RbC 24 CsC 24
6.4 Results
Table 6.1: Summary of peak positions and peak areas of the low-energy IINS spectra
Peak I Peak II Peak III Peak IV Peak V
Center Area Center Area Center Area Center Area Center Area xa (meV) (a.u.) (meV) (a.u.) (meV) (a.u.) (meV) (a.u.) (meV) (a.u.)
0.25 0.56 0.06 1.24 0.05 1.54 0.24
0.50 0.55 0.06 1.25 0.11 1.54 0.53
0.75 0.62 0.21 1.25 0.14 1.53 0.59 1.72 0.23
1.00 0.63 0.36 1.27 0.13 1.53 0.50 1.73 0.43
1.25 0.63 0.54 1.31 0.14 1.51 0.37 1.73 0.72
1.50 0.63 0.64 1.33 0.10 1.49 0.24 1.73 0.87
1.75 0.60 0.96 1.31 0.29 1.50 0.32 1.68 0.64 1.81 0.28
aDenotes the H2 composition of a KC24(H2)x sample
bErrors not listed for the fit parameters
6000
5000
4000
3000
2000
1000
0
Intensity (arb. units)
12 10 8 6 5 4 3
d-spacing (Å)
001 002 003
x = 0 x = 0.25 x = 0.5 x = 0.75 x = 1 x = 1.25 x = 1.5 x = 1.75
Figure 6.5: Diffraction pattern of KC24(H2)x measured on DCS at 4 K.
tration increases. However, the collapse of peak III, and associated growth of peak IV, may indicate a reconstruction of the in-plane KC24lattice. Similar behavior has been noted for the CsC24(H2)x system [112]. Peak positions and areas for the low-energy IINS spectra are summarized in Table 6.1.
6.4.2 Diffraction pattern from low-energy IINS spectra
The DCS instrument contains an angular array of detectors from which diffraction informa- tion can be obtained by the time-of-flight method. It should be emphasized that DCS isnot optimized as a diffractometer, and that the resolution in Q is quite coarse. Nevertheless, a qualitative diffraction pattern can be extracted from the measured S(Q, ω) by plotting the integrated intensity under the elastic peak as a function of momentum-transfer. The
diffraction pattern obtained from the low-energy IINS measured on DCS is illustrated in Fig. 6.5. For the x = 0 filling, the (001), (002), and (003) reflections have a d-spacing of 8.73 ˚A, 4.33 ˚A, and 2.90 ˚A, respectively. This translates to an average KC24interlayer spac- ing of 5.34 ˚A. As H2 is introduced to the sample, there is a gradual transfer of intensity to the second set of peaks with a slightly largerd-spacing. The fully hydrogenated sample has an interlayer spacing of 5.63 ˚A. In other words, the adsorption of H2 causes the KC24layers to expand by about 5%. These results are fully consistent with data reported in Ref. [64].
Given the lowQ-resolution of the instrument, a quantitative analysis of diffraction data is not appropriate. Nevertheless, the diffraction data verifies three things. First, the KC24 sample is not contaminated by stage-1 or stage-3 compounds. Second, hydrogen is being adsorbed between the layers of KC24 resulting in an expansion of the interlayer spacing.
Finally, the fact that there is a transfer of intensity between two distinct, co-existent peaks, rather than the shift of a single peak, implies that KC24(H2)x contains co-existent regions of the hydrogenated and pure KC24 phase.
6.4.3 Intermediate and high-energy IINS spectra
Intermediate-energy IINS spectra of KC24(pH2)x were measured as a function of hydrogen filling on the FANS instrument using the PG(002) monochromator. They are displayed in Fig. 6.6. As explained in the methods section, para-hydrogen was used instead of normal hydrogen to simplify the interpretation of spectral peaks. To determine peak positions and areas, the intermediate-energy spectra were fitted to a sum of Gaussian curves plus a flat background, and the fits are indicated in the figure. At the two lowest hydrogen fillings of x= 0.2 andx= 0.5, the spectra appear similar, except for the overall increase in intensity with hydrogen concentration. Peak I (11.9 meV) and Peak II (29.2 eV) are the dominant
3
2
1
0
Counts per 100 monitor
35 30 25 20 15 10 5
Energy loss (meV) 8
6
4
2
0
Counts per 100 monitor
35 30 25 20 15 10 5
Energy loss (meV)
12 10 8 6 4 2 0
Counts per 100 monitor
35 30 25 20 15 10 5
Energy loss (meV) 20
15 10 5 0
Counts per 100 monitor
35 30 25 20 15 10 5
Energy loss (meV) x = 0.2
x = 0.5 x = 1
x = 1.5
I
IV
III IV
I I I
II II IV
III
IV
Figure 6.6: Intermediate-energy IINS spectra of KC24(pH2)xas a function of hydrogen filling. Solid blue lines represent fits to a sum of Gaussian curves plus a flat background. Individual Gaussian curves are plotted as dashed red lines. Flat background is not shown. Data points below 8 meV and above 32 meV were removed prior to the nonlinear regression fit.
features. Nascent peaks at 23 meV and 25 meV are somewhat difficult to distinguish from the large background intensity. As hydrogen filling is increased to x = 1, two new peaks emerge at 23.7 meV (Peak II) and 26.5 meV (Peak III). As hydrogen composition is further increased to x= 1.5, there is a strong increase in Peak III, but little increase in the other peaks. The sharp feature that appears at Peak I at thex= 1.5 filling may be an instrument artifact fromλ/2 contamination of the incident beam, due to the large transition ca. 50 meV.
In all of the intermediate-energy spectra, there is a large background intensity which may be due to the overlap of closely-spaced peaks. With the modest energy resolution of FANS (i.e., 1.2 meV), however, individual peaks are often difficult to distinguish. Peak positions and areas for the intermediate-energy IINS are summarized in Table 6.2.
High-energy IINS spectra of KC24(pH2)xare plotted in Fig 6.7 as a function of hydrogen filling. Spectra were only measured forx= 0.5 andx= 1.0. The dominant feature in both spectra is Peak VII, which has a greater intensity than any other peak. It should be noted that the curves in Fig 6.7 are not artificially offset. The vertical offset is due to the large background intensity, which may indicate a large amount of H2 recoil associated with the scattering. At the higherx= 1.0 filling, upon closer examination, Peak VII appears to have a fine structure comprising two sub-peaks. The increase in intensity of the lower-energy sub- peak is what causes the apparent shift of the total peak from 50.9 meV atx= 0.5 to 49.4 meV atx= 1. Peak positions and areas for the high-energy IINS spectra are listed in Table 6.2.
6.4.4 IINS spectra of HD and D2 adsorbed in KC24
The richly-structured IINS spectra of KC24(pH2)x contain numerous overlapping peaks, making it difficult to accurately identify and interpret the origins of the spectral features.
One method of obtaining more information from the inelastic spectra is to substitute the
100
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Counts per 100 monitor
110 100
90 80
70 60
50 40
30
Neutron Energy Loss (meV) VIIa
KC24(H2)0.5 KC24(H2)1
KC24 V
VI VII
VIII IX
Figure 6.7: High-energy IINS spectra of KC24(pH2)xmeasured with the Cu(022) monochromator.
Solid lines represent fits to a sum of Gaussian curves plus flat background. Individual curves are not manually offset.
Table 6.2: Summary of peak positions and peak areas of the intermediate and high-energy IINS spectra
x= 0.2 x= 0.5 x= 1.0 x= 1.5
Center Area Center Area Center Area Center Area Peak (meV) (a.u.) (meV) (a.u.) (meV) (a.u.) (meV) (a.u.)
I 11.9 2.02 11.8 5.84 11.8 13.4 11.4 13.2
II 23.7 16.2 24.2 24.8
III 26.5 12.7 26.6 24.6
IV 29.2 4.94 29.3 8.71 29.2 13.3 29.2 7.10
V 39.4 2.83 39.4 71.6
VI 43.0 21.1 43.5 71.3
VII 50.9 93.8 49.4 360.
VIII 58.5 7.76 59.1 33.2
IX 85.2 27.2 84.7 37.9
aPeak parameters were obtained from fitting the spectra to a sum of Gaussian curves plus a flat background.
bPeaks I–IV are from the PG(002) spectra (see Fig. 6.6), while peaks V–IX are from the Cu(220) spectra (see Fig. 6.7). The integrated areas from the two different spectra are not directly comparable.
H2 adsorbate with a hydrogen isotope containing a different mass, specifically HD and D2. Shifts in peak positions as a function of mass can sometimes reveal the rotational or vibrational origin of a spectral peak. For a pure rotational transition of a free diatomic molecule, energy is proportional to the inverse of the reduced mass (see Eq. 6.2). Relative to H2, the rotational transitions of HD will be reduced by a factor of 0.75, and for D2 they will be reduced by a factor of 0.5. For a whole-molecule vibrational mode (i.e., governed by a power-law potential V(x) =Ax2), the energy levels scale with mass as m−1/2. Relative to H2, the vibrational transitions of HD will be reduced by a factor of p
2/3 ≈ 0.82, and for D2 the transitions will be reduced by a factor ofp
1/2≈0.71.
IINS spectra were collected for HD and D2 samples.1 These spectra are compared with thep-H2 spectra in the three panels of Fig. 6.8. Ratios between the peak positions for the three isotopes are summarized in Table 6.3. Unfortunately, it is difficult to identify the peaks for each isotope which correspond to the same transition. This is especially true for HD, which contains a complex spectrum due to the absence of symmetry restrictions on the rotational and nuclear spin states. Figure 6.8 contains my best guess for the peaks which correspond to equivalent transitions. Peaks are labeled with either an “a”, “b” or
“c” depending on whether the isotope is H2, HD, or D2, respectively.
The only peak ratio which can be easily categorized is Peak I, which seems to follow the m−1/2 scaling expected for a pure vibrational transition. However, the cross-section ofp-H2 for a pure vibrational transition (with no change in the rotational level) is proportional to σcand is very small (see Sec. 6.2.4). Peaks originating from pure phonon excitations should not be visible in the spectrum of KC24(pH2)0.5. Since the cross-section for a one-phonon
1Due to the smaller scattering cross-section of deuterium, it was necessary to collect data for a consider- ably longer time period. Even with longer collection times, the error bars on the D2 spectra are much larger than those of the other samples.
6
4
2
0 10 20 30 40
Neutron Energy Loss (meV) 0.6
0.5 0.4 0.3 0.2 0.1 0.0 3.0 2.5 2.0 1.5 1.0 0.5 0.0
KC24(H2)0.5 KC2424(HD)0.5 KC24(D2)0.5
Counts per 100 monitorCounts per 100 monitorCounts per 100 monitor
Ia
IIa IIIa
IVa Va Ic
Ib
IIc
IIb IIIc
IIIb IVb
Vb VIb
VIIb VIIc
Figure 6.8: Intermediate-energy IINS spectra of D2, HD, and p-H2 adsorbed in KC24. Solid lines represent fits to a sum of Gaussian curves plus a flat background. The Gaussian curves are shown as dashed, red lines. Fit components not corresponding to a clear, discrete peak are not illustrated.
Peaks thought to correspond to the same transition are labeled with the same Roman numeral, with an “a”, “b” or “c” to identify the isotope.
Table 6.3: Peaks positions in the intermediate IINS spectra for different hydrogen isotopes
H2 HD HD/H2 D2 D2/H2
Peak Positiona Position Ratio Position Ratio
I 11.9 9.36 0.79 8.02 0.68
II 24.1 18.1 0.75 15.9 0.66
III 29.3 20.2 0.69 18.5 0.63
IV 39.9 25.8 0.65
V 43.8 28.0 0.64
VI 33.0
VII 43.0 35.1
aH2 peak positions were obtained from thep-H2spectra.
bPeak positions are reported in units of meV.
cComposition wasx= 0.5 for all isotopes.
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1
00 10 20 30 40 50
Neutron Energy Loss (meV) 6
5 4 3 2
1 0
Counts per 100 monitor
50 40
30 20
10 0
Neutron Energy Loss (meV) KC24(HD)0.5
KC24(H2)0.5 Energy × 0.82
KC24(D2)0.5
KC24(H2)0.5 Energy × 0.5
KC24(H2)0.5 Energy × 0.71
KC24(H2)0.5 Energy × 0.75 I
III I II
HD D2 III
Figure 6.9: Comparison of the IINS spectra of the p-H2, HD, and D2 loaded samples. Thep-H2 spectra have been rescaled along the energy axis with theµ−1 factor (×0.75 for HD and ×0.5 for D2) of a pure rotational transition and them−1/2factor (×0.82 for HD and×0.71 for D2) of a pure phonon transition.
many of the spectra features may therefore be due to multi-excitation transitions.
Isotopic shifts in the IINS spectra are directly compared in Fig. 6.9. The p-H2 spectra are rescaled on the energy axis with the µ−1 factor of a pure rotational transition and the m−1/2 factor of a pure phonon transition. In this manner, peak positions for the isotopes can be directly compared to determine whether there are any good matches. Once again it is evident that none of the peaks (except for Peak I) follow the simple scaling relations expected for a pure phonon or rotational transition.