PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Temperature dependence of the propagation speed of a longitudinal
wave in different solids for use as a wedge material in an extremetemperature-resistant ultrasonic transducer
Oleg SHAPOVALOV1 ; Mate GAAL1 ; Gerald HÖNIG 1,2; Thomas GRADT 1; Sabine WEISS3
1 Federal Institute for Materials Research and Testing, Germany
2 currently at: TWT GmbH Science & Innovation, Germany
3 Brandenburg University of Technology Cottbus-Senftenberg, Germany

ABSTRACTIn special cases of angle beam ultrasonic measurement – e.g. defect detection in hot solids as well as
flow measurement of liquid gases or energy storage mediums [1] – the applied transducer has to withstandextreme temperatures. Since the irradiation angle into the specific material is determined not only by wedge
design, but also by the speed of sound in both the wedge material and the tested object, the developer musttake into account the speed of the wave propagation in a wedge material over the whole temperature rangeof transducers application.
In this study we investigate the temperature dependence of the speed of longitudinal wave propagation in 10
different materials in the range from -200 °C to 400 °C. The investigated materials belong to different material
classes (ceramics, glass, as well as ferrous and non-ferrous metals) and are all temperature-resistant up to atleast 600 °C, and therefore applicable as wedge materials in an ultrasonic transducer for use at extreme
temperatures.
Keywords: Ultrasonic Transducer, Speed of sound, Longitudinal Wave, Temperature

1. INTRODUCTION
Nowadays, the rapidly developing machining and energy industri es are often associated withextreme temperatures. At the same time, the constantly increasing safety standards require a nondestructive testing as well as structural health monitoring of most industrial systems and mechanisms.
Angle beam ultrasonic measurement is a commonly used method not only for non-destructive
testing of parts, but also for precise non-immersive flow measurement of liquids [1]. In both cases themeasurement process often demands knowledge about the applied irradiation angle, which can besimply calculated from the wedge angle and speed of wave propagation in both the wedge material
and the tested object or liquid. But since the speed of sound depends on the temperature of thepropagation medium, the changing temperature also affects the beam angle. Therefore, thedevelopment of an angle beam ultrasonic transducer for use at extreme temperatures must be guided
by precise knowledge of a temperature dependence of the speed of sound in a wedge material.
Besides overall temperature stability of all transducer parts, all adjacent materials must exhibit
similar thermal expansion to avoid cracking or decoupling during heating or cooling to the operationtemperatures. Thus, the investigated wedge materials exhibit thermal resistivity up to at least 600 °C
besides a wide range of coefficients of thermal expansion.

1oleg.shapovalov@bam.de4754

2. MATERIALS AND METHODS
2.1 Materials
The measurements were carried out on cylindric samples of each wedge material with room temperature-lengths L 20 of 120±1 mm. Table 1 summarizes the investigated materials and theirchemical compositions.

MulliteAlumina

Ohara S-PHM52

Haynes HR-120

Haynes 230

Hastelloy C-276

Hastelloy B-3FeNi46

W80Cu

W90NiFe

Table 1 – Chemical composition of investigated wedge materials ( wt. %) [2; 3; 4]

Al2O371

100--------

SiO229---------

P2O5--

40-50-------

BaO-

-

30-40-------

CaO--

2-10-------

B2O3-

-

2-10-------

ZnO--0-2-------

WO3--0-2-------

Sb2O3--0-2-------Fe---33<351.554-

4Ni---

3757

57

>65

46-

6Co

---

<3<5

<2.5

<3-

--

Cr---

25

22

16

1.5-

--

Mo-

-

-

<2.5216

28.5-

--

W---

<2.5

144

<3-

80

90

Nb-

--

0.7

<0.5-

<0.2-

--

Mn-

-

-

0.7

<0.5<1<3-

-

-

Si-

--

0.6

0.4

<0.-08 <0.1-

--

N---

0.2-

-----

Al---

0.1

0.3

-

<0.5-

--

C---

0.05

0.1

<0.5

<0.01---

B---

0.005 <0.015-----Ti----

<0.1-

<0.2-

--

La----

0.02-

----

V----

-

<0.35<0.2-

--Cu-

---

-

<0.5

<0.2-

20-

Ta-----

-

<0.2-

--

Zr-

----

-

<0.01---

4755

2.2 Measurement setup and calculation method
To generate a longitudinal ultrasonic impulse on one end of a specimen we used a high temperature
resistant piezo-crystal lithium niobate LiNbO3 (Curie-point at 1210 °C [6]) with the center frequencyof 2 MHz. The time of flight t of a longitudinal wave in each material at different temperatures (from-200 °C to 400 °C) was measured using the pulse-echo method. Fig. 1 represents the scheme of anexperimental setup.
To cool the specimens down to -196 °C we immersed the experimental setup shown in Fig. 1 intoa liquid nitrogen, which served at the same time as an acoustic couplant between the piezo materialand the measured part. For performing the high temperature measurements, we used the ether
Santovac® 5 as a couplant and heated the specimens in the standard atmosphere using a muffle furnace
Heraeus thermicon® P.

Figure 1 – Experimental setup
The temperature dependent length L T of each sample at each measurement temperature T is
estimated relative to the measured length of each sample at 20 °C, L20 by using the thermal expansion
coefficients, CTE listed in Table 2:(1)‫ ் ܮ‬ൌ ‫ܮ‬ଶ଴ ή ‫ ܧܶܥ‬ή ሺܶ െ ʹͲι‫ܥ‬ሻ

FeNi46

W80Cu

W90NiFe

Bismuth titanate

Langasite

Aluminium nitride

Bismuth titanate

Gallium phosphate

Gallium phosphate

Lithium niobate

Langasite

Langasite

Hastelloy B-3

6.0

Hastelloy C-276

Ohara S-PHM52

8.0

Haynes 230

Alumina

9.9 15.8 13.2 13.1 11.6 7.5

Haynes HR-120

Mullite

7.2

Piezo partner

CTE20-400, 5.0
Aluminum nitride

Wedge material

Table 2 – Coefficients of thermal expansion of investigated wedge materials (10 -6 K-1) [3; 4; 7-10]
and their possible piezo partners with matching CTEs [11-15]

Based on Eq. 1, the speed C of longitudinal wave propagation was calculated by:4756‫ ܥ‬ൌʹ‫் ܮ‬ʹ‫ܮ‬ଶ଴ ή ‫ ܧܶܥ‬ή ሺܶ െ ʹͲι‫ܥ‬ሻൌ‫ݐ‬‫ݐ‬(2)

Table 2 bottom shows possible high temperature resistant piezo -materials, which fit the CTE of
the respective wedge material in Table 2 top for a temperature range between 20 °C to 400 °C. As
explained in the introduction, matching CTEs of piezo and wedge material are the key for a durable
extreme temperature transducer operation.

3. EXPERIMENTAL RESULTS AND DISCUSSION
A representative example of an ultrasonic measurement of time of flight is shown on fig. 2.

Figure 2 – Example of a measurement on S-PHM52 at 24 °C (top) and 285 °C
It becomes obvious that the higher temperature of the propagation medium increases the time offlight of an ultrasonic signal not only because of a thermal expansion of a specimen but also due to adecrease of its propagation speed caused especially by a reduction of the elasticity modulus:‫ ܥ‬ൌ ඨ‫ܧ‬ሺͳ െ ‫ݒ‬ሻߩሺͳ ൅ ‫ݒ‬ሻሺͳ െ ʹ‫ݒ‬ሻ(3)where C is a speed of longitudinal wave propagation in a solid medium; E – modulus of elasticity;
ρ – density and v – Poisson’s ratio of a propagation medium. Since the elasticity modulus of mostmaterials decreases with increasing temperature much stronger than their density, the speed of soundis expected to decrease as well.
Besides the backwall echo being used to measure the time of flight, multiple following echoes –so called trailing echoes – appear on the ultrasonic images (Fig. 2) due to wave transformation on theside wall of a specimen [16].
As mentioned in Section 2.2, the acoustical coupling at high temperatures was carried out using apolyphenyl ether Santovac® 5, which already starts to evaporate at 250 -300 °C. Therefore, themagnitude of the received signal strongly decreases at higher temperatures and, as a result, thedetection of a backwall echo requires a higher gain. That leads to an increase in the relative magnitudeof acoustical noises and disturbances (Fig. 2, on the bottom).

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Figure 3 – Experimental results of the temperature dependence of longitudinal wave propagation
in investigated materials
The diagrams in Fig. 3 show the results of an investigation of a speed of the longitudinal wave
propagation in the chosen materials within the temperature range from -200 °C to 600 °C. The curves
on the left diagram represent the temperature dependence of the speed of sound in Ni/Fe/Cr-based
alloys with a quite characteristic temperature behavior of such metals – starting at 5700-5800 m/s atroom temperature, the curves have a slope of ca. 0.5 m/s·K.
The ceramic materials (Fig. 3 on the right) have much higher values of speed of sound (up to 7330m/s for alumina and 10620 m/s for mullite) because of their high elasticity moduli (E alumina = 403 GPa,E mullite = 227.5 GPa at 20 °C [17]) in conjunction with low densities (ρ alumina = 3.99 g/cm 3, ρmullite =3.16 g/cm3 [17]). Additionally, alumina has the lowest decrease rate among all the investigatedmaterials: the measured speed of sound has a slope of only approx. 0.2 m/s·K.
The very high density of W80Cu (15.2 g/cm 3 [5]) results in very low speeds of sound (Fig. 3 onthe right) between 4810 m/s and 4660 m/s. However, the speed of sound in another tungsten-based
alloy W90NiFe, despite of its even higher density (17 g/cm 3 [4]), is significantly higher because ofits much higher modulus of elasticity (340 GPa [4] compared to 235 GPa for W80Cu [5]).
As can be seen in Fig. 3, the glass material S-PHM52 could not be investigated at -196 °C: theimmersion process into liquid nitrogen caused temperature gradients, which inevitably lead to a
cracking of the glass due to its low resistance to thermal shock resulting from its fragility in
combination with a relatively high CTE (see Table 2). Fig. 3 presents a cracked glass specimen after
a failed low-temperature measurement. The high sensibility of this glass material speaks against its
application as a wedge material in a high-temperature-resistant ultrasonic transducer.

Figure 4 – A specimen of the glass S-PHM52 after a failure during cooling in liquid nitrogen (left)
and its comparison to an intact specimen (right)

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While the most materials investigated in this work have a nearly linear relation between speed ofsound and temperature, the FeNi46 alloy shows in the range from 300 °C a significant slowing of adecrease rate above 300 °C (Fig. 3 on the right and Fig. 5). This phenomenon can be explained by themagnetostriction of iron-nickel alloys [18] resulting in an accelerating decrease of the density ofFeNi46 from ca. 300 °C and thus the decelerating decrease of the speed of sound (Eq. 3).

Figure 5 – Temperature dependences of the speed of sound (black squares, left vertical axis) andthe density (empty squares, right vertical axis) of FeNi46 [9].

4. CONCLUSIONSIn the current study, we have investigated the speed of longitudinal wave propagation in severalsolids which can be used as wedge materials in a high-temperature-resistant ultrasonic transducer intemperature interval from -200 °C to 400 °C. The research has shown that the most of investigatedmaterials, except the temperature-sensible glass S-PHM52, are suitable for application as a wedge
material at extreme temperatures. The speed of sound in most investigated materials decreases evenlywith increasing temperature, while the decrease rate varies from 0,2 to 1 m/s·K depending on material.
However, we have noted and explained the pronounced non-linearity of a dependence of speed ofsound on temperature in the magnetostrictive FeNi46. Additionally, we have found that the major
effect on thermal change of the speed of wave propagation is provided by a change of elastic properties,
whereas the influence of a density change on the speed of sound is only rarely significant.

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