**Computational Mathematics, Algorithms, and Data Processing**

Printed Edition of the Special Issue Published in *Mathematics*  Daniele Mortari, Yalchin Efendiev and Boris Hanin Edited by

www.mdpi.com/journal/mathematics


Preface

This book aims to present an overview of the pertussis infection, focusing important issues about the diagnosis, the treatment of the disease, and the epidemiological and clinical as‐ pects in populations with high-vaccination rates.

Current proposals for vaccination against pertussis, as well as current strategies of immuni‐ zation programs, which primarily try to protect susceptible young children in the first year of life, who have not yet been immunized or are with incomplete vaccination schedule, will also be addressed.

Despite the effective and safe alternatives for immunoprevention, several challenges still have to be overcome for control of the disease, which remains a highly relevant problem in public health in terms of morbidity and mortality, with an increasing incidence even in countries with high-vaccine coverage.

We would like to thank all those who contributed to the realization of this work, especially the authors, for the content of the chapters of high-scientific value. We would also like to thank InTechOpen publishing team and Ms. Marijana Francetic for the technical support.

> **Waldely Dias and Isaias Raw** Instituto Butantan Center of Biotechnology Special Laboratory of Vaccine Development São Paulo, Brazil

**Section 1**

**Introduction**

**Section 1**


**5. Conclusions and future possibilities**

The results presented in these studies show that the best conditions established for the epoxidation of AGE to DGE on the Ti-SBA-15 catalyst in water solution are as follows: the temperature of 20°C, the molar ratio of AGE/H2O2 = 0.03:1, the content of the catalyst 3 wt%, and the reaction time of 60 min. At these mild and relatively safe conditions, the selectivity of DGE amounts to 100 mol%; the conversion of AGE and the selectivity of transformation to organic compounds in relation to hydrogen peroxide consumed amount to 4 mol% and 1 mol %, respectively. These studies also show that this process is very complicated because of the secondary reactions which proceed in reaction medium – hydration of epoxide ring in AGE (formation of 3A12PD), hydrolysis at the epoxide group in AGE, DGE, 3A12PD, epoxidation of the formed allyl alcohol, and hydration of the epoxide ring in glycidol and formation of glycerol. However, it is possible to choose such a way of carrying up this process in which only one product – DGE (the most desirable) – is obtained. The process of obtaining DGE is performed at very mild conditions, thus the danger of the explosive decomposition of hydrogen peroxide or compounds with epoxide group is very little, mainly taking into account the very low temperature of this process which amounts 20°C. Hydrogen peroxide used in this process is a relative cheap oxidizing agent and moreover, the methods of production of hydrogen peroxide are still developed and modernized. The method of AGE epoxidation with hydrogen peroxide is also ecologically friendly because only one product of its transformation is water. The presented studies showed that for this process hydrogen peroxide should be used in excess in relation to AGE. Mainly, it is connected with the phenomenon of ineffective decomposition of hydrogen peroxide (not explosive decomposition) at the active centers of Ti in the structure of the catalyst. This phenomenon causes that only a little amount of hydrogen peroxide takes part in epoxidation process and utilization of the excess of hydrogen peroxide in relation to AGE improves effective utilization of hydrogen peroxide molecules in the process of epoxidation. On the other hand, hydrogen peroxide undergoes very easy ineffective decomposition, thus even at the excess of hydrogen peroxide its concentration in reaction mixtures is low. The main cause of this situation is high content of the Ti-SBA-15 catalyst in reaction mixture (3 wt%). There are some possible ways of improving the hydrogen peroxide conversion efficiency by, for example, (1) addition of additives (CH3COOH, KHSO4, KH2PO4, KHF2, Na2SO4, NaHCO3, K2CO3, K3PO4, K2HPO4, or KH2PO4); (2) the changing of the way of hydrogen peroxide addition; (3) choosing the appropriate solvent (methanol, acetonitrile or acetone), or co-solvent (sulfolane); (4) increasing the acidity of the catalyst by the addition of metal oxide, for example, of TiO2, and utilization of the appropriate temperature of the calcination; and 5) the surface hydrophobization of mesoporous titanium silicates. We would like to test in our future works some of the ways of improving the efficiency of hydrogen peroxide conversion: choosing of the appropriate solvent, additives, and slow addition of hydrogen peroxide. A large advantage of the presented process is also performing the process of epoxidation in water solution without any other solvents. Moreover, water was not additionally introduced in the reactor, only with the solution of the oxidizing agent it was formed during the process. Water is now regarded as a very ecological solvent for organic processes.


**Author details**

Sebastián Andrés Crespo1 \*, Francisco Javier Fernandoy2 and Ariel Andrés Muñoz1,3

\*Address all correspondence to<EMAIL_ADDRESS>
1 Geography Institute, Pontifical Catholic University of Valparaiso, Valparaíso, Chile

2 Isotope Analysis Laboratory (LAI), Faculty of Engineering, Andrés Bello University, Viña del Mar, Chile

3 Center for Climate and Resilience Research [CR2], Chile


**1. Introduction**

Because of their low cost, flexibility, mobility, and ease of integration, Wireless Sensors (WS) are increasingly used in most computing systems. For example, WSs are used for ubiquitous structural monitoring [1]. Besides, one of WS's current major applications is the Internet of Things, in which WSs send their data to a base station that makes it available on the internet. WS provides endless opportunities and poses formidable challenges, such as the fact that energy is limited due to its battery's small size. In the quest for solutions to extend the lifespan of WSs, a new research field has evolved in recent years, known as Energy Harvesting (EH) [2]. Thanks to EH techniques, it is now possible to envisage WSs having a lifespan limited only by the hardware that constitutes them. These WSs are now well known in the literature as EH-WS [3]. The rise of the EH-WSs is due to the joint efforts in the fields of microelectronics and micro-mechanics, which today make it possible to dispose of ultra-low consumption WSs. An EH process involves identifying a primary energy source in the WS vicinity and converting it into electrical energy directly usable by the WS. This study deals with RF energy, which is ubiquitous due to the extension of telecommunications systems [4].

The proposed techniques about EH rely fully on the nature of the used primary energy sources. The main sources are the sun, vibration, thermoelectric gradient, wind, internal light, radio-frequency energy, etc. Vibration and sun sources are most considered in the literature because they generate more significant amounts of energy compared to the WS energy requirements. Recently, with the growth of radio communication systems deployment, it has become possible to consider harvesting significant quantities of RF energy in different environments. Besides, RF sources do not rely on weather conditions, as is the case with the sun source or engine operation, as would be the case with the vibration source.

This chapter presents the design considerations of energy-independent wireless sensor nodes under the base of a radiofrequency energy harvesting process. The main objective is to analyze the end-to-end conversion chain of radiofrequency waves into DC energy to define the design issues related to this growing field of research. For each stage, it will be reviewing the principles through design equations and optimization solutions. This main goal will guide the writing of the chapter, with the following specific objectives:

Firstly, the advantage of the RF energy source compared to the other commonly used primary energy sources is proposed in Section 2. The role of wireless sensors in the IoT and the capability of some currently marketed RF energy harvesters will be presented in Section 3. Section 4 dealt with the design issues of the RF energy harvesting systems. Each stage of the conversion chain will be analyzed, and the advantages and drawbacks of the proposed solutions will be established. Finally, Section 5 concludes this chapter.

#### **2. Comparison of RF source with other primary energy sources**

The primary energy sources considered for EH are vibration, sun, RF Energy, airflow, internal light, heat, and wind. Most computing systems require small and light WSs to influence the measurement environment as little as possible. Therefore, the power density metric is widely used by many researchers as a criterion for comparing the performance of micro-generators [5]. **Table 1** show some recent results obtained in the design of the various micro-generators [6]. These results indicate that the current RF micro-generators have power density comparable to sources such as airflow, heat, and indoor light.

Sources like vibrations and sunlight offer power densities 10 to 100 times higher than the RF source. However, in most studies on vibrations, to achieve these performances, it is necessary to increase the level of vibration, which is not desirable for many industrial applications, especially sensor applications. In [7], for instance, a piezoelectric micro-generator is designed to generate only *23:3 nW* for

*Radiofrequency Energy Harvesting for Wireless Sensor Node: Design Guidelines and Current… DOI: http://dx.doi.org/10.5772/intechopen.97627*

#### **Table 1.**

*Comparison of the some power density of Main energy harvesting methods.*

*0:25* g acceleration at a frequency of *68 Hz*. It is also foreseeable that the popularity of piezoelectric micro-generators will be declining in future years, as several research projects today are exploring solutions to reduce significantly or attenuate the vibration of engines [8].

Regarding solar energy, the achieved performance is inherently impacted during the night. Also, for WSs being deployed in indoor environments like buildings or factories, solar energy may not be available. Wind micro-generators share this constraint. These also often involve a substantial aperture [9], which is not suited to accommodate IoT applications'size design limitations. RF Energy, which, for some frequencies, can cross materials such as water, plastic, paper, and concrete, seems to be the only alternative in several situations. This research area is now expanding because this harvestable energy (RF energy) is almost always available, offering solutions to facilitate the supply of WS located in hard-to-reach environments.

Another asset of the RF source lies in the used transducer, as it can also be exploited to exchange data between sensors wirelessly. The primary transducers used are shown in **Figure 1**. The WS for transmitting and receiving information

**Figure 1.** *Some used transducers for the transformation of ambient energy.*

usually uses an antenna. The transducer for the RF source is, therefore, the same as that used by the WS to communicate. Thus, it is important for greater circuit miniaturization to consider using the RF source [10]. It is also the current trend of WS based on RF source referred to as Simultaneous Wireless Information and Power Transfer (SWIPT) technologies [11].

### **3. Autonomous wireless sensors in IoT and Mobile computing**

Setting up the IoT is now possible thanks to the convenience of placing or deploying many different sensors in an environment. **Figure 2** shows the end-toend IoT basic architecture elements [12]. The WS is the element that lays the foundation for IoT. Unlike other elements in **Figure 2** that can be placed in easily accessible locations, WSs must be able to be placed in locations such as battlefields, the deep ocean, or inhospitable terrains. Since WSs are battery-powered, it is often difficult and impossible to change or recharge their battery. Also, the WS's role in the figure below is to measure, process, and transmit data to a base station. More and more IoT applications require fast computational times, increasing the WS's energy budget. This further justifies the need for a ubiquitous charging solution such as the RF source for WS in mobile devices.

Regarding RF micro-generators, a product like the PCC110 [13] manufactured by Powercast, is a solution used to enable wireless power transmission. Its sensitivity is 17 dBm with a maximum conversion efficiency of 75%. Powercast also markets the P2110 [14], which harvests RF energy in the 915 MHz band while integrating efficient energy management solutions. This circuit can operate at incident powers below 11.5 dBm. It is also proposed in [15] the E-peas AEM40940, which offers RF energy harvesting solutions in three frequency bands 868 MHz, 915 MHz, and 2.45 GHz. This circuit offers usable DC output powers for incident RF powers between 19.5 dBm and 10 dBm. Due to the flexibility of the charging solution, these different circuits are a few examples that can be integrated into computing systems, particularly in mobile IoT applications.

**Figure 2.** *End-to end IoT architecture.*

#### **4. Design issues of rectenna circuit**

When observing at the end-to-end conversion efficiency of a rectenna, it is necessary to consider the energy propagation models, the receiving antenna, the characteristics of the rectifying diodes (RF/DC Converter), the matching filter design, and finally, the Storage Element as shown in **Figure 3**.

Energy propagation models can be used to estimate the harvestable energy levels depending on the propagation environment [16]. The receiving antenna must be designed to be optimal in the frequency band of the harvestable RF signals. The used rectifying diode must have the least loss in the targeted frequency band. The matching filter must be optimized to minimize reflection losses. A DC/DC converter is added to achieve Maximum Power Point Tracking (MPPT). Finally, when the rectenna is designed, its modeling is necessary to offer an efficient management *Radiofrequency Energy Harvesting for Wireless Sensor Node: Design Guidelines and Current… DOI: http://dx.doi.org/10.5772/intechopen.97627*

**Figure 3.** *Outline of design issues of rectenna.*

solution for the energy harvested. Note that once the components to achieve optimal performance are selected concerning the concepts overviewed, circuit manufacturing must be addressed; this chapter does not address this issue.

#### **4.1 Classification of the different techniques**

When considering the use of RF energy as a power source for WSs, it is important to distinguish the Ambient RF Energy Harvesting (A-RF-EH) from Wireless Power Transfer (WPT) [17, 18] (**Figure 4**). The A-RF-EH aims to recycle energy available in the environment that comes from wireless communication devices' surrounding activity, as shown in **Figure 4(a)**. Due to potential health concerns, the environment's naturally available RF power levels are too low. However, several designers have been able to propose solutions for harvesting usable quantities of power. These solutions rely mainly on circuits' design capable of harvesting RF energy through several frequency bands simultaneously [19].

Another way to exploit RF energy is to use the WPT, as illustrated in **Figure 4(b)**. The WPT can be done either using magnetic fields to carry the electrical energy with coils or by antennas. In the case of coils, the original proposal was made by Nicolas Tesla [20] and is based on the magnetic resonance of two coils to distribute large amounts of energy to locations far from the power source. Although this concept is used by many applications such as Radio Frequency IDentification (RFID) tags [21] and biomedical devices [22], it should be mentioned that its range is limited. It would, therefore, be challenging to implement for WSs placed in hard-to-reach locations. In addition to the constrained range, the power levels are too high, bringing health issues and effects [11] when someone is close to the transmitter.

The most popular way to power the WS by RF energy is by using antennas. As opposed to the near-field application, the use of antennas is known as the far-field application. Historically, this way of transferring energy via radio waves dates to the first works of Heinrich Hertz [23]. The block diagram of the conversion of RF into DC energy via antennas is depicted in **Figure 5** [17]. A transmitting antenna sends a signal at a given power and frequency. A receiving antenna operating on the same frequency then picks up the emitted signal. An RF/DC converter is used to transform the RF signal into a DC signal. To ensure maximum power transfer between the antenna and the RF/DC converter, it is essential to use a matching circuit. The rectifier's output DC voltage is generally very low and cannot be used directly for a given application. Moreover, the value of the output DC voltage changes depending on the input RF power level. A DC-to-DC converter is thus necessary to adapt the

**Figure 4.** *The technique of RF-EH. (a) A-RF-EH and (b) WPT.*

*Radiofrequency Energy Harvesting for Wireless Sensor Node: Design Guidelines and Current… DOI: http://dx.doi.org/10.5772/intechopen.97627*

**Figure 5.**

*Generalized RF energy harvesting systems for WS.*

rectifier voltage to the storage element's voltage requirement. The combination made up of these blocks is called *rectenna* for Rectifying Antenna. The rectenna circuits' design issues then concern the channel's modeling between the transmitting and the receiving antenna, the receiving antenna's designs, the matching circuit, the rectifying circuit, the DC-to-DC converter, and finally, the choice of the storage element [24].

#### **4.2 RF propagation models**

The energy amount and rate received by an antenna over time are two critical parameters to be considered before the circuit design [25]. Several propagation models exist to predict the average strength of the signal received at a given distance from the transmitting antenna [16]. These models are divided into two broad kinds: large-scale and small-scale fading models.

The large-scale models are used to assess the received signal's strength over large distances between the transmitting antenna and the receiving antenna; they are then suitable for designing a WS based on the WPT. The basic model is the free space model; it is an ideal model used when the transmitting antenna and the receiving antenna have an unobstructed path. The received power is evaluated by the Friis equation as follows:

$$P\_r = P\_t \frac{G\_t G\_r \lambda^2}{(4\pi d)^2} \tag{1}$$

where *Pt* is the transmitting power, *Pr* is the power received at distance *d*, *λ* is the wavelength of the transmitted signal, *Gt* and *Gr* represent the gains of the emitting and receiving antennas, respectively.

Practically, to evaluate the received power by an antenna, three basic mechanisms must be considered: reflection, diffraction, and scattering [16]. When considering ground reflection only, the Eq. (2) known as the two-ray model evaluates the received power as:

$$P\_r = P\_t G\_t G\_r \frac{h\_t^2 h\_r^2}{d^4} \tag{2}$$

where *Pr*,*Pt*,*Gt*,*Gr* and *d* are defined as above, *ht* and *hr* represent the heights of the transmit and receive antennas, respectively.

Considering all the factors influencing signal propagation (reflection, diffraction, and scattering) can be done through models derived from the combination of empirical and analytical methods [16], these models are widely used. The most popular is the path loss model, which defines the received power in a complex environment as follows:

$$P\_r(d, n) = P\_\mathbf{r}(d\_0) \left(\frac{d\_0}{d}\right)^n \tag{3}$$

*d0* is a is a reference distance (*d0* ¼ *1 m* [16]) and *n* is the path loss exponent. The value of *n* always relates to the propagation environment features. *Pr*ð Þ *d0* is the received power at the *d0* distance.

The current trend of WS powered by rectenna is the SWIPT, referred to as Simultaneous Wireless Information and Power Transfer [11]. The small-scale fading models are used to quantify the received power by a node, from a node close to it. The fading models allow evaluating the rapid fluctuations of the emitted signal's amplitude over a short period or for a short distance. Fading models consider the multiple versions of the emitted signal that reach the receiving antenna. If *N* is the total number of possible equidistant multi-path components, then the instantaneous power received when a continuous signal is emitted is given by [16]:

$$p(t) = \left| \sum\_{i=0}^{N-1} a\_i \exp\left( |j\theta\_i(t,\tau)| \right) \right|^2 \tag{4}$$

where *ai* and *θi* are respectively, the amplitude and phase of the ith received signal, and *τ* is the maximum delay.

The above summarizes some commonly used RF energy propagation models. Depending on the WPT or the A-RF-EH, deterministic models or stochastic models can be used, respectively. These models must be considered before circuit design because they make it possible to estimate the amount of harvestable energy.

#### **4.3 The receiving antenna**

Its role is to adequately capture the emitted signal with the right and high gain. However, the increase of the antenna gain goes with an increase in its dimensions through the equation:

$$G\_{\mathbb{R}} = \frac{4\pi A\_{\epsilon}}{\lambda^2} \tag{5}$$

*Ae* is the effective surface of the antenna, which is linked to its physical dimensions [16]. High-gain antennas are also obtained by favoring directional antennas over omnidirectional antennas. This has shown to be more effective in SWIPT [26].

To maximize the energy harvested by the antenna, particularly in the case of A-RF-EH, the studies report multi-band, broadband, and reconfigurable [27] antennas to overcome a lack of knowledge of the transmitting antennas' location and frequency.

Another important feature of the receiving antenna is its polarization, which must be circular to offer the possibility of keeping a constant DC output voltage even if the transmitting antenna or the rectenna [28] are rotating. The most widely used antennas are the dipole antennas, and the patch antennas. Since most applications have congestion as a design criterion, the patch antenna allows for easy integration; it is lightweight, low-cost, and widely considered in rectenna design. Also, these antennas are adapted to future 5G communication specifications [29]. The well-known structure of a patch antenna is shown in **Figure 6**.

The resonance frequency of the antenna, which must be the same as that of the transmitted signal, is related to length *L* of the patch by [30]:

*Radiofrequency Energy Harvesting for Wireless Sensor Node: Design Guidelines and Current… DOI: http://dx.doi.org/10.5772/intechopen.97627*

$$L = \frac{1}{2f\_r\sqrt{\mu\_0 \varepsilon\_0 \varepsilon\_\epsilon}} - 2\Delta L \tag{6}$$

*μ0* and *ε0* represent the permeability and the dielectric permittivity of the vacuum respectively, *ΔL* is the length extension of the patch defined as:

$$
\Delta L = 0.412h \frac{(\varepsilon\_\varepsilon + 0.3) \left(\frac{W}{h} + 0.264\right)}{(\varepsilon\_\varepsilon - 0.258) \left(\frac{W}{h} + 0.8\right)}\tag{7}
$$

where *εe* is the effective permittivity of the substrate, which is related to the relative permittivity as follow [31]:

$$
\varepsilon\_{\epsilon} = \frac{\varepsilon\_r + \mathbb{1}}{2} + \left(\frac{\varepsilon\_r - \mathbb{1}}{2}\right) \left(\mathbb{1} + \frac{\mathbb{1} 2h}{W}\right)^{-\frac{1}{2}} \tag{8}
$$

The thickness *h* of the substrate shall satisfy the following condition:

$$h \le \frac{1}{4f\_r\sqrt{\mu\_0\varepsilon\_0(\varepsilon\_r - 1)}}\tag{9}$$

The width *W* of the patch influences the impedance of the antenna as well as its bandwidth. It is also related to the resonance frequency *fr* of the antenna as follows:

$$\mathcal{W} = \frac{1}{2f\_r} \sqrt{\frac{2}{\mu\_0 \varepsilon\_0 (\varepsilon\_r + 1)}}\tag{10}$$

In most design strategies, the formulas (6) to (10) are used for the first sizing of the antenna, and then the optimization is done using an electromagnetic simulator. **Table 2** shows the gain capabilities for some patch antennas recently designed for rectenna applications.

#### **4.4 RF/DC converter**

To be able to supply the WSs with DC power, the RF power harvested by the antenna needs to be rectified. The RF/DC converter assumes this function. The rectification function can be implemented either by transistors or with Schottky diodes. Transistors are least-used because although they are more efficient at very

**Figure 6.** *3D view of the rectangular patch antenna.*

#### **Table 2.**

*Recent patch antennas gain for rectennas design.*

**Figure 7.** *Small signal model of a Schottky diode.*

low levels of RF input power [35], the achieved maximum conversion efficiency remains too low compared to that obtained with Schottky diodes [24]. For this reason, the subsequent writing deals only with design issues based on Schottky diodes. The fast switching and low threshold voltage diodes are the most considered by considering the high frequencies and the low voltage level of the incident or input RF signals. The small-signal Schottky diode model shown in **Figure 7** is very often used [36].

In this model, *RS* is the bulk series resistance, *RL* is the load resistance, *Rj* is the junction resistance, *VDC* is the voltage across the load resistance, and *Cj* is the junction capacitance, which depends on the RF input power as follows [36]:

$$\mathbf{C}\_{j} = \mathbf{C}\_{j0} \sqrt{\frac{\mathbf{V}\_{j}}{\mathbf{V}\_{j} + \mathbf{V}\_{\text{DC}}}} \tag{11}$$

with *C j0*, the zero-bias junction capacitance of the Schottky diode.

The leading manufacturers of the commonly used diodes are Avago, Skyworks, and Macon. **Table 3** gives the characteristics of some of the Schottky diodes most considered in the design of RF/DC converters.

In the previous subsection devoted to the receiving antenna, it was mentioned that patch antennas, being compact, lightweight, and low-cost, are the most suitable for the real applications of WSs for which congestion is one of the design constraints. However, compared to other antennas, patch antennas are narrowband and offer lower gains. Thus, the rectifying diode's conversion efficiency has become a critical design criterion for rectenna circuits [37].

*Radiofrequency Energy Harvesting for Wireless Sensor Node: Design Guidelines and Current… DOI: http://dx.doi.org/10.5772/intechopen.97627*

**Table 3.**

*Small-signal characteristics for commonly used Schottky diodes.*

**Figure 8.** *Efficiency link of RF/DC power conversion.*

#### *4.4.1 Conversion efficiency of the rectifying diode*

When considering the transformation of the RF signal into a DC signal, the energy harvested by the antenna undergoes the four-stage losses shown in **Figure 8**. These losses are a significant factor in the choice of the rectifying diode.

The matching efficiency *ηM* represents the losses due to the insertion of a matching filter between the antenna and the rectifier circuit, and it is defined in [17] by:

$$\eta\_M = \mathbb{1} - \left| \mathbb{S}\_{110} \right|^2 \tag{12}$$

where *S110* is the unmatched reflection coefficient defined in [38] as:

$$S\_{110} = \frac{Z\_D - Z\_0}{Z\_D + Z\_0} \tag{13}$$

*Z0* is the output impedance of the antenna, which is generally designed to be equal to *50 Ω*, and *ZD* is the diode input impedance seen from the antenna. Depending on the internal electrical elements of the diode (Cf. **Figure 7**), *ZD* is expressed as follows [36]:

$$Z\_{D} = \frac{\pi R\_{S}}{\cos \theta\_{\text{on}} \left(\frac{\theta\_{\text{on}}}{\cos \theta\_{\text{on}}} - \sin \theta\_{\text{on}}\right) + j\alpha R\_{S} C\_{j} \left(\frac{\pi - \theta\_{\text{on}}}{\cos \theta\_{\text{on}}} + \sin \theta\_{\text{on}}\right)}\tag{14}$$

with *ω* ¼ *2πf*, which is the pulsation of the rectenna, and *θ*on is the diode forward-bias turn-angle. *θ*on changes according to the incident power as follows:

$$
\tan \theta\_{\text{on}} - \theta\_{\text{on}} = \frac{\pi R\_S}{R\_L \left(1 + \frac{V\_j}{V\_{\text{DC}}}\right)} \tag{15}
$$

Considering Eqs. (13)–(15), an approximate expression of the unmatched reflection coefficient was established in [35] as follows:

$$|\mathbf{S}\_{\mathcal{H}0}| \approx \frac{\mathbf{R}\_j + (\mathbf{R}\_S - \mathbf{50}) \cdot \left(\mathbf{C}\_j^2, \mathbf{R}\_j^2, \alpha^2 + \mathbf{1}\right)}{\mathbf{R}\_j + (\mathbf{R}\_S + \mathbf{50}) \cdot \left(\mathbf{C}\_j^2, \mathbf{R}\_j^2, \alpha^2 + \mathbf{1}\right)} \tag{16}$$

From this expression, the conclusion is drawn that at high frequencies, when *C2 j :R2 j :ω2* ≥*1*, it is sufficient that *RS* is close enough to *50 Ω* to ensure a minimum reflection coefficient, and thus also to minimize the matching losses.

*ηP* in **Figure 8** is the efficiency associated with parasitic losses; parasitic being undesired mechanical and electrical characteristics that limit the performance of the circuit. The parasitic component efficiency defined in [39] as:

$$\eta\_P = \frac{1}{\left(\mathbb{1} + \left(\alpha \mathbf{C}\_{\bar{\jmath}}\right)^2 \mathbf{R}\_S \mathbf{R}\_{\bar{\jmath}}\right)^2} \tag{17}$$

*ηRF=DC* in **Figure 8** is the RF/DC conversion efficiency; it is related to the elements of the diode through the following Equations [33, 36].

$$
\eta\_{\rm RF/DC} = \frac{\mathbf{1}}{\mathbf{1} + \mathbf{A} + \mathbf{B} + \mathbf{C}} \tag{18}
$$

with

$$\begin{cases} A = \frac{R\_L}{\pi R\_S} \left( 1 + \frac{V\_j}{V\_{\rm DC}} \right)^2 \left[ \theta\_{\rm on} \left( 1 + \frac{1}{2 \cdot \cos^2 \theta\_{\rm on}} \right) - 1, 5 \tan \theta\_{\rm on} \right] \\\\ B = \frac{R\_S R\_L C\_j^2 \omega \sigma^2}{2 \pi} \left( 1 + \frac{V\_j}{V\_{\rm DC}} \right) \left[ \frac{\pi - \theta\_{\rm on}}{\cos^2 \theta\_{\rm on}} + \tan \theta\_{\rm on} \right] \\\\ C = \frac{R\_L}{\pi R\_S} \left( 1 + \frac{V\_j}{V\_{\rm DC}} \right) \frac{V\_j}{V\_{\rm DC}} [\tan \theta\_{\rm on} - \theta\_{\rm on}] \end{cases} \tag{19}$$

*ηDC=*Load in **Figure 8** represents the efficiency of DC power transfer; it is defined in [40] as follows:

$$
\eta\_{DC/Load} = \frac{R\_L}{R\_L + R\_T} \tag{20}
$$

where *RT* ¼ *RS* þ *RjI*Load [41] is the Thevenin resistance seen by the load, and *RL* is the load resistance. To maximize *ηDC=*Load, it is necessary to use a Maximum Power Point Tracking (MPPT) circuit.

Using Eqs. (12), (17), (18) and (20), a comparison of the RF/DC conversion efficiencies of the four Avago diodes, whose characteristics are reported in **Table 3**, was proposed in [33]; the obtained results are concise in **Table 4**. These results show that, for usable power levels [42], the HSMS 2850 diode is more suitable for circuit design.

#### *4.4.2 Rectifier topology selection*

Once the diode is selected, it is necessary to consider the topology of the rectifier circuit. Some rectifier topologies recently used in the rectenna design are shown in **Figure 9**. The most considered are the topologies Single Series Diode (SSD), Single Parallel Diode (SPD), Full Bridge (FB), and Voltage Doubler (VD) [43]. The SSD

*Radiofrequency Energy Harvesting for Wireless Sensor Node: Design Guidelines and Current… DOI: http://dx.doi.org/10.5772/intechopen.97627*

**Table 4.**

*Best Avago rectifier diode according to the incident power level.*

**Figure 9.**

*Most used rectifier topologies (a) SSD, (b) SPD, (c) FB, (d) VD, and (e) multistage VD.*

and SPD topologies are single-wave rectifiers, while the FB and VD topologies are full-wave rectifiers.

The characteristics of these basic topologies are proposed in **Table 5**. A comparison of the three topologies SSD, SPD, and FB, was proposed in [43] using a Rectenna Figure of Merit (RFoM) defined as follow:

$$\text{RFoM} \left( P\_{\text{in}} \right) = V\_{\text{OC}} \times \eta\_{\text{optimal load}} \tag{21}$$

where *V*OC is the open-circuit voltage of the rectifier and *η*optimal load is the conversion efficiency reached on the optimal load of the rectifier circuit. The results obtained in [43] are that the SSD topology is best suited for the low level of input power ð�*5* dBm to *0* dBm), while the SPD topology is the most efficient for medium input power level (*0* to þ*15* dBm); finally, the FB topology fits better for rectennas operating at so-called high incident power levels (> *15* dBm). However, in the literature, the most widely used topology is VD because of its voltage multiplier character [33].

It is also possible to amplify the rectified output voltage several times using several stages of voltage doubling (**Figure 9e**) [44]. When *n* voltage doublers are set in series and connected to the load *RL*, the output voltage across the load is expressed in [30, 45] as:

$$V\_{DC} = V\_{OC} \frac{nR\_L}{nR\_0 + R\_L} \tag{22}$$

where *RL* is the load resistance of the rectifier and *V*OC it open-circuit voltage.

#### **Table 5.**

*Comparison of main rectifier topologies.*

Although multi-stage VD can achieve significant voltage levels, the fact remains that they contribute to increasing the overall size of the rectenna. Also, the increase in components in the circuits contributes to an increase in losses. This is illustrated in **Figure 10**, in which up to 10 stages of voltage doublers were analyzed by simulation with Advanced Design System (ADS) software.

**Figure 10.** *Mutistage VD analysis. (a) Open circuit voltage, (b) efficiency, (c) RFoM.*

*Radiofrequency Energy Harvesting for Wireless Sensor Node: Design Guidelines and Current… DOI: http://dx.doi.org/10.5772/intechopen.97627*

#### **4.5 Impedance matching**

In addition to ensuring maximum power transfer between the antenna and the rectifier circuit, it also blocks the diode's harmonics. There are two main types of matching filters for rectennas: the transformer coupling and the LC network. LC networks are more popular and better suited for designing rectennas because of their ease of integration. The LC networks are made of reactive elements (coil and capacitor) which are non-dissipative [24]. The primary LC network is the low pass filter whose cutoff frequency is defined in [38] as:

$$f\_{\theta} = \frac{1}{2\pi\sqrt{\text{LC}}}\tag{23}$$

The parameter for qualitatively characterizing the adaptation is the reflection coefficient of the set consisting of the RF/DC converter and the input filter. A value of �*10 dB* is acceptable, according to [38], to ensure the maximum transfer of the harvested energy.

Very few analytical studies on the design of matching filters for rectenna circuits have been introduced in recent years. This is due to the power of the ADS software [33], which incorporates many tools to design and optimize the matching filter elements. In summing up the works [33, 46], the steps for creating a matching filter from the ADS software are shown in **Figure 11**.

It is shown (Cf. **Figure 11**) that from the reflection coefficient of the rectifier circuit, the ADS matching utility tool is used to generate the matching filter in a lumped component. These localized elements are the initial parameters that will then be optimized to achieve specific objectives. Three objectives are generally targeted simultaneously: the minimization of the reflection coefficient in the frequency band of interest, the maximization of the conversion efficiency, and the maximization of the DC output voltage for the expected input RF power level. The ADS software integrates several optimization techniques, the principal ones being: Hybrid, Newton, Quasi-Newton, Gradient, and Random technique. The gradient method search is the most widely used and allows for adjusting a set of variables according to an error function and its gradient. The error function usually used is the least-squares error function. Once the matching filter elements are optimized, the next step in the filter design is the transformation of the lumped component into a microstrip line. Then, the electromagnetic momentum simulator, always integrated into the ADS software, is used to predict the circuit's performance at high frequencies. This tool is used to create a physical layout to simulate the characteristics of the substrate.

Following the design steps, which are shown in **Figure 11**, it was proposed in [33], a Rectenna-based Schottky diode HSMS 2850, with a band-pass filter for an

#### **Figure 11.**

*Design step of an optimized matching filter in ADS software.*

**Figure 12.**

*Optimized rectifier performance at 2.45 GHz [33]. (a) DC output voltage, (b) Conversion Efficiency, (c) reflection coefficient.*

optimal RF harvesting at *2:45 GHz*. The results of the DC output voltage, the reflection coefficient and the conversion efficiency obtained by the gradient method search are shown in **Figure 12**. The local minimum is reached after 63 iterations, and at this point, the circuit demonstrates a conversion efficiency of nearly *71*% for an incident power of�*2:1 dBm 0*ð Þ *:61 mW* .

#### **4.6 DC/DC converter**

Most rectennas deployed in a real environment have low and variable DC output voltage due to slight fluctuations in RF input power. The voltage levels achieved cannot, therefore, directly feed the storage element. The DC / DC converter's function is then to adapt the output voltage of the rectifier to the charging voltage of the storage element. Several DC/DC converters are commercially available. For the case of rectennas design, the most suitable circuits are those with a low start-up voltage, a minimum operating power, and a high conversion efficiency over a wide range. The most appropriate circuits are then the TS3310 of TouchStone and bq25504 of Texas Instrument. A comparison of these two DC/DC converters has been proposed in [47], and it has emerged that the bq25504 converter offers better performance. However, it is less suitable for high dynamic variations of rectenna input power.

#### **4.7 Storage element**

Because the harvested RF energy is extremely low, it is difficult to use it to power the WS directly, hence the need for a storage element to accumulate this energy for later use. There are three main components currently used to store harvested energy: the battery, the capacitor, and the supercapacitor. Regardless of the type of the used component, the main features are capacity, voltage, energy density, power density, self-discharge, discharge depth, state of charge, and temperature effects. A comparison of the characteristics of these three components has been proposed in [48]. This study emerges that the supercapacitors can provide high power over a short time; however, the stored energy is ten times lower than that stored in a battery. This justifies the current trend of hybrid storage devices that combine both batteries and supercapacitors [49]. However, in the case of a rectenna, this solution would contribute to increasing the circuit sizes. Thus, for most rectennas involved in WSs, the energy density parameter is the most considered parameter, and it is the battery that offers the best energy density [48]. Depending on the output voltage levels of the DC/ DC converter and the desired energy *E* for the operability of the WS, the capacitance *Cb* of the battery is defined as:

$$C\_b = \frac{2E}{V\_h^2 - V\_\ell^2} \tag{24}$$

*Radiofrequency Energy Harvesting for Wireless Sensor Node: Design Guidelines and Current… DOI: http://dx.doi.org/10.5772/intechopen.97627*

where *Vh* and *Vℓ* represent the raising threshold voltage and the falling threshold voltage of the DC/DC converter, respectively.

The general design method of WS powered by rectenna is to enslave the WS operation to the available amount of energy. Therefore, one of the major design issues is the battery recharging time, known in the literature as the duty cycle strategy. The battery recharging time knowledge helps define the duty cycle of sensors powered by the harvested energy. Depending on the battery features used, the recharging time is defined in [50] by:

$$T\_r = \frac{C\_b D\_d V\_b}{\eta P\_r} \tag{25}$$

where *Cb* is the battery capacity, *Dd* is the discharge depth, *Vb* is the constant operating voltage (must be chosen equal to the output rectifier DC voltage), *Pr* is the power harvested by the receiving antenna and *η* is the overall conversion efficiency of the rectenna defined as:

$$
\eta = \eta\_{\text{M}}.\eta\_{\text{P}}.\eta\_{\text{RF}/\text{DC}}.\eta\_{\text{DC}/\text{Load}}\tag{26}
$$

*\* is an efficiency achieved without the use of a matching filter.*

*\*\*is the overall conversion efficiency considering the RF signal path losses.*

#### **Table 6.**

*Some recent rectenna circuit performances.*

For the WS's perpetual operation, the recharging time must be equal to the time delay spent, by sensor nodes, in the sleep mode, and the energy used during the active mode must avoid draining the battery.

All the above shows that the performance of rectenna circuits depends on several parameters that have been defined in this chapter. The most considered performance criterion is the conversion efficiency of the Rectenna. A comparison of efficiency for circuits designed between 2006 and 2014 was reported in [24]. In **Table 6**, the performances of recent designs are presented. Particular attention is paid to the rectifying diode used, as well as the rectifier topology.

## **5. Conclusion**

This chapter reports recent advances in the design of radiofrequency energy harvester circuits. To do this, we started by justifying the use of the RF source as a primary energy source for feeding the sensor nodes dedicated to the IoT networks. The need for completely energy-autonomous WSs in mobile computing systems has also been highlighted. We then gave an overview of the efforts carried out in the design of rectenna circuits. Current limitations due mainly to health concerns and circuit size were also mentioned. More specifically, a classification of harvesting techniques was defined, the different models of energy propagation were reviewed. The performance of the receiving patch antennas recently designed for IoT applications has been noted. The performance comparison of recently used rectifying diodes and the areas of use of the main rectifier topologies were also proposed.

### **Conflict of interest**

"The authors declare no conflict of interest."

## **Author details**

Alex Mouapi\*, Nadir Hakem and Nahi Kandil Underground Communications Research Laboratory, University of Quebec in Abitibi-Temiscamingue (UQAT), Val d'Or, Quebec, Canada

\*Address all correspondence to<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Radiofrequency Energy Harvesting for Wireless Sensor Node: Design Guidelines and Current… DOI: http://dx.doi.org/10.5772/intechopen.97627*


# **Molecular Biology of Selenium in Health and Disease**

Edited by Petra A. Tsuji and Dolph L. Hatfield

Printed Edition of the Special Issue Published in *International Journal of Molecular Sciences*

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## **Molecular Biology of Selenium in Health and Disease**

### **Molecular Biology of Selenium in Health and Disease**

Editors

**Petra A. Tsuji Dolph L. Hatfield**

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*Editors* Petra A. Tsuji Department of Biological Sciences, Towson University USA

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**1. Introduction**

Olivine is one of the simplest silicate minerals, and the general crystal chemical formula of which is (A)2SiO4, where A—Mg2+, Fe2+, Mn2+, etc. The olivine crystal structure is orthorhombic with a slightly distorted hexagonal close packing array of oxygen atoms. Si is on tetrahedral interstices and Mg and Fe ions are on octahedral sites (labeled M1 and M2). The M1 site is a distorted octahedra at the center of symmetry whereas M2 is a regular octahedra on the mirror plane [1–4]. Olivine is a general name of forsterite-fayalite sold solution [5]. In addition to the complete isomorphism of Mg and Fe, olivine also contains some petrogenetically significant minor components, such as B, Li, Co, P, and As [4,6,7].

A growing body of crystal structure and spectroscopy investigations have been carried out on both synthetic and natural olivine over the past few years. The majority of the previous studies have primarily focused on crystal structure refinement [3,4,8,9], the effect of temperature and pressure on the crystal structure [10–14], the chemical composition of the forsterite-fayalite series determination [15,16], residual pressure calculation [17], and water content estimation [18]. Although extensive studies have been conducted on olivine over a range of compositions, temperatures, and pressures using a variety of methods, more research is needed on several aspects of the properties of B-rich olivine.

Boron is a typical crustal element with high concentrations in rocks closely related to continents and rocks interacting with the hydrosphere, but low concentrations in mantle

**Citation:** Peng, B.; He, M.; Yang, M.; Wu, S.; Fan, J. Natural Forsterite Strongly Enriched in Boron: Crystal Structure and Spectroscopy. *Crystals* **2022**, *12*, 975. https://doi.org/ 10.3390/cryst12070975

Academic Editor: Carlos Rodriguez-Navarro

Received: 21 June 2022 Accepted: 11 July 2022 Published: 12 July 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

peridotite [19,20]. B-rich olivine, associated with clinohumite K-rich pargasite, uvite, spinel, magnetite, ludwigite, and sinhalite, was first described from the Tayozhnoye Fe deposit of Russia [21]. Sykes et al. [22] studied the infrared spectrum and transmission electron microscopy of B-rich olivine and presented the first direct evidence of coupled substitution of boron and hydrogen for silicon. More precise and complex coupled substitution mechanisms were presented by Kent and Rossman [6] and Gose et al. [23]. More recently, Ingrin et al. [24] identified the position of the OH bands associated with the boron substitution through the infrared spectrum. Unfortunately, due to the incompatibility of boron in olivine, the connection between boron and olivine is often neglected. Hence, we addressed the key question: Whether the incorporation of B in olivine will affect the structure of olivine? Whether the Raman spectrum and infrared spectrum of boron-containing olivine be different from those of boron-free olivine? Additionally, most previous studies on the B-contained olivine were performed on synthetic olivine. Therefore, it is inevitable to investigate the properties of natural B-rich olivine.

In this paper, we report a new occurrence of natural end-member forsterite in Jian forsterite jade from Jilin province, China. Besides the high content of Mg, this forsterite has another unusual feature, namely strong enrichment by B. We present chemical composition, single crystal X-ray diffraction, Raman spectrum, and infrared spectrum studies for B-rich forsterite. Our results refine the crystal structure of B-rich forsterite and provide strong evidence for the coupled substitution of H and B for Si in natural B-rich forsterite. This study presents a basis for understanding the formation of natural B-rich forsterite.

#### **2. Materials and Methods**

The natural B-rich forsterite crystals, directly selected from the Jian forsterite jade, were used for detailed data analyses. The Jian forsterite jade is a new type of jade that has been recently found in the Jian area of northeast China [25]. It is mainly composed of forsterite, serpentine, and brucite (Figure 1a,b). We crushed the jade to 60–80 mesh, and hand-picked crack-free and inter-transparent olivine particles under binoculars for analysis. The size of the selected forsterite is 0.3–1 mm (Figure 1c,d). Forsterite with Fo~91 in mantle peridotite xenolith from Jilin province, China was chosen for comparison (Sample O-1 and O-2).

**Figure 1.** Sample photographs. (**a**) the Jian forsterite jade. (**b**) 40× magnification observation of (**a**) under gem microscope. (**c**) and (**d**) hand-picked B-rich forsterite.

The chemical compositions of forsterite were obtained on polished thin sections using an EPMA-1720 electron microprobe at the Electron Probe Laboratory, China University of Geosciences (Beijing, China). The primary analyzing settings were a 5 μm beam spot diameter, 10 nA beam, and 15 kV acceleration voltage. The standards used to calibrate the electron microprobe were 52 standard minerals from the SPI Company of the United States, Washington, DC, USA.

In situ trace element analyses were carried out at the Mineral Laser Microprobe Analysis Laboratory (Milma Lab, Beijing, China), China University of Geosciences (Beijing) using Laser Ablation-Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS). An Agilent 7900 ICP–MS fitted with a NewWave 193UC excimer laser ablation system was used. A laser repetition rate of 8 Hz at 3 J/cm3 and a spot diameter of 50 μm were used in the analyses. NIST 610 was used as the external standard, Si was used as the internal standard, and ARM-1 and BCR-2G were used as the monitoring standards.

Single crystal X-ray diffraction measurements were obtained at ambient conditions with a Rigaku Xtalab PRO diffractometer system and HyPix-6000HE detector at the Laboratory of X-ray single crystal diffraction, China University of Geosciences (Beijing). The experiment was conducted with ϕ and Ω scanning mode, and the scanning step size was 0.5. Monocrystalline silicon array was used to conduct monochromatic processing on the wavelength, and X-ray (λ = 0.71073 Å) was used as the diffraction source to collect diffraction data. A 1.2 Kw water cooled microfocus source with a Mo rotor target and multilayer mirrors were used to collect intensity data. The atomic coordinates of samples are provided as CIF files in the Supplementary Materials. COD (entries 3000401) contains the supplementary crystallographic data for this paper.

The Raman spectrum was obtained using a Horiba HR-Evolution Raman microspectrometer with an Ar-ion laser operating at 532 nm excitation at the School of Gemmology, China University of Geosciences (Beijing). A 100 μm entrance slit and a grating with 1200 grooves per mm were used to collect the scattered light. Every Raman spectrum was acquired by 10 scans with 1 cm−1 resolution in the 4000–100 cm−1 range.

The infrared spectrum was obtained using the Tensor 27 Fourier infrared spectrometer at the School of Gemmology, China University of Geosciences (Beijing). All sample analyses adopted the transmission method. The experimental test conditions were as follows: test voltage was 220 V, the resolution was 4 cm−1 with 64 scans, the scanning range was 4000–400 cm−1, and the scanning speed was 10 kHz.

#### **3. Results**

#### *3.1. EPMA*

The chemical composition of olivine is end-member forsterite. All tested samples are compositionally homogeneous. The characteristics of zonation or exsolution lamellae are not observed. The Forsterite is Mg-rich (MgO > 57 wt%), and Fe-poor (FeOtot < 1 wt%). The Fo (100 × Mg/[Mg + Fe], mol%) of forsterite varies from 99.62 to nearly 99.74. The NiO content of this olivine is very low (<0.08 wt%), and the CaO content varies between 0.01 and 0.04 wt%. In addition, forsterite contains a certain amount of fluorine (0.13–1.06 wt%). Olivine in mantle peridotite xenolith is relatively iron-rich with Fo values of ~91. The content of NiO and CaO is higher than that of end-member forsterite. The chemical compositions are listed in Table 1.

**Table 1.** Chemical composition of B-rich forsterite and mantle olivine.

**Table 1.** *Cont.*

## *3.2. LA-ICP-MS*

The main trace element feature of the end-member forsterite is the extremely high content of B (1773.4–1795.91 ppm) (Figure 2). The content of compatible elements Cr, Co, and Ni is depleted. The concentrations of other trace elements are relatively low. Li and Ti concentrations range from 1.93 to 2.62 and 4.17 to 9.61 ppm, respectively. Other elements do not show any notable characteristics. The distribution of trace elements in olivine is very uniform [25]. Detailed trace elements contents are listed in Table 2. The trace element characteristics of B-rich forsterite are different from those of common mantle peridotite [26].

**Figure 2.** The B concentration of forsterite from the Jian forsterite jade compared with olivine from other origins.

**Table 2.** Trace element composition (ppm) of B-rich forsterite.

**Table 2.** *Cont.*

1 b.d.l., Below the detected line.

#### *3.3. Single Crystal X-ray Diffraction*

Crystal data for B-rich forsterite: orthorhombic, space group *Pnma*, a = 10.1918(7) Å, b = 5.9689(4) Å, c = 4.7484(3) Å, α = 90◦, β = 90◦, γ = 90◦, and V = 288.86(3) Å3, Z = 4, T = 293(2)K, μ(MoKα) = 1.16 mm−1, Dcalc = 3.25 g/cm3, 3161 reflections measured (7.998◦ ≤ 2Θ ≤ 60.592◦), 439 unique (Rint = 0.0824, Rsigma = 0.0500) which were used in all calculations. The final R1 was 0.0350 (I > 2σ(I)) and wR2 was 0.0948 (all data). In the crystal structure of forsterite, each structure unit contains one Si site, two cation sites, and three O sites (Figure 3). All the silicon atoms are coordinated to four oxygen atoms to form [SiO4] tetrahedrons and account for one-eighth of tetrahedral voids. Isolated [SiO4] tetrahedron (T) is surrounded by [MgO6] octahedra (M1 and M2). The Si–O bond distances vary from 1.613(3) to 1.6312(14) Å (Table 3). The average O–Si–O bond angle is 109.15◦. As shown in Figure 3, magnesium atoms are coordinated with six oxygen atoms to form [MgO6] octahedra. Two cation M sites M(1) and M(2) are occupied by magnesium atoms. The M(1) site is located at the center of symmetry, while the M(2) site is located on the mirror plane. The Mg1–O bond distances vary from 2.0622(14) to 2.1283(14) Å and the Mg2–O bond distances from 2.049(3) to 2.2068(16) Å. The O–Mg–O angles vary from 71.65(8)◦ to 109.93(9)◦ (Table 3). Table 3 shows bond distances and angles parameters for M1, M2, and T.

**Figure 3.** Unit-cell of B-rich forsterite structure viewed along c and b axes.

Compared with published olivine cell parameters [3,8,13,27–30], B-rich forsterite tested in this study shows the smallest unit cell parameters (Figure 4). As shown in Figure 4a–c, a negative and significant correlation between unit-cell parameters and the Fo value, which is in agreement with the results of Princivalle and Secco [3]. The parameter a is most affected by compositional changes (1/ka > 1/kb > 1/kc). Figure 4d–f show that cell volume and coordination polyhedron volume of tested forsterite are both inversely proportional to

**Bond Distance/Å Bond Angle** (O3–Mg1–O2) = 85.02(7) (O2–Mg1–O1) = 86.53(7) (O2–Mg1–O3) = 94.98(7) (O2–Mg1–O1) = 93.47(7) (Mg1–O1)[2] = 2.0622(14) Å (O3–Mg1–O2) = 94.98(7) octahedra (Mg1–O2)[2] = 2.0816(16) Å (O1–Mg1–O2) = 93.47(7) M1 (Mg1–O3)[2] = 2.1283(14) Å (O3–Mg1–O2) = 85.02(7) (O1–Mg1–O2) = 86.53(7) Average 2.0907 (O1–Mg1–O3) = 105.06(7) (O3–Mg1–O1) = 105.06(7) (O3–Mg1–O1) = 74.94(7) (O3–Mg1–O1) = 74.94(7) Average 90 (O1–Mg2–O3) = 96.76(7) (O3–Mg2–O3) = 88.83(4) (O3–Mg2–O2) = 80.97(7) (Mg2–O1)[1] = 2.049(3) Å (O3–Mg2–O3) = 71.65(8) (Mg2–O2)[1] = 2.175(3) Å (O1–Mg2–O3) = 90.79(6) octahedra (Mg2–O3)[2] = 2.2068(16) Å (O3–Mg2–O3) = 109.93(9) M2 (Mg2–O3 )[2] = 2.0674(14) Å (O2–Mg2–O3) = 90.82(6) (O3–Mg2–O3) = 88.83(4) (O1–Mg2–O3) = 90.79(6) Average 2.1286 (O3–Mg2–O2) = 90.82(6) (O2–Mg2–O3) = 80.97(7) (O1–Mg2–O3) = 96.76(7) Average 89.83 (Si–O3) = 1.6312(14) Å (O3–Si–O2) = 116.09(7) (Si–O1) = 1.656(3) Å (O2–Si–O1) = 114.46(11) tetrahedron (Si–O2) = 1.613(3) Å (O1–Si–O3) = 101.75(7) T (Si–O3) = 1.6312(14) Å (O3–Si–O3) = 104.72(11) (O2–Si–O3) = 116.09(7) Average 1.6327 (O1–Si–O3) = 101.75(7) Average 109.15

magnesium contents. Figure 4g,h show the shortening of M1–O, and M2–O bond distances

**Table 3.** Bond distances (Å) and bond angles of B-rich forsterite.

with increasing magnesium contents.

Numbers in square brackets represent the number of repeats of bonds and bond angles in a polyhedron.

#### *3.4. Raman Spectrum*

Laser Raman spectroscopy is a powerful method for structural and compositional characterization of minerals. The factor group analysis indicates that forsterite has 36 Ramanactive vibration modes: 11Ag + 11B1g + 7B2g + 7B3g [31,32]. Symmetry and assignment for the Raman modes of B-rich forsterite are listed in Table 4. A Raman spectrum of B-rich forsterite can be divided into three spectrum regions: (1) 700–1100 cm−1, (2) 400–700 cm−1, and (3) < 400cm−1 [15]. The bands of the region (1) (at approximately 824, 857, 882, 919, and 965 cm−1 for B-rich forsterite) are attributed to the internal symmetric and asymmetric stretching vibrational modes of the SiO4 ionic group [15]. Bands between 700 and 1100 cm−1 are the most characteristic peak of the olivine Raman spectrum, which can be used to identify olivine in the multi-phase spectrum [15,16,31]. Low intense bands of the region (2) (at 437, 544, 586, and 609 cm−1 for B-rich forsterite) are related to the internal bending vibrational modes of the SiO4 ionic groups [15]. The bands of the region (3) (at around 227, and 305 cm−1 for B-rich forsterite) are assigned to the lattice vibration modes, including rotational and translational vibrations of SiO4 tetrahedra, and translational vibrations of magnesium and iron cations [31]. In addition, bands associated with the vibration of B-O

are not detected, which is attributed to the concentration of boron. Generally speaking, boron has no effect on the Raman spectra of olivine.

**Figure 4.** (**a**–**c**) Unit-cell parameters **a**, **b**, **c** vs. Fo content of olivine. (**d**) Unit-cell volume vs. Fo content of olivine. (**e**,**f**) The volume of coordination polyhedron M1, and M2 vs. Fo content of olivine. (**g**,**h**) Average M1–O, and M2–O bond distances vs. Fo content of olivine.

**Table 4.** Assignment of bands in the Raman spectrum of the forsterite.

In our analysis, another feature of the Raman spectrum is that the systematic peak position shift towards higher Raman shift compared with Fo~91 olivine (820, 852 for Fo~91 olivine and 824, 857 for Fo~99 olivine, respectively) (Figure 5b). The behavior of atomics at the M2 octahedral site is the main factor affecting the Raman spectrum of olivine [33]. Our results indicate that the relative intensities and position of the Raman peak in olivine can be correlated with the type of atomic substitutions involved. Kuebler et al. [15] explained that systematic peak-position is related to the decrease in atomic mass and polyhedral volume in octahedral sites, and to the degree of coupling of the symmetric and asymmetric stretching vibrational modes of SiO4 groups.

**Figure 5.** Raman spectrum of B-rich forsterite compared with mantle olivine. (**a**) The Raman spectrum of samples. (**b**) The magnification of (**a**).

#### *3.5. Infrared Spectrum*

The characteristic peaks of B-rich forsterite appear mainly at approximately 1303, 1259, 1168, 990, 958, 883, 839, 761, 610, 508, 468, and 424 cm−1. The bands around 990, 958, and 883 cm−1 are related to the symmetrical stretching vibration of the Si−O−Si group. The bands near 468, 508, and 610 cm−1 represent the bending vibration of the Si−O group. Internal vibrations and lattice vibrations appear at 468 and 424 cm−1. The IR spectrum of B-rich forsterite displays strong OH band at 3696 cm−1 and weaker band at 3593 cm−1. Both bands are caused by OH stretching vibration, which indicates the existence of constitutional water in forsterite.

Figure 6 compares the IR spectra of B-rich forsterite from Jian forsterite jade and B-free olivine (Fo~91) from mantle peridotite. The spectra are similar, except for five bands at 761, 1168, 1259, 1303, and 3593 cm−1 in the spectrum of the B-rich forsterite. Similar bands have been reported in B-rich olivine samples [22,24]. The band at 761 cm−1 is close to the 758 cm−1 band observed in the infrared spectrum of B-rich olivine from Tayozhnoye, Russia. Sykes et al. [22] assigned the band at 758 cm−1 to the v1 symmetric stretching mode of the BO3 groups. The bands at 1168 and 1259 cm−1 in the B-rich forsterite spectra are assigned to ν3 asymmetric stretching vibration modes of BO3 groups [22,24]. The bands at 1301 cm−1 likely correspond to the isotopic shift of the bands at 1168 and 1256 cm−1, respectively, due to 10B [24].

**Figure 6.** The infrared spectrum of B-rich forsterite compared with mantle olivine.

#### **4. Discussion**