research papers
Practical measurement of the energy resolution
for meV-resolved inelastic X-ray scattering
ISSN 1600-5775

Daisuke Ishikawa* and Alfred Q. R. Baron*
Materials Dynamics Laboratory, RIKEN SPring-8 Center, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan.
*Correspondence e-mail: disikawa@spring8.or.jp, baron@spring8.or.jp
Received 18 January 2021
Accepted 26 March 2021

Edited by Y. Amemiya, University of Tokyo,
Japan
Keywords: inelastic X-ray scattering;
IXS; energy resolution; plexiglass;borosilicate glass.

Several different ways of measuring the energy resolution for meV-resolved
inelastic X-ray scattering (IXS) are compared: using scattering from poly(methyl methacrylate), PMMA, using scattering from borosilicate glass(Tempax), and using powder diffraction from aluminium. All of these methods
provide a reasonable first approximation to the energy resolution, but, also, in
all cases, inelastic contributions appear over some range of energy transfers.
Over a range of  15 meV energy transfer there is good agreement between
the measurements of PMMA and Tempax at low temperature, and roomtemperature powder diffraction from aluminium, so we consider this to be agood indication of the true resolution of our  1.3 meV spectrometer. The
resolution over a wider energy range is self-consistently determined using thetemperature, momentum and sample dependence of the measured response.
The inelastic contributions from the PMMA and Tempax, and their dependence
on momentum transfer and temperature, are then quantitatively investigated.
The resulting data allow us to determine the resolution of our multi-analyzer
array efficiently using a single scan. The importance of this procedure isdemonstrated by showing that the results of the analysis of a spectrum from a
glass are changed by using the properly deconvolved resolution function. The
impact of radiation damage on the scattering from PMMA and Tempax is
also discussed.

1. Introduction
Non-resonant inelastic X-ray scattering (IXS) is an accepted
method of investigating atomic dynamics at  nm1
momentum transfers with  meV resolution, as is useful forstudying phonons in crystals, and excitations in liquids andglasses (Dorner et al., 1986; Burkel et al., 1987; Sette et al.,1995). IXS provides relatively clean data with some advantages over other techniques [see discussion by Baron (2016)]
for measuring small (mm to mm scale) samples, and formeasuring liquids and glasses. Due to the relatively highincident X-ray energy ( 20 000 eV) compared with the energy
transfers of interest (typically < 0.1 eV), the momentum andenergy resolution for IXS are decoupled, so the influence ofthe finite energy resolution of a spectrometer can, in principle,
be simulated by a straightforward one-dimensional convolution of the energy resolution with a model. However, that
requires an accurate measurement of the energy resolution.
Various methods of measuring the resolution function havebeen mentioned (Masciovecchio et al., 1996a; Sinn et al., 2001;
Baron et al., 2001; Verbeni et al., 2005; Said et al., 2011;
Shinohara et al., 2019), but they usually involve the assumption that the scattering from some material, often a plastic, is apurely elastic, delta-function-like, line at zero energy transfer.
This assumption, while approximately true, and sufficientfor data analysis in some cases, is wrong in principle, as all
J. Synchrotron Rad. (2021). 28

https://doi.org/10.1107/S1600577521003234

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Figure 1
Schematic showing the setup/geometry with incident beam focused onto
the sample position, and scattering into a single analyzer. The analyzer isusually at an angle of 2 ’ 5 out of the vertical plane containing theincident beam. (Not to scale.)materials have some dynamical response at finite energy
transfer as is guaranteed on the meV scale, in a Born
approximation limit, by the first-moment sum rule of Placzek(1952). As the quality of IXS measurements then improves,
there is a greater need for understanding and carefully
determining the instrumental energy resolution for meV IXS.
This is especially important for the analysis of data fromsamples where inelastic excitations appear near a large(quasi-)elastic line (such as in glasses, or imperfect crystals, or
crystals with longer range density modulations), but is also
expected to be more generally useful, to, for example, investigate weak excitations that may appear on the tails ofstronger excitations.
In order to measure the energy resolution, one would,
ideally, like to uniformly illuminate the full analyzer solid
angle using elastic scattering in a geometry very similar to thatused to measure a sample (see Fig. 1): this gives the bestindication of the energy resolution of the spectrometer fora real measurement. However, the two requirements, pureelastic scattering and illumination over the full analyzer solid
angle, are not easily satisfied simultaneously. Bragg scatteringfrom a single crystal can provide an extremely favorable ratioof elastic to inelastic scattering, and effectively remove theinelastic components over a small solid angle. However, thesolid angle is badly mis-matched to typical IXS analyzer
acceptance: Bragg reflections have angular widths of 0.01 mrad, or less, and the analyzer solid angle is often
1 to 10 mrad. Therefore, using Bragg reflection from a single
crystal is not a practical way to measure the resolution of amrad-acceptance analyzer. More commonly one uses a disordered material measured at the momentum transfer corresponding to the structure factor (SF) maximum, also
sometimes called the first sharp diffraction peak. At thisposition one expects the scattering to be approximately elastic.
Further, the angular width of the SF maximum is usually large
enough so that the scattering results in relatively uniform
illumination over an analyzer.1 Previous work has mentioned
different samples used to measure the resolution including‘plastic’ (Masciovecchio et al., 1996a), more specificallypoly(methyl methacrylate) or PMMA/plexiglass (Sinn et al.,
2001; Baron et al., 2001; Verbeni et al., 2005) or Kr gas (Sette et1
Sometimes small-angle scattering (SAXS) has also been used. However,using spherical analyzers at small scattering angles is tricky in a typical setup as
it is easy to see scattering from a large volume around the sample, so thatwindow and air scattering can cause significant background. Also, SAXS
patterns usually change strongly with momentum transfer (e.g. they are often
displayed on a log scale), so it may be difficult to achieve uniform illuminationof a single analyzer and to measure more than one analyzer at a time.

2 of 8al., 1995), or borosilicate glass (Shinohara et al., 2019) usuallyat room temperature, and, in all cases, without discussion of
the inelastic contributions.
Here we investigate the inelastic contributions for scattering from two disordered materials that are interesting
for resolution measurements, PMMA and Tempax glass. We
compare these measurements with the use of powder
diffraction from a polycrystalline aluminium sample which
illuminates a line on the analyzer: by moving the analyzer sothat different portions are illuminated, we use the powder
scattering to estimate the resolution. We find good agreementof diffraction, and measurements of PMMA and Tempax at
low temperature, leading us to believe our resolution determination is good. We then quantitatively determine theinelastic contributions to the PMMA and Tempax response.
Using those data we can efficiently determine the energy
resolution for our array of analyzers using a single scan of asample at room temperature. The latter is important as IXS
spectrometers employ an array of multiple (4 to 28, dependingon the instrument) analyzers so that it is highly advantageous
if the resolution measurement can be made in parallel overmultiple analyzers at one time. We show how our procedure
improves the fit (and changes the best fit parameters) for a
low-Q spectrum from a glass.

2. Experimental setup, samples and methods
2.1. Spectrometer

All measurements were carried out at the high-resolution
spectrometer at the RIKEN Quantum NanoDynamics
beamline, BL43LXU (Baron, 2010, 2016), of the RIKEN
SPring-8 Center. The beam was focused onto the sample bya bent cylindrical mirror to a spot size of about 50 mm anddivergence of  0.2 mrad (V)  0.5 mrad (H) [unless otherwise specified, sizes and spectral widths will be given as the full
width at half maximum (FWHM)]. The BL43LXU spectrometer is designed for an array of up to 42 analyzers, but, in thepresent work, only the central 28 were active (see Fig. 2) in a
4  7 array at a 9.8 m radius from the sample. The analyzer
center-to-center spacing is 120 mm and each analyzer ispixelated (1 mm pitch) and operates in a slightly off-Roland
geometry with a temperature gradient applied to optimize theresolution (Ishikawa et al., 2015). By deliberate arrangement,
not all analyzers have the same deviation from backscatteringso there are systematic changes in the FWHM of the energy
resolution [see Fig. 2 and Ishikawa et al. (2015)]. In addition,
analyzer fabrication has process variations so that not all
analyzers are of the same quality. Thus, different analyzers
have different responses so it is desirable to measure theresolution of each analyzer for each experimental run, and foreach setting of the slits used to define the analyzer acceptance/
momentum resolution. It is then important that suchmeasurements be efficient.
2.2. Energy scans

Energy scans are performed by holding the analyzer
temperatures stable (typical variation < 0.12 mK r.m.s.) andIshikawa and Baron  Measurement of the energy resolution for meV-RIXS

J. Synchrotron Rad. (2021). 28

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Figure 2
Schematic of the analyzer array setup at BL43LXU. (Not to scale.)continuously scanning the temperature of the backscattering
monochromator. The energy transfer is then determined fromthe measured temperatures using the thermal expansion ofsilicon (approximately 17 mK meV1 near room temperature
at 21.7 keV) as calibrated by a known phonon line [seediscussion by Fukui et al. (2008)]. Typical scan speeds varyfrom 10 to 30 mK min1, with sampling times of 10 to 3 s. For
the resolution scans presented here, the data are sorted into
0.15 meV-wide bins near the elastic energy, though forexperimental data, or sometimes, at larger energy transfers,
larger bins (0.2 to 2 meV) are used to improve the statisticalquality (for fitting of spectra, of course, the resolution should
be binned with the same bin size as the data to avoid
introducing systematic errors in fitted linewidths). The dataprocessing (the ‘icscan’ program) includes corrections tocompensate for small changes in the incident power on thebackscattering crystal2 and for scan direction3. For the present
work, the beam was focused to a  50 mm spot using a bent
cylindrical mirror 5 m upstream of the sample position. The
position of the beam at the sample is held stable to better than
15 mm using feedback from a quadrant beam position monitor[see Baron et al. (2019)]. We note, for completeness, that the
bandwidth of the incident beam using the Si(11 11 11) backreflection monochromator at 21.7 keV is calculated to be 0.8 meV, though we only measure the resolution function of
the combined system of the analyzer and the monochromator.
2.3. Analyzer slits

The analyzer acceptance, or solid angle, is determined by aset of venetian-blind slits located about 0.9 m upstream of theanalyzer crystals (or about 8.9 m from the sample position).
The maximum aperture is 85 mm (V)  80 mm (H), while
the smallest gap is  2.5 mm  2.5 mm, though in practicalexperiments they have never been used with gaps smaller than2
The temperature sensor attached to the backscattering crystal is locatedabout 20 mm from the X-ray spot location and the power of the X-rays
incident onto the backscattering crystal creates a temperature gradient
between the X-ray beam and the sensor location. The temperature differenceis then dependent on incident power load, so that we apply a linear correctionthat is typically good for incident intensity variations of about 20%, as may
occur, for example, if upstream optics drift, or if the top-up of the storage ringis temporarily suspended (the typical stability is much better).
3This is put in as a ‘lag time’ – assuming the temperature readout lags behindthat at the X-ray spot by a small delay – typically 0.5 to 1 s. This correction
then allows scanning in both directions: when this correction is included,
peaks from scans upward or downward in energy transfer coincide to better
than 0.02 meV.

J. Synchrotron Rad. (2021). 28

4 mm  4 mm, and more typical values are 20 mm  20 mm tofully open. These slits have one motor to control all the gaps
in the vertical and one for the horizontal, and in the usual
operating configuration all analyzers have the same slit sizes[it is also possible to mount masks independently to set eachanalyzer aperture (Baron et al., 2019), but this is not done in
the present work]. All measurements presented here weremade with slit sizes of 80 mm (V)  40 mm (H), unless statedotherwise.
2.4. Samples

The samples used included commercially available poly(methyl methacrylate), PMMA, borosilicate glass (Tempax),
and a high-purity polycrystalline aluminium plate. Radiation
damage of the PMMA was an issue, with noticeable changes inthe structure factor occurring on  hour time scales in a beamof 4  1010 s1 into a 50 mm spot. Fig. 3 shows the progressionof a series of I(Q) measurements made one night. [I(Q) is used
to indicate that it is the measured intensity without correction
for atomic form factors, or for polarization.] The change in
response is clear. After X-ray exposure, visual inspection
showed structure (looking, sometimes, like a trail of bubbles)in the PMMA along the beam path. Therefore, all resolution
measurements using PMMA are made while scanning thesample through the incident beam, typically at a rate of
0.05 mm /5 minutes. This preserves the structure factor. No
equivalent issue was found for the Tempax despite >24 h ofillumination: color centers did form, leading to brown discoloration, but the structure factor was not noticeably affected
as is clear in Fig. 3(b). Fig. 3(c) shows the result of 2 scans of
one analyzer held at zero energy transfer: similar peak rates of 6 kHz are obtained at the SF maximum for 2 mm PMMA
and for 1.5 mm Tempax. For pristine PMMA the SF maximum
occurs at 9.6 nm1 and the peak width is about 5.9 nm1, while
for the Tempax glass the SF maximum is at 15.4 nm1 and thepeak width is about 7.2 nm1.

3. Resolution measurement
In order to determine the resolution of our system, we
measured the analyzer response under the following conditions:(i) Using the (111) powder diffraction ring from a sample
of pure aluminium, 1.2 mm thick. This was measured at five

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Figure 3
I(Q) for (a) PMMA and (b) Tempax, both at room temperature. The PMMA (Tempax) measurements were made with an incident beam intensity of
4  1010 (2  1010) 21.747 keV photons s1 into a 50 mm-diameter spot. (c) Measured intensity from one analyzer set at zero energy transfer from a
2 mm-thick sample of PMMA and a 1.5 mm-thick sample of Tempax. [2  1010 s1, 1.3 meV resolution at 21.747 keV, analyzer acceptance set to 4.5 mrad(H)  9 mrad (V).] The notation ‘0 h’, ‘24 h’, etc. indicate the time (in hours) of integrated illumination.

different 2 angles, effectively illuminating the analyzer
surface.
(ii) Using a 2 mm-thick PMMA sample at 11 and 300 K
measured at the SF maximum.
(iii) Using a 1.5 mm-thick Tempax sample at 20, 300 and
500 K measured at the SF maximum.
The excellent agreement, see Fig. 4, of the low-T
measurements of Tempax and PMMA and the 300 K Al
powder diffraction over the range of  15 meV leads us toconclude that this accurately represents the resolution function. However, beyond this range, various inelastic contributions begin to appear in the spectra, and are different foreach material.
At room temperature, both the PMMA and the Tempax
show inelastic contributions, albeit small, at the scale of a few
meV energy transfer. This can be seen in Fig. 5 (also Fig. 8) andnumerical values can be found in Table 1. However, notingthat there are not significant structural changes in thesematerials with temperature, we fit the results at 11 K and
300 K with a common set of inelastic excitations scaled by thesingle phonon Bose factor. This allows us to separate theinelastic contributions from the sample from the elastic scat-

Table 1
Fraction of the total scattering from the sample that is inelastic at theposition of the SF maximum for PMMA and TEMPAX at the indicatedtemperatures.
PMMA

TEMPAX

Energy range [min, max]
(meV)

11 K
(%)

300 K
(%)

20 K
(%)

300 K
(%)

500 K
(%)

Total
[10, +10]
[20, 10], [+10, +20][+20, +40][+40, +60][+60, +120]

0.48
0.30
0.04
0.04
0.04
0.04

4.86
4.41
0.25
0.07
0.05
0.05

0.24
0.07
0.04
0.03
0.03
0.04

1.01
0.66
0.16
0.05
0.04
0.05

1.80
1.24
0.30
0.09
0.05
0.06

Figure 5
Figure 4
Comparison of the direct measurement of the resolution using PMMA at
low temperature, Tempax at low temperature and powder diffraction at
the Al (111) diffraction ring, shown on (a) linear and (b) log scales.

4 of 8

Measured scattering from (a) PMMA and (b) TEMPAX at the indicatedtemperatures (points) compared with the derived resolution function
described in the text (green line). The inelastic contribution (convolved
with the resolution function) is given by the blue lines.

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Figure 6
Comparison of the measured resolution with a ray-tracing calculation
based on Ishikawa et al. (2015). The FWHMs are nearly the same, but the
tail is worse for the calculation. Insets show expanded views of the region
near zero energy transfer on (a) log and (b) linear scales.

tering, and then to self-consistently determine the resolution.
Table 1 indicates the contribution of inelastic excitations
integrated over the indicated energy ranges and sample
conditions at structure factor maximum.

4. Comparison with ray-tracing
We compare our measured resolution for this particularanalyzer with a ray-tracing calculation assuming dynamicaldiffraction from perfect thick silicon crystals [the same code as
used by Ishikawa et al. (2015)]. Examining Fig. 6, it is clear thatthe measured resolution is slightly worse than calculated,indicating that imperfections are introduced in the fabrication
process (previous tests of flat crystals suggest that the intrinsic
silicon quality is not an issue at this level). This is unsurprising
given long experience with analyzer-to-analyzer variations. It
also is consistent with the work of Said et al. (2011) where, forexample, some analyzers were seen to have better resolution
than others, and systematic improvements to resolution tails
are possible by increasing the thickness of the silicon used. At
the level of  1.3 meV resolution, spherical analyzer crystals
have process variations in their fabrication that lead to a
generally good, but still imperfect, response.

Figure 7
Momentum transfer (Q) dependence of the inelastic contribution to thetotal scattering for the indicates samples and temperatures, expressed
as a percentage of the integrated total intensity over an energy rangeof [20, 120] meV for (a) PMMA and (b) Tempax. Note the highest
momentum transfer in each case corresponds to the first minimum of thestructure factor and in included for reference only: all practical resolution
measurements are at momentum transfers close the SF maximum. See
also Fig. 8 where the I(Q, !) plane is shown.

excitation, and then optical bands that appear most strongly
for PMMA at  47, 75 and 100 meV (380, 605 and 807 cm1),
reasonably consistent with peaks observed in IR spectroscopy.

5. Inelastic excitations away from the SF maximum
The inelastic excitations in PMMA and Tempax were investigated by a series of measurements at different values of 2
with the same analyzer crystal. The analyzer resolution is thenconstant, allowing the inelastic contribution from the sample
to be extracted. Fig. 7 shows the fraction of the total scatteringfrom 20 to +120 meV that is from inelastic excitations as afunction of Q for the samples at different temperature: lowtemperatures, have, unsurprisingly, rather lower inelastic
contributions, especially above the SF maximum. Meanwhile,Fig. 8 shows the energy-resolved plots with a low-energy
J. Synchrotron Rad. (2021). 28

6. Efficient determination of the resolution
It is desirable to measure the resolution for each experiment.4
This provides the resolution in the conditions used in theexperiment, confirms that the spectrometer is performing as
expected, and gives a reference point for the evolution ofspectrometer performance. However, it is also highly desirable
4
We sometimes make one measurement under standard conditions at the startof an experiment and then an additional measurement at the end, where thelatter measurements are made with a reduced analyzer acceptance as may
have been used during the experiment to improve momentum resolution.

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Figure 8
I(Q, !) at room temperature for (a) PMMA and (b) Tempax after subtraction of the elastic contribution. Expressed as a fraction of the intensity at zeroenergy transfer. (Note that the intensity has been corrected for the incident X-ray polarization so this plot is for  scattering.)that such measurements do not take a large amount of beamtime: typical experimental runs are 3 to 8 days, so spending a
few hours measuring the resolution function is reasonable, but
to spend  1 day is too much. Therefore, after collecting data
to determine a self-consistent resolution function at the SF
maximum for one analyzer, we then went on to measure theresponse of the PMMA and Tempax over a wide range ofmomentum transfers, as is discussed in Section 5. This allows
us to determine the inelastic excitations in each material as afunction of momentum transfer. Once this is known, then we
can replace carrying out a longer series of measurements witheach analyzer near the SF maximum with a single scanfollowed by a deconvolution to remove the inelastic excitations. This approach is demonstrated in Fig. 9 where we show
the scattering from Tempax glass for all analyzers as measured
from a single scan. The analyzer resolution is then extracted
by fitting the measured response including the previously
determined inelastic excitations in Tempax where the freeparameters for the fit are the width, amplitude and center, of
one Gaussian and a set of 6 to 10 Lorentzians used to simulate
the resolution function, giving a smooth approximation to theresolution function (sarf). This allows the resolution to be
determined for each analyzer, as shown by the black lines in
the figure. One notes that there is some analyzer-to-analyzer
fabrication process variation as is clearly visible in the righthand column, where all resolutions for a given row of analyzers are collected.5

7. Comparison: PMMA versus Tempax for measuring
the resolution
PMMA and Tempax may both be used to measure the resolution function. At room temperature the phonon contribu5
The resolution of a09 shows a ‘bump’ at about 9 meV energy transfer. Thiscan appear if the analyzer diffraction plane (Psi-rotation about the Bragg
vector) is chosen such that one excites a multibeam condition, as canoccasionally happen after the spectrometer and detector alignment is changed.
This bump is consistent with 24-beam calculations of the full diffraction fromthe Si (11 11 11) back-reflection and integration over a range of Psi-angles
consistent with the experiment (Sutter & Baron, unpublished).

6 of 8tion from Tempax is about 1% of the total scattered intensity
while that of PMMA is about 5% near the SF maximum,
which suggests Tempax may be preferable. In addition, theTempax is less radiation sensitive than the PMMA. However,
PMMA is easier to cut/machine into specific shapes, andattenuates the beam less for a given thickness. Given these
considerations, we are now transitioning to using Tempax,
except in cases where a specific shape may be needed to,for example, measure the resolution with the PMMA placed
inside a specific sample cell.

8. Impact on analysis of a spectrum from a glass
As noted above, the impact of the corrections considered here
are most significant when observing weak modes on the tailsof strong modes, or near a strong elastic peak. This can beparticularly significant for the IXS spectra of glasses at small
momentum transfers, where it is not uncommon that the
acoustic mode intensity is only a few percent of the elastic
scattering. In Fig. 10 we show the measured spectrum of asilica-based glass at low momentum transfer (Q ’ 3 nm1).
From general considerations, this spectrum is expected to bewell approximated as the sum of a delta-function elastic peak
and a damped harmonic oscillator (DHO) function for the
acoustic mode, scaled by a one-phonon Bose factor, andconvolved with the resolution (e.g. Masciovecchio et al.,1996b). We then fit the measured spectrum using that model,
but taking the resolution function as either (a) the measured
spectrum from Tempax at room temperature, or (b) the
deconvolved (sarf) result from the process described in
Section 6. The results from minimizing (James & Roos, 1975)
2 are shown in the figure. As noted in the table inset in Fig. 10,
the deconvolved (sarf) resolution gives a smaller 2 andsignificantly different values for the acoustic mode width6 andintensity. Thus, the correction discussed here is important foranalysis of the spectra of glasses, even when using the rela6
The reported width in the table is the relevant parameter from the DHO
model which is approximately the half width at half-maximum (HWHM). See
Masciovecchio et al. (1996b) and Baron (2016).

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Figure 9
Scattering for all analyzers as measured using a single scan from Tempax glass. The data points are in blue, the red line shows the total fit, and the blacklines the derived resolution. Green numbers indicate momentum transfer in nm1 while other numbers give the full width at 1/2, 1/10 and 1/100
maximum. All the resolutions from each row are collected in the far right column. (A software error during this scan prevented a41 from being counted
so a40 is presented to fill the graph layout.) The detector/analyzer alignment is deliberately chosen so that the analyzers in the bottom row have thesmallest deviation from backscattering and therefore the best resolution (see Fig. 2).

tively good (see Sections 5 and 7)
response of Tempax to estimate theresolution.

9. Conclusion

Figure 10
Impact of different resolution functions on the fit to the spectrum from a glass sample. The points
are the measured spectra for Tempax (red circles) and the glass sample (back squares) while thesolid lines show the deconvolved resolution (sarf) and the fits and the contribution of the DHO
acoustic modes to the fits. The inset gives the 2 in 139 degrees of freedom and the optimized fit
parameters with errors. See the text for discussion.
J. Synchrotron Rad. (2021). 28

We have measured the resolution of
our meV spectrometer over a range[15, +15] meV and find essentially
identical results for low-temperature
PMMA, Tempax and powder diffraction
from aluminium, giving us confidence
that we know the real spectrometer
resolution over this range. Meanwhile,the consistency of results at 20 to 500 K
with a simple model suggests that theresolution is reasonably determined out
to  50 meV, and comparison between
different materials, and the assumption

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that the resolution function is smooth, then allows us someconfidence that we know the resolution function out to
120 meV energy transfer, or more. The measured response issimilar to ray-tracing calculation in the FWHM, but is somewhat worse in the tails. Scanning an analyzer over a wide Q
range then allowed us to measure the relative contributionof inelastic excitations for PMMA and Tempax. With that
information, we then can make an efficient and practicalmeasurement of the resolution for a multi-analyzer systemusing a single scan of Tempax or PMMA at room temperature– deconvolution of the inelastic contribution gives a smoothapproximation to the resolution function (sarf). The impact of
this approach is seen to be significant for analysis of a spectrum from a glass at low Q, and is generally expected to beimportant whenever a weak mode is measured on the tail ofstronger modes. We also have shown that PMMA, if used
incautiously, shows radiation damage on  1 hour time scales
even in our meV beam, while Tempax glass is relatively
radiation hard.

Acknowledgements
These experiments were carried out at BL43LXU, The
RIKEN Quantum NanoDynamics Beamline of the RIKEN
SPring-8 Center. While some of this work began in 2014, thebulk of the work became possible due to beam time that
became available during the disruption caused by the COVID19 pandemic in 2020.

Funding information
The following funding is acknowledged: RIKEN SPring-8
Center.

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