooth curves, due to much faster and 219 therefore finer sampling, the high-pressure data has been undertaken on temperature 220 holding steps with larger step size, representing sometimes larger jumps between 221 them, which could be interpreted as error fluctuations. Care has been undertaken by 222 validating the realty of such jumps re-visiting the original data -i.e. looking out for 223 changes of peak shape, overlapping etc and by the two kinds of fitting analysis both 224 Rietveld and single peak. We come up with the following estimate of error, 225 demonstrating the trend of the features we discuss on lattice strain evolution: 226  For the high-pressure setup [13] the energy calibration based on fluorescence 227 lines of Mo, Pb, Au, Ag, Pt, Ta and Cu and single peak fitting (see below) has 228 been calibrated to and accuracy of ~1E-4. Subsequently, the diffraction angle 229 was calibrated using MgO and Au as standard materials at ambient conditions. Note moreover, physically meaningful errors may originate from drifts in temperature 243 or pressure, as it will be discussed further in the paper. We exclude significant drifts 244 during a particular holding step, which would otherwise express in peak shape and 245 broadening. Single-peak fitting of the α 2 -201 reflection has been performed and con-246 firms the trends with an error of ~3E-4, even in the range around 1500 K, allowing a 247 qualitative interpretation of peak shifts due to various lattice variations, such as 248 change of phase composition, disorder transformation etc, as it will be discussed. 249 250

Lattice strains at standard atmospheric pressure 252
The evolving lattice strains were calculated by equation (1), 253 For a given reflection, G 0 are the reciprocal lattice vectors at 300 K and G are the 255 measured values at increasing temperature. The lattice strain discussed below is not 256 an absolute lattice strain but is merely the difference in strain with respect to a 257 reference value at 300 K. Lattice strains of the Ti-45Al-7.5Nb-0.5C alloy at standard 258 atmospheric pressure are shown in Figures 4 and 5 for the co-existing phases, α 2 /α 259 and γ, respectively. Both figures display an initial linear relationship between lattice 260 strain and temperature which then evolves abnormally and anisotropically. Also 261 shown is the average lattice strain, expressed as ∆ /3 of the atomic volume 262 expansion ( ∆ / = 2∆ / + ∆ / ), as a function of temperature. The changes in 263 lattice strain can be divided into four distinct temperature regions, which we discuss 264 for each phase. In region I, the strain evolution of the γ-phase is similar to that in the α 2 /α-phase. In 289 region II, the strain in both the aand c-directions increases almost linearly since the 290 dominant contributing factor to lattice strain is thermal expansion. In region III, the 291 strain in the -phase along the a-direction increases up to T eu whereas the strain in the 292 c-direction increases to a lesser extent, developing significant anisotropy. In region IV, 293 the strain in the a-direction decreases while the strain in the c-direction increases. The 294 volumetric strain deviates only slightly from linearity and at the T γ,solv of 1565 K, all 295 strain components meet as if they had expanded isotropically and linearly from room 296 temperature. 297 298

Lattice strain at high pressure 299
The experimentally determined lattice strains of the α 2 /α-and γ-phases are shown in 300 Figures 6 and 7 for the Ti-45Al-7.5Nb-0.25C alloy under a pressure of 9.6 GPa. It is 301 instructive to divide strain development into four regions. 302 Region I depicts the lattice strain evolution as a function of temperature in the range 303 300 K to 1003 K, where the α 2 -phase has not yet reached thermodynamic equilibrium. 304 Region II ranges from 1003 K to 1420 K (T γ,max ) and is divided into sub-regions II a 305 and II b , separated by the appearance of the β-phase at 1350 K (T β,start ) [13]. Region III 306 ranges from 1420 K to 1510 K (T eu ), while region IV covers the temperature range 307 above 1510 K. 308  Figure 6 shows the lattice strain evolution of the α 2 /α-phase along the cand a-316 directions respectively. In region I, the lattice strain evolution is linear with respect to 317 temperature. The strains along the aand c-directions in region II increase more than 318 those in region I. In region II b , the slope of the strain-temperature curve along the a-319 direction is higher than that along the c-direction, indicating a decrease in the c/a-320 ratio. A significant increase in strain occurs at 1420 K (the T γ,max ). In region III, a 321 maximum value of the lattice strain along c-direction is noticed at 1472 K. In region 322 IV, the lattice strain increases in the a-direction while there is an erratic behavior in 323 the c-direction. respectively. Noticeably, in region II a , the strain increases more along the a-direction 332 than in the c-direction, leading to a decrease of the c/a-ratio. In region II b , the strain 333 continues to increase but more so than in the previous region. In region III, the strain 334 increases but not as steeply as in the region II b . In region IV, the strain evolution trend 335 is almost the same as under standard atmospheric pressure. The transformation 336 temperatures T eu and T γ,solv shift to higher temperatures at high pressure, evidenced by 337 a comparison between Figures 5 and 7. The values of strain shown in Figure 7 are therefore higher than the true values of 371 lattice strain under 9.6 GPa by up to 25% and the isotropic lattice strain as a result of 372 temperature change has to be estimated. However, the anisotropic part, as will be 373 discussed later, is well representative.  Figure 9. Factors contributing to lattice strain evolution in the γ-phase at atmospheric pressure. 21 Figure 9 shows how temperature, aluminium content and the order parameter affect 424 strain evolution in the γ-phase at standard atmospheric pressure. 425 The thermal expansion is linear in region I along the aand cdirections due to the 426 linear temperature contribution. The small and anisotropic deviation from linearity in 427 Region II is due to the extent to which aluminium contributes to the disordering of the 428 TiAl-structure. It is observed that the lattice strain along the a-direction increases 429 faster than along the c-direction, and since the c-dimension is larger than the a-430 dimension, the unit cell approaches more closely an fcc unit cell, that of a fully 431 disordered -phase, revealing a higher degree of disorder and hence, a smaller order 432 parameter. Witusiewicz et al. [29] have shown earlier that the aluminium 433 concentration decreases well below stoichiometry in this temperature range as a 434 function of temperature and that the lowest aluminium concentration in the γ-phase is 435 attained at 1476 K, contributing to chemical disorder. Above 1476 K (in region IV), 436 the aluminium content in the partially ordered γ-phase increases, as shown in Figure  437 10(a). Yeoh et al. [21] have shown that the c/a ratio decreases sharply with increasing 438 temperature in Region III as shown in Figure 10(b). Hence, the strain along the a-439 direction increases more than in the c-direction and the TiAl-structure becomes highly 440 disordered. In region IV, the c/a ratio increases sharply as shown in Figure 10(b) and 441 the fully ordered TiAl-structure is approximated, due to the highest ordering energy of 442 the -phase, compared to all other Ti-Al configurations [30]. 443  Figure 4). There is a steep increase along the c-direction between 1462 K and 1472 K, 471 corresponding to the increase of the β-phase fraction (see Figure 3). The β-phase in 472 solid solution has a bcc structure and provides an opportunity for the co-existing α 2 -473 phase to drive closer to stoichiometry and order, increasing its c/a ratio. Moreover, 474 under the assumption that β orders to β 0 with a B2 structure, the latter would extract 475 Al from α 2 , again emphasizing a higher degree of order in the latter. The 476 transformation to β leads to a sharp decrease in the aluminium content of the 477 supersaturated α 2 /α-phase and hence, the α 2 /α-phase is increasingly ordered. The 478 change in the fraction of β-phase has a major influence on the aluminium 479 concentration in the α 2 /α-phase from region III onwards. These arguments explain 480 why the trend of the anisotropic strain in the α 2 /α-phase correlate well with the β-481 phase evolution. By contrast, the main contributor is a thermally driven α → α 2 order-482 disorder transition in region III under standard atmospheric pressure. The maximum 483 value of anisotropic strain along the c-direction at 1472 K is probably driven by the 484 appearance of an ordered β 0 -phase, leading to a lower aluminium content in the α 2 /α-485 phase. Under a pressure of 9.6 GPa, 1510 K, as a minimum of α-phase fraction, is 486 taken as eutectoid temperature, reported by Liss et al. [13]. It indicates that under high 487 pressure the eutectoid temperature would be increased. On approach to 1510 K, the 488 order-disorder transition α → α 2 occurs, the order parameter of the α 2 /α-phase 489 decreases, which results in the strain in the α 2 /α-phase along the c-direction having a 490 dramatic decrease. In region IV, up to 1529 K, the β-phase fraction increases sharply 491 (Figure 3), leading to a trend of an increase along the c-direction and a decrease in a-492 direction in the α 2 /α-phase, although questioned by large error bars. At higher 493 temperature, the anisotropic strain along the a-direction increases while that along the 494 c-direction decreases. 495 Figure 13 shows how temperature, aluminium content, order parameter and pressure 496 contribute to strain evolution in the γ-phase at a nominal pressure of 9.6 GPa in the 497 different regions respectively. Because of this observed pressure loss, the anisotropic 498 part of strain, ( / − /3 , / − /3 ) of the γ-phase is shown in Figure 14. 499 The sample pressure is from 9.6 GPa to 6.9 GPa -a very similar order of magnitude 500 which would not considerably change the phase transformation behavior. Moreover, 501 this anisotropic part of lattice strain is subtracted by the pressure influence, but 502 relevant features with respect to order parameter can be extracted. The significant 503 jumps in lattice parameter are definitely linked to phase transformations and not to 504 pressure release. The main features of the strain evolution in the -phase at a nominal 505 pressure of 9.6 GPa are discussed below: 506 507 Figure 13. Contributors to strain evolution of the γ-phase at nominal pressure of 9.6 GPa 508 509 510 Figure 14. Dependence of the anisotropic lattice strain in the -phase along a-(purple), c-(brown) 511 directions for Ti-45Al-7.5Nb-0.25C at 9.6 GPa 512 513 In region III, the transition of γ → α → β + α [13] results in an increased aluminium 514 content in the γ-phase, therefore, the strain increase is lower compared to atmospheric 515 pressure. The kink at 1472 K is attributed to the order parameter increase as a result of 516 the fact that the γ-phase fraction decreases sharply in the temperature range 1462 to 517 1472 K. In region IV, the trend in strain evolution is almost the same as at 518 atmospheric pressure, since the main contributing factor is the order parameter. 519

Phase sequence at high pressure 520
Based on our experimental observations and the Rietveld analyses outlined above, a 521 new version of the sequence of phase changes occurring in the Ti-Al-7.5Nb-0.25C 522 alloy under a pressure of 9.6 GPa, is shown in Figure 15 in the region of the alloy 523 composition (delineated by the area between the two vertical dotted lines). This is the 524 first experimental evidence suggesting that during heating under high pressure the 525 sequence of phase development is α 2 +γ, α 2 +α+γ, α 2 +α+γ+β, α+γ+β, α+β, L+α+β, L+β 526 and liquid L. Compared to the phase diagram suggested by Chladil et al. [19], it is 527 evident that the temperature range of the phase field α 2 +α+γ+β is extended under the 528 influence of a pressure of 9.6 GPa. 529 530 531 Figure 15

Comparison of the observations at low and high pressure 537
The quantitatively calculated contributions to strain evolution at standard atmospheric 538 pressure are listed in Table 1 [31] 542 543 The linear thermal expansion coefficients are η a = 12.075·10 -6 K -1 and η c = 544 12.047·10 -6 K -1 for α 2 /α-phase and η a = 12.412·10 -6 K -1 and η c = 11.847·10 -6 K -1 for γ-545 phase. They were extracted by fitting the curves of aand cdirections in region I of 546 Figures 4 and 5, since thermal expansion is proportional to the temperature change for 547 most solids, ℎ = η • ∆ [28,32]. In order to calculate the contribution of the 548 aluminium content of the α 2 /α-phase, the slope of the strain (Figure 4 and Figure 5) 549 and the slope of the phase boundary lines (Figure 10 no order parameter nor site occupation have been evaluated by Yeoh et al. [21]. The 570 fully disordered -phase would be fcc with a c/a axis ratio of one, and the atomic 571 volume is conserved during the order-disorder phase change. The lattice parameters of 572 the stoichiometric alloy have been reported by Beaven and Pfullman [31] and 573 extracted as a 50 = 4.0176 Å and c 50 = 4.0745 Å, for the fully ordered crystal structure. 574 a fcc = √a 50 2 ×c 50 3 leading to a fcc = 4.03648 Å. When the crystal structure changes from a disordered 575 (S = 0) to a fully ordered structure (S = 1), the influence of the structure parameter on 576 strain development is calculated as /S a = ( 50  a fcc )/ a fcc = 4677·10 -6 and 577 /S c = ( 50 a fcc )/a fcc = 9420·10 -6 , respectively. 578 Table 2 lists quantitative contributions to the strain evolutions at high pressure. The 579 thermal expansion coefficients are calculated by linear curve fitting based on the 580 strains in region I (Figures 6 and 7). They are η a = 8.126·10 -6 K -1 , η c = 9.030·10 -6 K -1 581 for the α 2 /α-phase and η a = 8.371·10 -6 K -1 , η c = 8.359·10 -6 K -1 for γ-phase. The 582 expansion coefficients are approximately 8×10 -6 K -1 under a compressive pressure of 583 9.6 GPa whereas it is 12×10 -6 K -1 under atmospheric pressure. Hence, a compressive 584 pressure of 9.6 GPa decreases the expansion coefficient to 67% of the value at 585 atmospheric pressure. An increase of aluminium content in the respective phases 586 would lead to a decrease in the strain along the aand cdirections, as well as a 587 decrease in the volumetric strain. The application of an applied compressive pressure 588 caused the strain to decrease in both phases. Liss et al. [13] has already calculated the 589 strain decrease in the α 2 /α-phase per 1 GPa is 2266·10 -6 along a-direction and 590 2189·10 -6 along the c-direction from the same experimental data. The corresponding 591 strain decrease in the γ-phase is 2206·10 -6 along a-direction and 2293·10 -6 in the c-592 direction [13]. 593 594

CONCLUSIONS 598
Lattice strain evolution in a Ti-45Al-7.5Nb-0.5C and a Ti-45Al-7.5Nb-0.25C alloy 599 respectively was determined by in-situ experiments using high-energy X-rays at 600 synchrotron storage rings. The temperature dependence of lattice strain evolution of 601 the Ti-45Al-7.5Nb-0.5C alloy was studied at atmospheric pressure while the lattice 602 strain evolution in a Ti-45Al-7.5Nb-0.25C was determined as a function of 603 temperature under a compressive pressure of 9.6 GPa. 604  Lattice strain evolution is determined by thermal expansion, changes in the 605 aluminium content of the respective phases and the extent to which the respective 606 phases are ordered under atmospheric pressure. Their interaction and respective 607 quantitative values to lattice strain changes have been obtained, which provides 608 valuable data to predict strain evolution in the future. 609  Pressure has a determining influence on strain evolution in the alloys. A 610 consequence of this finding is that the magnitude of the lattice strain can be 611 manipulated by these four factors during manufacture. Hence, inter-granular 612 stresses can be reliably predicted, minimized and controlled in order to manipulate 613 the mechanical properties of candidate titanium aluminide alloys. 614  The application of high pressure increases the eutectoid temperature T eu and the 615 temperature at which the transformation of the γ-phase is completed, T ,solv . The 616 linear thermal expansion coefficient of the alloy investigated is about 1/3 (4×10 -6 617 K -1 ) lower under a pressure of 9.6 GPa, than under standard atmospheric pressure. 618  Based on the experimental observations, a new version of the sequence of phase 619 changes occurring at high pressure is proposed and illustrated with reference to a 620 schematic phase diagram. This portion of the phase diagram shows that under 621 high pressure, the α 2 +α+γ+β phase field is stabilized over a wide range of temper-622 ature. 623  Lattice strains can be used to indicate the occurrence of phase transformations and 624 changes in composition, which are otherwise difficult to determine. 625  The c/a ratio of both the α 2 /α-and γ-phases provides valuable insight into the ex-626 tent to which these phases are ordered (as assessed by the order parameter). 627  A discontinuity in the c/a ratio is an indication of the order-disorder transition 628 α 2 → α. 629 The present findings are of generic importance with respect to lattice parameter 630 evaluation and are relevant to a multitude of intermetallic systems.