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In-situ monitoring of PVDF ultrasound transducers under gamma irradiation

T. Kelley*a, K. Hutchingsa, M. Jenkinsona, I. Dawsonb, K. Krawecb, P. S. Miyagawab,

J.H. Kernc, R. Edged

aPrecision Acoustics, Dorchester, UK; bDepartment of Physics, University of Sheffield,

Sheffield,UK; cTWI Ltd, Middlesborough, UK; dDalton Cumbrian Facility, University of

Manchester, Cumbria, UK

tom@acoustics.co.uk *corresponding author

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In-situ monitoring of PVDF ultrasound transducers under gamma irradiation

Ultrasonic transducer (UT) systems are used for non-destructive testing and evaluation across a wide

range of industries. In the nuclear industry, radiation damage of the UTs can lead to performance

degradation or even complete failure. We have investigated the radiation resilience of a new piezo-

polymer (PVDF) UT design. The irradiations were performed in a Cobalt-60 gamma facility with total

ionising doses up to 10.5 MGy. Continuous pulse-echo measurements were taken in-situ allowing the

performance as a function of time to be monitored. In addition to the UT irradiations and

measurements, high fidelity Monte Carlo particle transport simulations were performed to study the

radiation environments and the ionising dose profiles within the devices under test. These dose profiles

were used to gain insight into the behaviour of PVDF under irradiation. Results show that that all

sensors were able to withstand the doses achieved without suffering complete failure, with the best

performing device only losing 47% of its initial amplitude. Dose profiles for the PVDF show

piezoelectric performance to increase by up to 7% at doses around 500 kGy after which performance was

found to drop linearly at a rate of between 6.5 and 10% per MGy.

Keywords: ultrasound; transducer; NDT; nuclear; radiation; simulation

1 Introduction

Ultrasonic transducers (UTs) are routinely used for non-destructive testing (NDT) and evaluation of

both metallic and non-metallic components across a wide range of industry sectors, from aerospace

and energy to transport and utilities. Within the nuclear industry, a high proportion of this NDT

involves condition monitoring of safety critical components. This includes; pipework, valves, welds

and joints, nozzles, containers and vessels. Many of these components have high performance

requirements, and it is important to have a system that is capable of monitoring small changes.

Such a system may need to detect, for example, the formation and growth of cracks or the gradual

thinning of a section due to corrosion. Although signal processing and sensor design can be used to

good effect, there exists a fundamental physical limit on the imaging resolution that can be

achieved by an ultrasonic transducer of a particular frequency. As such the use of high frequency

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ultrasonic transducers is often required to meet requirements for a particular resolution. The

piezopolymer PVDF (Poly-vinylidene fluoride) is ideally suited for use as the piezo material in

high frequency ultrasonic transducers since it can readily achieve MHz frequencies in a thickness

mode resonance. Commercially available PVDF films are available in thicknesses as low as 9 µm

which, in theory and assuming a half wave resonance, have a thickness mode resonance around

140 MHz (based on a wave speed of 2560 m/s [1]). In practise, the frequency of a PVDF transducer

is dependent on a number of factors including sensor diameter, backing type, cable length and drive

impedance [2] and will typically be lower than the resonant frequency. However, PVDF transducers

can still achieve frequencies as high as 30 MHz with ease. This high-frequency operation is further

complemented by the inherently damping polymeric structure of PVDF which enables PVDF-based

ultrasonic transducers to exhibit exceptionally high bandwidth. The combination of high bandwidth

and high frequency is ideal for achieving very short impulse responses, often only 1–2 cycles, which

gives PVDF transducers a hard-to-rival ability to achieve a high imaging resolution.

In the nuclear industry, components requiring NDT are often exposed to high levels of

radiation. This is particularly the case for in-core components which in the most extreme case can

experience doses rates up to 10 MGy/h [3]. This harsh environment complicates the use of PVDF

transducers since its polymer structure is affected by radiation, and unlike piezoceramic materials

which can be doped and modified to improve radiation resilience, there is a more limited amount that

can be done to improve the radiation resilience of the piezopolymer.

The effect of irradiation on polymer is well understood. In summary, exposure will induce

additional crosslinking between the polymer chains and may also cause chain scission and the

formation of radicals [4]. Ionising radiations such as gamma will ionise the polymer. The resulting

high energy electrons will continue to collide with other molecules in the vicinity until they no

longer have sufficient energy for further ionisation and are eventually absorbed as thermal

electrons by an ion. These high energy electrons can impart enough energy to break one or more

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of the covalent bonds within the polymer. Whilst the severing of bonds in the main polymer chains

leads to shorter chains and a reduced average molecular weight, radiation also induces crosslinking

between the chains leading to an increased molecular weight. This additional crosslinking changes

the physical properties of the PVDF and is often manifested as a reduced elasticity, increased

stiffness or physical embrittlement.

A limited amount of material has been published on the piezoelectric performance of

PVDF under irradiation, but studies have shown that the relationship between performance and

cumulative dose is not linear. In heavy-ion and electron beam irradiations, PVDF has been shown

to retain its piezoelectric response up to at least 100 kGy [5]. Additionally, radiation induced

crosslinking has been shown to improve the thermal stability of PVDF by reducing the mobility of

the main polymer chains and improving the resistance of the dipoles to thermal relaxation [6, 7].

This phenomenon has been shown to positively impact thermal performance up to 400 kGy whilst

minimally affecting the level of polarisation [8]. It is however unlikely that this will adapt PVDF

to high temperature environments since its performance at high temperature is substantially poorer

than most piezoceramics [9]. Doses up to 450 kGy have also been shown to increase polarisation

levels in already polarised PVDF [7] and it is possible that this could lead to an improved sensor

performance.

Another organic material commonly used in the construction of ultrasonic transducers is epoxy

resin. Considering the large choice of commercially available adhesives, epoxies in particular have

been shown to offer good radiation resilience up to 10 MGy [10] and some epoxy families are

reported to maintain useful adhesive properties up to doses of 100 MGy [11]. However, as is typical

with organic compounds, irradiation of an epoxy by a gamma source will lead to the formation of

gasses. This can include, but is not limited to: H2, CO, CO2, CH4 and C2H6 [12, 11]. Since the

formation of these gasses occurs within the bulk of the material, extended exposure to radiation

may cause the formation of internal voids or the deformation and cracking of a material and the

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subsequent release of gas. In a situation where a material is confined and constrained by its

surroundings, the evolution of these gasses can lead to the formation of stresses within the material as

a result of the build-up of pressure. Since the primary function of an epoxy is often as an adhesive,

these radiation effects are very detrimental to performance, and as such the use of epoxy in a

radiation-rich environment must be carefully considered. The careful use of epoxy is addressed in the

sensor design reported in Section 2.

While the performance of ultrasonic transducers under irradiation has been previously

reported, the bulk of previously reported literature is focussed on piezoceramic sensors based

around materials such as: Lead Zirconate Titanate (PZT), Lithium Niobate and Barium Titanate

[13, 14], and there is limited data available on the performance of PVDF based sensors. At time of

writing, no published literature could be found on the effect of gamma irradiation on the

piezoelectric performance of PVDF at doses above 1 MGy. This paper presents a collection of

acoustic measurements on the performance of PVDF transducers obtained in-situ whilst under

gamma irradiation up to a cumulative dose of 10.5 MGy. An estimated dose received directly by

the PVDF itself is also derived to yield an insight into the performance of the piezopolymer in

isolation.

2 Device fabrication

Transducers were fabricated in a stainless-steel housing incorporating a 20 mm acoustic delay

line and a corresponding 20 mm stainless steel backing plate (see Figure 1). A circular disc of

PVDF film1 was sandwiched between the delay line and the backing which acted respectively as

the front and rear electrodes of the PVDF. Although a ‘dry’ acoustic coupling can be achieved

1 Measurement Specialities Inc. (TE Connectivity) Schaffhausen, Switzerland, and Kureha KF, Japan (40

µm only).

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between flat plates with the addition of sufficient pressure [15], a thin layer of epoxy2 was used

as an acoustic coupling medium between the PVDF and the delay line/backing to facilitate

improved transmission of ultrasound between the steel and piezopolymer to eliminate both the

need to polish electrode surfaces and to eliminate the risk of pressure fluctuations during operation

causing a variation in coupling efficiency of the probes. In addition, the extra sensitivity afforded

by this method over a dry coupling method allowed a higher signal to noise ratio to be achieved

during subsequent in-situ measurements.

Removing the reliance on adhesive bonds to hold the sensor together, all components were

designed to screw together mechanically. The delay line and backing plate were held in almost

direct contact (except for the PVDF and thin epoxy couplant) via a threaded section on the inside

of the housing and the outside of the backing plate which maintained a pressure on the PVDF. A

torque wrench was used to apply a measured force during assembly of these parts which

corresponded to a pressure of 104 kPa on the PVDF. This force was intended to counter the

pressures created by radiolytic gas production in the epoxy bondline which would cause

separation of the PVDF from its electrodes. However, owing to the extreme thinness of the

bondline (<1 µm), volumes of gas produced by radiolysis were expected to be small.

[Figure 1 here]

Three ultrasonic transducers were constructed in this identical manner with the exception of

the PVDF itself which was trialled in 3 different thicknesses (see Table 1). Additionally, a fourth

probe design was constructed (probe 4 in the table) which was a conventional PVDF probe design

comprising a steel housing and brass backing as described by Lewin & Schafer [2]. All transducers

2 Robnor resins, PX771C/NC

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were annealed at 70 ◦C for 5 hours prior to irradiation to stabilise the PVDF film for use up to this

temperature.

[Table 1 here]

3 Experimental set-up

Transducers were irradiated for approximately 14 days at the University of Manchester’s Dalton

Cumbrian Facility (DCF, Cumbria, UK) with a Cobalt-60 source, capable of supplying ionising

doses up to 476 Gy/min. Dose rates varied between probes based on their location in the irradiation

chamber but dose rate for each probe was constant over the 14 day duration. Cobalt-60 emits two

dominant gammas with energies 1.17 and 1.33 MeV, which are representative of the fission

gammas found in nuclear reactors. However, lower-energy photons and electrons will also be

present in the irradiation chamber due to interactions of the gammas with the material of the

irradiator chamber. The contribution to the total ionising dose from these lower energy sources has

not been studied. The transducers were mounted horizontally in an aluminium stand (see Figure 3)

and a 5 m length of coaxial cable (RG174) was attached to each via BNC connectors. The stand

was placed in the radiation chamber with the front of the acoustic delay line facing into the direction

of radiation. A pulser/receiver unit3 was used to drive the transducers in a pulse-echo mode, enabling

the acoustic echo from the front surface of the delay line to be monitored. Owing to the anisotropy of

the radiation, the dose received by transducers varied depending on the position in the chamber. The

maximum dose received was 10.5 MGy, whilst the minimum dose received by any sensor was 7.2

MGy. The dose received by the PVDF material was lower due to the self-shielding effect of the

transducer, which can only be determined through particle transport simulation as described in

3 JSR, DPR 300, Imaginant Inc, USA

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Section 4. A thermocouple was installed on one of the sensor bodies to monitor the temperature to

verify that the transducers did not exceed 70 ◦C, and that any degradation in sensor performance

should not be attributed to a thermal depolarisation of the PVDF. Transducer performance was

monitored throughout the 2-week period and voltage traces captured every 2 minutes for the duration.

The sensor design (described in Section 2) ensured that all materials which were likely to

suffer degradation, or have their properties significantly altered as a result of the irradiation, were

removed from the electrical and acoustic pathways in the sensor. Besides the PVDF, the only non-

metallic components in either of these pathways were the coaxial cable taking signals from the

sensor to oscilloscope and the thin acoustic coupling layer between PVDF and backing. Assuming

the acoustical and electrical properties of stainless steel and copper wire to remain constant up to

10 MGy, any changes in sensor performance can be attributed to either the PVDF, the cable or the

bond layer. To establish that the only variable affecting sensor performance during irradiation was the

PVDF itself, the performance of the cable was characterised before and after irradiation. Six identical

cables were tested in turn with the same sensor. Five of these cables had been used during the

probe irradiations, and one was a new unirradiated cable. Pulse-echo results, obtained in the same

manner as those taken in situ during irradiation, revealed that the cable performance was unchanged

in respect to this type of measurement as a result of the irradiation. Mean pulse-echo probe amplitude

from all six cables was measured as 140 mV with a range of 8 mV and a standard deviation of

3.7 mV. The spread of values can be attributed to pickup of random noise due to the 5 m cable

length.

[Figure 2 here]

Sectioning of the sensors post-irradiation was performed to yield an insight into the structure

of the bondline between PVDF and backing. A scanning electron microscope (SEM) was used to

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obtain high resolution images of the bondline (Figure 2). The bondline appeared intact with no

visible signs of delamination or thermally induced cracking and was measured to be 0.75 µm in

thickness. This sectioning process provided a unique insight into the integrity of the sensors’

internal components, in particular the bondlines between the PVDF and adjacent components and

has helped confirm the engineering design of these transducers to be effective at withstanding the

total accumulated dose of 10.5 MGy. Given the thickness of this layer, it can be assumed that any

changes in property as a result of irradiation will have had a very minimal impact on both the

acoustic and electric performance of the bondline and therefore will not have impacted significantly

on sensor performance. To qualify this, the epoxy had previously been characterised as having a

frequency (f) dependent attenuation (α) of;

α=3.4 × f 0.95 (1)

based on a broadband pulse, through-transmission characterisation measurement [16] over

the range 1-10 MHz, with α in units of dB cm-1 and f in MHz. Using the -20dB upper frequency

limit of the highest frequency probe (probe ‘2’, 21 MHz) to estimate the worst-case ultrasonic

attenuation in a 0.75 μm layer of the epoxy (as shown by the SEM measurements) yields a single-

trip loss of 0.005 dB (α = 61.3 dB cm-1). Even a significant increase in α as a result of irradiation

will therefore have a negligible effect on the transmission of ultrasound through this layer. As such,

it can be reasonably assumed that the in-situ measurements made on these sensors under irradiation

were monitoring the performance of the PVDF itself rather than any other aspect of the sensor

construction and can be used as a proxy for the behaviour of PVDF under irradiation.

4 Monte Carlo simulations

The Geant4 Monte Carlo simulation toolkit [17] was used to study the radiation dose profiles in

and around the UT probes, allowing also the dose received by the PVDF sensor material inside the

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housing to be determined. An accurate model of the irradiator and the UT probes was constructed in

Geant4, as shown in Figure 3. The Cobalt-60 sources were simulated in Geant4 using a radioactive

decay package [18], and gammas and electrons were transported throughout the simulation taking

into account scattering and absorption.

In order to validate the simulated predictions, simulations were also performed without the

UT probes so that comparisons could be made with ionising dose measurements4. An example of

these comparisons is presented in Figure 4. In general, good agreement is found, with variation

typically less than 30%. However the simulation is not perfect, with a tendency to under-predict the

dose rates close to the radioactive sources by around 30%, and over-predict towards the back of the

chamber, by some 50%. Also shown in this plot is the importance of including the steel chamber

walls into the simulation, which increases the ionising dose rates due to back-scattering.

[Figure 3 here]

The good agreement between the dose measurements and the simulated predictions gives

confidence in the Geant4 set-up and modelling. In the full simulations in which the UT probes are

included, the dose profile in and around each probe is obtained. Shown in Table 2 are the simulated

dose values at the front of the UT probes along with those at the location of the PVDF sensor. The

ratios can be used to scale the measured values and obtain values for the PVDF.

[Table 2 here]

[Figure 4 here]

4 Determined using a Radcal Corporation Accu-Dose+ base unit equipped with a 10x6-0.18 ion

chamber which was calibrated on 14th June 2018 to traceable international standards.

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5 Results

Shown in Figure 5 are the results of irradiating the transducers up to a maximum cumulative gamma

dose of 10.5 MGy. An initial fluctuation in performance was observed in all sensors at the onset of

irradiation. This fluctuation corresponded with the initial rapid temperature rise of the sensors from

ambient to 50 °C. Data from the in-situ thermocouples showed that the sensors reached a thermal

equilibrium at this temperature and this was maintained throughout the duration of the irradiation.

After this initial fluctuation in performance, which can be attributed to thermal effects within the

sensor structure, the performance was then found to improve up to doses of 1.1 MGy (on average).

The magnitude of this initial improvement in peak-peak amplitude was between 1 and 7 %, with

the largest improvements observed in sensors based on 40 µm PVDF. The smallest improvement

was seen in the sensor using 110 µm PVDF. At increasing doses, the performance begins to decrease

for new design probes 1–3, and complete failure occurred for both probes made to the conventional

design. For the probes 1–3 a linear decay was observed from around the 2–4 MGy mark, with

sensors losing between 6.5 and 10% of their initial (t0) amplitude per MGy. The best performing

sensor was based around the 110 µm PVDF, which exhibited a 6.5% loss per MGy. The worst

performing device (apart from the conventional probes) was based on the 40 µm PVDF which

exhibited a loss of 10% per MGy. Linearly extrapolating these rates of decay leads to an estimate of

sensors reaching complete failure at between 13 and 18 MGy.

The results of the Geant4 simulations reveal that dose received by the PVDF is reduced by 46-57%

compared to the measured values in air, depending on location in the irradiation chamber. This is

mainly due to the shielding effect of the 20 mm delay line.5 Scaling the measured dose rates by the

Geant4 predicted attenuation factors for each probe, the UT performance as a function of dose in the

PVDF can be investigated, and the results are given in Figure 6. The rate of decay in the linear

5 This is consistent with a simple attenuation calculation, which predicts a dose reduction of 57.3% due to

the 20 mm delay line, assuming a linear attenuation coefficient of 0.426 cm-1 [22]

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portion of the dataset above 1.5 MGy was found to be very consistent with all three sensors 1-3

dropping their pulse-echo performance by 17% of their t0 amplitude per MGy. A linear

extrapolation of the rates of decay determined through simulation indicates that piezoelectric

activity in the PVDF would drop to zero at a dose of between 6-7 MGy if the rate of decay remained

constant beyond the experimentally measured range.

An expanded section of Figure 6 is provided in Figure 7 to give a clearer indication of the

rise and fall in pulse-echo amplitude observed over the initial 1 MGy of irradiation. From this

figure it can be seen that the dose received by the PVDF corresponding to maximum UT output was

between 470 and 590 kGy.

A post-irradiation inspection of probe 4 revealed one of the causes of failure to be a

delamination between the PVDF and backing material. The nature of this delamination was so severe

that a gap of several mm was visible between parts of the PVDF and backing. Physical inspection of

the PVDF also revealed high levels of embrittlement, discolouration and cracking and peeling of the

sputter deposited gold/chrome electrode. This is consistent with the established view on the effects of

induced crosslinking, polymerisation and chain scission resulting from gamma irradiation [19, 20]. A

second probe made to the same design as probe 4 was also irradiated and appeared to fail after 0.95

MGy. Visual inspection of this probe yielded the same results as the first.

[Figure 5 here]

[Figure 6 here]

[Figure 7 here]

There were no outward differences upon inspection of the new UT designs after irradiation

besides a slight embrittlement of the polymer insulation in the BNC connector, however this had no

impact on sensor performance. Sectioning revealed a discolouration of the potting epoxy from its

original glasslike transparency to an opaque ‘chocolate’ brown. Although no quantitative tests

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were performed, a qualitative inspection indicated that there were no other signs of degradation

severe enough to affect the function of the epoxy and its integrity appeared unaffected. Unlike the

conventional design, the bondline between PVDF and delay line/backing appeared intact with no

voids evident, as shown in Figure 2.

To aid characterisation of the effect of radiation on PVDF, an analysis of the frequency

content of the in-situ data was performed (Figure 8). It was found that the -3dB centre frequency of

all new-design probes was reduced by up to 1% during exposure to the first 500 kGy of irradiation

(dose at PVDF). Continued radiation up to 4 MGy reversed this downshift and caused an overall

increase in frequency of between 3 and 4% for all probes of the new design. The largest downshift in

frequency was observed in probe 1, corresponding to the probe which showed the largest initial

improvement in signal amplitude. No frequency shift was observed in either of the standard design

probes.

[Figure 8 here]

In addition to the measurements made in-situ during irradiation, pulse-echo measurements were

made continuously over the initial 10 minutes post-irradiation and then again 20 days post-

irradiation. No evidence of signal recovery was observed at any stage.

6 Conclusions

The new UT designs show much greater radiation resilience compared to the conventional PVDF

design used in this study. The reason for the improved performance can be attributed to the new

mechanical design providing protection against the pressures exerted by radiolytic gas production.

Post-irradiation inspection suggests that the mechanical clamping aspect of the design was

sufficient to keep the sensor layers held together up to the full dose of 10.5 MGy against the

pressure forces of radiolytic gasses.

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The improvement in performance observed up to 1.1 MGy (corresponding to a dose at the

PVDF of 470-590 kGy) is consistent with previously published work [7] which shows both the

remnant and saturation polarisation of PVDF to be improved by radiation doses up to 450 kGy.

Results in this paper extend this dataset out to 4 MGy and confirm that doses above approximately

500 kGy lead to reduced sensor performance.

The link between frequency and probe performance indicates radiation induced chain

scission is significant within the PVDF. Since the PVDF in the new design is clamped between

two rigid plates it could be considered to have a fixed thickness once in thermal equilibrium, thus

any frequency shift would indicate a change in material velocity. We propose that this change in

velocity is evidence of the changing modulus of the PVDF as a result of irradiation and its

associated chain scission and crosslinking effects. In a previous study [21], polymer chain length

had been linked to dipole moment in PVDF based polymers. This could account for the performance

increase observed here if an increased dipole moment was established following scission. This

increase is short-lived however as chain scission and an increase in dipole moment cannot continue

indefinitely. As dose continues beyond 500 kGy the stiffening effects of additional crosslinking are

seen in the upwardly trending frequency, indicating an increase in modulus and an embrittlement of

the PVDF. In probes 1 and 2 and to a lesser extent in probe 3, the observed frequency shift continues

up to about 2 MGy at which point the frequency begins to stabilise. This stabilisation indicates that

embrittlement as a result of crosslinking may reach a peak at this point and there may be few sites

available for further crosslinking beyond this. The lack of frequency shift observed in probe 4

suggests the unclamped PVDF was able to deform during irradiation and therefore any change in

modulus did not manifest as a frequency shift due to the changing material thickness.

Further studies could be conducted to verify this hypothesis and might include ultrasonic

velocity measurements on both irradiated and unirradiated PVDF of sufficient thickness to

accurately quantify any velocity shifts. The linear extrapolation derived from Figure 6 to infer the

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point at which piezoelectric activity in PVDF drops to zero would also benefit from validation

through further experimentation.

The Monte Carlo simulation studies have shown the importance of full simulation to obtain

accurate dosimetry. Such simulations also allow studies of mitigating against the effects of radiation

through careful shielding design. This sensor design could provide a cost-effective and robust

alternative to piezoceramic based UTs for a variety of applications in high radiation environments.

This might include condition monitoring of nuclear waste storage containers or other ambient

temperature applications.

Acknowledgements

This work was supported by Innovate UK under grant 132953.

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Probe number PVDF Thickness (µm)

1234

524011052

Table 1: PVDF thicknesses of the ultrasound transducers tested in the gamma

irradiations.

Probe ID Dose PVDF Dose Front Ratio PVDF/Front123

3.93.84.5

7.37.210.5

0.530.540.43

Table 2: Dose values (MGy) in PVDF compared to front of probe, and their ratios.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 1: Schematic cross-section of transducer design. (1) Delay line, (2) Acoustic

coupling epoxy, (3) Backing, (4) BNC connector, (5) PVDF, (6) threaded section, (7)

Potting epoxy.

Figure 2: SEM micrographs of sectioned (irradiated) transducer to show PVDF bondline.

Main image showing; Delay line (A), PVDF (B) and backing (C). Inset: Expanded section

from main image, showing cross-section of bondline between PVDF and delay line (D).

Striations introduced into the edge of the PVDF by the sectioning process (E) are visible

at the boundary between PVDF and epoxy.

Figure 3: The DCF gamma irradiator as modelled in Geant4, indicating the nine

Cobalt-60 rods as well as the locations of the UTs.

Figure 4: Simulated Geant4 predictions of dose rate cover the regions y=58-68mm and

z =130-140mm whilst measurements were taken at y=60mm and z=132.5mm

Figure 5: Performance of probes 1-4 as a function of cumulative gamma dose. The

performance is measured using a normalised peak to peak pulse-echo probe amplitude.

Figure 6: Performance of probes 1-4 as a function of cumulative gamma dose in the

PVDF derived from the Geant4 simulations.

Figure 7: Expanded section of Figure 6 showing the performance of the UTs up to 1.2

MGy (dose at PVDF).

Figure 8: Shift in frequency as a function of Geant4 derived dose in the PVDF for

probes 1-4. Showing rapid thermal effects close to t0 and slower radiation induced

change up to 4 MGy.