Investigation of the spatial distribution of deformations in quartz piezo elements by x-ray topography

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Abstract

Using X-ray topography on laboratory and synchrotron X-ray sources, the distribution of deformations in the volume of two types of AT-cut quartz resonators of different sizes were obtained. From a comparison of X-ray data and the amplitude-frequency characteristics of the resonators, a correlation between the deformation patterns and the features of oscillatory processes for operating modes and their harmonics, as well as for parasitic modes, was established. A connection between oscillations in parasitic modes, which manifest themselves in the amplitude inhomogeneity, and the topology of the resonators is found. The applied significance of the obtained results for the development and optimization of new designs of piezoelectric elements and the development of their manufacturing technology is noted.

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About the authors

E. S. Ibragimov

Shubnikov Institute of Crystallography FSRC "Crystallography and photonics" RAS; NRC "Kurchatov Institute"

Email: ontonic@gmail.com
Russian Federation, 119333 Moscow, Leninskiy pr-kt 59; 123182 Moscow, Academician Kurchatov Sq. 1

F. S. Pilyak

Shubnikov Institute of Crystallography FSRC "Crystallography and photonics" RAS; NRC "Kurchatov Institute"

Email: ontonic@gmail.com
Russian Federation, 119333 Moscow, Leninskiy pr-kt 59; 123182 Moscow, Academician Kurchatov Sq. 1

A. G. Kulikov

Shubnikov Institute of Crystallography FSRC "Crystallography and photonics" RAS; NRC "Kurchatov Institute"

Author for correspondence.
Email: ontonic@gmail.com
Russian Federation, 119333 Moscow, Leninskiy pr-kt 59; 123182 Moscow, Academician Kurchatov Sq. 1

N. V. Marchenkov

Shubnikov Institute of Crystallography FSRC "Crystallography and photonics" RAS; NRC "Kurchatov Institute"

Email: ontonic@gmail.com
Russian Federation, 119333 Moscow, Leninskiy pr-kt 59; 123182 Moscow, Academician Kurchatov Sq. 1

Y. V. Pisarevsky

Shubnikov Institute of Crystallography FSRC "Crystallography and photonics" RAS; NRC "Kurchatov Institute"

Email: ontonic@gmail.com
Russian Federation, 119333 Moscow, Leninskiy pr-kt 59; 123182 Moscow, Academician Kurchatov Sq. 1

A. A. Kaloyan

NRC "Kurchatov Institute"

Email: ontonic@gmail.com
Russian Federation, 123182 Moscow, Academician Kurchatov Pl. 1

Y. A. Pershin

JSC "Lit-Fonon"

Email: ontonic@gmail.com
Russian Federation, 107076 Moscow, Krasnobogatyrskaya str. 44, bld. 1

Y. A. Glazunova

JSC "Lit-Fonon"

Email: ontonic@gmail.com
Russian Federation, 107076 Moscow, Krasnobogatyrskaya str. 44, bld. 1

S. A. Demin

JSC "Lit-Fonon"

Email: ontonic@gmail.com
Russian Federation, 107076 Moscow, Krasnobogatyrskaya str. 44, bld. 1

A. S. Yuzhalkin

JSC "Lit-Fonon"

Email: ontonic@gmail.com
Russian Federation, 107076 Moscow, Krasnobogatyrskaya str. 44, bld. 1

S. S. Pashkov

JSC "Lit-Fonon"

Email: ontonic@gmail.com
Russian Federation, 107076 Moscow, Krasnobogatyrskaya str. 44, bld. 1

G. N. Cherpukhina

JSC "Lit-Fonon"

Email: ontonic@gmail.com
Russian Federation, 107076 Moscow, Krasnobogatyrskaya str. 44, bld. 1

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Supplementary files

Supplementary Files
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2. Fig. 1. General appearance and overall dimensions of resonators (a) — РК563 (type 1) in a surface-mount housing and (b) — РК319 (type 2) in a quarter-wave resonator housing.

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3. Fig. 2. Measurement implementation schemes. (a) — White beam topography in a single-crystal diffraction scheme implemented at the Mediana synchrotron station of KISI-Kurchatov. 1 — bending magnet, 2 — white beam input mask, 3 — aluminum filter for absorption of the long-wavelength part of the spectrum, 4 — goniometric system, 5 — sample with holder, 6 — two-dimensional detector, 7 — electrical signal generator/analyzer. (b) — Monochromatic beam topography in a two-crystal diffraction scheme implemented on the TRS-K laboratory three-crystal X-ray spectrometer: 1 — X-ray tube, 2 — preliminary collimation slit, 3 — asymmetric single-crystal monochromator, 4 — goniometric system, 5 — sample with holder, 6 — two-dimensional detector, 7 — electrical signal generator/analyzer.

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4. Fig. 3. (a) — Schematic representation of the crystallographic orientation of the AT-cut quartz; (b) and (c) — initial topograms of the RK563 and RK319 resonators, respectively, obtained under normal conditions (without external influence).

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5. Fig. 4. (a) — Topogram and (b), (c) — graphs of the distribution in two directions of the amplitude of deformations of the piezoelectric element at the resonant frequency of 9.99217 MHz, corresponding to the 1st harmonic.

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6. Fig. 5. (a) — Topogram and (b), (c) — graphs of the distribution in two directions of the amplitude of deformations of the piezoelectric element of the 1st type resonator at a resonant frequency of 31.73469 MHz, corresponding to the 3rd harmonic.

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7. Fig. 6. (a) — Topogram and (b), (c) — graphs of the distribution in two directions of the amplitude of deformations of the piezoelectric element at the resonant frequency of 10.43383 MHz, corresponding to anharmonic oscillation.

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8. Fig. 7. (a) — Topogram and (b), (c) — graphs of the distribution in two directions of the amplitude of deformations of the piezoelectric element at the resonant frequency of 13.99129 MHz, corresponding to the 1st harmonic.

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9. Fig. 8. Amplitude-frequency characteristic of the resonator of the 2nd type.

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10. Fig. 9. (a) — Topogram and (b), (c) — graphs of distribution in two directions of deformations of the piezoelectric element at a resonant frequency of 12.91492 MHz.

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11. Fig. 10. (a) — Topogram and (b), (c) — graphs of distribution in two directions of deformations of the piezoelectric element at a resonant frequency of 13.42367 MHz, corresponding to anharmonic oscillation.

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