Sample 2: NbHo 7 5 Single Crystal Oise

Following the findings discussed in the previous section several attempts were made to prepare a single domain |3-NbH sample in order to remove the effect of averaging over different domain orientations. A brief description of the methods used is given below.

Sample Preparation

First, it is thought that if a single crystal presents a favourable fraction of its surface area having a (100) type plane and hydriding is achieved in one complete run, (i.e. a single exposure to hydrogen instead of the cycling found to be necessary in preparing sample 1) then one domain might be formed. For example Schone et al [4.10] explain their observed domain population ratio of 1:1.2 due to the fact that their crystal only exposed the (001) plane at the cylinder surface whilst the other planes subtended an angle between 45* and 90* to the surface. Hence domains along [110] and [liO] would be preferentially formed since these are in the plane of the surface. Schone et al also give

this as an explanation for similar relative signal intensities observed by Liitgemeier et al [4.17] for 2D in p-NbEJj.

A device for exposing a single surface of a single crystal disc was made in accordance with figure 4.13 to be used in a high pressure hydriding system at Warwick [4.18]. Using the device it was intended that the top surface be exposed to 0.4 MPa of hydrogen, the opposite side being exposed to only the evacuated cavity. Thus it was thought that hydriding could be achieved relatively quickly and with a preferential domain formation. The device was not found to be effective because of intrinsic problems in its fabrication and use. Firstly, and most importantly, the knife edge seals at the edge of the disc caused stressing of the sample due to restriction of sample expansion under heat treatment which caused samples to crack excessively. Secondly, heating of the device also led to problems with the copper o-ring seal and threads on the various parts which either fatigue easily or fuse with cooperating parts. A second method considered was to expose the desired surface of a sample by masking the rest of it with a non-hydridable material [4.5] and to assist hydriding by coating the desired surface with palladium black which is known to increase hydriding rates in certain cases due to its low enthalpy of absorption of hydrogen [4.19]. This method would be somewhat complex since after applying the desired coats it would also be necessary to remove them before the nmr study. This could be achieved by etching however, a further problem might be differential rates of etching of the different coating substitutes.

The method which was found to be successful was simply to cut a disc sample and expose it to a hydrogen atmosphere as previously described for sample 1. The success is thought to be due to the fact that the disc shape simply gives a greater exposure to a certain orientation due to the ratio of the surface areas of the disc faces to edge compared with the face to length ratio of a cylindrical sample. A single domain sample of NbHo,75 was prepared by cutting, by spark-erosion, a roughly 2mm thick circular disc from a cylindrical niobium single crystal with the same orientation as sample 1. The original crystal was 12mm in diameter and 25mm long. It has a [110] cylinder axis, a purity of 99.999% and was purchased from Goodfellow Metals. This crystal disc was etched to remove damage from spark-erosion leaving approximately a 1.5mm thick, 12mm diameter disc (the disc faces were not quite parallel however, and after etching the sample had an irregular thickness of 1.5 ± 0.2mm). A schematic drawing of the crystalline disc sample is given in figure 4.14.

It was, however, again found necessary to degas and hydride the sample repeatedly before it eventually formed a |3-phase composition of NbHo.ft. The concentration was confirmed by X-ray analysis which also showed the good crystalline quality of the hydrided sample. A crack developed from the outer edge to the centre of the disc along the [110] direction, which as has been demonstrated lies in an easy cleave plane of this phase [4.9]. The sample was subsequently found by the Knight shift measurements to contain only one type of domain with principal axis perpendicular to the [110] (disc face normal direction), that is along the [001] direction.

NMR Experimental Details

NMR measurements on this sample were made at 47MHz and approximately 1.1T. For the Tj study the disc was held in a PTFE former which was a rectangular plate (of dimension 210 x 15 x 2mm) with a central hole to hold the disc by friction. A 9.5 turn 24 swg copper wire coil was wound around the former and tuned to 47MHz using the tapped series matching probe. A signal to noise ratio of about 1:1 was observed on the oscilloscope for a simple 90° pulse. However, this coil was found to be problematical when studying the fH lineshape behaviour. In order to avoid any effects due to the coil shape the crystal was mounted in a cylindrical PTFE former, split longitudinally in to two sections and having a recess for the crystal. A 7 turn 24 swg copper wire, cylindrical coil was wound on the former. The former was then mounted in the holder used for a cylindrical crystal. This arrangement obviously led to a lower signal to noise due to the decreased sample filling factor but adequate measurements were achieved as described below.

Knight Shift Study

Knight shift studies of a disc-shaped sample are complicated by an anisotropic demagnetising field effect due to the sample shape winch produces an angular dependence [4.20]. It can be shown that the orientational dependent shift S(8) observed in such a case is:

S(9) - K A x iW e - l) - asin2© {4.5}

where @>0* when both the domain symmetry axis and disc faces are parallel with B0

as is the case for the sample prepared as shown in figure 4.14. The demagnetising factor a is shape dependent and varies from 0 to 4nxv (in c.g.s units), where the upper limit is valid for an “infinite plate” and this sample is expected to take some

intermediate value. Calculation of this factor is somewhat complex and only readily obtainable for rather simple shapes such as ellipsoids and not the irregular, tapered disc shape of this sample.

The absolute shift relative to a standard reference of bare protons can be calculated using the following expression

where Kjso is the observed shift relative to a signal from pure water. 4/3^v is the Lorentz cavity field [4.22] and -25.6ppm is the molecular shielding constant for protons in water [4.23].

The factor a was determined qualitatively by orientating the [001] direction parallel to the axis of rotation of the crystal thereby removing the Knight shift component of equation 4.5. The crystal was rotated between orientations having the disc faces and crystal [110] direction parallel to B0, and the disc face normal and crystal [liO] parallel toB0. As stated earlier, a single *H line was observed and the maximum observed separation of the *H line in the two positions was 39 t 2ppm. This value for the demagnetisation factor a is approximately 1/3 the value of HOppm observed by Fukai and Kazama [4.20] for a thin (50pm) foil of NbHo.771. From their measurements over a range o f sample angles and sample concentrations they observed a non-linear decrease in volume susceptibility of the systems with increasing hydrogen concentration which was in reasonable agreement with results obtained from ordinary susceptibility studies. From this it is reasonable to predict a value of a-120ppm for a 50pm sheet sample of NbHojs-

Returning the crystal to the orientation shown in figure 4.14 the orientational dependence of the *H Knight shift was measured and the results obtained are shown in figure 4.15. The orientational dependence observed was in good agreement with the predicted form given by equation 4.5.

The observation of a single resonance line from this sample and the Knight shift orientational dependence confirms the statements made earlier about the population of domains and the orientation within the disc. It was felt that achievable accuracy in determining Kjsq did not warrant its study since extensive measurements of this system in more suitably shaped samples already exist [4.10,4.14 & 4.20].

With the orientation indicated in figure 4.14 the shift observed is as shown in figure 4.15. The maximum separation of the line when 0=0° and 0=90° (ie [001] parallel and perpendicular to B0 respectively) was 101.6 ± 2ppm. Fitting the observed data to equation 4.5 we obtain a value for of -19.5 ± 2ppm in good agreement with previously quoted values. The linewidth observed was of the order of 20ppm and therefore, in similarly good agreement with previously obtained values. Again, however, a value for K^jj was not determinable from the data, except to say that it may be non-zero.

Tj Study

An extensive investigation of the *H Tj orientation and temperature dependence has been carried out and the results are shown in figures 4.16.4.17 and 4.18.

Due to the problem discussed earlier of maintaining a constant sample temperature whilst rotating the sample through a range of orientations, as with sample 1 a set of Ti measurements for one specific orientation at a time were made at various temperatures between ambient room temperature and about 217K. The data shown in figure 4.16 A, B, & C, are for 0*0°, 35° and 90° respectively and they are shown comparitively in figure 4.16D. These are, the approximate orientations predicted to give the maximum variation in Tj for single or multiple domain samples.

Typically, each Tj measurement consisted of about 50 sweeps of X , given in equation 2.4, from 0 to 5Ti, though this was less, say 32 or 16, for longer values of Tj. Several data sets (between 4 and 9) were taken at each temperature where a stability of better than IK was achieved during the period of gathering ail data sets. The error in the fittedTj value for each T j data set was of the order of or less than 5% and the standard deviation in the average of Tj from the gathered data was of the order of 2-3%.

The magnitude of the relaxation times is in good agreement with those obtained for sample 1 (given the increase in field, B, of study). As pointed out earlier, the gradient of T i v T-l is meaningless in terms of determining activation energies since it incorporates a divergence in T j for the various orientations as the low temperature limit is reached and maximum anisotropy occurs. Nevertheless they are consistent with increasing anisotropy with decreasing temperature and are given in table 4.3.

Tablet.3 Orientation, 9 0* 35* 90° Apparent Activation Energy, E* (eV). 0.209 ± 0.005 0.211 ± 0.005 0.229 ± 0.005

It can be seen that despite the fact that a consistently lower value of Tj was observed for 0=35° compared to 9*0°. the activation energies are very close to one another and ^(©«O®) is found to be lower.. This is probably due to the more limited range of temperatures over which the 9=35® measurements were made compared to 0=0°. which means that the full effect of the anisotropy was not observed for 0=35’ at very- low temperatures. The value for £4(0=90°) is however, appropriately larger than either of the other orientations. The average is in good agreement with previously reported values of E*, as was that obtained for sample 1.

By varying the sample orientation only slightly it was found that a constant sample temperature could be maintained across a range of angles. Accordingly a set of measurements for 9*30®, 45® and 60® were achieved, as shown in figure 4.17. at near constant temperature. Measurements were made at temperatures of 238K. 247K. and 263K. Additional Ti values for 0*0®, 35® and 90® are shown which were obtained from interpolation of the data shown in figure 4.16.

As shown in figure 4.16d and figure 4.17 the maximum relaxation rate is achieved when the [001] direction is approximately 35® to B0, the minimum rate occurs when 0*90® ([001] perpendicular to B,,), quite different from sample 1 but in excellent agreement with theory. Fitting Sholl’s theoretical predictions for each of the three models discussed earlier to the data, as shown in figure 4.18 for T=238K. we find a good agreement between experiment and theory. The anisotropy observed at 238K is, Ti ¡no] / T i <0«35») * (80 ± 2ms) / (66 + 2ms) * 1.21 ± 0.04 which is somewhat larger than the predicted anisotropy of 1.17 but not unacceptably so. The general trend in behaviour of Tj for different sample orientations with respect to B0 is very good.