Determination of the sonic properties of a Nigerian quartz for ultrasonic transducer

Abstract

BACKGROUND:

There is abundant quartz deposit in Nigeria which has been used for export and building purposes. However, its electrical and piezoelectric properties have not been studied. Thus, whether it can be used as raw material for the indigenous electric industries is unknown to date.

OBJECTIVE:

This study aims to characterize the piezoelectric properties of smoky quartz for ultrasonic transducer and determine its sonic properties.

METHOD:

In the research approach, the raw quartz was cut into six crystals of rectangular shape using a universal cutter. The crystals were purified with a 100 ml hydrofluoric and hydrochloric acid solution under a temperature of 250°C in a furnace. The sizes, weights, and capacitance of crystals were determined using the standard measuring instruments. The resonance method was used for the determination of the frequency of minimum and maximum impedance of the crystals. The piezoelectric constants of the crystals were derived using the standard formula for determination of piezoelectric constants.

RESULTS:

The results show that the sonic properties represented by the piezoelectric charge constant (d₃₁) and the piezoelectric voltage constant (g31) values are 2.52 (±1.075) ×10^-8c/m² and 1030.6114 ± 250.89v/m² respectively.

CONCLUSION:

The present study has characterized Nigerian quartz for its piezoelectric properties and found that it was suitable for use in the construction of ultrasonic transducers.

Keywords

Nigerian quartz piezoelectricity transducer sonic properties characterization

1 Introduction

The ability to visualize internal structures of the human body without any invasive procedure has revolutionized medical practice over the last century. Ultrasound is one of the many available imaging modalities enabling a substantial and unique imaging of the human internal organs. Its use in obstetrics, for the determination of fetal viability, dating and anomalies are its expanding role in medical applications and diagnosis.

Further advances have enabled assessment of blood flow (Doppler), where vascular studies hitherto achieved by angiography has been simplified and made non-invasive. Ultrasound is viewed in real time allowing assessment of body function such as heart movement, muscle, and tendon movement. More recently three dimensions (3D) and four-dimension (4D) ultrasound modes have been developed, providing even more lifelike representation [1 –3].

Ultrasound also plays a key role in interventional procedures. Its real-time capacity allows the direct visualization of needle tip placement in the body which is the first step in many interventional procedures such as biopsies, drainages and stent replacement [4]. The ultrasound machine can accomplish all of the above because of a physical phenomenon possessed by some materials termed piezoelectricity. The piezoelectric material is an essential component of any medical ultrasound unit, as it serves as the transducer to generating the high-frequency ultrasound used to probe the human body and also convert returning echoes to electrical signals for imaging [5].

The piezoelectric effect is an electromechanical interaction between mechanical and electrical states in some crystalline materials without inversion of symmetry. This is a reversible process in that materials exhibiting the direct piezoelectric effect also exhibit the reverse effect. When pressure is applied to the crystal they produce electric charge and when placed in an electric field the materials deform [6]. On the surfaces of the piezoelectric element, electrodes are affixed and a voltage applied. The element then oscillates repeatedly expanding and contracting, generating a sound wave. When the element is externally excited with vibration or ultrasonic wave, in turn, it generates a voltage [7].

The materials that exhibit this effect include naturally occurring crystals and laboratory made ones. The natural occurring crystals include Berlinite (AIPO₄) sucrose (table sugar), quartz (SiO₂) and Rochelle Salt. The laboratory elements include lead titanate (PbTiO₃), lead zirconate titanate (PZT), Potassium Niobate (KNbO₃) and lithium Niobate (LiN₆O₃) [8].

Quartz is one of the most common minerals in the Earth’s crust discovered by the Curie brothers in 1880 [9] to possess piezoelectric property. The first practical application of piezoelectric device using quartz was in sound navigation and ranging (SONAR) which was developed during the First World War in France, by Paul Langevin and co-workers in 1917. This was a transducer made from thin quartz crystal that was glued between two steel plates, and a hydrophone to detect the returned echo. By emitting a high-frequency chirp from the transducer and measuring the amount of time it takes to hear an echo from the sound waves bouncing off an object, one can calculate the distance to that object. Brazillian quartz was adjudged the best amongst the variety quartz found in Europe because it is pure, free from inclusions or mechanical defects such as veil or bubbles [10]. It became the choice raw material for many piezoelectric devices, such as in ceramic phonographs, transducers, cartridges of a simplified player design was cheap, accurate in performance and easy to maintain. Most ultrasonic transducers were made of quartz crystals mainly from Brazil.

Nigeria has an abundant deposit of quartz, its use has been limited to building construction and export purposes [11]. There is a paucity of study on the Nigerian quartz and moreover, it has not been characterized by its piezoelectric properties. The purpose of the present study is to determine the sonic properties of Nigerian Quartz for its application in the ultrasonic transducer. The sonic property of a piezoelectric element comprises the piezoelectric charge constant (d₃₁) and piezoelectric voltage constant (g₃₁). In the present study, the piezoelectric charge and voltage constant of Nigerian Quartz were determined and the values were compared with values from literature to assess its suitability for the ultrasonic transducer.

2 Materials and method

The experiment in this study involves the measurement of some relevant and important parameters of a locally sourced quartz variety for piezoelectric transducer application. The parameters obtained were compared with those obtained from the literature. The smoky quartz variety was chosen for the study amongst the others due to its abundance and availability. The material was supplied to the researchers by Sinai Globe limited Ibadan a solid mineral prospecting company. The raw quartz was obtained from their quartz mines in Ijero, Ekiti State, South West Nigeria. The study was done at Scientific Equipment Development Institute Akwuke Enugu, South East Nigeria.

2.1 Specimen preparation

The preparation for the study was carried out in stages. These are

Cutting out the quartz crystals from the rock samples.

Polishing of the quartz

Purification of the quartz crystals

Washing and drying of quartz crystals.

Electrode the crystals.

2.2 Cutting the quartz

The quartz crystals were cut using the universal cutter. Using the cutter six quartz crystals were cut from rock samples. The crystals were cut into requisite sizes required for the measurement of piezoelectric constants [12]. In the present study, six rectangular crystals cut out from different quartz rock samples were used for the study. The sizes of the crystals are shown in Table 1.

Table 1
Dimensions of quartz crystals used in the study

Samples Length (cm) Width (cm) Thickness (cm) Weight (g)

A 3.2 1.2 0.7 6.38

B 1.9 1.6 0.6 4.30

C 1.8 1.7 0.6 3.99

D 3.0 1.0 0.6 4.18

E 2.4 1.5 0.4 3.05

F 1.4 1.0 0.7 2.40

Samples	Length (cm)	Width (cm)	Thickness (cm)	Weight (g)
A	3.2	1.2	0.7	6.38
B	1.9	1.6	0.6	4.30
C	1.8	1.7	0.6	3.99
D	3.0	1.0	0.6	4.18
E	2.4	1.5	0.4	3.05
F	1.4	1.0	0.7	2.40

2.3 Polishing the crystals

The crystals were smothered by using sand slabs. The edges and surfaces of the crystals were polished ensuring that the rough edges were removed. The polishing and smoothening were done with simultaneous measurement of the crystals dimensions using the micrometer screw gauge.

2.4 Purification

The quartz crystals were purified using a mixture of Hydrofluoric and Hydrochloric acid solution. The solution with the crystals was hermetically sealed in a hard porcelain pot and deposited in the heating chamber of the furnace. The temperature of the furnace was raised to 250°C with a holding time of 60 minutes. Within this time frame the combined chemical reaction of acid in solution aided by the heat will leach out the impurities in the interstitial boundaries of the quartz crystals. The purification ensures that the quartz is pure for optimum utilization and results. At the end of the purification time, the furnace was turned off and crystals were left to cool.

2.5 Washing and drying

After the purification process, the crystals were immersed in distilled water for 24 hours to allow the chemicals used in the purification to be washed off. The washed crystals were then dried under normal room temperature in a dry and moisture free environment for 72 hours.

2.6 Electrode the crystals

After the preparation of the crystals, the next stage was the crystals being electrode. This was done using the vacuum silver electrode deposition machine. Both surfaces of each crystal were silver electrode. The crystals are shown in Fig. 1.

Fig.1

The Crystals after Purification and electroding.

2.7 Measurement of the vital parameters

The quartz crystal parameters to be measured include the (i) sizes (ii) weights (iii) Capacitance (iv) The Frequency of minimum impedance (v) Frequency of maximum impedance (vi) Magnitude of minimum impedance.

2.8 Size of crystals

The sizes of the quartz crystals were measured using a micrometer screw gauge. The sizes of the crystals are shown in Table 1.

2.9 Weighing

The crystals were weighed in both pre and post-purification processes. This was done using electronic weighing balance, the D – band model. The weights are shown in Table 2.

Table 2
Weights of the quartz samples before and after purification

Samples Weight before purification (g) Weight after purification (g) Weight difference (g) Percentage of of impurity (%)

A 6.38 5.70 0.68 10.649

B 4.30 4.21 0.09 2.093

C 3.99 3.89 0.10 2.506

D 4.18 4.09 0.09 2.153

E 3.05 3.03 0.02 0.656

F 2.40 2.31 0.09 3.750

Samples	Weight before purification (g)	Weight after purification (g)	Weight difference (g)	Percentage of of impurity (%)
A	6.38	5.70	0.68	10.649
B	4.30	4.21	0.09	2.093
C	3.99	3.89	0.10	2.506
D	4.18	4.09	0.09	2.153
E	3.05	3.03	0.02	0.656
F	2.40	2.31	0.09	3.750

2.10 Capacitance

The capacitances of the crystals were determined using the capacitance (and dissipation) bridges circuit. The values obtained are 2 pF for specimen A and 1 pF each for Specimens B to F. (pF is pico-Farad).

2.11 Determination of frequency of minimum impedance

The experimental set up for the determination of the frequency of minimum impedance, maximum impedance, and magnitude of minimum impedance are shown in Fig. 2a and b. The equipment used for the determination of the frequency of minimum and maximum impedance include the oscilloscope, AC millivoltmeter Oscillator, Decade Resistance boxes, and Double Pole Double Turn Switch (DPDT) box. The connections are as shown in the Fig. 2a and b above. The oscillator, frequency counter are serially connected with the quartz crystal using a coaxial cable which is fed into the input of AC Millivoltmeter. When the circuit is activated, the deflection of AC Millivoltmeter is noted and the frequency read off at the frequency counter. The measurements were made three times for each crystal and the mean value recorded.

Fig.2

(a) Experimental setup for determining the frequency of Minimum and Maximum Impedance. (b) Circuit for Frequency for Minimum and Maximum Impedance.

The values of frequency of minimum impedance and maximum impedance are shown in Table 4. The magnitude of minimum impedance was determined by connecting in series a variable resistor using the DPDT switch box to isolate the test specimen in the circuit and varying the resistor to obtain the same meter reading of the crystals in the AC millivoltmeter for the frequency of minimum impedance. The values for the magnitude of frequency of minimum impedance are shown in Table 5.

Table 3

Frequency of minimum and maximum impedance of quartz crystals, and dimensions

Samples	Dimensions in meters			Frequency of minimum impedance MHz (fm)	Frequency of maximum impedance MHz (fn)
	L	B	Thickness
A	0.032	0.012	0.007	7.625	3.83
B	0.019	0.016	0.007	7.66	4.92
C	0.018	0.017	0.006	7.545	5.9
D	0.03	0.01	0.006	7.645	5.915
E	0.024	0.015	0.004	7.515	6.495
F	0.014	0.01	0.007	7.66	6.05
Total				45.65	32.71
Mean				7.6083	5.4516

Table 4

Magnitude of frequency of minimum impedance

Test Specimen	Frequency of minimum impedance (MHz)	Magnitude of Frequency of Minimum Impedance Zm (Ω)
A	7.625	33
B	7.660	33
C	7.540	33
D	7.645	33
E	7.610	33
F	7.660	33

Table 5

Distribution of piezoelectric d₃₁ and g₃₁ constants

Sample	Piezoelectric d₃₁ (c/m²)	g₃₁ (v/m²)
A	2.4×10^–8	659
B	2.58×10^–8	1309.072
C	2.57×10^–8	1304.385
D	1.59×10^–8	797.06
E	1.31×10^–8	1182.27345
F	4.66×10^–8	932.0012
Total	15.12×10^–8	6183.66848
Mean	(2.52 ± 1.075) ×10^-8	1030.6114 ± 250.89

Using the measured values of the above parameters, the piezoelectric charge constant (d₃₁) and piezoelectric voltage constant (g₃₁) were determined using the standard equation for their determination. The equations and its derivatives are shown in the appendix. The values of d₃₁ and g₃₁ are shown in Tables 6 and 7 respectively.

3 Results

Table 1 shows the crystals dimensions. Specimen A has the longest length measures 3.2 cm followed by Specimen D, E, and B. The length of the crystal is a determinant variable in computing the coupling coefficient. Specimen C has the largest width dimension of 1.7 cm and Specimen D is the least with a value of 1.0 cm. The width of the crystal is a factor in determining the area and volume of the crystal. These parameters are used in computing the density and elastic constants of the crystal. Specimen A and F have a thickness value of 0.7 cm while Specimen E is the least in thickness with a value of 0.4 cm. This parameter is used in determining the capacitance and the dielectric constant of the crystal.

Table 2 shows the weight of the crystals pre and post-purification. Specimen A is the heaviest with a weight of 5.7 g and 10.65% level of impurities followed by specimen B which weighs 4.21 g and impurity of 2.09%. Specimen F is the least in weight with a value of 2.31 g and impurity of 3.75% Specimen E has the least impurity level of 0.656%. The purification ensures that the alkaline impurities which will impede the free flow of electrons are leached out. Impurities in quartz make it impossible for the preparation of quartz for electronic application and timing control [13]. The weight of the crystals and its volume will determine the density of the material.

The values of frequency of minimum and maximum impedance are shown in Table 3. Specimen B and F has the highest value of 7.66 MHz a piece, as the frequency of minimum impedance, while specimen E has the least value of 7.515 MHz. For the frequency of maximum impedance, the result shows that specimen A has the least value of 3.83 MHz while specimen E has the highest value of 6.495 MHz. The bandwidth of specimen A is wider than specimen E. The mean value of the frequency of minimum impedance is 7.608 MHz while the mean value of the frequency of maximum impedance is 5.452 MHz with a mean bandwidth of 2.156 MHz. The bandwidth determines the type of transducer application the crystal will be most suitable for. The frequency of minimum impedance represents the impedance value at which the crystal vibrates freely, while the frequency of maximum impedance represents the impedance value at which the crystal will not vibrate at all.

The piezoelectric charge constant values in Table 4 show that specimen F has the highest value of 4.66 × 10^-8C/M² while sample E has the least value of 1.31 × 10^-8C/M². The mean value of piezoelectric constant (d₃₁) is (2.52 + 1.075) ×10^-8C/M². The piezoelectric charge constant determines the magnitude of deformation when the crystal is placed in an electric field. This determines the generated piezoelectric pulse wave [14]. Specimen F will have better acoustic performance than the other crystals. Table 4 also shows the distribution of piezoelectric voltage constant (g₃₁). Sample B has the highest value of 1309.072 V/m² while Sample A is the least with a value of 659 V/m². The mean g₃₁ constant is 1030.6114±250.89 V/m². Specimen B will have better charge formation on pressure than the other crystals.

3.1 Calculating the piezoelectric constants

Using the governing equations, the values of piezoelectric charge and voltage constants were determined. Piezoelectric equations in strain-charge form¹⁹

S=S^ET+dE

D=ɛ^TE + dT

S = Mechanical Strain (N/m²)

T = Mechanical Stress (N/m²)

S^E = Elastic Compliance (Pa^–1)

d = Piezoelectric Coefficient C/N

D = Electric displacement C/m²

E = Electric field V/m

ɛ^T= Dielectric permittivity (F/m)

The equation and derivatives are shown below;

$\begin{matrix} d_{31} & = & K_{31} \sqrt{8.85 \times 10^{- 12} K_{3}^{T} \times S_{11}^{E}} coulomb / {meter}^{2} \\ g_{31} & = & \frac{d_{3}}{8.85 \times 10^{- 12} \times K_{3}^{T}} volts / meter \end{matrix}$

The values of d₃₁ and g₃₁ are shown in Tables 5 and 6.

4 Discussion

The sonic properties of the piezoelectric material represented by the piezoelectric charge constant (d₃₁) and piezoelectric voltage constant (g₃₁) are vital in ultrasonic image formation. These constants determine the frequency of the sound beam emitted by the transducer and the quality of ultrasound frequency produced⁹.

In the present study, the piezoelectric charge constant of quartz is 2.52 ± (1.075) ×10^-8C/m². This value is in agreement with the result obtained by Curie brothers [9], Dawson [15], Bottom [16]. The piezoelectric charge constant determines the frequency of the ultrasound generated when the crystal is activated and the mechanical displacement of the piezoelectric element. Higher values of the charge constant ensure a higher mechanical displacement or deformation of the crystal when in an electric field. The present value of d₃₁ is slightly higher than the values of Brazilian quartz obtained by Bottom. The value obtained by Bottom in their studies is 2.27 (±0.07) ×10^-12C/m², this value is slightly lower than the values in the present study. When this value is compared with PZT, the present value is quite low. PZT value for d₃₃ by Piezoceramic is -122 × 10^-12C/m². The difference is due to the fact that PZT is a synthetic material in which the properties are determined during manufacture while quartz is a natural piezoelectric material with its properties inherent to it.

The piezoelectric voltage constant (g₃₁) determines the quality and strength of the echoes from the subject to the transducer for ultrasound image formation. It is the returning echoes from the body that acts as pressure to the piezoelectric elements which in turn generates the voltage which is converted into images in the cathode ray tube of the ultrasound machine. The values of piezoelectric voltage constant (g₃₁) in the present study are 1030.61 ± 250.89 V/m². This value is not in agreement with the values obtained by Mohammadi [17], Piezoceramic [18] (2012) and Boston [19] (2013). The difference may be due to the inherent properties of the crystal controlled by the elastic constant, coupling coefficient and dielectric constant of the piezoelectric material. The present value of 1030.61 V/M² infers that the crystal will be sensitive to returning echoes from the body thus leading to higher charge generation from the crystals and quick or faster image formation.

The value of g₃₁ from this study is appreciably higher in value than the value of PZT by Mohammadi [17] and Piezoceramic [18] (2012). These values are 28.0 × 10^-3v/m² and -10.6 × 10^-12V/m² respectively. This implies that the present material will act as better receptors than PZT when used as an ultrasonic transducer.

5 Conclusion

The sonic properties of Nigerian Quartz comprising the piezoelectric charge constant (d₃₁) and piezoelectric voltage (g₃₁) with values of (2.52 ± 1.075) ×10^-8C/m² and (1030.61 ± 250.89) V/m² will satisfy the requirement for its application as a transducer for a medical ultrasonic transducer.

Footnotes

Acknowledgments

I want to thank Professor C. I. Nwajiagu the former Executive Director of Scientific Equipment Development Institute (SEDI) who gave approval for the study to be carried out in the institute and Professor Ndubuisi Samuel the present executive director who encouraged and supported the study to the end. This study would have fizzled out but for the expertise of Engr. Duke Kani the Head of Department Electrical R&D SEDI whose wealth of experience played a key role in the success of this study. He structured the team of scientists led by Gregory Agu, Emmanuel Enwereuzo, Obika Mike, Umoh Effiong, and Emmanuel Ufomba, who played key roles at various stages of the study.

The support of my colleagues cannot be overlooked; they are Dr. A. O Okaro, Dr. C. U. Eze, Dr. Ochie Kalu and Dr. Mrs. F. U. Idigo.

Notably, I appreciate profoundly, the wholistic support of my beautiful wife, Mrs. Gift Onyinyechi Nwadike who saw me through these years of study.

Finally, I thank our great God who led me all the way. Praise God and may His name be exalted forever Amen.

References

DiPietro

J.A.

, Costigan

K.A.

and Voegtline

K.M.

, Studies in fetal behaviour; revisited, renewed and reimagined; Monographs of the Society for Research in Child Development 80 (2015), 1–94.

Kuo

C.C.

, Chuang

H.C.

, Teng

K.T.

et al., An autotuning respiration compensation system based on ultrasound image tracking,, Journal of X-ray Science and Technology 24 (2016), 875–892.

, Xin

, Yang

et al., Breast osteoblastoma and recurrence after resection: Demonstration by color Doppler ultrasound, Journal of X-ray Science and Technology 25 (2017), 787–791.

Otto

R.C.

and Wellauer

, Localising the Biopsy needles in the sonographic image, Ultrasound-Guided Biopsy and Drainage (1985). DOI: 10.1007/978-3-C-2-70989-0

Kremkau

F.W.

and Forsberg

, Transducers Sonography Principles, and Instruments, Chapter 3; pp. 42–201.

Gautschi

, Piezoelectric Sensorics: Force, Strain Pressure Acceleration and Acoustic Emission, Materials and Amplifiers. Springer Publishers, Berlin, Heidelberg, New York, 2002, pp. 3.

Nihon Dempa Kogyo Corporation Limited, Basic Principle of Medical Ultrasonic Probes (Transducer). [Online] Available at: www.ndk.com/en/censor/ultrasonic/basic02.html [Accessed 15 April 2017].

Hepher

M.J.

, Natural and Synthetic piezoelectric material for chemical sensors. Dielectric Material Measurement and Applications, Sixth International Conference, 1992.

Curie

and Curie

, Sur I”electricite polaire dans cristaux hemiedres a face inclinees, Compt Rend Seances Acad Sci 91 (1880), 383–389. French.

10.

Gortze

and Mockel

, (Eds) Quartz: Deposits, Mineralogy and Analytics XVI 360. Hard Cover (2012), ISBN 978-3-642-22160-6.

11.

Bellis

, The History of SONAR, ThoughtCo Lifelong Learning Contact@thoughtco.com. 2017.

12.

Fayemi

, Neglect of solid minerals: Why Nigeria remains poor. Vanguard News, 2015.

13.

Loritsch

B.K.

and James

D.R.

, Inventors, Feldspar, Corporation, Assignee. Purified Quartz and Process for Purifying Quartz, US 4983370, 1990.

14.

Ceramics

, Measuring Properties of Piezoelectric Ceramics. [Online] Available at: <www.sparklerceramics.com> [Accessed 20 March 2012].

15.

Dawson

L.H.

, Piezoelectricity of crystal quartz,, Physics Review 29 (1927), 532–554.

16.

Bottom

V.E.

, Measurement of piezoelectric coefficient of quartz using fabry-perot dilatometer,, Journal of Applied Physics 41 (2003), 3941.

17.

Mohammadi

M.M.

, A comparison between quartz and PZT ceramic for sensoric applications, Research Desk 2 (2013), 321–325.

18.

American Piezo Ceramics (APC) International Limited, Physical and Piezoelectric Properties of APC Materials. [Online] Available at: <www.apc_materials_properties.pdf> [Accessed 12 May 2013].

19.

Boston Piezo-Optics Incorporation, Ceramic Materials (PZT) [Online] Available at: www.bostonpiezooptics.com/ceramic-materials-pzt [Accessed 12 September 2015].