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Isotope effect on hydrogen site energies for two metal dihydrides
45
Journal of the Less-Common Metals, 74 (1980) 45 - 54 0 Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
ISOTOPE EFFECT DIHYDRIDES”
ON HYDROGEN
SITE ENERGIES
FOR TWO METAL
E. L. VENTURXNI Sandra National Laboratories,
Albuquerque~
N.M. 87185
(‘U.S.A.)
Summary
The change in hydrogen site energy with isotope for dihydrides and dideuterides of scandium and yttrium was indirectly determined using electron spin resonance (ESR) of erbium ions in dilute concentration in the f.c.c. hosts. The ESR spectra measure the distribution of hydrogen adjacent to the erbium; the variations in this distribution with isotope and with hydrogen-tometal ratio were studied for several samples of both host metals. The data are accurately described by a lattice-gas model which yields the energy difference for protons or deuterons on octahedral and tetrahedral sites, both adjacent to the erbium impurities and in the bulk host lattice. This energy difference is 10% greater for deuterons, and the change with isotope can be attributed primarily to the mass dependence of the vibrational part of the total energy associated with each site.
1. Introduction
In the f.c.c. dihydrides of group IIEb metals hydrogen has two available sites which are.denoted as octahedral (0) and tetrahedral (T) from the arrangement of nearest-neighbor metal ions [l] . There are two T sites and one 0 site per metal atom, with the 0 sites having a higher total energy than the T sites. This leads to the formation of a metal dihydride with very few 0 sites occupied at low temperat~es. At low temperature the site energy of a hydrogen ion consists of an electronic part and a vibrational part, i.e., a well depth plus a zero-point energy; to a first approximation only the vibrational part changes with isotope, varying as the inverse square root, of the mass. Using electron spin resonance (ESR) of erbium ions in dilute concentration in scandium and yttrium dihydride and dideuteride hosts, we measured the occupation of 0 sites adjacent to the erbium as a function of hydrogen
*Paper presented at the International Symposium on the Properties and Applications of Metal Hydrides, Colorado Springs, Colorado, U.S.A., April 7 - 11, 1980.
46
and deuterium loading. The experimental details are presented in Section 2, while in Section 3 we outline a simple lattice-gas calculation which explains the ESR data and yields site energy differences for the hydrogen isotopes both next to the erbium impurity ions and in the bulk hydride/deuteride. The energy difference is approximately 10% greater for deuterium in both scandium and yttrium host lattices. In the final section we estimate the change in the vibrational part of the site energies with isotope mass using published inelastic neutron-scattering data and show that the change in total site energy determined from the erbium ESR data can be explained by the mass dependence of the vibrational energy for each site. This result supports the suggestion that the electronic part of the site energy is nearly independent of the hydrogen isotope [2] and allows extrapolation to find total site energies in metal tritides.
2. Experimental
details
The samples used in this study were prepared by arc melting 0.1 at.% Er into specially purified scandium or yttrium, loading with hydrogen or deuterium in a modified Sieverts’ apparatus and then grinding the brittle metal hydride into a fine powder for the ESR measurements. The loading ratio for each sample was determined both volumetrically and gravimetritally, the former method yielding a more accurate value, although both values agreed to better than 1%. We did not verify directly that no hydrogen was lost during grinding of the bulk samples, but bulk loading ratios were used together with ESR data from the corresponding crushed powders for the plots in Figs. 2 and 3. The excellent agreement between the measurements and the predicted (lattice-gas) dependence on hydrogen-to-metal ratio, as shown by the data points and calculated curves respectively, suggests that any hydrogen deficiency due to grinding is less than the loading uncertainty indicated by the error bars. Of much greater concern in preparing the samples was the problem of obtaining a homogeneous hydrogen distribution in non-stoichiometric materials; this requires very careful temperature-pressure cycling during loading. The hydrogen-to-metal ratio ranged from 1.89 to 1.995 in the scandium samples and from 1.90 to 2.10 in the yttrium samples. The yttrium samples with the highest loading contained a very small amount of the trihydride phase (easily detected as a new signal in the erbium ESR spectrum), but all other samples were single phase within the accuracy of our measurements. Figure 1 shows derivative ESR absorption spectra for 0.1 at.% Er in samples of YH,_ss and YD,,a, powder. The data were obtained at 9.8 GHz and 2 K, the low temperature yielding narrow resonance lines and a good signal-to-noise ratio. Both spectra reveal two distinct sites for the erbium ions, one with cubic symmetry and one with axial symmetry. Similar spectra [ 3, 41 have been observed for erbium in ScH, . The erbium ESR data in Fig. 1 are dominated by a large isotropic resonance with ag factor of 6.778 &
47
I cbo
Hype-fine
Lines
Applred
I 15’00
1000
Magnetic
Field
zobo
in Oe
Fig. 1. ESR absorption derivative us. applied magnetic field for erbium in YHl.99 and YD,,g, powder samples. The inset shows T (0) and 0 (0) hydrogen sites surrounding an erbium ion in the f.c.c. host lattice.
0.003, consistent with a r7 doublet ground state for trivalent erbium in a cubic crystal field [ 51. This field is produced by the configuration shown in the inset in Fig. 1 in which the erbium ion is surrounded by a cube of eight nearest-neighbor T-site hydrogen ions (0) and the next-nearest-neighbor 0 sites (0) are vacant. The r, ground state indicates that these hydrogen ions are negatively charged [ 51. There are eight hyperfine lines approximately centered on the large isotropic resonance due to erbium ions in cubic sites with a nuclear spin of g (23% of the erbium ions have this nuclear spin). The positions of the hyperfine lines are indicated at the bottom of Fig. 1. In addition to the cubic erbium ESR signal and its eight hyperfine lines, the spectra in Fig. 1 have a resonance at a higher field labeled g, and a barely distinguishable peak at a lower field shown as gll. These two signals arise from erbium ions in a distinct axial site; in a powder sample a magnetic ion with axial surroundings produces an ESR spectrum with a positive peak and a “normal” derivative resonance at gll and gl respectively, where gll is the g factor with the applied magnetic field along the symmetry direction and gl is the g factor with the field normal to this axis [6]. The hyperfine lines arising from erbium ions with a nuclear spin on an axial site are too weak to be resolved. The strength of the axial erbium resonance increases with increasing hydrogen loading for both scandium and yttrium host lattices, and we associate this signal with an erbium ion surrounded by eight T-site hydrogen ions plus one and only one hydrogen on an adjacent 0 site [4]. There is no evidence for erbium ions with less than eight adjacent T-site hydrogens in the ESR spectra studied to date. This is consistent with a lower T-site energy for hydrogen adjacent to an impurity than for hydrogen at bulk sites. In the case of erbium in ScH, or ScD, there is a second distinct axial resonance which is
48
attributed to erbium ions with two adjacent O-site protons or deuterons on opposite sides of the erbium [4]. This second axial signal was not resolved for erbium in YH, or YD, and will not be considered here. The spectra in Fig. 1 were analyzed with a least-squares computer fit [3,6] to determine the number of erbium ions with a neighboring 0 site occupied compared with the number on cubic sites; the results are plotted uersus the hydrogen-to-metal ratio in Figs. 2 and 3. The large isotropic resonance plus its associated hyperfine lines are accurately described by a lorentzian line shape containing both absorptive and dispersive components (due to the metallic powder sample). The four adjustable parameters for a least-squares fit to the cubic erbium signal are the halfwidth at half-maximum (HWHM), the resonance field, the relative amounts of absorption and dispersion and an overall amplitude which is directly proportional to the number of ions in cubic sites. The smaller axial erbium ESR signal is described by a lorentzian line shape with the same absorption-to-dispersion ratio as the cubic signal but with an arbitrary HWHM (assumed to be isotropic), two resonance fields and an overall amplitude. This axial signal must be integrated, using the proper intensity variation with angle, over all angles between the applied magnetic field and the axial direction because of the powder form of the sample [6] . This two-step least-squares fitting procedure is repeated iteratively until the adjustable parameters converge; the amplitude of the axial signal divided by the amplitude of the cubic signal then determines directly the probability for O-site occupation shown in Figs. 2 and 3. In Fig. 1 the ESR signal attributed to erbium ions with one occupied adjacent 0 site has a greater intensity for YH,.a, than for YDr.ee, but it appears at the same magnetic field (g,_ = 5.00 + 0.01) for both samples.
Hydrogen to Metal Ratio x
Fig. 2. The fraction of erbium ions with one adjacent O-site hydrogen ion us. the proton (0) and the deuteron (0) concentrations for scandium host metal. The curves were calculated from the relation shown with A = 0.0029for ScH, and A = 0.0017 for ScD, (see text).
49
L .90
1.0*
2.00
2.01
2.
LO
Hydrogen to Metal Ratio x
Fig. 3. The fraction of erbium ions with one adjacent O-site hydrogen ion us. the ,’ proton (0) and the deuteron (0) concentrations for yttrium host metal. The curves were calculated from the relation shown with A = 0.020 and B = 0.0040 for YH, and A = 0.011 and B = 0.0025 for YD, (CO(X) is given by eqn. (1)).
Similarly the axial erbium signal in a ScH, sample is greater than that in a ScD, sample for a given hydrogen-to-metal ratio but occurs at the same g factor (gL = 5.44 f 0.01). These results indicate that the effective charge on the neighboring hydrogen ions and their distance from the erbium ion do not vary significantly with isotope. This is consistent with the small difference in lattice constant for a hydride and a deuteride of the same metal [l] . It also supports the assumption that the electronic properties of these materials are relatively insensitive to isotope [ 21 .
3. Lattice-gas calculation In this section we summarize the results of a lattice-gas calculation described in a previous paper [ 71. The calculation assumes an equilibrium distribution of hydrogen among the available sites in a host lattice containing erbium impurities. The equations contain two parameters which are adjusted to describe the ESR data in the different hosts. These parameters in turn involve the difference in site energies for the hydrogen divided by an equilibrium temperature. At the experimental temperature of 2 K the hydrogen cannot move to establish equilibrium between the sites, so the equilibrium temperature is estimated to be the temperature below which motion among the sites does not occur on the experimental time scale. This point is discussed further at the end of this section. Our lattice-gas model assumes that the erbium ions are well separated in the host lattice and that the hydrogen distribution around one erbium ion is independent of all other erbium ions. The f.c.c. dihydride lattice has four metal atoms per cubic cell, and at 0.1 at.% Er the impurities are separated by
50
six cells on average. We studied samples with both more and less erbium; the ESR linewidth increases linearly with concentration, indicating isolated impurity ions. Furthermore the ratio of erbium ions in cubic sites to erbium ions in axial sites does not vary significantly with erbium concentration, supporting a model with independent impurity ions. This allows a distinction between those hydrogen ions on a site adjacent to an erbium ion (nearest or next-nearest neighbors) and those on sites in the bulk host lattice. Three site energies for hydrogen ions are involved: the energy Ur for hydrogen on a bulk T site, the bulk O-site energy iJo and the energy Uo for an 0 site next to an erbium impurity (T sites next to an erbium ion are always filled and the ESR data do not give their energy). Neglecting protonproton interactions, the equilibrium occupation probability for each site can be written in terms of the site energy, the temperature and the chemical potential [ 71. (The effect of interactions is discussed elsewhere [ 81. Interactions do not significantly alter the form of eqn. (2) or the value of A obtained from a fit to the ESR data.) By requiring that the amount of bulk hydrogen on T sites plus the amount of bulk hydrogen on 0 sites should equal the hydrogen-to-metal ratio X, we can eliminate the chemical potential to obtain the following equation for the probability co(x) that a bulk 0 site is occupied : ~~(~)=x-4x/(2+x+B(1-x)+[8B+{2-x-B(1-x)}~]~’~) where B = exp {(Ur - U,)/h,T). probability pr(3t) for occupation Pl@)
=
AIx -co(x)) 2 -x
+ Co(X)
(1)
Similarly we can obtain a relation for the of one and only one impurity 0 site: (2)
where A = 6 exp {(UT - U&)/k& (there are six equivalent 0 sites) [ 71. Since the samples are single phase and the lattice spacing is relatively constant for the concentrations studied here, we make the simplifying assumption that the site energies UT., U. and Ub are independent of the hydrogen-to-metal ratio x. This neglects any mean-field contributions from H-H interactions to the effective site energies. Hence there are two adjustable parameters, A and B, for fitting eqn. (2) to our ESR data. In Fig. 2 the experimental impurity O-site occupation probability pi(x) is plotted uersus x for erbium in ScH, (0) and ScD, (0). The curves are calculated from eqn. (2) with A = 0.0029 and B = 0 for ScH, and A = 0.0017 and B = 0 for ScD,, corresponding to a 7% increase in the site energy difference Ur for the heavier isotope. (The value of A given here for ScH, is G slightly smaller than that reported earlier [4, 71 which was obtained using a less rigorous fitting procedure.) From eqn. (l), when B = 0 the probability co(x) of the bulk O-site occupation is zero for x < 2. The error bar on our hydrogen-to-metal ratio x is kO.005, and this sets an upper limit on B of 10V5 for both ScH, and ScD,. The experimentalp data for YH, (0) and YD, (0) are shown in Fig. 3. In contrast with the scandium data which rise rapidly as x approaches 2, the
51
yttrium data vary smoothly from x = 1.9 to x = 2.1. This means that co(x) is not negligibly small for the yttrium samples as it is for scandium. The curve for YH, was calculated from eqn. (2) with A = 0.020 and I3 = 0.0040; the values for YD, are A = 0.011 and B = 0.0025. This corresponds to a 10% increase in the site energy difference Uo - U, for the heavier isotope and to a 9% increase in the bulk difference U, - U,. As discussed elsewhere [ 71, the temperature T which appears in eqns. (1) and (2) is an equilibrium temperature at which the hydrogen distribution among the available sites can be described by a lattice-gas model. Since equilibrium does not exist at our experimental temperature of 2 K, we must use a “freezing” temperature Tf below which the hydrogen distribution does not change on an experimental time scale. Each sample was cooled from room temperature to 10 K at 2 - 5 K min- r, so a reasonable estimate for Tf is the temperature at which the proton jump time is 1 min. Proton motion in metal hydrides is characterized by activation energies of 400 - 500 meV, which makes the jump time a strong function of temperature. Using proton nuclear magnetic resonance diffusion data [9] for ScH,, the jump times are estimated (by extrapolation) to be 1 s at 180 K and 1 h at 135 K, and we choose Tf = 150 K (1 min jump time). This value of Tf will vary with the isotope mass and the host metal; however, in the following discussion these changes are not important, and we use a single freezing temperature for all samples. With Tf = 150 K the values for A and B given already for the four host materials yield the site energy differences listed in Table 1. The bulk site energy difference for the two yttrium hosts can be substituted into eqn. (1) to obtain the O-site occupation fraction at room temperature for a hydrogento-metal ratio of 2: co(x = 2) is 0.28 in YH, and 0.25 in YD,. For T below the freezing temperature the corresponding values are 0.08 and 0.07. It should be noted that the latter occupation fractions are obtained directly by applying eqns. (1) and (2) to the ESR data in Fig. 3 and are independent of the actual value of Tf (assuming that it is higher than the experimental temperature of 2 K). TABLE 1 Site energy differences for a freezing temperature Z’f = 150 K using the parameters A and B which fit the lattice-gas model to the ESR pl data Sample
Ub - UT (meV)
UO - UT (meV)
ScH, ScD, YH, YDx
98 106 14 81
>150 >150 71 78
4. Vibrational energy shift and conclusions From Table 1 it can be seen that the bulk site energy difference U, U, increases from 71 to 78 meV on substituting deuterons for protons in the
52
yttrium system. If the choice of 150 K for the freezing temperature were in error by 50 K, this increase would change by 2 meV. Hence we must explain a site energy shift of 5 - 9 meV with isotope in the yttrium samples. The site energy for a hydrogen ion in these materials can be divided into an electronic part and a vibrational part, i.e. into a well depth plus a zero-point motion. This is shown schematically in Fig. 4 for a T site where the well depth (i.e. the electronic part of the total site energy) is -ET and the vibrational part is 4 fiw F for a proton and $ R, !i?for a deuteron. Hence the T-site energy for a proton is U!i!= -ET + 4 tie F with an analogous expression for T-site deuterons. The energy of protons and deuterons on 0 sites can be divided into an electronic part and a vibrational part in an identical manner. From energy band considerations, the electronic energy for either an 0 site or a T site is expected to be relatively insensitive to isotope [2]. In addition, our ESR results show that the axial g factor splitting of an erbium ion due to an adjacent O-site proton or deuteron is independent of isotope, indicating a similar effective charge and a similar lattice spacing. Hence we look to the change in vibrational energy with mass to explain the 5 - 9 meV shift determined from impurity ESR. Recent inelastic neutron-scattering results [ 10, 111 give a direct measure of the proton vibrational energy on a T site in YH,: tiw: = 116 f 2 meV. Unfortunately no direct measurement of the corresponding O-site vibrational energy has been reported, but we can estimate this energy from inelastic neutron-scattering data for an isomorphic hydride. LaH, has vibrational energies of 103 meV for T-site protons and 78 meV for O-site protons [ 12, 131. Taking into account that the corresponding T-site vibrational energy in YH, is roughly 13% higher, we can estimate that hw:! = 88 ? 5 meV for O-site protons in YH2. This argument is based on the fact that the vibrational energies in these materials are correlated with the lattice spacing [ 141. Data for deuterons in several dideuterides show that the vibrational energy varies as the inverse square root of the isotope mass, as expected [ 10, 131.
Fig. 4. A schematic representation of various energies associated with protons and deuterons on a T site in the bulk host lattice. The site energy U, is the difference between the electronic energy (well depth) -I$ and the vibrational energy (zero-point motion) p fiw,.
53
Using these values, we find that the T-site vibrational energy is approximately 42 meV higher than the O-site vibrational energy for protons in YH,. From our lattice-gas model, the total T-site energy U$ is 71 meV lower than the O-site energy UE for protons. Hence the electronic part of the site energy (--ET in Fig. 4) must be roughly 113 meV lower for protons on T-sites than for protons on O-sites. From the inverse square root mass dependence, the T-site vibrational energy is approxima~ly 30 meV higher than the O-site value for deuterons, If the electronic site energies are independent of isotope, this means that the total site energy difference should be 42 - 30 = 12 meV greater in YD, than in YH,. This is in reasonable agreement with the shift of 7 * 2 meV obtained from impurity ESR assuming a freezing temperature Tf = 150 K. The discrepancy may result from a small change in electronic energy with isotope, a value for Tf that is too low or an O-site vibrational energy that is higher than our estimate of 88 meV. If the last explanation holds, the O-site vibrational energy in YH, must be roughly 100 meV; however, this is about 30% above the co~espond~g value in LaH, [ 131, an unreasonably large shift. Clearly more info~ation concerning hydrogen and deuterium motion at low temperatures is needed to obtain better definition of the freezing temperature. In summary, ESR measurements of the hydrogen and deuterium distributions around erbium ions in dilute concentration in samples of scandium and yttrium hydrides and deuterides together with a lattice-gas model yield total site energy differences for the hydrogen isotopes both adjacent to the erbium and in the bulk host lattice. Inelastic neutron-scattering data give the vibrational part of the site energies for hydrogen and deuterium, and there is reasonable agreement between the isotope dependences of the total site energy and of the energy from vibrations motion alone. This supports the assertion that the electronic part of the energy is relatively insensitive to the particular hydrogen isotope. As discussed elsewhere [ 81, the H-H interactions deduced from the ESR data for ScH, and ScD, also appear to be isotope independent. Acknowledgments Discussions of this work with A. C. Switendick and P. M. Richards are gratefully acknowledged. A. M. Gutierrez recorded several ESR spectra. Sandia National Laboratories is a U.S. Department of Energy facility. This work was sponsored by the U.S. Department of Energy under Contract No. DE-AC04-76-DP00789. References 1 W. M. Mueller, in W. M. Muelter, J. P. Blackiedge and G. G. Libowitz (eds.), Mefaf Hydrides, Academic Press, New York, 1968, Chap. 9. 2 A. C. Switendick, personal communication, 1979.
54 3 4 5 6 7 8 9 10 11 12 13
14
E. L. Venturini, J. Appl. Phys., 50 (1979) 2053. E. L. Venturini and P. M. Richards, Solid State Commun., 32 (1979) 1185. K. R. Lea, M. J. M. Leask and W. P. Wolf, J. Phys. Chem. Solids, 23 (1962) 1381. R. Aasa and T. Vanngard, J. Magn. Reson., 19 (1975) 308. E. L. Venturini and P. M. Richards, Phys. Lett. A, 76 (1980) 344. P. M. Richards, Proc. Int. Symp. on the Properties and Applications of Metal Hydrides, Colorado Springs, Colorado, April 7 - 1 I, 1980; J. Less-Common Met., 74 (1980) 81. H. T. Weaver, Phys. Rev., Sect. B, 5 (1972) 1663. J. J. Rush, H. E. Flotow, D. W. Connor and C. L. Thaper, J. Chem. Phys., 45 (1966) 3817. V. K. Brand, Atomkernenergie, 17 (1971) 113. D. G. Hunt and D. K. Ross, J. Less-Common Met., 49 (1976) 169. P. P. Parshin, M. G. Zemlyanov, M. E. Kost, A. Yu. Rumyantsev and N. A. Chernoplekov, Izv. Akad. Nauk SSSR, Neog. Mater., 14 (1978) 1653; Inorg. Mater. (USSR), 14 (1978) 1288. M. Moss, personal communication, 1979.
Journal of the Less-Common Metals, 74 (1980) 45 - 54 0 Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
ISOTOPE EFFECT DIHYDRIDES”
ON HYDROGEN
SITE ENERGIES
FOR TWO METAL
E. L. VENTURXNI Sandra National Laboratories,
Albuquerque~
N.M. 87185
(‘U.S.A.)
Summary
The change in hydrogen site energy with isotope for dihydrides and dideuterides of scandium and yttrium was indirectly determined using electron spin resonance (ESR) of erbium ions in dilute concentration in the f.c.c. hosts. The ESR spectra measure the distribution of hydrogen adjacent to the erbium; the variations in this distribution with isotope and with hydrogen-tometal ratio were studied for several samples of both host metals. The data are accurately described by a lattice-gas model which yields the energy difference for protons or deuterons on octahedral and tetrahedral sites, both adjacent to the erbium impurities and in the bulk host lattice. This energy difference is 10% greater for deuterons, and the change with isotope can be attributed primarily to the mass dependence of the vibrational part of the total energy associated with each site.
1. Introduction
In the f.c.c. dihydrides of group IIEb metals hydrogen has two available sites which are.denoted as octahedral (0) and tetrahedral (T) from the arrangement of nearest-neighbor metal ions [l] . There are two T sites and one 0 site per metal atom, with the 0 sites having a higher total energy than the T sites. This leads to the formation of a metal dihydride with very few 0 sites occupied at low temperat~es. At low temperature the site energy of a hydrogen ion consists of an electronic part and a vibrational part, i.e., a well depth plus a zero-point energy; to a first approximation only the vibrational part changes with isotope, varying as the inverse square root, of the mass. Using electron spin resonance (ESR) of erbium ions in dilute concentration in scandium and yttrium dihydride and dideuteride hosts, we measured the occupation of 0 sites adjacent to the erbium as a function of hydrogen
*Paper presented at the International Symposium on the Properties and Applications of Metal Hydrides, Colorado Springs, Colorado, U.S.A., April 7 - 11, 1980.
46
and deuterium loading. The experimental details are presented in Section 2, while in Section 3 we outline a simple lattice-gas calculation which explains the ESR data and yields site energy differences for the hydrogen isotopes both next to the erbium impurity ions and in the bulk hydride/deuteride. The energy difference is approximately 10% greater for deuterium in both scandium and yttrium host lattices. In the final section we estimate the change in the vibrational part of the site energies with isotope mass using published inelastic neutron-scattering data and show that the change in total site energy determined from the erbium ESR data can be explained by the mass dependence of the vibrational energy for each site. This result supports the suggestion that the electronic part of the site energy is nearly independent of the hydrogen isotope [2] and allows extrapolation to find total site energies in metal tritides.
2. Experimental
details
The samples used in this study were prepared by arc melting 0.1 at.% Er into specially purified scandium or yttrium, loading with hydrogen or deuterium in a modified Sieverts’ apparatus and then grinding the brittle metal hydride into a fine powder for the ESR measurements. The loading ratio for each sample was determined both volumetrically and gravimetritally, the former method yielding a more accurate value, although both values agreed to better than 1%. We did not verify directly that no hydrogen was lost during grinding of the bulk samples, but bulk loading ratios were used together with ESR data from the corresponding crushed powders for the plots in Figs. 2 and 3. The excellent agreement between the measurements and the predicted (lattice-gas) dependence on hydrogen-to-metal ratio, as shown by the data points and calculated curves respectively, suggests that any hydrogen deficiency due to grinding is less than the loading uncertainty indicated by the error bars. Of much greater concern in preparing the samples was the problem of obtaining a homogeneous hydrogen distribution in non-stoichiometric materials; this requires very careful temperature-pressure cycling during loading. The hydrogen-to-metal ratio ranged from 1.89 to 1.995 in the scandium samples and from 1.90 to 2.10 in the yttrium samples. The yttrium samples with the highest loading contained a very small amount of the trihydride phase (easily detected as a new signal in the erbium ESR spectrum), but all other samples were single phase within the accuracy of our measurements. Figure 1 shows derivative ESR absorption spectra for 0.1 at.% Er in samples of YH,_ss and YD,,a, powder. The data were obtained at 9.8 GHz and 2 K, the low temperature yielding narrow resonance lines and a good signal-to-noise ratio. Both spectra reveal two distinct sites for the erbium ions, one with cubic symmetry and one with axial symmetry. Similar spectra [ 3, 41 have been observed for erbium in ScH, . The erbium ESR data in Fig. 1 are dominated by a large isotropic resonance with ag factor of 6.778 &
47
I cbo
Hype-fine
Lines
Applred
I 15’00
1000
Magnetic
Field
zobo
in Oe
Fig. 1. ESR absorption derivative us. applied magnetic field for erbium in YHl.99 and YD,,g, powder samples. The inset shows T (0) and 0 (0) hydrogen sites surrounding an erbium ion in the f.c.c. host lattice.
0.003, consistent with a r7 doublet ground state for trivalent erbium in a cubic crystal field [ 51. This field is produced by the configuration shown in the inset in Fig. 1 in which the erbium ion is surrounded by a cube of eight nearest-neighbor T-site hydrogen ions (0) and the next-nearest-neighbor 0 sites (0) are vacant. The r, ground state indicates that these hydrogen ions are negatively charged [ 51. There are eight hyperfine lines approximately centered on the large isotropic resonance due to erbium ions in cubic sites with a nuclear spin of g (23% of the erbium ions have this nuclear spin). The positions of the hyperfine lines are indicated at the bottom of Fig. 1. In addition to the cubic erbium ESR signal and its eight hyperfine lines, the spectra in Fig. 1 have a resonance at a higher field labeled g, and a barely distinguishable peak at a lower field shown as gll. These two signals arise from erbium ions in a distinct axial site; in a powder sample a magnetic ion with axial surroundings produces an ESR spectrum with a positive peak and a “normal” derivative resonance at gll and gl respectively, where gll is the g factor with the applied magnetic field along the symmetry direction and gl is the g factor with the field normal to this axis [6]. The hyperfine lines arising from erbium ions with a nuclear spin on an axial site are too weak to be resolved. The strength of the axial erbium resonance increases with increasing hydrogen loading for both scandium and yttrium host lattices, and we associate this signal with an erbium ion surrounded by eight T-site hydrogen ions plus one and only one hydrogen on an adjacent 0 site [4]. There is no evidence for erbium ions with less than eight adjacent T-site hydrogens in the ESR spectra studied to date. This is consistent with a lower T-site energy for hydrogen adjacent to an impurity than for hydrogen at bulk sites. In the case of erbium in ScH, or ScD, there is a second distinct axial resonance which is
48
attributed to erbium ions with two adjacent O-site protons or deuterons on opposite sides of the erbium [4]. This second axial signal was not resolved for erbium in YH, or YD, and will not be considered here. The spectra in Fig. 1 were analyzed with a least-squares computer fit [3,6] to determine the number of erbium ions with a neighboring 0 site occupied compared with the number on cubic sites; the results are plotted uersus the hydrogen-to-metal ratio in Figs. 2 and 3. The large isotropic resonance plus its associated hyperfine lines are accurately described by a lorentzian line shape containing both absorptive and dispersive components (due to the metallic powder sample). The four adjustable parameters for a least-squares fit to the cubic erbium signal are the halfwidth at half-maximum (HWHM), the resonance field, the relative amounts of absorption and dispersion and an overall amplitude which is directly proportional to the number of ions in cubic sites. The smaller axial erbium ESR signal is described by a lorentzian line shape with the same absorption-to-dispersion ratio as the cubic signal but with an arbitrary HWHM (assumed to be isotropic), two resonance fields and an overall amplitude. This axial signal must be integrated, using the proper intensity variation with angle, over all angles between the applied magnetic field and the axial direction because of the powder form of the sample [6] . This two-step least-squares fitting procedure is repeated iteratively until the adjustable parameters converge; the amplitude of the axial signal divided by the amplitude of the cubic signal then determines directly the probability for O-site occupation shown in Figs. 2 and 3. In Fig. 1 the ESR signal attributed to erbium ions with one occupied adjacent 0 site has a greater intensity for YH,.a, than for YDr.ee, but it appears at the same magnetic field (g,_ = 5.00 + 0.01) for both samples.
Hydrogen to Metal Ratio x
Fig. 2. The fraction of erbium ions with one adjacent O-site hydrogen ion us. the proton (0) and the deuteron (0) concentrations for scandium host metal. The curves were calculated from the relation shown with A = 0.0029for ScH, and A = 0.0017 for ScD, (see text).
49
L .90
1.0*
2.00
2.01
2.
LO
Hydrogen to Metal Ratio x
Fig. 3. The fraction of erbium ions with one adjacent O-site hydrogen ion us. the ,’ proton (0) and the deuteron (0) concentrations for yttrium host metal. The curves were calculated from the relation shown with A = 0.020 and B = 0.0040 for YH, and A = 0.011 and B = 0.0025 for YD, (CO(X) is given by eqn. (1)).
Similarly the axial erbium signal in a ScH, sample is greater than that in a ScD, sample for a given hydrogen-to-metal ratio but occurs at the same g factor (gL = 5.44 f 0.01). These results indicate that the effective charge on the neighboring hydrogen ions and their distance from the erbium ion do not vary significantly with isotope. This is consistent with the small difference in lattice constant for a hydride and a deuteride of the same metal [l] . It also supports the assumption that the electronic properties of these materials are relatively insensitive to isotope [ 21 .
3. Lattice-gas calculation In this section we summarize the results of a lattice-gas calculation described in a previous paper [ 71. The calculation assumes an equilibrium distribution of hydrogen among the available sites in a host lattice containing erbium impurities. The equations contain two parameters which are adjusted to describe the ESR data in the different hosts. These parameters in turn involve the difference in site energies for the hydrogen divided by an equilibrium temperature. At the experimental temperature of 2 K the hydrogen cannot move to establish equilibrium between the sites, so the equilibrium temperature is estimated to be the temperature below which motion among the sites does not occur on the experimental time scale. This point is discussed further at the end of this section. Our lattice-gas model assumes that the erbium ions are well separated in the host lattice and that the hydrogen distribution around one erbium ion is independent of all other erbium ions. The f.c.c. dihydride lattice has four metal atoms per cubic cell, and at 0.1 at.% Er the impurities are separated by
50
six cells on average. We studied samples with both more and less erbium; the ESR linewidth increases linearly with concentration, indicating isolated impurity ions. Furthermore the ratio of erbium ions in cubic sites to erbium ions in axial sites does not vary significantly with erbium concentration, supporting a model with independent impurity ions. This allows a distinction between those hydrogen ions on a site adjacent to an erbium ion (nearest or next-nearest neighbors) and those on sites in the bulk host lattice. Three site energies for hydrogen ions are involved: the energy Ur for hydrogen on a bulk T site, the bulk O-site energy iJo and the energy Uo for an 0 site next to an erbium impurity (T sites next to an erbium ion are always filled and the ESR data do not give their energy). Neglecting protonproton interactions, the equilibrium occupation probability for each site can be written in terms of the site energy, the temperature and the chemical potential [ 71. (The effect of interactions is discussed elsewhere [ 81. Interactions do not significantly alter the form of eqn. (2) or the value of A obtained from a fit to the ESR data.) By requiring that the amount of bulk hydrogen on T sites plus the amount of bulk hydrogen on 0 sites should equal the hydrogen-to-metal ratio X, we can eliminate the chemical potential to obtain the following equation for the probability co(x) that a bulk 0 site is occupied : ~~(~)=x-4x/(2+x+B(1-x)+[8B+{2-x-B(1-x)}~]~’~) where B = exp {(Ur - U,)/h,T). probability pr(3t) for occupation Pl@)
=
AIx -co(x)) 2 -x
+ Co(X)
(1)
Similarly we can obtain a relation for the of one and only one impurity 0 site: (2)
where A = 6 exp {(UT - U&)/k& (there are six equivalent 0 sites) [ 71. Since the samples are single phase and the lattice spacing is relatively constant for the concentrations studied here, we make the simplifying assumption that the site energies UT., U. and Ub are independent of the hydrogen-to-metal ratio x. This neglects any mean-field contributions from H-H interactions to the effective site energies. Hence there are two adjustable parameters, A and B, for fitting eqn. (2) to our ESR data. In Fig. 2 the experimental impurity O-site occupation probability pi(x) is plotted uersus x for erbium in ScH, (0) and ScD, (0). The curves are calculated from eqn. (2) with A = 0.0029 and B = 0 for ScH, and A = 0.0017 and B = 0 for ScD,, corresponding to a 7% increase in the site energy difference Ur for the heavier isotope. (The value of A given here for ScH, is G slightly smaller than that reported earlier [4, 71 which was obtained using a less rigorous fitting procedure.) From eqn. (l), when B = 0 the probability co(x) of the bulk O-site occupation is zero for x < 2. The error bar on our hydrogen-to-metal ratio x is kO.005, and this sets an upper limit on B of 10V5 for both ScH, and ScD,. The experimentalp data for YH, (0) and YD, (0) are shown in Fig. 3. In contrast with the scandium data which rise rapidly as x approaches 2, the
51
yttrium data vary smoothly from x = 1.9 to x = 2.1. This means that co(x) is not negligibly small for the yttrium samples as it is for scandium. The curve for YH, was calculated from eqn. (2) with A = 0.020 and I3 = 0.0040; the values for YD, are A = 0.011 and B = 0.0025. This corresponds to a 10% increase in the site energy difference Uo - U, for the heavier isotope and to a 9% increase in the bulk difference U, - U,. As discussed elsewhere [ 71, the temperature T which appears in eqns. (1) and (2) is an equilibrium temperature at which the hydrogen distribution among the available sites can be described by a lattice-gas model. Since equilibrium does not exist at our experimental temperature of 2 K, we must use a “freezing” temperature Tf below which the hydrogen distribution does not change on an experimental time scale. Each sample was cooled from room temperature to 10 K at 2 - 5 K min- r, so a reasonable estimate for Tf is the temperature at which the proton jump time is 1 min. Proton motion in metal hydrides is characterized by activation energies of 400 - 500 meV, which makes the jump time a strong function of temperature. Using proton nuclear magnetic resonance diffusion data [9] for ScH,, the jump times are estimated (by extrapolation) to be 1 s at 180 K and 1 h at 135 K, and we choose Tf = 150 K (1 min jump time). This value of Tf will vary with the isotope mass and the host metal; however, in the following discussion these changes are not important, and we use a single freezing temperature for all samples. With Tf = 150 K the values for A and B given already for the four host materials yield the site energy differences listed in Table 1. The bulk site energy difference for the two yttrium hosts can be substituted into eqn. (1) to obtain the O-site occupation fraction at room temperature for a hydrogento-metal ratio of 2: co(x = 2) is 0.28 in YH, and 0.25 in YD,. For T below the freezing temperature the corresponding values are 0.08 and 0.07. It should be noted that the latter occupation fractions are obtained directly by applying eqns. (1) and (2) to the ESR data in Fig. 3 and are independent of the actual value of Tf (assuming that it is higher than the experimental temperature of 2 K). TABLE 1 Site energy differences for a freezing temperature Z’f = 150 K using the parameters A and B which fit the lattice-gas model to the ESR pl data Sample
Ub - UT (meV)
UO - UT (meV)
ScH, ScD, YH, YDx
98 106 14 81
>150 >150 71 78
4. Vibrational energy shift and conclusions From Table 1 it can be seen that the bulk site energy difference U, U, increases from 71 to 78 meV on substituting deuterons for protons in the
52
yttrium system. If the choice of 150 K for the freezing temperature were in error by 50 K, this increase would change by 2 meV. Hence we must explain a site energy shift of 5 - 9 meV with isotope in the yttrium samples. The site energy for a hydrogen ion in these materials can be divided into an electronic part and a vibrational part, i.e. into a well depth plus a zero-point motion. This is shown schematically in Fig. 4 for a T site where the well depth (i.e. the electronic part of the total site energy) is -ET and the vibrational part is 4 fiw F for a proton and $ R, !i?for a deuteron. Hence the T-site energy for a proton is U!i!= -ET + 4 tie F with an analogous expression for T-site deuterons. The energy of protons and deuterons on 0 sites can be divided into an electronic part and a vibrational part in an identical manner. From energy band considerations, the electronic energy for either an 0 site or a T site is expected to be relatively insensitive to isotope [2]. In addition, our ESR results show that the axial g factor splitting of an erbium ion due to an adjacent O-site proton or deuteron is independent of isotope, indicating a similar effective charge and a similar lattice spacing. Hence we look to the change in vibrational energy with mass to explain the 5 - 9 meV shift determined from impurity ESR. Recent inelastic neutron-scattering results [ 10, 111 give a direct measure of the proton vibrational energy on a T site in YH,: tiw: = 116 f 2 meV. Unfortunately no direct measurement of the corresponding O-site vibrational energy has been reported, but we can estimate this energy from inelastic neutron-scattering data for an isomorphic hydride. LaH, has vibrational energies of 103 meV for T-site protons and 78 meV for O-site protons [ 12, 131. Taking into account that the corresponding T-site vibrational energy in YH, is roughly 13% higher, we can estimate that hw:! = 88 ? 5 meV for O-site protons in YH2. This argument is based on the fact that the vibrational energies in these materials are correlated with the lattice spacing [ 141. Data for deuterons in several dideuterides show that the vibrational energy varies as the inverse square root of the isotope mass, as expected [ 10, 131.
Fig. 4. A schematic representation of various energies associated with protons and deuterons on a T site in the bulk host lattice. The site energy U, is the difference between the electronic energy (well depth) -I$ and the vibrational energy (zero-point motion) p fiw,.
53
Using these values, we find that the T-site vibrational energy is approximately 42 meV higher than the O-site vibrational energy for protons in YH,. From our lattice-gas model, the total T-site energy U$ is 71 meV lower than the O-site energy UE for protons. Hence the electronic part of the site energy (--ET in Fig. 4) must be roughly 113 meV lower for protons on T-sites than for protons on O-sites. From the inverse square root mass dependence, the T-site vibrational energy is approxima~ly 30 meV higher than the O-site value for deuterons, If the electronic site energies are independent of isotope, this means that the total site energy difference should be 42 - 30 = 12 meV greater in YD, than in YH,. This is in reasonable agreement with the shift of 7 * 2 meV obtained from impurity ESR assuming a freezing temperature Tf = 150 K. The discrepancy may result from a small change in electronic energy with isotope, a value for Tf that is too low or an O-site vibrational energy that is higher than our estimate of 88 meV. If the last explanation holds, the O-site vibrational energy in YH, must be roughly 100 meV; however, this is about 30% above the co~espond~g value in LaH, [ 131, an unreasonably large shift. Clearly more info~ation concerning hydrogen and deuterium motion at low temperatures is needed to obtain better definition of the freezing temperature. In summary, ESR measurements of the hydrogen and deuterium distributions around erbium ions in dilute concentration in samples of scandium and yttrium hydrides and deuterides together with a lattice-gas model yield total site energy differences for the hydrogen isotopes both adjacent to the erbium and in the bulk host lattice. Inelastic neutron-scattering data give the vibrational part of the site energies for hydrogen and deuterium, and there is reasonable agreement between the isotope dependences of the total site energy and of the energy from vibrations motion alone. This supports the assertion that the electronic part of the energy is relatively insensitive to the particular hydrogen isotope. As discussed elsewhere [ 81, the H-H interactions deduced from the ESR data for ScH, and ScD, also appear to be isotope independent. Acknowledgments Discussions of this work with A. C. Switendick and P. M. Richards are gratefully acknowledged. A. M. Gutierrez recorded several ESR spectra. Sandia National Laboratories is a U.S. Department of Energy facility. This work was sponsored by the U.S. Department of Energy under Contract No. DE-AC04-76-DP00789. References 1 W. M. Mueller, in W. M. Muelter, J. P. Blackiedge and G. G. Libowitz (eds.), Mefaf Hydrides, Academic Press, New York, 1968, Chap. 9. 2 A. C. Switendick, personal communication, 1979.
54 3 4 5 6 7 8 9 10 11 12 13
14
E. L. Venturini, J. Appl. Phys., 50 (1979) 2053. E. L. Venturini and P. M. Richards, Solid State Commun., 32 (1979) 1185. K. R. Lea, M. J. M. Leask and W. P. Wolf, J. Phys. Chem. Solids, 23 (1962) 1381. R. Aasa and T. Vanngard, J. Magn. Reson., 19 (1975) 308. E. L. Venturini and P. M. Richards, Phys. Lett. A, 76 (1980) 344. P. M. Richards, Proc. Int. Symp. on the Properties and Applications of Metal Hydrides, Colorado Springs, Colorado, April 7 - 1 I, 1980; J. Less-Common Met., 74 (1980) 81. H. T. Weaver, Phys. Rev., Sect. B, 5 (1972) 1663. J. J. Rush, H. E. Flotow, D. W. Connor and C. L. Thaper, J. Chem. Phys., 45 (1966) 3817. V. K. Brand, Atomkernenergie, 17 (1971) 113. D. G. Hunt and D. K. Ross, J. Less-Common Met., 49 (1976) 169. P. P. Parshin, M. G. Zemlyanov, M. E. Kost, A. Yu. Rumyantsev and N. A. Chernoplekov, Izv. Akad. Nauk SSSR, Neog. Mater., 14 (1978) 1653; Inorg. Mater. (USSR), 14 (1978) 1288. M. Moss, personal communication, 1979.