Comparison of magnetic and microwave absorbing properties between multiwalled carbon nanotubes...

6
World Journal of Engineering World Journal of Engineering 11(4) (2014) 317-322 World Journal of Engineering 1. Introduction The demands to develop radar absorbing materials (RAM) are increased due to the rapid development in telecommunication technologies. Their applications could be implied in both civil and Comparison of magnetic and microwave absorbing properties between multiwalled carbon nanotubes nanocomposite, nickel zinc ferrite nanocomposite and hybrid nanocomposite L.J. YU 1* , S. H. Ahmad 2 , Sivanesan Appadu 3 , I. Kong 4 , Mou’ad A Tarawneh 2 and Moayad Husein Flaifel 2 1 UCSI University, Kuala Lumpur Campus (North Wing), Lot 12734, Jalan Choo Lip Kung, Taman Tayton View, 56000 Cheras, Kuala Lumpur, Malaysia 2 School of Applied Physics, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia 3 Department of Technology Processing Radiation, Nuclear Agency of Malaysia, 43000 Bangi, Selangor, Malaysia 4 Department of Mechanical, Materials and Manufacturing Engineering, University of Nottingham Malaysia Campus, Jalan Broga, 43500 Semenyih, Selangor, Malaysia E-mail: [email protected] (Received 21 January 2014; accepted 22 June 2014) Abstract Three types of fillers were incorporated in the thermoplastic natural rubber by melt blending process. They are NiZn ferrite, multiwalled carbon nanotubes, and hybrid NiZn ferrite/multiwalled carbon nanotubes followed by weight ratio of 1:1. Their magnetic properties and microwave absorbing properties were investigated. The ball-milled techniques, resulted good filler dispersion in hybrid nanocomposite, proven by the matching saturation magnetization experimental values with the theory calculation. It was found that the magnetic property strongly depends on the amount of magnetic particles in the nanocomposites. The mixing of two different types of filler (multiwalled carbon nanotubes and NiZn ferrite) showed an enhancement of the microwave properties at lower filler loading. Key words: Magnetic property, Microwave absorbing property, Thermoplastic natural rubber composite World Journal of Engineering military field, aim to suppress the electromagnetic interference, protective shielding of electronic devices and reduce radar signal detected from a target. The microwave absorbers can be categorized into magnetic and dielectric absorbers based on their ISSN:1708-5284

Transcript of Comparison of magnetic and microwave absorbing properties between multiwalled carbon nanotubes...

Page 1: Comparison of magnetic and microwave absorbing properties between multiwalled carbon nanotubes nanocomposite, nickel zinc ferrite nanocomposite and hybrid nanocomposite

World Journal of

EngineeringWorld Journal of Engineering 11(4) (2014) 317-322

World Journal of

Engineering

1. IntroductionThe demands to develop radar absorbing

materials (RAM) are increased due to the rapiddevelopment in telecommunication technologies.Their applications could be implied in both civil and

Comparison of magnetic and microwaveabsorbing properties between multiwalled

carbon nanotubes nanocomposite, nickel zincferrite nanocomposite and hybrid

nanocomposite

L.J. YU1*, S. H. Ahmad2, Sivanesan Appadu3, I. Kong4,Mou’ad A Tarawneh2 and Moayad Husein Flaifel2

1UCSI University, Kuala Lumpur Campus (North Wing), Lot 12734, Jalan Choo Lip Kung,Taman Tayton View, 56000 Cheras, Kuala Lumpur, Malaysia

2School of Applied Physics, Faculty of Science and Technology, Universiti KebangsaanMalaysia, 43600 Bangi, Selangor, Malaysia

3Department of Technology Processing Radiation, Nuclear Agency of Malaysia, 43000Bangi, Selangor, Malaysia

4Department of Mechanical, Materials and Manufacturing Engineering, University ofNottingham Malaysia Campus, Jalan Broga, 43500 Semenyih, Selangor, Malaysia

E-mail: [email protected]

(Received 21 January 2014; accepted 22 June 2014)Abstract

Three types of fillers were incorporated in the thermoplastic natural rubber by melt blendingprocess. They are NiZn ferrite, multiwalled carbon nanotubes, and hybrid NiZn ferrite/multiwalledcarbon nanotubes followed by weight ratio of 1:1. Their magnetic properties and microwaveabsorbing properties were investigated. The ball-milled techniques, resulted good filler dispersionin hybrid nanocomposite, proven by the matching saturation magnetization experimental valueswith the theory calculation. It was found that the magnetic property strongly depends on theamount of magnetic particles in the nanocomposites. The mixing of two different types of filler(multiwalled carbon nanotubes and NiZn ferrite) showed an enhancement of the microwaveproperties at lower filler loading.

Key words: Magnetic property, Microwave absorbing property, Thermoplastic naturalrubber composite

World Journal of

Engineering

military field, aim to suppress the electromagneticinterference, protective shielding of electronicdevices and reduce radar signal detected from atarget. The microwave absorbers can be categorizedinto magnetic and dielectric absorbers based on their

ISSN:1708-5284

Page 2: Comparison of magnetic and microwave absorbing properties between multiwalled carbon nanotubes nanocomposite, nickel zinc ferrite nanocomposite and hybrid nanocomposite

318 L.J. YU et al./World Journal of Engineering 11(4) (2014) 317-322

lossy characteristic. Magnetic absorbers, such asferrite and metal composites required high fillingratio in the matrix to achieve expected absorbingproperties. The absorbers made from thesecomposites are typically high density. Meanwhile,composites filled with carbon, graphite, carbonnanotubes or glass fibers are categorized asdielectric absorbers. Carbon nanotubes (CNTs)nanocomposites are very promising due to their highaspect ratio and special conductive properties forexcellent absorption level with low CNTsconcentration (Saib et al., 2006). However, CNTsdo not show magnetic loss in the microwaveabsorbing process, which limits their absorbingcharacteristics (Wang et al., 2009). Therefore,composites combining with both magnetic fillersand dielectric fillers provide an opportunity tosatisfy the requirements of a good absorber withstrong absorption, low density and flexible. Manyreports have been published focus on modificationof CNTs by coating or filling the CNTs with othernanomaterials through chemical methods, aimed toenhance their microwave properties (Wang et al.,2009; Hubber and Makkeiff, 2006; Zhang et al.,2008; Kang et al., 2008; Zhao et al., 2007).However, the control of this method is crucial toenable sufficiently filling nanomaterials in CNTs.

In this paper, we report the effect of incorporatingball-milled hybrid fillers (nickel-zinc ferrite/multiwalled nanotubes) into thermoplastic matrixvia a simple melt blending process. The reason ofusing thermoplastic natural rubber as the matrix isdue to its flexibility in shaping and recyclable. Themagnetic properties and microwave properties ofthis ball-milled hybrid nanocomposite werecompared with nickel-zinc ferrite nanocompositeand multiwalled nanotubes nanocomposite of samefiller concentration.

2. Materials and methods2.1. Material

Nickel zinc ferrite nanoparticles(Ni0.5Zn0.5Fe2O4), with 98.5% purity, averageparticle size 10–30 nm, were obtained fromcommercial suppliers in powder form. Multiwalledcarbon nanotube (MWNT) with 90% purity, averagediameter 9.5 nm, and average length 1.5 µm wereobtained from Nanocy l. Natural Rubber (NR) andpolypropylene (PP) were supplied by RubberResearch Instituted of Malaysia (RRIM) and Mobile(M) Sdn. Bhd., respectively. Liquid natural rubber

(LNR) was prepared by photosynthesizeddegradation of NR in visible light.

2.2. Samples preparationThe thermoplastic natural rubber (TPNR), blends

of PP, NR and LNR was prepared according to theweight ratio of 70:20:10. LNR was used as thecompatibilizer in the mixture. The fillers: NiZnferrite, MWNT and hybrid fillers (mixture of NiZnferrite/ MWNT) were prepared according to theweight ratio as Table 1.

2.3. MethodsBoth NiZn ferrite and MWNT fillers were mixed

in a tubular mixing machine followed the powder toporcelain balls weight ratio of 1:10 for 1 hour. Themixture of NiZn ferrite/ MWNT was incorporatedinto TPNR matrix by melt blending technique. Allnanocomposites were prepared by incorporating2 wt% of fillers into TPNR using Thermo Haakeinternal mixer with a mixing speed of 100 r.p.m., at180 oC for 13 minutes. After that, the samples werehot-pressed into a thin sheet of 1 mm in thicknessusing a hydraulic press at 185 oC. Field emissionscanning electron microscopy (FESEM) was used toexamine the fractured morphology of samples.Magnetization measurements were carried out usinga vibrating sample magnetometer (VSM Model7404), to obtain the M-H loop at room temperature(25 oC). Microwave vector network analyzerAnritsu 37247D was used to measure microwaveabsorption property. The nanocomposites werepressed into toroid with an outer diameter and innerdiameter of 6.97 mm and 3.05 mm respectively.

3. Results and discussionMagnetic hysteresis loops of nanocomposites are

shown (Fig. 1). Saturation magnetization (Ms),remanence (Mr) and the coercive force (Hc) weredetermined from the loop and the values are shown inTable 2. NiZn ferrite nanocomposite exhibits thehighest Ms value and Mr value among the threecomposites. MWNT nanocomposite shows highest Hc

Table 1.Weight percent of fillers

Nanocomposite Wt% of NiZn ferrite Wt% of MWNT

NiZn ferrite 100 0MWNT 0 100Hybrid 50 50

Page 3: Comparison of magnetic and microwave absorbing properties between multiwalled carbon nanotubes nanocomposite, nickel zinc ferrite nanocomposite and hybrid nanocomposite

L.J. YU et al./World Journal of Engineering 11(4) (2014) 317-322 319

value, followed by hybrid nanocomposite and NiZnferrite nanocomposite. Kang et al., 2008 concludedthat the Ms of composite is dependent on the weightratio of magnetic filler in composite, given by:

Ms (composite) = Ms (pure magnetic filler) xweight ratio of magnetic filler in composite (1)

The experimental Ms value for NiZn ferritenanocomposite obtained (0.791 emu/g) is closed tothe calculated Ms value (0.823 emu/g) according to itsweight ratio in the composite. The consistency Ms

value obtained by experiment and calculationindicating that ZiNn ferrite particles are welldispersed polymer matrix. However, this relation isnot applicable for the MWNT composite. At roomtemperature, diamagnetic properties are dominant inMWNTs. The MWNT possess a weak magnetizationtoward applied magnetic field. Therefore, the Ms

value of the MWNT nanocomposite is negligible dueto its low MWNT loading. The enhancement of Ms isshown in the hybrid nanocomposite. This reveals thatthe NiZn ferrite has greater influence towards thesaturation magnetization than MWNT in TPNRmatrices. The Mr indicates the magnetization of thecomposites in the absence of magnetic field afterbeing magnetized. The Mr values of the samples are

relatively small compared to the saturationmagnetization. This implying that, most of the spinmoments has returned to its original state. In Table 2,it was noticed that larger Hc is needed to demagnetizethe MWNT (67.71 Oe) than NiZn ferrite (20.35 Oe).NiZn ferrite is known as soft ferrite which its Hc

value is small. The Hc value of MWNT and NiZnferrite has increased after incorporating the filler intothe thermoplastic matrix. Similar observation hasbeen reported by (Dwi et al., 2007; Kong et al., 2010;Makled et al., 2005.; Sun et al., 2010). This isbecause the matrix restricts the alignment of themagnetic moment of the ferrite (Kong et al., 2010). Itwas found that Hc value is proportional to the MWNTcontent exhibits in nanocomposite (Chen et al.,2009). The Hc value of MWNT nanocomposite hasincreased 3.4 times of hybrid nanocomposite whenthe MWNT content is doubled. This implies thatincrement content of MWNT in polymer composite isfurther restricting the re-alignment of magneticmoment under applied field.

Electromagnetic wave absorption depends on theefficient complement between the relative permittivityand the permeability of materials. Electromagneticwave energy can be completely absorbed anddissipated to heat energy through magnetic anddielectric losses. This electromagnetic wave losseffectiveness can be quantitatively shown byreflection loss. The reflection loss can be expressed as:

RL (dB) = 20 log (PrPi), (2)

Where the Pr is power reflected being detectedand Pi is the input power. The greater minimumvalue obtained from reflection loss value indicatingbetter microwave absorbing properties. Themicrowave reflection obtained from the preparedsamples. For all three nanocomposite samples, thefrequency was studied in the range from 0.5 GHz to12.5 GHz (Figure 2). The RL performance

a

b

cM (

emu

/g)

10.80.6

−12 −8 −4 0

H (kOe)

4 8 12

0.40.2

0−0.2−0.4−0.6−0.8

−1

Fig. 1. Magnetization curve of the nanocomposites: (a) NiZnnanocomposite. (b) Hybrid nanocomposite (c) MWNT

nanocomposite.

Table 2.Magnetic properties of materials

Materials Ms (emu/g) Mr (emu/g) Hc (Oe)

NiZn ferrite 41.176 1.494 20.35MWNT 3.139 0.916 67.71NiZn ferrite nanocomposite 0.791 1.394 22.06MWNT nanocomposite 0.016 0.222 134.6Hybrid nanocomposite 0.556 1.053 39.58

aa bb

c

c

RL

(dB

)

00.5 2.5 4.5 6.5

Frequency (GHz)

8.5 10.5 12.5−10

−20

−30

−40

Fig. 2. Reflection loss (RL) of nanocomposite: (a) NiZn ferritenanocomposite. (b) Hybrid nanocomposite (c) MWNT

nanocomposite.

Page 4: Comparison of magnetic and microwave absorbing properties between multiwalled carbon nanotubes nanocomposite, nickel zinc ferrite nanocomposite and hybrid nanocomposite

320 L.J. YU et al./World Journal of Engineering 11(4) (2014) 317-322

characteristics of these nanocomposites weresummarized in Table 3. Based on the results showed(Figure 2), the RL dips of the hybrid nanocompositefalls in between the two nanocomposites whichcontain single type of filler. Do take note that thehybrid filler (50 wt% ferrite/ 50 wt% MWNT) iscontaining half weight percent of the single typefiller (100 wt% ferrite or 100 wt% MWNT). Thisshows that hybrid nanocomposite exhibiting goodRL performance by combining NiZn ferrite andMWNT. Numerous reported the improvement ofmicrowave absorption are significantly originatedfrom the combination of the diamagnetic CNTs andmetallic nanomagnet, which had better match of thedielectric loss and magnetic loss (Wang et al., 2009;Hubber and Makkeiff, 2006; Zhang et al., 2008).This indicated that both dielectric loss and magneticloss were contributed to the enhancement of thereflection loss of the hybrid nanocomposite. Thehybrid filler loading alter both the permeability andpermittivity, hence leading to the changes ofabsorption properties, resulted in the changes of thematching frequency and absorbing peaks.

Referring to table 3, the second RL dip of hybridnanocomposite falls in between the NiZn ferrienanocomposite and MWNT nanocomposite. Theoccurrence of second peaks at a higher frequency(>9 GHz) is conclusive from the quarter waveprinciple. When the electromagnetic wave isincident on an absorber backed by metal plate, thewaves undergo multi reflection in the sample.Partially microwave reflected for the air absorberinterface while residue microwave is reflected fromthe absorber-metal interface. These multi reflectedwave are out of phase when the quarter wavethickness for lower frequencies. The bandwidth ofthe hybrid nanocomposite turns to become narrowerfor RL below -20 dB showed the same bandwidthwidth as MWNT nanocomposite.

A shift in minimum RL frequency is observedwith increase in thickness is shown (Figure 3). The

microwave properties can be modulated bymanipulating the thickness of the sample to meetrequired frequency. The maximum absorption ofmicrowave energy occurs when the matchingthickness, dm is equal to the quarter of propagationwavelength in a material, λm. It is expressed by:

λm = λ0 / (εr µr)1/2, (3)

Where λ0 is the free space wavelength, εr and µr

are the relative permeability and permittivity. It canbe found from the relationship above, the frequencycorresponding to the maximum reflection loss isnearly inversely proportional to the thickness of theabsorber. Besides, the frequency in where the hybridnanocomposites has the minimum RL, is positionedin between the minimum RL obtained from bothsingle filler nanocomposites (NiZn ferritenanocomposite and MWNT nanocompositerespectively). We plot a line by using averageequation:

(fm + fn)/2, (4)

Where fm and fn are the frequency of RL peaks forMWNT nanocomposite and NiZn nanocompositerespectively. In figure 3, it was found that theexperimental frequency of minimum RL (crossmarked) of the hybrid composites are closely matched

Table 3.Reflection loss (RL) of nanocomposite

Bandwidh Minimium reeflection loss Matching freqencyNanocomposite (GHz) (dB) (GHz)

RL dips 1 2 1 2 1 2

NiZn 1.1 1.5 31.35 30.66 5.03 10.13Hybrid 0.6 0.7 30.59 30.03 4.70 9.69MWNT 0.6 0.7 28.28 30.23 4.53 9.08

ab

c

Fre

quen

cy o

f min

imum

RL

(GH

z)

10 12 14Matching thickness (mm)

16 18 20

10

87

4

9

65

Fig. 3. Relationship between minimum reflection loss (RL)frequency and matching thickness of nanocomposite: (a) NiZnferrite nanocomposite (b) hybrid nanocomposite (c) MWNT

nanocomposite.

Page 5: Comparison of magnetic and microwave absorbing properties between multiwalled carbon nanotubes nanocomposite, nickel zinc ferrite nanocomposite and hybrid nanocomposite

L.J. YU et al./World Journal of Engineering 11(4) (2014) 317-322 321

with the plotted line by using average equation, at allmatching thickness from 10 mm–20 mm.

The electromagnetic shielding effectiveness (SE)is another measurement to show the efficiency of amaterial to attenuate the incident electromagneticwave. The electromagnetic shielding effectivenesscan be expressed as:

SE (dB) = 20 log (PtPi), (5)

Where the Pt is transmitted power and Pi are theinput power. The greater minimum value obtainedfrom the SE plot indicating better microwaveattenuation properties, which mean lesselectromagnetic waves were being transmittedthrough the material. Figure 4 shows the SEperformance characteristics of the prepared samplesin the range of frequency from 0.5 GHz to 12.5 GHz.The good SE performance is attributed to the filler’sintrinsic conductivity (Huang et al., 2007). It can beseen that the SE performance of the three samplesare weak (<2.5 dB) and exhibited in wave form.The maximum SE values of these three samples wereobtained around 4.5 GHz and 9–10 GHz, werematching with the minimum RL frequency (as shownin Figure 3). This indicating most of the incidentwaves were being absorbed and transmitted throughthe sample at the mentioned frequency. Therefore,less reflected waves were detected. MWNTnanocomposite exhibits the minimum SE value alongthe studied frequency, followed by the hybridnanocomposite and NiZn ferrite nanocomposite. Thehigh aspect ratio MWNTs possesses goodconductivity to the applied electromagnetic waves,forming a good conducting network system in theTPNR phases and intercepts with the incident waves.Hence, MWNT nanocomposite tends to attenuatemore electromagnetic wave than NiZn ferrite

nanocomposite and the hybrid nanocomposite. Incontrast, the attenuation of the electromagnetic wavesis relatively weak for the NiZn nanocompositebecause NiZn ferrite is an insulator, possesses a highresistivity towards the electrical component inelectromagnetic waves. A similar result was reportedby (Annadurai et al., 2002), where ferrite compositeshown poor attenuation in shielding effectiveness. Asfor the hybrid nanocomposite, the SE performance isbetter than NiZn ferrite nanocomposite as it contentboth MWNTs and NiZn ferrite, with lower weightpercent.

4. ConclusionThe comparison was made between the hybrid

nanocomposite and single type filler nanocomposites.The magnetic properties (magnetization saturation,remanance, and coercive force) are depending on thecontent of magnetic particles in the composite. Thecombination of magnetic filler and of dielectric fillerin the hybrid nanocomposite, exhibited anintermediate microwave absorbing property betweenthe single type filler nanocomposites, when the singletype filler content is decreased by half in the hybridfiller. The frequency of minimum reflection (RL)were depending on the thickness of nanocomposites.A formula was purposed to determine the minimumreflection of the hybrid fillers, the results showed thatexperimental values were matched by the calculation.As a conclusion, the magnetic properties andmicrowave properties can be alter according to theamount of fillers and the types of fillers. The ball-milled mixing hybrid nanocomposites were assumedto achieve a homogenous distribution due to theclosely matched experimental values of saturationmagnetization with the calculation values.

AcknowledgementsAuthor would like to thank scholarship sponsored

by National Science Fellowships (NSF), MOSTI,Malaysia.

ReferencesAnantharam M.R., Vijutha S., Philip K., Mohana P., Joy P.A.,

2010. A flexible microwave absorber based nickel ferrite

nanocomposite. Journal of Alloys and Compounds 489,

297–303.

Annadurai P., Mallick A.K., Tripathy D.K., 2002. Studies on

microwave shielding materials based on ferrite and carbon

abc

0.5 2.5 4.5

Frequency (GHz)

SE

(dB

)

6.5 8.5 12.50

−3−3.5

−5

−2.5−2

−1.5−1

−0.5

−4−4.5

10.5

Fig. 4. Shielding effectiveness (SE) of nanocomposite:(a) NiZn ferrite nanocomposite (b) Hybrid nanocomposite

(c) MWNT nanocomposite.

Page 6: Comparison of magnetic and microwave absorbing properties between multiwalled carbon nanotubes nanocomposite, nickel zinc ferrite nanocomposite and hybrid nanocomposite

322 L.J. YU et al./World Journal of Engineering 11(4) (2014) 317-322

black-filled EDPM rubber in the X-band frequency. Journal

of Applied Polymer Science 83, 145–150.

Chen C.S., Liu T.G., Chen X.H., Lin L.W., Liu Q.C., Qing X.,

Ning Z.W., 2009. Preparation and magnetic property of

multi-walled carbon nanotube/α-Fe2O3 composites.

Transactions of Nonferrous Metals Society 19, 1567–1571.

Dwi P., Ahmad S.H., Abdullah M.H., Yusoff A.N., 2007. Effect

of Nickel cobalt zinc ferrite filler on magnetic and thermal

properties of thermoplastic natural rubber composites.

International Journal of Polymeric Materials 56(3), 327–338.

Huang Y., Li N., Ma Y.F., Du F., Li F.F., He X.B., Lin X., Gao

H.J., Chen Y.S., 2007. The influence of single-walled carbon

nanotube structure on the electromagnetic interference

shielding efficiency of its epoxy composites. Carbon 45(8),

1614–1621.

Hubber T., Makeiff D.A., 2006. Microwave absorption by

polyaniline-carbon nanotube composites. Synthetic metals

156, 497–505.

Kang F.Y., Lv R.T., Cai D.Y., Wang C., Gu J.L., Wang K.L.

Wu D.H., 2008. Long continuous FeNi nanowires inside

carbon nanotubes: Synthesis, property and application.

Journal of Physics and Chemistry of Solids 69, 1213–1217.

Kong I., Ahmad S.H., Abdullah M.H., David H., Yusoff A.N.,

Dwi P., 2010. Magnetic and microwave absorbing propertirs

of magnetite-thermoplastic natural rubber nanocomposites.

Journal of Magnetism and Magnetic Materials 322(21),

3401–3409.

Makled M.H., Morji K., Matsui T., Mabuchi H., El-Mansy

M.K., 2005. Magnetic and dynamic mechanical properties of

barium ferrite-natural rubber composites. Journal of

Materials Processing Technology 160, 229–233.

Saib A., Bednarz L., Daussin R., Bailly C., Thomassin J-M.,

Pagnoulle C., Detrembleur C., Jerome R. Huynen I., 2006.

Carbon nanotube composites for broadband microwave

absorbing materials. IEEE Transactions Microwave Theory

54 (6), 2745–2754.

Sun Y.Y., Zhou X., Liu Y.Q., Zhao G.Z., Jian Y., 2010. Effect

of magnetic nanoparticles on the properties of magnetic

rubber. Materials Research Bulletin 45, 878–881.

Wang C., Lv R.T., Kang F.Y., Gu J.L., Gui X.C., Wu D.H.,

2009. Sythesis and application of iron-filled carbon

nanotubes coated with FeCo alloy nanoparticles. Journal

of Magnetism and Magnetic Materials 321 (13),

1924–1927.

Zhang L., Zhu H., Song Y., Zhang Y.M., Huang Y., 2008. The

electromagnetic characteristic and absorbing properties of

multi-walled carbon nanotubes filled with Er2O3

nanoparticles as microwave absorbers. Materials Science

and Engineering B-solid State Materials for Advanced

Technology 153, 78–82.

Zhao D.L., Li X., Shen Z.M. 2007. Preparation and

electromagnetic and microwave absorbing properties of Fe-

filled carbon nanotubes. Journal of Alloys and Compounds

471, 457–460.