**1. Introduction**

Any method for the solution of crystal structures or for Rietveld refinement of such structures needs at least the set of symmetry matrices of the given space group (SG). In data bases and concise standard descriptions of crystal structures, the complete list of atoms is reduced to atoms representatives and a space group symbol. Since symmetry operations are tensor objects and their matrix form depend on the origin and the orientation of the coordinate system, the symbol must identify not only the *space group type* but also the *space group description*. For this reason standard space group descriptions called *conventional* were tabulated since the year 1935. Contemporary descriptions are based on the 3rd series of the *International Tables for Crystallography* [1], frequently referred to as ITA83. In a common practice one takes a space-group symbol, usually an international Hermann-Mauguin (H-M) symbol, as the index and obtains the symmetry operators from the printed tables. This approach guarantees the conventional descriptions of space groups, 'standard' ordering of symmetry matrices, its geometric interpretation, etc. but has a disadvantage of being limited to the tabulated representations of space groups. Moreover, huge amount of data and a possibility of human errors in transferring the symmetry information to applications involving crystal symmetry [2,3] leads to the generally accepted conclusion, that the automated derivation of space-group information becomes essential when this information is routinely required, especially in the case of higher symmetry. In the years 1960-1980 welldocumented algorithms [4,5] translating H-M symbols into a set of generators, which are then used to build a full set of symmetry matrices, were developed. Differences in the generated space group descriptions, caused by ambiguities in H-M symbols prompted in [6- 8], brought to procedures based on explicit-origin generators, that is on symmetry operations with specified complete translation vectors not only on its characteristic components – glide or screw vectors. The explicit-origin generators were organized into lengthy [7,8] or concise space-group symbols and used for the SG generation. The latter

© 2012 Stróż, licensee InTech. This is an open access chapter 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. © 2012 Stróż, licensee InTech. This is a paper 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.

#### 246 Recent Advances in Crystallography

symbol, known as the *Hall symbol*, was applied in [6,9]. It should be also noted, that according to the transformational concept [10], the one from equivalent sets of generators published in ITA83 can serve as the 'starting point' for any space group description in the ITA83-style.

The efficiency of space groups construction from the generators is also considered in the literature. Trivial approaches based on any symmetry operations, treated as the group generators, are redundant and completely ineffective. For example, the number of matrix multiplications and matrix comparisons needed for the generation of space group F*m*3�*m* has been estimated in [9] at 18528 and 1.7 million, respectively. Such huge number of mathematical operations can be drastically reduced at the expense of an algorithm complexity. In the approach described in reference [9], the improved algorithm was approximately 100 times faster than the simplistic method. The natural limit of such improvements corresponds to the non-redundant methods, that is procedures in which each matrix multiplication gives a new symmetry operation and thus matrix comparisons are not needed at all. Such method was based on representation of 32 crystallographic point groups in terms of cyclic groups and their products [7,8]. The 'composition series' method [11], successfully adapted to conventional space group descriptions in ITA83 [12], can also be modified to a non-redundant form [13]. This method is especially interesting, since it repeats the ITA83-type order of symmetry operations, assuming the published sets of generators are used. Basing on the composition series, all space group descriptions, that is conventional or not conventional, may be standardized [13-15].

For specific purposes justified in [8,9], the set of symmetry matrices should be complemented by the 'secondary symmetry information' which originates from the geometric characterizations of the symmetry operations given in ITA83 in the form of the operation symbols and the diagrams of symmetry elements. The symmetry operations are the foundation for the Hermann-Maugin symbols and to derive information important in understanding the Wyckoff positions, to find equivalent descriptions of crystal structures or to find transformations between different algebraic descriptions of the same space group.

The matrix-column pair of a space-group operator contains all the information that is needed for a geometrical characterization of the space-group operator and the corresponding symmetry element. Procedures for doing this are well documented in the literature [8,9,16-18]. Algorithms for the determination of (i) the type of rotation, (ii) the rotation angle φ given as n = 360/ φ, (iii) the sense of rotation, (iv) the orthogonal decomposition of the translation vector of the space group operator into its intrinsic and location-dependent components, (v) the orientation and the location of a geometric element, (vi) the inversion point on a geometric element in case of a rotoinversion symmetry operation, are given in the above references.

Even though the recipes are clear, the geometric meaning of symmetry matrices needs some additional conventions [18] to obtain a unique form, not necessarily presented in algorithms. Difficulties are connected with the positive direction of an axis line or plane traces specifications, or the selection of a point which fixes a geometric element in the space. Moreover, coding some glide vectors by the letters *a*, *b*, *c*, *g* causes that operation symbols are difficult to generate and are not generally understood, also in the community of crystallographers. Even though there are critical opinions like '*The symbols written under the heading Symmetry operations are actually descriptive symbols which repeat part of the information given by the diagram – actually they correspond to cosets representatives in the decomposition of the space group with respect to its translation subgroup….Solid state physicists would appreciate much more if these symbols are replaced by Seitz operators*' [19], the deriving of geometric descriptions, especially without any relations to the Crystallographic Tables, is crucial. It must be also remembered that symbols were used to give a scientific definition to a term '*symmetry element*' – the collective designation for a number of geometric concepts widely used by crystallographers, mineralogists and spectroscopists [20-22]. They were recommended by the *Ad-hoc committee on the nomenclature of symmetry* [21] for general use.

246 Recent Advances in Crystallography

not conventional, may be standardized [13-15].

operation, are given in the above references.

ITA83-style.

symbol, known as the *Hall symbol*, was applied in [6,9]. It should be also noted, that according to the transformational concept [10], the one from equivalent sets of generators published in ITA83 can serve as the 'starting point' for any space group description in the

The efficiency of space groups construction from the generators is also considered in the literature. Trivial approaches based on any symmetry operations, treated as the group generators, are redundant and completely ineffective. For example, the number of matrix multiplications and matrix comparisons needed for the generation of space group F*m*3�*m* has been estimated in [9] at 18528 and 1.7 million, respectively. Such huge number of mathematical operations can be drastically reduced at the expense of an algorithm complexity. In the approach described in reference [9], the improved algorithm was approximately 100 times faster than the simplistic method. The natural limit of such improvements corresponds to the non-redundant methods, that is procedures in which each matrix multiplication gives a new symmetry operation and thus matrix comparisons are not needed at all. Such method was based on representation of 32 crystallographic point groups in terms of cyclic groups and their products [7,8]. The 'composition series' method [11], successfully adapted to conventional space group descriptions in ITA83 [12], can also be modified to a non-redundant form [13]. This method is especially interesting, since it repeats the ITA83-type order of symmetry operations, assuming the published sets of generators are used. Basing on the composition series, all space group descriptions, that is conventional or

For specific purposes justified in [8,9], the set of symmetry matrices should be complemented by the 'secondary symmetry information' which originates from the geometric characterizations of the symmetry operations given in ITA83 in the form of the operation symbols and the diagrams of symmetry elements. The symmetry operations are the foundation for the Hermann-Maugin symbols and to derive information important in understanding the Wyckoff positions, to find equivalent descriptions of crystal structures or to find transformations between different algebraic descriptions of the same space group.

The matrix-column pair of a space-group operator contains all the information that is needed for a geometrical characterization of the space-group operator and the corresponding symmetry element. Procedures for doing this are well documented in the literature [8,9,16-18]. Algorithms for the determination of (i) the type of rotation, (ii) the rotation angle φ given as n = 360/ φ, (iii) the sense of rotation, (iv) the orthogonal decomposition of the translation vector of the space group operator into its intrinsic and location-dependent components, (v) the orientation and the location of a geometric element, (vi) the inversion point on a geometric element in case of a rotoinversion symmetry

Even though the recipes are clear, the geometric meaning of symmetry matrices needs some additional conventions [18] to obtain a unique form, not necessarily presented in algorithms. Difficulties are connected with the positive direction of an axis line or plane traces specifications, or the selection of a point which fixes a geometric element in the space. The analysis of symbol derivations as well as the contents of geometric features in the symbols, given in [15, 18, 23], suggests the possibility of defining new symbols, easier to calculate, universal and richer in geometric meaning.

Taking into account all above remarks, the most important features for the computer generation of space groups and their geometric characterization are: (i) a possibility of unique naming of any SG descriptions, (ii) an easy interpretation of SG symbols, that is a derivation of generators, (iii) effectiveness (non-redundancy) of group generation, (iv) reduced amount of predefined data, (v) full consistency with ITA83, (vi) an effective geometric characterization of obtained set of symmetry matrices. The generators selected by H. Wondratschek and used for the conventional space group descriptions in ITA83 meet some demands from the above list, but the geometric symbols need some modifications.

In this chapter a complete, effective and unique approach to the automated derivation of space-group information for a conventional as well as for a non-conventional space group description is proposed.


**4.1 Overview of HSE-TDOC**

HSE-TDOC refers to the specialty-specific HSE guidance (HSE guidance), project-specific HSE plan (HSE plan), and position-specific HSE checklist (HSE checklist) [11]. Among them, the HSE guidance may have much content, while the HSE plan may either have much content or just a few pages depending on the project.


**1. Introduction**

Ionospheric scintillation has significant impacts on space-based radio communication, wave propagation, and navigation system performance. The main effects of scintillation on the transionospheric radio system are signal loss and/or phase cycle slips, which cause difficulties in regard to locking the receiver signal. There is no doubt that satellite radio signal scintillation is a consequence of a scattering mechanism, as radio waves are propagating through random electron density (*Ne*) fluctuations, especially within the F-region ionosphere, where the irregularity layer is sufficiently thick. Many excellent ionospheric scintillation theory and observation reviews have been published [1–4]. Comprehensive studies on the physics and theories of ionospheric irregularities and scintillations can also be found in books by [5,6].

The effects of ionospheric scintillation are most intense in the equatorial region, moderate at high latitudes, and minimum at middle latitudes [7]. At equatorial latitudes and the time near and/or soon after sunset, the zonal neutral wind and conductivity gradient caused by the sunset terminator interact develop an enhanced eastward electric field, called

**Citation:** Tsai, L.-C.; Su, S.-Y.; Lv, J.-X.; Bullett, T.; Liu, C.-H. Multi-Station and Multi-Instrument Observations of F-Region Irregularities in the Taiwan–Philippines Sector. *Remote Sens.* **2022**, *14*, 2293. https:// doi.org/10.3390/rs14102293

Academic Editors: Serdjo Kos, José Fernández and Juan F. Prieto

Received: 30 March 2022 Accepted: 7 May 2022 Published: 10 May 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**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/).

pre-reversal enhancement (PRE), generally at F-region heights [5,8,9]. As a result, the ionosphere moves upward, develops steep density gradients and large-scale plasma depletions in the bottom side F-region, and becomes unstable, triggering the Rayleigh–Taylor (R–T) instability. The plasma depletions, called plasma bubbles, become populated with mesoscale or small-scale irregularities and rise to great heights. These plasma bubbles, extended in altitude, also map out along magnetic field lines to the north and south of the magnetic equator, i.e., higher magnetic latitudes. These structured irregularities generally move eastward by the action of a vertical oriented polarization electric field. Undergoing a non-linear cascade process of electric field driving and wave-wave coupling [10], irregular structures drift and vary from large- to small-scale. The spectral distribution of irregularities includes a broad component associated with waves. Equatorial spread-F (ESF) thus stems from high-frequency radar observations of the "spread" of the ionospheric echoes in ionograms and can be used to describe equatorial and low-latitude F-region instability phenomena. Scintillation and ESF activities attain a maximum value during high sunspot activity periods, especially during equinoxes (March, April, September, and October), owing to the increased value of the background ionization density [11]. In particular, low-latitude scintillation can be dictated by solar transients, such as magnetic storms [11].

Several techniques have been used to observe and study ionospheric irregularities and scintillations. These include sounder, radar backscatter, in-situ measurements onboard rockets or satellites, ground-based satellite beacon signal observations, space-based navigation beacon observations using radio occultation (RO) techniques, etc. Earlier investigations [12] developed an operational system, named the SCIntillation Network Decision Aid (SCINDA), to nowcast and forecast scintillation. At the operator terminal, the SCINDA data were combined with an empirical plasma bubble model to generate three-dimensional maps of irregularity structures and two-dimensional outage maps for the equatorial region in the American sector. In this study, another multi-station and multi-instrument system, developed for ionospheric scintillation and ESF specification in the Taiwan–Philippines sector, is outlined. The issues related to the scintillation and ESF event observed on 26 October 2021, are presented and discussed. We shall first indicate the existence of a plasma bubble in the Taiwan–Philippines sector using the FS7/COSMIC2 Global Positioning System (GPS) or GLObal NAvigation Satellite System (GLONASS) RO observations. We shall verify the latitudinal extent of the tracked plasma bubble using the recorded ionograms from the Vertical Incidence Pulsed Ionospheric Radar (VIPIR) located at Hualien (23.89◦N, 121.55◦E, dip latitude 17◦N), Taiwan. We further discuss the spatial and temporal variabilities of two-dimensional scintillation index maps based on the simultaneous GPS L1-band signal measurements from 133 ground-based receivers located in Taiwan and the surrounding islands. We also operate two high-sampling, software-defined GPS receivers and characterize the targeted plasma irregularities by carrying out spectrum analyses of the received signal. Overall, we summarize the derived plasma irregularity and ESF characteristics and point out a potential precursor for post-sunset scintillation and ESF events.

#### **2. System Description**

Since June 2019, the Taiwanese American FS7/COSMIC2 program has been executing active limb sounding of the Earth's neutral atmosphere and ionosphere via GPS/GLONASS RO observations from low-Earth orbiting (LEO) satellites. Similar to the prior mission, FS3/COSMIC, the FS7/COSMIC2 is a six-LEO-satellite constellation mission but orbits at 24◦ inclination and ~550 km altitudes (~720 km altitudes for parking orbits). It enhances the Global Navigation Satellite System (GNSS) receiver's capability to receive multi-channel (1.5 GHz and 1.2 GHz) GPS and GLONASS satellite signals and can provide more than 5000 RO observations per day within the region between the geographic latitudes of ±40◦. Each RO observation can provide a set of limb-viewing measurements on GNSS signal intensity and phase from the LEO satellite altitude to the Earth's surface. Those measurements can be further retrieved into *Ne* and limb-viewing scintillation index

*S*4 profiles in altitudes [13,14]. In this study, we propose to identify a plasma bubble in the Taiwan–Philippines sector by using the FS7/COSMIC2 GPS/GLONASS RO observations. Meanwhile, the Taiwan–Philippines sector is defined as the ionospheric region located in 20◦ ± 15◦ N and 120◦ ± 15◦ E geographic coordinates, where the geomagnetic latitudes are from ~−3◦ to 25◦.

The Hualien VIPIR is a modern ionospheric radar (also termed ionospheric sounder or ionosonde) that fully digitizes complex signal records and uses multiple parallel receiver channels for simultaneous signal measurements from multiple spaced receiving antennas [15]. As a usual ionospheric sounder, the Hualien VIPIR transmits pulsed waveforms in the medium- and high-frequency (MF/HF) bands and measures the envelope group delays, i.e., virtual ranges, of ionospheric echoes to produce ionograms with ionospheric trace h'(f) as a function of the radio carrier frequency. Details of the system can be found in [16].

Other sources of scintillation observations are the 133 ground-based GPS receivers located in Taiwan and the surrounding islands. They are operated and maintained by the Central Weather Bureau (CWB) of Taiwan and routinely provide 1-Hz satellite navigation system data (in the RINEX format). The online processing includes determinations of scintillation index *S*4 and the two-dimensional vertical *S*4 map in the Taiwan–Philippines sector. Based on earlier investigations [17], the theoretical and experimental analyses show that scintillation index *S*4 values become underestimated when a sampling spatial scale is larger than the first Fresnel zone (FFZ). We note that the 1-Hz sampling rate from ground-based GPS receivers is high enough to determine complete *S*4 values but not to characterize the signal scintillation spectrum. Thus, we have designed and implemented a software-defined receiver in order to acquire and track GPS (and Satellite-Based Augmentation System, SBAS) L1-band C/A code signals [18,19]. Compared with most commercial GPS receivers, software-defined GPS receivers offer added flexibility and versatility by implementing most functions in software. Another advantage of a software-defined GPS receiver is that it could have a maximum sampling rate of 1000 Hz due to the L1-band Coarse Acquisition (C/A) code duration of 1 millisecond, and the executing sampling rate can be much higher than that of a usual commercial GPS receiver. Spectrum analyses on the received signals of two software-defined GPS receivers located at Chungli (24.97◦N, 121.19◦E) and Hualien (23.89◦N, 121.55◦E), Taiwan will be used to characterize the targeted ionospheric irregularities.

#### **3. Results**

This section presents the multi-station and multi-instrument observations of a scintillation event that occurred in the Taiwan–Philippines sector on 26 October 2021, which was at magnetic quiet conditions, referring to Kp indexes between 0+ and 2+. Figure 1 shows the geographical geometry of the F-layer irregularity observations obtained during 13:00~15:30 UT, i.e., 21:00~23:30 LT in Taiwan, on 26 October 2021, by the FS7/COSMIC2 GPS/GLONASS RO sounding experiment. Six (#1 to #6 observations) out of fourteen RO observations were recorded and classified as scintillation observations according to their maximum limb-viewing L1-band *S*4 values larger than 0.1 [14]. Their recording times, which are the FS7/COSMIC2 LEO satellite orbiting times at the peak altitudes of RO observations, are used to identify the scintillation event period, at least from 13:54 to 14:59 UT. For each RO scintillation observation, a set of RO limb-viewing links at a 15 s sampling rate (between 150 and 450 km altitudes), which connects the occultation points to their conjugate points, is shown in coded colors of L1-band *S*4 values to present the possible projection area of ionospheric irregularities, and the trace of perigee points (or tangent points) is also shown. We note that the first three (#1, #2, and #3) RO observations are located near the magnetic equator and experience strong scintillations. The later three (#4, #5, and #6) RO observations are located in the northeast directions of the observations #1, #2, and #3 and could be their latitudinal mapping-out cases; thus, they experience weaker scintillations. In contrast, as shown in Figure 1, the peak tangent point positions of the other

eight RO observations without definable scintillations are located outside of the aimed scintillation area covering observations #1 to #6.

**Figure 1.** Geographical geometry of the F-layer irregularity observations during 13:00~15:30 UT on 26 October 2021, by the FS7/COSMIC2 GPS/GLONASS RO sounding experiment. Six out of fourteen RO observations were obtained and classified as the scintillation observations #1 to #6. Sets of limb-viewing links (at a de-sampling rate of 15 s and altitudes between 150 to 450 km) connecting the occultation points to their conjugate points are shown in coded colors by L1-band *S*4 values to present the possible projection area of ionospheric irregularities. The traces of limb-viewing tangent points are also shown in black. The peak locations of the other eight RO observations without scintillation are shown by green squares, the location of the Hualien VIPIR position is shown by a black square, and two magnetic latitude lines at dip 0◦ and 17◦ are shown in brown.

Figure 2 shows the RO scintillation observations #1 and #4 with more information, including the limb-viewing L1-band signal-noise-ratio (SNR) amplitude profiles at both the occulting and calibrating sides, the resulting undersampling *S*4 profiles, and the retrieved *Ne* profile. We note that the L2-band signals are much weaker and thus do not have enough sensitivity to derive reliable *S*4 values to be shown in this paper. On the other hand, the derived *S*4 values are from "undersampling" measurements because *S*4 values become saturated and completed when a sampling spatial scale is less than the FFZ, but otherwise, *S*4 values could be underestimated at undersampling conditions [17]. The FFZ is defined by *DF* = √*λL* , where *λ* is the radio wavelength and *L* is the distance from the irregularity position, which is assumed to be the tangent point position along a limb-viewing GPS/GLONASS-LEO ray, to an LEO satellite position in this study. For those tangent-point altitudes from 400 to 200 km, the FFZ scale sizes for the L1-band signals are between 516 and 643 m. Therefore, the Fresnel frequency can be obtained via *fF* = *v*/ √2 *DF*, where *v* is the relative radio-scanning speed to the ionosphere. The derived Fresnel frequency is thus approximately 2.1 (2.6) Hz at 400 (200) km altitude for a frozen ionosphere. We note that the upward drift velocity of plasma irregularities is usually less than 50 m/s [4], which is much lower than the vertical component (~2 km/s) of LEO satellite velocity at F-region altitudes and can be ignored to estimate the corresponding Fresnel frequency. We conclude that the sampling rate of FS7/COSMIC2 RO observations on the

ionosphere is 1 Hz and less than the possible Fresnel frequencies of plasma irregularities, and thus the derived *S*4 values should be underestimated at undersampling conditions.

**Figure 2.** Results of FS7/COSMIC2 RO scintillation observations #1 (**left panel**) and #4 (**right panel**) as in Figure 1. Both figures show the limb-viewing L1-band SNR amplitude profiles at the occulting (calibrating) side in black (grey) and the resulting undersampling *S*4 profiles in cyan. The retrieved *Ne* profiles are shown in red.

As shown in Figure 2, strong and moderate fluctuations occur in the L1-band SNR amplitudes of observations #1 and #4, respectively, from the occulting-side observations but not from the calibrating-side observations. It indicates that the amplitude fluctuations are induced by the ionospheric irregularities, which are located along the limb-viewing links between the occultation points and their conjugate points, as shown in Figure 1. We note that the strong amplitude fluctuations, i.e., large undersampling *S*4 values, as well as the *Ne* fluctuations from observation #1, were distributed over a wider altitude region up to the LEO orbiting altitude than those from observation #4, and the peak scintillations and *Ne* irregularities happened around the F-layer electron density peaks. This is consistent with the observations from the theoretic descriptions in the Introduction section.

Equatorial spread-F (ESF) features usually accompany equatorial plasma bubbles and have been observed by numerous authors using ionosonde. In this study, we operated the Hualien VIPIR, a modern ionosonde, and observed spread-F features from the ionograms recorded between 13:19~15:04 UT, i.e., 21:19~23:04 LT, on 26 October 2021. The observed ESF event lasted for approximately one hour and forty-five minutes. In Figure 3, the upper ionogram shows two traces of one-hop F-layer echoes, where the upper trace is weaker than the main trace and has higher altitudes with approximately 25 km differences at the start (13:19 UT) of the ESF event. Furthermore, the lower ionogram shows a weak range spread-F, which was recorded during the middle (13:49 UT) of the ESF event. We note that the spread-F frequencies ranged from ~1.7 MHz up to 11.5 MHz, which presents the top frequency of ordinary ionospheric echoes, i.e., *foI*. It is usually difficult to retrieve a critical plasma frequency *foF2* from ionograms with ESF, but not difficult to retrieve *foI*. Multi-trace echoes could be interpreted as being due to the large-scale plasma depletion that happened before an ESF event. Meanwhile, the range-type spread-F indicates the existence of small-scale irregularities on the whole bottom side ionosphere.

**Figure 3.** Two typical ionograms showing multi-trace echoes (**upper panel**) and weak range spread-F (**lower panel**) observed at the start (13:19 UT) and mid (13:49 UT) of an ESF event by the Hualien VIPIR on 26 October 2021. Note that the signals throughout all virtual ranges are radio frequency interferences from other radio sources.

Figure 4 shows the geographical geometry of the ionospheric pierce points (IPP) of the simultaneous GPS signal measurements at 14:42 UT on 26 October 2021, using the CWB GPS receiving network. The IPP altitudes were designed to be 300 km in accordance with the statistical peak scintillation or irregularity altitude retrieved from the FS7/COSMIC2 limb-viewing *S*4 and/or *Ne* profiles, as shown in Figure 2. Furthermore, the IPPs were obtained at and limited by a minimum elevation angle of 45◦ from receivers to avoid multi-path signals. In this study, we define the vertical scintillation index *VS*4 as the vertical component of the normalized variance of the signal power intensity *I* as follows:

$$VS\_4 = \sin(\theta) \times sqrt{\left(\left\langle \frac{\left(\left(I - \langle I\right)\right)^2\right\rangle}{\left\langle I\right\rangle^2}\right)},\tag{1}$$

where *θ* is the line-of-sight elevation angle from the receiver. We calculate *VS*4 values by applying (1) and a 30-s duration window to 1-Hz L1-band signal amplitudes from the CWB GPS data archives. We note that the use of *VS*4 to represent a vertical scintillation index is based on an assumption in which irregular *Ne* distribution is a function of altitude only along a transionospheric radio path. However, equatorial plasma bubbles are plume-like structures from low altitudes [4], and the shapes of bubbles are extended vertically upward and also stretched in the north-south direction along the magnetic field lines. Ref. [20] shows

that GPS RO observations with high *S*4 values are much more likely to occur when the ray paths are distributed in certain bubbles and more nearly aligned with the magnetic field. The details of two-dimensional and even three-dimensional irregular *Ne* structures should be figured out in future studies. Meanwhile, we can assume the observing irregularities located at altitudes around 300 km to be the IPP altitude, and the corresponding FFZ scale sizes (*DF*) of L1-band signals are between 239 and 275 m for elevation angles from 90◦ to 45◦. We note that GPS satellites have orbiting velocities of approximately 3.9 km/s, and thus the corresponding IPP velocity is ~60 (80) meter/s at an elevation angle of 90◦ (45◦) from the receiver. If we assume a frozen ionosphere, the resulting Fresnel frequencies *fF* are between 0.18 and 0.2 Hz. Ref. [11] shows that, using extensive incoherent scatter radar observations from Jicamarca, the daytime westward drifts are significantly smaller than the nighttime eastward drifts, and during solar maximum, the maximum nighttime eastward velocity increases up to about 160 m/s. Even if we include a 160 m/s IPP trace component of plasma irregularity drift velocity, the resulting Fresnel frequencies *fF* are approximately 0.66 Hz and are also lower than the 1-Hz sampling rate for the CWB GPS receivers. This means that the derived *S*4 values from the CWB GPS data are at complete conditions. As a result, Figure 5 shows three developed structures on a two-dimensional *VS*4 map taken at 13:24, 13:49, and 14:42 UT, which are approximately at the start, middle, and end of the scintillation and ESF event. Referring to Figure 4 and the bottom panel of Figure 5 based on the same CWB GPS data at 14:42 UT, we derive a two-dimensional extended *VS*4 map deduced through relaxation by applying the red-black smoothing technique [21] on point-distributed *VS*4 measurements. We execute one pass through the mesh updating the "red" cells (like the red squares of a checkerboard) and another pass updating the "black" cells (like the black squares) and so forth for two loops. It produces two more cell extents on derived *VS*4 maps where the cell (latitudinal or longitudinal) resolution is 0.1◦, determined approximately by the medium distance between neighboring GPS stations.

**Figure 4.** Geographical geometry of the IPPs of the simultaneous GPS signal measurements at 14:42 UT on 26 October 2021, and from 133 ground-based receivers located in Taiwan and the surrounding islands. The dots colored in light blue, yellow, and red show the IPP positions at 300 km altitudes for the lines of sights connecting GPS satellite #8, #21, and #27, respectively, which have a minimum elevation angle of 45◦ from receivers. The positions of another two software-defined GPS receivers located at Chungli (24.97◦N, 121.19◦E) and Hualien (23.89◦N, 121.55◦E), Taiwan, are shown and labeled by "R1" and "R2", respectively.

**Figure 5.** Three developed structures in two-dimensional *VS*4 map taken at 13:24 (**upper panel**), 13:49 (**middle panel**), and 14:42 UT (**lower panel**) on 26 October 2021, and derived by the simultaneous GPS signal measurements from the CWB GPS receiving network.

It is now generally accepted that radio scintillation caused by ionospheric plasma irregularities can be characterized by fitting a power-law function with the spectral index *p* to the derived signal spectrum [2,22–24]. According to the scintillation theory and power spectra analyses [2,25], the intensity spectrum of weak and moderate scintillations and power-law ionospheric irregularities should have more or less a flat portion at low frequencies and start to roll off around the Fresnel frequency in the form *f* 1−*p*, where *p* is defined as the spectral index and is near 4 in the irregularity power-law relationship. Furthermore, the higher the spectral index, the stronger the scintillation intensity and the smaller the irregularity scale.

As described in the last section, we also operate two high-sampling, software-defined GPS receivers located at Chungli and Hualien, Taiwan separately to simultaneously receive GPS signals. The locations of the Chungli and Hualien software-defined GPS receivers are shown in Figures 4 and 5 and labeled by "R1" and "R2", respectively. In this study, L1-band C/A code signal amplitudes were recorded at a sampling rate of 50 Hz and for a 70-s duration every five minutes. We obtain three L1-band signal scintillation patches recorded by the Chungli software-defined GPS receiver at different data segments, which are from 13:29 to 13:44 UT, 14:29 to 14:49 UT, and 13:44 to 14:19 UT on 26 October 2021, for GPS satellites #8, #21, and #27 signal observations, respectively. The derived *VS*4 values are consistent with CWB GPS observation results and are from 0.19 to 0.25, 0.16 to 0.22, and 0.14 to 0.19 for GPS satellites #8, #21, and #27 signal measurements, respectively. Figure 6 shows the corresponding signal spectrums obtained via a Lomb periodogram algorithm [21]. We note that above approximately 1 Hz, the power spectral densities (PSD) are near the noise level where the minimum frequency of the noise level is defined as the deviation frequency of the signal intensity spectrum [26,27]. The 50-Hz sampling rate is approximately one order higher than the derived deviation frequency. Below 1 Hz, the PSDs are more or less a flat portion at low frequencies and decay from their maxima at a break frequency of *fB* toward the noise level in an approximately linear fashion on the log-log scale shown. This indicates and confirms a power-law variation *f* 1−*p* of the plasma irregularity PSD with the frequency as discussed. We note that the spectrum break frequencies of *fB* can be treated as the experimental Fresnel frequencies and are approximately 0.07, 0.15, and 0.12 Hz, and the derived spectral index *p* values are 3.57, 4.36, and 3.59 for the L1-band signal scintillation patches from GPS satellites #8, #21, and #27, respectively. Comparing with the corresponding IPP positions shown in Figure 4 and the derived *VS*4 maps shown in Figure 5, we note that the area with a higher spectral index *p* has a stronger scintillation intensity. The spectrum analysis results of the L1-band signal scintillation patches recorded by the Hualien software-defined GPS receiver are similar to those from the Chungli system and are not shown in this study.

**Figure 6.** Power spectrums and their spectral index *p* values of the L1-band signal scintillation patches recorded by the Chungli software-defined GPS receiver from GPS satellites #8 (**upper panel**), #21 (**middle panel**), and #27 (**lower panel**). Three data segments are from 13:29 to 13:44 UT, 14:29 to 14:49 UT, and 13:44 to 14:19 UT on 26 October 2021, for GPS satellites #8, #21, and #27 signal observations, respectively.


*Supporting open minds since 2005*

Functional Materials http://dx.doi.org/10.5772/intechopen.76823 Edited by Dipti Sahu

#### Contributors

Denisse Ortiz-Acosta, Tanya Moore, Sabah Abdelbasir, Ahmed Esmail Shalan, Jiyong Fu, Wei Wang, Minghua Zhang, Nor Hapishah Abdullah, Muhammad Syazwan Mustaffa, Mohd Nizar Hamidon, Farah Nabilah Shafiee, Rabaah Syahidah Azis, Jeetendra Kumar Banshiwal, Durgesh Nath Tripathi

#### © The Editor(s) and the Author(s) 2019

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*3.2. Characterization and Selection of Mesoporous Carriers as Adsorbent Carrier*

The powder materials used as a carrier for preparation of liquisolid systems should have high liquid adsorbent power, and, at the same time, good flow and compaction properties, to allow uniform feed and reproducible filling of tablet dies and good tableting. Then, the flow and compaction properties of the mesoporous silicas and clay materials considered as potential adsorbent carriers for preparation of liquisolid systems, namely Aeroperl®300, Zeopharm®5170 and Neusilin®US2, were firstly investigated. The results of these studies, in terms of apparent and tapped density, Carr's Index and Hausner ratio, flowability (Copley test) and compactability (Wells test) are presented in Table 1.

**Table 1.** Apparent (DA) and tapped (DT) Density, Carr Index % (CI), Hausner Ratio (HR), flowability (as flow through an orifice), and compactability (determined by Wells test A, B and C) of Aeroperl®300, Neusilin®US2, Zeoparm®5170.

Based on Carr's Index and Hausner Ratio values, Zeopharm®5170 showed the best fluidity level, followed by Neusilin®US2 and then by Aeroperl®300. However, according to the flow Copley test, all powders presented excellent flowability, freely falling through the smallest apparatus hole (4 mm diameter). As for the compaction properties, the results of the Wells test showed that all powders samples exhibited a fragmenting behavior since similar crushing strength values were obtained in the different conditions of the test (A≈B≈C). This is considered a desirable characteristic of powders to be compressed, since the crushing strength of tablets made with fragmenting materials should be less negatively affected by the presence of hydrophobic lubricant, such as Mg stearate, with respect to plastic-deforming materials [55,56]. Neusilin®US2 gave rise to the tablets with the highest hardness, but acceptable breaking strength values (around 30 N) were obtained also with Aeroperl®300. On the contrary, the crushing strength values of Zeopharm®5170 tablets were very low, probably due to its poor binding properties, and then this excipient was discarded in subsequent studies.

The selected mesoporous clay and silica were then further characterized by BET analysis. Both compounds showed a very extended specific surface area, which confirmed their highly porous nature. However, the chosen clay Neusilin®US2 showed a clearly greater surface area (355.5 vs. 268.4 m2/g) and also a significantly higher volume (1.0 vs. 0.5 cm3/g) of mesopores (i.e., pores in the 2.0–50 nm range) compared to the chosen silica Aeroperl®300.

#### *3.3. Preparation and Characterization of Liquisolid Systems*

Liquisolid systems were then prepared by dissolving 5 mg GLY (drug therapeutic single dose) in 0.05 mL of the selected solvents (DMA or 2-PYR), and then gradually adding, under continuous mixing, Neusilin®US2 or Aeroperl®300, selected as carrier-coating materials. The strong adsorptive power of the selected mesoporous clay and silica allowed to use a liquid load factor (i.e., the w/w ratio of liquid medication to the carrier powder) of 1.1, clearly higher than the values commonly used in conventional liquisolid systems [22,27,29,47], and obtain dry-looking powders, with practically unchanged flow properties (measured according to the Copley flow test) compared to the respective pure carriers.

The obtained liquisolid systems were then characterized by LPS for granulometric distribution and compared with the corresponding pure carriers. As can be observed in Figure 2, both Aeroperl®300 and Neusilin®US2 exhibited a satisfactorily homogeneous distribution curve, with a mean volumetric diameter of 31 μm and 76 μm, respectively. The formation of liquisolid systems did not substantially change the original granulometric distribution of the corresponding carriers, irrespective of the type of solvent used, indicating in all cases the absence of appreciable aggregation phenomena and the obtainment of homogeneous systems looking as dry powders.

**Figure 2.** Granulometric analysis, by Laser Particle Size (LPS), of pure Aeroperl®300 and Neusilin®US2, and of the corresponding liquisolid systems with glyburide (GLY) containing 2-pyrrolidone (2-PYR) or dimetylacetamide (DMA) as non-volatile water miscible solvent.

DSC analyses were performed on pure drug and mesoporous clay and silica and on the corresponding liquisolid systems, in order to evaluate possible solid-state modifications or interactions between the components (Figure 3). The DSC curve of GLY was typical of a crystalline, pure, anhydrous compound, showing a flat profile before the sharp endothermic peak at 175 ◦C (ΔH 180 J/g) due to the drug melting. On the contrary, the thermal curves of both carriers indicated their amorphous nature, being characterized by a broad endothermal band in the range 70–140 ◦C, due to evaporation of associated water molecules, followed, in the case of Neusilin®US2, by another endothermic effect at a higher temperature (240 ◦C), due to decomposition phenomena.

**Figure 3.** Differential Scanning Calorimetry (DSC) curves of pure glyburide (GLY), Aeroperl®300 and Neusilin®US2 and of the corresponding liquisolid systems with 2-pyrrolidone (2-PYR) or dimetylacetamide (DMA) as non-volatile water miscible solvent.

DSC curves of liquisolid systems containing 2-PYR as a solvent showed two broad endothermic effects: the first, which peaked around 100 ◦C, was due to the carrier (Neusilin®US2 or Aeroperl®300) dehydration, while the second one, which peaked around 240 ◦C, was due to the solvent evaporation (boiling point 245 ◦C), partially superimposed, in the case of Neusilin®US2, to the carrier decomposition phenomena. An analogous thermal behavior was displayed by liquisolid systems prepared with DMA as a solvent; however, in this case, due to the lower boiling point of this solvent (165 ◦C), a partial superimposition of the carrier dehydration band to that of solvent evaporation happened. Interestingly, in all cases the complete disappearance of the drug melting peak was observed, which can be considered indicative of drug amorphization and/or solubilization in the liquisolid system, i.e., its almost molecular dispersion within the liquisolid matrix [26,27].

The results of PXRD studies were substantially in agreement with those of DSC analysis. In fact, as can be observed in Figure 4, the diffraction pattern of pure GLY exhibited the presence of numerous sharp peaks, in particular at 18.8, 19.4, 20.8 and 22.9◦ 2Θ, indicative of its crystalline nature, while a diffuse halo pattern, characteristic of amorphous powders, was shown by both mesoporous clay and silica.

The typical diffraction peaks of the drug were no more detectable in the X-ray spectra of all the liquisolid formulations, thus confirming the conversion of the drug in an amorphous or solubilized form within the liquisolid matrix, as suggested by DSC analysis, and allowing to exclude any possible artifact of this last technique, due to the sample heating during the scan.

**Figure 4.** X-Ray powder diffraction patterns of pure glyburide (GLY), Neusilin®US2 and Aeroperl®300 and of the corresponding liquisolid systems with 2-pyrrolidone (2-PYR) or dimetylacetamide (DMA) as non-volatile water miscible solvent.

The ESEM outcomes (Figure 5) further supported the results of DSC and XRPD analyses. The ESEM image of pure micronized GLY showed its crystalline nature and its very homogeneous particle size. Neusilin®US2 appeared instead as particles of almost spherical form, with a highly porous surface,

and Aeroperl®300 as spherical particles, many of which characterized by the presence of an internal cavity. The morphology of liquisolid systems obtained with both Neusilin®US2 or Aeroperl®300 as carrier-coating material was very similar to that of the corresponding pure samples, thus confirming their excellent adsorbent power and the absence of agglomeration phenomena.

**Figure 5.** ESEM images of pure glyburide (**A**), Aeroperl®300 (**B**) and Neusilin®US2 (**C**) and of the corresponding liquisolid systems (**B'** and **C'**).

Dissolution studies were then performed to evaluate the ability of the various liquisolid systems to improve the GLY dissolution rate and select the more effective ones for the preparation of liquisolid tablets. As can be seen in Figure 6, all the developed liquisolid systems showed a very marked improvement of GLY dissolution rate compared to the plain GLY, with an about 27 times increase of percent drug dissolved after only 2 min, and an about 4 times increase at the end of the test (60 min). No statistically significant (*p* > 0.05) differences were found among the different kinds of liquisolid systems and then they were all employed for tablet preparation.

**Figure 6.** Dissolution profiles of glyburide (GLY) as such or from the different liquisolid systems.


**2. Introduction to thermography**

Infrared thermography is the recording of temperature distribution of a body using the infra‐ red radiation emitted by the surface of that body at wavelengths between 7 and 14 μm. With this information, it is possible to create a visual map or thermogram of the distribution of temperatures on the surface of the object imaged. The sensitivity of modern infrared cameras is such that temperature differences to 0.025°C can be detected.

Thermography can be used for breast cancer screening based on the fact that the tempera‐ ture of the tumor is about 2°C higher than the neighboring tissues and blood vessel activ‐ ity surrounding a developing cancer is almost always higher than in normal breast tissue. Since breast tissue is part of the skin, vascular alterations due to cancer result in tempera‐ ture changes on the surface of the breast which can be captured with infrared thermography. Thermal abnormalities identified with thermal imaging are among the earliest signs of a pre‐ cancerous or cancerous lesion of the breast.

Thermal imaging is a noncontact, noninvasive and extremely privacy aware. Since thermal cameras are small, they are very portable and can be used for screening in rural camps.

There are many certified thermographers and thermologists who continue to practice using thermal analysis for breast cancer diagnosis [4].


*Article* **Ab Initio Study of Ferroelectric Critical Size of SnTe Low-Dimensional Nanostructures**

#### **Takahiro Shimada 1,\*, Koichiro Minaguro 1, Tao Xu 2, Jie Wang 3 and Takayuki Kitamura 1**

Received: 12 February 2020; Accepted: 8 April 2020; Published: 11 April 2020

**Abstract:** Beyond a ferroelectric critical thickness of several nanometers existed in conventional ferroelectric perovskite oxides, ferroelectricity in ultimately thin dimensions was recently discovered in SnTe monolayers. This discovery suggests the possibility that SnTe can sustain ferroelectricity during further low-dimensional miniaturization. Here, we investigate a ferroelectric critical size of low-dimensional SnTe nanostructures such as nanoribbons (1D) and nanoflakes (0D) using first-principle density-functional theory calculations. We demonstrate that the smallest (one-unit-cell width) SnTe nanoribbon can sustain ferroelectricity and there is no ferroelectric critical size in the SnTe nanoribbons. On the other hand, the SnTe nanoflakes form a vortex of polarization and lose their toroidal ferroelectricity below the surface area of 4 × 4 unit cells (about 25 Å on one side). We also reveal the atomic and electronic mechanism of the absence or presence of critical size in SnTe low-dimensional nanostructures. Our result provides an insight into intrinsic ferroelectric critical size for low-dimensional chalcogenide layered materials.

**Keywords:** ferroelectricity; SnTe; nanoribbon; nanoflakes; critical size; density-functional theory

#### **1. Introduction**

Ferroelectrics exhibit spontaneous polarization that can be reversed by an external electric field, due to their noncentrosymmetric crystal structure having a relative displacement of cations and anions in a ferroelectric (FE) phase. Ferroelectric properties have attracted attention due to their technological applications such as ferroelectric memory (FeRAM), sensors, MEMS/NEMS, and actuators [1–3]. To enhance the performance of these devices, it is necessary to reduce the size of ferroelectrics and integrate them at a high density. In recent years, with the progress of manufacturing technology, nanoscale ferroelectric materials with low-dimensional structures such as nano-thin films [4,5] (two-dimensional; 2D), nanowires [6,7], nanotubes [8,9] (one-dimensional; 1D), and nanodots [10,11] (zero-dimensional; 0D) have been synthesized for the high-performance, high-integration of nano-devices.

However, ferroelectricity disappears when the size of the ferroelectric material becomes nanoscale (ferroelectric critical size): in perovskite oxide PbTiO3 and BaTiO3 nanofilms, ferroelectricity disappears when the thickness of the films becomes 2 nm or less [12–15]. The appearance of ferroelectric critical size was explained by two aspects: (I) effect of electrostatic (depolarization) field and (II) the reconstruction and rearrangement of atomic and electronic structure at surfaces or edges. At the surface of ferroelectric materials, the surface polarization charge is formed due to the termination of polarization, and the depolarization field formed in the opposite direction of spontaneous polarization suppresses the ferroelectricity [16]. In particular, when the material dimensions become nanoscale, the ratio of the surface or edge to the entire volume increases, the influence of the depolarization field formed by the surface charge becomes dominant, and the ferroelectricity of the entire material disappears. This is factor (I). In general, ferroelectricity originates from a delicate balance between long-range interaction due to Coulomb force, which is the driving force for the relative displacement (ferroelectric displacement) of cations and anions in the crystal, and short-range interaction due to covalent bonds that stabilize the centrosymmetric structure [17]. In nanoscale materials, the long-range interaction is reduced due to the absence of atoms outside of material surfaces, and thereby the balance between long-range and short-range interaction is broken. In particular, such interactions are also changed due to the reconstruction and rearrangement of atomic and electronic structures at surfaces or edges. This is factor (II). For these reasons, the ferroelectric critical size appears. This physical limitation prevents the miniaturization of ferroelectric materials beyond the critical size.

In recent years, however, ferroelectricity was discovered in the monolayer structure of chalcogenide SnTe in the in-plane direction [18]. This indicates that ferroelectricity can exist in a structure with an atomic thickness. Obviously, this discovery is beyond the long-believed ferroelectric critical thickness of several nanometers. Since the nanostructure is commonly utilized in a low-dimensional form, it is scientifically interesting and technologically important to investigate whether ferroelectricity is also sustained in ultimate SnTe nanoribbons (1D) and SnTe nanoflakes (0D) in addition to the discovered monolayer (2D) form. However, the ferroelectric critical size for SnTe nanoribbons and nanoflakes has not yet been reported.

In this study, we investigate whether a ferroelectric critical size exists in low-dimensional structure of SnTe, the nanoribbons (1D) and nanoflakes (0D) using first-principle, density-functional theory (DFT) calculations.

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

We focus on SnTe nanoribbons and nanoflakes with an edge structure. SnTe has two types of edges formed along the [110] and [100] directions. Henceforth, these edge structures are called [110] edge and [100] edge, respectively. Table 1 shows the preliminarily calculated formation energies of the [110] and [100] edges. Here, the edge formation energy is calculated by *E*edge = (*E*nanoribbon – *E*monolayer)/2*l*, where *E*nanoribbon and *E*monolayer are the total energies of SnTe nanoribbons and SnTe monolayer, respectively, and *l* is the length of edge in the nanoribbon model, shown later. The formation energy of the [110] edge is lower, and thus more stable, than that of the [100] edge. In addition, the [110] edge structure was experimentally observed at the edge of the SnTe monolayers [18–20]. Following these experimental and theoretical results, we thus analyze the nanoribbons and nanoflakes consisting of the [110] edges, as shown in Figure 1. Figure 1 shows the paraelectric phase of SnTe monolayer with a space group of *Fm3m*. In the ferroelectric phase, Sn and Te atoms are spontaneously displaced along the [110] direction. The space group of the ferroelectric SnTe monolayer is *Pmn*21. The following SnTe nanoribbons and nanoflakes are in the ferroelectric phase, and thus modeled with a small initial displacement along [110]. Note that the electronic origin of ferroelectricity and alternating short and long bonds has already been discussed by Liu et al. [21], and they revealed that the stabilization of the ferroelectric phase and large distortion originates from an interplay between hybridization interactions of Sn-Te, which act as a driving force for the ferroelectricity, and Pauli repulsions, which tend to suppress the ferroelectricity.

**Table 1.** Calculated edge formation energy *E*edge of [110] and [100] edge in layered SnTe.

**Figure 1.** Schematic illustration of (**a**) SnTe nanoribbon and (**b**) SnTe nanoflake.

Figure 2 shows the simulation model of the SnTe nanoribbons. Here, *m*110 denotes the number of unit cells constituting the nanoribbon width. To explore the critical ferroelectric size, we calculate several SnTe nanoribbons with different widths of *m*110 = 1 to 10 (6 to 65 Å). The model of a nanoribbon width 3-unit-cells width (*m*110 = 3) is shown in Figure 2 as an example. In this simulation model, there are 4*m*110 + 2 Sn and Te atoms each, for a total of 8*m*110 + 4 atoms. The three-dimensional periodic boundary condition is applied to the simulation cell. To prevent undesirable interactions between the nanoribbons in the neighboring image cells, a vacuum region of *l*v = 20 Å in the *y*- and *z* directions. *a*1, *a*2, and *a*3 in the figure are the simulation cell vectors, and are represented by

$$a\_1 = (a, 0, 0),\tag{1}$$

$$a\_2 = (0, m\_{110}b + l\_{\forall}, 0)\_\prime \tag{2}$$

$$\mathfrak{a}\_{\mathbb{S}} = (0, 0, \mathfrak{c} + l\_{\mathrm{v}}),\tag{3}$$

where *a*, *b*, and *c* are the equilibrium lattice constants of the SnTe monolayer, *a* = 6.520 Å, *b* = 6.479 Å, and *c* = 3.240 Å.

Figure 3 shows the simulation model of SnTe nanoflakes. Here, *m*f denotes the number of unit cells constituting each side of the SnTe nanoflake. To explore the critical ferroelectric size, we calculate several SnTe nanoflakes with *m*f = 1 to 7 (6 to 45 Å) on one side. The model of a SnTe nanoflake with 5 × 5 unit-cells surface area (*m*f = 5) (hereinafter referred to as a 5 × 5 nanoflake) as an example. In this simulation model, there are (2*m*f + 1)2 Sn and Te atoms each, for a total of 2 × (2*m*f + 1)2 atoms. The three-dimensional periodic boundary condition is applied to the simulation cell. To avoid undesirable interactions from neighboring nanoribbons in image cells, a vacuum region of *l*v = 20 Å is introduced to the *x, y,* and *z* directions of the simulation cell. *a*1, *a*2, and *a*3 in the figure are the simulation cell vectors, and are represented by

$$a\_1 = (m\_{\text{fr}}a + l\_{\text{rv}}, 0, 0), \tag{4}$$

$$a\_2 = (0, m\_\text{f}b + l\_\text{v}, 0),\tag{5}$$

$$\mathfrak{a}\_{\mathfrak{B}} = (0, 0, c + l\_{\mathrm{v}}),\tag{6}$$

where, *a*, *b*, and *c* are the equilibrium lattice constants of the SnTe monolayer.

**Figure 2.** Simulation models of SnTe nanoribbon with 3-unit-cells width. The gray area and solid lines indicate edges of SnTe nanoribbon. The solid boxes represent the simulation cells. *a*1, *a*2 and *a*3 indicate the simulation cell vectors.

We perform first-principle, density-functional theory (DFT) calculations [22,23]. The effects of nuclei and inner shells are expressed by the project-augmented wave (PAW) method [24,25], and the Sn 4*d*, 5*s*, 5*p* orbitals and the Te 5*s*, 5*p* orbitals are explicitly treated as valence electrons. The electronic wave function is expanded in plane-waves, and the cutoff energy of the plane waves is set to 450 eV. The Brillouin zone integration is performed using a 10 × 1 × 1 Monkhorst-Pack *k*-point mesh for the nanoribbon models and a 1 × 1 × 1 *k*-point mesh for the nanoflake models [26]. The PBE-D3 functional is used for the evaluation of the exchange correlation term [27]. The stable structure is determined by relaxing atomic positions using the conjugate gradient method until the force acting on the atoms became 1.0 × 10−3 eV/Å or less. All the first-principles calculations are performed using the Vienna Ab-initio Simulation Package (VASP) code [28,29]. The present calculation condition was confirmed to reproduce the electronic (band structure) and ferroelectric properties of SnTe monolayer via the comparison of experimental data [18].

**Figure 3.** Simulation models of the SnTe nanoflake with a surface area of 5 × 5 unit cells. The gray area and solid lines indicate edges of the SnTe nanoflake. The solid boxes represent the simulation cells. *a*1, *a*2 and *a*3 indicate the simulation cell vectors.

#### **3. Results and Discussion**

#### *3.1. Ferroelectric Critical Size of SnTe Nanoribbons*

Figure 4 shows the change in the spontaneous polarization *P* of the nanoribbon with respect to the width of the SnTe nanoribbon. The polarization of SnTe nanoribbons are aligned along the longitudinal direction ([110] direction). The black dashed line indicates the polarization value of the SnTe monolayer. Here, the ferroelectric polarization is calculated by the Berry phase approach [30]. Note that, in this study, the indeterminacy of spontaneous polarization via the Berry phase calculations is treated by using the paraelectric phase SnTe structure as the reference (zero-polarization) state. The SnTe nanoribbons with a 10-unit-cells width exhibits the polarization of *P* = 26.6 μC/cm2, which is almost the same magnitude as the SnTe monolayer, *P* = 26.5 μC/cm2. This indicates that there is no size effect in the nanoribbons with a 10-unit-cell width (65 Å). Even when the nanoribbon width is reduced, the ferroelectric polarization is almost constant at *P* = 26.6 to 27.9 μC/cm2, and all simulated nanoribbons show ferroelectric polarization comparable to that of the SnTe monolayer. This means that the SnTe nanoribbon does not exhibit any size-dependence, unlike conventional three-dimensional ferroelectrics such as BaTiO3 and PbTiO3. In addition, the SnTe nanoribbon with the minimum one-unit-cell width exhibits non-zero ferroelectric polarization. Our result indicates that ferroelectricity does not disappear even in the smallest nanoribbon, and there is, therefore, no critical dimension in which the ferroelectricity disappears in the SnTe nanoribbons.

**Figure 4.** Polarization P in SnTe nanoribbon as a function of the width. The red dotted line shows the ferroelectric polarization of 2D SnTe monolayer. UC denotes the unit cells.

Conventional three-dimensional crystalline ferroelectrics, such as the perovskite oxides BaTiO3 and PbTiO3, exhibit remarkable size-dependence, and the ferroelectricity disappears when the material size reaches several nanometers [31–33]: for example, the critical ferroelectric size of BaTiO3 nano-films was reported to be 2-nm thickness [12,13], that of PbTiO3 nano-films was 1.2-nm thickness [14,34], and Pb(Zr,Ti)O3 nanodot lost its ferroelectricity when it became 3.2 nm in diameter [10]. Regardless of the material and shape, the ferroelectricity is reduced and finally disappears as the material size decreases. As was explained in the introduction, such size effects and critical dimensions on ferroelectricity originate from two factors: (I) electrostatic effects due to the formation of a depolarization field [16,35–38], and (II) the reconstruction and rearrangement of atomic and electronic structures due to the low coordination number at the surface (or edge) [36–39].

Considering the above discussion on the conventional ferroelectrics, here we investigate the absence of a critical ferroelectric size of SnTe nanoribbons in terms of factors (I) and (II). Considering factor (I), the ferroelectric polarization direction of the SnTe nanoribbon is almost parallel to the edge line, and thereby, no surface polarization charge is induced and no depolarization field is generated. Therefore, the electrostatic factor (I) due to the depolarization field does not occur in SnTe nanoribbons. Next, the dangling bond formation at the edge of the SnTe nanoribbon is examined to consider factor (II). Here, we first refer the bonding structure of the SnTe monolayer (i.e., without dangling bonds) as a reference, as shown in Figure 5. In the SnTe monolayer, spontaneous polarization *P* appears in the [110] direction due to the relative displacement of Sn2+ ions in the [110] direction with respect to Te2− ions in the ferroelectric phase (see Figure 5a). Due to the ionic displacement, the SnTe monolayer forms an Sn-Te bond along the [110] direction, which is the same as the direction of spontaneous polarization. This means that the relative displacement and bonding of the Sn2+ and Te2− ions in the [110] direction in the SnTe monolayer corresponds to the spontaneous polarization and, thereby, is a characteristic of the ferroelectric manifestation of the SnTe monolayer. Figure 6 compares the bonding situation between in the SnTe monolayer and the SnTe nanoribbon. The white lines in the figure indicate Sn-Te bonds, while the white dashed circles and lines in the SnTe nanoribbon indicate the imaginary Sn or Te position and bond, respectively, which were formed in the SnTe monolayer. As described above, the SnTe monolayer forms an armchair-shaped Sn-Te bond along the [110] direction (see Figure 5b-2), and this situation can be seen alternately appearing on the Sn-Te bond from the top view of the monolayer, as shown in Figure 6a. In general, near the surface or edge, the rearrangement of electrons occurs due to the presence of dangling bonds, which affects ferroelectricity [36–38]. On the other hand, focusing on the electron density distribution at the edge of the SnTe nanoribbon in Figure 6b, Sn-Te is also found along the [110] direction, which is almost the same as the electron density distribution of the SnTe monolayer; i.e., the absence of a dangling bond at the edge of SnTe monolayer. This is because the bonding sequence in the SnTe monolayer is mainly along the polar direction of [110], and thereby, the formation of the [110] edge does not introduce any dangling bond. The absence of a dangling

bond at the [110] edge in the SnTe nanoribbons makes the ferroelectricity same as that in the SnTe monolayer. Therefore, the absence of factors (I) and (II) leads to the absence of critical ferroelectric size in SnTe nanoribbons.

**Figure 5.** (**a**) Crystal structure of SnTe monolayer and (**b**) charge density distributions in SnTe monolayer. The covalent Sn-Te bonds are shown by white lines. Red arrows *P* indicate the direction of spontaneous polarization in the SnTe monolayer. Yellow and blue arrows indicate the displacement of Sn and Te atoms, respectively.

**Figure 6.** Charge density distributions (**a**) in the SnTe monolayer and (**b**) in the SnTe nanoribbon with 6-unit-cells width. Red arrows *P* indicate the spontaneous polarization. The covalent Sn-Te bonds are shown by white lines. White dotted circles and lines indicate the imaginary Sn or Te atom positions and Sn-Te bonds formed in the SnTe monolayer.

#### *3.2. Ferroelectric Critical Size of SnTe Nanoflakes*

Figure 7 shows the local polarization distribution in the 5 × 5 nanoflakes. Spontaneous polarization exists and forms a vortex polarization order in the counterclockwise direction. Similar vortex polarization distributions are also observed in the other 6 × 6 and 7 × 7 nanoflakes. Such a polar vortex is characteristic of the polarization order in ferroelectric nanostructures [11,40] because the surface component of polarization is aligned along a surface or edge to prevent the formation of the depolarization field and minimize the electrostatic energy efficiently. Since SnTe nanoflakes are surrounded by edges on all sides, a surface polarization charge is induced at the edges, and a depolarization field is generated inside the SnTe nanoflakes. Since the parallel polarization to the edge of the nanoflake does not produce any surface polarization charge or depolarization field, the formation of vortex polarization is more energetically stable than the original straight form of ferroelectric polarization.

**Figure 7.** Vector-field representation of local polarization distribution in the 5 × 5 nanoflake. Red arrows indicate the spontaneous polarization.

To evaluate the critical dimension of the ferroelectricity in SnTe nanoflakes with vortex polarization, here we consider the toroidal moment *G*. The toroidal moment *G* is used as a physical quantity that characterizes vortex polarization appearing in nanoscale ferroelectric materials [10,41,42], and is given by the following equation [42]

$$G = \frac{1}{2N} \sum\_{\mathbf{k}} r\_{\mathbf{k}} \times P\_{\mathbf{k}} \tag{7}$$

where **r***k* is the position vector of the *k*-th local unit cell, *Pk* is the local spontaneous polarization at position **r***k*, and *N* is the number of local unit cells included in the simulation cell. The sum is taken of all unit cells in the simulation cell. The local polarization is evaluated using the Born effective charge tensors [30]. The site-by-site local polarization can be calculated by

$$P\_i = \frac{\mathcal{e}}{\Omega\_{\mathcal{C}}} w\_j Z\_j \mu\_j \tag{8}$$

where Ω*c* is the volume of the local unit cell *i*; *e* and *uj* denote the electron charge and the atomic displacement vector relative to the ideal lattice site (paraelectric lattice site) of atom *j*, respectively. The index *j* covers all atoms in the local unit cell *i*. *Zj* is the Born effective charge tensor of atom *j* and *wj* is a weight factor.

Figure 8 shows the toroidal moment *Gz* and the average polarization *P* for each SnTe nanoflake size. Note that we show the *z* component of toroidal moment *G* because all of the vortex polarization appears on the *xy* plane. The toroidal moment *Gz* decreases as the size of the SnTe nanoflakes decreases. When the size of the SnTe nanoflakes become 4 × 4 unit-cell size or less, the toroidal moment *Gz* becomes zero. Here, we also show the averaged polarization in panel (b), as defined by

$$\overline{P} = \frac{1}{N} \sum\_{\mathbf{k}} |P\_{\mathbf{k}}| \tag{9}$$

Such size-dependent behavior is also seen in the averaged polarization. The average polarization value decreases as the size of the SnTe nanoflakes decreases, and the polarization becomes 0 when one side is less than four unit cells (25 Å). These results indicate that, in contrast to the SnTe monolayer (2D) and nanoribbons (1D), the SnTe nanoflakes (0D) exhibit remarkable size-dependence and a critical dimension at which ferroelectricity disappears. The critical dimension is evaluated to be four unit cells on one side (about 25 Å). This suggests that structural low-dimensionality can affect the ferroelectricity of SnTe system and lead to the appearance of a ferroelectric critical size.

**Figure 8.** (**a**) Toroidal moment, *G*, and (**b**) averaged polarization, *P*, in SnTe nanoflake as a function of SnTe nanoflake size. The green dotted line indicates the polarization of the SnTe monolayer. PE indicates the paraelectric phase.

In the following, we discuss the appearance of critical dimension of the vortex polarization in the SnTe nanoflakes. As discussed in Section 3.1, the factors that cause the size effect and critical dimension appear are: (i) the electrostatic effect, due to the formation of a depolarization field [16,35], and (ii) the reconstruction and rearrangement of the atomic and electronic structure due to a lower coordination number at a surface or edge [36–38]. In order to examine the effect of these factors, we calculate an imaginary model of an edge-free SnTe monolayer with a vortex polarization that is the same as the nanoflakes, as shown in Figure 9, and compare the results. This model consists of periodically arranged clockwise and counterclockwise polarization vortices in a SnTe monolayer, and each polarization vortex mimics a nanoflake with a vortex polarization but without any edge structures. Since this imaginary edge-free SnTe monolayer model is free from the edge and the resulting (coinciding) electrostatic depolarization field and dangling bonds, through comparison between the SnTe nanoflakes and this imaginary edge-free model, one can extract how the existence of edge and electrostatic field and/or dangling bonds affect the ferroelectricity of the SnTe nanoflakes. Figure 10 shows the calculated local polarization field of the imaginary edge-free SnTe models with polarization-vortex periodicity of 5 × 5 and 4 × 4 unit cells. The edge-free SnTe model with a 5 × 5 unit cell size exhibits a quasi-stable vortex polarization, as shown in Figure 10a, which is almost same as that observed in the 5 × 5 SnTe nanoflake, as shown in Figure 7. On the other hand, no spontaneous polarization is observed in the edge-free SnTe model with a 4 × 4 unit cell or less (Figure 10b). This is also consistent with the absence of polarization and paraelectric nature of the 4 × 4 SnTe nanoflake. These results indicate that the presence or absence of edges does not affect the appearance of a ferroelectric critical size of SnTe nanoflakes. Therefore, the effects of factors (i) the depolarization field and (ii) the dangling formation at the edges are not the

primary causes of the disappearance of the vortex polarization in the SnTe nanoflakes. The situation of the SnTe nanoflakes is clearly different from that of the conventional ferroelectrics, where the critical size appears due to these two factors.

**Figure 9.** Simulation model of the edge-free SnTe with periodic polarization vortices. Red arrows indicate the direction of vortex polarization.

**Figure 10.** Vector-field representation of the spontaneous polarization of the imaginary edge-free SnTe models with a polarization-vortex periodicity of (**a**) 5 × 5 and (**b**) 4 × 4 unit cells. Red arrows indicate spontaneous polarization.

From the above discussion, there is the possibility that the critical size of SnTe nanoflakes is not due to the presence of edges, but the intrinsic size dependence of the vortex polarization itself. To confirm this possibility, we investigate the energetics of the edge-free SnTe models with different

vortex sizes. Again, this model is free from the edge and can only extract the effect of the size of vortex polarization. Figure 11 shows the total energy difference of the polar vortex phase from the total energy of the paraelectric (PE) phase Δ*E*vortex as a function of periodic vortex size. For comparison, the ferroelectric (FE) phase with straight polarization (single domain) is also shown in Figure 11. Here, the total energy difference Δ*E*vortex is normalized by dividing by the number of unit cells in each system. Δ*E*vortex is negative at 7 × 7 vortex size, and the vortex size is more stable than the paraelectric phase. Δ*E*vortex increases with decreasing vortex polarization size, and, finally, Δ*E*vortex may reach the energy of the PE phase at the 4 × 4 vortex size or less. As shown in Figure 10b-2, the 4 × 4 vortex model becomes paraelectric, and thus the total energy of 4 × 4 size or less is same as that of the PE phase. This indicates that the vortex polarization increases its total energy as the vortex size decreases, and finally the vortex polarization with a smaller than 5 × 5 size becomes more energetically unstable than the PE phase and the vortex polarization cannot be formed. We thus confirm that the vortex form of polarization intrinsically exhibits the size dependence, and there exists a critical size of vortex polarization itself. Therefore, the ferroelectric critical size observed in the SnTe nanoflakes originates from the intrinsic size limit of polarization vortices.

**Figure 11.** Total energy difference of the vortex polarization Δ*E*vortex and the ferroelectric phase of the SnTe monolayer on the basis of the paraelectric phase as a function of the size of vortex polarization.

The increase in the total energy of vortex polarization due to the decrease in the size of vortices is due to the increase in domain wall densities. As shown in Figure 12, the vortex structure has four domains (white area), and they are separated by four 90◦ domain walls (green area). As the size of the vortex polarization decreases, the ratio of the domain wall per unit surface area increases, and the total energy increases. Such a high density of domain walls in the smaller vortex polarization is the primary cause of the loss of polarization in the smaller SnTe nanoflakes.

With the recent advance in manufacturing technology for two-dimensional materials, such as graphene, there are numerous experimental studies which reported the fabrication of various nanostructures of 2D materials, including graphene nanoribbons, nanoflakes, nanotubes and nanohorns. Using the fabrication techniques of graphene and its nanostructures, the fabrication of SnTe nanoribbons and nanoflakes presented in this study should be experimentally feasible. Thus, our results may stimulate an experimental study to fabricate and characterize the unique ferroelectric properties of SnTe monolayer and nanostructures.

**Figure 12.** Schematic illustration of domain structure in the SnTe nanoflake consisting of 90◦ domain walls. Red arrows indicate spontaneous polarization and green areas indicate domain walls.

#### **4. Conclusions**

In this study, we investigated a ferroelectric critical size of low-dimensional SnTe nanostructures such as nanoribbons (1D) and nanoflakes (0D) using first-principle density-functional theory calculations. We demonstrated that the smallest (one-unit-cell width) SnTe nanoribbon could sustain ferroelectricity and there was no ferroelectric critical size in the SnTe nanoribbons. On the other hand, the SnTe nanoflakes formed a vortex of polarization and lost its toroidal ferroelectricity below the surface area of 4 × 4 unit cells (about 25 Å on one side). We also revealed the atomic and electronic mechanism of the absence or presence of critical size in SnTe low-dimensional nanostructures. Our result provides an insight into intrinsic ferroelectric critical sizes for low-dimensional chalcogenide layered materials.

**Author Contributions:** Conceptualization, T.S. and T.K.; methodology, T.S. and K.M.; formal analysis, T.S. and K.M.; investigation, T.S. and K.M.; writing—original draft preparation, T.S. and K.M.; writing—review and editing, T.S., T.X. and J.W.; visualization, T.S. and K.M.; supervision, T.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by JSPS KAKENHI, grant number 17H03145, 18H05241, 18K18806, and 19K21918.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).


*3.5. Antioxidant Activity*

RA exhibited free radicals scavenging activity in hepatic stellate cells (HSCs) as a result of its antioxidant e ffects by boosting GSH synthesis and participating in NF-κB-dependent inhibition of MMP-2 activity. It also has the ability to reverse activated HSCs to quiescent cells and ultimately inhibits MMP-2 activity. RNA interference-imposed knockdown of NF-κB abolished MMP-2 down-regulation by RA. NF-κB inactivation mediated by RA could be blocked by the diphenyleneiodonium chloride, a potent inhibitor of NADH/NADPH oxidase. Moreover, transfection of dominant-negative (DN) mutant JNK1, p38 α kinase, or extracellular signal-regulated kinases 2 (ERK2) had no such e ffect. At once, RA suppresses lipid peroxidation (LPO) and ROS generation, whereas in HSC-T6 cells it increases cellular GSH. Additionally, it significantly increases Nrf2 translocation and catalytic subunits from glutamate cysteine ligase (GCLc) expression but was not able to modulate GCL (GCLm) subunits and antioxidant response element (ARE)-mediated luciferase activity. GClc up-regulation mediated by RA is inhibited by shRNA-induced Nrf2 knockdown. The knocking down of Nrf2 abolished RA-mediated inhibition of ROS [16,62].

On the other hand, lycopene and RA administration reduced elevated blood urea nitrogen, renal malondialdehyde (MDA), proapoptotic protein (Bax) immuno-expression, serum creatinine, inducible nitric oxide synthase (iNOS), and autophagic marker protein (LC3/B) levels induced by gentamicin. This combination also increased the reduced SOD, an antiapoptotic protein (Bcl2) immuno-expression, GPx, and GSH levels and ameliorated gentamicin-induced histopathological changes. Moreover, it also evidenced a greater protective e ffect than corresponding monotherapy [63].

The in vivo antioxidant defense system consists of antioxidant enzymes including CAT, GPx, SOD, and nutritional antioxidants. Any disturbance in normal antioxidant defense system triggers several diseases, including diabetes, cancer, atherosclerosis, and degenerative diseases [64]. In experimental animals, carbon tetrachloride (CCl4) induced neurotoxicity, whereas CCl4 skin absorption, inhalation, and ingestion increased lipid peroxidation and reduced protein and antioxidant enzymes contents. This molecule produces free radicals in the lungs, heart, blood cells, and kidney. Under aerobic conditions, CCl4 is converted into highly reactive trichloromethyl radicals through the action of the cytochrome P450 system [65].

Brain amyloid-β (Aβ) accumulation is a hallmark of Alzheimer's disease (AD) and has an important role in cognitive dysfunction [66]. At a dose of 0.25 mg/kg, RA significantly enhanced cognitive function and object discrimination and recognition test. Furthermore, RA decreased the time to reach the platform and increased the number of crossings over the removed platform, when compared with Aβ25-35-induced group in Morris water maze test; moreover, it reduced NO and MDA levels in kidney, brain, and liver [67]. RA also suppresses AD development by reducing amyloid β aggregation by increasing monoamine secretion in mice [68].

RA also prevented oxidative stress in C6 glial cells by increasing cell viability and inhibiting lipid peroxidation. It also decreased H2O2-induced COX-2 and iNOS expression at the transcriptional level and down-regulated COX-2 protein expression and iNOS in C6 glial cells treated with RA [67]. It significantly reduced oxidative stress and increased antioxidant status in Wistar rats post-spinal cord injury (SCI). RA also facilitated the inflammatory process through pro-inflammatory post-SCI and down-regulated NF-κB [69]. It also exerted a significant cytoprotective effect through covering the intercellular ROS in HaCat keratinocytes. RA also increased CAT, SOD, heme oxygenase-1 (HO-1), and transcription factor Nrf2 expression and activity, markedly reduced by UVB radiation [70].

On the other hand, in G93A-SOD1 transgenic mice with amyotrophic lateral sclerosis (ALS), RA application at a daily dose of 400 mg/kg significantly increased their survival by reliving function motor neurons deficits. These types of systematic changes were closely correlated with a decrease in neuronal loss and oxidative stress in ventral horns of G93A-SOD1 mice [71]. RA also increased SOD, GSH and GPx activities and decreased MDA levels in kidney and liver of sepsis-induced rats [72].

RA also reduced threshold shift, attenuated noise-induced hearing loss, and promoted hair cells survival. Moreover, it enhanced the endogenous antioxidant defense system by decreasing SOD production and up-regulation and decreased 4-HNE expression [73,74]. SOD, CAT, and GPx activities were increased through RA application at a dose of 50, 100, and 200 mg/kg. Furthermore, it induced structural changes in the kidney and liver at a dose of 200 mg/kg [75,76].


**5. Conclusions**

We analyzed the climate feedback on vegetation using CMIP5 model experiments for each climate-limited region. In contrast to the climate trend induced by the radiative effect, the positive trend in GPP and LAI can be attributed mainly to the CO2 fertilization effect. While CO2 fertilization was the main driver of the increasing trend in vegetation, the climate feedback on vegetation also contributed to 17% and 7% of vegetation growth in temperature-limited and radiation-limited regions, respectively. These feedbacks provide additional sensitivity to the CO2 fertilization, and can explain the discrepancy of the β factor between models and observation. The observed trend corroborates the importance of the climate feedback in explaining the greening earth.

**Author Contributions:** Conceptualization, H.H., R.R.N., G.B., L.C., S.G., W.W., C.M., R.E., T.L. and R.M.; data curation, A.R.M.

**Funding:** This research was funded by the NASA Earth science program.

**Acknowledgments:** Computational resources from NASA Earth Exchange helped facilitate the analysis.

**Conflicts of Interest:** The authors declare no conflict of interest.


*3.2. BMI z-Score Change for Children with Overweight and (Severe) Obesity on the Mid-Long Term after the Start of the COVID-19 Pandemic*

In 2020, 30 (51.7%) children had an increase in BMI z-score at T6 when compared to T0, while there were 19 children (48.7%) with an increase in the control group of 2019.

At T12, 29 (60.4%) and 18 (58.1%) children had an increase of the BMI z-score in 2020 and 2019, respectively. The change in BMI z-score at T6 and T12 in the 2020 group shows an increasing trend, compared to a decreasing trend in 2019 (Figure 2).

Based on model 1, the mean difference in BMI z-score change was not significant at T6 (+0.05 in 2020 versus −0.05 in 2019, difference = +0.10, 95% CI −0.01, +0.21, *p* = 0.061), while it was significant at T12 (+0.07 in 2020 versus −0.09 in 2019, difference = +0.16, 95% CI 0.02, 0.30, *p* = 0.022).

The same model was re-applied for the different subgroups of children that had an increase in their BMI z-score and children that had a decrease in BMI z-score. This showed significant differences at both T6 and T12 when 2020 was compared to 2019 for children with a BMI z-score increase (mean difference at T6 = 0.10, 95% CI 0.00, 0.21, *p* = 0.047 and mean difference at T12 0.22, 95% CI 0.11, 0.34, *p* < 0.001). It also showed a significant difference at T6 for children with a BMI z-score decrease when 2020 was compared to 2019 (mean difference 0.11, 95% CI 0.03, 0.20, *p*-value = 0.010) (Table 2).

**Figure 2.** Change in BMI z-score for children with overweight and (severe) obesity at T6 and T12 in 2019 and 2020.

**Table 2.** Mean change for subgroups that had an increase or decrease/stabilisation in the BMI z-score at T6 and T12 in 2020, when compared to 2019.

\* Statistically significant, *p* ≤ 0.05. ˆ based on model 1, which means that the differences in mean change from baseline scores (at T6 and T12) are corrected for centre, measurement moment, year\*measurement moment.

#### *3.3. Lifestyle Intervention Changes during the COVID-19 Pandemic*

When characteristics of the lifestyle intervention between the group in 2020 and 2019 were compared, no significant differences in total consultations per month or no-show consultations were observed. However, significant differences were observed in the number of outpatient clinic visits and remote consultations when 2020 and 2019 were compared (Figure 3).

**Figure 3.** Characteristics of the lifestyle intervention: different consultations at T6 (**a**) and T12 (**b**) in 2020 and 2019.

According to model 2, i.e., after correction for the lifestyle intervention characteristics, the mean change in BMI z-score was significantly higher in 2020 when compared to 2019 at both T6 and T12 (see Table 3).

**Table 3.** Estimated fixed effects in the model for BMI z-score difference for children with overweight and (severe) obesity.

\* Significant, *p* ≤ 0.05.

A significant contributing lifestyle factor in this model was the frequency of no-show consultations per month. With every missed consultation per month, the change in BMI z-score at both time points increased by +0.43 (95% CI 0.07, 0.80, *p* = 0.021).


**4. Conclusion**

DM is an important risk factor along with other diabetic complications for cognitive decline, which leads to loss of independence and nonadherence to medication and results in high healthcare cost. It is still controversial how early the age of cognitive impairment is, although there is enough documented links between diabetes and cognitive function. The standard glycaemic control is better than intensive glycaemic control in the prevention of cognitive decline. The challenge for treatment is to maintain the cognitive function by reduction of hypoglycaemic events.


*4.2. Collaboration*

A majority of the ONSOs (75.6%, M = 4.07, SD = 0.72) and even more of the OFFSOs (88.1%, M = 4.44, SD = 0.87) considered the exercises to be focused on collaboration. Less than half of the ONSOs (41.4%, M = 3.13, SD = 1.11) and 63.5% of the OFFSOs (M = 4.00, SD = 1.19) experienced that the collaboration began without an unnecessary waiting time. Additionally, 42.6% (M = 3.34, SD = 0.98) of the ONSOs and 57.2% (M = 3.97, SD = 1.22) of the OFFSOs considered that the exercises encompassed alternative strategies to collaborate. Moreover, 53.2% (M = 3.70, SD = 1.01) of the ONSOs and 79.7% (M = 4.40, SD = 0.99) of the OFFSOs considered that staff who needed to practice collaboration were engaged in the exercises. Discussions took place after the practical activities in the studied exercises; however, 33% of the ONSOs thought these discussions were insufficient, and they wanted more seminar activities after the practical actions (M = 3.17, SD = 1.00). In contrast, 29.8% of the OFFSOs considered the discussions to be insufficient, while 20.6% remained neutral (M = 3.42, SD = 1.42). Out of all the ONSO respondents, 44.6% did not consider the exercises to be those they usually practiced (M = 2.82, SD = 1.30), while only 5.2% of the OFFSOs considered the same (M = 4.46, SD = 0.93). The mean for all items within the collaboration dimension was 3.52 (SD = 1.01) for the ONSOs and 4.06 (SD = 0.64) for the OFFSOs (Figure 1).


**7. Conclusion**

and skin. Cardiac cCK has two forms as a homodimer (MMCK and/or BBCK) or heterodimer (MBCK), which is a cardiac-specific form [24]. According to this knowledge, it is said that MBCK can usually be determined as an indicator of a heart attack. sMtCK is the mainly octameric form [24] and places the outer intermembrane space and mitochondrial cristae between membranal protein ANT in the inner membrane and VDAC in the outer layer [24]). MtCK has high affinity to cardiolipin [14] and the outer surface of the inner mitochondrial membrane [24]. It must not be forgotten that DOX has a great relationship with cardiolipin. So, one of DOX's targets is MtCK. Moreover, DOX oxidizes MtCK at cysteine residues. Besides oxidation, DOX leads to inactivation of MtCK, resulting in enhanced embryonic CK isoform

MtCK can efficiently produce PCr from creatine [24, 43]. Transformation of creatine to PCr firmly binds between energy generation and utilization. MtCK, an octameric, accompanies ANT, and VDAC (porin) [43]. ANT can transfer ADP to matrix space. Then, ADP resynthesizes ATP through oxidative phosphorylation. However, PCr can be sent to the cytosol via VDAC [24]. PCr is utilized by cCK to maintain the subcellular local ATP/ADP ratio [24].

Although DOX inactivates all CK, MtCK is especially destroyed [43] by the drug through dissociation of its structure from octamer to dimer [24, 43] or infusion of binding MtCK at mitochondrial membranes, such as cardiolipin [24]. Moreover, cardiac MtCK has been reported to be more sensitive to DOX than uMtCK, leading to selective toxicity in heart tissue. The inactivation of MtCK by DOX is linked to the drug's dosage. At a low dose below 100 μM, MtCK's inactivation occurs because of DOX's redox modification from its cysteine residues. Its high treatment, however, depresses MtCK due to ROS production. Furthermore, DOX and MtCK have been indicated to have a standard feature, they tend to attach an inner mitochondrial membrane, providing high DOX concentration around the MtCK. Additionally, when DOX

to oxidative and nitrous stress, which means that CK is very vulnerable to the redox status of cells. Even a 2 μM DOX concentration has been reported to lead to dimerization of MtCK (ordinarily octameric), and augment the inhibition and dimerization at a 20 μM intensity. Also, it is indicated that total CK activity has been noticed to reduce (by nearly 20%) for DOX treatment concentrated at 20 μM. Under this circumstance, CK has still been maintaining its function due to a compensatory mechanism, which reduces MCK (a myofibrillar isoform) and high BCK (a fetal isoform) that is elevated by heart failure or cardiac hypertrophy. It is vital to know that CK shift is reported to be within 1 h at 2 μM of DOX. So, CK system dysfunction might probably participate in DOX-mediated heart failure. MtCK inhibition by dimerization not only causes energy transfer from mitochondria to the cytosol but also influences the mitochondrial respiratory chain. Moreover, this inhibition destroys the three-modal interaction between MtCK, ANT, and VDAC, which means that MtCK plays a role in MPT. So, damage to the modal interaction could first trigger apoptosis. Besides programmed cell death, myofibrillar CK functionally integrates with SERCA. When a CK defect occurs, cytosolic Ca2+ balance is destroyed, leading to defects in contraction and relaxation coupling due to Ca2+ accumulation. Ca2+accumulation could also trigger apoptosis. This is why dysfunction of CK causes innate

, CK inhibition via DOX accelerates. The inhibition is linked

expression [14].

352 Mitochondrial Diseases

is activated by peroxidase/H2

apoptosis in two ways [43].

O2

It is impossible to ignore DOX therapy from cancer patients' treatment due to its inevitable chemotherapeutic efficiency on a variety of cancers. Unfortunately, there is limited knowledge available on DOX's cardiotoxicity, particularly mitochondriopathy. This is why the molecular clarifying mechanism of DOX's myocardial and mitochondrial toxicities will hopefully overcome the side effects and increase the survival rate of cancer patients as well. Therefore, further studies are needed to evaluate the detrimental effects of DOX on mitochondria to restore its limited utilization in cancer patients' therapy.


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