Complex permittivity, complex permeability and reflection loss of Co-Zr substituted La-Sr hexaferrites in 18–40 GHz frequency range

Journal Pre-proofs Research articles Complex Permittivity, Complex Permeability and Reflection Loss of Co-Zr substituted La-Sr Hexaferrites in 18 – 40 GHz frequency range Pawandeep Kaur, S. Bindra Narang, Shalini Bahel PII: DOI: Reference:

S0304-8853(19)32953-1 https://doi.org/10.1016/j.jmmm.2020.166456 MAGMA 166456

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Journal of Magnetism and Magnetic Materials

Received Date: Revised Date: Accepted Date:

22 August 2019 26 November 2019 15 January 2020

Please cite this article as: P. Kaur, S. Bindra Narang, S. Bahel, Complex Permittivity, Complex Permeability and Reflection Loss of Co-Zr substituted La-Sr Hexaferrites in 18 – 40 GHz frequency range, Journal of Magnetism and Magnetic Materials (2020), doi: https://doi.org/10.1016/j.jmmm.2020.166456

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Complex Permittivity, Complex Permeability and Reflection Loss of Co-Zr substituted La-Sr Hexaferrites in 18 – 40 GHz frequency range Pawandeep Kaur*, S. Bindra Narang*, Shalini Bahel Department of Electronics Technology, Guru Nanak Dev University, Amritsar

ABSTRACT In this research, electromagnetic and microwave absorption properties of the hexagonal ferrites with chemical composition, Sr0.85La0.15(CoZr)xFe12-2xO19 (x = 0.00, 0.25, 0.50, 0.75 and 1.00) were studied in the K-band (18 – 26.5 GHz) and Ka-band (26.5 – 40 GHz) frequency range. Minimum reflection loss (RL) was successfully optimized in the studied frequency range by tuning sample thickness using quarterwavelength criterion. Absorption results of synthesized hexagonal ferrites show minimum RL in the range of -18.15 dB to -28.69 dB and absorption bandwidth (-10 dB) in the range of 1.04 GHz to 5.87 GHz. The microwave absorption significantly improved with absorption bandwidth (-10 dB) of 5.87 GHz for the composition x = 1.00 at a sample thickness of 2.2 mm. These newly synthesized ferrites have high potential as microwave absorbing material for military applications such as camouflaging of the target and also as EMI (Electromagnetic Interference) suppressor.

*Corresponding authors E-mail addresses: [email protected] (P. Kaur), [email protected] (S.B. Narang)

1. Introduction: Now-a-days the level of electromagnetic (EM) pollution has increased due to a rapid growth in the modern electronic and information technology. The unwanted electromagnetic radiation causes electromagnetic interference (EMI) which results in poor performance of the electronic and microwave

devices. Furthermore, this increased electromagnetic pollution has shown sign of harmful effects on human beings and environment [1]. The microwave absorber is the best solution to reduce such unwanted microwave radiations. M-type hexagonal ferrites can effectively work as EM wave absorbers due to their better dielectric and magnetic properties [2-3]. In this respect, the design of efficient microwave absorbers in X-, Ku-band is of great interest to the researchers in the last two decade [3-8]. Two prerequisite conditions for EM wave suppression by the material must be satisfied: First, the EM wave must enter the material without front-end reflection and second, the EM wave which entered the material must be attenuated to acceptable level. Strong absorption, wide bandwidth and small sample thickness are the significant features of efficient microwave absorbers. However, relatively few papers have investigated hexagonal ferrites as efficient microwave absorbers in K and Ka-band frequency range qualitatively [9-11]. Many researchers have modified the structural, dielectric, magnetic and electromagnetic properties of M-type hexagonal ferrites by substitution of Fe3+ ions with various divalent-tetravalent ion combinations [2-11] and/or substitution of Sr2+ ion with La3+ ion [12-13]. Narang et al. [9] investigated the electromagnetic and microwave absorption properties of M-type Co-Ti doped barium hexagonal ferrites in 18–40 GHz frequency range and observed that the sample with x = 0.2 achieved minimum reflection loss of -44.56 dB. Dong et al. [10] studies microwave absorption properties of Co-Ti doped barium hexaferrites and results showed low reflectivity of these ferrites in the Ka-band. Pubby et al. [11] prepared hexaferrites with general formula Sr(CoZr)xFe12-2xO19 using so-gel auto-combustion method and observed that the sample with x= 0.2 has maximum absorption capacity with reflection loss peak of -37.2 dB at 24.3 GHz frequency. Chemical methods for synthesis of ferrites are based on low sintering temperatures, which are known to enhance the magnetic properties of hexagonal ferrites due to transition of grain size from micrometer to nanometer range [14]. The aim of this research work is to investigate microwave absorption performance of the synthesized hexagonal ferrite with composition formula, Sr0.85La0.15(CoZr)xFe12-2xO19 (x = 0.00, 0.25, 0.50, 0.75 and 1.00) in 18 - 40 GHz frequencies for their usage in electronic material industry as

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microwave absorbers with wide absorption bandwidth. To the best of author’s knowledge K- and Kaband study on this composition using citrate auto-combustion method has not been studied so far. 2. Experimental procedure M-type hexaferrites with chemical composition, Sr0.85La0.15(CoZr)xFe12-2xO19 (x = 0.00, 0.25, 0.50, 0.75 and 1.00) were synthesized using citrate auto-combustion method and the detailed procedure of synthesis was previously published along with its structural, magnetic and microwave absorption properties in X- and Ku-band frequency range [15]. This is the extended investigation of the synthesized ferrites on microwave absorptive properties in K- and Ka-band frequency range. The synthesized powders were shaped into rectangular pellets to fit exactly into WR-42 (K-Band) and WR-28 (Ka-Band) waveguide respectively. The complex permittivity (ɛ′-jɛ′′) and complex permeability (µ′-jµ′′) were determined from measured scattering parameters using vector network analyzer (Agilent N5225A PNA Series) in 18–40 GHz frequencies. Scanning electron microscope (SEM) and X-ray diffraction (XRD) analysis of synthesized ferrites have resulted in average grain size 120 nm – 544 nm and crystallite size 34 nm – 40 nm respectively [15]. XRD for samples x = 0.00, 0.25 and 0.75 is shown in Figure 1 and SEM for samples x = 0.00 and 0.75 is shown in Figure 2. The grain shrinkage from micrometer scale to nanometer scale may induce change in the surface state and grain surface energy level [12]. The interface polarization and multiple scattering will enhance microwave absorption property of the synthesized ferrite [13]. 3. Result and Discussion 3.1. Complex Permittivity and Complex Permeability In order to investigate the reasons for microwave absorptive behavior of synthesized ferrites, complex permittivity and permeability were studied in 18 – 40 GHz frequencies. The real part (ɛ′) of permittivity and real part (µ′) of permeability represent the storage capability of electric and magnetic energy respectively. Fig. 3(a) and 4(a) exhibits the frequency dependence of ɛ′ and µ′ over 18 – 40 GHz frequency respectively. The imaginary part (ɛ′′) of permittivity and (µ′′) permeability represents the loss of electric and magnetic energy respectively. Fig. 3(b) and 4(b) exhibits the frequency dependence of ɛ′′ and µ′′ in 18 – 40 GHz frequency range. The dispersion in complex permittivity (ɛ′-jɛ′′) with frequency may be attributed to the difference in the relaxation frequencies of various dipoles generated due to substitution of Co2+ and Zr4+ in place of Fe3+ and substitution of La3+ in place of Sr2+ ions in synthesized ferrites [8]. Similarly, with substitution of such ions dispersion in complex permeability (µ′ - jµ′′) may be attributed to the change in direction of the magnetization vector which shift towards basal plane [16].

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Similar trend in (ɛ′-jɛ′′) and (µ′ -jµ′′) was reported by the other researcher [10]. It has been observed that the peaks in ɛ′ corresponds to dips in µ′ occurred at same frequency and their numerical values become closer to each other at that frequency in studied frequency range. Such numerically close values of ɛ′ and µ′ lead to impedance matching which is favorable to achieve strong microwave absorption [17]. The average increase in µ′ of all the synthesized ferrites as compared to composition x = 0.00 may be attributed to the increase in grain size with CoZr substitution in synthesized ferrite. Large grain size reduces the resistance to domain wall motion, thereby enhancing permeability with Co-Zr substitution [7]. It is clear from Figures 3(b) and 4(b), that the values of ɛ′′ and µ′′ are larger for the synthesized ferrites as compared to composition x = 0.00. The electron hopping between Fe3+ and Fe2+ ions results in the enhancement of the interfacial polarization for Co-Zr substituted ferrites due to which average dielectric loss (ɛ′′) increases. Resonance peaks observed in µ′′ represents energy absorption which may be attributed to the ferromagnetic resonance (fr) and exchange resonance of the synthesized ferrites [18]. The ferromagnetic resonance is closely related with the magnetic anisotropy field (Ha) by the following relation [19]: 2πfr = γHa, where γ is the gyromagnetic ratio. The anisotropy field (Ha) decreases with increase in Co-Zr substitution in synthesized ferrites as reported in previous paper [15], thereby shifting the resonance peak from higher frequency for composition x = 0.00 to the lower side for Co-Zr substituted ferrites. Furthermore, the enhancement ɛ′′ and µ′′ values with Co-Zr substitution, improves miniaturization capability of a material i.e. strong absorption can be observed at small sample thickness [20]. 3.2. Microwave Absorption performance According to transmission-line theory, when an electromagnetic wave is normally incident on an absorbing layer of a material backed with a metal plate (Figure 5), the reflection loss (RL) at a given absorber thickness is determined using the following equations [15]: RL (dB) = 20log[(Zin – Z0)/ (Zin+ Z0)]

(1)

Zin = Z0(µr/ ɛr)1/2tanh[j(2πft(µrɛr)1/2)/c)]

(2)

Where Zin is the input impedance, Z0 is the characteristic impedance of free space, f is the frequency, c is the velocity of light in vacuum and t is the thickness of samples. The reflection loss is measured at the optimum values of the matching thickness (tm) which is expressed by the following equation [22]; tm = nλ/4 = nc/ (4fm(µr/ ɛr)1/2)

(n = 1 and 3)

where λ is the wavelength inside the absorber.

4

(3)

Figure 6 (a)-(e) represents the simulated and calculated matching thickness for all the synthesized ferrites at different nλ/4 curves (n = 1, 3 and 5) along with variation of minimum reflection loss at particular matching thickness (tm) and matching frequency (fm) in the studied frequency range (18-40 GHz). Furthermore, long vertical dash lines are drawn from the minimum RL for a simulated thickness to the corresponding calculated nλ/4 (1, 3 and 5) curves.

The calculated sample thicknesses are in

agreement with the simulated sample thicknesses in for all the synthesized ferrites, which fulfills quarter wavelength mechanism at nλ/4 (1, 3 and 5). Moreover, for a few thicknesses, the RL spectra shows more than one dip, this may be due to matching of impedance at more than one point [23]. For composition x = 0.00 in Figure 6 (a), the minimum RL value of -20.58 dB, -18.8 dB, -17.05 dB and -27.12 dB have been observed at sample thickness 1 mm, 2.9 mm, 3.7 mm and 4 mm respectively. The -10 dB absorption bandwidth has been obtained in the range 2.04 –3.8 GHz. The values of reflection loss peak, matching frequency, sample thickness and bandwidth (-10 dB) for the Co-Zr substituted La-Sr hexagonal ferrites in the 18 ‒ 40 GHz frequency are presented in Table 1. From Figure 6 (b) for composition x = 0.25, RL<-10 dB have been observed for the sample thicknesses 1.5 mm, 2.2 mm, 2.9 mm, 3.5 mm, 3.7 mm, 3.8 mm and 4.0 mm. The enhancement in -10 dB bandwidth from 2.62 GHz for composition x = 0.00 to 2.8 GHz for composition x = 0.25 has been observed at same thickness t = 2.9 mm. Maximum bandwidth of value 3 GHz has been obtained at sample thickness of 4 mm. For composition x = 0.50, minimum RL value of -17.78 dB, -18.36 dB, -18.38 dB, -18.15 dB and -17.6 dB are obtained at sample thickness 1.2mm, 1.7 mm, 3 mm, 3.8 mm and 4.0 mm respectively as shown in Figure 6 (c). Microwave absorption bandwidth (-10 dB) for this composition has been obtained in the range of 1.04 – 2.83 GHz. For composition x = 0.75, Figure 6(d) shows that the highest value of minimum RL -28.69 dB at 23.3 GHz have been obtained for sample thickness 1.4 mm. The -10 dB BW of 1.83 GHz, 1.49 GHz, 2.68 GHz, 2.31 GHz and 2.20 GHz has been obtained for sample thickness 1.2 mm, 1.4 mm, 3.0 mm, 3.9 mm and 4.0 mm respectively. For this composition, minimum RL values with large absorption bandwidth of value 3.10 GHz and 2.87 GHz have been obtained for sample thickness of 3.9 mm and 4 mm at 34.31 GHz and 35.6 GHz respectively. In Figure 6 (e), for composition x = 1.00, minimum RL of value -19.50 dB, -25.57 dB, -15.08 dB and -20.50 dB have been obtained for sample thickness 1.1 mm, 2.2 mm, 3.0 mm and 4.0 mm respectively. Enhancement in -10 dB absorption bandwidth has been achieved for this composition as

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compared to other compositions of this series. Highest absorption bandwidth of 5.87 GHz has been observed at sample thickness of 2.2 mm at 34.30 GHz in the studied frequency range (18 – 40 GHz). 3.3 Absorption power When an electromagnetic wave is incident on the synthesized sample backed with metal plate, the wave can either get reflected or absorbed in the material. The percentage of absorbed power can be calculated from reflection loss using equation (4) [24]: Absorption (%) = 100 – reflected power = [100 – (100 *10-RL/10)]

(4)

Figure 7 (a-b) presents the absorption power of Co-Zr substituted La-Sr hexagonal ferrites for their respective nλ/4 (n = 1 or 3) matching thickness in the 18 – 40 GHz frequency range. In 18 ‒ 26.5 GHz frequency range, (Figure 7 (a)), the compositions x = 0.75, 0.00 and 0.25 absorb 99.9 %, 99.8 % and 99.7 % of incident power at 21.99 GHz, 24.9 GHz and 21.38 GHz respectively, followed by other compositions x = 1.00 and x = 0.50 which show 99.2 % and 98.6 % absorption of power at 21.7 GHz and 21.4 GHz respectively. Power absorption of more than 90 % was observed from 24.2 GHz to 26.15 GHz for composition x = 0.00, 20.62 GHz to 21.94 GHz for x = 0.25, 20.51 GHz to 21.73 GHz for x = 0.50, 20.89 GHz to 23.29 GHz ad 23.3 GHz to 24.7 GHz for x = 0.75 and 20.63 GHz to 22.29 GHz for x = 1.00 respectively. In 26.5 ‒ 40 GHz frequency range, for composition x = 1.00, Figure 7 (b) shows that maximum absorption of 99.9 % with absorption bandwidth range from 33.8 GHz to 34.2 GHz, followed by compositions x = 0.25, 0.00, 0.75 and 0.50 which absorb 99.7 % , 98.8 %, 98.6 % and 98.5 % of incident power respectively. It has been observed that more than 90 % absorption bandwidth range has increased with Co-Zr substitution for the synthesized ferrites which further support their strong microwave absorption in 18 – 40 GHz frequency range. 4. Conclusions Synthesized ferrites were investigated for electromagnetic and microwave absorbing properties. Absorption bandwidth is enhanced with Co-Zr substitution in La-Sr hexagonal ferrites which is attributed to the multiple resonance peaks in ɛ′′ and µ′′. The peaks in ɛ′ correspond to dips in µ′ at same frequency and their numerical values become closer to each other at that frequency in the studied frequency range. Such numerically closer values of ɛ′ and µ′ lead to impedance matching which is favorable to achieve strong microwave absorption. In K-band, the microwave absorption of more than 99% was obtained with absorption bandwidth of 3 GHz and 1.27 GHz for compositions 0.25 and 0.75 respectively. In Ka-band, the composition x = 1.00 shows minimum RL of value of -25.57 dB with enhanced absorption bandwidth

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of 5.87 GHz at sample thickness of 2.2 mm. Therefore, synthesized ferrites are the potential candidates of MW absorbers in 18 – 40 GHz with good absorption, small sample thickness and broad bandwidth range.

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[12] C.J. Li, B.Wang and J.N. Wang, Magnetic and Microwave Absorbing Properties of Electrospun Ba(1x)LaxFe12O19

Nanofibers. J. Magn. Magn. Mater. 324 (2012) 1305.

[13] N. Chen, K. Yang and M. Gu, Microwave absorption properties of La-substituted M-type strontium ferrites, Journal of Alloys and Compounds.490 (1–2) (2010) 609. [14] F.M. Idris, M. Hashim, I. Ismayadi, I.R. Idza, M. Manap and M.S.E. Shafie, Broadeneing of EM Energy-Absorption Frequency Band by Micrometer-to-Nanometer Grain Size Reduction in NiZn Ferrite. IEEE Trans. Magn. 49 (2013) 5475. [15] P.Kaur, S.B. Narang and S. Bahel, Modulation of microwave properties of La-Sr hexagonal ferrite with doping of Co-Zr and change in thickness, J Mater. Sci: Mater. Electron. 28 (2017) 16077. [16] X.Z. Zhou, Co‐Sn substituted barium ferrite particles. J. Appl. Phys. 75 (1994) 5556.

[17] P. Meng, K. Xiong, L.Wang, S. Li, Y. Cheng and G. Xu, Tunable complex permeability and enhanced microwave absorption properties of BaNixCo1−xTiFe10O19. J. Alloys Compd. 628 (2015) 75. [18]Z. Ma, Y. Zhang, C.T. Cao, J. Yuan, Q.F. Liu and J.B. Wang, Attractive microwave absorption and the impedance match effect in zinc oxide and carbonyl iron composite, Physica B. 406 (2011) 4620. [19] C. Stergiou and G. Litsardakis, Electromagnetic properties of Ni and La doped strontium hexaferrites in the microwave region. J. Alloys. Compd. 509 (2011) 6609. [20] C. Stergiou and G. Litsardakis, Y-type hexagonal ferrites for microwave absorber and antenna applications, J. Magn.Magn.Mater. 405 (2016) 54. [21] T. Inui, K. Konishi and K. Oda, Fabrications of broad-band RF-absorber composed of planar hexagonal ferrites, IEEE Trans. Magn. 35 (1999) 3148. [22] B. Wang, J. Wei, Y. Yang, T. Wang, and F. Li, Investigation on peak frequency of the microwave absorption for carbonyl iron/epoxy resin composite, J. Magn. Magn.Mater. 323 (2011) 1101. [23] X. H. Li, J. Feng, Y. P. Du, J. T. Bai, H. M. Fan, H. L. Zhang, Y. Peng and F. S. Li, One-pot synthesis of CoFe2O4/graphene oxide hybrids and their conversion into FeCo/graphene hybrids for lightweight and highly efficient microwave absorber, J. Mater. Chem. A. 3 (2015) 5535.

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[24] P. Kaur, S. Bahel and S.B. Narang, Microwave absorption behavior and electromagnetic properties of Ni-Zr doped La-Sr hexagonal ferrite synthesized by auto-combustion method, Mater. Res. Bull. 100 (2018) 275- 281.

CRediT author statement: S. Bindra Narang: Supervision and Conceptualization. S. Shalini Bahel: Supervision, Writing: Review and Editing. P. Kaur: Methodology, Investigation, Validation, Writing-Original Draft.

Figure Captions Figure 1. X-ray diffraction patterns of Sr0.85La0.15(CoZr)xFe12-2xO19 ferrites for different Co-Zr contents (x = 0.00, 0.25 and 0.75). Figure 2 SEM micrographs of Sr0.85La0.15(CoZr)xFe12-2xO19 ferrites for (a) x = 0.00 and (b) x = 0.75. Figure 3 Variation of (a) real part (ɛ′) and (b) imaginary part (ɛ′′) of permittivity of Sr0.85La0.15(CoZr)xFe122xO19

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ferrites (for different Co-Zr contents) with respect to 18 ‒ 40 GHz frequency range.

Figure 4 Variation of (a) real part (μ′) and (b) imaginary part (μ′′) of permeability of Sr0.85La0.15(CoZr)xFe12-2xO19 ferrites (for different Co-Zr contents) with respect to 18 ‒ 40 GHz frequency range. Figure 5 Ferrite (as microwave absorbing material) backed with a metal plate. Figure 6 (a-e) Variation of minimum reflection loss (RL) of Sr0.85La0.15(CoZr)xFe12-2xO19 ferrites (for different Co-Zr contents) with respect to frequency (18 – 40 GHz) for various sample thicknesses (upperhalf) and calculated λ/4, 3λ/4 and 5 λ/4 thicknesses (lower-half). Figure 7 Absorption power of Sr0.85La0.15(CoZr)xFe12-2xO19 ferrites (for different Co-Zr contents) with respect to frequency (a) 18–26.5 GHz and (b) 26.5 –40 GHz.

11

Figure 1. X-ray diffraction patterns of Sr0.85La0.15(CoZr)xFe12-2xO19 ferrites for different Co-Zr contents

(x = 0.00, 0.25 and 0.75).

(a)

x = 0.00

(b) x = 0.75

Figure 2 SEM micrographs of Sr0.85La0.15(CoZr)xFe12-2xO19 ferrites for (a) x = 0.00 and (b) x = 0.75.

12

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Figure 3 Variation of (a) real part (ɛ′) and (b) imaginary part (ɛ′′) of permittivity of Sr0.85La0.15(CoZr)xFe122xO19

14

ferrites (for different Co-Zr contents) with respect to 18 ‒ 40 GHz frequency range.

15

Figure 4 Variation of (a) real part (μ′) and (b) imaginary part (μ′′) of permeability of Sr0.85La0.15(CoZr)xFe12-2xO19 ferrites (for different Co-Zr contents) with respect to 18 ‒ 40 GHz frequency range.

Figure 5 Ferrite (as microwave absorbing material) backed with a metal plate.

16

(a)

17

(b)

(c)

18

(d)

19

(e) Figure 6 (a-e) Variation of minimum reflection loss (RL) of Sr0.85La0.15(CoZr)xFe12-2xO19 ferrites (for different Co-Zr contents) with respect to frequency (18 – 40 GHz) for various sample thicknesses (upperhalf) and calculated λ/4, 3λ/4 and 5 λ/4 thicknesses (lower-half).

20

(a)

(b)

Figure 7 Absorption power of Sr0.85La0.15(CoZr)xFe12-2xO19 ferrites (for different Co-Zr contents) with respect to frequency (a) 18–26.5 GHz and (b) 26.5 –40 GHz.

Highlights: 

Synthesized ferrites show microwave absorption of more than 99%



Minimum RL in the range of -18.15 dB to -28.69 dB.



Bandwidth (-10 dB) of 5.87 GHz obtained for x = 1.00 in Ka-band.



These ferrites can be used as efficient microwave absorbing material.

Table 1 Reflection loss (RL), matching frequency (fm), matching thickness (tm) and -10 dB bandwidth (BW) of Sr0.85La0.15(CoZr)xFe12-2xO19ferrites with composition x in 18 – 40 GHz frequency range. Frequency

Quarter

Composition

Band

Wavelength

x

21

Peak Value

Matching

-10 dB

Reflection

Matching

thickness

Bandwidth

loss

frequency

tm (mm)

BW (GHz)

λ/4

K-Band

3λ/4

λ/4

Ka-Band

3λ/4

5λ/4

22

RL (dB)

fm (GHz)

0.25

-15.80

21.10

1.50

1.18

0.50

-18.36

19.22

1.70

1.04

0.75

-28.69

23.30

1.40

1.27

1.00

-18.89

21.11

1.70

1.42

0.00

-27.14

24.97

4.00

2.30

0.25

-25.80

28.67

4.00

3.00

0.50

-17.60

21.06

4.00

1.40

0.75

-23.90

22.20

3.90

2.20

1.00

-20.80

21.68

4.00

1.65

0.00

-20.58

29.70

1.00

3.80

0.25

-22.38

28.28

1.50

2.73

0.50

-17.78

29.25

1.20

2.01

0.75

-28.69

23.30

1.40

1.49

1.00

-19.50

26.82

1.10

1.36

0.00

-18.80

31.07

2.90

2.62

0.00

-27.12

25.02

4.00

2.04

0.25

-21.20

28.56

2.90

2.80

0.25

-25.64

28.70

4.00

3.10

0.50

-18.29

29.73

3.00

2.60

0.75

-18.17

28.21

3.00

2.68

1.00

-25.57

34.30

2.20

5.87

1.00

-15.08

27.42

3.00

2.10

0.00

-17.05

37.66

3.70

2.70

0.25

-17.50

36.09

3.70

2.51

0.50

-18.15

35.70

3.80

2.83

0.75

-23.16

34.31

3.90

3.10

1.00

23

-20.50

32.00

4.00

2.87