Interação da matéria de vórtices com estruturas de defeitos em filmes de Nb

!

"#$%& '# (# )" # '

*+"

&(

"

"#

' '

&

( ,(

'

!-.

!

/ 00

&

1

23 ' 3 4

#

& 5

- 6

7 0 0

-' 3

Ficha catalográfica elaborada pelo DePT da Biblioteca Comunitária/UFSCar

K17im

Kapp, Juliana Sens Nunes.

Interação da matéria de vórtices com estruturas de defeitos em filmes de Nb / Juliana Sens Nunes Kapp. -- São Carlos : UFSCar, 2009.

121 f.

Tese (Doutorado) -- Universidade Federal de São Carlos, 2009.

1. Supercondutividade. 2. Transição de fase. 3. Diagrama de fases. 4. Defeitos colunares. 5. Dinâmica de vórtices. I. Título.

Juliana Sens Nunes Kapp

Tese de Doutorado submetida à

Coordenação do Programa de Pós-Graduaçio em Física, da Universidade Federal de São Carlos, como requisito parcial para a obtençio do titulo de Doutor em aências.

Aprovada em 30 de Março de 2009.

BANCA EXAMINADORA

!{":"

~

Universidade Federal de São Carlos

-

E//()~

~~t0

Prof. Dr. Edson Sardella

Universidade Estadual Paulista - FC (Bauru)

/~L/l~A1

Prof. Dr. Rubens de Andrade Junior Universidade Federal d"'Rio tk Janeiro -DEE

! " # $ %& '

" ( " ) * + " ,

) " ( * $ - . / .

! " . " 0 1 / 2 0 / "

! 0 ) . / .

" " " " 0 /

! " 0 / 0

) " ( # *- . " 3 4

5 6 . $

5 7, 77 8+

5 . 9 ! ! ) .

' : : , " ; 7 6< 7 %

-$ " = " $

. ! # $ ( *

- )8 :> ( * ? $

2 ( $ @ : * ( *

. : ) = # $ "

" ) 9 A ) '

. 8 . : .

: /===0

" ! .

$ # $ ) =

. - B 6 .

" 2 : , . " "

9

2 6 . " . 3

. $ 6 8

7 = 2 8" . " .

! 3 = ! 6

!

"

"

"

#

$

%

C . <

: 7 .

8 / 0 ) !

2 / 0 ) " > χD

×

χ :

( )

> " 2 !

9 " 8 7 $

$ - ) "

< " " )

$ " 8

> " 9

9 , ) "

. / 0 : $ ?

C . )

" ; 2 9 7 2

9 " × .

9 _E . 8 / 0 $

2 8 9! !F$ < "

" )

G . H I H . . J "

H . J + . H . 8

0

/ H. . " . 6. / 0 H

. ". . " J χD . J χ×

H. I

( )

. H. . " . " " 8

" + . J H . " J "

. . - J " . . ! J . "

" 8 J " . " H . .

. " . " J H "

. " " . . . J .

I I . + H . "

" J . / 0 : H . H 8 H?

. ". " J . .

: J J G . H I H

. " H . . . J . + .

. 8 / 0 J " . . 8 ! H .

. ! J " . " .

" " " .

KL

EM

K K , EM

K E 6 #2 NM

K N G #2 NN

K L + + H 7 " NL

K O , 9 NP

K Q # . I " LM

K R < ) #2 LQ

K P A I 6 4 8" ON

!

E K " ) OP

E K K " QE

E K E QN

E E QO

E N K + C 7 9 QQ

E N E + C G (6. ". @ * QR

E N N + C G (4 @ * QP

E N L + C (+ G 4 * RM

"

#

$

N K " + " ) RE

N E % . 6 8 RP

N E K A I 6 RP

N E E $ , PE

N E N $ + ! $ PO

N E N $ S " " ) PQ

N N + 7 " TK

N N K $ S " " ) TK

N N E $ 6 TL

N N N , TR

N L " U KMK

%

#

$

$

&

! " # !

$

% &$ '

'

( )

% *+$

)

% *&$ '

&

% ,*$ ! "# $

- .)

% +//&$ % $ & ' ! ! ! (

00

1 )

2 ' 3

. 4 ' 5

! ! " 2 )

& &) !

* _{" 2 && "}

6

" 7 8 9

' "

#

' " 2

&1 * +

"

" 2 1/ $ & ' &

* & :

" # 1*

.

' ;

6 % 7" 2 1

( ' : $ & ', &

< "

2 1* ! ! ! (

' " = ! ( >

' 5 5

; " ? ;

" @ ! ( > !

: '

> ; '

5 Φ =+"/*× /−1*"-+ 6 (07" A

' 6 7 ' '

. ) " B % 0

" 00 ' '

" # ' '

- $ & ', & κ

! ! ! ( 5 '

: 5

1

" C ' !

+//&" @ 00

' 5 ;

> ' ' ' % < '

; % " )/ %. ) ;

5 " D

-- '

! ! ! (

# ' %

> " = '

,E "# $ !

- > ! ;

&/ 4 ' " #

'

-!

' ; "

A

" =

'

; /. /E #F +

' E" ( % '

'

" = 5 '

E

>

: " #

'

%

'" D " )/ %. )

'

>

! "

2 ; ' '

- " )/ %. ) "

%

H ' H

" #

% 5

% ' < 5

: F ' < "

A ' ; 5

'

!

*

'

*% "

D

> " )/ %. )

5 ' :

6+ & % I0J7" D 0

+

5

" 2 5

%

-< 5 "

-" )/ %. ) % 5

! ( B ' >

> % % "

2 % !

; $

'

" @ 8 9

'

> 0 " =

; '

,

#B ; '

- 6 ' 8 9

7" 0 ' ( (

% *( " 2

(

* _{' '}

' ' ' " B

% > 5

< 5 "

@ B 5

00

5 "

D B + ' 5 5

' " #

;>

-

-" )/ %. ) " = '

5 "

@ B &

;> " B ×*

% >

" )/ %. ) !

K ' '

" # '

"

# : : 5

B ."

D

5 $

% K = 5 = B L L % I B L

M @ ( 2 ( I N

( O = ( " = $% ) 1 - )) )

2 ' ) ) ') # $ N" (" @ ?" P O #"

#" M" D B" M" Q R 2" = S M" T" J U" #" D 5 #

( ,% . +//*"

% N" (" @ ?" P O #" #" M" D B" M" Q R 2" = S M" T"

J U" #" D 5 """ &+/ 6+//,7 1 E"

% N" (" @ ?" P O #" #" M" D B" M" Q R 2" = S M" T"

J U" #" D 5 3 2 .E, 6+//,7 ,+/"

% N" (" @ %4 ?" P O B" M" Q R 2"= S #" = M" T"

J ("#" M R #" ?" L 5 U" #" D 5 , ) 1

- )) 2 - - 4 ) ) &- ) '

1.1 Estados Meissner e Misto

! " #

$% &

' '' ( '

$ #

*

+

+

$ , ! $

'

( ''

+ !

$ # #

$ , # $

- - #

+ _* ( +

( . / # $

$ # !

/ # _* $

( . ''

! "# "# $

% $ ×& ' (

# ) * + ((

,

**

0 .

. / )

# )

"0 12 #- + $

! # . &

3 3

1 1* * ₌

∇

2 % _' 3 1 1

. *

1 1

λ = # . !

# &

3 3

.

* *

λ =

∇ _*

-*

0 3

) $ 4 λ_.

+ , * 2

! #

. / 5 " 6

7 # $

) + &

.

6

6 _*

*

λ = ∇

.

λ ,

+

7 6 ) +

$

) %

*8

7 # . .

/ < = > !8 . * . 9:

> !8 9. ? ! > !8 9.

. 3 ' @ A 9 . > B *4C

#- #- > !8 9.

) .

) < = > !8 . * .

( > !8 9. # 4

.

/ 4 .

+ $ #

. *

1 1

λ = > !8 . / # /

4 ψ ψ *

+ 6 &

* =

ψ 8

! #- ψ / #

! 6 ; <

= 4 .

#-# =

> !8 9. &

* 8

*

*ψ γ ψ

β ψ α

ψ & = & + & + + ∇

*9

& % α β γ 4 .

! # > !8 9. ) / #

! # +) : = ∂ ∂ = ∂ ∂

∫

ψ ) % &

αψ ψ

ψ β

ψ + =−

−

∇ ∗

∗

* *

* D >

0 ) * # > !8 9. /

! # D $&

D 6 * ∇− + = × ∇ = ∗ ∗ ∗ ∗ ψ ψ ? D

6 ψ ψ ψ ψ ψ ψ∗ψ

∗ ∗ ∗ ∗ ∗ ∗ − ∇ − ∇ = * * @ ! - ? @

#-7 # > !8 9.

. 3 ' ) /

/ ) #

:

Φ 5 B

* * *

: = =

*>

) #

> !8 9. $

A .

) B . B

#

#- .

0 .

8' 4 , 8 ) / , 9

- 1

1 $ ! ) E & 8' 4 & E @

F+ ;

7 # 3 3 )

'' / # #- > !8 9

. # / βψ *ψ #

*?

/ $ $ #- / ψ

) ψ 2 + ) C'

+ # +

# λ_. = ξ 9 3 "

# . &

* *

*

&

ξ π

Φ

= _:

/ ( "# *: ) +

D8 B * ) + 1 ! !

1 $ 3 $ "# $

(

(

)

)

' $ $ λ $ "# . ξ $

*@ C * * . & & π λ

ξ = Φ '

+ 4 > !8 9.

& & . ξ λ κ =

# : _* =κ * '

* D

=

κ _* > ''

<

* '

D8 B * ) ) / # ''

/ # > !8 9. 3≈3 _* !

;ψ_>. * < , > ) 3 = !

4 +

. ! . D8 B *44

, > +

; * H* 1 = Iψ_>. * J ) +

*

0 + $

$ > !8 9.

) ( #- / D8 B *

6 .

$ E F ) * *8 >8

6 $ +

#-. , ?

? ' "# F D * 1

! K & L 8 4- >?

= # . .

/ ! ) , 8

; D8 B *< $ ) #

:

F D8 B * . '' $

$ <: "

$ .

1.2 Tipos de Vórtice

( . = /

<: D8 B * 0

=

& 7 . .)

$ 6

. .) ( 4

+ +

, @ 4

<: D8 B * 3

# $

0 - )

) ; <

6 "0 6 8 *> *? ! =

) % 4

6 # G= 4 .

@ D ! M3 _{* ?−δ} N #

& 6 "0 6 4/

A "# 6 "# 6 8

$ ) + )8+ O *

<: 6

*

C 6 "# 6

. , $ $

) & $

# 6 #- λ₆

" ) 6

#-, E . #

6 "# 6 . <:

6 , )

( # 6 λ₆ ,

& * D * * _     + Φ = 6

6 _{π λ}

λ

0 % <: 6

Φ ( 3

. 3 ! &

∫

∫

Φ 3 = = *λ 3 = = _*

C = = 3 γ λ π * * + Φ

= γ ) " #

# * #

* &

[

]

Φ = Φ

H % # 4

. *π 0

/ <: 6 Φ

3 / λ₆I <: D8 B *

3

1.3 Interação entre Vórtices

2 . '' #

, : C %

. # # 1 . ) . *

# ! $ "

. &

=

1 6

* =Φ 8

C ( "# * *: 4?

8

( )

6 ×Φ

= _* 9

0 . # )

#-&

'

6 ×Φ

= >

'

6 . #

. .

# +) 6 . $

D8 B *

1.4 Flux Flow, Pinning e Creep

C # . 6 $

# # > ) /

$ # #

9

" . ! 1 8 *:

8 *?

! ) # # . ! )

1 2 ! # . ! # . !

#

) . &

6× Φ

= ?

3

6×

= @

! "

* / 6 &

* 3

K= ×

! # .

>

*

.

. *

* =η ⋅ − = *: η . . *

A # /

#

'' J . ) )

/ #

" #

( /

4 =

#-. / 6 $

0 %

ξ C

. /

C " # . !

1 2

( ) +)

4 ) ' )

× ×& + $

" * 8

?

$

1 $ .

!

# * ω_: G=

+ ) # _: #

) &

B&

D :

:

−

=ω *

) )

. /

#- C # #

# $ , *

; + < 3 .

. 6

-4 "# G K

@

1.5 Modelo de Estado Crítico

E / # =

) #

0

) ) #

E +

$ &

+ 6 ( 3 4@ % 6

+ /

# 8 *?

+ 4 7 # "

+ 4 " +

,

1 3

0 D $ # #

# D $

&

76

*

= **

E / # ) /

6 ! / # ) $

&

B=

∫

∫

*

* *

A 3= + C' #

3 6

" # %

/ #

# &

6 =*⋅% D _*8

4 + %

0

, =7

K ' ) :

3 6

&

:

8:

6 _D⋅ −* _{% D}

! ) # *9 ) .

*

1.6 Vortex Shaking

! #

+ 2A )

!A ) # L )

) 8% > D* ) 9

"

ω

=

# / # #

* 1 B

3 B B ? * 1 B

+ 3 6_⊥

+ # 3

⊥

6 3 ! %

- 1 ≤2 =〈. ! ≤ D* 〈〈2 .

, 9 0 ; <

(

)

! $ & B M

8

/ < 1 B *

P J "# = ;

) ; < .

K ' ) ) # / =

+

B B 0 B

. ) "

; <

# #

+ N$ B

8*

; $ K 6 * 1 B

3 B B ? D : K !

Q α 6

! # 3 B B - #

K + 6 , >

#- &

% B & K 6 = ωDπ 66 *>

% B &

8

( )

( )

* 1 B =

; <

? 7 G $

P J 3 B B ?

L B $ =

/ # 3 &

% B & ≈ : −8: D *@

88

D

26 ω

π _⊥

= ) /

$ , >

, ? # *@ +

# # * $ )

( * 1 B #

3 B B ) /

4 ? , @

89

A 1 "# $ * * 1 B

@ .D2= ) + .D2= ) +

: D2=

8>

! * 1 B ) #

@%8

) #

#-

#-) %!A ) ) $ ) )

.

B

1.7 A Dinâmica da Matéria de Vórtices

! $ <: $ .

D8 B * # # )

. )

! # $

. # . ! 6

#

&

× '' 0

4 ×& #

6 . 6 +

)

M ) 8*

#-# % . _*−1' _{1 8}

= # $ . #

8?

# #

#

4C ' "# $ R "#

B& K

K = + D "# 9

* γ " ) 8 R +-4

! , * %

M M3 . ' % )

!= ) 8 +

( ) ) #- /

8@

4 . 9

M3 . ' "# R !

8 1 4C / B 4;C > @ B * %

R ! & E A 4; 4 F *

-! % $ =

. % !

● Sem defeitos

( . . D8 B * +

# . # )

8

● Baixa densidade/ baixa eficiência

( * . B * B *

--= ) #- 5

O %

) # 5 /

. . + . #

! % " $ .

+

44 "# R *

. B * B * S

*: . * G

= .

, ** % . ; <

9:

# + P C

#-) %

# 3 #

4 = / , *

4 K ) + )8+ ) + :

3' 4 $ *

"# H % ) + : M3 -@%

) + 8' 4

-A

% ) + : M3 /C% ) +

S * 8 8 1

9

● Alta densidade/ alta eficiência

( /4 # + .

= = #

* 19 / M # + *P

$ .

; < , *

) # +

&

ν = # * 19

&

ν

ξ_> Q & −& − _:

L ) ! #

> τ & ! > > ξ τ Q

C 4 7 K 6

I # &

(

)

! >

− ± + _{≈ε ξ}

ξ _*

±

ε #- R ) % &

# *

<

(× ; <

9*

F ) 9 * 19

4- ' * (9< 8 F /

M3 A * & T &

& U & 8 * ! E - @± C 4 ν V ?

"# E 4 - &

● Defeitos colunares

( .

. $ 3 3 9 +

/-# + *

9

! # . % +

#

< B 99 3 9 "

* 19 ) $ <: 3

+ . 3 9 &_3> !

# . 3 9

3 # . ξ⊥

DD

ξ _{2 $ " < B &}

(

)

S _{ξ ξ}

ξ⊥+ ∝ ± 6 ⊥

K !

* 19 _± #

( )

( )

# &_3> 0 3 9 < B .

) , *8

1.8 O Kink na Transição Bose9glass

E ) * 9> 9? 3 9 =

B B ) #

/

7 / 3 N ) *

3' #

98

7 , *9

) , *>

4/ D 3' H N R

0 Q AC 8

) + D # H )8+

K ) + R 8 "# *:

) 8 7 = + 4

3 N ) ) ;

. <

) &_B + B B

.

, *> - * ! , *?

99

4; . # 3' H

58 $ 3φ E / C 4C /C >

8$ H 8 * 9 B B

* W P J $

4

4? B B $ * * %& ) "

# # 9 +

3

9>

J ) ) + ;

< 3_φ .

! # + % +

, *> 3_φ % B B !

; <

> 3_φ =9:

"

7 . / . < B /@ ).

- 3 47+ #- #

. 7

) = B B #

4@ 7 R *:

. < B /@ 8 * 3 $

# R % $ 3

" #

8 1 B B &_B !

B

&

9?

! # 8 ) ) $

) # , *@ 6 6

. < B ε_: =

(

)

ε _{. . / #}

: &

(

)

, *@ ; < 3

6 3 B B &_B

! = %

3 3

3: < < &_B #

!

! %

= < B 99 # 9 _: &_:

4 )

(

)

: − D

= 9

N$ /

< B ) 99 9@

!!!" " # $ %&'& (

) * "

2

! "

3

# ) & 4

5467 # $ % & " )

8 9 !

' & : $ %&% ) 0 5467

; " #

Φ = − (

%

γ

γ γ γ( # ; ( . 3

0 # ; " )

# ) %&'" ) γ =γ +γ₍ '₎ 8 ; "

!

$ * + , # -$ # ' !

' ./

     

Φ Φ =

! !

%'₎ γ π

' _%&'

3 # ) < # " $ %&% <

# Φ 0 0 # )

!

Φ

Φ = & #

) 0 " )

# ) &

90 2 *

'

' ( " )./ # '! 1 '! ?1 & 4

# ) 8 "

&

) " #

)./ "

# 8# &

3 @# A B "

) " ) 0 &

# C

" & D $

%&-% ; @ E

E #0 E E A" ; 0 $

%&>" ) & ( ;

" &

0 ) # 1 .2 32 4.2 # + # # 5

# 6 # # 7 312 7 " # &, E

%

4 < # % 8 ; ( " # &, 8 ; ( +

80; % % " 84; # = # 8.; # 83; #

* 8>;

? # @"

@

× ) " F

" " F

%

)

@ @ & # )

8# 8

" G 8 '&

?

× " "

-A ) @ A ) @ A

8 ?₎ # ? & D

A ) " "

B @ A B 8

& 3 )

) & 90 )

# H

&

( # #

? ?

? = ₎ − _{A )} & ( ) ?

" # 8# "

# ? & 6 ) #

) # ) # A )&

3 #

/ # " ) I

∂ ∂ χ

χ = = _%&%

G @

@

>

{ }

ω = J

= 7G @ & 3 "

@

@ = _! + _!

ω

{

}

! J

φ ϖ+

=

%&-φ # K I L &

3 "

( )

! !

= _%&>

M " # " 0 I

χ χ

χ = ′+ ′′ _%&>

3 χ′ 0 L "

" χ′′ 0

% % ! ω χ′′ = #

8 & 6 " χB 0 L

" ) χ 0 L

C &

3 <3G" χ

( )

C " 0 χ′′

" " # ," # * #

" # L # # #B & #

" " L <

C # DE 31F 3 D

0 ? < @_G ?

# " I K # "

K B & G 8 B "

) 9(" ) #

# &

( B B ; )

# 0 %!!! # " )

) # 8# & P ) )

" & ( B

B 9 H 311

I # ) J C # - & # # # # * )

90 B K # M:

8 B " " ) 8 "

" & 3

& ( ) " # "

" # & 3 )

# 8 " <

& D M: #

& ( )

) # ) # K -9$)< Dual-Beam

( B K 3$ <

8 8

; # 0 & M

) & 3

3$ ) Shimadzu SPM9500 J3, pertencente ao

# L # - & # # # # ,&

! "

( 9( B 0 "

# 41: 7G< '!! "

C / 8) '!! )

- '!<2 ( " / '!<'' ( & M

9( 8 B "

" # & * / '

% H I : %

- & % ) ( # F-M

5 L 8 " " # "

8 !! & M 8 "

" & (

" )

Q

# $%& & '

D 9( *1 )

-! -! " ) @ A

8 " %!! & M

'! N

'N " # $ %& &

. # 9( # # ?@ # + # # # 01 " 01 # %

8 # E ;

3 % ) L

O H # L # - & # # # # ,"

) 9 # P # ? # $ %& & (

+

$ %& I M) 9 # P # ?

# $( '

D 9( ( # R1 " )

% % " ) )

" 8 ( # "

!! &

( 8

# $ %&Q" 9( R1& 3 #

L " # =

" ;

& 3 # L S 1

" " # )

) -!! & G !!

" ) " 0 *1"

2

> $ < 8 # % Q ; # * # # %

% # * L # % # % = # !

# (

R # 9( # # :@ # + # # # 3 " 3 # %

8 # E ;

M "

*1" '! N

' N & 3 R1 # $

Q!

) $ # ( '

( 9( # $ : $6R " '%! +!

& ( )

Dual-Beam # NOVA 200 Nanolab #

FEI) # $ %&2" # 8 "

0 " 0 # "

"

# K # &

/ Dual-Beam (FIB-MEV).

4 8 I !! "

@ A ) " # $ %&'!& P

8 ) / C !! " ) 0

Q'

1 # 9( $: # = # # 1 " R1 # %

S # * # % " # L 8 #

Q # & # K D;

M ) # )

# K -9$)< < % # T D = & <

×

! _" #

$

% "

& '

(

)

% =) ≤%( $ ! ' * *

+,

- !

( )

.

/ , %

/ , % , "

( )

×

χ $

0

1

( )

2

χ

$ ' $ 3 0

!" !#

$

0 4%

( )

)+ 4(

$

%× 4% 4, . 1

2

χ 0

( )

+5

& ' ($)* χ× &%+ , ! - , ( , )""

.$ ' '

( )

( )

& ' ($#* χ2× + , ( , )"" .

/ /

$

χ

χ

+)

& ' ($(* = _& − _0& . × /

' , )""

1' $

# ×

0& 6* 7 & 6 7 8

9 ! " # / , ,

0 * ×

:; , )""

-* 0

1' <

$

5

"

= / , 5 :; / , ) >; / , 4 /?> /

!

"##

"##

+4

, + ! '

* @ 8 !

*

$

' =,A , )"" 2"" . #

' $ 3 * B

* 9 !

& ' ($3* 4 =,A , 2"" . 5

$

$

$

%& '

"##

++

& ' ($2* 4 =,A , )"" . 5

+ $

& ' ($!* 4 =,A , )"" . 5

&%+$

$

$

%& '

"##

(

)

$

$

"##

((

+A

& ' ($6* 4 =,A , )"" . 5

7 $

# $ $ '

!

'

$

$

%& '

"##

(

+C

4) 44

.

-+ 8 + 9 %" :

-' 2; $ ! 9 ! %

9 / , A , %% =,A

- - _- $

= <

' <

' B 0

. $ 3 1

$

$ < -' 22

: -' 2;$

& ' ($;* =9' ' / =,A $

$

(α 1 2

' 3 '

(α 4 2 5

/

' 3 '

/ ' 3 '

A(

& ' ($>* =9' ' / =,A + $

& ' ($)"* =9' ' / =,A &%+$

%& '

(α 1 2

' 3 '

(α 4 2 5 /

' 3 '

/ ' 3 '

*)

%& '

(α 4 2 5 /

' 3 '

/ ' 3 '

(α 1 2

' 3 '

A%

& ' ($))* =9' ' / =,A

7 $

D 8

3 = ₍

(

)

< -' )) F ' ' = " '

(

)

% ,4 9 ! % 8 * 8

* -' )) )A

8 / , A

:; / , C >; / , %( /?> / , %% !

A ,

= # - -

-8

' ' = ₍

(

)

8 : %

%& '

(α 1 2

' $3 '

(α 4 2 5

/

' 3 '

/ ' 3 '

A"

G , ) ' ? )

' : % ' %

' $ G - - H $

0 @ ' '

5"

/ % "( '

& : %

$ $ ' 8

= $

" # .' 8 =,A $

"$!6 ± "$") &%+ "$6; ± "$")

+ "$;! ± "$")

A 7 )$"3 ± "$"(

$ % $ &'

' '

= ' _- @

- *

$ 1

A,

' )+ 4( 4) 44

* ' 3 - - ? $

- 8 0 8 1

/ , %" :; $ $

- - *

? $ '

(

)

- & $ 6 7

1 $

B 1

& ' ($)#* B 8

$

$

"##

( %& '

( %&

( %&

( %& '

A5

& ' ($)(* B

( )

$

/ , %" $

' * $

( )

$ I

$ !

/ C 0 8 $ $

1 6 7

$ $ $

' B

1 $

( )

$ ' 8 F

%&

A)

! ' $

* - -$ < ≈( '

# 3 '

$ % ( %

* 3 $ 3

' / , %5

'

$ 3 ' >;$

$ * '

%(( ;* )(( ;* D

$ 3 ' / , %5

$ $ 3

( )

$ * ?

$

$ 3 '

' $ $

A4

& ' ($)3* ' C '

4 5 C ' 1'B

+ $

D

( )

* $ 3 5( )(( ;* 8 JH J JH

# < '

' =± )( K

) $ % * # $ $#

# 3 - - 8 0 -'

' 6 1 7

+ 9 %" # / % "+ % "A 9 ! % $

-χ

%&

#0

' $

$

%&

%& %&

%&

A+

0 $ $ 6 7

# 0$ ' B θ

/ , %)

$

3 0 $

6 74)

# 3 _⊥

/ , %4 & :;@ , %+

>; , %A & /?> =,A #

8 D - . '

' ! ' J JH - - '

' 3

& ' ($)2* E / F ' B θ

' ' _{⊥ EE}

AA

& ' ($)!* B

' _⊥ =,A

& ' ($)6* B

' _⊥ + =,A

AC

& ' ($);* B

' _⊥ &%+ =,A

1 _⊥

θ 0 $ B θ * θ L

C(M $ 1 ' _EE * _EE

6 ' 7 * $

/ , %4 , %+ , %A $

N _- ' $

'

-B 1 3

# & θ $

6 7 θ #

$

⊥⊥⊥⊥

((θ 0

((θ 0

((θ 0

((θ 0

((θ 0

"##

*)

C(

1 $

⊥

×

&

" # .' 8 θ =,A

θ 8 + 8&%+ 8

" "$;! ± "$") "$6; ± "$") "$!6 ± "$") )2 "$;6 ± "$") "$6; ± "$"# "$!; ± "$"2 #! "$;6 ± "$"3 "$;6 ± "$"# "$!6 ± "$"! 32 "$>) ± "$"3 "$;; ± "$"( "$6) ± "$)" !" "$>) ± "$"( )$() ± "$)" )$(" ± "$("

& ' ($)>* G ' F ' θ ( $

: 8 3

(

)

( %− E

= ' ' $

0 8 # : "

, ) B 9

)

*)

/

C%

B

-$ ' 8 θ

/ , %C 3

θ θ O $

0 @ ' '

5"

$ * : %

: " $ = $ B θ

$

+

$ % * # $ $#

#

× / , "(

$ % %A % ") 9 ! % $ G$

0 / 44 & - $

< * ± # - 3 4+=

' 6 ! 7

$ $

' !

&

⊥ / , "% & :;@ / , "" & >; / , ", &

C"

& ' ($#"* : × &%+ , 2$2

( =

θ C B 8 / ' & $

& ' ($#)* & & '

' _⊥ F '

, 2 $

$ $

$ $

!

!

'

0 0 0 0 0

"/

6

'&

'

C,

& ' ($##* & & '

' _⊥ F '

+ , ! $

& ' ($#(* & & '

' _⊥ F '

&%+ , ! $

C5

. ' $

' '

- - _- : / , "% , ", *

' _⊥ L(""" * $ '

'

θ L 4(M ' $

×

⊥ $ $ θ

& $ $

0 $ B '

* * $

& 1 * θ

? $ / , %4 , %+ , %A

- × $ * $

'

$ % $

:

3 ' = ' <

- θ =( ? * * &

-C)

* # & × :;

/ , "5@ >; & / , ")@ /?> & / , "4

# &

1

: . # 1 3

6 7 1

0

& ' ($#3* & × , 2 ! 6 $

"/

6

'&

C4

& ' ($#2* & × + , ! 6$6 ;$( $

& ' ($#!* & × &%+ , ! 6$( 6$6 $

)

' '

"/

6

'&

'

*)

' '

"/

6

'&

C+

' $ _- '

8 $

@ * $

' $

θ ' .

-$ * 6 7

& × 3

$ &

# / , "+

A ,

= # / , "A

! B

D 1

B

. $

* * 0 < /

, "A$

/ , "A ' = E ₍ = E _- $

-- -- 9

CA

/?> _- =A%) ! . =% =

-, "A ₍ 8 '

(

)

( %− E

= $ B

& ' ($#6* : 8

× =,A * 4 5 4C5 &%+ 4 5 +

4 5 7 $

$ %

7 *) & )

8 +#,-"."/0

CC

& ' ($#;* : 8

. '. = E ₍ = E _- =,A H = _- =%

- $

/ , "A $

' /?> ' C

0 9

$ *

:; ! 6 ! 7

6 7 $ /?> D

/ , "A $ & N& C N& N&

! #

%& '

2

.

2

% 7 *) & ) 8 +#"-."/0

%((

! * $

$ 0 3 1

$

* ' = E

-/ , "C . =(A, $

- * $ ? )

1 # / , "C

& * = E ₍

$ & N& C N& N& 8 / , "A

& ' ($#>* & & ' '.

(

E

= ' C =(A,$

"/

2

%(% D       -( '

)

,

#

- .

#

P $ '

3 = ₍

(

)

*

(

)

2

E

' −

= - !

$ 8 ' .

! $ $

!

/ , ,( :;@ / , ,% & /?>@ /

, ," >; _{E -×}τ

(

)

-E

(

=

τ

θ O $ = E ₍ = E _-H _{( (}

B 8 $ 0

< '

. <

%("

& ' ($("* I ' /

θH =% = _-$

& ' ($()* I ' /

&%+ θH =% = _-$

$ $

.

*)

τ 2/

.

0

0 0 0 0

.

τ 2/

.

0

0

0

0

%(,

& ' ($(#* I ' /

+ θH =% = _-$

P / , ,, :;@ / , ,5 & /?>@

/ , ,) >; _⊥× " '

(

)

θ :

' $

8 -'

$

$

_.

)

0

0

0

0

0

τ 2/

%(5

& ' ($((* I ' / θ

' / '. '

H =% = _-$

& ' ($(3* I ' / θ

' / '. '

&%+H =% = _-$

$

%

1

2

$

.

⊥⊥⊥⊥

0 0 0 0 0

$

.

0 0 0 0 0

%

1

2

⊥⊥⊥⊥

%()

& ' ($(2* I ' / θ

' / '. '

+ H =% = _-$

*

/ , "A = E _- = E ₍$#

/ , ,4

, ,+

$

.

⊥⊥⊥⊥

)

0 0 0 0 0

%(4

& ' ($(!* I ' /

( =

θ H =% = _-$

& ' ($(6* I ' /

'. ' θ =( H =% = _-$

.

.

τ

7 +#"-."/0 %

& ) 8 *)

$

$

.

7 +#"-."/0 %

& ) 8 *)

%(+

/ , ,4 , ,+

$ '

$ 1

! "

# $

% ! &' ( )

* + & ', #

+ - &. / 0 !

1 23456% - &78

! "# $ % &

' & !

9 ! :

; ( ) *+

. /

1 23456% - &&7

%

! ! < ,

$ #

" # _-."/

= < . . " "_. !

#

%

2 # _-."/ " "_.

" : 2 ( *

# >

? / $

. ( * / @

. . ! <

5 #

# ) "

; + - &. / ) ) . /

40 ! ; "

, 0

. < /

0 !

+ - &. /

% 1 +@=

+ ' &7

1 23456% - &&&

40 ? %

=0 :

, A " ! "

)

# ;

! "

! ?

" > "#B 1 B #B 2

C 4 & D'

! ? # _-."/

E

2 3 -' + & '7

%

4 ' 87

θ> $

9 ! !

< # _-."/ #

"

#× 5

: 1 # :

! # _-."/ "_. "

% 3

1 23456% - &&'

! # _-."/ " 3 9

! <

) 2 ( ) *+

$

3 1 "

) <

5 1 # "_.

: ! # _-."/ "_. " ?

(

)

# = ₇ &− F ₇

, * . ,, :

(

)

'

F" " "

# = − * . ,D

G-$

: ! # _-."/

2 " ?

: :

" #

1 23456% - &&H

I ! $ ( ) *+

5

)

5

<) 5

6 ( 7

- " # 8 3 6 9 : 9 3 7 6 9 & 0

, ; 9

! " ! # $%%&'

$ ($ !

" ! # $%%&'

( !

" ! # $%%&'

) &( !

" ! # $%%&'

* $%% !

" ! # $%%&'

+ , - . ! / 0 1 2 3 . $& &('

( 4 5 , 4!! 6 / 7 3 4 8 9

*

& 7 : ; " . , 1 8 < / = ! 8 6 8 > 4# ! &

$%% ' )( *

3 : 6 ? 8 9 6 9 > / , 8 . !

& $%% ' $+ & $+$

% < ! @ : (

$%% ' )$( )$

7 ; 8 / : " . @ 7 5 1 4 ; # +&

$%% ' %+)* &

$ . . 6 A 4 . < 8 # " 8 5 > B # " 8 8

< - - # 9 9 / " # 6 2 8 = 2 C 2 # 3 3 !

% $%% ' %&(%%)

1 8 # 5 D E # $ ' (&(

) 9 / : 4 - 5 / 9 C 2 ! " #

*

* - , # # : , # , # ' ( *' 4 )

+ . # " , F " E D C 8 D

?! E . # !$%% % ! %# % ! " ! #

+

( 0 , ; # , 7 , # & ' ! ( ) *$% *%' %+)

& / 6 # , 9 # / 5 . EE %& *(' (*

, 9 %) *+' &

$% , ; 2 " + ( * ' +)

$ 7 5 3 / 3 ! ! ? E

6 # # &

$$ 4 4 4 2 " + ( * *(' * (

$ 1 : = , 8 5 # . : 4 +)' 4 $$+

$) F > ! # : 3 G $) 4 +(' *$+

$* / . ,- . /0 1 # # #

! # 3 _$ 2₍−δ 7 HI 8 # !

-J ' K 9 # 9 L >M # 3 F " # # - # # .I

9 .I 9 $%%*

$+ 6 7 / +$' $*

$( 8 3 2 ! ! . # ># 7 "

(

$& 9 6 45 +)'

$ !$%% ' ! %! %6 ' 7 ! ! " ! #

$%%&'

% > . EE 5 " < < 4 . " "!! N &$ (' ))

> : 6 # # 8 0 ? # ! )& ' $&

$ 6 D 8 4 4 5 8 5 6 3 : ; 5 :

: !! # # 4 = 2 "!! * &(' &*$

< < 8 1 8 > E 4 8 ! EE / : 3 C C /

8 - : # ; 0 9 # 2 ) )' &%$

) 8 1 ! 9 5 / : E : = # 4 > > 1 2

*& &' 5* )%

* 8 1 ! 4 . : = 9 5 / : E F 1 1 = =C 2

5 / D ; 1 9 & &' )$ +

+ 4" ! 6 = 2 " < 8 # " 8 5 : . 2! 7 >

- #! 3 3 ! : = 8 , 8 = 2 C 2 = " # 6 2 > B # "

) $%% ' )*

&

& > : 6 # # ; 8 2 2 ! ( $% $%%(' .

7 . : 4 = " ## 6 < . 6 5 4 , # 6

6 " 2 ? . # 3 3 ! (( $%%&' $ )*$$

)% 7 . : 4 = " ## 4 , # 6 5 6 < . ?

. 3 3 ! # 6 6 " 2 (( $%%&' % )*%&

) 6 ! < 6 # ; 7 # 4 = 2 ( / 8

= C 4 # ! . 9 8 ! # . K 0 ) &

#

)$ < < 4 8 ! EE 4 . " +& +'

) < 5 # 4 . " # < < +* $%%$' %%*%

)) ? , 2 < D" 2 " ( #! ) ( ' )%

)* 7 5 : . . & ' *

)+ 3 = ? / ! # . 6 # / 8 5 9 3 ; ! # ,

7 ) $%% ' )%*

)& . # " 9 4 ,

!$%% ! %) % # % 97 1! !

" ! # $%%&'

) ? # . #

!$%% ! !# % 8 :%; ! <=>? ? %"8 =9# % % ( !

9 % # >:@ ! " ! # $%%&'

*% . # " 9 4 ,

!$%% ! %) % # % 1! !

" ! # $%%&'

* ; 1 9 F 1 B , @ / . / 0 = 0 2 0 " . 7

6 # / , : 9 2 # / 8 @ &( $%% ' )

*$ 7 . - ) ' %

* 5 : = + & ' * N 5 : =

+) %' $*&+

*) . ; , " 2 # . . ) )' $ &

** 7 5 0 8 0 2 +& $' $ &

*+ 3 = 9 8 . 6 # / 8 9 6 5 6 9 /

$%

*( 4 4 8 D " 4 . ! : . 1 9 # 1 4 D

)+& $%%&' (*

*& 4 0 , # 0 8 0 2 $ $%%)' %+(%%&

* !$%% ! ! ! + %A " % % ? # !

" ! # $%%&'

+% 4 4 8 D " , - 4 # 1 4 D $% $%%&'

>* % >* $

+ , = > ! ($ )' )

+$ 4 0 . ! " # 8 = 2 C 2 N (* *' &+

+ , = > ! N (* *' &(

+) / = E # # 0 8 0 2 N ) $%%*' %((%%*

+* / . 5 B # 4 4 8 D " 9 8 , 2 > O 8

; 6 ! 1 4 D $% $%%&' * +

++ / . 5 B # 4 4 8 D " 9 8 , 2 > O 8

$

+( / . = 5 B # 9 8 , 2 > O 4 8 ;

6 ! . 4 8 2 " 4 5 0 # 1 4 D / 8 # # 7

# 7 ! ! HI

+& / . = 5 B # 9 8 , 2 > O 4 8 ;

6 ! . 4 8 2 " 4 5 0 # 1 4 D 2 + 8

# # # 7 # ! HI

+ > B # " / 5 9 ! 8 8 > E # 8 7 " ) )' &%$

(% !$%% ? #% %! %#!# !! %:>:@+B=> ! !