Experimental constraints on the phase diagram of titanium metal

ARTICLE IN PRESS Journal of Physics and Chemistry of Solids 69 (2008) 2559– 2563

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Experimental constraints on the phase diagram of titanium metal Jianzhong Zhang a,, Yusheng Zhao a, Robert S. Hixson a, George T. Gray IIIa, Liping Wang b, Wataru Utsumi c, Saito Hiroyuki c, Hattori Takanori c a b c

Los Alamos National Laboratory, Los Alamos, NM 87545, USA Mineral Physics Institute, State University of New York, Stony Brook, NY 11794, USA Synchrotron Radiation Research Center, Japan Atomic Energy Research Institute, Hyogo 679-5148, Japan

a r t i c l e in fo

abstract

Article history: Received 9 January 2008 Received in revised form 18 April 2008 Accepted 27 May 2008

The phase transformations of titanium metal have been studied at temperatures and pressures up to 973 K and 8.7 GPa using synchrotron X-ray diffraction. The equilibrium phase boundary of the a– o transition has a dT/dP slope of 345 K/GPa, and the transition pressure at room temperature is located at 5.7 GPa. The volume change across the a– o transition is DV ¼ 0.197 cm3/mol, and the associated entropy change is DS ¼ 0.57 J/mol K. Except for DV, our results differ substantially from those of previous studies based on an equilibrium transition pressure of 2.0 GPa at room temperature. The a– o– b triple point is estimated to be at 7.5 GPa and 913 K, which is comparable with previous results obtained from differential thermal analysis and resistometric measurements. An update, more accurate phase diagram is established for Ti metal based on the present observations and previous constraints on the a– b and o– b phase boundaries. & 2008 Elsevier Ltd. All rights reserved.

Keywords: A. Metals C. High pressure C. X-ray diffraction D. Phase transitions D. Thermodynamic properties

1. Introduction Theoretical and experimental studies of phase stability trends in the periodic table have been one of the important subjects in chemistry and computational physics. It is now generally accepted that structural phase stability in transition and rare-earth metals is controlled by the valence d electrons per atom [1,2]. In other words, crystal structures in these elemental metals tend to have certain sequences when viewed as functions of atomic number. All three transition series, excluding the four magnetic 3d metals, for example, show the canonical hcp-bcc-hcp-fcc sequence of structures as their atomic number increase [2]. Since compression would lead to an increase in d-electron population by transfer of electrons from the s-orbital, similar structure sequences are expected to occur in individual transition metals with increasing pressure [2,3]. As one of the group IV transition metals, titanium (Ti) metal has been the subject of extensive experimental studies at high pressure and temperature. At ambient conditions, Ti metal crystallizes in a hexagonal close packed structure (hcp or a phase), and transforms to a bodycentered cubic structure, commonly referred as b phase, at temperatures higher than 1155 K. With increasing pressure at room temperature, the hcp phase transforms into a hexagonal structure called o phase, which is not close packed and has three

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E-mail address: [email protected] (J. Zhang). 0022-3697/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2008.05.016

atoms per unit cell. The pressure induced transition from a to the o phase in Ti was first observed by Jameison [4], and has since been studied extensively with static high pressure [5–14] and shockwave [15–19] techniques. The onset of the transition at room temperature has been observed over a wide range of pressures from 2.95 to 11 GPa, as recently summarized in Ref. [14]. This discrepancy is in part due to the difference in sample purities, which has been observed to influence both the onset pressures of the transition and the transformation kinetics of group IV transition metals (Ref. [20] and references therein). For experiments performed under non-hydrostatic conditions, the stress concentration at grain corners of polycrystalline materials will typically enhance the transition to lower pressures, and the onset pressure of the phase transformation depend on the extent of applied shear or uniaxial stress [14,21,22]. In addition, the new phase formed under high pressure has a different density. This misfit creates elastic stresses and would therefore consume some energy. As a result, the transformation cannot start immediately at the equilibrium phase boundary but only after some metastable overshoot in pressure to overcome activation energy needed for transformation to occur [23]. Because of these observations and because many of previous investigations were conducted at room temperature, the equilibrium phase boundary for the a– o transition and hence the phase diagram of Ti remain unclear for this fundamentally as well as technologically important metal. Temperature affects the solid-state phase transformations in a number of important ways. Firstly, as expected from the kinetic theory of phase transformation, the kinetic barriers would

ARTICLE IN PRESS J. Zhang et al. / Journal of Physics and Chemistry of Solids 69 (2008) 2559–2563

become smaller with increasing temperature. Secondly, heating would relax the deviatoric stress built up during the room temperature ‘‘cold’’ compression and hence minimize the observed influences of stress on phase transitions in Ti and other materials. Last but not the least, our recent study demonstrates that the impurity effect on the onset pressure of the transition in group IV transition metals is substantially reduced at elevated temperature [20]. In this work, we investigated the phase transformations in Ti metal at simultaneously high pressure (P) and temperature (T), with a focus on the a– o transformation.

2. Experimental The starting Ti metal has an hcp structure (a-phase) and is in a form of crystalline bulk with a grain size of 20 mm. The sample is of high purity, with 360 ppm of O, 60 ppm of C and o15 ppm of H, N, Al, V and Fe as impure ions. Synchrotron X-ray diffraction experiments were conducted using a cubic anvil apparatus [24] at beamline X17B2 of the National Synchrotron Light Source (NSLS), Brookhaven National Laboratory and at beamline BL14B1 of the Spring-8, Japan. An energy-dispersive X-ray method was employed with diffracted X-rays collected at the fixed Bragg angles of 2y ¼ 6.49231 at NSLS and 2y ¼ 5.99401 at Spring-8. The cell assemblies used in the experiments are similar to those described in Ref. [24]. Briefly, a mixture of amorphous boron and epoxy resin was used as pressure-transmitting medium and amorphous carbon was used as furnace material. The Ti samples were surrounded by NaCl powders and packed into a cylindrical container of boron nitride, 1.0 mm inner diameter and 2.0 mm length. In each of the two experiments we performed, NaCl was used as an internal pressure standard and temperatures were measured by a W/Re25–W/Re3% thermocouple. The temperature variations over the entire length of sample container at 1500 K were of the order of 20 K, and the radial temperature gradients were o20 K at this condition [24]. X-ray diffraction patterns were obtained for both samples and NaCl in close proximity to the thermocouple junction; errors in temperature measurements were thus estimated to be approximately 10 K. Pressures were calculated from Decker’s equation of state for NaCl [25] using lattice parameters determined from X-ray diffraction profiles at each experimental condition. Five NaCl diffraction lines, 111, 200, 220, 222 and 420, were usually used for determination of pressure. The uncertainty in pressure measurements is mainly attributed to statistical variation in the position of diffraction lines and is o0.2 GPa in the P– T range of this study. The effect of deviatoric stress on pressure determination or onset pressures of the phase transitions is minimal because a majority of the data reported here was collected at elevated temperature or on cooling from 900 K, under which the deviatoric stress is expected to be fully relaxed in NaCl [26].

3. Results and discussion Two experiments have been performed at pressure and temperature conditions up to 8.7 GPa and 973 K, and the experimental P– T paths are shown in Fig. 1. At ambient conditions, the a phase of Ti metal has a unit-cell volume of 35.3 A˚3 or a molar volume of 10.63 cm3/mol and a c/a ratio of 1.586, which are in agreement with previously published values. Throughout this work, the relative standard deviations for the unit-cell volumes are within 0.1% of the refined values for both the a and o phases. With stepwise increases in temperature at selected pressures, the Ti metal remains as an hcp phase at pressures up to 6.0 GPa at 902 K (i.e., heating-cooling cycle ] 4 in

1100 NSLS experiment SPring-8 experiment

1000

(1)

(2) (3)

(4)

(5)

(6)

900 800 Temperature, K

2560

700 600 500 400 300 200 0.0

2.0

4.0

6.0

8.0

10.0

Pressure, GPa Fig. 1. Pressure–temperature paths for the two experiments conducted in this work. All symbols indicate the conditions at which X-ray diffraction data were collected. In the experiment performed at NSLS (solid symbols), the Ti metal was first compressed at room temperature to a desired pressure, followed by stepwise heating to the maximum temperature of 900 K and subsequent cooling to room temperature. The same procedure was repeated several times at progressively higher pressures, as indicated sequentially by the numbers in parentheses. In the experiment carried out at SPring-8 (open symbols), the Ti sample was first compressed at 298 K to the maximum pressure of 7.8 GPa and then heated at a constant loading force. This experiment was cut short due to a thermocouple failure after reaching 973 K.

Fig. 1). On heating at the next higher pressure (heating-cooling cycle ] 5 in Fig. 1), the a-phase Ti was observed to transform partially to the o-phase, which coexists with the a-phase over the temperature range of 900-300 K on cooling. On heating at the highest pressures of the NSLS experiment (heating-cooling cycle ] 6 in Fig. 1), the a-phase transformed completely to the o-phase. Xray diffraction patterns under selected P– T conditions are shown in Fig. 2, indicating that the transition between a and o phases can readily be distinguished by the appearance and disappearance of their characteristic diffraction peaks. The key experimental constraints on the equilibrium a– o phase boundary are summarized in Fig. 3. Fig. 3a shows the phase stability of Ti metal at selected pressure and temperature conditions. For mixed phases of Ti, the relative diffraction intensities, hence the apparent volume fractions, between a and o phases are observed to vary with temperature (Fig. 3b). An inspection of Fig. 3b reveals that with increasing temperature along the experimental path ] 5 in Fig. 1, the a-phase becomes more stable than the o-phase above 700 K, which provides additional constraints on the construction of a– o phase boundary. Based on these observations, the phase boundary is determined to have a dT/dP slope of 345 K/GPa, and the equilibrium transition pressure at room temperature is located at 5.7 GPa, which is 3.7 GPa higher than generally believed in previous studies [6,7,27]. Previously reported transition pressure of 2 GPa at room temperature for the a– o transition is likely due to the shear deformation in the sample [7], which typically leads to the lower transition pressure [14,21,22]. In this regard, the present transition pressure at 300 K should be viewed

ARTICLE IN PRESS J. Zhang et al. / Journal of Physics and Chemistry of Solids 69 (2008) 2559–2563

ω-220

ω-300

ω-200

α-103+ω-300 α-103

α-112

α-110

ω-002

α-112

80

90

100

Fig. 2. Selected X-ray diffraction patterns showing the phase stability of Ti metal at 673 K and indicated pressures, all from the NSLS experiment. An independent experiment conducted at Spring-8 indicates that Ti metal remains as the o-phase at 7.3 GPa upon heating to 673 K.

1200

1.0

0.8

800 α

600

ω

400

ω phase more stable

0.6

0.4

-1.87

0.2

-1.98

Temperature, K

1000

P = 5.7 + 0.0029×(T-300)

Ιω201/ (Iω201+Iα102)

α ω α+ω

Heating Ti

Ti

at 6.1 - 7.2 GPa

200

α-phase more stable

60 70 Energy, keV

-1.87

50

-1.97 -1.88

40

5.60 GPa 673 K

α-110

α-002

Ti

30

ω-201

α-102

ω-111 α-102

α-002+ω-110 α-101

α-100

ω-001

Intensity, a.u.

6.76 GPa 673 K

-1.91

ω-002

ω−111

NaCl-220

ω-110 BN

673 K

α-101

NaCl-200

ω-201

ω−001

7.94 GPa

volume refinements. The average volume change is 0.197 cm3/ mol, and the percentage volume reduction is 1.92%, which is in good agreement with the recent findings of 1.5–1.9% obtained using in-situ X-ray diffraction techniques [14,28]. Based on Clausius–Clapeyron equation for the first-order phase transition, dT/dP ¼ DV/DS, where DV and DS are molar volume and entropy changes of the transition, respectively, we obtain DS ¼ 0.57 J/ mol K. For comparison, DS was previously estimated to be 1.49 J/ mol K [29]. In the experiment performed at Spring-8, the a-Ti was found to be stable on room temperature compression to 7.8 GPa (Fig. 4a). Because Ti metal was surrounded by soft NaCl powders and then contained in a boron nitride capsule, the sample pressure environment can generally be viewed as quasi-hydrostatic. Although no transition was observed in the present experiment at room temperature, our finding appears to support the results of recent experiments under uniaxial loading, which reports an onset pressure of 4.9 GPa for the a-to-o transition without pressure medium (i.e., non-hydrostatic loading) and of 10.5 GPa with an argon pressure medium (i.e., hydrostatic loading) [14]. Upon heating at 7.8 GPa, we observed the a-to-o phase transition at 323 K (Fig. 4b), which was complete within a short period of 6 min (Fig. 4c). These observations indicate that the onset as well as kinetics of the a-to-o phase transition is significantly influenced by a small temperature increment (DT ¼ 23 K!). The pressure difference for the a– o transition at 323 K between the observations of Fig. 3 (P ¼ 5.8 GPa) and Fig. 4 (P ¼ 8.0 GPa) is a kinetically driving phenomenon. Formation of a new phase is typically accompanied by the creation of the interface between new and original phases, which would require energy [30]. For transformation occurred at high pressures, the new phase usually has a different density. This misfit creates elastic stress around nuclei and also consumes additional energy. As a result, the phase transformation cannot start immediately at the equilibrium phase boundary but only after some metastable overshoot in pressure (DP), which provides a sufficiently large driving force (DG) to overcome activation energy needed for transformation to occur. The thermodynamic driving force is described by DG ¼ DVDP, where DV is the volume change upon transformation and DP the difference between the observed pressure of the phase transformation and the pressure at

-1.97

as a more accurate value because it is established from the observations over a temperature range of 300–900 K. The calculated volume reduction across the a– o phase transition is also shown in Fig. 3b, which does not vary with temperature within the standard deviations of the unit-cell

2561

0.0 2.0

4.0

6.0 8.0 Pressure, GPa

10.0

200

400

600 800 1000 Temperature, K

1200

Fig. 3. (a) Experimental constraints of the present study on the a– o phase boundary of Ti metal. (b) Variation of the relative intensities with temperature between the (2 0 1) diffraction line of o-phase and the (1 0 2) diffraction line of a-phase. These observations indicate that with increasing temperature along the experimental path #5 of Fig. 1, the a-phase becomes more stable than the o-phase above 700 K. The numbers next to symbols refer to the percentage differences in molar volume between the oand a-phases, defined as (Vo–Va)  100/Va.

ARTICLE IN PRESS J. Zhang et al. / Journal of Physics and Chemistry of Solids 69 (2008) 2559–2563

Ti

7.96 GPa, 323 K

8.66 GPa 973 K

50

β-310

β-211

β-220

β-200 BN

110

Energy, keV Fig. 4. Selected X-ray diffraction patterns showing the phase stability of Ti metal upon heating at 7.8 GPa. A small temperature increment of 23 K from room temperature results in complete transformation from the a- to o-phase.

equilibrium for a given temperature, also referred as kinetic barrier of the transformation [31]. As expected from kinetic theory of phase transformation, DP decreases with increasing temperature. Our experimental results show that DP is relatively small at 323 K (DPE2.2 GPa), which can be attributed to a small volume change across the a– o transition (DVE1.9%). For comparison, kinetic barriers of phase transition can be substantially larger in other systems such as silicates. Taking the coesite–stishovite phase transition in SiO2 as an example, [23] no transformation can be observed at temperatures below 773 K, primarily due to a substantially large volume difference between the two SiO2 polymorphs (DVE32%) as well as to the large activation energy associated with the Si coordination change from four-fold in the low-pressure phase of coesite to six-fold in the high-pressure phase of stishovite. The key observations for the o– b transition of Ti metal are shown in Fig. 5. Because the b phase is formed by the splitting of alternating (0 0 1) plane along the c-axis of an o structure into two (111) planes of the b-phase, [32] diffraction patterns of the o-phase contain all diffraction lines of the b-phase and some characteristic lines associated its superlattice structure (Fig. 5a). In this work, the transition from the o-phase to the b-phase is identified by the disappearance of the diffraction lines, (0 0 1), (111) and (0 0 2) of the o-phase. Due to the limited pressure range of the current experimental technique, the o– b transition was only studied at one pressure condition for Ti metal. As demonstrated in Fig. 5, at 8.5 GPa, the o– b transition is bracketed between 873 and 973 K. Consistent with the results of previous studies (e.g., Refs. [4,14,28]), the o-phase was retained after cooling and subsequent pressure release, indicating that the o-phase can be quenched as a metastable phase at ambient conditions.

60

80 Energy, keV

100

ω-302

ω-220

ω-111 BN BN

α-004

40

ω-300

ω-201

90

α-112+201

α-103

α-110

α-102

70

ω-110

Intensity, a.u.

ω-001

α-002

7.75 GPa 300 K

α-101 α-100

30

8.36 GPa 873 K

ω-220

ω-300

α-110 ω-002

ω-111

ω-201

7.96 GPa 323 K

α-102

α-101

ω-001

α-100

(a)

BN BN

ω-220

ω-300

ω-002

ω-110

Intensity, a.u.

(b)

ω-111

ΒΝ ΒΝ

ω-001

ω-201

6 min. after pattern (b)

ω-002

ω-110

(c)

β-110

2562

120

Fig. 5. Selected X-ray diffraction patterns showing the transition from o- to bphase of Ti metal on heating. The o-(0 0 1), (111) and (0 0 2) peaks are characteristic lines of o-phase.

The experimental results for the a– o and o– b phase transitions are summarized in Fig. 6 and compared with the phase diagram of Ti commonly referred to in literature [32]. Although the a– o transition at room temperature was previously observed over a wide range of pressures (semi-filled hexagons in Fig. 6), application of shear stress was found to reduce the hysteresis of the a– o phase transformation, allowing the equilibrium transition pressure at room temperature to be estimated at 2.070.3 GPa [6,7]. Such estimated pressure, however, is substantially lower than the present value of 5.7 GPa, determined from the high P– T diffraction data. As a result, the slope as well as entropy change of the transition of previous studies (dT/dP ¼ 93 K/GPa and DS ¼ 1.49 J/mol K) [27,28] are substantially different from the present findings (dT/dP ¼ 345 K/GPa and DS ¼ 0.57 J/mol K). These discrepancies demonstrate that careful studies at simultaneously high pressure and temperature are essential to derive the equilibrium transition pressure at room temperature and thermodynamic properties associated with the phase transformation. The a– b phase transformation in Ti has previously been studied by differential thermal analysis (DTA) up to 4.0 GPa [33] and resistometrically to 8.0 GPa [5]. The o– b transition was also observed up to 12.0 GPa in the latter study, which reported an average slope of 20 K/GPa and a transition temperature of 1023 K at 12.0 GPa. To date, the Ti phase diagram, [27] as illustrated in Fig. 6, is essentially based on the observations of Ref. [5] and an equilibrium transition pressure of 2.0 GPa for the a– o transition at room temperature, [6,7] with an estimated a– o– b triple point at 8.070.7 GPa and 913750 K. Although the present study does not provide sufficient constraints on the a– o– b triple point as well as o– b phase boundary, our observations of the o– b transitions are consistent with the phase boundary determined in Ref. [5]. In addition, the extrapolated pressure to the triple-point temperature (T ¼ 913 K) from our a– o boundary is located at 7.5 GPa,

ARTICLE IN PRESS J. Zhang et al. / Journal of Physics and Chemistry of Solids 69 (2008) 2559–2563

LLC under DOE Contract DE-AC52-06NA25396. The experimental work was carried out at the beamlines X17B2 of the National Synchrotron Light Source of Brookhaven National Laboratory, which is supported by the Consortium for Materials Properties Research in Earth Sciences (COMPRES) under NSF Cooperative Agreement EAR 01-35554, and at the beamline BL14B1 of SPring8, which is supported by Synchrotron Radiation Research Center, Japan Atomic Energy Research Institute.

1400 this study Tonkov, 1992

Ti

ω-phase, this study

1200

2563

β-phase, this study β

1000 Temperature, K

References

800

α

ω

600

α-ω phase boundary: dT/dP = 345 K/GPa ΔV = 0.197 cm3/mol ΔS = 0.57 J/mol K

400

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

Pressure, GPa Fig. 6. Phase diagram of Ti metal. Semi-filled hexagons refer to the onset pressures of the a– o transition previously determined at room temperature [14]. The dash lines denote the phase boundaries of a– b, a– o and o– b transitions of Tonkov [27]. The solid lines indicate the phase boundaries constrained from the present work. The a– o– b triple point was previously estimated at 8.070.7 GPa and 913750 K [27]. Based on our new phase boundary for the a– o transition as well as agreement between the present observations and the boundary determined in the Ref. [5] for the o– b transition, the a– o– b triple point is slightly modified and located at 7.5 GPa and 913 K. The a– b and o– b phase boundaries of Tonkov are adjusted to this updated triple point.

which is comparable to previous estimation. Based on this slightly adjusted triple point (P ¼ 7.5 GPa and T ¼ 913 K) and previous constraints on the phase boundaries for the a– b and o– b transitions, an update and more accurate phase diagram is established for Ti metal, which is shown in Fig. 6. The consistency among the observations of the present and previous studies in the vicinity of the triple point indicates that adequate heating would reduce both the hysteresis and the kinetic barrier of the phase transformation and hence make it easier and more accurate to determine phase transformations near equilibrium conditions.

Acknowledgments This research is supported by the Los Alamos National Laboratory, which is operated by Los Alamos National Security

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