# Growth and characterization of thorium-doped calcium fluoride single
crystals

Kjeld Beeks  Tomas Sikorsky  Veronika Rosecker  Martin Pressler  Fabian
Schaden  David Werban  Niyusha Hosseini  Lukas Rudischer  Felix Schneider
Institute for Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020,
Vienna, Austria  Patrick Berwian  Jochen Friedrich  Fraunhofer-Institut für
Integrierte Systeme und Bauelementetechnologie IISB, Schottkystraße 10, 91058
Erlangen, Germany  Dieter Hainz  TRIGA Center Atominstitut, TU Wien,
Stadionallee 2, 1020, Vienna, Austria  Jan Welch  Johannes H. Sterba  CLIP,
TRIGA Center Atominstitut TU Wien, Stadionallee 2, 1020, Vienna, Austria
Georgy Kazakov  Thorsten Schumm  Institute for Atomic and Subatomic Physics,
TU Wien, Stadionallee 2, 1020, Vienna, Austria

###### Abstract

We have grown 232Th:CaF2 and 229Th:CaF2 single crystals for investigations on
the VUV laser-accessible first nuclear excited state of 229Th. To reach high
doping concentrations despite the extreme scarcity (and radioactivity) of
229Th, we have scaled down the crystal volume by a factor 100 compared to
established commercial or scientific growth processes. We use the vertical
gradient freeze method on 3.2 mm diameter seed single crystals with a 2 mm
drilled pocket, filled with a co-precipitated CaF2:ThF4:PbF2 powder in order
to grow single crystals. Concentrations of $4\cdot 10^{19}$ cm-3 have been
realized with 232Th with good ($>$10%) VUV transmission. However, the
intrinsic radioactivity of 229Th drives radio-induced dissociation during
growth and radiation damage after solidification. Both lead to a degradation
of VUV transmission, limiting the 229Th concentration to $<5\cdot 10^{17}$
cm-3.

##  .1 Introduction

The radioisotope thorium-229 has a unique nuclear structure in which the first
excited state is long-lived and exceptionally low in energy: few electron
volts (eV), instead of the common keV-MeV range for nuclear excited states Von
der Wense (2017). The radiative lifetime of this isomeric state (229mTh) is
expected to exceed 1000 seconds Tkalya  _et al._ (2015) for the bare nucleus.
Owing to its low energy in the range of electronic shell transitions, an
interaction between the nucleus and its chemical environment is expected
Tkalya (2011); Borisyuk  _et al._ (2019); Bilous  _et al._ (2017); Nickerson
_et al._ (2020, 2021). Studying the interaction of the nucleus with its
chemical surrounding presents a unique research opportunity.

The 229Th nucleus has attracted many ideas for applications Tkalya  _et al._
(1996), most of them based on nuclear laser spectroscopy. Our main interest is
to perform optical nuclear spectroscopy of vacuum ultraviolet (VUV)
transparent single crystals containing 229Th as a dopant Dessovic  _et al._
(2014).

The energy of this nuclear isomer state was indirectly measured only recently
by two independent methods Seiferle  _et al._ (2019); Sikorsky  _et al._
(2020) to $8.15\pm 0.45$ eV (averaged). This corresponds to a wavelength of
$152\pm 8$ nm, which is in the VUV range and thus absorbed in air. The
measurements of the isomer energy used internal conversion (IC) and gamma
emissions from the nucleus respectively. Internal conversion is a common
nuclear decay process, where the energy of the excited nucleus is transferred
to a shell electron which is ejected if the decay energy exceeds the binding
energy. The internal conversion decay channel can have a dramatically
different lifetime compared to the radiative decay. The IC lifetime of
$7(1)\,\mu$s was measured for neutral 229mTh on a metal surface von der Wense
_et al._ (2016).

To exploit the many prospects of the 229Th system, internal conversion and
other non-radiative decay channels need to be suppressed. For solid-state
approaches, this requires the bandgap of the 229Th-doped crystal material to
exceed the isomer excitation energy. Hehlen et al. categorized, which large
bandgap materials would be suitable, pointing out the relevance of fluoride
crystals Hehlen  _et al._ (2013). Excitation and fluorescence of commercially
grown, 232Th-containing crystals was explored by Rellergert  _et al._ (2010)
(Th:NaYF, Th:YLF, Th:LiCAF, Na2ThF6, Th:LiSAF) to investigate VUV irradiation
induced background and optical transparency.

The approach in our laboratory is to use CaF2 crystals with an 11.8 eV direct
bandgap Rubloff (1972). The cutoff of this material is however dominated by a
broad indirect exciton bound state at 11.2 eV Letz  _et al._ (2009) which
diminishes the VUV transmission for photons with energy above 9.8 eV or
wavelength below 126 nm. These exciton states are higher in energy than the
8.15 eV isomer energy and thus non-radiative de-excitation should be
prevented.

Crystal doping will ensure a high amount of addressable nuclei, of the order
of 1019 cm-3. The presence of the dopant will however modify the band
structure of the host crystal and lead to additional electronic defect states
Dessovic  _et al._ (2014). Interactions between the nucleus and the local
crystal fields will lead to line shifts and broadenings Kazakov  _et al._
(2012).

In this work, we describe the in-house growth and characterization of 229Th-
doped CaF2 single crystals. Severe challenges are connected with the inherent
radioactivity of the dopant (on the order of 106 Bq), its extreme scarcity
(milligrams) and general purity requirements of the used materials. To
accommodate these, we developed a modified vertical gradient freeze (VGF)
machine to grow small-volume crystals ($<0.1$ cm-3) in vacuum with minimal
losses. We demonstrate that the doped material maintains VUV transparency in
the range of the expected isomer excitation wavelength and investigate the
relation between VUV transmission and the effect of different doping
concentrations on both surface and bulk absorption. These crystals are
currently used in several attempts to excite the 229Th using X-ray irradiation
Masuda  _et al._ (2019) or VUV irradiation Jeet  _et al._ (2015); Stellmer
_et al._ (2018).

##  .2 Preparation of 229ThF4:PbF2:CaF2 growth material

In an exemplary fashion, the following describes the preparation of 45 mg of
229ThF4:PbF2:CaF2 powder for growing 3 crystals (15 mg each) with 3.2(1) mm
diameter and 11(1) mm length. PbF2 acts as a scavenger for oxygen removal (see
below) and as a carrier that facilitates the handling of the minuscule
(micrograms) amounts of 229ThF4 during the wet chemistry preparation process.

229Th (7.9 MBq, Oak Ridge National Laboratory, in dried nitrate form) was
dissolved in 0.1 M HNO3 Suprapure grade (Sigma Aldrich) prior to use. All
reagents CaF2 (Alfa Aesar), Pb(NO3)2 (Sigma Aldrich), PbF2 (Alfa Aesar), 40 %
HF (Sigma Aldrich) were purchased from commercial suppliers in trace metal
grade and were used as received. Water was purified in-house by triple
distillation. Using higher quality CaF2 powder increased the VUV transmission
of the grown crystals.

In a centrifugation vial, lead(II) nitrate (2.9 mg) was added to and dissolved
in a solution of 229Th in 0.1 M HNO3 (9 mL, 5.5 MBq). Subsequently,
229ThF4:PbF2 was precipitated by addition of hydrofluoric acid (40 %, 1 mL). A
white precipitate appeared immediately and was allowed to rest overnight. The
supernatant was carefully removed using a pipette after centrifugation and the
precipitate was washed with triple distilled water (2 mL, 6 times). After the
fourth washing step, the supernatant was tested for remaining free fluoride
ions by adding a small portion of an aqueous solution of CaCl2. No appearance
of any white material confirmed the absence of free fluoride ions, and two
additional washing steps were performed.

The 229ThF4:PbF2 was then poured into an aluminum container to avoid powder
sticking to the wall, reducing losses when the powder is transferred into the
crystal growing machine later. A small portion of water was added and the
whole was then dried in an oven at 80 ℃ until weight was constant (4 days).
Then CaF2 (28.3 mg) was added to the 229ThF4:PbF2, mixed thoroughly and
measured via $\gamma$-spectroscopy. The $\gamma$-spectroscopy was performed
with a 151 cm3 HPGe detector from Canberra Industries (1.8 keV resolution at
the 1332 keV 60Co peak; 50.1 % relative efficiency), connected to a PC-based
multi-channel analyzer with preloaded filter and Loss-Free Counting (LFC)
system.

The powder was then combined with a previous batch of 229ThF4:PbF2:CaF2 (15
mg, containing 0.3 MBq 229Th) to give a total amount of 45 mg
229ThF4:PbF2:CaF2 with a weight ratio of 0.33:1:14 and a total activity of 5.8
MBq 229Th used. The previous batch originated from a trial run of above
mentioned method. The stock powder was then split in 3 parts of equal amounts
by weight (15 mg) to give three aluminum containers with equivalent material
(No. 1, No. 2, No. 3). All vials were measured with $\gamma$-spectroscopy in
the same geometry to check the distribution of activity between the containers
(0.33:1:14, as above) and stored in a desiccator until used. Due to losses
during the process 4.7 MBq out of 5.8 MBq 229Th were obtained as usable
powder.

##  .3 Preparation of 232ThF4:PbF2:CaF2 growth material

For calibration purposes, process optimization, and many measurements, which
do not probe nuclear properties (e.g. VUV transmission measurements),
commercially available 232Th can be used as a proxy.

Two different methods for the 232ThF4:PbF2:CaF2 sample preparation were used.
Method A was used to prepare 232Th containing powder analogous to the 229Th
powder. Then conditions (ratios between components, water content,
contamination, etc.) were kept constant between growing 232Th:CaF2 and growing
229Th:CaF2. Method B was used when different ratios between components should
be tested. This approach avoided the lengthy coprecipitation which allowed for
quick testing. Losses of Th were not important in this method due to the use
of the abundant 232Th isotope. The two methods were:

  * A:

The sample was prepared analogous to the 229ThF4:PbF2:CaF2 procedure described
above using 232ThNO3 instead of 229ThNO3. A small amount of 229ThF4:PbF2:CaF2
was added (1 kBq of 229Th) to the 232ThF4:PbF2:CaF2 powder for tracing
purposes.

  * B:

The sample was prepared by mixing commercially available CaF2, PbF2 and
232ThF4. Then 1 kBq of 229ThF4 was added by letting a spoon touch first the
produced 229ThF4 then the 232ThF4 for tracing the location of the dopant after
growth.

##  .4 Vertical gradient freeze growth process

To grow 3.2 mm diameter, 11 mm long crystals, we use a modified vertical
gradient freeze method. It was first developed in 1924 by Stöber Stöber
(1924), inspired on the Bridgman method. This method was adapted to our needs
in cooperation with the Fraunhofer institute for integrated systems and device
technology (IISB) to grow crystals with minimal dopant losses Schreitl (2016).
The main advantage of the VGF method over other methods like Czochralski is
that the growth speed is decoupled from the crystal diameter. Very small
diameter crystals and hence high (1018 cm-3) doping concentrations can be
realized with the extremely scarce 229Th isotope while maintaining low growth
speed ($<$0.5 mm/h) which promotes high quality crystals and improved VUV
transparency.

In the vertical gradient freeze method, a temperature gradient is slowly
driven across the starting growth material (powder and seed) to control the
liquid-solid interface, as illustrated in figure 1. In our implementation,
sub-millimeter control of this interface layer is required, imposed by the
small crystal dimensions (see figure 2). The gradient is realized by
electronically controlling the currents in two ohmic heaters on top of and
below the crucible containing powder and seed (see figure 3). The entire
system is kept under vacuum during the growth process, approximately 10-4 mbar
at the start of the growth (see figure 5). The vacuum prevents oxidation of
the graphite and CaF2 powder. Inert gases could also be used for this purpose,
however achieving a steep temperature gradient (20 K/cm) is then very
challenging.

Figure 1: Simplified schematic representation of the vertical gradient freeze
method applied to the seed crystal in figure 2 filled with dopant powder.
While applying a steep temperature gradient, the top of the crystal melts and
becomes a liquid while the bottom remains solid. By slowly cooling and moving
the melting interface upwards, a doped single crystal can be grown on the seed
crystal.

A stationary graphite crucible is filled with a CaF2 seed crystal together
with the starting material in the seed pocket. A temperature gradient of
$\approx$ 20 ℃/cm should be around the melting temperature of the chosen
material, which is 1418 ℃ for CaF2. In this way, the powder in the pocket of
the seed crystal can be molten together with the top part of the seed. Due to
the rather steep gradient the bottom of the seed does not melt. The freezing
interface is then slowly moved upward such that the melt can crystallize on
top of the seed crystal, and thus grow a single crystal following the
orientation of the seed.

The diameter and length of the crystals grown in our laboratory has been
successively reduced from 17 mm to 3.2 mm and from 40 mm to 11 mm,
respectively, by careful calibration and using smaller seeds. This implements
a volume reduction and corresponding concentration increase by a factor
$\approx$100\. Seed crystals of 5 mm diameter (with different, single crystal
orientations) were purchased from Korth, Matek, and Alkor. Hyperion Optics
milled the seeds down from 5 mm to 3.2 mm diameter and drilled a 2 mm diameter
hole (5 mm deep) into the top, to accommodate the doping material. Figure 2
shows a photograph of such a prepared seed, and the DETAIL in figure 3 shows
the positioning of the seed inside the graphite crucible.

Figure 2: Seed crystals with 3.2 mm diameter, 11 mm length and a 2 mm
diameter, 5 mm deep pocket used for growing highly doped 229Th:CaF2. A caliper
with inch and mm scales is shown as well.  Figure 3: Crystal growing device
used to grow 3.2 mm diameter crystals. On the left side is a horizontal cut
displaying the graphite heating element with the isolated thermocouple through
the center. The right image displays a vertical cut that shows all of the main
components of the vertical gradient freeze growing machine and zooms into the
crystal location. The thermocouples are platinum/rhodium (Pt30Rh-Pt6Rh) with
an alsint casing. The vacuum seals for the thermocouples are made of FKM,
which is able to withstand both the low pressure fluorine atmosphere and the
high temperatures which are present at the ends of the thermocouple. Water is
circulated through the steel vacuum chamber to provide cooling.

The pocket is filled with the co-precipitated growth material. Special care
was taken to use metallic funnels just as the containers to avoid material
losses due to electrostatic adsorption to the wall. The pocket within the seed
ensures minimal losses and easy handling of the crystals before starting the
VGF process. The filled seed is placed into the VGF furnace (figure 3) inside
of a carbon crucible. The phase diagram of CaF2 and ThF4 at low vacuum has not
been measured to our knowledge, but we observe evaporation. Fluorine was
detected by using a Pfeiffer quadrupole mass spectrometer and traces of
radioactive Th and U in the graphite show that these partly evaporate during
growth. The volume above the seed in which material can be evaporated is small
in our setup. We observed that this small volume increases doping efficiency
as opposed to a larger volume or direct connection to the vacuum pump. We
hypothesize that when the vapor is actively pumped away more of the material
is evaporated which reduces doping concentration.

The seed is then grown to a single crystal: Two ohmic carbon heaters (see left
side of figure 3) are used to create the steep temperature gradient over the
crystal, partially melting it. Short-term temperature stability is maintained
with short horizontal alsint-insulated thermocouples close to the heaters and
absolute calibration is done with long vertical thermocouples close to the
crucible.

The temperature at the crystal pocket is not exactly the same as the one
indicated by the bottom thermocouple, thus we employ an iterative temperature
calibration process to ensure that the temperature is such that the crystal
only melts midway. Important here is to carefully monitor the in and outside
temperature of the thermocouples to get an accurate temperature measurement
and avoid drifts in the system (e.g. by room temperature or cooling water).
The graphite thermal isolation and alsint isolation of the thermocouples must
not touch, since at high temperatures these two chemically react, which slowly
degrades the casing of the thermocouples which can create vacuum leaks.

The temperature cycle of the growing process (shown in figure 4) is divided
into five sections: 1) 18 hours of heating up the system, outgassing, and
restoring pressure (see figure 5) 2) 6 hours of scavenging oxygen through
reaction with PbF2 3) 22 hours of melting the top half of the crystal and also
slowly freezing it 4) 18 hours of annealing the crystal 5) 14 hours of cooling
down. A vacuum of at least 10-4 mbar is obtained before growth. During growth
(especially during section 1) the pressure can go up to 10-2 mbar. The
complete growth process typically takes 3 days.

Figure 4: Temperature cycle versus time to grow 3.2 mm diameter crystals as
set and measured by the thermocouples indicated in figure 3. The sections as
described in the text are indicated as well. The entire process takes about 80
hours or approximately 3 days. Note that only the horizontal thermocouples are
used to actively control the temperature, and thus only these have set
temperatures. Their temperatures are lower than the vertical thermocouples as
they are further from the center of the crucible. The lines of the set
temperatures are almost completely hidden by the actual measured lines. Figure
5: Pressure evolution during the temperature cycle versus time to grow 3.2 mm
diameter crystals. Temperature was taken from the top vertical thermocouple.
One can see that every increase in temperature increases the pressure, which
after temperature stabilization decreases again. Interestingly the pressure
does not significantly increase anymore at temperatures above 1000 ℃.

Due to the radioactive nature of the dopant, special security measures are
implemented in the growth process. On the pre-pump, carbon filters are
installed to absorb any evaporated material. The dopant material also is
absorbed into the graphite insulation, which becomes radioactive after several
growth cycles. In every growth, the insulation absorbs and also releases some
dopant; cross-contamination of dopants was observed in a pure CaF2 crystal,
grown after growth of a radioactively doped crystal. The growth of undoped
crystals can be used to reduce cross-contaminations by absorbing them, we
observe a reduction of roughly a factor 10 per growth process.

One important aspect in growing CaF2 crystals is the probability of
incorporating oxygen, especially at higher temperatures Molchanov  _et al._
(2005); Ko  _et al._ (2001). Oxygen contamination is known to reduce the
transparency of CaF2, especially in the VUV region. At elevated temperatures,
the carbon crucible should react with any background gaseous O2 and H2O to
form CO in the system. The H2O that is adsorbed on the surface of the crystal
powder, however, will first react with the CaF2. The H2O will react with the
CaF2 to CaO (Tmelt=2613 ℃ Haynes  _et al._ (2016)) and HF according to

$\text{CaF}_{2}^{s}+\text{H}_{2}\text{O}^{a}\xrightarrow{}\text{CaO}^{s}+2\text{HF}^{g}.$
(1)

To mitigate this, oxygen scavengers are used: Fluoride compounds (PbF2
Tmelt=830 ℃ Haynes  _et al._ (2016)) in the powder that before melting CaF2
react preferentially with oxygen and water to volatile oxygen containing
compounds (PbO Tmelt=887 ℃ Haynes  _et al._ (2016)) which are evaporated at
higher temperatures and transported away such that the oxygen is replaced by
fluoride:

$\text{CaO}^{s}+\text{PbF}_{2}^{g}\xrightarrow{}\text{CaF}_{2}^{s}+\text{PbO}^{g},$
(2)
$\text{H}_{2}\text{O}^{a}+\text{PbF}_{2}^{g}\xrightarrow{}2\text{HF}^{g}+\text{PbO}^{g}.$
(3)

The gaseous lead(II) oxide will then react with cooler carbon in the
insulation walls where they form metallic lead (Tmelt=328 ℃ Haynes  _et al._
(2016)) and CO (not CO2 according to the Boudouard equilibrium)

$\text{PbO}^{g}+\text{C}^{s}\xrightarrow{}\text{Pb}^{s}+\text{CO}^{g}.$ (4)

##  .5 Temperature calibration

Melting a mixture of CaF2 and ThF4 will lead to a modified melting temperature
compared to the separate constituents, as investigated in Capelli  _et al._
(2015). Since the amount of available 229Th will not allow growing doping
concentrations higher than 0.05 wt % (1 MBq) to 0.5 wt % (10 MBq) we do not
expect (and did not observe) significant changes in the melting temperatures.
The temperature calibration could be used independent of the doping
concentration, and a partial phase transition into CaThF6 occurring at 19 wt %
can be ignored.

To finely adjust the temperature settings of the growth process, low
concentrations of uranium-238 were used as a colorant. As shown in figure 6,
the coloring allows to accurately determine the lowest position of the liquid-
solid interface, in other words, how deeply the melting progressed into the
seed crystal. For a typical gradient of 20 ℃/cm and a peak (set) offset
temperature of 1418 ℃, the precision (reproducibility) of the melting boundary
is 1 mm with a change in 2.5 ℃ in set temperature shifting by 1 mm. The
calibration can be transferred from uranium to thorium without adaptation due
to the low doping concentrations. The calibration is obtained in an iterative
process involving 5-10 growth processes. The temperature interval between
obtaining a fully molten crystal and not melting the seed at all is about 15
K, the temperature relation is not fully linear and the drilled top part of
the seed crystal containing the growth material is more susceptible to melting
than the lower bulk of the seed crystal.

Crystals grown with 229Th and 232Th doping are optically fully transparent, so
it is less obvious to determine the melting depths. Here, the radioactivity of
229Th can be used to extract spatial information on the doping distribution
(see below). For doping with 232Th, which is used as a proxy in experiments
not focusing on nuclear properties, the growth material is ”spiked” with a low
(few Bq) activity of 229Th to produce a measurable signal on a
$\gamma$-detector. Both thorium isotopes are chemically identical and
therefore distribute identically during the growth process.

##  .6 Doping efficiency and homogeneity

Before and after growth, 229Th-doped crystals are measured on a
$\gamma$-spectrometer in a reproducible geometry (in the crucible) to
determine the efficiency of the doping process by comparing the intensity of
the 193 keV $\gamma$-line. We observe a 20-30% doping efficiency of the
starting material where we attribute the losses to evaporation. The highest
doping concentration realized so-far was with a 229Th activity of 1 MBq
(3.6$\cdot 10^{17}$ nuclei) in the starting material, reaching a concentration
of 2.4$\cdot 10^{17}$ cm-3 (see figure 11).

The doping concentration is homogeneous over the molten part of the crystal
and decays over 2-3 mm in the interface to the not molten seed, as illustrated
in figure 7. For this investigation, a crystal doped with 232Th, spiked with
229Th, was grown. After growth the crystal was cut into 1 mm disks and each
disk was measured in a reproducible geometry in the gamma-detector. Again, the
193 keV line activity was detected and from this the concentration was
calculated by measuring a reference sample. The seed crystal was molten to a
depth of around 6 mm, in which the concentration is approximately homogeneous
(within 2$\sigma$ as seen in figure 7). Beyond, we observe diffusion of dopant
into the not molten part on a length scale of about 2 mm, until no doping can
be detected in the not molten region of the seed crystal.

Figure 6: 238U:CaF2 single crystal grown during temperature calibration. The
crystal lies on a caliper where the mm scale is indicated below. The melting
boundary can be clearly seen in the color difference. The bottom (left) part
is only slightly colored due to Uranium outgassing from the carbon crucible
that accumulated there in earlier growth cycles and penetrating the outer
layer of the CaF2 crystal. The top of the crystal on the right is strongly
colored due to the incorporation of the dopant material during melting and re-
solidification. Figure 7: Doping concentration versus position in a (”spiked”)
232Th:CaF2 crystal. The red color indicates the doped and undoped parts,
although the thorium is colorless. The grown crystal was cut in 1 mm pieces
and the activity of each piece was determined with the $\gamma$-detector and
related to concentration through a reference sample. In the figure, 0 mm
corresponds to the top and thus doped part of the crystal. Error bars indicate
the uncertainty in the obtained count rate in the $\gamma$ detector. Figure 8:
229Th:CaF2 single crystal grown with an activity of 1 MBq in the growth
material. On the left, the crystal as it was inspected immediately after
growth. On the right, the crystal after 3 days. The orange coloring is due to
the agglomerations of defects, F-centers, produced by the radioactivity Beeks
and Schumm (2022). The melting boundary can be clearly seen in the color
difference. The top of the crystal is on the right.

##  .7 VUV transmission

Good transmission of the obtained crystals in the VUV range around 150 nm is
imperative for all attempts to optically manipulate (or detect) the 229Th
isomeric state. We therefore performed a series of characterization
experiments described below, with a special emphasis on the behavior of the
VUV absorption with doping concentration.

Doping Th into the CaF2 matrix should not reduce the bandgap and therefore the
optical transmission window significantly, as theoretically calculated
Dessovic  _et al._ (2014) and measured Schreitl (2016). However, additional
electronic states (often referred to as color centers or defect states) can
emerge within the bandgap Nickerson  _et al._ (2020).

In order to measure the VUV transmission, the crystals were cut and polished.
Cutting was done using a Wiretec DWS100 with a 0.08 mm diamond coated wire.
Facets cut with the wire saw were flat enough to be polished in a 1-step
process. Polishing was done with a Buehler crystal polishing machine and a
Buehler SiC P4000 grit Silicon Carbide polishing paper. The polishing paper
was wetted with isopropanol. As CaF2 is hygroscopic and adsorbed water
decreases transmisson, the polishing paper was wetted with isopropanol instead
of water Reiterov  _et al._ (1980).

Figure 9: Experimental setup to measure the wavelength-dependent transmission
of a crystal. The light produced by a deuterium (D2) VUV lamp is focused by a
mirror onto a monochromator which, using a rotating focusing reflective
grating, can image different colors of light through a sample in a filter
wheel on a PMT detector. By comparing the light output at a set wavelength
with and without crystal in the optical path, a transmission spectrum can be
measured.

Transmission measurements were performed using a dedicated setup as
schematically depicted in figure 9. The light of a Hamamatsu L15094 D2 lamp is
focused with a toroidal mirror onto the entrance slit of a McPherson 234/302
monochromator. Part of the light does not hit the focusing mirror. The light
is separated into its spectral components by the grating and is focused onto
the exit slit. By rotating the grating the exit wavelength can be selected.
The exit slit cuts out a small portion of the spectrum effectively creating a
narrow wavelength light source with a linewidth down to 0.1 nm. The linewidth
can be changed by changing the entrance/exit slit width (0.01 mm to 2.50 mm).
This light travels through the crystal, and is recorded by a Hamamatsu R6835
head-on CsI photomultiplier tube (PMT) which is mounted close to the crystal.

Although conceptually simple, measuring a wavelength-dependent absolute
absorption is burdened with several experimental challenges. These are
connected with geometrical changes in the beam paths due to the presence of
the sample (beam shifts and astigmatism), strong spectral intensity
modulations and overall intensity instabilities in the VUV source (deuterium
lamp). These lead to an overall systematic error on the following transmission
measurements of $\pm$5 %.

Figure 10: Spectral transmissions of 232Th:CaF2 with different thicknesses and
concentrations for different wavelengths. A sample of VUV grade CaF2 produced
and polished by Korth GmbH is displayed for comparison, thickness 5 mm. It can
be seen that the 232Th doped crystals all absorb heavily below 130 nm, but
pure CaF2 only below 125 nm. Due to the different thicknesses of the samples
the transmission might be different, but the absorption coefficient not.
Figure 11: Spectral transmissions of 229Th:CaF2 with different thicknesses and
concentrations for different wavelengths. A sample of VUV grade CaF2 produced
and polished by Korth GmbH is displayed for comparison (not remeasured),
thickness 5 mm. It can be seen that the 229Th doped crystals are consistently
less transparent than pure CaF2, but otherwise follow the same behavior.
Figure 12: Relative absorption coefficient of 232Th:CaF2 with different
concentrations for different energies and wavelengths. Main features are
general increase in absorption for higher concentrations, absorption around
150 nm and below 130 nm or after 9.5 eV. The thickness of the crystal limits
how well high absorption can be measured which is an artefact in the figure:
the thinnest crystals have the highest absorption around 10 eV. Figure 13:
Relative absorption coefficient of 229Th:CaF2 crystals with different
concentrations for different energies and wavelengths. The crystal grown with
1 MBq activity, was only 0.5 mm thick. The thickness allowed an absorption
measurement of only the high wavelength region. The absorption profile of
these crystals is flat with few features. The bandgap edge of CaF2 after 10 eV
is seen. With higher activity during growth, more absorption is observed
independent of concentration.

To compare measurement results between different samples, we account for the
thickness of the crystal, surface reflections, and absorption at the surface
by normalizing the absorption coefficient to pure (undoped) CaF2. This
relative absorption coefficient $\mu_{rel}$ then is a measure for the
absorption caused by Th doping in the bulk and at the surface. Although
generally relevant in CaF2, we expect two-photon absorption processes to be
negligible in these measurements, due to the very low intensities used. It is
also assumed that surface quality is similar for all measured crystals.
However, this is hard to guarantee due to the hygroscopic nature of calcium
fluoride, which leads to water adsorption Denks  _et al._ (2000)

The relative absorption coefficient is defined as

$\mu_{rel}=\frac{-\log{(T/T_{CaF_{2}})}}{d},$ (5)

where $T$ is the transmission, $T_{CaF_{2}}$ the transmission of pure CaF2 and
$d$ the thickness of the crystal. We measure the transmission and subsequently
calculate the relative absorption of 229/232Th:CaF2, for the wavelength region
of interest 120-160 nm.

Non-normalized transmission measurements for 232Th- and 229Th-doped crystals
can be seen in figures 10 and 11, respectively. Figures 12 and 13 show the
corresponding relative absorption coefficients.

From figures 10 and 11 it can clearly be seen that all grown single crystals
have a transmission above 1 % around 150 nm, some reaching $\approx$ 40 %. In
cases where the seed crystal was fully molten during the growth process, we
obtain completely VUV-opaque samples (transmission $<0.1\,\%$, independent of
doping concentration). We conjecture that in these cases, a polycrystal is
formed, which suppresses VUV transmission due to the presence of grain
boundaries.

Doping concentrations up to 2.6$\cdot$1020 cm-3 for 232Th and up to
5.4$\cdot$1017 cm-3 229Th were grown with good transparency.

The 232Th doped crystals often show an absorption around 150 nm, which we
attribute to Ca metallic particles Rix  _et al._ (2011). In undoped CaF2 they
absorb around 160 nm but the presence of Th changes the refractive index of
the crystal, thereby changing the absorption wavelength of these centers.
Higher doping concentrations generally seem to lead to more absorption.

In Angervaks  _et al._ (2018), sharp absorption bands around 160-170 nm were
observed and attributed to calcium metallic precipitates or colloids
incorporated in the CaF2 matrix. These precipitates can form due to crystal
damage or a deficiency of fluoride.

All grown Th:CaF2 crystals seem to absorb starting from 130 nm and have very
low transmission below 125 nm, earlier than the transmission edge of CaF2
which starts at 125 nm and has little transmission below 122 nm.

In the absorption of 232Th (figure 12) it can be seen that crystals with
similar concentrations have similar absorption. Three features can again be
identified: Increasing absorption around 150 nm or 8.2 eV, a general increase
of absorption with increasing doping concentration and very strong absorption
starting at $<$130 nm or 9.5 eV. These features are all compared to pure CaF2,
so they are an effect of the dopant.

In figure 11 it can be seen that the 229Th doped crystals are transparent up
until the transmission edge of undoped CaF2. The overall transmission of these
crystals is lower. In the absorption of 229Th:CaF2 (figure 13) some common
features can be detected. Similar concentration does not give similar
absorption and the absorption profile is flat. The measurement of the crystal
grown with the highest activity is uncertain due to its strong absorption.
Following the spectral absorption of the other crystals we can expect its
profile to be flat as well with a relative absorption higher than 6 mm-1. From
figure 13 it can be concluded that crystals grown using similar activity have
similar absorption and at these low concentrations (compared to figure 12) the
absorption does not heavily depend on concentration.

Figure 14: Relative absorption coefficient of Th:CaF2 and undoped CaF2
crystals with different concentrations for different energies and wavelengths.
In the legend the crystal number, doping concentration and thickness is
indicated. The highly doped 232Th doped crystal was made by manually mixing
ThF4 with CaF2, not by coprecipitation as described above. The differences in
absorption between radioactive and not radioactive are clearly seen throughout
the spectrum.

The 229Th doped crystals display a different behavior from the 232Th doped
crystals, which can be clearly seen when comparing figure 10 and 11. This was
not expected as it is assumed that different isotopes behave identically
concerning the electronic interactions. Most probably, the isotope itself does
not change the characteristics but the radioactivity of the isotope does. The
229Th doped crystals only stop transmitting at the bandgap edge of CaF2, the
125 nm absorption is not observed. The absorption around 150 nm seems to have
disappeared. The general transmission of the 229Th doped crystals is lower,
despite the lower doping concentration.

To confirm the different absorption spectra of 229Th and 232Th doped crystals,
drifts and changes between measurements of the VUV transmission setup were
excluded. For this, a low doped 232Th:CaF2, a high doped 232Th:CaF2 and a high
doped 229Th:CaF2 were measured in the same experimental run. The results are
seen in figure 14. Here we can see several effects. There seems to be an
activity-related broadband VUV absorption, independent of doping
concentration. The 229Th:CaF2, just as undoped CaF2, heavily absorbs at $>$10
eV, the transmission edge of CaF2. The 232Th:CaF2 absorbs heavily at $>$9.5
eV, earlier than the other crystals. The intensity of this absorption is
concentration-dependent, whereas the absorption of the radioactive crystals is
almost concentration independent.

If we now combine the information contained in all figures, a few observations
can be made:

  * •

Crystals grown with increasing activity have an activity-dependent broadband
VUV absorption, independent of Th concentration. This is clearly seen in the
absorption of 229Th doped crystals and even in 232Th doped crystals probably
due to the small amounts of added 229Th in combination with the weak activity
of 232Th. The activity of the crystal with the highest 232Th doping
concentration is still only 1 Bq.

  * •

Thorium doping with low activity creates a concentration-dependent absorption
around 150 nm and a strong absorption around 122 nm. This is mainly visible
for crystals with doping concentration of $>$7$\cdot$1019 cm-3.

The thorium-related absorption around 122 nm does not seem to be present in
crystals grown with high activities. It is conjectured, that the thorium is in
a different electronic state, either oxidation state or paired with a defect,
if a crystal is grown in the presence of high radioactivity. Because of this
change in electronic state, the absorption around 122 nm disappears. The
hypothesis connected with this observation is that the radioactivity induces
loss of fluoride which produces non-stoichiometric, or fluoride-deficient
crystals.

Figure 15: Cuts made in the crystal grown with 1 MBq of 229Th, named X2. As
can be seen from the orange coloring due to radioactively induced damage, only
X2.1 and X2.2 are doped with 229Th.

##  .8 Fluoride deficiency

The strongest evidence for a fluoride deficiency in the 229Th:CaF2 crystals
was the transmission of the crystal named X2, containing a high activity of 1
MBq. A thin slice taken from the undoped side of X2, named X2u (see figure
15), was measured to be completely VUV opaque. At first the suspicion was
radiation damage: Annealing to 600 ℃ did not decrease VUV absorption of any
part of X2 whereas it should remove radiation damage. The annealing did
however remove the orange color of parts X2.1 and X2.2 in figure 15, the
healing of F centers. Not responding to annealing indicated that the VUV
opaqueness of X2u was not radiation induced damage in the crystal. Another
observation hinting towards fluoride-deficiency was that when growing CaF2
crystals in vacuum (doped or not) outgassing of F2 was measured by a mass
spectrometer.

Figure 16: Schematic representation of the radioactively induced loss of
fluoride during the growth process (compare to figure 1), taking crystal X2 as
an example (see figure 15). First the crystal is filled with the radioactive
powder. During growth, a part of the crystal is molten and a part of the
crystal is in the superionic state. In the liquid, the 229Th is dissolved and
the $\alpha$-decay locally provides the energy to dissociate CaF2, producing
F2 that is pumped away. The superionic crystal has extremely mobile F- atoms
which will diffuse to the liquid phase, supplying it with more F-. The
resulting crystal will have a homogeneous deficiency of F due to its high
mobility during growth, but only a partial doping of Th due to its low
mobility during growth. As is seen in figure 7, only a small fraction of the
Th penetrates the not molten crystal.

Our conjecture of the process that leads to the fluoride deficient crystals is
depicted and detailed in figure 16. By growing CaF2 with radioactive
materials, the loss of fluoride in the liquid phase is enhanced and non-
stoichiometric crystals are produced. The dissociation of fluoride compounds
to produce gaseous F2 through radioactivity, radiolysis, has been observed in
UF6 Dmitrievskii and Migachev (1960). The nuclear chemical reaction describing
this process is

$\text{CaF}_{2}\xrightarrow[]{\alpha\text{ 5
MeV}}\text{Ca}^{s}+\text{F}_{2}^{g},$ (6)

where the metallic Ca is dissolved in the solid phase, and F2 leaves the
liquid melt as a gas. The energy for a chemical reaction is $\approx$ eV, the
energy of $\alpha$-decays is $\approx$ MeV. Because of this, every single
$\alpha$-decay could drive many chemical reactions. In a conservative
estimate, if 1 % of all reactions with an $\alpha$ particle drive radiolysis,
which costs 10 eV per reaction, then 5000 dissociation events can take place
per $\alpha$-decay. At an activity of 1 MBq of 229Th this would mean at least
5$\cdot 10^{9}$ radiolysis events per second. In a growing cycle where a part
of the crystal is molten for 22 hours, there are 2$\cdot 10^{15}$ radiolysis
events as compared to the $\approx 10^{21}$ F atoms in the crystal. This would
lead to a defect concentration of 4$\cdot 10^{16}$ cm-3, which should indeed
be visible in a transmission measurement.

Between 1370 K and 1450 K Voronin and Volkov (2001); Derrington  _et al._
(1975), the solid CaF2 undergoes a phase transition into the superionic state.
Therefore, the superionic part of the crystal becomes fluoride deficient due
to fluoride transfer to the melt. In the superionic state, the fluorides are
highly mobile inside the crystal Ca+ matrix. The highly mobile F- can migrate
from the superionic phase to the molten phase, where the radioactivity induces
further dissociation. After freezing, the entire crystal is left fluoride
deficient. The crystal compensates for F- loss by producing Ca metallic
colloids which increase the VUV absorption. The top liquid thus loses fluoride
supplied by the bottom solid. The mobile superionic fluorides evenly spread
throughout the solid and liquid crystal, causing homogeneous fluoride-
deficiency throughout the crystal explaining our observations. This fluoride
deficiency causes a strong broadband absorption in the VUV spectral range.

##  .9 Cherenkov radiation

A second characterization was performed where the radioluminescence of the
229Th:CaF2 crystal, grown with 100 kBq of 229Th, was measured in the VUV
spectral range. This crystal was chosen due to its high concentration and
transparency. The inherent radioactivity of the 229Th produces two main types
of luminescence: Luminescence of CaF2 by creating electron-hole pairs which
form self-trapped excitons (STE) Rodnyi (1997) and Cherenkov radiation through
beta emission with energies larger than 158 keV. Stellmer et al. Stellmer  _et
al._ (2016) measured both these emission types by using undoped CaF2 and a
solid 233U sample. The Cherenkov radiation dominates the low wavelength region
up until 200 nm. Above 200 nm the luminescence of the STEs dominate. Both can
produce a background for further experiments and thus merit characterization.

For the luminescence measurement, the chosen crystal was placed in the focal
point of the entrance of a 234/302 McPherson spectrometer as depicted in
figure 17. Any radioluminescence was then spectrally resolved and imaged on a
Hamamatsu R7639 PMT cooled to -30 °C. The PMT is cooled to reduce dark noise
to 0.5 cps, otherwise Cherenkov radiation could not be detected. A shutter was
used to take continuous dark measurements while the signal was integrated for
9 hours per wavelength setting. The result of this measurement for a 1 mm long
3.2 mm diameter 229Th:CaF2 crystal with a concentration of 5.4$\cdot 10^{17}$
cm-3 can be seen in figure 18.

Figure 17: Schematic drawing of the detector-spectrometer combination used to
measure the fluorescence of activated crystals. The fluorescence produced by
the crystal goes through the entrance slit and is then imaged by a focusing
grating in a Seya-Namioka spectrometer model onto the exit slit. Only a slit
size-dependent fraction of wavelengths will fall onto the PMT. Directly after
the exit slit a fast (18.0 ms opening time) shutter is installed. Figure 18:
The detected VUV spectrum of a 229Th:CaF2 crystal compared to a theoretically
computed Cherenkov spectrum that takes into account the spectral efficiency of
the system (figure 17). The calculation was slightly scaled to experimental
results (see text for calculated discrepancy) to accentuate the differences
between the curves. A 1 mm slit size was used for the measurement. The maximum
count rate was 0.7 cps. The absorption edge of CaF2 below 122 nm can be seen,
as well as loss of efficiency of the PMT and grating for higher wavelengths.
The measured transmission of the crystal was used to calculate the theoretical
Cherenkov spectrum. The sharp peaks at low wavelength in the theoretical
spectrum are artefacts due to lines in the D2 lamp used to measure the
transmission of this crystal.

The Cherenkov background at 150 nm was measured to be 0.5 cps. As can be
calculated Stellmer  _et al._ (2016), every single decay event (1 Bq) of 229Th
produces 0.1 Cherenkov photon per second at 150 nm in a 1 nm bin. Considering
9.4 kBq (the amount of nuclei visible through a narrow slit) of 229Th, and
0.05 % total efficiency of the spectrometer system, the Cherenkov flux at 150
nm would be 0.4 cps. The small discrepancy between prediction and measurement
can be due to the (lack of) accuracy in the measured amount of 229Th in the
crystal, or the characterization of the numerous experimental efficiencies. In
this spectral efficiency the measured transmission of the crystal, the
efficiency of the grating with its MgF2 coating and the efficiency of the PMT
with its MgF2 window were considered.

The calculated Cherenkov spectrum does not fully reproduce the measured values
for higher wavelengths $>$170 nm. This could be caused by measurement errors
in the transmission of the crystal, which is used in the calculation of the
spectrum. The mismatch can also be VUV luminescence of color centers induced
by the radioactivity, radioluminescence. It is known that due to the
scavenger, all crystals are slightly contaminated with Pb which has a
luminescence peak at 180 nm Babin  _et al._ (2004). A more detailed
investigation on the luminescence properties (radioluminescence and VUV-
induced) is under way with the aim to identify contaminants as well as the
additional electronic levels (defect centers) connected to Th doping in
different charge states.

##  .10 Discussion and Conclusion

We have grown highly doped ($5.4\cdot 10^{17}$ cm-3) 229Th:CaF2 crystals with
low absorption ($\mu$ = 0.9 mm-1 or 20 % transmission at 150 nm and 2 mm
thickness) and highly active (1 MBq) 229Th:CaF2. This was done by careful co-
precipitation of ThF4 and PbF2 and mixing with CaF2 to form a powder of growth
material. The powder was then placed in a specially machined, millimeter-scale
single CaF2 seed crystal which was used to grow a single Th:CaF2 crystal on
top of the seed crystal using the vertical gradient freeze method. At high
activities, these crystals seem to lose VUV transmission due to radioactivity-
induced fluoride losses during the growth process (radiolysis). Even the not
molten and undoped parts of this crystal lose transparency due to the high
mobility of fluoride in the superionic state realized during crystal growth.
Still, even at 1 MBq total doping activity, a transmission of several percent
remains. In the future, attempts will be made to regain the undoped CaF2
transmission profile by re-feeding fluoride during growth or by annealing
after growth.

The thorium-related spectral absorption feature at 122 nm decreased for
radioactive crystals and the same crystals showed unidentified emission
features. It is highly likely this is caused by a change in the electronic
configuration of Th due to fluoride deficiency. By adding fluoride to the
crystal it is expected that the electronic configuration changes to one
similar to the non-radioactive crystals with high transparency. The highly
active 229Th:CaF2 crystals emit Cherenkov radiation which was quantified in
this work, as it which will constitute a constant background for the future
nuclear spectroscopy of 229Th in the crystal matrix.

##  .11 Acknowledgements

###### Acknowledgements.

We acknowledge the tireless support for over a decade by Kurth Semmelroth,
Rainer Apelt, and the scientific and technical staff of the Fraunhofer
Institute for Integrated Systems and Device Technology IISB. We also thank
Reinhard Uecker from the Institute for Crystal Growth for first explorations
into Th:CaF2 and invaluable advice. We are grateful to Mauro Tonelli from
University of Pisa and the team from MEGA Materials for sharing their
experience and insights. This work received funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme under the ThoriumNuclearClock grant agreement No. 856415. The
research was supported by the Austrian Science Fund (FWF) Projects: I5971
(REThorIC) and P 33627 (NQRclock).

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