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Determination of the hydrogen site occupation in the α phase of zirconium hydride and in the

α and β phases of titanium hydride by inelastic neutron scattering

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1982 J. Phys. F: Met. Phys. 12 15

(http://iopscience.iop.org/0305-4608/12/1/003)

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J. Phys. F: Met. Phys., 12(1982)15-24. Printed in Great Britain

Determination of the hydrogen site occupation in the a phase of zirconium hydride and in the a and f l phases of titanium hydride by inelastic neutron scattering

R Khoda-Bakhsht and D K Ross Department of Physics, Unicersit j of Birmingham. Birmingham. B l 5 2TT. Engldnd. U K

Received 19 February 1981. in final form 21 Ju ly 1981

Abstract. Inelastic neutron scattering measurements have been used to determine the site occupied by hydrogen in 2 Zr-H and 1 and /3 Ti- H. The measured optical peak frequen- cies were only consistent with hydrogen being located on the tetrahedral sites in all cases. The significance of the energy shift between the hldr ide phase and the solid-solution phase is discussed.

1. Introduction

Many transition metals are exothermic absorbers of hydrogen and form both solid solutions and hydride phases (Mueller et al 1968, Alefeld and Volkl 1978). In the hydride phase, the site occupation is generally easily determined by neutron diffrac- tion. Thus, it is well known that in p Pd-H, hydrogen occupies the octahedral site in FCC palladium giving a defect NaCl structure (Worsham et al 1957, Bergsma and Goedkoop 1960, Ferguson et al 1965, Mueller et a1 1975) whereas with many other metals, including titanium and zirconium, dihydrides are formed with the fluorite structure, in which the hydrogen occupies a site with regular tetrahedral symmetry (Ross et a1 1979). A further common hydride structure is the 2’ phase in BCC metals (e.g. Nb and Ta) in which tetragonally distorted tetrahedral sites are occupied at random (Alefeld and Volkl 1978). At low temperatures the hydrogens in both p Pd-H (Anderson et a1 1978) and in the 2’ phases of the BCC hydrides (Schober and Wenzl 1978) form superlattice structures indicating the presence of repulsive H-H forces. They do not, however, with the exception of V-H, change site occupation, although some distortion of the metal lattice is induced in the BCC systems.

Neutron diffraction measurements in the solid-solution phases are rather more difficult due to the much smaller H(D) concentrations, but it has been reported that hydrogen occupies tetrahedral sites in the a (HCP) phases of ZrH,,,,2 (Narang et al 1977) and TiH,,,, (Pinto et a1 1979) at room temperature whereas for TiD, 0 7 5 at 375 “C, Alperin et al (1976) have reported that 687; of the deuterons were on the octahedral site with the remainder on the tetrahedral site. For CY Pd-H(D) i t has been

t Present address: Department of Physics. Unibersity of Urmia. P O Box 32. Urmia. Islamic Republic of Iran.

0305-4608/82/010015 + 10$01.50 @ 1982 The Institute of Physics 15

16 R Khodn-Bakhsh and D K Ross

shown that the octahedral site in the FCC structure is occupied at various temperatures (Nelin 1971).

Other methods have also been applied to the determination of site occupation. Thus incoherent quasi-elastic neutron scattering can be used to determine the individ- ual steps in the diffusion of the proton through the lattice while the direction and length of these steps taken together define the site occupation. Thus octahedral site occupation has been confirmed in the x (Carlile and Ross 1974) and fl (Anderson et al 1978) Pd-H systems and tetrahedral site occupation in x Nb-H (Lottner er a1 1979). The location of D can also be inferred by comparing measured coherent elastic scattering from single crystal samples with calculations based on models of the lattice distortion around the interstitials (Bauer 1979). ESR methods have been used to detect small concentrations (about 0.5%) of octahedral protons around Er ions in ScHz (Venturini et U / 1979) and similarly Mossbauer methods have been used to establish hydrogen location around an Er ion in ZrH, (Shenoy et a1 1976). These two methods, however, suffer from the need to introduce a probe nucleus into the sample which gives rise to some doubt as to whether the environments of the probe are typical. NMR measurements can also be interpreted to indicate site occupation. Thus Korn and Zamir (1970) have deduced that above 125 'C, hydrogen is on the tetrahedral sites in x titanium. Another recently developed method is fast ion channelling in crystals (Carstanjen et ul 1980. Carstanjen 1980. Takahashi et N I 1978). This is particularly appro- priate to very low hydrogen concentrations and also yields thermal cloud parameters for the protons. The method is less applicable to HCP crystals, however.

Site occupation can also be established by means of inelastic neutron measure- ments of the local mode frequencies of the proton because measurements on known structures show that the spectrum will consist of one or more peaks which are charac- teristic of the various site geometries. Thus, for the fluorite and other structures having regular tetrahedral sites. it has been shown that the peak energy E varies with the hydrogen-metal distance R as (Ross et a1 1979)

where A = 410 meV A3 '. whereas for octahedral sites, the frequency is certainly much lower (4036 of this value for Pd-H). For the x' phase in BCC metals, the tetrahedral site is compressed along one axis and this leads to a splitting in the peak, the compressed axis now having a lower frequency than the other two axes. Experimentally it is found that the peak energies split in the ratio of about , 2: 1 (Richter and Shapiro 1980) and it may be shown that if we assume that the H potential well is generated by central pairwise interactions between the hydrogen and the nearest neighbour Nb atoms, V(r) , and we neglect third and higher derivations of V(r ) , then for d2V,/dr2 >> (ljr)/(dV/dr) the frequency ratio o f , 2: 1 is in fact obtained (Ross et al 1981). It has also been noted that for these systems, the measured frequencies are apparently independent of the M-H distances (Yamada et a1 1976). Given that the frequencies of vibration in inter- stitial sites are remarkably independent of the detailed electronic structures involved, it is reasonable to suggest that the same relationships will apply approximately in the x phases, although some deviation may be expected because the lattice can now relax away from the interstitial, thus yielding an actual M-H distance rather larger than the value obtained from the lattice parameter. Further, because of the large incoherent cross section of hydrogen, because the inelastic scattering cross section is proportional to the square of the vibration amplitude, which is necessarily large for a light

Hydrogen site occupation in Zr-H and Ti-H 17

interstitial atom, and because the local mode vibration frequency normally comes above the acoustic cut-off of the metal lattice, the frequency distribution of the proton can be measured down to very low hydrogen concentrations. Thus Wagener et a1 (1980) have established that hydrogen occupies the tetrahedral sites in cx Ce-H and Drexel et a / (1976) have shown that the octahedral sites are occupied in z Pd-H. On the basis of the above considerations it is clear that inelastic neutron scattering provides a power- ful and direct method of establishing which site is occupied even at very low hydrogen concentrations-as low as 0.2% has been quoted (Drexel et al 1976tbeyond the range of neutron diffraction and quasi-elastic scattering, and a method which, in contrast to the channelling technique, is available for all lattices.

A further reason for making inelastic neutron scattering measurements to deter- mine hydrogen site occupation is that electron band calculations are rapidly reaching the point where not only can the occupation site be determined but the frequency of vibration on the site can also be predicted. Thus, carrying on from the pioneering calculations of Switendick (1978), Gelatt et a1 (1978) have recently been able to calcu- late energies of absorption of hydrogen into an FCC monohydride structure for 3d and 4d transition metals which agree well with measured enthalpies of formation of dilute (McLellan and Oates 1973) and non-dilute (Mueller et a1 1968) hydrides. Compared with the variation of this energy across the series, energy differences due to the occupation of alternative sites and to changes in the hydrogen concentrations are fairly small and it would seem that these have not yet been calculated in a realistic way. However, it is interesting to note that the calculations of the electron charge around the proton (Gelatt et al 1978) do not correlate with earlier charge transfer models (Hauck and Shenk 1977) and therefore the correlations with site occupation obtained from these models were probably coincidental.

Quite independently of this approach, which applies to the non-dilute case, pro- gress has also been made in treating isolated interstitial protons using Kohn-Sham self-consistent theory and Green function methods. Detailed calculations are now available for a free electron gas (Sholl and Smith 1977, Norskov 1979) while both a Thomas-Fermi (Darby et a1 1978) and a parameterised version of the potential obtained from the free electron gas (Sholl and Smith 1977) have been used to estimate the preferred site occupation in zirconium and palladium respectively. The above palladium calculations (Sholl and Smith 1978), however, indicate that the tetrahedral site is occupied, contrary to experiment. A more basic approach (Khan et a1 1981) attempts the whole calculation for Pd self-consistently, making due allowance for lattice relaxation. It is interesting to note that this calculation predicts that if equal octahedral and tetrahedral relaxations are assumed then the tetrahedral site is preferred, whereas if the distance from the centre of the site to the relaxed atom is assumed to be the same for each type of site, then the octahedral site is preferred. This result is in fact consistent with the Sholl and Smith (1978) result above because these authors neglected lattice distortion.

Finally, it may be noted that for simple metals even more detailed calculations can be performed. Thus Taylor (1980) has recently calculated vibrational frequencies for both octahedral and tetrahedral sites in aluminium both for unrelaxed and relaxed lattices. Here it is of interest to note that the frequency obtained for hydrogen in the unrelaxed tetrahedral site (152meV) is not too dissimilar to the value of 177meV obtained from the experimental correlation (equation (l)), while the equivalent value for the octahedral site (78 meV) can be compared with the measured value of 58 meV in /3 Pd-H which has an almost identical metal-metal hydrogen distance.

18 R Khodu-Bakhsh and D K Ross

For the above reasons, we have measured the vibration frequencies of hydrogen in the cx phase of zirconium hydride and in the z and fi phases of titanium hydride.

2. Experimental method

The samples were prepared from zirconium and titanium metal in the form of poly- crystalline sponge, having quoted purities of 99.8% and 99.9%, which was obtained from Koch Light Laboratories Ltd. Hydrogenisation was carried out in a standard rig, details of which are given elsewhere (Khoda-Bakhsh 1981). The initial vacuum was

Torr and a liquid nitrogen cold trap was incorporated into the rig. High-purity commercial hydrogen was used for making the titanium samples but it was found necessary to use hydrogen produced within the rig by decomposition of titanium hydride for the zirconium sample. The hydrogen concentrations in the samples were measured both by weight gain and from the equilibrium pressure at a given tempera- ture by reference to the published isotherms (Mueller et a1 1968). The concentrations so obtained agreed within experimental error and the mean values are recorded in table 1.

The measurements were carried out using a beryllium filter spectrometer (BFS), namely INlb, at the Institut Laue-Langevin at Grenoble. This spectrometer, being mounted on a beam from the hot source, provides a high incident neutron flux beyond the maximum energy required in the present experiment (about 200 meV). Descrip- tions of the spectrometer and details of the flux and resolution for different mono- chromator planes can be found elsewhere?. For the energy transfers of interest, the resolution is dominated by the monochromator contribution (AEIE = 7% for Cu (200) and 10% for Cu (220)). The (200) plane could only be used up to 110 meV.

The samples were contained in disc shaped stainless steel capsules which were pressurised with hydrogen to the equilibrium pressure expected for the particular samples at the operating temperatures. The discs were electrically heated and wrapped in aluminium foil to ensure a uniform temperature. Background runs were performed using the same capsules filled with an equivalent amount of the metal sponge which had been baked out under vacuum to remove any hydrogen. The sample thickness was chosen to give not more than 10% scatter; as only a proportion of the neutrons

Table 1. Hydrogen concentrations in Zr and Ti, peak positions and resolution-corrected widths.

Peak positions Resolution-corrected widths (meV) (FWHH) (meV)

Temperature Sample ( C) First Second Third First Second Third

144 i 1 - - 4 1 i 3 - - ZrHo o 5 = o o l TIHO 05 = o 01 315 k 10 141 & 1 - - 3 0 2 3 - -

TiHo 1 4 z o o 2 715 i 10 1 2 0 i 2 1 4 1 i 3 1 7 1 2 2 1 6 k 3 1 0 0 + 1 0 2 0 + 3

600 i 5

t ILL Manual 1977 The Neutron Beam Facilities and Instrument Specifcations (Grenoble: Institut Max Von Laue-Paul Langevin).

Hydrogen site occupation in Zr-H and Ti-H 19

scattered once will be scattered inelastically, the proportion of inelastically scattered neutrons that have more than one energy transfer will be very small. Thus the pos- itions and relative intensities of the inelastic features will not be significantly affected by multiple scattering and therefore no correction was applied.

3. Results

Measurements were made on ZrH,,,, at 600 i 5 T, on TiHo,05 at 315 k 10 “C and on TiH0,14 at 715 f 10 “C. The corresponding data for the (220) scans, after back- ground and filtering corrections, are given in figures 1-3. The (200) scans (45-90 meV) had no structure and are therefore not shown. The spectra are plotted for fixed monitor counts-the monitor being a l/c detector in the incident flux. Q varies little across the measuring range and multi-phonon effects are small in the vicinity of the local mode peak. Hence the coordinate is proportional to the amplitude weighted frequency distribution. The energy loss is obtained by assuming that the mean scattered energy is 4 meV.

As the resolution function is expected to be Gaussian in this energy range (Gamlen et a1 1974) the widths of the experimental peaks have been unfolded on the assump- tion that they also are approximately Gaussian. Peak positions and widths are given in table 1. For the single peaks (figures 1 and 2) , the values were obtained directly from the plotted spectra. For the complex spectra in figure 3 they were obtained using a least-squares fitting routine.

X l O k

4

2 3 3 U

2

z 0

4

100 150 200 Energy loss ImeV)

Figure 1. Amplitude weighted frequency distribution for ZrHo,os at 600 T.

20 R Khoda-Bakhsh

I d o 3

and D K Ross

D

e

*e. I I

100 150 200 Energy Loss ( m e V )

Figure 2. Amplitude weighted frequency distribution for TiH,,,, at 315 'C.

80 100 150 200

Energy loss ( m e V 1

Figure 3. Amplitude weighted frequency distribution for TiHO.,L at 715 -C. The full curve shows a least-squares fit using a three Gaussian model and the arrows indicate the fitted peak positions. The first and third peaks are due to the split vibrations of the distorted tetrahedral site in the BCC phase while the middle peak is due to the regular tetrahedral site in the HCP r phase.

Hydrogen site occupation in Zr-H and Ti-H 21

4. Discussion

All the sites involved in the present study are somewhat distorted from cubic sym- metry, The metal lattices have c/a ratios of 1.588 (Ti) and 1.593 (Zr) compared with the ‘ideal’ value of 1.633, whereas the dihydride phases have c/a ratios of 0.945 (Ti) and 0.889 (Zr) at 80 K (Mueller et U / 1968). (c ia = 1 for a regular tetrahedron.) In the c(

phase, the distortion is small enough to ignore. In the titanium hydride case, it has been suggested that the tetragonal distortion at the hydrogen site is sufficient to account for the splitting of the observed peak (Zemlyanov et al 1978). However, both the cubic, 6, and tetragonal, E, phases of zirconium hydride (which at room tempera- ture exist in the composition ranges 1.59 < H/Zr < 1.66 and 1.66 < HjZr < 2.00 respectively) (Mueller et a / 1968) show splitting of the hydrogen vibration peak (Couch et al 1971) indicating the presence of hydrogen-hydrogen forces which presumably give rise to the tetragonal distortion at higher concentrations. The mean frequency is therefore quoted in table 1.

The first conclusion to be drawn from the results is that in the solid solutions of hydrogen in titanium and zirconium the hydrogens are situated in the tetrahedral rather than the octahedral sites. Thus, as mentioned above, it is to be expected that the vibration frequency in a given site geometry will increase with decreasing metal- hydrogen distance R (the R - 3 ’ 2 dependence (Ross et a / 1979) has only been demon- strated for the regular tetrahedral site geometry). Reference to table 2 will show that the metal-hydrogen distances in Ti and Zr in the x phase tetrahedral site are less than 10% smaller than in the hydride phase, and this difference in R will be reduced by lattice distortion. It will also be seen that the measured frequencies are within 5% of each other. The R dependence of octahedral site frequencies is not known but would be expected to be similar. Thus as the octahedral sites in cy Ti-H and x Zr-H are somewhat larger than the equivalent site in x Pd-H one would expect hydrogen in this site to have a frequency of vibration somewhat less than for x Pd-H (68.5 meV) (Drexel et (11 1976). This conclusion about the relative vibration frequencies of the two sites is also supported by the electron band calculations of Taylor (1980) for alumin- ium (see table 2). The evidence is thus overwhelmingly in favour of tetrahedral site occupation. This result contrasts with that of Alperin et al (1976) for cy TiD0,075 at 315 ‘C. One must therefore conclude that the site occupation can be influenced by the isotope involved. This must presumably be due to the smaller zero point energy of deuterium.

It is also of interest to consider the small changes in frequency of a given site between the solid solution and the hydride phase for different metals. Data for cerium (Wagener et ul 1980) and palladium (Drexel et a / 1976, Khoda-Bakhsh 1981) are therefore also included in table 2.

Without carrying out the complete lattice dynamical calculation it is difficult to extract unambiguously the metal-hydrogen longitudinal force constants, as has been done by Vorderwisch et a / (1978) for CeD2,12. The values given in table 2 are the mean values, while the quoted errors give the split peak positions as upper and lower bounds. In spite of these possible errors it is clear that the three materials behave in rather different ways. In zirconium, the r phase peak is to the high side of the hydride peak, in titanium it is clearly on the low-energy side, while in cerium it is some 10% down. It is interesting to compare this sequence with the fact that zirconium gives the smallest change and cerium the largest change in lattice parameter between metal and hydride.

22 R Khoda-Bakhsh and D K Ross

ri P a F

w

0" z

c a .-

z

s c a 8

Hydrogen site occupation in Zr-H and Ti-H 23

To date there have been no electron band structure calculations that could be compared with the present observed shifts. It may, however, be useful to anticipate such calculations by splitting up the change in energy into, firstly, an increase due to the reduction in the lattice parameter going from the hydride to the solid solution AE,,, and secondly, a reduction due to the relaxation of the lattice about a given interstitial AEre,. Thus the total change AE is

AE = AEIP - AE,,,. (2)

AEIp/E = - ~ o p t A V / V . (3)

Here AElp can be expressed in terms of the optical Gruneisen constant yopt

Unfortunately there seem to be no values of yap, for the present systems. For palla- dium hydride values in the range 3-4 have been obtained (Abbenseth and Wipf 1980, Khoda-Bakhsh 1981). Similarly there have been no estimates of AE,,, for the present system although Taylor (1980) has calculated values for aluminium (see table 2) which show 26% relaxation for the tetrahedral site and 11% for the octahedral site. Although the actual values for aluminium are not directly relevant, they show that AErel can be large, particularly for the tetrahedral site. The smaller relaxation at the octahedral site arises because it is a larger site and presumably this fact contributes to the large positive AE value that exists for palladium (see equation (2)).

Finally figure 3 shows the data for a sample that was in the mixed phase region, partly the hexagonal solid-solution r phase and partly the BCC /3 phase. Firstly, we can attribute the central peak to the tetrahedral site in the HCP phase and the first and third peaks to the tetrahedral site in the BCC phase. As Yamada er a1 (1976) have pointed out, all the BCC tetrahedral sites that have been investigated yield remarkably similar frequencies independent of lattice parameter and related by the J2 factor mentioned above. The mean values quoted (Yamada et al 1976) are 120meV and 175 meV, which are remarkably close to the present values. The other notable feature of figure 3 is the dramatic increase in the width of the 2 phase peak with the increase in temperature, presumably due to phonon damping, either by hydrogen diffusion or phonon-phonon interactions.

5. Conclusions

Neutron inelastic scattering measurements from hydrogen dissolved in zirconium and titanium show that hydrogen occupies the tetrahedral site in the metal HCP phases ct

Zr-H and ct Ti-H and the distorted tetrahedral site in the metal BCC phase. The observed shifts in the vibration frequency between the solid solution and the hydride phases are consistent with being due to the net effect of contributions from the optical Gruneisen constant and lattice relaxation around the defect.

Acknowledgments

This work was supported by the Science Research Council, London and the Institute Laue-Langevin, Grenoble. The authors would like to acknowledge the assistance of staff at ILL-in particular Dr I S Anderson and Dr J Tompkinson. RK-B would also like to acknowledge financial support from the Ministry of Science and Higher Education of the Islamic Republic of Iran.

R Khodu-Bukhsh and D K Ross

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