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Kinetic study of the hafnium-hydrogen reaction
Journal LCM
of the Less-Common
Metals,
219
175 (1991) 219-234
1280
Kinetic study of the hafnium-hydrogen
reaction
Y. Levitin and J. Bloch Nuclear
Research
Center
-
Negev,
PO Box 9001, Beer-Sheva
(kra&
M. H. Mink Nuclear Research University
Cater of the Negev,
- Negev, PO Box 9001, Beer-Sheva Department of Nuclear Engineering,
and Ben Gurion PO Box 653, Beer-Sheva
clsraeu
(FIeceived January 7, 1991)
Abstract The kinetics of hafnium hydride formation were studied utilizing conventional rate measurements (Sieverts system) combined with metallographic examinations of partially hydrided samples. The rate measurements were performed at 700 TorrH, over a temperature range 200-550 “C. Two types of hafnium samples (polycrystalline and crystal bar) were compared. The progression of the massive stage of the reaction is characterized by a contracting-envelope morphology with a constant hydride front velocity. The anisotropy in the reaction front velocity regarding different crystalline orientations of the metal is small, resulting in similar results for the different types of hafnium. The temperature dependence of the front velocity obeys an Arrhenius-type relation over the temperature range 250-450 “C, with an apparent activation energy of 0.50*0.05 eV. Considering a diffusion-controlled model, a diffusion activation barrier of about 0.4 eV is evaluated, which agrees with the average reported value for the diffusion of hydrogen in hafnium hydride. At temperatures above about 500 “C, deviations from the Arrhenius relation are displayed, possibly owing to a change of mechanism.
1. Introduction Group IVb metals (titanium, zirconium and hafnium) form hydrides containing very high volume densities of hydrogen (NH = 9.1 X 10z2, 7.3 X 1O22 and 7.6 X 1O22H atoms cm-3 for titanium, zirconium and hafnium respectively). These hydrides have some applications in nuclear technologies [ 11. The phase diagrams of the corresponding metal-hydrogen systems display certain similar characteristics and systematic trends [ 1 ] : (1) the formation of f.c.c. non-stoichiometric hydrides in the low temperature regions of the phase diagrams (the so-called a-phase for the Ti-H system and the 6 phase for the Zr-H and Hf-H systems) which transform into f.c.t. structures upon additional absorption of hydrogen - this transformation is probably second order in the Ti-H system and first order in the Zr-H and Hf-H systems (the formation of the so-called E phase); (2) eutectoid decomposition of the low temperature f.c.c. hydrides, occurring in the high temperature regions of the phase diagrams - the eutectoid transition temperatures display a systematic trend, increasing with
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0 1991 -
Elsevier Sequoia, Lausanne
increasing atomic number of the metal (about 280 “C for TCH, 550 “C for Zr-H and actually no transition has been observed in the Hf-H system up to 900 “C). Besides these systematic trends in the M-H phase diagrams, there is also a systematic behaviour in the structural misfit between the f.c.c. hydrides and the parent metals (volume expansion v /vM of 24%, 17% and 15% for the titanium, zirconium and hafniurn f.c.c. hydrides respectively). It is thus interesting to compare the kinetic behaviour of the corresponding metal-hydrogen reactions within this group and establish if some trends exist regarding the mechanisms controlling the hydride formation. The kinetic parameters which should be compared must characterize the intrinsic nature of the reaction as defined in ref. 2. These parameters may be evaluated by a careful kinetic study of well-defined geometrical shapes of the reacting samples incorporating conventional rate measurements with metallographic examinations of partially hydrided samples [ 2, 31. Such a study has recently been made on the titanium~hydrogen reaction [3] within the temperature range below the eutectoid decomposition (25-250 “C). In the present work the kinetics and mechanism of hafnium hydride formation are studied. The corresponding study of the zirconium~ hydrogen reaction and the comparison within this group of metals will be published in a separate paper [4). 2. Experimental
details
2.1. The apparatus A conventional constant-volume glass-made Sieverts system was utilized for the overall rate measurements. The time dependence of the pressure drop in the system due to the reaction was continuously recorded. The weight of the reacting sample was adjusted so that the total pressure change at the completion of the reaction would not exceed approximately 10% of the applied initial pressure in order to attain the kinetic behaviour under almost constant-pressure conditions. It is note worthy that the equilibrium pressure of the hydride in the uppermost temperature range studied in the present work is less than 0.1% of the applied hydriding pressure. Under such conditions the pressure dependence of the kinetic parameters is quite small and the 10% variation in pressure is not anticipated to induce any significant changes in the reaction kinetics. Temperature control was achieved with a chromel-ahunel thermocouple placed against the outer wall of the quartz reactor. In some experiments another thermocouple was inserted inside the reactor, touching the hafnium specimen. In no case did the difference between the readings of the two thermocouples (resulting either from temperature gradients across the reactor or self-heating due to the exothermic nature of the hydriding reaction) exceed about 10 “C within the studied temperature range (250-550 “C). To prepare partially hydrided samples, the reaction was allowed to proceed to some predetermined extent (at a certain temperature), then
221
hydrogen was quickly (within a few seconds) evacuated cooled to room temperature. Metallographic examinations on the partially hydrided samples.
and the sample were performed
2.2. Specimens Two types of hafnium samples were studied, a polycrystalline rod and a crystal bar. Both types were of about the same purity, the dominant contamination as detected by chemical analysis being zirconium (1.7% in the rod and 1.5% in the crystal bar). The main difference between the two types was in their microstructure, as demonstrated in Fig. 1. The polycrystalline rod was characterized by small (10-30 pm) regularly shaped grains whereas the crystal bar consisted of very large (l-3 mm) grains. Hence the results observed for the former samples represented an average over all crystalline orientations whereas the crystal bar samples represented an assembly of a very few single-crystal orientations. This difference will be discussed further in the following sections. For each of these two types of hafnium, samples with well-defined geometrical shapes were prepared by saw cutting the original rods. Two types of geometrical shapes were utilized, discs with a diameter of 5 mm and a thickness of about 0.5 mm, and cubes of about 2X 2X 2 mm”. The analysis methods of the kinetic data obtained for these geometries are described in Section 2.4. 2.3. Experhental procedure In order to attain reproducible hydriding kinetics and to eliminate initial induction periods (which under certain experimental conditions are so long that they practically impede the initiation of the reaction), the samples were
Fig. 1. Metallographic
pictures of (A) polycrystalline
and (B) crystal bar hafnium samples.
thermally activated by vacuum (about 10e6 Torr) annealing at 900 “C for 2 h. This thermal activation affects mainly the characteristics of the thin surface passivation layer, increasing its permeability to hydrogen [5, 61. It should be remembered that for certain metals high temperature annealing may affect not only the surface layer properties but also the bulk microstructure [3, 61, introducing in some cases changes in the measured kinetic parameters [6]. However, in the present case, owing to the very high melting point of hafnium, no such changes were introduced by the applied thermal pretreatments. It is interesting to note that unlike titanium [3] and uranium [5, 61 where pretreatment temperatures of about 450 “C or below were sufficient to activate the samples, for hafnium much higher temperatures were needed. After the vacuum pretreatment the samples were cooled to the desired reaction temperature (in the range 250-550 “C) and high purity hydrogen at a pressure of about 700 Torr was admitted. The reaction usually initiated immediately without significant induction periods. For planar samples (discs) the reaction kinetics followed a linear time dependence over most of the reaction course (about lo%-90%) whereas for the cubes a non-linear time behaviour was observed (as demonstrated in Fig. 2(a). Both geometrical shapes, however, fitted contracting-envelope progression kinetics with a constant hydride front velocity, as discussed in Section 2.4. The use of two different geometrical shapes (i.e. discs and cubes) of samples had two reasons. First, it confirmed the validity of a contractingenvelope constant-velocity-type progression of the reaction (see Section 2.4). Secondly, the initial deviations of the reaction kinetics from a contractingenvelope time dependence (eqns. (1) and (2)) occur within a certain reaction range corresponding to the establishment of a product hydride layer with a minimum thickness X0 (which may be temperature dependent). In order to obtain the contracting-envelope-type kinetics over the largest possible reaction range, it is desirable that X,/L -K 1, where L is the initial thickness of the sample. From this point of view it is beneficial to utilize samples with relatively large thicknesses.However, since the largest diameter of the sample is limited by the design of the reactor (which in our system was about 5 mm), increasing the thickness converts it from a planar into a box-like (or cubic) shape. Hence the samples with a cubic geometry enable us to obtain contracting-envelope kinetics over a reaction range larger than that obtained for the planar discs. This latter argumentation is less significant in systems where either X0 is small (i.e. the rapid formation of a thin continuous product layer) or L is large (i.e. working with samples with large diameters, where the planar approximation is valid even for larger thiclmesses). 2.4. Data processing 2.4.1. Evaluation of reactionjknzt velocities For a contracting-envelope progression of a gas--solid reaction, simple analytical relations exist [ 2 ] relating the reacted fraction (Y and the reaction
223
-, Cl
q
i
(a>
TIME[mlnl
6
8
z
2
(b) Fig. 2. (a) Reacted fraction vs. time kinetics obtained for diierent geometrical shapes of hafnium: 0, cube (about 2 x 2 x 2 mm3); + , disc (about 5 X 0.5 mm’). The solid lines represent the fit of the contracting-envelope expressions (eqns. (1) and (2)) to the experimental data. (b) Reaction front displacement X vs. time obtained from the kinetic curves of (a) (see text).
front displacement X. Thus for example, for planar samples (i.e. samples with thicknesses L much smaller than the lateral dimensions) a simple linear relation is fulfilled: 2 (Y= -x L For a box-like sample (initial dimensions a,
(1) X a2 X as)
a=C,X-c2x2+c3x3
with Ci constants depending on a,, u2 and u3:
(2)
224
1 -+al a2
(
c,=4
c,=
1 al a3
+-
1 a2 a3
(3) )
8 ala2a3
The reaction displacement X is given by t
X(t) =
$
U(t ‘) dt ’ +X0
(4)
to
where t is the tune measured from the admission of hydrogen, t,,.is the time required to establish a continuous hydride layer (including the induction time, when it occurs, and the time required for the spread and overlap of the hydride nuclei formed on the surface until a continuous front is developed) and X0 is the initial thickness of the hydride layer formed at to. U is the velocity of the hydride front, which may be either time dependent (e.g. for certain diffusion-controlled mechanisms) or constant. For a constant velocity, assuming X,, -=KX, the reaction displacement time dependence is linear: x=
UT
7=t--to
(5) (6)
The evaluation of X(t) from the experimental a(t) values is accomplished via analytical expressions such as equations (1) and (2). Hence for planar samples (eqn. (1)) a simple linear relation is obtained whereas for a boxlike geometry (eqn. (2)) a more complex cubic relation is fuElled. In the latter case, knowing the constants Ci, then for each measured a(t) the corresponding X(t) can be calculated (solving the cubic eqn. (2)). According to eqns. (5) and (6), plotting X(t) vs. t should yield a straight line with a slope equal to the reaction velocity U. Figure 2(b) demonstrates such a linear dependence obtained for a cubic sample by the above procedure. The solid lines in Fig. 2(a) represent the fit of the calculated equations (1) and (2) (utilizing eqns. (5) and (6)) with the U value evaluated above substituted in these equations. 2.4.2. Evaluaticm of reacted fractions For metal-hydrogen systems which form either non-stoichiometric hydrides with a wide homogeneity range or more than a single hydride phase (e.g. dihydrides and trihydrides), a certain ambiguity may be encountered when the reacted fraction a(t) is determined from the P-V-T data (i.e. by calculating the amount of hydrogen absorbed by the sample at a given time). A similar problem may arise also when the hydrogen solubility in the metal is large under the given experimental conditions.
225
The usual approach to calculate (y(t) is by a relation of the type
a(t) =
A%(t) Anu(t = 03)
where An,(t) is the amount of hydrogen absorbed by the sample at time t and An,(t = co) is the saturation value measured at a sulhciently long time when equilibrium is reached. For non-stoichiometric hydrides this saturation value may depend on the reaction temperature and in certain cases may vary (for a given temperature) with the final hydrogen pressure attained at equilibrium. Obviously, under equilibrium conditions (i.e. at the time the reaction is completed) only the hydride phase that is thermodynamically stable (under the experimental P-T conditions) exists. However, during the kinetic process non-equilibrium forms may also exist; e.g. if the higher trihydride is the stable form, a lower dihydride can still be a precursor state constituting the reaction product layer that progresses into the metal. The exact distribution of hydrogen accommodated within the sample at a given time, An,(t), is thus unknown. For example, the absorbed hydrogen can form a hydride layer with a composition corresponding to the thermodynamic value, it can form a different (thicker) layer of a lower composition intermediate phase or it can form a two-phase mixture of both. Similar uncertainties are encountered for systems which form extensive solid solutions of hydrogen in either the product hydride phase or in the parent metal. It is thus important to realize that the correct definition of a(t) is the fraction of parent metal that has reacted with hydrogen to form a hydride phase (regardless of the composition of that hydride). The uncertainty in the type of distributions of the absorbed An,(t) results in an uncertainty in the evaluation of the correct reacted fraction, since for different distributions of the same An,, different amounts of the parent metal are consumed. Only for cases when either a layer of a single hydride phase with a composition near the equilibrium value is formed or the solubilities of hydrogen in the metal and in the hydride phase are small does the application of eqn. (7) yield the correct a(t) values. For example, when the solubility of hydrogen in the metal is significant, eqn. (7) will yield a(t) values which are larger than the real ones, whereas for the case when a lower composition hydride precursor is formed, eqn. (7) will yield a(t) values which are smaller than the actual ones. In order to check the validity of eqn. (7) for the present case, a series of partially hydrided samples (see e.g. Fig. 3) were examined metallographically. The corresponding reacted fractions were determined by two procedures; by applying eqn. (7) (denoting the corresponding LYas CQ,)and by measuring the actual dimensions of the um-eacted metal from the metallographic pictures (denoting the corresponding (Y as (Y,). Figure 4 presents the (Ye VS. (Y, curve, which turned out to be a straight line intersecting the origin with a slope of 45”. The applicability of eqn. (7) was thus confirmed.
226
Fig. 3. Metallographic
0
cl..?
cross-section
of a partially hydrided sa
0.6
Ll.L(
0.E
all-l Fig. 4. Relation between reacted fraction calculated from P-V-T metallographic examinations (CT,).
3. Experimental
data (CT,) and estimated from
results
Figure 5 presents metallographic pictures of samples (top, polycrystalline; bottom, crystal bar) which were partially hydrided at different temperatures (200,350 and 550 “C). It is seen that for both types of hafnium the progression of a continuous hydride front characterizes the reaction topochemistry. These metallographic observations confirm the validity of contracting-envelope expressions to represent the measured kinetic curves (cy VS. t). Figure 6 demonstrates typical X(t) VS. t kinetics (where X is the reaction front displacement) obtained at different temperatures for the polycrystalline (Fig. 6(a)) and crystal bar (F’ig. 6(b)) samples. Within the applied temperature range 250-550 “C a constant-velocity progression of the hydride front was displayed. At each temperature within the range 250-450 “C the velocity U
227
(4
TlMECmlnl
i
2’
01
TIME[minl
Fig. 6. Reaction front displacement vs. time obtained at different reaction temperatures for (a) polycrystailine (discs) and (b) crystal bar (cubes) samples: X, 350 “C; A, 400 “C; 0, 550 “C.
obtained for the polycrystalline sample was somewhat higher thanthat obtained for the crystal bar. At higher temperatures the velocities obtained for both types of samples were about the same. Apart from the slight difference in U values, there are some differences in the morphological details characterizing the hydride progression in the two types of hafnium samples. As can be seen in Fig. 5 (ZOO “C), there is a certain Herence in the structure of the hydride front boundary progressing into different crystallmeorientations (in the crystal bar). This effect is illustrated more pronouncedly in Fig. 7, where the boundary between two grains is enlarged, displaying a textured (needle-like extensions) hydride front advancing into one grain and a smoother hydride front advancing into the
229
Fig. 7. F’rogression of hydride performed at 200 “C).
front in two different
grains
in crystal bar hafnium
(reaction
other grain. Although the average front velocity in both grains is about the same, these observations point to some preferred orientations for either hydrogen diffusion or hydride precipitation, which for certain crystal planes produce the textured needle-like patterns. These anisotropies, however, are not significant, which is consistent with the similarity in the kinetic characteristics of the crystal bar as compared with the polycrystalline hafnium. As demonstrated in Fig. 5 (bottom), the extent of anisotropy (as reflected by the size of the needle-like extensions of the hydride front) increases with decreasing reaction temperature (compare the 200 and 350 “C patterns). At temperatures exceeding about 500 “C the textured shape of the needle-like hydride front (for the crystal bar) is replaced by a relatively smooth zone consisting of small hydride precipitates, advancing the continuous hydride layer. The thickness of this zone is about 60 pm (Fig. 5 (bottom)). In this high temperature region the limiting composition of the 6 hydride phase (i.e. the ((w+ 8):s composition limit) decreases significantly with increasing temperature 11, 71. Since the composition of the hydride formed near the hydride-metal boundary is close to the (a+ 8):s limit (at the reaction temperature), cooling the sample to room temperature transforms the system into the two-phase (Y+ S field in the corresponding phase diagram [ 1, 71. Thus the two-phase pattern of small hydride precipitates that characterizes the above-mentioned zone is displayed. The existence of a continuous hydride layer above this two-phase zone may point to the existence of hydrogen concentration gradients within the hydride layer. As the distance from the gas-hydride surface is decreased, a higher hydrogen concentration is maintained in the layer (at the reaction temperature). Consequently, cooling the sample keeps the system within the homogeneity region of the S field, producing a continuous one-phase hydride structure.
230
Comparing the 550 “C reacted samples of the two types of hafnium (Fig. 5) reveals the absence of a two-phase zone in the case of the polycrystalline hafnium sample (where only a single-phase structure of the hydride layer is displayed). A possible explanation of the difference between the two hafnium samples may be postulated by assuming a faster (possibly grain boundary) hydrogen diffusion taking place within the hydride formed on the polycrystalline metal. The hydrogen concentration gradients along the hydride layer are then diminished, leading to the formation of a higher composition hydride, even near the hydride-metal boundary. The implications of these observations with regard to the possible mechanisms controlling the hydride formation will be discussed further in Section 4. As indicated by Fig. 6, the initial stage of the reaction involved in some cases a short induction period followed by a stage that was more rapid than the linear massive reaction. The extent of this initial rapid stage, however, was relatively small (i.e. equivalent to a reaction displacement of about 30-50 pm); thus the exact functional time dependence of this stage could not be determined accurately. 4. Discussion As mentioned in Section 3, the massive part of the reaction was characterized by the progression of a hydride front moving at a constant velocity. Such a constant velocity progression may correspond to different mechanisms [2], of which two are possible in the present case. One mechanism involves a rate-determining step controlled by the permeation of hydrogen through a protective hydride layer with an apparently constant thickness Ir,. The other mechanism is associated with a rate-controlling step occurring at the hydride-metal interface (e.g. phase transformation or boundary hydrogen transfer). In some cases it is possible to substantiate the former (diffusion-controlled) mechanism by the tune dependence displayed during the initial hydriding stage preceding the massive linear stage. In such cases (e.g. the titanium-hydrogen reaction [ 31) a parabolic, t In , time relation is obtained initially, transforming after a certain reaction fraction into a linear tune dependence (i.e. the so-called par-a-linear kinetics). In order to observe this distinct parabolic stage, it is necessary that a measurable fraction of the reaction proceed by the thickening of a continuous protective product (hydride) layer. Such a requirement is not always fuElled. In some cases the apparently constant thickness of the layer is established immediately after the completion of the lateral coverage of the surface (by the spread of the hydride nuclei). Consequently, the linear stage is not preceded by a measurable parabolic stage, though the controlling mechanism may still be diffusion. Thus, even though the existence of para-linear kinetics may support a diffusion-controlled mechanism, the absence of the parabolic initial stage does not rule out that possibility. In our present case, where the initial non-
231
linear stage is too short to determine the existence of a definite parabolic stage, it is not possible to distinguish between the two above-mentioned mechanisms (i.e. diffusion or interface controlled) on the basis of the functional tune relation of the kinetic curves. Figure 8 illustrates Arrhenius plots of In U VS. 1 /T for both polycrystallme and crystal bar samples. In the lower temperature regime (below about 450 “C) a linear relation is displayed with slopes corresponding to apparent activation energies of 10.8 kcal mole-’ (0.47 eV) and 12.2 kcal mole-’ (0.53 eV) for the polycrystalline and crystal bar samples respectively. At higher temperatures above about 500 “C deviations from a linear Arrhenius relation are displayed for both types of hafnium samples. Table 1 summarizes the available data [S-l 31 on the activation barriers of hydrogen (and its isotopes) diffusion in hafnium hydrides. These data
I OOO/T[°Kl
Fig. 8. Arrhenius plots of ln U vs. 1 /T for (+) polycrystalline and (Cl) crystal bar hafnium samples hydrided under about 700 TorrH, pressure. The front velocity U is given in units of micrometres per minute.
TABLE
1
Activation energy barriers for the diffusion of hydrogen and its isotopes (deuterium and tritium) in hafnium hydrides Hydride composition
Phase
Temperature range (“C)
Experimental method
Ed (ev)
Ref.
Hm1.70
6 6
Hf-H,.9a
e
HfH1.64 HfD_2
6 l
Hf-H1.90
tz
Hfl1.90
E
1B&430 180-430 170-400 130-240 70-230 20-230 130-480
NMR NMR NMR TDPAC TDPAC TDPAC TDPAC
0.55 0.55(2) 0.55-0.65 0.43(5) 0.33 0.53 0.36(6)
I31
HfD1.W
IsI
191
(101 Ill1 I121 1131
were obtained by two experimental techniques, namely time differential perturbed angular correlations (TDPAC) [lo-131 and nuclear magnetic resonance (NMR) [8, 91. Although some scatter is obtained in the data, which may arise from different characteristics of the hydride samples utilized (e.g. different H:Hf composition ratios, different hydrogen isotopes, different sample purities, etc.), most of the results indicate an activation barrier of about 0.50 + 0.15 eV. This value closely resembles the apparent activation energy obtained from Fig. 8, which may point to a diffusion mechanism controlling the hydriding reaction in the lower temperature regime (below about 450 “C). Such a conclusion, however, should be considered cautiously, since the apparent activation barriers as obtained from the In U 7)s. 1 /T Arrhenius plots do not necessarily coincide with the diffusion activation barrier, even for diffusion-controlled reactions [ 2, 141. For a diffusion-controlled model of a hydride layer with an apparently constant thickness I,,moving at a constant velocity U, the pressure-temperature dependence of U is given by a relation of the type [2] U(P,
q
=K
W? 7?
Dm
hl(T)Y(T)
where K is a constant (depending on the densities and molecular weights of the metal and hydride), Y is the limiting composition of the hydride phase, 2 is the excess hydrogen dissolved in the hydride (beyond the limiting composition Y) and D is the diffusion constant for hydrogen in the hydride. It is seen from eqn. (8) that only for the case when the temperature dependence of all the parameters 2, Y and Ii, is negligible does the Arrhenius relation of In U vs. 1 /T yield a slope corresponding to the activation barrier for diffusion. Otherwise, either deviations from Arrhenius behaviour are introduced or, even for the case when Arrhenius-type curves are displayed, the corresponding slopes are not simply correlated with the diffusion barriers only. It has been pointed out [ 141 that under certain assumptions a simplilled diffusion model neglecting the possible temperature dependence of I,, leads to an apparent energy value given by Eapp= 6(AW +&
(9)
where Eapp is the apparent activation energy as determined from the In U W. 1 /T Arrhenius plot, Ed is the diffusion activation barrier (of hydrogen in the hydride) and S(m is a thermodynamic parameter associated with some enthalpy difference quantities. It is possible to estimate the value of the additional 6(m parameter from the temperature dependence of the normalized hydride phase composition limit pho), dellned as
where NHoj is the limiting composition of the hydride phase (e.g. the (a+ 6):s limit in the present case) and Ns is the saturation composition at infinite pressure as deduced from structural considerations (e-g. H:M=2 in the
233
present case). Under certain assumptions the following relation may be derived [ 141: ln
AK11 -=-
1 --A(l)
6(Af-o +c
(11)
RT
where C is a constant. Figure 9 presents the ln[phc,,/(l -P,,(~))] vs. 1 lT plot for the present Hf-H system. The experimental phc,,(Q values were calculated from the data in refs. 1 and 7. It is seen that the actual temperature dependence is more complex than that anticipated by eqn. (11). However, for the low (below 400 “C) and high (above 500 “C) temperature regimes such expressions may be approximately fitted, yielding a(AEQLT=1.3 kcal mole-’ (0.11 eV) and 6(AEQ,= 7.6 kcal mole-’ (0.66 eV) respectively. Hence in the temperature range where In U vs. 1 /T obeys an Arrhenius relation, the value of 6(w, is relatively low and the apparent activation energy may correspond closely to the diffusion activation barrier. Utilizing eqn. (9) and the estimated values of &pp and Xhly)i.~, diffusional activation barriers of 0.36 and 0.42 eV are obtained for the polycrystalline and crystal bar hafnium respectively. These values are still within the range of reported values summarized in Table 1, which substantiates the diffusion-controlled mechanism in this temperature range. For temperatures above about 500 “C deviations from the 1inearArrhenius relation are displayed in fig. 8. It might be argued that the enhanced temperature dependence of &AEQ, as displayed in Fig. 9 for this higher temperature regime, introduces a temperature dependence in E,, (eqn. (9)), leading to the observed deviations. However, since the absolute value of S(wHT is increased with increasing temperature, the above consideration should result in an increase in the absolute value of Ear_,,whereas the opposite trend is actually displayed in Fig. 8 (a decrease in the slope of In U vs. 1 /T in the high temperature
0.9
1.1
1.3
I.5
1.7
1.9
IOOO/TC°Kl Fig.
9. Temperature
dependence
of limiting hydride
composition
(eqn. (11))
(see text).
234
range). In principle, a temperature dependence of Ed may be postulated with a trend opposite to that of 6(AE!), resulting in an overall decrease of E,, with increasing temperature. However, substituting the values of E,, = 0.3 eV (at 450-550 “C) and S(hll)m=O.66 eV in eqn. (9) yields E,= - 0.36 eV, which physically is not possible. It thus seems that the diffusion-controlled mechanism which is consistent with the lower temperature hydriding regime cannot be adapted to the higher temperature range. One possibility which may account for the observed kinetic behaviour in the high temperature range is still based on a diffusion-controlled mechanism but with the apparent constant hydride thickness I,, being temperature dependent [ 31. According to eqn. (8), an enhanced increase in 1,(T) occurring with increasing temperature may lead to a decrease in the slope of the ln U U.S. 1 /T curve as observed in Fig. 8. In that case, however, a significant increase in the extent of the initial non-linear stage should be displayed in the X UUS.t curves (Fig. 6). Another consideration which is inconsistent with a diffusion-controlled mechanism prevailing in the higher temperature regime is the different hydrogen concentration gradients across the hydride layer deduced for the polycrystalline and crystal bar samples (as discussed in Section 3). It is not probable that even though different concentration gradients are established in these different types of samples (in that temperature regime), the same U values are still obtained with a diffusion-controlled reaction (which should be very sensitive to such concentration gradient differences). Another possibility which may result in the observed deviations in the In U vs. 1 lT curves is a change in the controlling mechanism. It is possible that at higher temperatures the diffusion process becomes sufficiently rapid that it is no longer a rate-determining step. An interface-controlled mechanism may then take place, leading to a different temperature dependence. References 1 W. M. Mueller, J. P. Blackledge and G. G. Libowitz (eds.), Metal Hydrides, Academic, New York/London, 1968. 2 M. H. Mints and J. Bloch, Prog. Solid State Chem., 16 (1985) 163. 3 A. Efron, Y. Lifshitz, I. Lewkowicz and M. H. Mints, J. L.ess-Common Met., 153 (1989) 23. 4 J. Bloch, I. Jacob and M. H. Mintz, to be published. 5 J. Bloch, E. Sw-issa and M. H. Mintz, 2. Phys. Chem. N.F., 164 (1989) 1193. 6 J. Bloch and M. H. Mintz, J. Less-Common Met., 166 (1990) 241. 7 R. K. Edwards and E. Veleckis, J. Phus. Chem., 66 (1962) 1657. 8 H. T. Weaver, J. Magn. Res., 15 (1974) 84. 9 J. R. Pope, P. P. Narang and K. R. Doolan, J. Phys. Chem. Solids, 42 (1981) 519. 10 0. de Damasceno, A. L. de Oliveria, J. de Oliveria, A. Baudry and P. Boyer, Solid State Commun., 53 (1985) 363. 11 M. Forker, L. Freise, D. Simon, H. Saitovitch and P. R. J. Silva, Z. NC&@ A, 41 (1986) 403. 12 M. Forker, L. Freise, D. Simon, H. Saitovitch and P. R. J. SiIva, Hyperfke Intemct., 35 (1987) 829. 13 M. Forker, W. Hen, D. Simon and R. Lasser, Z. Phus. Chem. N.F., 164 (1989) 889. 14 J. Bloch and M. H. Mlntz, J. Less-Common Met., 81 (1981) 301.
of the Less-Common
Metals,
219
175 (1991) 219-234
1280
Kinetic study of the hafnium-hydrogen
reaction
Y. Levitin and J. Bloch Nuclear
Research
Center
-
Negev,
PO Box 9001, Beer-Sheva
(kra&
M. H. Mink Nuclear Research University
Cater of the Negev,
- Negev, PO Box 9001, Beer-Sheva Department of Nuclear Engineering,
and Ben Gurion PO Box 653, Beer-Sheva
clsraeu
(FIeceived January 7, 1991)
Abstract The kinetics of hafnium hydride formation were studied utilizing conventional rate measurements (Sieverts system) combined with metallographic examinations of partially hydrided samples. The rate measurements were performed at 700 TorrH, over a temperature range 200-550 “C. Two types of hafnium samples (polycrystalline and crystal bar) were compared. The progression of the massive stage of the reaction is characterized by a contracting-envelope morphology with a constant hydride front velocity. The anisotropy in the reaction front velocity regarding different crystalline orientations of the metal is small, resulting in similar results for the different types of hafnium. The temperature dependence of the front velocity obeys an Arrhenius-type relation over the temperature range 250-450 “C, with an apparent activation energy of 0.50*0.05 eV. Considering a diffusion-controlled model, a diffusion activation barrier of about 0.4 eV is evaluated, which agrees with the average reported value for the diffusion of hydrogen in hafnium hydride. At temperatures above about 500 “C, deviations from the Arrhenius relation are displayed, possibly owing to a change of mechanism.
1. Introduction Group IVb metals (titanium, zirconium and hafnium) form hydrides containing very high volume densities of hydrogen (NH = 9.1 X 10z2, 7.3 X 1O22 and 7.6 X 1O22H atoms cm-3 for titanium, zirconium and hafnium respectively). These hydrides have some applications in nuclear technologies [ 11. The phase diagrams of the corresponding metal-hydrogen systems display certain similar characteristics and systematic trends [ 1 ] : (1) the formation of f.c.c. non-stoichiometric hydrides in the low temperature regions of the phase diagrams (the so-called a-phase for the Ti-H system and the 6 phase for the Zr-H and Hf-H systems) which transform into f.c.t. structures upon additional absorption of hydrogen - this transformation is probably second order in the Ti-H system and first order in the Zr-H and Hf-H systems (the formation of the so-called E phase); (2) eutectoid decomposition of the low temperature f.c.c. hydrides, occurring in the high temperature regions of the phase diagrams - the eutectoid transition temperatures display a systematic trend, increasing with
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increasing atomic number of the metal (about 280 “C for TCH, 550 “C for Zr-H and actually no transition has been observed in the Hf-H system up to 900 “C). Besides these systematic trends in the M-H phase diagrams, there is also a systematic behaviour in the structural misfit between the f.c.c. hydrides and the parent metals (volume expansion v /vM of 24%, 17% and 15% for the titanium, zirconium and hafniurn f.c.c. hydrides respectively). It is thus interesting to compare the kinetic behaviour of the corresponding metal-hydrogen reactions within this group and establish if some trends exist regarding the mechanisms controlling the hydride formation. The kinetic parameters which should be compared must characterize the intrinsic nature of the reaction as defined in ref. 2. These parameters may be evaluated by a careful kinetic study of well-defined geometrical shapes of the reacting samples incorporating conventional rate measurements with metallographic examinations of partially hydrided samples [ 2, 31. Such a study has recently been made on the titanium~hydrogen reaction [3] within the temperature range below the eutectoid decomposition (25-250 “C). In the present work the kinetics and mechanism of hafnium hydride formation are studied. The corresponding study of the zirconium~ hydrogen reaction and the comparison within this group of metals will be published in a separate paper [4). 2. Experimental
details
2.1. The apparatus A conventional constant-volume glass-made Sieverts system was utilized for the overall rate measurements. The time dependence of the pressure drop in the system due to the reaction was continuously recorded. The weight of the reacting sample was adjusted so that the total pressure change at the completion of the reaction would not exceed approximately 10% of the applied initial pressure in order to attain the kinetic behaviour under almost constant-pressure conditions. It is note worthy that the equilibrium pressure of the hydride in the uppermost temperature range studied in the present work is less than 0.1% of the applied hydriding pressure. Under such conditions the pressure dependence of the kinetic parameters is quite small and the 10% variation in pressure is not anticipated to induce any significant changes in the reaction kinetics. Temperature control was achieved with a chromel-ahunel thermocouple placed against the outer wall of the quartz reactor. In some experiments another thermocouple was inserted inside the reactor, touching the hafnium specimen. In no case did the difference between the readings of the two thermocouples (resulting either from temperature gradients across the reactor or self-heating due to the exothermic nature of the hydriding reaction) exceed about 10 “C within the studied temperature range (250-550 “C). To prepare partially hydrided samples, the reaction was allowed to proceed to some predetermined extent (at a certain temperature), then
221
hydrogen was quickly (within a few seconds) evacuated cooled to room temperature. Metallographic examinations on the partially hydrided samples.
and the sample were performed
2.2. Specimens Two types of hafnium samples were studied, a polycrystalline rod and a crystal bar. Both types were of about the same purity, the dominant contamination as detected by chemical analysis being zirconium (1.7% in the rod and 1.5% in the crystal bar). The main difference between the two types was in their microstructure, as demonstrated in Fig. 1. The polycrystalline rod was characterized by small (10-30 pm) regularly shaped grains whereas the crystal bar consisted of very large (l-3 mm) grains. Hence the results observed for the former samples represented an average over all crystalline orientations whereas the crystal bar samples represented an assembly of a very few single-crystal orientations. This difference will be discussed further in the following sections. For each of these two types of hafnium, samples with well-defined geometrical shapes were prepared by saw cutting the original rods. Two types of geometrical shapes were utilized, discs with a diameter of 5 mm and a thickness of about 0.5 mm, and cubes of about 2X 2X 2 mm”. The analysis methods of the kinetic data obtained for these geometries are described in Section 2.4. 2.3. Experhental procedure In order to attain reproducible hydriding kinetics and to eliminate initial induction periods (which under certain experimental conditions are so long that they practically impede the initiation of the reaction), the samples were
Fig. 1. Metallographic
pictures of (A) polycrystalline
and (B) crystal bar hafnium samples.
thermally activated by vacuum (about 10e6 Torr) annealing at 900 “C for 2 h. This thermal activation affects mainly the characteristics of the thin surface passivation layer, increasing its permeability to hydrogen [5, 61. It should be remembered that for certain metals high temperature annealing may affect not only the surface layer properties but also the bulk microstructure [3, 61, introducing in some cases changes in the measured kinetic parameters [6]. However, in the present case, owing to the very high melting point of hafnium, no such changes were introduced by the applied thermal pretreatments. It is interesting to note that unlike titanium [3] and uranium [5, 61 where pretreatment temperatures of about 450 “C or below were sufficient to activate the samples, for hafnium much higher temperatures were needed. After the vacuum pretreatment the samples were cooled to the desired reaction temperature (in the range 250-550 “C) and high purity hydrogen at a pressure of about 700 Torr was admitted. The reaction usually initiated immediately without significant induction periods. For planar samples (discs) the reaction kinetics followed a linear time dependence over most of the reaction course (about lo%-90%) whereas for the cubes a non-linear time behaviour was observed (as demonstrated in Fig. 2(a). Both geometrical shapes, however, fitted contracting-envelope progression kinetics with a constant hydride front velocity, as discussed in Section 2.4. The use of two different geometrical shapes (i.e. discs and cubes) of samples had two reasons. First, it confirmed the validity of a contractingenvelope constant-velocity-type progression of the reaction (see Section 2.4). Secondly, the initial deviations of the reaction kinetics from a contractingenvelope time dependence (eqns. (1) and (2)) occur within a certain reaction range corresponding to the establishment of a product hydride layer with a minimum thickness X0 (which may be temperature dependent). In order to obtain the contracting-envelope-type kinetics over the largest possible reaction range, it is desirable that X,/L -K 1, where L is the initial thickness of the sample. From this point of view it is beneficial to utilize samples with relatively large thicknesses.However, since the largest diameter of the sample is limited by the design of the reactor (which in our system was about 5 mm), increasing the thickness converts it from a planar into a box-like (or cubic) shape. Hence the samples with a cubic geometry enable us to obtain contracting-envelope kinetics over a reaction range larger than that obtained for the planar discs. This latter argumentation is less significant in systems where either X0 is small (i.e. the rapid formation of a thin continuous product layer) or L is large (i.e. working with samples with large diameters, where the planar approximation is valid even for larger thiclmesses). 2.4. Data processing 2.4.1. Evaluation of reactionjknzt velocities For a contracting-envelope progression of a gas--solid reaction, simple analytical relations exist [ 2 ] relating the reacted fraction (Y and the reaction
223
-, Cl
q
i
(a>
TIME[mlnl
6
8
z
2
(b) Fig. 2. (a) Reacted fraction vs. time kinetics obtained for diierent geometrical shapes of hafnium: 0, cube (about 2 x 2 x 2 mm3); + , disc (about 5 X 0.5 mm’). The solid lines represent the fit of the contracting-envelope expressions (eqns. (1) and (2)) to the experimental data. (b) Reaction front displacement X vs. time obtained from the kinetic curves of (a) (see text).
front displacement X. Thus for example, for planar samples (i.e. samples with thicknesses L much smaller than the lateral dimensions) a simple linear relation is fulfilled: 2 (Y= -x L For a box-like sample (initial dimensions a,
(1) X a2 X as)
a=C,X-c2x2+c3x3
with Ci constants depending on a,, u2 and u3:
(2)
224
1 -+al a2
(
c,=4
c,=
1 al a3
+-
1 a2 a3
(3) )
8 ala2a3
The reaction displacement X is given by t
X(t) =
$
U(t ‘) dt ’ +X0
(4)
to
where t is the tune measured from the admission of hydrogen, t,,.is the time required to establish a continuous hydride layer (including the induction time, when it occurs, and the time required for the spread and overlap of the hydride nuclei formed on the surface until a continuous front is developed) and X0 is the initial thickness of the hydride layer formed at to. U is the velocity of the hydride front, which may be either time dependent (e.g. for certain diffusion-controlled mechanisms) or constant. For a constant velocity, assuming X,, -=KX, the reaction displacement time dependence is linear: x=
UT
7=t--to
(5) (6)
The evaluation of X(t) from the experimental a(t) values is accomplished via analytical expressions such as equations (1) and (2). Hence for planar samples (eqn. (1)) a simple linear relation is obtained whereas for a boxlike geometry (eqn. (2)) a more complex cubic relation is fuElled. In the latter case, knowing the constants Ci, then for each measured a(t) the corresponding X(t) can be calculated (solving the cubic eqn. (2)). According to eqns. (5) and (6), plotting X(t) vs. t should yield a straight line with a slope equal to the reaction velocity U. Figure 2(b) demonstrates such a linear dependence obtained for a cubic sample by the above procedure. The solid lines in Fig. 2(a) represent the fit of the calculated equations (1) and (2) (utilizing eqns. (5) and (6)) with the U value evaluated above substituted in these equations. 2.4.2. Evaluaticm of reacted fractions For metal-hydrogen systems which form either non-stoichiometric hydrides with a wide homogeneity range or more than a single hydride phase (e.g. dihydrides and trihydrides), a certain ambiguity may be encountered when the reacted fraction a(t) is determined from the P-V-T data (i.e. by calculating the amount of hydrogen absorbed by the sample at a given time). A similar problem may arise also when the hydrogen solubility in the metal is large under the given experimental conditions.
225
The usual approach to calculate (y(t) is by a relation of the type
a(t) =
A%(t) Anu(t = 03)
where An,(t) is the amount of hydrogen absorbed by the sample at time t and An,(t = co) is the saturation value measured at a sulhciently long time when equilibrium is reached. For non-stoichiometric hydrides this saturation value may depend on the reaction temperature and in certain cases may vary (for a given temperature) with the final hydrogen pressure attained at equilibrium. Obviously, under equilibrium conditions (i.e. at the time the reaction is completed) only the hydride phase that is thermodynamically stable (under the experimental P-T conditions) exists. However, during the kinetic process non-equilibrium forms may also exist; e.g. if the higher trihydride is the stable form, a lower dihydride can still be a precursor state constituting the reaction product layer that progresses into the metal. The exact distribution of hydrogen accommodated within the sample at a given time, An,(t), is thus unknown. For example, the absorbed hydrogen can form a hydride layer with a composition corresponding to the thermodynamic value, it can form a different (thicker) layer of a lower composition intermediate phase or it can form a two-phase mixture of both. Similar uncertainties are encountered for systems which form extensive solid solutions of hydrogen in either the product hydride phase or in the parent metal. It is thus important to realize that the correct definition of a(t) is the fraction of parent metal that has reacted with hydrogen to form a hydride phase (regardless of the composition of that hydride). The uncertainty in the type of distributions of the absorbed An,(t) results in an uncertainty in the evaluation of the correct reacted fraction, since for different distributions of the same An,, different amounts of the parent metal are consumed. Only for cases when either a layer of a single hydride phase with a composition near the equilibrium value is formed or the solubilities of hydrogen in the metal and in the hydride phase are small does the application of eqn. (7) yield the correct a(t) values. For example, when the solubility of hydrogen in the metal is significant, eqn. (7) will yield a(t) values which are larger than the real ones, whereas for the case when a lower composition hydride precursor is formed, eqn. (7) will yield a(t) values which are smaller than the actual ones. In order to check the validity of eqn. (7) for the present case, a series of partially hydrided samples (see e.g. Fig. 3) were examined metallographically. The corresponding reacted fractions were determined by two procedures; by applying eqn. (7) (denoting the corresponding LYas CQ,)and by measuring the actual dimensions of the um-eacted metal from the metallographic pictures (denoting the corresponding (Y as (Y,). Figure 4 presents the (Ye VS. (Y, curve, which turned out to be a straight line intersecting the origin with a slope of 45”. The applicability of eqn. (7) was thus confirmed.
226
Fig. 3. Metallographic
0
cl..?
cross-section
of a partially hydrided sa
0.6
Ll.L(
0.E
all-l Fig. 4. Relation between reacted fraction calculated from P-V-T metallographic examinations (CT,).
3. Experimental
data (CT,) and estimated from
results
Figure 5 presents metallographic pictures of samples (top, polycrystalline; bottom, crystal bar) which were partially hydrided at different temperatures (200,350 and 550 “C). It is seen that for both types of hafnium the progression of a continuous hydride front characterizes the reaction topochemistry. These metallographic observations confirm the validity of contracting-envelope expressions to represent the measured kinetic curves (cy VS. t). Figure 6 demonstrates typical X(t) VS. t kinetics (where X is the reaction front displacement) obtained at different temperatures for the polycrystalline (Fig. 6(a)) and crystal bar (F’ig. 6(b)) samples. Within the applied temperature range 250-550 “C a constant-velocity progression of the hydride front was displayed. At each temperature within the range 250-450 “C the velocity U
227
(4
TlMECmlnl
i
2’
01
TIME[minl
Fig. 6. Reaction front displacement vs. time obtained at different reaction temperatures for (a) polycrystailine (discs) and (b) crystal bar (cubes) samples: X, 350 “C; A, 400 “C; 0, 550 “C.
obtained for the polycrystalline sample was somewhat higher thanthat obtained for the crystal bar. At higher temperatures the velocities obtained for both types of samples were about the same. Apart from the slight difference in U values, there are some differences in the morphological details characterizing the hydride progression in the two types of hafnium samples. As can be seen in Fig. 5 (ZOO “C), there is a certain Herence in the structure of the hydride front boundary progressing into different crystallmeorientations (in the crystal bar). This effect is illustrated more pronouncedly in Fig. 7, where the boundary between two grains is enlarged, displaying a textured (needle-like extensions) hydride front advancing into one grain and a smoother hydride front advancing into the
229
Fig. 7. F’rogression of hydride performed at 200 “C).
front in two different
grains
in crystal bar hafnium
(reaction
other grain. Although the average front velocity in both grains is about the same, these observations point to some preferred orientations for either hydrogen diffusion or hydride precipitation, which for certain crystal planes produce the textured needle-like patterns. These anisotropies, however, are not significant, which is consistent with the similarity in the kinetic characteristics of the crystal bar as compared with the polycrystalline hafnium. As demonstrated in Fig. 5 (bottom), the extent of anisotropy (as reflected by the size of the needle-like extensions of the hydride front) increases with decreasing reaction temperature (compare the 200 and 350 “C patterns). At temperatures exceeding about 500 “C the textured shape of the needle-like hydride front (for the crystal bar) is replaced by a relatively smooth zone consisting of small hydride precipitates, advancing the continuous hydride layer. The thickness of this zone is about 60 pm (Fig. 5 (bottom)). In this high temperature region the limiting composition of the 6 hydride phase (i.e. the ((w+ 8):s composition limit) decreases significantly with increasing temperature 11, 71. Since the composition of the hydride formed near the hydride-metal boundary is close to the (a+ 8):s limit (at the reaction temperature), cooling the sample to room temperature transforms the system into the two-phase (Y+ S field in the corresponding phase diagram [ 1, 71. Thus the two-phase pattern of small hydride precipitates that characterizes the above-mentioned zone is displayed. The existence of a continuous hydride layer above this two-phase zone may point to the existence of hydrogen concentration gradients within the hydride layer. As the distance from the gas-hydride surface is decreased, a higher hydrogen concentration is maintained in the layer (at the reaction temperature). Consequently, cooling the sample keeps the system within the homogeneity region of the S field, producing a continuous one-phase hydride structure.
230
Comparing the 550 “C reacted samples of the two types of hafnium (Fig. 5) reveals the absence of a two-phase zone in the case of the polycrystalline hafnium sample (where only a single-phase structure of the hydride layer is displayed). A possible explanation of the difference between the two hafnium samples may be postulated by assuming a faster (possibly grain boundary) hydrogen diffusion taking place within the hydride formed on the polycrystalline metal. The hydrogen concentration gradients along the hydride layer are then diminished, leading to the formation of a higher composition hydride, even near the hydride-metal boundary. The implications of these observations with regard to the possible mechanisms controlling the hydride formation will be discussed further in Section 4. As indicated by Fig. 6, the initial stage of the reaction involved in some cases a short induction period followed by a stage that was more rapid than the linear massive reaction. The extent of this initial rapid stage, however, was relatively small (i.e. equivalent to a reaction displacement of about 30-50 pm); thus the exact functional time dependence of this stage could not be determined accurately. 4. Discussion As mentioned in Section 3, the massive part of the reaction was characterized by the progression of a hydride front moving at a constant velocity. Such a constant velocity progression may correspond to different mechanisms [2], of which two are possible in the present case. One mechanism involves a rate-determining step controlled by the permeation of hydrogen through a protective hydride layer with an apparently constant thickness Ir,. The other mechanism is associated with a rate-controlling step occurring at the hydride-metal interface (e.g. phase transformation or boundary hydrogen transfer). In some cases it is possible to substantiate the former (diffusion-controlled) mechanism by the tune dependence displayed during the initial hydriding stage preceding the massive linear stage. In such cases (e.g. the titanium-hydrogen reaction [ 31) a parabolic, t In , time relation is obtained initially, transforming after a certain reaction fraction into a linear tune dependence (i.e. the so-called par-a-linear kinetics). In order to observe this distinct parabolic stage, it is necessary that a measurable fraction of the reaction proceed by the thickening of a continuous protective product (hydride) layer. Such a requirement is not always fuElled. In some cases the apparently constant thickness of the layer is established immediately after the completion of the lateral coverage of the surface (by the spread of the hydride nuclei). Consequently, the linear stage is not preceded by a measurable parabolic stage, though the controlling mechanism may still be diffusion. Thus, even though the existence of para-linear kinetics may support a diffusion-controlled mechanism, the absence of the parabolic initial stage does not rule out that possibility. In our present case, where the initial non-
231
linear stage is too short to determine the existence of a definite parabolic stage, it is not possible to distinguish between the two above-mentioned mechanisms (i.e. diffusion or interface controlled) on the basis of the functional tune relation of the kinetic curves. Figure 8 illustrates Arrhenius plots of In U VS. 1 /T for both polycrystallme and crystal bar samples. In the lower temperature regime (below about 450 “C) a linear relation is displayed with slopes corresponding to apparent activation energies of 10.8 kcal mole-’ (0.47 eV) and 12.2 kcal mole-’ (0.53 eV) for the polycrystalline and crystal bar samples respectively. At higher temperatures above about 500 “C deviations from a linear Arrhenius relation are displayed for both types of hafnium samples. Table 1 summarizes the available data [S-l 31 on the activation barriers of hydrogen (and its isotopes) diffusion in hafnium hydrides. These data
I OOO/T[°Kl
Fig. 8. Arrhenius plots of ln U vs. 1 /T for (+) polycrystalline and (Cl) crystal bar hafnium samples hydrided under about 700 TorrH, pressure. The front velocity U is given in units of micrometres per minute.
TABLE
1
Activation energy barriers for the diffusion of hydrogen and its isotopes (deuterium and tritium) in hafnium hydrides Hydride composition
Phase
Temperature range (“C)
Experimental method
Ed (ev)
Ref.
Hm1.70
6 6
Hf-H,.9a
e
HfH1.64 HfD_2
6 l
Hf-H1.90
tz
Hfl1.90
E
1B&430 180-430 170-400 130-240 70-230 20-230 130-480
NMR NMR NMR TDPAC TDPAC TDPAC TDPAC
0.55 0.55(2) 0.55-0.65 0.43(5) 0.33 0.53 0.36(6)
I31
HfD1.W
IsI
191
(101 Ill1 I121 1131
were obtained by two experimental techniques, namely time differential perturbed angular correlations (TDPAC) [lo-131 and nuclear magnetic resonance (NMR) [8, 91. Although some scatter is obtained in the data, which may arise from different characteristics of the hydride samples utilized (e.g. different H:Hf composition ratios, different hydrogen isotopes, different sample purities, etc.), most of the results indicate an activation barrier of about 0.50 + 0.15 eV. This value closely resembles the apparent activation energy obtained from Fig. 8, which may point to a diffusion mechanism controlling the hydriding reaction in the lower temperature regime (below about 450 “C). Such a conclusion, however, should be considered cautiously, since the apparent activation barriers as obtained from the In U 7)s. 1 /T Arrhenius plots do not necessarily coincide with the diffusion activation barrier, even for diffusion-controlled reactions [ 2, 141. For a diffusion-controlled model of a hydride layer with an apparently constant thickness I,,moving at a constant velocity U, the pressure-temperature dependence of U is given by a relation of the type [2] U(P,
q
=K
W? 7?
Dm
hl(T)Y(T)
where K is a constant (depending on the densities and molecular weights of the metal and hydride), Y is the limiting composition of the hydride phase, 2 is the excess hydrogen dissolved in the hydride (beyond the limiting composition Y) and D is the diffusion constant for hydrogen in the hydride. It is seen from eqn. (8) that only for the case when the temperature dependence of all the parameters 2, Y and Ii, is negligible does the Arrhenius relation of In U vs. 1 /T yield a slope corresponding to the activation barrier for diffusion. Otherwise, either deviations from Arrhenius behaviour are introduced or, even for the case when Arrhenius-type curves are displayed, the corresponding slopes are not simply correlated with the diffusion barriers only. It has been pointed out [ 141 that under certain assumptions a simplilled diffusion model neglecting the possible temperature dependence of I,, leads to an apparent energy value given by Eapp= 6(AW +&
(9)
where Eapp is the apparent activation energy as determined from the In U W. 1 /T Arrhenius plot, Ed is the diffusion activation barrier (of hydrogen in the hydride) and S(m is a thermodynamic parameter associated with some enthalpy difference quantities. It is possible to estimate the value of the additional 6(m parameter from the temperature dependence of the normalized hydride phase composition limit pho), dellned as
where NHoj is the limiting composition of the hydride phase (e.g. the (a+ 6):s limit in the present case) and Ns is the saturation composition at infinite pressure as deduced from structural considerations (e-g. H:M=2 in the
233
present case). Under certain assumptions the following relation may be derived [ 141: ln
AK11 -=-
1 --A(l)
6(Af-o +c
(11)
RT
where C is a constant. Figure 9 presents the ln[phc,,/(l -P,,(~))] vs. 1 lT plot for the present Hf-H system. The experimental phc,,(Q values were calculated from the data in refs. 1 and 7. It is seen that the actual temperature dependence is more complex than that anticipated by eqn. (11). However, for the low (below 400 “C) and high (above 500 “C) temperature regimes such expressions may be approximately fitted, yielding a(AEQLT=1.3 kcal mole-’ (0.11 eV) and 6(AEQ,= 7.6 kcal mole-’ (0.66 eV) respectively. Hence in the temperature range where In U vs. 1 /T obeys an Arrhenius relation, the value of 6(w, is relatively low and the apparent activation energy may correspond closely to the diffusion activation barrier. Utilizing eqn. (9) and the estimated values of &pp and Xhly)i.~, diffusional activation barriers of 0.36 and 0.42 eV are obtained for the polycrystalline and crystal bar hafnium respectively. These values are still within the range of reported values summarized in Table 1, which substantiates the diffusion-controlled mechanism in this temperature range. For temperatures above about 500 “C deviations from the 1inearArrhenius relation are displayed in fig. 8. It might be argued that the enhanced temperature dependence of &AEQ, as displayed in Fig. 9 for this higher temperature regime, introduces a temperature dependence in E,, (eqn. (9)), leading to the observed deviations. However, since the absolute value of S(wHT is increased with increasing temperature, the above consideration should result in an increase in the absolute value of Ear_,,whereas the opposite trend is actually displayed in Fig. 8 (a decrease in the slope of In U vs. 1 /T in the high temperature
0.9
1.1
1.3
I.5
1.7
1.9
IOOO/TC°Kl Fig.
9. Temperature
dependence
of limiting hydride
composition
(eqn. (11))
(see text).
234
range). In principle, a temperature dependence of Ed may be postulated with a trend opposite to that of 6(AE!), resulting in an overall decrease of E,, with increasing temperature. However, substituting the values of E,, = 0.3 eV (at 450-550 “C) and S(hll)m=O.66 eV in eqn. (9) yields E,= - 0.36 eV, which physically is not possible. It thus seems that the diffusion-controlled mechanism which is consistent with the lower temperature hydriding regime cannot be adapted to the higher temperature range. One possibility which may account for the observed kinetic behaviour in the high temperature range is still based on a diffusion-controlled mechanism but with the apparent constant hydride thickness I,, being temperature dependent [ 31. According to eqn. (8), an enhanced increase in 1,(T) occurring with increasing temperature may lead to a decrease in the slope of the ln U U.S. 1 /T curve as observed in Fig. 8. In that case, however, a significant increase in the extent of the initial non-linear stage should be displayed in the X UUS.t curves (Fig. 6). Another consideration which is inconsistent with a diffusion-controlled mechanism prevailing in the higher temperature regime is the different hydrogen concentration gradients across the hydride layer deduced for the polycrystalline and crystal bar samples (as discussed in Section 3). It is not probable that even though different concentration gradients are established in these different types of samples (in that temperature regime), the same U values are still obtained with a diffusion-controlled reaction (which should be very sensitive to such concentration gradient differences). Another possibility which may result in the observed deviations in the In U vs. 1 lT curves is a change in the controlling mechanism. It is possible that at higher temperatures the diffusion process becomes sufficiently rapid that it is no longer a rate-determining step. An interface-controlled mechanism may then take place, leading to a different temperature dependence. References 1 W. M. Mueller, J. P. Blackledge and G. G. Libowitz (eds.), Metal Hydrides, Academic, New York/London, 1968. 2 M. H. Mints and J. Bloch, Prog. Solid State Chem., 16 (1985) 163. 3 A. Efron, Y. Lifshitz, I. Lewkowicz and M. H. Mints, J. L.ess-Common Met., 153 (1989) 23. 4 J. Bloch, I. Jacob and M. H. Mintz, to be published. 5 J. Bloch, E. Sw-issa and M. H. Mintz, 2. Phys. Chem. N.F., 164 (1989) 1193. 6 J. Bloch and M. H. Mintz, J. Less-Common Met., 166 (1990) 241. 7 R. K. Edwards and E. Veleckis, J. Phus. Chem., 66 (1962) 1657. 8 H. T. Weaver, J. Magn. Res., 15 (1974) 84. 9 J. R. Pope, P. P. Narang and K. R. Doolan, J. Phys. Chem. Solids, 42 (1981) 519. 10 0. de Damasceno, A. L. de Oliveria, J. de Oliveria, A. Baudry and P. Boyer, Solid State Commun., 53 (1985) 363. 11 M. Forker, L. Freise, D. Simon, H. Saitovitch and P. R. J. Silva, Z. NC&@ A, 41 (1986) 403. 12 M. Forker, L. Freise, D. Simon, H. Saitovitch and P. R. J. SiIva, Hyperfke Intemct., 35 (1987) 829. 13 M. Forker, W. Hen, D. Simon and R. Lasser, Z. Phus. Chem. N.F., 164 (1989) 889. 14 J. Bloch and M. H. Mlntz, J. Less-Common Met., 81 (1981) 301.