This document discusses magnetic susceptibility and types of magnetic materials. It defines magnetic susceptibility as the ratio of magnetism induced in a substance to the applied magnetic field. There are four main types of magnetic materials: diamagnetic, paramagnetic, ferromagnetic, and antiferromagnetic. Diamagnetic materials have a negative susceptibility and produce a magnetization opposite to the applied field. Paramagnetic materials have a positive susceptibility and are weakly attracted by magnetic fields. Ferromagnetic materials have a high positive susceptibility and can retain magnetization after removing the applied field. Antiferromagnetic materials also have positive susceptibility but their magnetic moments cancel out above a certain temperature.

1. 1
Title : Magnetic Susceptibility of magnetic
materials
A graduation project submitted to the Department of Physics in partial fulfillment of
the requirements for the degree of Bachelor of Science in Applied Physics
Prepared by: Samia Abdullah A_lotaibi
Supervisor: Dr. Mohamed Alamen
AIMISIU/COS/DOP/
Riyadh- KSA- Dec. 2014
Kingdom of Saudi Arabia
Al-Imam Mohammad Ibn Saud Islamic University
College of Sciences
Department of Physics

2. 2
Table of contents
1- Introduction……………………………………………………………………………..7
2- Magnetic susceptibility………………………………………………………………….8
3. Types of magnetic materials………………………………….………………………....8
3.1. Diamagnetic Materials. ……………………………...…....…………………..8
3.1.1. Definition……………………………….…………………………………...9
3.1.2. Properties of diamagnetic materials………….…….………………………10
3.1.3. Examples of diamagnetic materials are…………………………..………..10
4.1 Paramagnetic Materials…………………………....................……………………...10
4.1.1 Definition…………………………………………………………………...11
4.1.2.Properties of Paramagnetic materials susceptibility………………………..12
4.1.3.Examples of paramagnetic materials………………………………….……13
5.1 Ferromagnetic Materials………………………….....................................………….13
5.1.1 Definition………………………………………..…………………………13
5.1.2 Curie temperature…………………………………………………………..14
5.1.3. Properties of ferromagnetic materials……………………………………...14
5.1.4. Examples of ferromagnetic materials are………………………………….15
6.1 Anti-ferromagnetic materials ………………………………………………………...15
6.1.1 Definition……………………………………………………………...……15
6.1.2 Neel temperature…………………………………………………………....15
6.1.3 Properties of antiferromagnetic materials…………………………………..16
6.1.4 Examples of antiferromagnetic materials are……………................………16
4.Experimental results……………………………………………………………..……..17
4.1. ZnO powder………………………………………………………………….17
4.2.ZnO:Mn powder……………………………………………………….….18,19
4.3.Ni powder………………………………………………………………….....20
5.Conclusion……………………………………………………...………………………21
6.References……………………………………………………………………………....22
7.Appendix …………………………………….……………………………………..23-29

3. 3
List of Tables
1 A Curie temperatures for some ferromagnetic materials……………...........................14
2 Neel temperatures for some crystalline ferromagnetic materials……………………...16
List of Figures
1 Relationship between temperature and magnetic susceptibility for diamagnetic
materials…………………………………………………………………………………..9
2 The orientation of spin in paramagnetic materials………………………….................10
3 Spin orientation in paramagnetic materials before and after applying magnetic
field…………………………………………............…………………………………….11
4 Relationship between temperature and magnetic susceptibility for paramagnetic
materials.....……………………………………………………………………………….11
5 Spin orientation in ferromagnetic materials…………………………………………..13
6 Relationship between magnetic susceptibility and temperatures for ferromagnetic
materials…………………………………………………………………………………..14
7 Spin orientation of anti-ferromagnetic material ……………………….……………...15
8 Relationship between susceptibility and temperatures for antiferromagnetic…………15
9 Magnetization of ZnO powder………………………………..…………..…….………17
10 Magnetization of ZnO doped Mn powder………………………...………………….19
11 Magnetization of Ni…………………………………………….…………………….20

4. 4
Acknowledgements .
I thank God who gave me the mind and made me able to think in everything
around me and helped me in my studies and my lives .
I express my immense gratitude to my supervisor Dr Mohamed Abdellah Lemine for
helping me during this project.
I thank my Family who gave me support from my childhood to the last level in
the University , and I thank the national also .
I thank the Imam Mohamed Bin Saud Islamic University ,which has given me
an opportunity to study physics , I thank every member of the faculty at this
University, and helped me from my friends.

5. 5
ABSTRACT
Magnetic materials attracted the interest during the last years due to their applications in many
fields such as media, biomedical, water treatment..etc.
This final project will be dived into parts:
In the first part, we will study each type of magnetic materials by giving the definition, magnetic
susceptibility, the properties and some examples. Four type of magnetic materials are reviewed:
diamagnetic , paramagnetic , ferromagnetic and anti-ferromagnetic.
In the second part, we will determine experimentally the type of some magnetic materials based
on the magnetic susceptibility by using vibrator sample magnetometer (VSM) located at physics
department –Al imam University.
and based on the magnetic susceptibility experimental values, we determined the magnetic nature
of different powders. It was found that ZnO materials have a negative susceptibility and from that
we concluded that is diamagnetic materials. By adding Mn impurity to ZnO, it is transformed to
paramagnetic materials with a positive magnetic susceptibility. We showed also that Ni is
ferromagnetic with high and positive magnetic susceptibility.

6. 6
‫الخال‬‫صه‬:
‫جذبت‬‫المواد‬‫المغناطيسية‬‫اإلهتمام‬‫خالل‬‫السنوات‬‫الماضية‬‫بسبب‬‫تطبيقاتها‬‫في‬‫العديد‬‫من‬‫المجاالت‬‫مثل‬‫وسائل‬
،‫اإلعالم‬‫الطب‬،‫الحيوي‬‫معالجة‬... ‫المياه‬..‫ألخ‬
‫هذا‬‫المشروع‬‫سيغوص‬ ‫النهائي‬‫إلى‬‫األجزاء‬:
‫في‬‫الجزء‬،‫األول‬‫وسوف‬‫ندرس‬‫كل‬‫نوع‬‫من‬‫المواد‬‫المغناطيسية‬‫من‬‫خالل‬‫إعطاء‬،‫تعريف‬‫الحساسية‬،‫المغناطيسية‬
‫والخصائص‬‫وبعض‬‫األمث‬‫لة‬‫على‬‫ذلك‬.‫تتم‬‫مراجعة‬‫أربعة‬‫أنوع‬‫من‬‫المواد‬‫المغناطيسية‬:‫مغناطيسية‬ ‫ديا‬،‫بارا‬
،‫مغناطيسي‬‫فيرو‬‫مغناطيسية‬‫ومكافحة‬‫المغناطيسية‬.
‫في‬‫الجزء‬،‫الثاني‬‫وسوف‬‫نحدد‬‫تجريبيا‬‫نوع‬‫من‬‫بعض‬‫المواد‬‫المغناطيسية‬‫على‬‫أساس‬‫القابلية‬‫المغناطيسية‬‫باستخدام‬
‫مغنطيسية‬‫عينة‬‫هزاز‬(VSM)‫الموجود‬‫في‬‫قسم‬‫إمام‬ ‫جامعة‬ ‫الفيزياء‬.
‫واستنادا‬‫إلى‬‫القيم‬‫التجريبية‬‫للقابلية‬،‫المغناطيسية‬‫توصلنا‬‫إلى‬‫الطبيعة‬‫المغناطيسية‬‫للمساحيق‬‫المختلفة‬.‫وقد‬‫وجد‬‫أن‬
‫المواد‬‫أكسيد‬‫الزنك‬‫لديها‬‫القابلية‬‫السلبية‬‫ومن‬‫خلصنا‬ ‫ماحسبناه‬ ‫خالل‬‫إلى‬‫مواد‬ ‫أنها‬‫مغناطيسيه‬ ‫دايا‬.‫بإضافة‬‫شوائب‬
‫المنجنيز‬ ‫من‬‫أكسيد‬ ‫إلى‬،‫الزنك‬‫يتم‬‫تحويله‬‫إلى‬‫مواد‬‫ذات‬‫قابلية‬‫مغناطيسية‬‫إيجابية‬.‫أظهرنا‬‫أيضا‬‫أن‬‫فيرو‬ ‫هو‬ ‫النيكل‬
‫قابلية‬ ‫له‬ ‫مغناطيسية‬‫مغناطيسية‬‫عالية‬‫وإيجابية‬.

7. 7
1. Introduction
Magnetic materials attracted the interest during the last years due to their applications in
many fields such as media, biomedical, water treatment..etc.
This final project will be dived into parts:
In the first part, we will study each type of magnetic materials by giving the definition,
magnetic susceptibility, the properties and some examples. Four type of magnetic
materials are reviewed: diamagnetic, paramagnetic, ferromagnetic and anti-ferromagnetic.
In the second part, we will determine experimentally the type of some magnetic materials
based on the magnetic susceptibility by using vibrator sample magnetometer (VSM)
located at physics department –Al imam University.

8. 8
2. Magnetic Susceptibility.
Magnetic Susceptibility is the ratio of the intensity of magnetism induced in a substance
to the magnetizing force or intensity of field to which it is subject.
The magnetic susceptibility per unit volume is defined mathematically by:
χ =
M
B
(CGS) , χ =
μ0M
B
(SI) , note: the magnetic field intensity have two
expression which are equally (B = H)
In both systems units of χ is dimensionless. We shall sometimes for convenience refer to
M/B as the susceptibility without specifying the system of units .
Where :
χ : it is the magnetic susceptibility of material is the ratio of M to H .
μ0
: it is the magnetic permeability of a vacuum in H. m−1
is the ratio of B to H
M : it is the Magnetization of material or the total magnetic moment per unit volume .
B : it is the macroscopic magnetic field intensity (applied magnetic field).
Magnetic susceptibility reflects a material's degree of sensitivity to magnetic fields. Some
materials are highly susceptible and other materials are slowly susceptible and will
become magnetized in response to a magnetic field, while others resist magnetism,
depending on their composition.
We will see in the experimental part of this report the magnetic susceptibility of some
materials characterized by vibrator sample magnetometer (VSM) located at department of
physics.
3. Types of magnetic materials
3.1. Diamagnetic Materials.
3.1.1. Definition.
Diamagnetism is due to the non-cooperative behavior of orbiting electrons when exposed
to an applied magnetic field and. Diamagnetic substances are composed of atoms which
have no net magnetic moments (ie., all the orbital shells are filled and there are no
unpaired electrons). A negative magnetization is produced when the material is exposed
to external magnetic field, thus the susceptibility is negative (Figure 1).

9. 9
Figure 1. : Relationship between temperature and magnetic susceptibility for
diamagnetic materials
When an external magnetic field H is applied to a diamagnetic material (or diamagnet ),
the atomic electronic orbitals are strongly modified owing to the deviation of electron
trajectory by the magnetic field according to Laplace’s law. Therefore, a spontaneous
induced magnetic field appears and it opposes the variations of the external magnetic field
as predicted by Lenz’s law.
In general, diamagnetism originates from an induced current opposing the external
applied magnetic field. For this reason, their relative magnetic permeabilities are slightly
below unity (μr < 1). As a general rule, because diamagnetism originates from orbital
deformation under an applied external magnetic field, all materials obviously have a basic
diamagnetic component.
In diamagnetic materials, the magnetic susceptibility can be accurately predicted by
Langevin's classical theory of electromagnetism as follows :
χm
=
−μ0
n Z e2
< r2
>
6m0
Where :
χm
: frequently a susceptibility is defined referred to unit mass or to a mole of the
substance ,which means The molar susceptibility .
μ0
: the magnetic permeability of a vacuum in H.m−1
.
Z : the atomic number of the atom .
n: the atomic density in m−3
.
e : the elementary charge in C .
< 𝐫 𝟐
> ∶ the root mean square of the square of the atomic radius in m2
.

10. 10
3.1.2. Properties of diamagnetic materials:
• Diamagnetic materials exhibit small and negative magnetic susceptibility in the
range 𝑜𝑓 ∶ −10−6
to −10−5
• Relative magnetic permeability of diamagnetic materials is always less than unity that is
μr < 1
• Magnetic susceptibility of diamagnetic materials does not change with temperature
3.1.3. Examples of diamagnetic materials are:
1) Gases such as hydrogen, nitrogen, chlorine, and bromine and noble gases such as He,
Ne, Ar, Kr, Xe .
2) The chemical elements from group IIA(2): Be; group IIIA(13): B, Ga, In, Tl; group
IVA(14): C, Si, Ge, Pb; group VA(15): P, As, Sb, Bi, group VIA(16) S, Se, Te; group
IA(11): Cu, Ag and Au; group IIA(12): Zn, Cd, Hg .
3) Crystalline solid materials such as (MgO) and diamond .
4.1 Paramagnetic Materials.
4.1.1 Definition
In the paramagnetic materials, the magnetic moments do not interact with each other and
they are randomly arranged in the absence of a magnetic field (figure 2).
Figure.2. The orientation of spin in paramagnetic materials

11. 11
When a field is applied, the atomic magnetic moments are aligned in the direction of the
field and that will induce a net positive magnetization and positive susceptibility.
Figure 3: Spin orientation in paramagnetic materials before and after applying
magnetic field
The efficiency of the field in aligning the moments is opposed by the randomizing effects
of temperature. This results in a temperature dependent susceptibility, known as the Curie
Law. At normal temperatures and in moderate fields, the paramagnetic susceptibility is
small (but larger than the diamagnetic contribution). Unless the temperature is very low
(<<100 K) or the field is very high paramagnetic susceptibility is independent of the
applied field.
Figure 4: Relationship between temperature and magnetic susceptibility for
paramagnetic materials.

12. 12
The magnetic susceptibility of paramagnetic materials decreases with an increase in
temperature. The temperature dependence of the magnetic susceptibility of paramagnetic
materials is given by the Curie–Weiss law described by the following equation:
χm
=
μ0
n m2
[3k(T − TC)]
=
C
(T − TC)
where:
μ0
: it is the magnetic permeability of a vacuum in H.m−1
n : it is the atomic density in m−3
m: it is the microscopic dipolar magnetic moment of an atom in A.m2
k : it is the Boltzmann constant in J.K−1
T : it is the absolute thermodynamic temperature in K
TC: it is the the paramagnetic Curie temperature in K at which the susceptibility reaches
its maximum value
C : it is the the paramagnetic Curie constant in K−1
4.1.2.Properties of Paramagnetic materials susceptibility:
1) The magnetic lines of forces due to the applied field are attracted towards the
paramagnetic material.
2) When placed in a non-uniform magnetic field, the paramagnetic materials move from
weaker parts of the field to the stronger parts.
3) Permeability of paramagnetic material is greater than 1.
4) Magnetic susceptibility of paramagnetic material is positive (10−5
to 10−3
) .
5) Susceptibility of paramagnetic materials varies inversely with the temperature (Curie –
Weis law).
6) Arises from permanent dipole moments on the atoms.

13. 13
4.1.3.Examples of paramagnetic materials:
Gases for example: oxygen and all the chemical elements dealing with diamagnets for
example :Li, Na, Mg, Al, Ti, Zr, Sn, Mn, Cr, Mo, and W and all the platinum-group
metals: Ru, Rh, Pd, Os, Ir, Pt. On.
5.1 Ferromagnetic Materials .
5.1.1Definition
Ferromagnetic materials has a spontaneous magnetic moment- a magnetic moment even
in zero applied magnetic field. The existence of a spontaneous moment suggests that the
electron spin and magnetic moments are arranged in a regular manner.
Figure 5 : Spin orientation in ferromagnetic materials
Ferromagnetic materials have magnetic dipolar moments aligned parallel to each other
even without an external applied magnetic field.

14. 14
5.1.2 Curie temperature
The Curie temperature is the temperature above it the ferromagnetic materials become
paramagnetic.
Figure 6 : Relationship between magnetic susceptibility and temperatures for
ferromagnetic materials
Examples of Curie temperature for some materials:
Materials Co Fe Ni Gd Fe2O3 MnAs
Curie temperature(K) 1388 1043 627 292 948 318
Table 1 : A Curie temperatures for some ferromagnetic materials
5.1.3. Properties of ferromagnetic materials:
1) A ferromagnetic materials has a spontaneous magnetic moment- a magnetic moment
even in zero applied magnetic field (at H = 0) below 𝑇𝐶 .
2) All ferromagnetic materials become paramagnetic above a temperature called Curie
temperature Tc
3) Permeability is greater than 1 .
4) Magnetic susceptibility is large and positive .
5) Magnetic susceptibility decreases with the rise in temperature according to Curie-
Weiss law.
6) The source of ferromagnetism is the spin of the electrons.

15. 15
5.1.4. Examples of ferromagnetic materials are:
Nickel , cobalt, iron and aluminum-nickel-cobalt alloy.
6.1 Anti-ferromagnetic materials:
6.1.1 Definition
In the antiferromagnetic materials, the alignment of the spin moments of neighboring
atoms or ions in exactly opposite directions
Figure 7: Spin orientation of anti-ferromagnetic materials
6.1.2 Neel temperature
The Neel temperature is the temperature above it the anti-ferromagnetic materials become
paramagnetic.
Figure 8: Relationship between susceptibility and temperatures for
antiferromagnetic materials

16. 16
Examples of the Neel temperature for some materials:
Materials Cr NiO FeO MnO CoO MnS
Neel temperature(K) 308 525 198 116 291 160
Table 2 : Neel temperatures for some crystalline ferromagnetic materials
6.1.3 Properties of antiferromagnetic materials:
1) The antiferromagnetism will not produce any magnetisation because of the two
opposing spin components.
2) When we applied external field, the net magnetization will be different of zero due to
that the maximum of spin are in the same direction .
3) Antiferromagnetism is a special case of ferrimagnetism .
4) Neel temperature (𝑇 𝑁) is the critical temperature for the antiferromagnetic materials .
6.1.4 Examples of antiferromagnetic materials are:
MnO, FeO, CoO, NiO, Cr, Mn,MnO4, MnS, FeCl3, MnF2 .

17. 17
4. Experimental results
In this part, we studied the magnetic properties of three materials by using vibrator sample
magnetometer (VSM) equipment located at physics department.
An external magnetic field is applied on the powders materials and the magnetization
values are registered. Based on the definition of magnetic susceptibility in the first part of
this report, we will determine the type of each materials by calculating the value for each
materials.
4.1. ZnO powder
Fig.9 shows the magnetization of ZnO powders. If we compare this figure to Figure 1 in
the first part of this report, we can conclude that the behavior is similar to diamagnetic
materials.
Figure 9. : Magnetization of ZnO powder
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
-6000 -4000 -2000 0 2000 4000 6000
Moment(emu)
Magnetic Field (G)
Graph of ZnO material

18. 18
We can confirm this conclusion by calculating also the magnetic susceptibility for this
materials. The magnetic susceptibility is : χ =
M
B
If we take : (x , y) = (m ,B) , where : m = Magnetic Field(G) , B = Moment(emu)
When we calculate the magnetic susceptibility for two points from the figure:
First point (-0.01055 , 5000) : χ =
M
B
=
−0.01055
5000
= −0.00000211
Second point (-0.0082,4000) : χ =
M
B
=
−0.0082
4000
= −0.00000205
So we conclude from the calculation of the magnetic susceptibility of the Zno
materials which are negative that ZnO is diamagnetic materials.
4.2.ZnO:Mn powder
We showed in Fig.9 that ZnO is diamagnetic materials. If we doped it with
ferromagnetic materials, we are expecting that this magnetic behavior changes.
Fig.10 shows the magnetization of ZnO doped with 5% of Mn. It can be seen that
ZnO change behavior comparing to Fig.9. If we compare Fig.10 to Fig.4 of the first
part, we can conclude that ZnO doped Mn is a paramagnetic material.
This calculation can be confirmed quantitavely by deducing the magnetic
susceptibility from figure 10.
From the data table the magnetic susceptibility: χ =
M
B
If we take : (x , y) = (m ,B) , where : m = Magnetic Field(Oe) , B = Moment(emu)
When we calculate the magnetic susceptibility for tow points :
First point (0.12228, 50000.15234) : χ =
M
B
=
0.12228
50000.15234
= 0.00000244559
Second point (0.11734, 47999.85547) : χ =
M
B
=
0.11734
47999.85547
=0.00000244459

19. 19
We conclude from the figure and from the positive value of the magnetic
susceptibility that ZnO:Mn powder is paramagnetic material
Figure 10. : Magnetization of ZnO doped Mn powder
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
-60000 -40000 -20000 0 20000 40000 60000
Moment(emu)
Magnetic Field (Oe)
Graph of ZnO:Mn material

20. 20
4.3.Ni powder
Fig.11 shows the magnetization of Ni powders. It is clear that the behavior is different
from the previous materials (ZnO and ZnO doped Mn).
Figure 11. : Magnetization of Ni
From the data table the magnetic susceptibility: χ =
M
B
If we take : (x , y) = (m ,B) , where: m = Magnetic Field(G) , B = Moment(emu)
When we calculate the magnetic susceptibility tow points :
First point (4.0213, 9904.58) : χ =
M
B
=
4.0213
9904.58
=0.00040600409
Second point (4.02031 , 9706. 91 ) : χ =
M
B
=
4.02031
9706.91
=0.0004141699
So we conclude from the calculation the magnetic susceptibility of the Ni powder
which is a positive and high that Ni materials is ferromagnetic materials.
-6
-4
-2
0
2
4
6
-15000 -10000 -5000 0 5000 10000 15000
Moment(emu)
Magnetic Field (G)
Graph of Ni metal

21. 21
5. Conclusion
We reported the definition of the magnetic susceptibility, the different types of magnetic
materials and theirs properties. In the second part and based on the magnetic susceptibility
experimental values, we determined the magnetic nature of different powders. It was
found that ZnO materials have a negative susceptibility and from that we concluded that
is diamagnetic materials. By adding Mn impurity to ZnO, it is transformed to
paramagnetic materials with a positive magnetic susceptibility. We showed also that Ni is
ferromagnetic with high and positive magnetic susceptibility.

22. 22
6. References:
1. Charles kittel ,introduction to solid state physics, united states of American
,2005 john
2. Book of Physics of Magnetism and Magnetic Materials
K.H.J.Buschow, F.R.de Boer , Springer; 2003 .
3. http://www.irm.umn.edu/hg2m/hg2m_b/hg2m_b.html .

23. 23
7. Appendix of Data table
Ni powder Zno powder ZnO:Mn powder
Magnetic Field(G) Moment (emu)
Magnetic Field(G) Moment (emu) Moment (emu/g) Magnetic Field (Oe)
9904.58 4.0213
5000 -0.01055
0.12228
50000.15234
9706.91 4.02031
4000 -0.0082
0.11734
47999.85547
9509.19 4.01902
3000 -0.00588
0.11251
45999.86328
9311.48 4.01768
2500 -0.00474
0.10773
43999.85547
9113.76 4.0162
2000 -0.00362
0.10295
41999.69922
8916.07 4.0148
1500 -0.00256
0.09817
39999.84375
8718.38 4.01295
1000 -0.00159
0.09338
37999.85938
8520.73 4.01113
500 -8.48E-04
0.08859
35999.83984
8323.03 4.00929
0 5.29E-04
0.08384
33999.83594
8125.26 4.00779
-500 8.23E-04
0.07905
31999.82813
7927.36 4.00605
-1000 0.00167
0.07426
29999.85938
7729.52 4.00405
-1500 0.00263
0.06948
27999.72656
7531.68 4.00215
-2000 0.00367
0.06467
25999.92383
7333.82 4.00016
-2500 0.00477
0.05989
23999.77734
7135.96 3.99762
-3000 0.00588
0.05509
21999.87109
6938.12 3.99522
-4000 0.0082
0.0503
19999.88867
6740.24 3.9928
-5000 0.01027
0.0455
17999.89648
6542.38 3.98993
-4000 0.00819
0.04069
15999.78906
6344.51 3.98705
-3000 0.00573
0.03589
13999.76855
6146.65 3.98405
-2500 0.00461
0.03108
11999.85059
5948.8 3.98093
-2000 0.00352
0.02626
9999.78027
5750.92 3.97738
-1500 0.00248
0.02506
9499.74805
5553.02 3.97318
-1000 0.00154
0.02385
8999.84082
5355.23 3.96916
-500 8.35E-04
0.02265
8499.88379

24. 24
5157.37 3.96458
0 -5.41E-04
0.02144
7999.78711
4959.5 3.95943
500 -7.96E-04
0.02023
7499.71582
4761.64 3.95386
1000 -0.00161
0.01902
6999.73389
4563.79 3.94777
1500 -0.00255
0.01781
6499.77588
4365.93 3.94061
2000 -0.00357
0.0166
5999.83105
4168.09 3.93273
2500 -0.00463
0.01538
5499.98682
3970.17 3.92342
3000 -0.00573
0.01416
4999.86572
3772.22 3.91276
4000 -0.00797
0.01296
4499.83203
3574.24 3.90039
5000 -0.01028
0.01171
3999.88745
3178.33 3.86899
3499.75342 0.01047
2980.4 3.84871
2999.8208 0.00922
2782.43 3.82363
2499.90112 0.00795
2584.49 3.79204
1999.83032 0.00666
2386.54 3.75152
1799.71631 0.00612
2188.61 3.69861
1599.82886 0.00559
1990.63 3.62836
1399.89124 0.00503
1792.62 3.53359
1199.86536 0.00445
1594.63 3.40563
999.77649 0.00385
1396.62 3.23387
799.77588 0.00322
1198.56 3.0091
599.8382 0.00258
1000.65 2.72422
399.81235 0.00185
802.663 2.374
199.83688 0.00113
604.645 1.95472
-0.20158 8.39E-05
406.639 1.46151
-200.11404 -9.35E-04
208.636 0.87878
-400.20291 -0.00183
10.6019 0.18021
-600.1532 -0.00263
-187.412 -0.57088
-800.05304 -0.00334
-385.434 -1.2149
-1000.2049 -0.00397
-583.438 -1.75974
-1200.12988 -0.00458
-781.456 -2.22482
-1399.89124 -0.00517
-979.568 -2.61456
-1599.96753 -0.00574
-1177.44 -2.93082
-1799.90527 -0.00627

25. 25
-1375.45 -3.17883
-2000.12 -0.00681
-1573.46 -3.36703
-2499.98926 -0.0081
-1771.46 -3.50626
-2999.93433 -0.00935
-1969.46 -3.60891
-3499.84155 -0.01059
-2167.45 -3.68454
-4000.22729 -0.01182
-2365.45 -3.74111
-4500.05908 -0.01305
-2563.44 -3.784
-5000.10498 -0.01427
-2761.43 -3.81743
-5499.99951 -0.01548
-2959.5 -3.8443
-6000.07031 -0.0167
-3157.44 -3.86577
-6500.09082 -0.01791
-3355.42 -3.88347
-6999.87207 -0.01912
-3553.42 -3.89838
-7500.01855 -0.02032
-3751.4 -3.91094
-8000.07666 -0.02152
-3949.42 -3.92207
-8499.97168 -0.02273
-4147.36 -3.93162
-8999.90332 -0.02393
-4345.34 -3.93974
-9499.9873 -0.02513
-4543.28 -3.94686
-9999.86914 -0.02634
-4741.22 -3.95347
-11999.81348 -0.03114
-4939.15 -3.95924
-13999.80762 -0.03595
-5137.17 -3.96452
-15999.7373 -0.04074
-5335.13 -3.96915
-17999.8457 -0.04555
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-5730.94 -3.97737
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-6126.85 -3.98475
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-6324.8 -3.98764
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-6720.69 -3.99319
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-7314.53 -4.00058
-37999.76172 -0.09339
-7512.5 -4.00274
-40000.00391 -0.09819

26. 26
-7710.38 -4.00498
-41999.94922 -0.10298
-7908.34 -4.00686
-43999.90625 -0.10773
-8106.27 -4.00874
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-8502.01 -4.0125
-50000.02734 -0.12211
-8699.85 -4.01436
-47999.98438 -0.1172
-8897.69 -4.01592
-45999.96484 -0.11243
-9095.51 -4.01753
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-9293.38 -4.01925
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-9491.2 -4.02097
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-9689.13 -4.02232
-37999.79688 -0.09324
-9886.88 -4.02401
-35999.95703 -0.08849
-9890.59 -4.02409
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-9284.29 -4.02
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-9082.27 -4.0183
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-8880.28 -4.01643
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-8678.28 -4.01492
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-8274.32 -4.01178
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-8072.24 -4.00975
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-7870.35 -4.00773
-13999.89453 -0.03588
-7668.4 -4.00557
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-8999.76563 -0.02383
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-6456.6 -3.99082
-7500.19482 -0.02022
-6254.65 -3.9878
-6999.93506 -0.01901
-6052.66 -3.98431
-6499.97705 -0.0178

27. 27
-5850.65 -3.98071
-5999.90674 -0.01658
-5648.78 -3.97723
-5499.87305 -0.01536
-5446.81 -3.97306
-5000.14258 -0.01415
-5244.84 -3.96837
-4499.88281 -0.01292
-5042.9 -3.96318
-4000.06372 -0.01169
-4840.92 -3.95761
-3499.69019 -0.01046
-4638.97 -3.95142
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-4437.01 -3.94452
-2499.86353 -0.00801
-4235.05 -3.93661
-1999.94373 -0.00665
-4033.09 -3.92747
-1799.77917 -0.00612
-3831.13 -3.91705
-1599.84155 -0.00558
-3629.08 -3.90508
-1399.75269 -0.00502
-3427.24 -3.89116
-1199.97876 -0.00445
-3225.25 -3.87431
-1000.06635 -0.00385
-3023.31 -3.85411
-799.93964 -0.00321
-2821.34 -3.82948
-600.01459 -0.00255
-2619.38 -3.79848
-400.10211 -0.00182
-2417.43 -3.75899
-200.16444 -0.00102
-2215.47 -3.7071
-0.07559 -8.04E-05
-2013.51 -3.63807
200.03845 9.46E-04
-1811.52 -3.54439
399.95093 0.00183
-1609.45 -3.41691
599.85083 0.00262
-1407.46 -3.24531
799.86407 0.00332
-1205.52 -3.01919
999.91516 0.00396
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1199.87793 0.00458
-801.498 -2.37443
1399.70227 0.00525
-599.492 -1.94603
1599.77844 0.00573
-397.482 -1.43993
1799.84204 0.0063
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1999.9563 0.00681
6.5766 -0.11491
2499.83813 0.0081
208.533 0.64586
2999.92163 0.00935
410.586 1.28967
3499.84155 0.0106

28. 28
612.585 1.83425
4000.02563 0.01183
814.711 2.29679
4499.73145 0.01306
1016.61 2.68043
4999.84033 0.01428
1218.61 2.98879
5499.79785 0.0155
1420.62 3.2274
5999.80566 0.01671
1622.61 3.4062
6499.88916 0.01792
1824.59 3.53747
6999.74609 0.01914
2026.62 3.63326
7499.729 0.02034
2228.6 3.70355
7999.76172 0.02155
2430.62 3.75629
8499.76953 0.02276
2632.62 3.79629
8999.72754 0.02397
2834.71 3.82729
9499.79883 0.02518
3036.66 3.85214
9999.89453 0.02638
3238.61 3.8726
11999.87598 0.0312
3440.62 3.8894
13999.74414 0.03603
3642.64 3.9034
15999.72461 0.04084
3844.63 3.91511
17999.82031 0.04566
4046.6 3.92564
19999.83984 0.05048
4248.58 3.93477
21999.73242 0.05529
4450.54 3.9427
23999.81445 0.06011
4652.49 3.94953
25999.73242 0.06493
4854.42 3.95588
27999.70117 0.06973
5056.42 3.9615
29999.75781 0.07454
5258.4 3.9665
31999.75391 0.07936
5460.29 3.97087
33999.84766 0.08419
5662.24 3.97494
35999.70313 0.08901
5864.17 3.9789
37999.98828 0.09382
6066.14 3.98237
39999.74219 0.09861
6268.1 3.98577
41999.89844 0.10345
6470.03 3.98874
43999.86719 0.10826
6671.99 3.99139
45999.86328 0.11306
6873.93 3.99415
47999.90625 0.11791

29. 29
7075.89 3.99692
49999.84766 0.12273
7479.83 4.00131
7681.72 4.0034
7883.66 4.00553
8085.61 4.00743
8287.56 4.00915
8489.52 4.011
8691.42 4.01317
8893.37 4.01484
9095.33 4.01646
9297.26 4.01791
9499.24 4.01942
9701.24 4.02082
9903.04 4.02223