**Concomitant** *TP53* **Mutation Confers Worse Prognosis in** *EGFR***-Mutated Non-Small Cell Lung Cancer Patients Treated with TKIs**

**Matteo Canale 1, Elisabetta Petracci 2, Angelo Delmonte 3, Giuseppe Bronte 3, Elisa Chiadini 1, Vienna Ludovini 4, Alessandra Dubini 5, Maximilian Papi 6, Sara Baglivo 4, Nicoletta De Luigi 7, Alberto Verlicchi 3, Rita Chiari 8, Lorenza Landi 9, Giulio Metro 4, Marco Angelo Burgio 3, Lucio Crinò 3 and Paola Ulivi 1,\***

Received: 2 March 2020; Accepted: 3 April 2020; Published: 7 April 2020

**Abstract:** Background: Non-small cell lung cancer (NSCLC) is the primary cause of cancer-related deaths worldwide. Epidermal Growth Factor Receptor (*EGFR*)-mutated patients usually benefit from TKIs treatment, but a significant portion show unresponsiveness due to primary resistance mechanisms. We investigated the role of *TP53* mutations in predicting survival and response to *EGFR*-TKIs in EGFR-mutated NSCLC patients, to confirm, on an independent case series, our previous results. Methods: An independent retrospective cohort study was conducted, on a case series of 136 *EGFR*-mutated NSCLC patients receiving first or second generation TKIs as a first line therapy, and a smaller fraction of patients who acquired the T790M resistance mutation and were treated with third generation TKIs in the second or further line of treatment. *TP53* mutations were evaluated in relation to disease control rate (DCR), objective response rate (ORR), progression-free survival (PFS) and overall survival (OS) of the patients. Results: Forty-two patients (30.9%) showed a *TP53* mutation. Considered together, *TP53* mutations had no significant impact on time-to-event endpoints. Considering the different *TP53* mutations separately, exon 8 mutations confirmed their negative effect on PFS (HR 3.16, 95% 1.59–6.28, *p* = 0.001). In patients who developed the T790M resistance mutation, treated with third generation TKIs, the *TP53* exon 8 mutations predicted worse PFS (even though not statistically significant), and OS (HR 4.86, 95% CI: 1.25–18.90, *p* = 0.023). Conclusions: *TP53* exon 8 mutations confirmed their negative prognostic impact in patients treated with first and second generation TKIs and demonstrated a role in affecting clinical outcome in patients treated with third generation TKIs.

**Keywords:** non-small-cell lung cancer; epidermal growth factor receptor; tyrosine kinase inhibitors; *TP53* mutations; responsiveness; prognosis


**Determination of Chemical State and External Magnetic Field Effect on the Energy Shifts and X-Ray Intensity Ratios of Yttrium and Its Compounds**

Sevil Porikli1 and Yakup Kurucu2

*Erzincan University, Faculty of Art and Sciences, Department of Physics Atatürk University, Faculty of Sciences, Department of Physics Turkey*

#### **1. Introduction**

88 Radioisotopes – Applications in Physical Sciences

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The term 'X-ray fluorescence analysis' (XRF) refers to the measurement of characteristic fluorescent emission resulting from the deexcitation of inner shell vacancies produced in the sample by means of a suitable source of radiation. For a particular energy (wavelength) of fluorescent light emitted by a sample, the number of photons per unit time (generally referred to as peak intensity or count rate) is related to the amount of that analyte in the sample. The counting rates for all detectable elements within a sample are usually calculated by counting, for a set amount of time, the number of photons that are detected for the various analytes' characteristic X-ray energy lines. It is important to note that these fluorescent lines are actually observed as peaks with a semi-Gaussian distribution because of the imperfect resolution of modern detector technology. Therefore, by determining the energy of the X-ray peaks in a sample's spectrum, and by calculating the count rate of the various elemental peaks, it is possible to qualitatively establish the elemental composition of the samples and to quantitatively measure the concentration of these elements.

XRF is an analytical method to determine the chemical composition of all kinds of materials. The materials can be in solid, liquid, powder, filtered or other form. XRF can also sometimes be used to determine the thickness and composition of layers and coatings. The method is fast, accurate and non-destructive, and usually requires only a minimum of sample preparation. Applications are very broad and include the metal, cement, oil, polymer, plastic and food industries, along with mining, mineralogy and geology, and environmental analysis is of water and waste materials. XRF is also a very useful analysis technique for research and pharmacy.

For routine XRF analysis, two major approaches are distinguishable based on the type of detector used to measure the characteristic X-ray emission spectra. Wavelength dispersive X-ray fluorescence (WDXRF) analyses depend upon the use of diffracting crystal to determine the characteristic wavelength of the emitted X-rays. Energy dispersive X-ray fluorescence (EDXRF) employs detectors that directly measure the energy of the X-rays by collecting the ionization produced in suitable detecting medium.

Determination of Chemical State and External Magnetic Field

compounds for *Kβ*1,3 and *Kβ*2 components.

experimental support.

configuration.

Effect on the Energy Shifts and X-Ray Intensity Ratios of Yttrium and Its Compounds 91

electron configuration. Although some investigations have been made to study their electronic structures individually, no systematic study has been made so far for understanding the valence electronic structure of all the 3*d* transition metals. With a deeper theoretical understanding of the underlying processes and further improving X-ray sources, sophisticated experiments have been developed (e.g., resonant inelastic scattering, magnetic dichroism (Groot, 1994a,b)) that give detailed information on the valance electron

In a number of X-ray spectral studies of 3*d* transition metals it has been observed that the *Kβ*-to-*Kα* X-ray intensity ratios are dependent on the physical and chemical environments of the elements in the sample. In the earlier studies of 3*d* metal compounds (Küçüköder et al., 1993; Padhi et al., 1993, 1995), the influence of chemical effects has shown difference in the *Kβ*-to-*Kα* X-ray intensity ratios up to nearly 10%. Such chemical effects can be caused either by a varying 3*d* electron population or by the admixture of *p* states from the ligand atoms to the 3*d* states of the metal or both. Brunner et al. (1982) explained their experimental results by the change in screening of 3*p* electron by 3*d* valance electrons as well as the polarization effect. They also pointed out that the chemical effect is almost the same order of magnitude as the effect of excitation mode and both effects should be studied separately. However, most of these measurements have been performed with solid-state X-ray detectors and the change in the satellite peaks in the *Kβ* X-ray region has not been studied because of poor energy resolution. Urch (1979) discussed the chemical effect on the *K* X-ray spectra based on molecular-orbital (MO) theory. Similar studies on the chemical effect on the X-ray spectra have already been done extensively. However, these studies are concerned mostly on with transition energies and profiles of X-rays, and qualitative discussions on the intensities have not yet been made. Tamaki et al. (1979) studied Cr and 55Mn-labeled compounds and reported that the *Kβ*/*Kα* ratio increases with increasing formal oxidation number of the element in the compound. Kataria et al. (1986) found deviations of up to 10% for the same ratio in the case of Mn compounds. Mukoyama et al. (1986) experimentally confirmed the theoretical predictions following Brunners' (1982) model in the case of Te and Mo

Wide employed applications and the intriguing asymmetry of the Cu Kα and Kβ line shapes (Deutsch&Hart, 1982) along with those of all 3d transition elements, led in turn to a century of extensive spectrometric studies of the Cu *Kα* and *Kβ* spectra. In spite of these extensive studied, recent studies reveal that surprises still lurk under the skewed *Kα*1,2 and overlapping *Kβ*1,3 lines, and the related multi-electronic satellite (S) and hypersatellite (HS) spectra. The asymmetric lineshape of the copper emission lines were attributed in the past to a number of different processes: Kondo-like interaction of the conduction electrons with the core holes, final state interactions between the core holes and the incomplete 3*d* shell, 2*p*/3*d* shell electrostatic exchange interaction, and most importantly, shake-up and shake-off of electrons from the 3*l* shells. The last process, in particular, received in the past strong

Raj et al. (1998) were carried studies on CrB, CrB2 and FeB forms in order to look into the electronic structure of the transition metals in monoborides and diborides. In order to understand the valence electronic structure of the transition metals in the compounds, they have tried to compare the measured *Kβ*-to-*Kα* ratios with the multiconfiguration Dirac±Fock calculations assuming different electronic configurations for the transition metal. Such a comparison would provide information on the valence electronic structure of the transition metals in the compounds, which could in turn provide information on

X-ray emission spectra are known to be influenced by chemical combination of X-ray emitting atoms with different ligands. The effect of the chemical combination, however are not large and a theoretical interpretation of these effects has not been established completely. Therefore, chemical effects have rarely been utilized in the characterization of materials. The purpose of this work was to study chemical effects and discuss their applications to Yttrium (Y) in various compounds. So much so that, this paper presents and discusses the measured spectra both energy dispersive and wave-length dispersive X-ray spectrometer. In the first part of the study, the effect of the 0.6T and 1.2T external magnetic field and chemical state on the *Kα*, *Kβ*1,3 and *Kβ*2,4 X-ray energies and relative intensity ratios for Y, YBr3, YCl3, YF3, Y(NO3)3.6H2O, Y2O3, YPO4, Y(SO4)3.8H2O and Y2S3 have been investigated, using the 22.69 keV X-rays from a 109Cd and 59.54 keV γ-ray from a 241Am as photon sources. The measurements were done using an energy dispersive Si(Li) detector with photon excitation by radioisotopes. For B=0, the present experimental results were compared with the experimental and theoretical data in the literature.

The results show that Y2O3, YF3 and Y2S3 can change owing to the applied magnetic field. In addition, we found that the energy of characteristic X-ray series is totally independent of the excitation source and mode. However, changes have been observed in X-ray spectra when the element studied in the sample is chemically bonded to others. The development of high resolution spectrometers allows for the characterization and study of these effects.

In the second part of the study, energies and full width at half maximum (FWHM) values of the *Kα*, *Kβ*1,3 and *Kβ*2,4 X-ray of Y and its compounds were measured by a wavelength dispersive spectrometer. An accurate analytical representation of each line, obtained by a fit to a minimal set of Gaussians, is presented. The absolute energies and FWHM values derived from the data, agree well with previous measurements. Possible origins of chemical shifts are discussed. It was found that the chemical shifts of Y *Kα* line in pure Y and its some compounds relatively small (less than 0.1 eV with pure Y as reference). The influence of crystal symmetry on the energy shifts of X-ray lines is an interesting aspect of our study. The results demonstrate a clear dependence of the energy shifts on the chemical state of the element in the sample. The relative intensities are more susceptible to the chemical environment than the energy shifts.

It is well known that the chemical environment of an element affects and modifies the various characteristics of its X-ray emission spectrum. Most of the works suffer from neglecting chemical influences, and usually theoretical atomic values (Scofield, 1974a, 1974b) are used as a reference even for quite different chemical compounds of certain element. However, some papers deal with chemical effects (Berenyi et al., 1978; Rao et al., 1986), mostly in connection with X-ray emission after an electron capture process (EC) and partially after photoionisation (PI). Paic &Pecar (1976) found that for first-row transition elements the *Kβ*/*Kα* ratio depends on the mode of excitation. The difference between the ratios for electron-capture decay and photoionization becomes almost 10%. Similar results were obtained by Arndt et al., (1982) and they pointed out that the difference comes from a strong shake-off process accompanying photoionization.

The 3*d* transition metals have played an important role in the development of modern technology, and knowledge of their valence electronic structure is very important for understanding their physical properties. X-ray spectroscopy is an established tool for probing the electronic structure of 3*d* transition metal compounds (Meisel et al., 1989). A number of techniques, such as photoemission spectroscopy, X-ray absorption and X-ray emission spectroscopy create a hole in an inner shell in order to investigate the valance

X-ray emission spectra are known to be influenced by chemical combination of X-ray emitting atoms with different ligands. The effect of the chemical combination, however are not large and a theoretical interpretation of these effects has not been established completely. Therefore, chemical effects have rarely been utilized in the characterization of materials. The purpose of this work was to study chemical effects and discuss their applications to Yttrium (Y) in various compounds. So much so that, this paper presents and discusses the measured spectra both energy dispersive and wave-length dispersive X-ray spectrometer. In the first part of the study, the effect of the 0.6T and 1.2T external magnetic field and chemical state on the *Kα*, *Kβ*1,3 and *Kβ*2,4 X-ray energies and relative intensity ratios for Y, YBr3, YCl3, YF3, Y(NO3)3.6H2O, Y2O3, YPO4, Y(SO4)3.8H2O and Y2S3 have been investigated, using the 22.69 keV X-rays from a 109Cd and 59.54 keV γ-ray from a 241Am as photon sources. The measurements were done using an energy dispersive Si(Li) detector with photon excitation by radioisotopes. For B=0, the present experimental results were

The results show that Y2O3, YF3 and Y2S3 can change owing to the applied magnetic field. In addition, we found that the energy of characteristic X-ray series is totally independent of the excitation source and mode. However, changes have been observed in X-ray spectra when the element studied in the sample is chemically bonded to others. The development of high

In the second part of the study, energies and full width at half maximum (FWHM) values of the *Kα*, *Kβ*1,3 and *Kβ*2,4 X-ray of Y and its compounds were measured by a wavelength dispersive spectrometer. An accurate analytical representation of each line, obtained by a fit to a minimal set of Gaussians, is presented. The absolute energies and FWHM values derived from the data, agree well with previous measurements. Possible origins of chemical shifts are discussed. It was found that the chemical shifts of Y *Kα* line in pure Y and its some compounds relatively small (less than 0.1 eV with pure Y as reference). The influence of crystal symmetry on the energy shifts of X-ray lines is an interesting aspect of our study. The results demonstrate a clear dependence of the energy shifts on the chemical state of the element in the sample. The relative intensities are more susceptible to the chemical

It is well known that the chemical environment of an element affects and modifies the various characteristics of its X-ray emission spectrum. Most of the works suffer from neglecting chemical influences, and usually theoretical atomic values (Scofield, 1974a, 1974b) are used as a reference even for quite different chemical compounds of certain element. However, some papers deal with chemical effects (Berenyi et al., 1978; Rao et al., 1986), mostly in connection with X-ray emission after an electron capture process (EC) and partially after photoionisation (PI). Paic &Pecar (1976) found that for first-row transition elements the *Kβ*/*Kα* ratio depends on the mode of excitation. The difference between the ratios for electron-capture decay and photoionization becomes almost 10%. Similar results were obtained by Arndt et al., (1982) and they pointed out that the difference comes from a

The 3*d* transition metals have played an important role in the development of modern technology, and knowledge of their valence electronic structure is very important for understanding their physical properties. X-ray spectroscopy is an established tool for probing the electronic structure of 3*d* transition metal compounds (Meisel et al., 1989). A number of techniques, such as photoemission spectroscopy, X-ray absorption and X-ray emission spectroscopy create a hole in an inner shell in order to investigate the valance

resolution spectrometers allows for the characterization and study of these effects.

compared with the experimental and theoretical data in the literature.

environment than the energy shifts.

strong shake-off process accompanying photoionization.

electron configuration. Although some investigations have been made to study their electronic structures individually, no systematic study has been made so far for understanding the valence electronic structure of all the 3*d* transition metals. With a deeper theoretical understanding of the underlying processes and further improving X-ray sources, sophisticated experiments have been developed (e.g., resonant inelastic scattering, magnetic dichroism (Groot, 1994a,b)) that give detailed information on the valance electron configuration.

In a number of X-ray spectral studies of 3*d* transition metals it has been observed that the *Kβ*-to-*Kα* X-ray intensity ratios are dependent on the physical and chemical environments of the elements in the sample. In the earlier studies of 3*d* metal compounds (Küçüköder et al., 1993; Padhi et al., 1993, 1995), the influence of chemical effects has shown difference in the *Kβ*-to-*Kα* X-ray intensity ratios up to nearly 10%. Such chemical effects can be caused either by a varying 3*d* electron population or by the admixture of *p* states from the ligand atoms to the 3*d* states of the metal or both. Brunner et al. (1982) explained their experimental results by the change in screening of 3*p* electron by 3*d* valance electrons as well as the polarization effect. They also pointed out that the chemical effect is almost the same order of magnitude as the effect of excitation mode and both effects should be studied separately. However, most of these measurements have been performed with solid-state X-ray detectors and the change in the satellite peaks in the *Kβ* X-ray region has not been studied because of poor energy resolution. Urch (1979) discussed the chemical effect on the *K* X-ray spectra based on molecular-orbital (MO) theory. Similar studies on the chemical effect on the X-ray spectra have already been done extensively. However, these studies are concerned mostly on with transition energies and profiles of X-rays, and qualitative discussions on the intensities have not yet been made. Tamaki et al. (1979) studied Cr and 55Mn-labeled compounds and reported that the *Kβ*/*Kα* ratio increases with increasing formal oxidation number of the element in the compound. Kataria et al. (1986) found deviations of up to 10% for the same ratio in the case of Mn compounds. Mukoyama et al. (1986) experimentally confirmed the theoretical predictions following Brunners' (1982) model in the case of Te and Mo compounds for *Kβ*1,3 and *Kβ*2 components.

Wide employed applications and the intriguing asymmetry of the Cu Kα and Kβ line shapes (Deutsch&Hart, 1982) along with those of all 3d transition elements, led in turn to a century of extensive spectrometric studies of the Cu *Kα* and *Kβ* spectra. In spite of these extensive studied, recent studies reveal that surprises still lurk under the skewed *Kα*1,2 and overlapping *Kβ*1,3 lines, and the related multi-electronic satellite (S) and hypersatellite (HS) spectra. The asymmetric lineshape of the copper emission lines were attributed in the past to a number of different processes: Kondo-like interaction of the conduction electrons with the core holes, final state interactions between the core holes and the incomplete 3*d* shell, 2*p*/3*d* shell electrostatic exchange interaction, and most importantly, shake-up and shake-off of electrons from the 3*l* shells. The last process, in particular, received in the past strong experimental support.

Raj et al. (1998) were carried studies on CrB, CrB2 and FeB forms in order to look into the electronic structure of the transition metals in monoborides and diborides. In order to understand the valence electronic structure of the transition metals in the compounds, they have tried to compare the measured *Kβ*-to-*Kα* ratios with the multiconfiguration Dirac±Fock calculations assuming different electronic configurations for the transition metal. Such a comparison would provide information on the valence electronic structure of the transition metals in the compounds, which could in turn provide information on

Determination of Chemical State and External Magnetic Field

chemical environments is appreciable.

1973; Makarov, 1999; Batrakov et al., 2004).

metallic cases.

Effect on the Energy Shifts and X-Ray Intensity Ratios of Yttrium and Its Compounds 93

al. (1986) studied the variation of the relative *K* X-ray intensity ratios for compounds involving Tc isotopes, 95mTc, 97mTc and 99mTc. They found that the chemical effect on the *Kβ*/*Kα* ratios for 4*d* elements is small but the dependence of the *Kβ*2/*Kα* ratios on the

Mukoyoma et al. (1986) have calculated the *Kβ*2/*Kα* intensity ratios for chemical compounds of 4*d* transition elements by the use of the simple theoretical method of Brunner et al. (1982), originally developed for 3*d* elements. Although they obtained good agreement between theories and experimental, it was found that their model is inadequate for the

These investigations on the effect of 3*d* and 4*d* electrons were performed only to understand the chemical effect on the X-ray intensity ratios. However, if the dependence on the excitation mode is also caused by the difference in the number of 3*d* electrons, as shown in our previous work, both effects, i.e. the dependence on the chemical environment and on the excitation mode, can be treated simultaneously to estimate the *Kβ*/*Kα* ratios in terms of the number of 3*d* electrons. However it may also be possible that these ratios are also expressed as a function of other parameters, such as bond length and effective number of 4*p* electrons. Considering these facts, it is interesting to study the dependence of the *Kβ*2/*Kα*

Iiahara et al. (1993) measured the *L* X-ray intensity ratios for some Nb and Mo compounds. When the measured *Lγ*1/*Lβ*1 ratios were plotted as a function of the effective number of 4*d* electrons, they found that the experimental data are experimental data are almost on a straight line. However, it should be noted that the 4*d*→2*p* transitions are allowed dipole transition and the 4d electron is the valance shell electron which participates directly in the X-ray emission. In this case the X-ray emission rate is proportional to the number of 4*d*

The chemical behavior of actinide atoms (in particular, that of uranium) is determined by valance nl-electrons of three types: 7s, 6d and 5f. Although the bond energies of these electrons are almost equal, their wave-function differs greatly in distribution in the radial direction (Katz et al., 1986; Balasubramanian et al., 1994). It can be said that the 5f electrons have an only core arrangement in the atom. Therefore, when actinides chemical bonding is studied, several questions should be raised: (1) the possibility and form of 5f electrons participation in chemical bonding; (2) the necessity for taking into account the splitting of valance levels of the atom into two sublevels nl+ and nl- with total angular momentum j=1±1/2 because of the relativistic effect of spin-orbital splitting (SOS) (Pyykko,1988; Pepper et al., 1991); (3) the energetic stabilization of the specific chemical state of the heavy atom due to fine effects of electron density redistribution on valance orbital; (4) the possibility of independent participation of split subshells in chemical bond formation. One of the methods of modern precise spectroscopy capable of providing a correct description of chemical bonding process is the chemical shift (CS) method of X-ray emission lines, i.e. the change in their energy when the chemical state of the emitting atom is changed (Gohshi&Ohtsuka,

Atomic theory has shown that the magnetic dipole moments observed in bulk matter arise from one or two origins: one is the motion of the electrons about their atomic nucleus (orbital angular momentum) and the other is the rotation of the electron about its own axis (spin angular momentum). The nucleus itself has a magnetic moment. Except in special types of experiments, this moment is so small that it can be neglected in the consideration of the usual macroscopic magnetic properties of bulk matter. When the atom is placed in an

ratio in 3*d* elements on various parameters of chemical compounds.

electrons and increases with increasing effective number of 4*d* electrons.

the rearrangement of electrons between 3*d* and 4*s* states of the metal or electron transfer from the 3*d* state of the metal to the ligand atoms or vice-versa.

The chemical environment has a strong effect on the transitions originated in valence band and its influence could clearly be observed in the emission spectrum structure. The P-*Kβ* spectrum has been studied by many authors (Takashi, 1972; Taniguchi 1984; Torres Delluigi et al., 2003), who used both single-crystal and two-crystal spectrometers with conventional X-ray sources. These authors showed some modifications in the *Kβ* spectra and its relation with P chemical environment. Compounds with oxygen as ligand atom, a relationship between the ratio of the Kβ' line intensity to the total intensity of the Kβ line and the energy shift of the Kα1,2 lines was found by them. Fichter (1975) discussed the *Kα*-line shifts related to the oxidation number of the P-atom. The chemical shift of X-ray emission lines is usually interpreted with the effective charges or oxidation number of the X-ray emitting atom (Leonhardt&Meisel, 1970; Meisel et al., 1989). For example, the Al *Kα* lines shift to higher energy in going from the metal to the oxide (Nagel et al., 1974). By comparing the measured chemical shifts with those of the reference compounds, Gohshi et al. (1973, 1975) determined the chemical state of S, Cr and Sn. They obtained not only qualitative, but also quantitative results.

Theoretical studies of emission spectra were performed mostly to study atoms with simple electronic configurations (see, e.g., the review by Mukoyama et. al., 2004). Theoretical calculations for solids and molecules have been done mainly to predict transition energies and line profiles, but evaluation of transition probabilities is rather scarce. This is due to two reasons: Firstly, molecular orbital methods and band theories are originally developed for ground states and sometimes difficult to apply to excited states with an inner-shell vacancy. Secondly, matrix elements for absorption and emission processes in molecules include multi-center integrations, which are tedious and require long computing times. Most individual authors indicate that their results favor the Dirac-Hartree-Fock calculations of Scofield (1974a), rather than the significantly lower predictions of the same author's earlier Dirac-Hartree-Slater calculations (Scofield, 1969). Both of these describe the de-excitation of a single *K* vacancy in a neutral atom. However careful examinations (Salem et al., 1974; Khan&Karimi, 1980) of all available data reveal a tendency for *Kβ*/*Kα* to fall somewhat below the DHF predictions in the atomic number region 21<Z<32 where the 3*d* subshell is filling.

Band et al. (1985) applied the scattered-wave (SW) X*α* MO method to calculate the chemical effect on the *Kβ*/*Kα* intensity ratios. They performed the MO calculations for different chemical compounds of Mn and Cr using the cluster method and obtained the spherically averaged self-consistent potential and the total charge of the valance electrons in the central atom region. Chemical effect on the *Kβ*/*Kα* X-ray intensity ratios or some Mn and Cr compounds has been studied both theoretically and experimentally by Mukoyama et al. (1986). The *K* X-ray spectra were measured by the use of a double crystal spectrometer with high energy resolution. The theoretical calculations were made with the use of the discretevariational X*α* molecular-orbital method and the X-ray intensities were evaluated in the dipole approximation using molecular wave functions. Mukoyoma et al. (2000) have calculated the electronic structures of tetraoxo complexes of 4*d* and 5*d* elements with the discrete-variational *Xα* (DV-*Xα*) MO method. They found that the for Tc compounds, the calculated values were in good agreement with the measured values. In the case of Mo *K* Xrays, the agreement theory and experiment is not as good as with Tc compounds. Yamoto et

the rearrangement of electrons between 3*d* and 4*s* states of the metal or electron transfer

The chemical environment has a strong effect on the transitions originated in valence band and its influence could clearly be observed in the emission spectrum structure. The P-*Kβ* spectrum has been studied by many authors (Takashi, 1972; Taniguchi 1984; Torres Delluigi et al., 2003), who used both single-crystal and two-crystal spectrometers with conventional X-ray sources. These authors showed some modifications in the *Kβ* spectra and its relation with P chemical environment. Compounds with oxygen as ligand atom, a relationship between the ratio of the Kβ' line intensity to the total intensity of the Kβ line and the energy shift of the Kα1,2 lines was found by them. Fichter (1975) discussed the *Kα*-line shifts related to the oxidation number of the P-atom. The chemical shift of X-ray emission lines is usually interpreted with the effective charges or oxidation number of the X-ray emitting atom (Leonhardt&Meisel, 1970; Meisel et al., 1989). For example, the Al *Kα* lines shift to higher energy in going from the metal to the oxide (Nagel et al., 1974). By comparing the measured chemical shifts with those of the reference compounds, Gohshi et al. (1973, 1975) determined the chemical state of S, Cr and Sn. They obtained not only

Theoretical studies of emission spectra were performed mostly to study atoms with simple electronic configurations (see, e.g., the review by Mukoyama et. al., 2004). Theoretical calculations for solids and molecules have been done mainly to predict transition energies and line profiles, but evaluation of transition probabilities is rather scarce. This is due to two reasons: Firstly, molecular orbital methods and band theories are originally developed for ground states and sometimes difficult to apply to excited states with an inner-shell vacancy. Secondly, matrix elements for absorption and emission processes in molecules include multi-center integrations, which are tedious and require long computing times. Most individual authors indicate that their results favor the Dirac-Hartree-Fock calculations of Scofield (1974a), rather than the significantly lower predictions of the same author's earlier Dirac-Hartree-Slater calculations (Scofield, 1969). Both of these describe the de-excitation of a single *K* vacancy in a neutral atom. However careful examinations (Salem et al., 1974; Khan&Karimi, 1980) of all available data reveal a tendency for *Kβ*/*Kα* to fall somewhat below the DHF predictions in the atomic number region 21<Z<32 where the 3*d* subshell is

Band et al. (1985) applied the scattered-wave (SW) X*α* MO method to calculate the chemical effect on the *Kβ*/*Kα* intensity ratios. They performed the MO calculations for different chemical compounds of Mn and Cr using the cluster method and obtained the spherically averaged self-consistent potential and the total charge of the valance electrons in the central atom region. Chemical effect on the *Kβ*/*Kα* X-ray intensity ratios or some Mn and Cr compounds has been studied both theoretically and experimentally by Mukoyama et al. (1986). The *K* X-ray spectra were measured by the use of a double crystal spectrometer with high energy resolution. The theoretical calculations were made with the use of the discretevariational X*α* molecular-orbital method and the X-ray intensities were evaluated in the dipole approximation using molecular wave functions. Mukoyoma et al. (2000) have calculated the electronic structures of tetraoxo complexes of 4*d* and 5*d* elements with the discrete-variational *Xα* (DV-*Xα*) MO method. They found that the for Tc compounds, the calculated values were in good agreement with the measured values. In the case of Mo *K* Xrays, the agreement theory and experiment is not as good as with Tc compounds. Yamoto et

from the 3*d* state of the metal to the ligand atoms or vice-versa.

qualitative, but also quantitative results.

filling.

al. (1986) studied the variation of the relative *K* X-ray intensity ratios for compounds involving Tc isotopes, 95mTc, 97mTc and 99mTc. They found that the chemical effect on the *Kβ*/*Kα* ratios for 4*d* elements is small but the dependence of the *Kβ*2/*Kα* ratios on the chemical environments is appreciable.

Mukoyoma et al. (1986) have calculated the *Kβ*2/*Kα* intensity ratios for chemical compounds of 4*d* transition elements by the use of the simple theoretical method of Brunner et al. (1982), originally developed for 3*d* elements. Although they obtained good agreement between theories and experimental, it was found that their model is inadequate for the metallic cases.

These investigations on the effect of 3*d* and 4*d* electrons were performed only to understand the chemical effect on the X-ray intensity ratios. However, if the dependence on the excitation mode is also caused by the difference in the number of 3*d* electrons, as shown in our previous work, both effects, i.e. the dependence on the chemical environment and on the excitation mode, can be treated simultaneously to estimate the *Kβ*/*Kα* ratios in terms of the number of 3*d* electrons. However it may also be possible that these ratios are also expressed as a function of other parameters, such as bond length and effective number of 4*p* electrons. Considering these facts, it is interesting to study the dependence of the *Kβ*2/*Kα* ratio in 3*d* elements on various parameters of chemical compounds.

Iiahara et al. (1993) measured the *L* X-ray intensity ratios for some Nb and Mo compounds. When the measured *Lγ*1/*Lβ*1 ratios were plotted as a function of the effective number of 4*d* electrons, they found that the experimental data are experimental data are almost on a straight line. However, it should be noted that the 4*d*→2*p* transitions are allowed dipole transition and the 4d electron is the valance shell electron which participates directly in the X-ray emission. In this case the X-ray emission rate is proportional to the number of 4*d* electrons and increases with increasing effective number of 4*d* electrons.

The chemical behavior of actinide atoms (in particular, that of uranium) is determined by valance nl-electrons of three types: 7s, 6d and 5f. Although the bond energies of these electrons are almost equal, their wave-function differs greatly in distribution in the radial direction (Katz et al., 1986; Balasubramanian et al., 1994). It can be said that the 5f electrons have an only core arrangement in the atom. Therefore, when actinides chemical bonding is studied, several questions should be raised: (1) the possibility and form of 5f electrons participation in chemical bonding; (2) the necessity for taking into account the splitting of valance levels of the atom into two sublevels nl+ and nl- with total angular momentum j=1±1/2 because of the relativistic effect of spin-orbital splitting (SOS) (Pyykko,1988; Pepper et al., 1991); (3) the energetic stabilization of the specific chemical state of the heavy atom due to fine effects of electron density redistribution on valance orbital; (4) the possibility of independent participation of split subshells in chemical bond formation. One of the methods of modern precise spectroscopy capable of providing a correct description of chemical bonding process is the chemical shift (CS) method of X-ray emission lines, i.e. the change in their energy when the chemical state of the emitting atom is changed (Gohshi&Ohtsuka, 1973; Makarov, 1999; Batrakov et al., 2004).

Atomic theory has shown that the magnetic dipole moments observed in bulk matter arise from one or two origins: one is the motion of the electrons about their atomic nucleus (orbital angular momentum) and the other is the rotation of the electron about its own axis (spin angular momentum). The nucleus itself has a magnetic moment. Except in special types of experiments, this moment is so small that it can be neglected in the consideration of the usual macroscopic magnetic properties of bulk matter. When the atom is placed in an

Determination of Chemical State and External Magnetic Field

**2. Experimental**

discussion below).

**2.1 Experimental set up (EDXRF)**

Effect on the Energy Shifts and X-Ray Intensity Ratios of Yttrium and Its Compounds 95

to have been measured here for the first time. Secondly, spectra of *K* X-rays emitted from a Y target were measured in high resolution wave-length dispersive X-ray spectrometer (WDXRF). After the measurement, characteristic quantitative such as peak energy, indices of asymmetry, FWHM are determined. The measured spectra were described in terms of a background function (a straight line) and peaks having Gaussian profiles. The Microcal

Yttrium compounds can serve as host lattices for doping with different lanthanide cations and they used as a catalyst for ethylene polymerization. As a metal, it is used on the electrodes of some high-performance spark plugs. Yttrium is also used in the manufacturing of gas mantles for propane lanterns as a replacement for thorium, which is radioactive. Developing uses include yttrium-stabilized zirconia in particular as a solid electrolyte and as an oxygen sensor in automobile exhaust systems. Yttrium is used in the production of a large variety of synthetic garnets. Small amounts of yttrium (0.1 to 0.2%) have been used to reduce the grain sizes of chromium, molybdenum, titanium, and zirconium. It is also used to increase the strength of aluminium and magnesium alloys. The addition of yttrium to alloys generally improves workability, adds resistance to high-temperature recrystallization and significantly enhances resistance to high-temperature oxidation (see graphite nodule

The studied elements were Y, YBr3, YCl3, YF3, Y(NO3)3.6H2O, Y2O3, YPO4, Y(SO4)3.8H2O and Y2S3. The purity of commercially obtained materials was better than 99%. For powdered samples, particle size effects have a strong influence on the quantitative analysis of infinitely thick specimens. Even for specimens of intermediate thickness, in which category the specimens analyzed in the present study fall, these effects can be significant. Therefore, to circumvent particle size effects all samples were grounded and sieved through a -400 mesh (<37 μm) sieve. The powder was palletized to a uniform thickness of 0.05-0.15 g cm-2 range by a hydraulic press using 10 ton in-2 pressure. The diameter of the pellet was 13 mm. All of the lines were excited using a 100 mCi Am-241 annular radioactive source and Cd-109 point source of 10 mCi strength (providing 5.0x103 steradian-1 photon flux of Ag Xradiation). The fluorescent X-rays emitted from the targets were analyzed by a Si(Li)

detector (effective area 12.5 mm2, thickness 3 mm, Be window thickness 0.025 mm).

For each sample three separate measurements have been made just to see the consistency of the results obtained from different measurements agreed with a deviation of less than 1%. The experimental setup consist of a Si(Li) detector and Cd-109 radioactive source as shown in Fig. 1. The mechanical arrangement to house the source-sample-detector combination in a definite geometry was shown in Fig. 1. An Al, Pb conical collimator was used between the sample and the detector for the excitation to obtain a large beam of emergent radiation and to avoid the interaction of the X-rays emitted by the component elements of the radioactive capsule and detector.An Al, Pb conical collimator was used between the sample and the detector for the excitation to obtain a large beam of emergent radiation and to avoid the interaction of the X-rays emitted by the component elements of the radioactive capsule and detector. This collimator has an external diameter of 13 mm and it was placed in the internal diameter of the radioactive source (8 mm). A graded filter of Pb, Fe and Al to obtain a thin beam of photons scattered from the sample and to absorb undesirable radiation shielded the

Orgin 7.5 was used for peak resolving and background subtraction of *K* X-rays.

external magnetic field, the magnetic field produces a torque on the magnetic dipole. The torque is tending to align the dipole with the field, associated with this torque; there is a potential energy of orientation:

$$
\Delta E = \text{-} \mu\_l B \tag{1}
$$

*μl* is the orbital magnetic dipole moment of an electron. According to the quantum theory, all spectral lines arise from transitions of electrons between different allowed energy levels within the atom and the frequency of the spectral line is proportional to the energy difference between the initial and final levels. The slight difference in energy is associated with these different orientations in the magnetic field. In the presence of a magnetic field, the elementary magnetic dipoles, whether permanent or induced, will act to set up a field of induction of their own that will modify the original field.

Today investigations of magnetic effects on X-ray spectra became actual both from theoretical and experimental points of view. The numbers of works on this subject deal with magnetic circular dichroism (MCD) in X-ray absorption spectroscopy (XAS), that gives information on empty electron states in a valence band and their spin configurations (Thole et al., 1992, Stöhr&Wu, 1994). Several experiments have been performed on the external magnetic field effect on the *K* shell X-ray emission lines. Demir et al., (2006a) determined how the radiative transitions and the structures of the atoms in a strong magnetic field are affected, K*α* and K*β* X-ray production cross sections, the *K*-shell fluorescence yields and *I*(*Kβ/Kα*) intensity ratios for ferromagnetic Nd, Gd, and Dy and paramagnetic Eu and Ho were investigated using the 59.5 keV incident photon energy in the external magnetic fields intensities ± 0.75 T. On the other hand, Demir et al., (2006b) measured *L*3 subshell fluorescence yields and level widths for Gd, Dy, Hg and Pb at 59.5 keV incident photon energy in the external magnetic field of intensities ± 0.75 T. Porikli et al. (2008a; 2008b; 2008c) conduct measurements using pure Ni, Co, Cu and Zn and their compounds. Characteristic quantities such as position of line maxima, full widths at half maximum (FWHM), indices of asymmetry and intensity ratio values were determined in the values of external magnetic field 0.6 T and 1.2 T. Several experiments have been performed on the external magnetic field effect on the *K* shell X-ray emission lines. Commonly, experimental *L* X-ray intensities are measured using radioisotopes as excitation sources (Han et al., 2010; Porikli, 2011b). They have the advantages of stable intensity and energy and of small sizes, which allow compact and efficient geometry, and they operate without any external power.

Our motivation in performing this experiment has been two fold. First, with the aim of a better understanding of the chemical effect and external magnetic field effect, we conduct measurements using pure yttrium (Y) and its compounds. Characteristic quantities such as position of line maxima, full widths at half maximum (FWHM), indices of asymmetry and *Kβ*1/*Kα*, *Kβ*2/*Kα*, *Kβ*2/*Kβ*1 and *Kβ*/*Kα* intensity ratio values are determined in the values of external magnetic field 0.6 T and 1.2 T. In the present work, the measurements were done using a filtered 22.69 keV from Cd-109 and 59.54 keV from Am-241 point source and Si(Li) detector. Particle size effects were circumvented. Peak areas were determined using Gaussian fitting procedures and the errors in various corrections such as self-absorption and detector efficiency were minimized. The measured values were compared due to the external magnetic field and chemical effect. The measured values for B=0 were compared with other experimental and theoretical results. To our knowledge, these intensity ratio values of Y in the external magnetic field have not been reported in the literature and appear to have been measured here for the first time. Secondly, spectra of *K* X-rays emitted from a Y target were measured in high resolution wave-length dispersive X-ray spectrometer (WDXRF). After the measurement, characteristic quantitative such as peak energy, indices of asymmetry, FWHM are determined. The measured spectra were described in terms of a background function (a straight line) and peaks having Gaussian profiles. The Microcal Orgin 7.5 was used for peak resolving and background subtraction of *K* X-rays.


**1. Introduction**

In order to solve the environmental problems caused by automobile exhaust, some automobile companies cooperate with the government to implement the new energy "shared car" services in urban areas, with a maximum speed of no more than 70 km/h. Shared cars have more microsensors than ordinary fuel vehicles. Currently, microsensors are mainly powered by chemical batteries [1,2]. Chemical batteries have the characteristics of a large volume, low energy density, and short service life, and they also need to be replaced regularly [3,4]. These features increase the maintenance cost of shared vehicles. If the renewable energy that exists in the ambition environment can be directly converted into electricity to power microsensors, this problem can be solved very well [5,6]. The process of driving a car produces a lot of energy that can be recycled, such as heat energy [7,8], vibration energy [9–11] and wind energy [12]. Wind-induced vibration energy, which occurs when the car is driving, can be directly converted into electrical energy [13,14]. In recent years, there has been much research on wind-induced vibration energy recovery. There are three main types of electromechanical energy conversions, namely, piezoelectric, electromagnetic, and electrostatic [15,16]. Among them, the piezoelectric energy collecting device has the advantages of having good system compatibility, a simple

structure, and a high energy density [17]. This makes piezoelectric energy harvesting a promising approach to energy recovery.

Researchers have developed many e ffective miniature wind-capacitor energy harvesting devices using electromagnetic or piezoelectric principles. The wind energy harvesters are mainly classified into turbine harvesters [18,19], windmill harvesters [20], reed harvesters [21–27], and other new structures [28–33]. Florian Herrault et al. [18] designed a microturbine electromagnetic generator. The four-pole six-turn/pole NdFeB generator exhibits up to 6.6 mW of AC electrical power across a resistive load at a rotational speed of 392,000 r/min. This milliwatt-scale power generation indicates the feasibility of such ultra-small machines for low-power applications. Sardini [19] et al. designed a turbo-type microgenerator to supply energy to the sensor that measures air temperature and speed. When the wind speed is 9 m/s, the electromagnetic generator matches the resistance of 500 Ω, and electric power with an average power of 45 mW can be obtained. Priya [20] designed a windmill-type piezoelectric energy harvester with a maximum output power of 7.5 mW when the wind speed is 10 mph and the matching resistance is 6.7 k Ω. Tan Y. K. et al. [21] designed a reed-type wind energy recovery device that uses a PZT (lead zirconate titanate) piezoelectric material to power the wind speed sensor. The wind energy harvester can start with a cut-in wind speed of 2 m/s and a cut-o ff wind speed of 7.5 m/s. When the wind speed is 6.7 m/s and the load is 220 k Ω, the maximum output voltage is 8.8 V, and the maximum output power is 155 μW.

The reed-type wind energy piezoelectric energy harvester can be divided into three types according to the excitation mode, namely, the resonant cavity type [22–24], blunt body spoiler type [25,26], and direct excitation type [27]. D. St. Clair et al. [22] proposed a wind-pressure energy-capturing device based on self-excited airflow oscillation using a single reed and a cavity structure. When the wind speed is 7.5–12.5 m/s, the wind pressure-capture device can obtain an output power of 0.1 mW to 0.8 mW. They found that the resonant cavity-based piezoelectric energy harvester does not require any external vibration sources, thus eliminating the bandwidth problems associated with vibratory energy harvesters. Bibo Amin et al. [23] established an analytical electromechanical model to predict the response characteristics of a wind-pressure energy-capturing device based on self-excited airflow oscillation using a single reed and a cavity structure, and the e ffectiveness of the model was verified by experiments. In order to improve the vibration response of the wake excitation and increase the output power, L. A. Weinstein et al. [25] added a fin device at the end of the piezoelectric vibrator to make the natural frequency close to the vortex a shedding frequency. Song Rujun et al. [26] proposed a vortex-induced vibration-type piezoelectric energy-trapping device, composed of a piezoelectric cantilever beam and a terminal cylinder. They established its mathematical model and carried out experiments. The results show that this piezoelectric energy harvester can obtain the maximum energy output during vortex-induced resonance.

The wind speed of a piezoelectric energy harvester based on the turbulent vibration of the spoiler cylinder has a narrow adaptive range, and its natural frequency needs to be matched. However, the role of the spoiler cylinder is to increase the degree of chaos in the fluid flow field, and it can increase the pressure of the local fluid. It is not necessary to match the wind speed of the resonant cavity piezoelectric energy harvester. The amplitude response characteristics of the resonant cavity piezoelectric energy harvester are as follows: When the wind speed is low, the fluid kinetic energy cannot overcome the damping of the fluid flowing in the cavity, and the displacement response of the cantilever beam and voltage output is 0. When the wind speed exceeds a certain threshold, the cantilever beam produces self-sustaining and finite period oscillates, and as the wind speed increases, both the amplitude response and the voltage output increase.

In this paper, in order to achieve the purpose of continuous and stable power supply for the vehicle-mounted sensor on the shared car, the traditional resonant cavity piezoelectric energy harvester was improved: A Helmholtz resonant cavity was added to the end of the main cavity, and a spoiler cylinder was added at the entrance of the main cavity. Both the spoiler cylinder and the Helmholtz resonator increase the gas pressure in the main cavity to improve the energy capture e fficiency of the

harvester. The resonant cavity piezoelectric energy harvester has an effective wind speed range, in which the piezoelectric energy harvester can work effectively, otherwise the energy harvester will not work or even be destroyed. In order to discuss whether the harvester can be installed on a shared car, the effective wind speed range of this harvester has been studied. The energy conservation method was used to solve the cut-in wind speed (threshold wind speed required to start the harvester), and the critical stress method was used to solve the cut-out wind speed (maximum wind speed above which operating could result in harm to the structure) of the energy harvester. Herein, the experimental research that has been carried out is described in detail.

#### **2. Structure and Working Principle**

This piezoelectric energy harvester was designed as a composite reed resonator structure, consisting of a structural module and two piezoelectric power generation modules, as shown in Figure 1. The structural module is composed of a main cavity, a spoiler cylinder, a Helmholtz cavity short tube, and a Helmholtz resonator. The two piezoelectric power generation modules are symmetrically distributed on the left and right sides of the main cavity, where one end of which is fixed to the main cavity body, and the other end is free to form an elastic cantilever beam structure. The spoiler cylinder is fixed at the inlet of the main cavity, and the Helmholtz cavity is fixed at the tail of the main cavity. The piezoelectric power generation module is composed of a metal substrate and piezoceramics, and the piezoceramics are attached to the root of the fixed end of the substrate.

**Figure 1.** Schematic of the resonant cavity piezoelectric energy harvester: (**1**) Spoiler cylinder; (**2**) main cavity; (**3**) piezoceramics; (**4**) substrate; (**5**) Helmholtz cavity short tube; (**6**) Helmholtz resonator cavity.

When the car is running, the airflow enters the main cavity of the harvester from the air inlet of the main cavity (*U*in). The air in the main cavity is compressed, then the pressure is increased, the cantilever beam is bent and deformed, and the air outlet of the main cavity (*U*out) is opened. As a result, the air pressure in the main cavity is reduced, the elastic beam is reset, and the air outlet is closed. Thus, a repeating process is formed. The piezoelectric cantilever beam is periodically and repeatedly deformed to generate charges of opposite polarities in cycles on the upper and lower surfaces of the piezoelectric ceramic sheet. The piezoelectric ceramic sheets and loads form a closed energy output circuit that outputs electrical energy, thereby converting wind pressure energy into electrical energy.

#### **3. Research on Cut-in Wind Speed**

The piezoelectric energy harvester has an e ffective wind speed range, and the minimum wind speed that enables the piezoelectric energy harvester to start capturing energy is called the cut-in wind speed, which is also called the lower critical wind speed. In this paper, the energy conservation method is used to solve the cut-in wind speed.

#### *3.1. Energy Conservation Analysis of the Harvester in one Cycle*

The airflow enters the piezoelectric energy harvester from the inlet of the main cavity and flows out from the outlet. In this process, the reduced wind pressure energy is partially consumed by the piezoelectric damper's own damping force, and the other part acts on the piezoelectric harvester converted into electrical energy. Suppose there is a critical wind speed, at which the kinetic energy of the airflow is just consumed by the damping of the piezoelectric trap itself, so that the piezoelectric trap cannot capture energy. This critical velocity of the airflow entering the cavity is the cut-in wind speed.

The damping of the piezoelectric energy harvester consists of three parts, namely, the damping of the material used in the piezoelectric energy harvester (the phenomenon of mechanical energy loss caused by the friction among the internal grains of the material caused by the action of the trap in the wind field), the fluid damping generated by the various structures of the piezoelectric energy harvester after the fluid enters it, and piezoelectric damping produced by piezoelectric ceramic when piezoelectric cantilever beam vibrates. The material of piezoelectric energy harvester produces little damping and can be neglected during the research process. When the wind speed acting on the piezoelectric cantilever beam is equal to the cut-in wind speed, the piezoelectric cantilever beam is not deformed, and the piezoelectric ceramic piece does not generate electric energy. As such, there is no piezoelectric damping.

The cut-in wind speed can be obtained by the energy conservation method. When the energy conservation method is used to calculate the starting wind speed, the work done by the fluid damping force generated by each part of the structure is equal to the kinetic energy of the fluid entering the cavity. The damping of the piezoelectric energy harvester mainly includes the fluid damping force generated by the turbulent cylinder and the fluid damping force generated by the inner surface of the cavity.

The fluid kinetic energy in one cycle is calculated by Equation (1):

$$E\_p = \frac{1}{2}m\upsilon^2 = \frac{1}{2}\rho(A\_0 \cdot \upsilon T)\upsilon^2 = \frac{1}{2}\rho A\_0 \upsilon^3 T \tag{1}$$

where *Ep* is defined as the kinetic energy of the fluid in a cycle, ρ is defined as the density of the air, *A*0 is defined as the inlet area of the main cavity, *v* is defined as the velocity of the fluid at the entrance of the harvester, and *T* is defined as the vibration period of the piezoelectric cantilever.

The work done by the piezoelectric energy harvester structure damping in one cycle is calculated by Equation (2):

$$\mathcal{W} = \mathcal{W}\_d + \mathcal{W}\_q \tag{2}$$

where *W* is defined as the work done by the structural damping force in a cycle, *Wd* is defined as the work done by the fluid damping force generated by the spoiler cylinder in a cycle, *Wq* is defined as the work done by the fluid damping force generated on the inner surface of the main cavity and the Helmholtz resonator.

#### *3.2. Work Done by the Spoiler Damping Force*

## 3.2.1. Theoretical Analysis

The average resistance coefficient of the cylinder unit length is [34]:

$$\mathcal{C}\_d = \frac{F\_d}{\frac{1}{2}\rho D v^2} \tag{3}$$

The fluid damping force generated by the spoiler cylinder of length *L* is:

$$F\_d = \frac{1}{2} \rho \mathbf{C}\_d D L v^2 \tag{4}$$

where *Cd* is defined as the resistance coefficient of the spoiler cylinder (*Cd* is 1.11, according to the empirical value [34]), and *D* and *L* are respectively defined as the diameter and length of the spoiler cylinder.

The work of the damping force generated by the spoiler cylinder in a cycle is given by Equation (5):

$$\mathcal{W}\_d = F\_d \cdot \mathbf{x} = F\_d \cdot vT = \frac{1}{2} \rho C\_d D L v^3 T \tag{5}$$

where *x* represents the displacement of the spoiler cylinder relative to the fluid for a cycle.

#### 3.2.2. Simulation Verification of the Value of Resistance Coefficient

The resistance coefficient is a function of the Reynolds number [34]. The Reynolds number is related to the velocity, so the resistance coefficient is related to the speed.

In order to verify the accuracy of the resistance coefficient selected according to the empirical value when solving the starting wind speed, the resistance coefficient of the spoiler cylinder is calculated by the Fluent software package, then compared with the empirical value resistance coefficient selected. If the error is within ±5%, it shows that the resistance coefficient obtained by the empirical value is reasonable when the energy conservation method is used to calculate the wind speed of the resonant cavity piezoelectric harvester.

In order to facilitate the study, this paper neglects the influence of the length of the cylinder. By simplifying the three-dimensional model of the main cavity into two-dimensional model, the influence of the disturbing cylinder on the model is studied. The simplified model is shown in Figure 2.

**Figure 2.** Simplified flow field model of the main cavity.

The Kármán vortex street effect occurs when the fluid passes through a cylinder. At this time, the shedding frequency of the fluid vortex in the flow channel [35] is:

$$f = S\_l \frac{v}{\varepsilon D} \tag{6}$$

where

$$\varepsilon = 1 - \frac{2}{\pi} \left[ \frac{D}{\mathcal{O}} \sqrt{1 - \left(\frac{D}{\mathcal{O}}\right)^2} + \arcsin\frac{D}{\mathcal{O}} \right] \tag{7}$$

where *St* is the Strouhal number, which indicates the relative relationship between the fluid kinetic energy and the inherent energy of the system. When the fluid flows over the spoiler cylinder, according to the calculation formula of Reynolds number, *Re* = ρ*vD*μ (*v* takes the values of 1–30 m/s; ρ is air density; μ is hydrodynamic viscosity; *D* is the diameter of the spoiler cylinder), where the range of *Re* is from 336.7 to 10,101.2. It is common practice to assume *St* = 0.21 in the sub-critical range, 300 < *Re* < 1.5 × 105 [36]; ε represents the ratio of the area of the arcuate faces on both sides of the cylinder to the cross-sectional area of the intake passage; Φ represents the hydraulic diameter of the inlet.

When the flow field dynamic characteristics of the spoiled cylinder are analyzed, the boundary conditions are as follows.

The inlet wind speed is set from 2 m/s to 10 m/s, and the step length is 1 m/s. The remaining parameters are not changed. Finally, the resistance coefficient of the spoiler can be calculated. The results from our analysis are shown in Figure 3.

**Figure 3.** Relationship between inlet wind speed and resistance coefficient.

It can be seen from Figure 3 that when the inlet wind speed is different, the resistance coefficient also changes, but the change is not obvious. Therefore, the influence of wind speed on the resistance coefficient of the turbulent cylinder can be ignored. The average value of the coefficient of resistance of the turbulent cylinder is 1.07. The error is 3.6% when compared with the empirical value of 1.11, and is less than 5%, which is within the allowable range. Therefore, it can be verified that the empirical value of the resistance coefficient selected by the empirical value is reasonable when the energy method is used to solve the cut-in wind speed.

*3.3. Work Done by the Damping Force Generated by the Main Cavity and the Inner Surface of the Helmholtz Resonator*

The friction of the flat wall surface per unit area [34] is calculated by Equation (8):

$$
\pi\_f = 0.3232 \sqrt{\frac{\mu \rho v^3}{x}} \tag{8}
$$

where μ represents the air viscosity coefficient.

The fluid damping force produced on the upper and lower surfaces of the inner wall of the main cavity is calculated by Equation (9) [34]:

$$F\_f = 2\left(\int\_0^{L\_B} \tau\_f \cdot B d\mathbf{x} - 2\int\_0^{2R} \tau\_f \cdot \sqrt{R^2 - \left(R - x\right)^2} d\mathbf{x}\right) \tag{9}$$

Equation (8) can be substituted for Equation (9) and then simplified:

$$F\_f = 1.2928 \sqrt{\mu \rho v^3} (\sqrt{L\_B} \cdot B - \frac{2}{3} (2R)^{\frac{3}{2}}) \tag{10}$$

where *LB* and *B* denote the length and width of the main cavity, respectively, and *R* denotes the radius of the spoiler cylinder (2*R* = *D*).

Similarly, the fluid damping force generated on the left and right surfaces of the inner wall of the main cavity is given by Equation (11) [34]:

$$F\_h = 2(\int\_0^{L\_B} \tau\_f \cdot h \mathrm{d}x - 2 \int\_{L\_2}^{L\_3} \tau\_f \cdot \Delta h \mathrm{d}x - \int\_{L\_3}^{L\_3 + \Delta h} \tau\_f \cdot h \mathrm{d}x) \tag{11}$$

where *h* denotes the height of the main cavity; *b* denotes the width of the substrate; Δ*h* denotes the gap between the main cavity and the substrate in the width direction; Δ*b* denotes the gap between the main cavity and the substrate in the length direction; *L*2 and *L*3 denote the distance from the entrance of the main cavity to the front end and the end of the substrate, respectively.

Then, the fluid damping generated on the inner wall surface of the main cavity can be expressed by Equation (12):

$$F\_h = 1.2928 \sqrt{\mu \rho v^3} (\sqrt{L\_3} \cdot h - 2(\sqrt{L\_2} - \sqrt{L\_3}) \cdot \Delta h - (\sqrt{L\_3 + \Delta h} - \sqrt{L\_3}) \cdot b) \tag{12}$$

Similarly, the fluid damping generated on the inner surface of the Helmholtz resonator at the end of piezoelectric energy harvester can be calculated by Equation (13):

$$F\_m = 1.2928\pi \sqrt{\mu\rho v^3} ((\sqrt{L\_4} - \sqrt{L\_B}) \cdot R\_1 + (\sqrt{L\_5} - \sqrt{L\_4}) \cdot R\_2) \tag{13}$$

where *L*4 is defined as the distance from the entrance of the main cavity to the end of the short tube, *L*5 is defined as the distance from the entrance of the main cavity to the end of the Helmholtz resonator cavity, *R*1 is defined as the radius of the short tube, and *R*2 is defined as the radius of the Helmholtz cavity.

#### *3.4. Numerical Calculation of Cut-in Wind Speed*

The work done by the fluid damping force of the main cavity in one cycle can be calculated by Equation (14):

$$\mathcal{W}\_{\emptyset} = (F\_f + F\_h + F\_m) \cdot \mathbf{x} = (F\_f + F\_h + F\_m) \cdot \mathbf{v}T \tag{14}$$

According to the law of conservation of energy:

$$E\_p = \mathcal{W} = \mathcal{W}\_d + \mathcal{W}\_q \tag{15}$$

Substituting Equations (1), (5), and (14) into Equation (15), Equation (15) can be converted into Equation (16):

$$\frac{1}{2}\rho A\_0 \upsilon^3 T = F\_d \cdot \upsilon T + (F\_f + F\_h + F\_m) \cdot \upsilon T \tag{16}$$

Substituting Equations (4), (10), (12), and (13) into Equation (16), the cut-in wind speed can be obtained by solving Equation (17).

$$
\rho \mathbf{C}\_{4} \text{DL} + 2.5856 \sqrt{\mu \rho v} \begin{bmatrix}
(\sqrt{L\_{\text{B}}} \cdot \mathbf{B} - \frac{2}{3} (2R)^{\frac{2}{3}}) + (\sqrt{\mathsf{L}\_{\text{B}}} \cdot \mathbf{h} - 2(\sqrt{\mathsf{L}\_{\text{B}} - \mathsf{L}\_{2}}) \cdot \Delta \mathbf{h} - (\sqrt{\mathsf{L}\_{3} + \Delta \mathbf{b}}) \\
\end{bmatrix} - \rho A\_{0} = \mathbf{0} \tag{17}
$$

The values of the parameters in Equation (17) are shown in Table 1.

Equation (17) can be solved by mathematics software, and the cut-in wind speed of the piezoelectric energy harvester obtained here was 5.29 m/s.

#### **4. Solution of Wind Cut-o**ff **Velocity by Stress Critical Value Method**

When the airflow enters the cavity of the piezoelectric harvester, the piezoelectric cantilever beam arranged on both sides of the cavity will bend and deform. When the piezoelectric cantilever beam can work normally and is not damaged, the maximum airflow speed that it can withstand is called the cut-out wind speed, also called the upper critical wind speed. If the inlet wind speed is higher than this critical wind speed, the cantilever beam or the piezoelectric ceramic piece may break and cause a failure. On the contrary, if the airflow velocity is lower than the cut-off wind speed, the piezoelectric cantilever beam will not be destroyed. Therefore, the cut-out wind speed can be obtained by solving the wind speed at the point of critical stress of the piezoelectric beam.

The piezoelectric module is composed of a substrate and a piezoelectric ceramic piece, both of which must be able to work normally within the allowable range of allowable stress. The substrate material used was beryllium bronze, whose strength is 1035 MPa [37]. The piezoelectric ceramic sheet was PZT-5H, where the tensile strength under the d31 working mode is 75.845 MPa [38]. Taking a safety factor of 1.3 [39], the allowable stresses for the substrate and the piezoelectric ceramic piece are 796 MPa and 58.345 MPa, respectively. Therefore, it is necessary to ensure that the maximum stress of the substrate and the piezoelectric piece when the piezoelectric cantilever is in operation does not exceed their respective allowable stresses.

The Fluent software package was used to analyze the pressure distribution on the elastic beam of the piezoelectric trap when the airflow acted on the elastic beam in the flow field.

The specific process of fluid simulation was as follows:

1. Model import and establishment of the flow field: The resonant cavity piezoelectric energy harvester structure model was modeled by SolidWorks and saved in the IGS format and then imported into Fluent. The flow field was established according to the size parameters of the energy harvester. Generally, the flow field size was about 5 to 10 times that of the research object. The length, width, and height of the flow field established in this paper was 1000 mm, 400 mm, and 200 mm, respectively. Finally, the fluid inlet and the fluid outlet were set.

Boundary condition setting: The inlet wind speed was 15 m/s, outlet pressure was the standard atmospheric pressure, and wall surface was set to no slip. The monitoring was set to monitor the pressure value of the cantilever beam on both sides of the piezoelectric energy harvester.

4. Initialization calculation and postprocessing: Global initialization was required before starting the calculation. The initialization method for this article was standard initialization. The initial pressure was set to the standard atmospheric pressure. Here, the postprocessing mainly extracts and collates the pressure data of the cantilever beams on both sides.

The pressure distribution of each node on the inner surface of the substrate in the wind field was extracted from the analysis results. The pressure distribution law is shown in Figure 4, where the *x*-axis is the length of the substrate, with a range of 30–120 mm, the *y*-axis is the width of the substrate, with a range from −7.5 mm to 7.5 mm, and the *z*-axis is the pressure value, with a range from 0 Pa to 150 Pa.

As can be seen from Figure 4, the pressure in the x-direction was increased first and then decreased, but the change was small. When the y-coordinate range was from −7.5 mm to −2.5 mm, the pressure increased linearly with the increase of the y-coordinate value. When the y-coordinate range was from −2.5 mm to 2.5 mm, the pressure did not obviously change with the increase of the y-coordinate value. When the y-coordinate range was from 2.5 mm to 7.5 mm, the pressure decreased linearly with the increase of the y-coordinate value. According to the distribution of wind pressure on the substrate in the wind field, the substrate can be divided into 12 regions, as shown in Figure 5.

**Figure 4.** Distribution of the pressure on the substrate in the wind field.

**Figure 5.** Division of substrates.

As shown in Figure 5, the pressure values of regions 4, 5, 6, 7, 8, and 9 are not much different, and approximate a rectangular area of equal value. The four regions of regions 1, 3, 10, and 12 are approximately triangular. Regions 2 and 11 are approximately rectangular. For the approximate isosurface area, a plurality of values may be averaged, and the triangular region can take the corresponding pressure value at the median line as the average value of the region, and the rectangular region takes the pressure value at the intermediate symmetry axis as the average value of the region.

The pressure of each region at different wind speeds is obtained by changing the inlet wind speed. The static analysis of the piezoelectric cantilever beam was performed using the Ansys software package according to the above loading method. The specific simulation details are described below:

After the simulation calculation, since the maximum Mises stress generated on the substrate did not exceed 200 MPa, which is much smaller than its allowable stress, the relationship between the maximum Mises stress on the substrate and the wind speed is not listed here. Figure 6 is a graph showing the relationship between the maximum Mises stress of the piezoelectric piece and the wind speed.

It can be seen from Figure 6 that the maximum Mises stress value of the piezoelectric piece increases with the increase of the wind speed. When the wind speed is lower than 5 m/s, the maximum Mises stress value of the piezoelectric piece approaches 0. When the wind speed is greater than 25 m/s, the maximum Mises stress of the piezoelectric piece exceeds 61.7 MPa, which is greater than the allowable stress of the piezoelectric piece. When the wind speed is between 24 m/s and 25 m/s, there is a wind speed value such that the maximum Mises stress of the piezoelectric piece is exactly equal to the allowable stress of the piezoelectric piece. In order to ensure the safety of the piezoelectric cantilever beam structure, the cut-out wind speed of the piezoelectric energy harvester was determined to be 24 m/s. This speed is greater than the maximum speed that a shared car travels in the city, so the piezoelectric energy harvester installed on the shared car can work properly.

**Figure 6.** Relationship between wind speed and Mises stress of piezoelectric piece.

## **5. Experimental Study**

In order to determine the output characteristics of the resonant cavity piezoelectric energy harvester and verify the correctness of the critical wind speed calculation results, a prototype of the resonant cavity piezoelectric energy harvester was fabricated, as shown in Figure 7. The thickness of the piezoelectric piece and substrate were both 0.5 mm, and the remaining dimensions were the same as in Table 1.

The resonant cavity piezoelectric energy harvester model is mainly composed of wires, a main cavity, a spoiler cylinder, a bolt, two piezoelectric ceramic pieces, two substrates, and a Helmholtz resonant cavity. The main cavity, the spoiler cylinder, and the Helmholtz resonator were modeled in SolidWorks and then processed separately using 3D printing technology, where the material used was PLA. The left and right sides of the main cavity both have a rectangular groove, with a length of 96 mm and a width of 16 mm, for fixing the piezoelectric cantilever beams. The material of the substrates used was beryllium bronze, which was cut by a cutter. The piezoelectric ceramic pieces used the PZT-5H piezoelectric ceramic pieces produced by the Hebei Hongsheng Acoustic Electronic Equipment Co., Ltd. The size of the piezoelectric piece was 10 mm × 15 mm × 0.4 mm. A through-hole was formed at the entrance of the main cavity and was assembled with the spoiler cylinder. The main cavity has a round hole at the end was assembled with the Helmholtz cavity. The piezoelectric cantilever beam was fixed on both sides of the main cavity by M3 bolts. The piezoelectric cantilever beam was made by bonding the PZT-5H to the substrate by epoxy resin containing copper powder. Two wires were spot-welded on the positive surface of PZT-5H and the substrate.

The experiment platform, as shown in Figure 8, was constructed. The experimental study on the output characteristics of the resonant cavity piezoelectric energy harvester was carried out.

**Figure 7.** Resonant cavity piezoelectric energy harvester prototype.

**Figure 8.** Resonant cavity piezoelectric energy harvester experimental platform.

The equipment used in the experiment were as follows: A blower (LKW315L-4, Shandong Qineng Ventilator Co., Ltd., Zibo, China), with the maximum adjustment frequency of 50 Hz and a maximum speed of 1350 r/min, a NI acquisition card (NI-cDAQ-9174, National Instruments, Austin, TX, USA), an oscilloscope (ADS 1102CAL, Guorui Antai Technology Co., Ltd., Nanjing, China), a frequency converter (VFD 110B 43A Shanghai Xinyu Automation Equipment Co., Ltd., Shanghai, China), an anemometer (CTV100, Beijing Oubai Keyi Instrument Co., Ltd. Beijing, China), with a wind speed measurement range of 0–30 m/s and a sensitivity of 0.1 m/s, and a PC.

Since two piezoelectric cantilever beams were symmetrically mounted on both sides of the piezoelectric energy harvester, only the vibration of one side piezoelectric cantilever beam was studied. Figure 9 shows the average open circuit voltage of the piezoelectric energy harvester at different wind speeds.

**Figure 9.** Curve of open circuit voltage with wind speed.

As can be seen from Figure 9, the open circuit voltage of the piezoelectric harvester increases nonlinearly with the increase of the wind speed. When the wind speed increases from 0 m/s to 5 m/s, the open circuit voltage increases slowly. When the wind speed is greater than 5 m/s, the open circuit voltage increases rapidly. In the actual experiment, the external small vibration can also cause the vibration of the energy absorbing device. Considering the influence of the actual factors, the cut-in wind speed of the piezoelectric energy harvester is 5 m/s. The blower can provide a maximum wind speed of 25 m/s, and the trap can still operate at this wind speed. However, in the experiment, it was found that after the harvester worked at a large wind speed for a long time, the piezoelectric cantilever beam would undergo a slight bending deformation. Therefore, the cut-out wind speed of the piezoelectric energy harvester should be 24 m/s. The effective wind speed range of the harvester is 1.58 times that of the micropiezoelectric wind energy harvester with a resonant cavity (with an effective wind speed range of 4–16 m/s), which has a cavity size of 64 mm × 22 mm × 14 mm, with a piezoelectric beam length of 8 mm and a flexible beam length of 30 mm, as described by Du Zhigang [24].

The power generation performance of a piezoelectric energy harvester needs to be measured by a load resistor [40,41]. Figure 10 is a plot of output power as a function of load resistance at the wind speed of 10 m/s.

**Figure 10.** Relationship between output power and load resistance at the wind speed of 10 m/s.

It can be seen from Figure 10 that when the wind speed is 10 m/s, the output power firstly increases and then decreases with the increase of the load resistance. When the load resistance is 60 kΩ, the output power of one side piezoelectric cantilever beam reaches a maximum of 45 μW. In this experiment, the optimal resistance of the piezoelectric energy harvester was 60 kΩ.

Figure 11 shows the relationship of the output voltage with time at a wind speed of 22 m/s when the resistance was 60 kΩ.

**Figure 11.** Variation of output voltage at a wind speed of 22 m/s.

It can be seen from Figure 11 that the peak output voltage of the single-sided piezoelectric cantilever beam of the piezoelectric energy harvester can reach 9.6 V when the wind speed is 22 m/s, and the peak output power obtainable at this time is 1.536 mW. The average voltage of one side of the piezoelectric cantilever beam was 2.0877 V, and the corresponding total power and power density here were 0.145 mW and 1.2 mW/cm3, respectively.