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Contents lists available at ScienceDirect Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys Improved microstructure and ferroelectric properties in B-site Ti 4+ - substituted (Bi 0.86 Sm 0.14 )FeO 3 polycrystalline ceramics Haidee Mana-ay a,,1 , Jesuraj Anthoniappen a , Chi-Shun Tu b , Raymund Sarmiento Jr. a , Cheng-Sao Chen c , Pin-Yi Chen d , Flora Mae Ruiz a a Department of Physics, University of San Carlos, Talamban Campus, Cebu City, 6000, Philippines b Department of Physics, Fu Jen Catholic University, New Taipei City, 24205, Taiwan c Department of Mechanical Engineering, Hwa Hsia University of Technology, New Taipei City, 23567, Taiwan d Department of Mechanical Engineering, Ming Chi University of Technology, New Taipei City, 24301, Taiwan HIGHLIGHTS Reduction of grain size upon Ti 4+ doping. Ti 4+ doping stabilized phase coexistence in (Bi 0.86 Sm 0.14 )FeO 3 ceramics. Enhanced ferroelectric order due to Ti 4+ doping. Ti 4+ doping enhanced ferroelectric and piezoelectric properties. Ti 4+ doping resulted in dielectric homogeneity and reduced dielectric loss. ARTICLEINFO Keywords: BiFeO 3 Multiferroics Morphotropic phase boundary Dielectric homogeneity Ferroelectric order ABSTRACT Multiferroic (Bi Sm )(Fe Ti )O 0.86 0.14 1 x x 3 ceramics (BFO14Sm100xTi) for = x 0.000, 0.005, and 0.010 were synthe- sized using solid-state reaction method to investigate the influence of Ti 4+ doping on their microstructure, di- electric, and ferroelectric behaviors. Scanning electron micrographs reveal that the Ti 4+ doping facilitates slow oxygen ion diffusion leading to reduced grain size (2.13, 1.75, and 1.50 μm for BFO14Sm, BFO14Sm0.5Ti, and BFO14Sm1Ti, respectively). High-resolution synchrotron X-ray diffraction (HR-XRD) analysis and Rietveld re- finements confirm the phase coexistence of polar R3c rhombohedral and nonpolar PbZrO 3 -like Pbam orthorhombic phases. The temperature dependent HR-XRD shows that the Ti 4+ ions stabilize phase coexistence up to ° 250 C .The enhanced dielectric homogeneity and decreased conductivity are caused by Ti 4+ substitution, which are attributed to reduction of oxygen vacancies. The improved piezoelectric coefficients (d 33 ) and symmetric P–E hysteresis loops of BFO14Sm0.5Ti, and BFO14Sm1Ti indicate enhanced ferroelectric order due to Ti 4+ ion doping. 1. Introduction Multiferroics are a group of smart materials which exhibit coupling between two or more ferroic orders, such as ferroelectricity and ferro- magnetism, making them potential candidates for technological applica- tions in multistate information-storage devices, modern electronics, energy harvesting, spintronics, and sensors [1–3]. Among these multiferroics, bismuth ferrite (BiFeO 3 , BFO) has gained enormous research interest due to the presence of magnetoelectric coupling at room temperature [2,4]. Thus, BFO is a promising alternative for a “green” multifunctional material as compared with lead-based compounds, such as Pb(Zr Ti )O (PZT), x 1 x 3 Pb(Mg Nb )O PbTiO , 1/3 2/3 3 3 and Pb(Zn Nb )O 1/3 2/3 3 PbTiO 3 [5]. It has a high ferroelectric Curie temperature ° T of 830 C C and anti- ferromagnetic Néel temperature ° T of 370 C N [6], enabling it to be utilized reliably at and above room temperature. It has been well established that many perovskites exhibit maximal electromechanical responses in the vicinity of the morphotropic phase boundary (MPB) [7,8]. The A-site samarium substitution (Bi 1- x Sm x FeO 3 ) at room temperature exhibits a ferroelectric rhombohedral phase for = x 0 12% , a coexistence of ferroelectric triclinic and orthor- hombic phases for = x 12.5 20% , and a non-polar orthorhombic phase for = x 25% [9]. It has been also proved that the smaller ionic radius of https://doi.org/10.1016/j.matchemphys.2018.12.092 Received 2 July 2018; Received in revised form 3 December 2018; Accepted 28 December 2018 Corresponding author. Physics Department, SC 341, 3rd Floor, Science Complex, Silliman University, 1 Hibbard Avenue, Dumaguete City, 6200, Philippines. E-mail address: [email protected] (H. Mana-ay). 1 Department of Physics, Silliman University, Dumaguete City, 6200, Philippines. Materials Chemistry and Physics 225 (2019) 272–278 Available online 04 January 2019 0254-0584/ © 2018 Elsevier B.V. All rights reserved. T

Transcript of Materials Chemistry and Physics

Contents lists available at ScienceDirect

Materials Chemistry and Physics

journal homepage: www.elsevier.com/locate/matchemphys

Improved microstructure and ferroelectric properties in B-site Ti4+-substituted (Bi0.86Sm0.14)FeO3 polycrystalline ceramicsHaidee Mana-aya,∗,1, Jesuraj Anthoniappena, Chi-Shun Tub, Raymund Sarmiento Jr.a,Cheng-Sao Chenc, Pin-Yi Chend, Flora Mae Ruizaa Department of Physics, University of San Carlos, Talamban Campus, Cebu City, 6000, PhilippinesbDepartment of Physics, Fu Jen Catholic University, New Taipei City, 24205, Taiwanc Department of Mechanical Engineering, Hwa Hsia University of Technology, New Taipei City, 23567, TaiwandDepartment of Mechanical Engineering, Ming Chi University of Technology, New Taipei City, 24301, Taiwan

H I G H L I G H T S

• Reduction of grain size upon Ti4+ doping.

• Ti4+ doping stabilized phase coexistence in (Bi0.86Sm0.14)FeO3 ceramics.

• Enhanced ferroelectric order due to Ti4+ doping.

• Ti4+ doping enhanced ferroelectric and piezoelectric properties.

• Ti4+ doping resulted in dielectric homogeneity and reduced dielectric loss.

A R T I C L E I N F O

Keywords:BiFeO3

MultiferroicsMorphotropic phase boundaryDielectric homogeneityFerroelectric order

A B S T R A C T

Multiferroic (Bi Sm )(Fe Ti )O0.86 0.14 1 x x 3 ceramics (BFO14Sm100xTi) for =x 0.000, 0.005, and 0.010 were synthe-sized using solid-state reaction method to investigate the influence of Ti4+ doping on their microstructure, di-electric, and ferroelectric behaviors. Scanning electron micrographs reveal that the Ti4+ doping facilitates slowoxygen ion diffusion leading to reduced grain size (2.13, 1.75, and 1.50 µm for BFO14Sm, BFO14Sm0.5Ti, andBFO14Sm1Ti, respectively). High-resolution synchrotron X-ray diffraction (HR-XRD) analysis and Rietveld re-finements confirm the phase coexistence of polar R3c rhombohedral and nonpolar PbZrO3-like Pbam orthorhombicphases. The temperature dependent HR-XRD shows that the Ti4+ ions stabilize phase coexistence up to °250 C. Theenhanced dielectric homogeneity and decreased conductivity are caused by Ti4+ substitution, which are attributedto reduction of oxygen vacancies. The improved piezoelectric coefficients (d33) and symmetric P–E hysteresis loopsof BFO14Sm0.5Ti, and BFO14Sm1Ti indicate enhanced ferroelectric order due to Ti4+ ion doping.

1. Introduction

Multiferroics are a group of smart materials which exhibit couplingbetween two or more ferroic orders, such as ferroelectricity and ferro-magnetism, making them potential candidates for technological applica-tions in multistate information-storage devices, modern electronics, energyharvesting, spintronics, and sensors [1–3]. Among these multiferroics,bismuth ferrite (BiFeO3, BFO) has gained enormous research interest dueto the presence of magnetoelectric coupling at room temperature [2,4].Thus, BFO is a promising alternative for a “green” multifunctional materialas compared with lead-based compounds, such as Pb(Zr Ti )O (PZT),x 1 x 3

Pb(Mg Nb )O PbTiO ,1/3 2/3 3 3 and Pb(Zn Nb )O1/3 2/3 3 PbTiO3 [5]. It has ahigh ferroelectric Curie temperature °T of 830 CC and anti-ferromagnetic Néel temperature °T of 370 CN [6], enabling it to beutilized reliably at and above room temperature.

It has been well established that many perovskites exhibit maximalelectromechanical responses in the vicinity of the morphotropic phaseboundary (MPB) [7,8]. The A-site samarium substitution (Bi1-xSmxFeO3) at room temperature exhibits a ferroelectric rhombohedralphase for =x 0–12%, a coexistence of ferroelectric triclinic and orthor-hombic phases for =x 12.5–20%, and a non-polar orthorhombic phasefor =x 25% [9]. It has been also proved that the smaller ionic radius of

https://doi.org/10.1016/j.matchemphys.2018.12.092Received 2 July 2018; Received in revised form 3 December 2018; Accepted 28 December 2018

∗ Corresponding author. Physics Department, SC 341, 3rd Floor, Science Complex, Silliman University, 1 Hibbard Avenue, Dumaguete City, 6200, Philippines.E-mail address: [email protected] (H. Mana-ay).

1 Department of Physics, Silliman University, Dumaguete City, 6200, Philippines.

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Sm3+ (1.079 ) compared to Bi3+ (∼1.4 ) [10] induces structuraldistortions which may significantly change the ferroelectric phase be-havior [11,12]. The existence of MPB in 14% samarium-doped BFO thinfilms was reported by many researchers [7,13–17] highlighting struc-tural stability up to °400 C and nanoscale twinned triclinic domains[14]. A recent report by Chen et al. [18] confirmed the coexistence ofR3c and Pbam structures in 14% Sm3+-doped BFO ceramics. The ef-fective piezoelectric value displays a rapid increase around=x 13 15% peaking at =x 14% with d 110 pm/V33 ) [14], which arecomparable to the values for epitaxial thin films of Pb-based com-pounds such as PZT [19]. A square-shaped FE hysteresis loop with goodsaturation and robust switchable polarization ( 70 µC/cm2) was re-ported for compositions from =x 0 up to x 14% [14]. Although Sm3+-doped BFO ceramics exhibited improved polarizations, the P–E hys-teresis loops did not show saturation due to the leaky nature [20]. Theelectrical conduction in Sm3+-doped BFO was suggested to be due tooxygen vacancies and irrespective of Sm3+ compositions [21].

Interestingly, B-site substitution with transition metals (Mn, Zr, Sn,and Ti) in BFO has showed enhanced multiferroic properties [22–25].Among these transition metals, a great interest is given to Ti4+ sub-stituent as it readily reacts with Bi2O3 [26] and is a highly polarizableion which might couple with Bi displacements [25]. The Ti4+ ions inthe d state allow 3d–O 2p hybridization which is essential for stabilizingferroelectric distortion [27]. Hence, enhanced ferroelectricity is ex-pected in the Ti4+-doped BFO. Secondly, the high leakage current andresistivity in BFO-based ceramics are due to the reduction of Fe3+ toFe2+ ions, resulting in formation of oxygen vacancies [7,28–30]. It ispostulated that the donor dopants could reduce concentration ofoxygen vacancies by compensating for Fe2+, hence reducing number ofcharge carriers [22–24]. Shi et al. reported that the Ti4+ has loweredconcentration of oxygen vacancies in BFO thin films by charge com-pensation which remarkably reduced conductivity [24]. In a study byKalantari et al., the dielectric and impedance spectroscopy data showedthat the Ti4+ doping reduced conductivity in the (Bi0.85Nd0.15)(Fe1-yTiy)O3 system [25]. Qi et al. also reported decreased leakage current inBFO by more than three orders of magnitude with Ti4+ ion doping [23].

In this work, 14% Sm3+-doped BFO is chosen to study effects of theB-site Ti4+ substitution on the microstructure, dielectric, piezoelectric,and ferroelectric properties. Small Ti4+ doping concentrations of 0.5%and 1% were chosen to stabilize the phase coexistence in 14%Sm3+-doped BFO and ensure a homogeneous distribution of Ti4+ ions intoBFO matrix. This study reveals that the Ti4+ ions facilitate a sloweroxygen ion diffusion resulting in reduced oxygen vacancies. It alsoenhanced dielectric homogeneity by effectively reducing the ionicconductivity caused by space charges. The higher d33 values and sym-metric P-E loops of the Ti4+-doped samples indicate enhanced ferro-electric order.

2. Materials and methods

Bi Sm Fe Ti O( )( )x x0.86 0.14 1 3 ceramics with =x 0.0, 0.005, and 0.01(labelled as BFO14Sm, BFO14Sm0.5Ti, and BFO14Sm1Ti, respectively)were fabricated using solid-state reaction method. High-purity (> 99%)powders of Bi O2 3, Sm O2 3, Fe O2 3, and TiO2 were used as starting re-agents. Stoichiometric amounts of powders were mixed thoroughlywith zirconia balls in an agate mortar for 48 h with ethanol as medium.The mixture was calcined at °830 C (3 h) for BFO14Sm andBFO14Sm0.5Ti and °810 C (3 h) for BFO14Sm1Ti with a heating rate of

° min5 C/ . A high-energy planetary ball-mill (Retsch PM100) was usedto reduce particle sizes. The powders were uniaxially pressed (2MPa)and pelletized into ∼1 cm disks and sintered at °870 C (4 h) forBFO14Sm and °880 C (3 h) for BFO14Sm0.5Ti and BFO14Sm1Ti. Theas-sintered samples were polished and then were annealed at °650 C for30min in order to remove the residual stress. In situ XRD analysis wasconducted using Rigaku Multiplex X-Ray Diffractometer with radiationsof K (1.5444 )1 and K 2 (1.5406 ). The Rietveld refinements were

performed using HighScore Plus software to determine structural spacegroups. Temperature-dependent in situ HR-XRD was performed at theNational Synchrotron Radiation Research Center in Taiwan (BL17B1).Morphologies of as-sintered ceramics were obtained using a scanningelectron microscope (HITACHI S-3400N FE-SEM) equipped with energydispersive X-ray (EDS) spectroscopy system. Raman spectroscopy wasconducted using a micro-Raman instrument (Nanobase, XperRam 200)equipped with a green laser of = 532 nm. Wayne-Kerr AnalyzerPMA3260A was used to obtain dielectric permittivity at zero-fieldheating and cooling. Direct piezoelectric coefficients d33 were measuredusing ZJ-6B piezometer at various dc poling E fields. Curves of polar-ization versus E field (P–E hysteresis loop) were studied using Sawyer-Tower circuit at f= 46 Hz.

3. Results and discussion

Fig. 1(a–c) shows the cross-sectional SEM micrographs of all sam-ples. The micrographs reveal dense but inhomogeneous distribution ofgrains. The average grain size (D̄) of BFO14Sm ( 2.13 µm) is sig-nificantly higher than BFO14Sm0.5Ti ( 1.75 µm) and BFO14Sm1Ti( 1.50 µm). It has been argued that Ti4+ plays the role of a donordopant due to its higher valence compared to Fe3+; thus, Ti4+ ionsuppresses the formation of oxygen vacancies leading to a sloweroxygen ion diffusion and consequently slower grain growth rate[31–33]. The EDS spectra of the samples found in Fig. 1(d–e) show thepresence of the individual elements of the basic chemical compositionof each sample. Furthermore, Fig. 2 shows the Raman spectra of TiO2

powder and BFO14Sm100xTi (x = 0, 0.005, 0.01) ceramics taken atroom temperature. The peaks marked by asterisk (*) are attributed tothe characteristic peaks of TiO2. The EDS and Raman spectra reveal thattitanium was successfully doped in BFO14SM0.5Ti and BFO14SM1Ti.

Fig. 3 shows the in situ XRD spectra at room temperature forBFO14Sm1Ti, BFO14Sm0.5Ti, and BFO14Sm. The spectra confirm the

Fig. 1. (a–c) Cross-sectional SEM micrographs of BFO14Sm, BFO14Sm0.5Ti,and BFO14Sm1Ti ceramics at room temperature with the corresponding (d–f)energy dispersive X-ray analysis spectra showing the constituent elementspresent.

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perovskite structure with minor secondary phases (Bi25FeO40 andBi2Fe4O9) as indicated by the pound sign (#) [18]. These secondaryphases are likely due to phase decompositions at high-temperaturesintering process [34]. There is no obvious 2 shift position of reflectionpeaks due to similar atomic radii of Ti4+ (0.605 ) and Fe3+ (0.64 ) atthe B-site [10]. All three samples exhibit similar peak splitting, in-dicating R3c rhombohedral and Pbam orthorhombic phase coexistenceas evidenced by visible splitting of the peaks at (110), (111), and (200)positions [7,34–37]. The Pbam orthorhombic phase is shown by anasterisk (*). The phase coexistence is clearly visible from the short anglescans of (111) and (200) peaks obtained from synchrotron HR-XRD asshown in the insets of Fig. 3(a–c). These phases are indicated by the letters “R” (rhombohedral R3c) and “O” (orthorhombic Pbam). This is

further supported by the Rietveld refinements shown in Fig. 4 con-firming that Ti4+-doping stabilized the phase coexistence in 14%Sm3+-doped BFO. Table 1 shows the calculated space groups and their phaseratios for each composition. Rietveld refinements suggest that therhombohedral R3c phase is most dominant at 1% Ti4+ dopant con-centration, indicating that Ti4+ doping induces a more polar order.Although a phase coexistence of R3c and Pnma has been predictedtheoretically at a critical dopant concentration (14% for samarium) [7],the present results are consistent with recent reports by Chen et al. andKhomchenko et al. which confirmed the coexistence of polar R3c andantipolar PbZrO3-like orthorhombic Pbam structures in BFO14Sm byTEM diffraction and Rietveld refinements [19,38].

Fig. 5 shows temperature-dependent synchrotron XRD spectra of(111) and (200) peaks for the samples. The spectra reveal that theroom-temperature phase coexistence is stable until °250 C in all three

Fig. 2. Raman spectra of TiO2 powder and BFO14Sm100xTi (x = 0, 0.005,0.01) ceramics taken at room temperature. Asterisk (*) denote characteristicpeaks of TiO2.

Fig. 3. In situ XRD diffraction patterns of BFO14Sm, BFO14Sm0.5Ti, andBFO14Sm1Ti ceramics at room temperature. Insets are the short angle (111)and (200) diffractions patterns obtained from high-resolution synchrotron XRDat room temperature.

Fig. 4. Experimental XRD patterns (Iobs), Rietveld refinements (Icalc), and de-viations (Iobs-Icalc) are represented by black lines, red “×” symbols, and greenlines, respectively. Rwp, Rexp, and 2 denote weighted R profile, statisticallyexpected R value, and goodness-of-fit, respectively. The peak ticks of Rietveldrefinements for various space groups are given under each sample.

Table 1Space groups and their phase ratios in BFO14Sm, BFO14Sm0.5Ti, andBFO14Sm1Ti ceramics determined by the Rietveld refinements.

Space groups Phase Ratio (%)

BFO14Sm BFO14Sm0.5Ti BFO14Sm1Ti

Rhombohedral R3c 11.8 14.4 74.7PbZrO3-like orthorhombic Pbam 85.6 82.2 23.7Orthorhombic Pbam (Bi2Fe4O9) 0 0.8 0Cubic I23 (Bi25FeO40) 2.4 2.5 1.6SmFeO3-like orthorhombic Pnma 0.2 0.1 0

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compositions. Above °250 C, three peaks (R and O phases) at the (111)diffraction merged into 2 peaks (R phase) and four peaks (R and Ophases) at the (200) diffraction converged into a single peak (R phase).This indicates a possible phase transition from two-phase coexistence toa single R3m rhombohedral structure around °300 C as evidenced byJeong et al. [39]. This suggests that Ti4+ doping does not affect thephase stability in BFO14Sm.

Fig. 6(a–c) shows the frequency dependence of the dielectric per-mittivity ( ) at room temperature measured in the frequency range of500 Hz–1MHz. At lower frequencies, BFO14Sm shows a large fre-quency-dependent dispersion of the dielectric permittivity compared tothe Ti4+-doped samples and attains a nearly constant value at higherfrequencies, in agreement with the report of Gu et al. [40]. This be-havior is typically attributed to space charge contributions [41]. It wassuggested that in polycrystalline ceramics, the displacement of chargecarriers takes place when the field is applied and they align at grainboundaries if resistance of grain boundaries is large. At grain bound-aries, space charge polarization governed by free charges is built up,resulting to the large value of dielectric permittivity [42]. However, thismechanism only takes place at low frequencies due to the large inertial

mass of space charges. At higher fields, the space charges no longerrespond to the field and have no contribution to the polarization.Therefore, the frequency dispersion of dielectric permittivity inBFO14Sm is caused by space charges lagging behind the applied field athigher frequencies, hence contributing less to the polarization [43]. Incontrast, Ti4+-doped samples only show a minimal frequency disper-sion behavior, indicating that the reduction of oxygen vacancies evi-denced by the decreased grain sizes in the Ti4+-doped samples resultsin the suppression of space charge polarization [36]. The minimal de-crease in dielectric permittivity with increasing frequency was alsoobserved by Shi et al. for (Sm/Ti) co-doped BFO ceramics [44].

The right insets in Fig. 6(a–c) show the temperature dependence ofdielectric permittivity ( ) and dielectric loss (tan ) of Ti4+-doped andundoped samples. The room-temperature dielectric permittivities at1MHz for BFO14Sm, BFO14Sm0.5Ti, and BFO14Sm1Ti are 143, 108,and 131, respectively. The enhanced room-temperature dielectric per-mittivity in BFO14Sm1Ti as compared with BFO14Sm0.5Ti is attributedto the more dominant polar rhombohedral structure in BFO14Sm1Ti asrevealed by the phase ratios in Table 1 determined through the Rietveldrefinements. As the temperature increases, the dielectric permittivityincreases sharply in BFO14Sm, exhibiting sharp frequency-dependentpeaks around °200 C , which is likely due to thermally inducedhopping conduction and space charge polarization [42,43]. A similarbehavior was also observed for other BFO-based materials reported inliteratures [42,45]. In contrast, the Ti4+-doped samples show fre-quency-independent broad peaks, which suggests that Ti4+ doping canenhance dielectric homogeneity [46].

The room-temperature dielectric loss at 1MHz decreases with Ti4+

Fig. 5. Temperature-dependent high-resolution synchrotron (111) and (200)diffraction patterns of BFO14Sm, BFO14Sm0.5Ti, and BFO14Sm1Ti ceramics.Peak labelled with + is attributed to minor secondary phase.

Fig. 6. (a–c). Frequency-dependent dielectric permittivity at room temperatureof BFO14Sm, BFO14Sm0.5Ti, and BFO14Sm1Ti. Right insets are the tempera-ture-dependent dielectric permittivity and dielectric loss at 500 kHz and 1MHz.Left insets are the thermal hysteresis taken at 1MHz.

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doping from ∼0.5360 in BFO14Sm to ∼0.0140 and ∼0.0170 inBFO14Sm0.5Ti and BFO14Sm1Ti, respectively. This suggests that Ti4+

doping has effectively reduced leakage current and electrical con-ductivity, in agreement with the reports of Wang et al. and Deng et al.[33,35]. At higher temperatures, the thermally activated process asso-ciated with oxygen vacancies results in the increase in conductivity andthus leads to an exponential increase of dielectric loss [47]. The strongthermal dielectric hystereses at 1MHz shown in the left insets ofFig. 6(a–c) indicate a first-order transition in these compositions.

Fig. 7 shows piezoelectric coefficient (d )33 for Ti4+-doped and un-doped samples measured at room temperature for different polingelectric fields. The maximal piezoelectric coefficients (d33) obtained at100 kV/cm are 43, 51, and 53 pC/N for BFO14Sm, BFO14Sm0.5Ti, andBFO14Sm1Ti, respectively. These values are comparably higher thanthose reported by Chen et al. for Sm-doped BFO ceramics [9] and Shiet al. for (Sm/Ti)-codoped BFO ceramics [44]. The enhanced piezo-electric coefficients can be correlated to reduced grain size in the Ti4+-doped samples and enhanced ferroelectric order as observed from theSEM micrographs and Rietveld refinements, respectively. It has beenreported that the increase in piezoelectric properties with decreasinggrain size is influenced by domain-wall contributions. The domainwidth decreases with decreasing grain size, resulting in increased do-main wall density and activity, and thus contributing to enhancedpiezoelectric properties [48,49].

The effects of Ti4+ doping in ferroelectric polarization have beenstudied from polarization–electric field (P–E) loops at various polingelectric fields as shown in Fig. 8. Due to the higher dielectric loss,BFO14Sm can only withstand the applied field up to 50 kV/cm, whereasTi4+-doped samples can withstand applied field as high as 80 kV/cm.The BFO14Sm exhibits asymmetric and rounded hysteresis loops whichare characteristics of materials with higher leakage current and electricalconductivity [50,51], as reported in Sm-doped BFO [40] and Ba-dopedBFO [33]. The gap between the initial and final values of the polarizationat negative fields can be attributed to an asymmetric space-charge dis-tribution between the top and bottom electrodes. Positively-chargedoxygen vacancies tend to be more concentrated near the bottom surfacewhich generate high leakage current contributing to more polarizationloss during the negative cycle of the applied field. Similar behavior wasalso observed by Lee et al. in Na0.5K0.5NbO3 thin films attributing to anasymmetric oxygen vacancy and Na/K vacancy charge distribution be-tween bottom and top electrodes, respectively [52]. On the other hand,Ti4+-doped samples show the tendency of a typical hysteresis loop withan ellipse-like feature which is consistent with those reported in the lit-erature [31,33,53–55], suggesting enhanced ferroelectric nature incomparison with BFO14Sm. The improvement in the shape of the

ferroelectric hysteresis loops observed with the addition of Ti4+ can beattributed to the decrease of oxygen related defects brought about byTi4+ doping, which reduces the leakage current and thus improves thepolarization [56]. Shi et al. also reported enhanced ferroelectricity inBi0.86Sm0.14FeO3 ceramics with 1% Ti-doping although they argued thatsuch enhancement cannot be attributed to the generally believed me-chanism of suppression of leakage current [24]; further investigation isworth conducting on this issue. It should be noted that all three sampleswere not able to reach a saturated polarization before the leakage cur-rents became significant. Similar unsaturated and lossy loop behaviorwas observed for (Eu/Sr)-doped BFO even under large electric field [57].It has been reported that hysteresis loop in BFO-based polycrystallineceramics does not attain saturation at low poling fields due to its highcoercive field (150 kV/cm) [44,58–60]. The problem on BFO's highcoercive field and low resistance makes it very difficult to achieve asaturated hysteresis loop [29,61–63].

Fig. 7. Piezoelectric coefficient (d33) at different poling electric fields ofBFO14Sm, BFO14Sm0.5Ti, and BFO14Sm1Ti ceramics.

Fig. 8. Room-temperature polarization hysteresis (P–E) loops of BFO14Sm,BFO14Sm0.5Ti, and BFO14Sm1Ti ceramics at various poling electric fields.

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4. Conclusions

SEM micrographs reveal reduced grain sizes in (Sm, Ti) co-dopedbismuth ferrite ceramics due to slower oxygen ion diffusion and loweroxygen vacancies by the B-site Ti4+ substitution. EDS and Ramanspectra confirm the presence of titanium in the doped ceramic samples.In situ XRD spectra and Rietveld refinements confirm a phase coex-istence of rhombohedral R3c and orthorhombic Pbam phases. Rietveldrefinements further reveal that Ti4+-doping stabilizes the phase coex-istence and induces a more polar structure. High-resolution synchrotronXRD reveals that the phase coexistence was stabilized up to °250 C forall three samples. The Ti4+-doped samples have enhanced dielectrichomogeneity and reduced dielectric loss. This suggests that Ti4+ dopinghas effectively reduced electric conductivity caused by space charges.The enhanced d33 values and symmetric P–E hysteresis loops in theTi4+-doped samples indicate enhanced ferroelectric order. This worksuggests that the Ti4+ ions could effectively enhance dielectric andferroelectric properties in multiferroics which are important from theapplication perspective.

Declarations of interest

None.

Acknowledgment

This work is supported by the Research Enrichment Program Grantunder the Accelerated Science and Technology Human ResourceDevelopment Program of the Department of Science and TechnologyPhilippines. The authors express their sincere thanks to the MultiferroicResearch Laboratory at Fu Jen Catholic University (Taiwan), theMaterials Research Laboratory at Ming Chi University of Technology(Taiwan), and the National Synchrotron Radiation Research Center(Taiwan).

References

[1] A. Kumar, P. Sharma, D. Varshney, Structural and ferroic properties of La, Nd, andDy doped BiFeO3 ceramics, J. Ceram. 2015 (2015) 869071 https://doi.org/10.1155/2015/869071.

[2] M. Fiebig, Revival of the magnetoelectric effect, J. Phys. Appl. Phys. 38 (2005)R123 https://doi.org/10.1088/0022-3727/38/8/R01.

[3] S. Priya, R. Islam, S. Dong, D. Viehland, Recent advancements in magnetoelectricparticulate and laminate composites, J. Electroceram. 19 (1) (2007) 149–166https://doi.org/10.1007/s10832-007-9042-5.

[4] J.-P. Rivera, A short review of the magnetoelectric effect and related experimentaltechniques on single phase (multi-) ferroics, Eur. Phys. J. B 71 (2009) 299 https://doi.org/10.1140/epjb/e2009-00336-7.

[5] Z.-G. Ye (Ed.), Handbook of Advanced Dielectric, Piezoelectric and FerroelectricMaterials, Woodhead Publishing, Cambridge, 2008.

[6] S.R. Shannigrahi, A. Huang, N. Chandrasekhar, D. Tripathy, O. Adeyeye, Sc mod-ified multiferroic BiFeO3 thin films prepared through a sol-gel process, Appl. Phys.Lett. 90 (2007) 022901 https://doi.org/10.1063/1.2430652.

[7] J.-H. Lee, M.-A. Oak, H.J. Choi, J.Y. Son, H.M. Jang, Rhombohedral–orthorhombicmorphotropic phase boundary in BiFeO3-based multiferroics: first-principles pre-diction, J. Mater. Chem. 22 (4) (2012) 1667–1672, https://doi.org/10.1039/C1JM13582A.

[8] M. Ahart, M. Somayazulu, R.E. Cohen, P. Ganesh, P. Dera, H.-K. Mao, R. Hemley,Y. Ren, P. Liermann, Z. Wu, Origin of morphotropic phase boundaries in ferro-electrics, Nature 451 (2008) 545–548 https://doi.org/10.1038/nature06459.

[9] X. Chen, Y. Wang, Y. Yang, G. Yuan, J. Yin, Z. Liu, Structure, ferroelectricity andpiezoelectricity evolutions of Bi1-xSmxFeO3 at various temperatures, Solid StateCommun. 152 (6) (2012) 497–500 https://doi.org/10.1016/j.ssc.2011.12.044.

[10] R. Shannon, Revised effective ionic radii and systematic studies of interatomicdistances in halides and chalcogenides, Acta Crystallogr. A 32 (1976) 751–767https://doi.org/10.1107/S0567739476001551.

[11] H. Singh, K. Yadav, Structural, dielectric, vibrational and magnetic properties of Smdoped BiFeO3 multiferroic ceramics prepared by a rapid liquid phase sinteringmethod, Ceram. Int. 41 (8) (2015) 9285–9295 https://doi.org/10.1016/j.ceramint.2015.03.212.

[12] D. Kan, C.-J. Cheng, V. Nagarajan, I. Takeuchi, Composition and temperature-in-duced structural evolution in La, Sm, and Dy substituted BiFeO3 epitaxial thin filmsat morphotropic phase boundaries, J. Appl. Phys. 110 (1) (2011) 014106 https://doi.org/10.1063/1.3605492.

[13] D. Kan, L. Pálová, V. Anbusathaiah, C.-J. Cheng, S. Fujino, N. Valanoor, K. Rabe,I. Takeuchi, Universal behavior and electric‐field‐induced structural transition inrare‐earth‐substituted BiFeO3, Adv. Funct. Mater. 20 (2010) 1108–1115, https://doi.org/10.1002/adfm.200902017.

[14] S. Fujino, M. Murakami, V. Anbusathaiah, S.-H. Lim, V. Nagarajan, C.J. Fennie,M. Wuttig, L. Salamanca-Riba, I. Takeuchi, Combinatorial discovery of a lead-freemorphotropic phase boundary in a thin-film piezoelectric perovskite, Appl. Phys.Lett. 92 (20) (2008) 202904 https://doi.org/10.1063/1.2931706.

[15] C.-J. Cheng, D. Kan, S.-H. Lim, W.R. McKenzie, P.R. Munroe, L.G. Salamanca-Riba,R.L. Withers, I. Takeuchi, V. Nagarajan, Structural transitions and complex domainstructures across a ferroelectric-to-antiferroelectric phase boundary in epitaxial Sm-doped BiFeO3 thin films, Phys. Rev. B 80 (1) (2009) 014109 https://doi.org/10.1103/PhysRevB.80.014109.

[16] C.-J. Cheng, D. Kan, V. Anbusathaiah, I. Takeuchi, N. Valanoor, Microstructure-electromechanical property correlations in rare-earth-substituted BiFeO3 epitaxialthin films at morphotropic phase boundaries, Appl. Phys. Lett. 97 (21) (2010),https://doi.org/10.1063/1.3520642 212905.

[17] A.Y. Borisevich, E.A. Eliseev, A.N. Morozovska, C.-J. Cheng, J.-Y. Lin, Y.H. Chu,D. Kan, I. Takeuchi, V. Nagarajan, S.V. Kalinin, Atomic-scale evolution of modu-lated phases at the ferroelectric-antiferroelectric morphotropic phase boundarycontrolled by flexoelectric interaction, Nat. Commun. 3 (2012) 775 https://doi.org/10.1038/ncomms1778.

[18] C.-S. Chen, C.-S. Tu, P.-Y. Chen, W.S. Chang, Y. Idzerda, Y. Ting, J.-M. Lee, C.W. Yu,Micro-to-nano domain structure and orbital hybridization in rare-earth-dopedBiFeO3 across morphotropic phase boundary, J. Am. Ceram. Soc. 101 (2) (2017)883–896 https://doi.org/10.1111/jace.15226.

[19] V. Nagarajan, A. Stanishevsky, L. Chen, T. Zhao, B.-T. Liu, J. Melngailis,A.L. Roytburd, R. Ramesh, Realizing intrinsic piezoresponse in epitaxial submicronlead zirconate titanate capacitors on Si, Appl. Phys. Lett. 81 (22) (2002) 4215–4217https://doi.org/10.1063/1.1516857.

[20] H. Dai, Z. Chen, T. Li, Y. Li, Microstructure and properties of Sm-substituted BiFeO3ceramics, J. Rare Earths 30 (11) (2012) 1123–1128 https://doi.org/10.1016/S1002-0721(12)60191-4.

[21] Y.B. Yao, W.C. Liu, C.L. Mak, Pyroelectric properties and electrical conductivity insamarium doped BiFeO3 ceramics, J. Alloy. Comp. 527 (25) (2012) 157–162https://doi.org/10.1016/j.jallcom.2012.02.182.

[22] K. Abe, N. Sakai, J. Takahashi, H. Itoh, N. Adachi, T. Ota, Leakage current prop-erties of cation-substituted BiFeO3 ceramics, Jpn. J. Appl. Phys. 49 (9S) (2010),https://doi.org/10.1143/JJAP.49.09MB01 09MB01.

[23] X. Qi, J. Dho, R. Tomov, M. Blamire, J. MacManus-Driscoll, Greatly reduced leakagecurrent and conduction mechanism in aliovalent-ion-doped BiFeO3, Appl. Phys.Lett. 86 (6) (2005) 062903 https://doi.org/10.1063/1.1862336.

[24] X.X. Shi, Y. Qin, M. Chen, Enhanced ferroelectric properties in Bi0.86Sm0.14FeO3-based ceramics, Appl. Phys. Lett. 105 (19) (2014) 192902 https://doi.org/10.1063/1.4901901.

[25] K. Kalantari, I. Sterianou, S. Karimi, M. Ferrarelli, S. Miao, D. Sinclair, I. Reaney, Ti-doping to reduce conductivity in Bi0.85Nd0.15FeO3 ceramics, Adv. Funct. Mater. 21(19) (2011) 3737–3743 https://doi.org/10.1002/adfm.201100191.

[26] A. Srinivas, D.-W. Kim, K.S. Hong, Observation of ferroelectromagnetic nature inrare-earth-substituted bismuth iron titanate, Appl. Phys. Lett. 83 (11) (2003)2217–2219 https://doi.org/10.1063/1.1610255.

[27] R. Cohen, Origin of ferroelectricity in perovskite oxides, Nature 358 (1992)136–138 https://doi.org/10.1038/358136a0.

[28] Y.P. Wang, L. Zhou, M.F. Zhang, X.Y. Chen, J.-M. Liu, Z.G. Liu, Room-temperaturesaturated ferroelectric polarization I BiFeO3 ceramics synthesized by rapid liquidphase sintering, Appl. Phys. Lett. 84 (10) (2004) 1731–1733 https://doi.org/10.1063/1.1667612.

[29] V.R. Palkar, R. Pinto, BiFeO3 thin films: novel effects, Pramana 58 (5–6) (2002)1003–1008 https://doi.org/10.1007/s12043-002-0207-0.

[30] S.T. Zhang, M.H. Lu, Y.F. Chen, B. Ming, Larger polarization and weak ferro-magnetism in quenched BiFeO3 ceramics with a distorted rhombohedral crystalstructure, Appl. Phys. Lett. 87 (26) (2005) 262907 https://doi.org/10.1063/1.2147719.

[31] S.J. Kim, S.H. Han, H.G. Kim, A.Y. Kim, J.S. Kim, C.I. Cheon, Multiferroic propertiesof Ti-doped BiFeO3 ceramics, J. Kor. Phys. Soc. 56 (12) (2010) 439, https://doi.org/10.3938/jkps.56.439.

[32] P. Kumar, C. Panda, M. Kar, Effect of rhombohedral to orthorhombic transition onmagnetic and dielectric properties of La and Ti co-substituted BiFeO3, Smart Mater.Struct. 24 (2015) 045028 https://doi.org/10.1088/0964-1726/24/4/045028.

[33] H. Deng, M. Zhang, Z. Hu, Q. Xie, Q. Zhong, J. Wei, H. Yan, Enhanced dielectric andferroelectric properties of Ba and Ti co-doped BiFeO3 multiferroic ceramics, J.Alloy. Comp. 582 (2014) 273–276 https://doi.org/10.1016/j.jallcom.2013.07.187.

[34] M.S. Bernardo, T. Jardiel, M. Peiteado, A.C. Caballero, M. Villegas, Reactionpathways in the solid state synthesis of multiferroic BiFeO3, J. Eur. Ceram. Soc. 31(16) (2011) 3047–3053 https://doi.org/10.1016%2Fj.jeurceramsoc.2011.03.018.

[35] T.-H. Wang, C.-S. Tu, Y. Ding, T.-C. Lin, C.-S. Ku, W.-C. Yang, H.-H. Yu, K.-T. Wu, Y.-D. Yao, H.-Y. Lee, Phase transition and ferroelectric properties of xBiFeO3–(1-x)BaTiO3 ceramics, Curr. Appl. Phys. 11 (3) (2011) S240–S243 https://doi.org/10.1016/j.cap.2011.01.037.

[36] Y.F. Cui, Y.G. Zhao, L.B. Luo, J.J. Yang, H. Chang, M.H. Zhu, D. Xie, T.L. Ren,Dielectric, magnetic, and magnetoelectric properties of La and Ti codoped BiFeO3,Appl. Phys. Lett. 97 (22) (2010) 222904 https://doi.org/10.1063/1.3524225.

[37] D. Alikin, A. Turygin, J. Walker, T. Rojac, V. Shvartsman, V. Shur, A. Kholkin,Quantitative phase separation in multiferroic Bi0.88Sm0.12FeO3 ceramics via pie-zoresponse force microscopy, J. Appl. Phys. 118 (2015), https://doi.org/10.1063/1.4927812 072004.

H. Mana-ay et al. Materials Chemistry and Physics 225 (2019) 272–278

277

[38] V. Khomchenko, L.C. Pereira, J. Paixão, Substitution-driven structural and magneticphase transitions in Bi0.86(La,Sm)0.14FeO3 system, J. Phys. Appl. Phys. 44 (18)(2011) 185406 https://doi.org/10.1088/0022-3727/44/18/185406.

[39] Y.K. Jeong, C.W. Bark, S. Ryu, J.-H. Lee, H.M. Jang, R3c-R3m octahedron-tiltingtransition in rhombohedrally-distorted BiFeO3 multiferroics, J. Kor. Phys. Soc. 58(4) (2011) 817–820, https://doi.org/10.3938/jkps.58.817.

[40] Y. Gu, J. Zhao, W. Zhang, H. Zheng, L. Liu, W. Chen, Structural transformation andmultiferroic properties of Sm and Ti co-doped BiFeO3 ceramics with Fe vacancies,Ceram. Int. 43 (17) (2017) 14666–14671 https://doi.org/10.1016/j.ceramint.2017.07.187.

[41] S. Karimi, I.M. Reaney, I. Levin, I. Sterianou, Nd-doped BiFeO3 ceramics with an-tipolar order, Appl. Phys. Lett. 94 (2009) 112903 https://doi.org/10.1063/1.3097222.

[42] P. Godara, A. Agarwal, N. Ahlawat, S. Sanghi, Crystal structure refinement, di-electric and magnetic properties of Sm modified BiFeO3 multiferroic, J. Mol. Struct.1097 (2015) 207–213 https://doi.org/10.1016/j.molstruc.2015.05.022.

[43] C.C. Wang, H.B. Lu, K.J. Jin, G.Z. Yang, Temperature-dependent dielectric strengthof a Maxwell-Wagner type relaxation, Mod. Phys. Lett. B 22 (13) (2008) 1297–1305https://doi.org/10.1142/S0217984908015310.

[44] X.X. Shi, X.Q. Liu, X.M. Chen, Structure evolution and piezoelectric propertiesacross the morphotropic phase boundary of Sm-substituted BiFeO3 ceramics, J.Appl. Phys. 119 (2016) 064104 https://doi.org/10.1063/1.4941820.

[45] D. Bochenek, P. Niemiec, P. Guzdek, M. Wzorek, Magnetoelectric and electricmeasurements of the (1-x)BiFeO3 –(x) Pb(Fe1/2Nb1/2)O3 solid solutions, Mater.Chem. Phys. 195 (2017) 199–206 https://doi.org/10.1016/j.matchemphys.2017.04.022.

[46] C.-S. Tu, R.R. Chien, T.-H. Wang, J. Anthoniappen, Y.-T. Peng, Dielectric responseand origin in antiferromagnetic/ferroelectric (1-x)BiFeO3-(x)BaTiO3 ceramics, J.Appl. Phys. 113 (2013) 17D908-3 https://doi.org/10.1063/1.4795420.

[47] H. Singh, K.L. Yadav, Synthesis and thermal, structural, dielectric, magnetic andmagnetoelectric studies of BiFeO3-MgFe2O4 nanocomposites, J. Am. Ceram. Soc. 98(2) (2014) 574–579 https://doi.org/10.1111/jace.13316.

[48] Y. Tan, J. Zhang, Y. Wu, C. Wang, V. Koval, B. Shi, H. Ye, R. McKinnon, G. Viola,H. Yan, Unfolding grain size effects in barium titanate ferroelectric ceramics, Sci.Rep. 5 (2015) 9953, https://doi.org/10.1038/srep09953.

[49] T. Hoshina, S. Hatta, H. Takeda, T. Tsurumi, Grain size effect on piezoelectricproperties of BaTiO3 ceramics, Jpn. J. Appl. Phys. 57 (2018), https://doi.org/10.7567/JJAP.57.0902BB.

[50] J. Walker, P. Bryant, V. Kurusingal, C. Sorrell, D. Kuscer, G. Drazic, A. Bencan,V. Nagarajan, T. Rojac, Synthesis-phase–composition relationship and high electric-field-induced electromechanical behavior of samarium-modified BiFeO3 ceramics,Acta Mater. 83 (2015) 149–159 https://doi.org/10.1016/j.actamat.2014.09.058.

[51] Y.-H. Gu, Y. Liu, C. Yao, Y.-W. Ma, Y. Wang, H.L.-W. Chan, W.-P. Chen, Ho and Tico-doped BiFeO3 multiferroic ceramics with enhanced magnetization and ultrahigh

electrical resistivity, Chin. Phys. B 23 (3) (2014) 037501 https://doi.org/10.1088/1674-1056/23/3/037501.

[52] H.J. Lee, C.W. Ahn, S.S. Won, A. Tange, B.C. Park, H.J. Seog, I.W. Kim, Pure fer-roelectric polarization of lead-free Na0.5K0.5NbO3 thin films by using the doublewave method, J. Kor. Phys. Soc. 66 (9) (2015) 1401–1405, https://doi.org/10.3938/jkps.66.1401.

[53] M.S. Bernardo, T. Jardiel, M. Peiteado, F.J. Mompean, M. Garcia-Hernandez,M.A. Garcia, M. Villegas, A.C. Caballero, Intrinsic compositional inhomogeneities inbulk Ti-doped BiFeO3: microstructure development and multiferroic properties,Chem. Mater. 25 (2013) 1533–1541, https://doi.org/10.1021/cm303743h.

[54] M. Kumar, K.L. Yadav, Study of room temperature magnetoelectric coupling in Tisubstituted bismuth ferrite system, J. Appl. Phys. 100 (2006), https://doi.org/10.1063/1.2349491 074111.

[55] Y. Tian, F. Xue, Q. Fu, L. Zhou, C. Wang, H. Gou, M. Zhang, Structural and physicalproperties of Ti-doped BiFeO3 nanoceramics, Ceram. Int. 44 (4) (2017) 4287–4291https://doi.org/10.1016/j.ceramint.2017.12.013.

[56] G.S. Lotey, N.K. Verma, Structural, magnetic, and electrical properties of Gd-dopedBiFeO3 nanoparticles with reduced particle size, J. Nanoparticle Res. 14 (3) (2012)742, https://doi.org/10.1007/s11051-012-0742-7.

[57] W. Mao, W. Chen, X. Wang, Y. Zhu, Y. Ma, H. Xue, L. Chu, J. Yang, X. Li, W. Huang,Influence of Eu and Sr co-substitution on multiferroic properties of BiFeO3, Ceram.Int. 42 (11) (2016) 12838–12842 https://doi.org/10.1016/j.ceramint.2016.05.048.

[58] J. Li, J. Wang, M. Wuttig, R. Ramesh, N. Wang, B. Ruette, A.P. Pyatakov,A.K. Zvezdin, D. Viehland, Dramatically enhanced polarization in (001), (101), and(111) BiFeO3 thin films due to epitaxial-induced transitions, Appl. Phys. Lett. 84(25) (2004) 5261–5263, https://doi.org/10.1063/1.1764944.

[59] J. Wang, J.B. Neaton, H. Zheng, V. Nagarajan, S.B. Ogale, B. Liu, D. Viehland,V. Vaithyanathan, D.G. Schlom, U.V. Waghmare, N.A. Spaldin, K.M. Rabe,M. Wuttig, R. Ramesh, Epitaxial BiFeO3 multiferroic thin film heterostructures,Science 299 (5613) (2003) 1719–1722, https://doi.org/10.1126/science.1080615.

[60] K.Y. Yun, D. Ricinschi, T. Kanashima, M. Noda, M. Okuyama, Giant ferroelectricpolarization beyond 150 μC/cm2 in BiFeO3 thin film, Jpn. J. Appl. Phys. 43 (5A)(2004) L647–L648 https://doi.org/10.1143/JJAP.43.L647.

[61] Y.P. Wang, L. Zhou, M.F. Zhang, X.Y. Chen, J.-M. Liu, Z.G. Liu, Room-temperaturesaturated ferroelectric polarization in BiFeO3 ceramics synthesized by rapid liquidphase sintering, Appl. Phys. Lett. 84 (10) (2004) 1731–1733, https://doi.org/10.1063/1.1667612.

[62] S. Karimi, I. Reaney, Y. Han, J. Pokorny, I. Sterianou, Crystal chemistry and domainstructure of rare-earth doped BiFeO3 ceramics, J. Mater. Sci. 44 (19) (2009)5102–5112 https://doi.org/10.1007/s10853-009-3545-1.

[63] J.-R. Cheng, L. Cross, Effects of La substituent on ferroelectric rhombohedral/tet-ragonal morphotropic phase boundary in (1−x)(Bi, La)(Ga0.05Fe0.95)O3–x PbTiO3piezoelectric ceramics, J. Appl. Phys. 94 (2003) 5188, https://doi.org/10.1063/1.1610802.

H. Mana-ay et al. Materials Chemistry and Physics 225 (2019) 272–278

278