calorimetrically measured enthalpies for the reaction of h2(d2) (g) with ti and ti-ni alloys at 323...

Calorimetrically Measured Enthalpies for the Reaction of HdD2) (g) with Ti and Ti-Ni Alloys at 323 K

W. LUO, J.D. CLEWLEY, and TED B. FLANAGAN

Reaction enthalpies have been measured calorimetrically at 323 K for the reaction 1/2H2 (g) + Ti (t~, hcp) ~ TiHLs and for the partial molar solution of H 2 in the 6 phase. The magnitude of the enthalpy decreases from 68 at H /T i = 0 to 65 kJ/mol H at H /T i = 1.5. The enthalpy continues to slowly fall in magnitude with the increase of H content, and then, for (H/Ti) > 1.9, it fails more precipituously. 2ff/~y(TiH~.5) = - 9 8 . 4 kJ and 2ff-/~y(TiH2) = - 130.3 kJ evaluated at 323 K. No differences in enthalpies were found between H and D. The results are discussed in terms of the existing solvus data for this system, which are important for the quantitative understanding of hydride-induced fracture. Enthalpies of reaction with H2 have been determined for several Ti-Ni alloys which lie in the (Ti(~) + TizNi ) two-phase field. The reaction with H2 initially occurs with the Ti phase and then with the Ti2Ni phase. The enthalpies are similar for the Ti phase as for pure Ti, indicating that this phase is relatively pure Ti. Reaction with the TizNi phase shows a plateau region with an enthalpy of reaction with 1/2H2 of about - 3 0 kJ / mol H.

I. I N T R O D U C T I O N

D E S P I T E the increasing technological importance of titanium and its alloys, some basic thermodynamic data are lacking for its reaction with the ubiquitous interstitial element, hydrogen. Below the eutectoid temperature, titanium-hydrogen forms the 6 phase (Figure 1) Iu if the H saturated ~-Ti is cooled or if H2 is reacted isother- mally with the H-saturated solution. The enthalpy for this reaction with H2 has not been measured directly nor, because of their extremely low hydrogen pressures, has it been determined from Van't Hoff plots of plateau pressures of the two solid-phase region. This enthalpy value is of importance because of its relation to the solvus enthalpy for hydride precipitation in Ti. Stress- induced hydride precipitation is believe to be a significant cause of fracture in titanium and its alloys. For this reason, the thermodynamics of this important system should be established if possible.

As noted previously, over large concentration and temperature regions of the phase diagram, the extremely low equilibrium hydrogen pressures make it impossible to employ the usual pressure-concentration-temperature (p-c-T) method for obtaining thermodynamic data for this system, e.g., below about 650 K and H / T i < 1.0 (Figure 1). Other routes for obtaining thermodynamic data in the low-pressure regions of the phase diagrams of metal-hydrogen systems, such as Ti-H or Zr-H, are consequently of importance. These other methods are as follows:

(1) solvus determinations; (2) calorimetric measurements of the heats of combustion or solution of the hydrides; and

W. LUO, formerly Graduate Student, Department of Chemistry, University of Vermont, is Research Associate, Department of Applied Science, Brookhaven National Laboratory, Upton, NY. J.D. CLEWLEY, Research Assistant Professor, and TED B. FLANAGAN, Professor of Chemistry, are with the Department of Chemistry, University of Vermont, Burlington, VT 05405.

Manuscript submitted September 3, 1992.

(3) calorimetry for the direct reaction of H 2 with the solid phase.

The last method has never been utilized for bulk Ti at moderate temperatures, but data are available at elevated temperatures [21 and for Ti films at 273 K. [3]

Solvus data (the relationship between the terminal solubility of hydrogen (TSH) and temperature) can be determined from the appearance of the hydride phase at various temperatures by changes of an appropriate physical parameter, such as internal friction or electrical resistance, upon hydride precipitation or dissolution. If the nonideality of the hydrogen solution is unimportant, m then the temperature dependence of the solvus gives the enthalpy for transfer of one mole of H from the hydride to the dilute phase: i.e.,

L~knsolv = ]~/plat] "~ ~ [ l ]

where A indicates relative to 1/2H2 at 1 atm. The thermodynamic quantity which will be determined in this research is the first one on the right-hand side of the equal sign and corresponds to Reaction [2]; i.e.,

1 2 H2 (g) + Ti (c0 ~ Tills5 (6) [2]

The last term on the right-hand side of Eq. [1] is the enthalpy for solution of hydrogen in a-T at infinite dilution which can be schematically indicated by the reaction

1 - H2 (g) + Ti (~) ~ [H] in Ti ( a ) [3] 2

If Eq. [ 1 ] is applied where nonideality is a factor, then the derived solvus enthalpy does not have a simple thermodynamic significance. Iaj

The calorimetric method employed here gives enthalpies which are unaffected by hysteresis, IS1 and therefore, when its value, A/4o~a, is employed in Eq. [1], a so- called "unconstrained" solvus enthalpy should result, t6j According to Puls, t61 this should also correspond to the

METALLURGICAL TRANSACTIONS B VOLUME 24B, OCTOBER 1993-- 867

:x5

!1oo

/

700

'-I ~nr 573 K

5 0 0 [

3QO / I I 0 Q2 0.4

/ / /

\ / / / \ / \k..// / J / 0.64 1.05 ~ ~

\ \ ct+ ~ \ \

0 .6 0.8 1.0 1.2 1.4 1,6 i .8

H / T i

Fig. 1 - - T h e phase d i ag ram for t i t an ium-hydrogen , m

solvus enthalpy determined when the hydride phase dis- appears, i .e . , during heating. Models where the hydride phase is considered to be an inclusion in the surrounding metal matrix have been employed, e .g . , by Puls, 161 to discuss the effect of elastic and plastic constraints on the solvus thermodynamics. When Z~k/-/plat is determined by reaction calorimetry, relatively large amounts of hydride phase form as compared to the situation for most solvus measurements. If the experimental value of AHso,, is compatible with the calculated value using Eq. [1] and the calorimetric value of AHplat, then it seems that there is no basic difference between the thermodynamics of hydride formation (or dissolution) when only a very small amount of hydride phase forms (as in solvus measurements) or when relatively large amounts are present (as in calorimetric measurements). If this is the case, then elastic constraints, which are unimportant for the latter conditions, are also unimportant for the former conditions.

II. EXISTING THERMODYNAMIC DATA

The TSH results for Ti-H given by Paton et al . 171 lead to AHso~v = 18.6 kJ /mol H with no difference found between heating and cooling although the TSH values themselves are greater for the former, and consequently, the solvus enthalpies should differ but the data are ap- parently not accurate enough to detect any differences. On the other hand, they did find a large difference between the solvus enthalpies for heating and cooling for Ti0.9oA10~0 - H. In his analysis of the solvus results for Ti-H, Puls t6J employed the data of Paton e t a / . [7] for Ti0.9oAlo.z0 finding AHso~v --- 18.26 kJ /mol H from their heating data and 10.23 kJ /mol H from their cooling data, Ivl Vitt and Ono tSJ found a value of 18.7 kJ /mol H for Ti-H, but when their data, the data of Paton and co- workers, [7J and the data of Krster et al. ~91 are fit by a common least-squares line, they obtain 21.0 kJ /mol H. This fit includes data for both heating and cooling. Numakura and Koiwa u~ used internal friction measurements to obtain TSH data, and they found a large hysteresis with AHso~v = 31.5 (heating) and 27.4 (cooling) kJ /mol H. Values about 2 kJ /mol H smaller were found

for D. These are considerably larger than the values found from the resistivity results of Paton et al. ~71 and Vitt and Ono Isj The data of Numakura and Koiwa for cooling fall, more or less, among the results of other investigators, but their heating data fall much lower and, although they state that they agree with those of Krster et al.,19J much of the data of Krster et al. were omitted in the comparison. If the internal friction data of Numarkura and Koiwa u~ are examined, it would seem difficult to select a temperature for hydride decomposi- tion during heating; the temperature where hydride forms during cooling seems less ambiguous. It is concluded that the TSH data based on techniques other than internal friction are probably most reliable, at least for the results obtained during heating. The solvus data, which Kivilahti and Miettinen l~} determined from all of the available thermodynamic data for this system for their calculation of the phase diagram, have considerably greater H contents than the experimental values.

With regard to the thermodynamic values on the right- hand side of Eq. [ 1], Mrowietz and Weiss u21 obtained a value of -46 .01 kJ /mol H for ~ from p-c -T data from 773 to 1 123 K using pressures which were corrected for the effects of thermal transpiration. They also reviewed the results in the literature up to 1985 for A/-~H. More recently, Kivilahti and Miettinen, u~l who used available thermodynamic data to compute the phase diagram of the Ti-H system, concluded for AH~ that the results of McQuillan t~3j and Veleckis and Rogers t141 using the p - c - T method are probably the most reliable and Dantzer 's results from calorimetry 121 must also be judged to be reliable; they remarked, however, that Dantzer 's value may have been influenced by residual hydrogen in the Ti. In any case, they chose a value of

= - 4 6 . 8 kJ /mol H for infinite dilution of hydrogen. This is actually close to the average of all of the values which have been determined and to the value reported by Mrowietz and Weiss u21 and the value of - 4 5 . 3 kJ /mol H recently obtained by Yamanaka. uSl

Relative to A/-/~ there are few values of AHp~,~ available for Reaction [2] to employ in Eq. [1]. At temperatures _>737 K, Dantzer 121 carried out a valuable, detailed reaction calorimetric investigation of this system using bulk Ti. This study illustrates the power of the calorimetric method for delineating phase boundaries, etc. A value for AHp~a~ for Reaction [2] equal to -63 .1 kJ /mol H is obtained if we integrate Dantzer 's t21 calorimetric enthalpies at 737 K after their correction to 298 K using the Einstein model for the heat capacity of H in the solid. Frornm and Gebhardt t~61 derived from McQuillan's p-c -T data a value of AHp~a, = - 6 6 . 9 kJ /mol H tl3] which is based upon data for different phases at higher temperatures.

Methods which rely on heats of combustion or solution of the metal hydrides are time consuming, requiring a separate sample which is consumed during each determination. The combustion method was employed by Stalifiski and Biegafiski. I~71 They reported values for different stoichiometries in the range from TiH~.6o7 to TiHl 974. The magnitudes of these values decrease nearly linearly with r = (H/Ti) from 71.1 to 62.6 kJ /mol H with a value of 74 kJ /mol H for r = 1.5.

868- -VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B

The calorimetric method has not been previously employed in the moderate temperature range with bulk Ti because of the belief that this gas-solid reaction would not be facile enough under these conditions to allow reaction calorimetry to be successfully carried out. Wedler and Strothenk, TM however, performed reaction calorimetry at 273 K for this system using Ti films. They find a minimum in the magnitude of the enthalpy at r --~ 0.05 which they believe corresponds to solution in the a phase and then the enthalpy increases in magnitude to 63 kJ /mol H at r = 0.35; the values then fall, reaching 60 kJ /mol H at r = 1.45, and there is then a more abrupt decline in magnitudes. The average value for Reaction [2] is then - 6 1 . 5 kJ /mol H which is somewhat smaller in magnitude than the other values which have been reported.

III. RESEARCH TO BE CARRIED OUT

In this research, we will undertake an investigation similar to that done with Ti films by Wedler and Strothenk TM in the moderate temperature range below the eutectoid where the a, 6, and e phases exist, t~l The only reaction which occurs below the eutectoid temperature in the range of stoichiometries from r ~- 0 to 1.5 is Reaction [2] where the hydrogen concentration in the dilute phase is essentially zero according to the most recently compiled phase diagram, t~l After complete formation of the 6 phase, further hydrogen dissolves in it and then finally it dissolves in the e phase (Figure 1).

In this proposed research, bulk rather than films of titanium will be employed; we have found that hydrogen will readily react with the bulk form at room temperature provided that it has been previously hydrided and dehydrided several times at elevated temperatures.

In the Ti-rich part of the phase diagram for Ti-Ni, a two-phase field of a-Ti and Ti2Ni is shown below 1043 K without an indication of any solubility of Ni in Ti. t~Sl In this research, we have prepared several alloys in this two-phase field and characterized them through their reaction with H2 utilizing the calorimetric enthalpies and the equilibrium hydrogen pressures. We have recently carried out similar experiments in the two-phase field of (Zr + ZrMn2) and found that H2 readily reacted with the Zr phase at moderate temperatures ~9~ whereas it does not react with pure, bulk Zr unless the metal is activated by hydriding and dehydriding at elevated temperatures. It has been reported t2~ that Ti2Ni reacts slowly and irre- producibly. The highest (H/Ti2Ni) ratio reached at room temperature was 2.7. t2~

IV. EXPERIMENTAL

Titanium of 99.99 pct purity (from Aesar Inc., Ward Hill, MA) has been employed for this investigation. It was hydrided in situ within the calorimetric vessel. A 0.6 g sample of Ti was mixed with copper powder and placed into the reaction cell; the blank cell of the calorimeter contains the calibration heater and copper powder of about the same heat capacity as the (Ti + Cu) on the reaction side.

A heat-leak twin cell differential calorimeter was employed for this research. The two cells are quite closely matched thermally. In order to demonstrate this, electrical heaters of equal resistance were placed in each of two dummy cells which were replicas of those actually employed. They were placed in the calorimeter block and connected in series, and when a current was passed through them, no signal was detected. This demonstrates that the two cells are very closely matched thermally.

The cells could be removed from the massive A1 block of the calorimeter and reinserted into the block repro- ducibly, i .e. , with respect to the calorimetry. This re- moval is essential for the activation of the sample. The first activation was difficult, and the sample had to be evacuated at ~673 K to a vacuum of ~ 10 -4 Pa, exposed to several atmospheres of H2 (g), and then re-evacuated. The sample was hydrided to the stoichiometry Till2 in situ at ~823 K and then dehydrided at 823 K by evac- uation for various times up to 12 hours. This procedure was carried out several times until the sample was suf- ficiently active to absorb hydrogen rapidly at room temperature. One sample was evacuated at 1000 K after activation, but there seemed to be no difference in its final H content after complete hydriding and the contents of the others which had been evacuated at 823 K, indicating that at 823 K, almost all of the H had been removed prior to the calorimetric runs. A dose of hydrogen was generally completely absorbed in about 5 to 10 minutes near room temperature. The time for the two cells to thermally equilibrate was about 50 minutes, i.e., the time for a calorimetric determination.

Once the hydrogen was absorbed by the solid phase, chemical processes within the solid no longer gave rise to any heat evolution. This was clearly seen in the recorder tracings of a few runs which were relatively slow, because when their hydrogen pressures fell to zero, the recorder tracings, AT, exhibited concomitant changes: i.e., the slow decay of the signal was determined only by the heat conduction. In the first plateau region for the V-H system, it was found that internal processes gave rise to a heat evolution even after the hydrogen had been completely absorbed by the metal. I2~J

Thermal analysis was carried out (PERKIN-ELMER*

*PERKIN-ELMER is a trademark of Perkin-Elmer Physical Electronics, Eden Prairie, MN.

DSC-4) using foil samples which had been loaded vol- umetrically from the gas phase. For each determination, several different samples were analyzed from the same H-loaded specimen and the average values were employed.

The Ti-Ni alloys, Ti0.833Ni0A76 and Tio75Nio.25, were prepared by arc-melting the pure components. The resulting buttons were annealed for several days in vacuo at 1000 K.

V. RESULTS AND DISCUSSION

A. Ti-H Solvus

The solvii for systems, such as Ta-H, Pd-H, and V- H, exhibit deviations from linearity when the data are plotted as In a against T -~ in the temperature region of

METALLURGICAL TRANSACTIONS B VOLUME 24B, OCTOBER 1993--869

the plots where the values of a are greatest and the nonideality of most importance, m22-24] This nonideality arises principally from the H-H interaction in the dilute phase of these systems; equations have been given to allow for this influence provided; that the extent of nonideality is known from experimentJ 4J It has been im- plicitly assumed by previous workers that the solvus plots for the Zr-H and Ti-H are unaffected by nonideality and that therefore the slope of In a plotted against T - accurately represents the enthalpy for the transfer of one mole of H from the hydride to the dissolved state (Eq. [1]). In this research, we wish to examine this assump- tion for Ti-H in some detail because it has been shown that this is not the case for some other metal-hydrogen systems. [4,22 24]

The nonideality in the a phase (hcp) has been evaluated by Kivalahti and Miettinen, [11] who give the follow- ing equation derived from evaluation ofp-c-T data in the literature:

a /x~ = [27,300 - 28.6T] 2 (J /mol H) [4]

for the excess chemical potential in this phase. I f this equation is employed for the calculation of the difference between the ideal and experimental value of log a, the dashed line is obtained, as shown in Figure 2 where the TSH data of literature data are plotted. It can be seen that there is very little difference between the ideal and experimental data, indicating that the role of nonideality

l t.O

X ce "~

1.5 - ~o~, " ~ N

S

2.5 - a A X ~

\ 3.O I I I

1,7 2.0 2.5 3.0

( 1 / T x I O S / ( K -1)

Fig. 2 - - T h e solvus plot for Ti-H. Filled symbols during heating and open ones during cooling. V, present data; 4, Ref. [7]; D, Ref. [9]; �9 Ref. [8].

is small, at least according to Eq. [4] given by Kivalahti and Miettinen, who analyzed hydrogen solubility data above the eutectoid temperature. The difference between this metal-hydrogen system and some others, where nonideality is an important factor leading to nonlinear plots of log a against T-I, [4'22-24] is that both the H-H interaction enthalpy is more negative and the temperature range is higher for this system (Figure 1) as compared to the others. For example, the solvus plot for the Pd-H system commences to deviate from linearity at a = 0.0045 (235 K). At this H / P d value, the calculated deviation of In a from its ideal value is 6 pct using the expression for nonideality of H given by Kuji et al. [2sl or 5.6 pct using the nonideal terms given by Wicke and Nernst. t26j The deviation for Ti-H at the same value of a, which now occurs at 350 K, is only 0.5 pct based on Eq. [3]. H~l This means that the solvus plot for Ti-H should yield a thermodynamically significant solvus enthalpy; i.e., Eq. [1] should be valid.

In this research, two different specimens were employed and the results are shown in Figure 2 along with the other solvus data. The two data points, which are at relatively high temperatures, are shown by the filled and empty V symbols which agree quite well with those from References 8 and 27 in the same temperature range. There is seen to be a significant hysteresis, as shown by the filled (cooling) and empty (heating) symbols. Using all of the solvus data available from both heating and cooling results (Figure 2) a value of M4sojv = 22.9 kJ /mol H is obtained. (Since we want to use a value of zSJ-/solv unaffected by hysteresis for use in Eq. [ 1 ], we employ the average solvus enthalpy for both the heating and cooling data).

B. Hysteresis of the Eutectoid Reaction

In their assessed phase diagram, San-Martin and Manchester u] report the eutectoid reaction to occur at 573 K based on the results of McQuillan t13] and Beck I281 although they show it as a dashed line on the phase diagram which indicates that, in their opinion, some experimental uncertainty exists in the value. Thermal analysis LeTI using heating and cooling rates of 1 ~ per minute gave 592 and 554 K, respectively, but San- Martin and Manchester m believed that these rates are too large and therefore the results are suspect. Veleckis and Rogers u4j extrapolate the (a + /3) and (/3 + 6) Van ' t Hoff lines, finding that they intersect at a eutectoid temperature of 554 K which corresponds with the cooling value found by Lenning et al. t27] In their phase diagram synthesis from thermodynamic data, Kivilahti and Miettinen u ~] arrived at a eutectoid temperature of 553 K.

It seems timely to repeat determinations of this eutectoid temperature using modern thermal analysis equip- ment. In the present investigation, 10 different TiHr samples with values of r in the range from 0.154 to 1.0 were prepared by loading foil or, in one case, powder Ti with H from the gas phase. Each sample was then heated and cooled at specified rates several times over the temperature interval from 475 to 675 K. The eutectoid reaction was clearly shown by an endothermic peak during heating and an exotherrnic peak during cooling (Figure 3). The onset of the peak was chosen as each

870--VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B

L) W tO

,I (9 E

10.00 --50~

20 .00

J 0 ,00 I I I I I I I I I I

210 230 250 270 290 310 330 350 370 390

T (':'C)

Fig. 3 - -Di f fe ren t i a l scanning calorimeter scans for a 17.08 mg specimen of TiHo.466 during its heating (endothermic) and subsequent cooling (exothermic). A thermal hysteresis of 50 ~ is shown.

transition temperature in accord with standard practice. The 10 different samples of different compositions gave 595 -+ 1 K for heating and 545 - 2 K for cooling with no trend found with r. Scans were carried out at 5, 10, 20 and 40 ~ m -1, and there was no systematic difference in the transition temperatures observed with the different scan rates; therefore, the objections to the results of Lenning et al. [271 raised by San-Martin and Manchester lq do not seem to be valid. These two temperatures for the eutectoid transition give a thermal hysteresis of 50 deg; Lenning et al. [271 reported a 38 deg hysteresis with 592 and 554 K as the heating and cooling temperatures, respectively. The former is in good agreement with the present value, but the latter is somewhat larger. The average of these values corresponds rather closely to the value 573 K given by San-Martin and Manchester. ul The value of 554 K, which Veleckis and Rogers tl4~ obtained indirectly, corresponds to the cooling value obtained by Lenning et al. t27~ It is now clear that there is a large hysteresis for the eutectoid reaction.

C. Calorimetric Data for Ti-H

Calorimetrically measured enthalpies as a function of r are shown in Figure 4 (323 K) for Ti-H and Ti-D. As noted in the Introduction, the calorimetric values are not directly affected by hysteresis, as has been shown ex- perimentally; ~SJ the values shown in Figure 4 have all, however, been determined during absorption. The equilibrium hydrogen pressures are too small to measure at the temperature of the calorimetry (50 ~ except for one or two determinations at the highest hydrogen contents. The enthalpy for the plateau (Reaction [2]) falls in magnitude steadily with r from about 67.5 to 64 kJ /mol H from r = 0 to 1.9, and it then declines more abruptly as r approaches 2.0. It should be noted that 40 or more determinations were carried out with several samples across the plateau region, r --< 1.5. The (a + 6)~6-phase boundary is located in Figure 1 at r = 1.5, and it is apparent that there is no marked change in the enthalpy at this boundary. This is in keeping with the shape of the phase boundary shown in the phase diagram; i.e., it is nearly vertical at the temperature where the determinations were made, although the shape is rather uncer- tain in this region. A vertical boundary requires that the

; ! __ . T

I 6 0

E

< ] 5 O

4 0 - - ~ I i i I ~ I 0 0 , 4 1 . 6 2 . 0

} i I

0 . 8 1 . 2 H ( D ) / T i

I

Fig. 4 - -Ca lo r ime t r i c enthalpies for Reaction [2] showing four separate sets of determinations using two different Zr samples (323 K). The arrows show where sample were heated to 623 K and to 750 K between the calorimetric determinations. The filled symbols refer to Ti-H and the empty ones to Ti-D.

thermodynamic parameters are continuous across the boundary. For r ----- 1.5, the reaction corresponds to a solution of 1/2H2 in the 6 phase and the enthalpy change becomes a relative partial molar one. Several different series of runs were made with both H and D, and there is no discernable difference seen between the two iso- topes (Figure 4).

During the calorimetric determinations, the cells were removed from the calorimeter block at the H content r = 0.57 and the cell which contained the sample was heated briefly to 623 K, i.e., to above the eutectoid temperature. The cells were then reinserted into the alumi- num calorimeter block, and the calorimetry was continued. This heating treatment had no effect on the subsequent calorimetric results. The heating procedure was employed again at r = 1.25, but in this case, the sample was heated to 750 K, and again there was no obvious effect on the subsequent sloping of the AHpla, values. It can be concluded that the morphology of the H-containing phases within the Ti resulting from the pro- gressive loading of the Ti with H from the exterior of the sample from the gas phase is not the source of the decline in I~plat[ values. This also suggests that sloping is not due to elastic stresses building up during conversion to the hydride phase because they should be elim- inated during the heating and recooling procedure. In the calorimetric results reported by Wedler and Strothenk p] for Ti films, a decline of enthalpies is also found. In principle, the plateau enthalpies (to r -- 1.5) should be invariant and we have no explanation for their decrease in magnitude. The initial value as r ~ 0 of IAHp~a,I for Reaction [2] is 67.5 kJ /mol H, and the average over the interval from r = 0 to 1.5 is 66 --- 1 kJ /mol H. The values are actually rather constant, 65 kJ /mol H, in the composition range between r = 0.6 to 1.5.

If Dantzer 's t2] enthalpy values, obtained above the eutectoid temperature, are integrated from r = 0 to 1.5, f~.5 AHHdr, where r = H/Ti , we obtain a value of - 9 7 . 6 kJ /mol for AHOy(Till15). In order to compare Dantzer 's value with the present results the former


should be corrected for the difference in temperatures between the two determinations, but the heat capacity data for Ti-H do not extend beyond about 363 K [17] so

we have employed the Einstein model with the vibra- tional frequency of hydrogen determined from inelastic neutron scattering to estimate the heat capacity correction. This correction gives M-/?(TiH1.5) = - 9 4 . 6 kJ (298 K). The present data give M-/~y(TiH~5) = - 9 8 . 4 kJ at 323 K; a negligible difference between the enthalpies of formation at 298 and 323 K is expected on the basis of the heat capacities. For Till2, we obtain AH?(TiH2) = - 1 3 0 . 3 kJ at 323 K compared to Dantzer 's value of - 1 3 3 . 0 kJ after correction to 298 K. San- Martin and Manchester lu give values of - 1 2 3 . 4 and - 144.35 kJ /mol for A/-/~y(TiH2) at 298 K from Stalinski and Bieganski I~7~ and derived by them from the results of Sieverts and Gotta, [29~ using an extrapolation based on the data of G i b b e t al.,13~ respectively. It can be seen that these two values bracket both the value obtained here and Dantzer 's value.

If the present value of AHplat = - 6 7 . 5 kJ /mo] H (as (H/Ti) --* 0) is employed in Eq. [i] and - 4 5 . 3 for A/~H, then AHsolv = 22.2 kJ /mol H, which is close to the experimental value of 22.9 kJ /mol H obtained from the solvus plot (Figure 2). This indicates tbat the solvus data are ideal and, consequently, meaningful thermodynamic data can be obtained from the slope of the solvus plot (Figure 2); e.g., the solvus enthalpy corresponds to the transfer of one mole of H from the hydride to the dilute phase. It also suggests that the value of AHplat which we have obtained is a reasonable one. This also indicates that there is essentially no difference in the thermodynamic values for the solvus as (H/Ti) ~ 0 determined from physical changes and the thermodynamic parameters which apply for the plateau Reaction [2] which occurs at larger amounts of hydride conversion and where models of hydride occlusions are not expected to be validJ 6I The small decline in IAHp~a,I (Figure 4) is not believed to be related to changing amounts of elastic vs plastic accommodation because of the results of the "stress release" experiments noted previously, i.e., the results indicated by the arrows in Figure 4.

D. Enthalpy for the Eutectoid Reaction

The enthalpy change for the eutectoid reaction can be determined from thermal analysis: i.e., the area of the scan for the transition gives its enthalpy (Figure 3). At the eutectoid composition of (H/Ti) = 0.64, we obtain for the transition enthalpy, IAHt, I = 4.7 + 0.5 kJ /mol Ti; the same values are obtained for both the heating and cooling transitions. This value is related to the thermodynamic parameters for reaction with H2. Thus, it can be shown that at the eutectoid composition, the enthalpy for the eutectoid transition (reaction) is given by

AHt~ = (b - a) [~f-/plat(O{ --~ /3) - - ~ p l a t ( C ~ -"'> 8)] [5]

Using AHp~at(a --> /3) = - 5 3 kJ /mol H from Veleckis and Rogers u41 and AHplat(a --> 6) = - 6 6 kJ /mol H from the present work, we obtain from Eq. [5], using b = 0.64 and a = 0.072 (from Figure 1), AH,, = 7.4 kJ /mol Ti which is about one-half of the experimental value of

14.7 kJ /mol Ti. Mrowietz and Weiss us found a value for AHplat(a --> /3) = - 5 7 . 6 kJ /mol H from p-c-T data (773 to 1298 K); this gives even poorer agreement with the experimental value for AH,r. If different values of b and a are used, e.g., those employed by Kivilahti and Miettinen, EIu the agreement with the experimental value is somewhat better but still poor.

Experimental values of AH,, have been obtained for the 10 different compositions of Till, used for the determination of the eutectoid temperature. These transition enthalpies were all too large in comparison to the predictions of an equation similar to Eq. [5] but with r substituted for b. The discrepancy is puzzling and may be related to a larger than anticipated error in the value of AHp~a,(c~ --*/3) and to a large uncertainty in the value of b.

E. Ti-Ni Alloys

When doses of Hz are added to the two-phase alloys, Ti0.833Ni0J67 and Ti0 75Ni0.25, they should first react with the Ti phase present and then with the TizNi phase. This means that the equilibrium pressures will initially be negligible, i.e., they should correspond to the plateau pressure for the (c~ + 6) two-phase region of Ti. If the Ti phase is pure, then the enthalpies corresponding to Eq. [2] should have the same values as for pure Ti (Figure 4). Figure 5 shows some results for Ti0.83Ni0.~7 at 323 K. The pressures are too small to measure below about H / M = 1.2, but for greater hydrogen contents, they were measured. The enthalpies of reaction from r = 0 to 1.0 are similar to those for pure Ti, indicating that the Ti phase must be nearly pure (Figure 5). After the Ti phase is fully hydrided ( H / M = 1.0, Figure 5), the Ti2Ni phase commences to be hydrided and the magnitude of the enthalpy of reaction falls. It appears to be about - 3 0 kJ /mol H in a plateau region for the TieNi region.

This region is enlarged in Figure 6 where data are shown for a Ti0.75Ni0.25 and a Ti0.833Ni0J67 alloy at 323 K. The experimental data have been evaluated on the basis of the amount of the Ti2Ni phase present in each alloy. For example, in one mole of Ti0.s33Ni0J67, there are

3 F

8 0 k �9 5 i

Ti H 2

?~176176176176176176176176176176 o o z 6 o . ~ 1 7 6 1 7 6 1 7 6 1 7 6 o ~ 4

- ~ 4 0 �9 3

0 <] ~ 0 --

- - i I ~ 0 O 0

2 0 L o o

b i I

0 L 01,2 ~ I. _ t L I 11.4 Q 0 . 4 0 6 0 8 1 .O 1 . 2

HIM(TI NI ) �9 83 ,I 7

Fig. 5- -Ti t ra t ion calorimetry of Ti0 83Nio.z7 with H2. The filled symbols are the equilibrium pressures and the open symbols the enthalpies.

872--VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B

8 0

'35 "6 6O

E

T

_!_< 4o t

O.0

D

O

| ' C30

OGO,' 0

1'

o l e , O ~ " ~ ~,,/

. , - 0 - �9 . l "

,e~D O QOO O O ~O

O

Q,

O�9

i'.o Lo 3'.0 H/Ti2Ni

5.0

4.0

3.0

2s

Fig. 6- -T i tra t ion calorimetry of Ti0.83Ni0.17 (C)) and Ti075Ni0.25 (~) with H2. The H contents for both alloys have been expressed as the reaction of the Ti2Ni phase with H2. The filled symbols are the equilibrium pressures and the open ones the enthalpies.

0.167 moles of Ti2Ni, and therefore, after Till2 forms in this alloy, the experimental data are multiplied by a factor of (1 /0 .167) to express the data as H/Ti2Ni (Fig- ure 6). The results for the two alloys are seen to agree quite well. The lower pressure points with the dashed line through them correspond to those which were al- lowed to equilibrate for 12 hours, indicating that equilibrium is established very slowly. The plateau region of the pressures corresponds to enthalpies of about - 30 kJ/ mol H. Attempts to carry out calorimetry directly with Ti2Ni were unsuccessful because of the slow rates.

VI. CONCLUSIONS

The enthalpy for the reaction of a-Ti with H 2 has been measured directly by calorimetry across the two-phase region at moderate temperatures. The magnitude of the enthalpy is found to decline with conversion to the hydride phase similarly as found for Ti filmsJ 3] This should not occur in the ideal case, because the reaction would be the same across the two-phase coexistence region, i.e., Reaction [2]. It is not due to the morphology of the two phases, since heating above the eutectoid temperature and subsequent cooling yielded the same decline. The average magnitude from 0 to r = 1.5 is, 66 kJ/mol H, and z~f(TiH2) = - 1 3 0 . 3 at 323 K.

Two-phase alloys (Ti + Ti2Ni) have been reacted with

H2, yielding enthalpies of reaction for the Ti-rich phase and for the Ti2Ni phase (323 K).

A C K N O W L E D G M E N T

The authors thank H. Noh for preparation of specimens for thermal analysis.

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calorimetrically measured enthalpies for the reaction of h2(d2) (g) with ti and ti-ni alloys at 323...

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