537.226.

2014 .. , .. , .. , ..

07.04.2014
() . , , , P (T) .
: , , , .
1.
, , P, , Ps E. (E, ) Ps(E, ) (), . . , - [1, 2]. Ps, , .
(E << E) [3-5], (E > E). , -
, - , . E-mail: a.milinskiy@mail.ru
, - , . E-mail: shack4@mail.ru
, . E-mail: piligrim.a3@gmail.com
, - , . E-mail: svbar2003@list.ru
, , .. - , . : - - 8; - 3; -8(2)2; - 23. , , .
2.

= 0 + ( + + 3 + %5 5 +...), (1)
- , 1 , 3 5 - , .
-, -, , [6]
=^ + - 2+- 4+- 6+,
2 4 6 (2)
= ( - X
- , - , , , [ . (gradP)2 , . (2) , [ > 0 > 0 , [ < 0 > 0 - .
. , << , . (2), -
= [ + 2 + 4]. (3)
, -- X, (3) :
= X =
1

X =

(4)
X = = + 2 + 54

X = ~= =
1
+ 32 + 54
(5)
_

= -3[6(, + ) + 20( , + )3]. (7)
. ,
= sin( 2 )-

(9)
5 - , . = ^( , (9) (8)
2 2 1
I = -[^- (2?)6 X3 + 6 4 -(^() - ^() + 2
1
+ ^-^- 20 8(20 + -^60/ E 4 - (^() - +
+ -^60, -(2(2) - sin(4f)) + 4
2 1
+ 8 -2- 200~16- (2 ^() - 3 ^(3) + ^(5))]. 8
, (2 , 3, 4, ...),

.
2 =-2[5-^ ^^ + 10/) + 155-^}],(10)
3 15 5
= 3408(3/){ + 10/} + S-^y6 8(3/),(11)
2
4
1 = 155-4-,X^(4) , (12)
, (4),
5 5 15 = ~ IX 6^ ^5^). 2
(13)
= -X 3(6 + 203)
(5) (2),
- + X, (6)
5 - . (6), (5)
. , [5]
() ,
1 =-- = -+ 2(0--, (8)
v '
= ( = 0). -
. , , (6) , .. 0. .
, , , , , . /^) , , = 2 ] ( = 1, 2, 3.). - [7]
1() = - + X 1 ^^ -) , (14)
2 =1
/ - , /- - .
Jo =
11(), 1 2 + 2, tg:


(15)
= -11 (),(), = 1)$().
,
7
I = 12 + 2 =
\
2 7

. (, I -
V 2
, (16)
./ - , , .
(16), / , , ( > ) , /2, (16) , .
3.
10 20. 2000 /. , , , -
24- 2 230 ^. 2 , . [8]. 1- . , . 1 /. 0.2 .
. . ( = 322 ) 8 2/. 2 ( ). 2- . 8 100 . 8 22 84, -... - [9].
.1 8 -
2,5

3 !'5
0,5
0
- 1,6 " 1,4 " 1,2 - 1
3
- 0,8 - 0,6
- 0,4
- 0,2 0
290 295 300 305 310 315 320 325 330
()
. 1. 8 : << (), (), > () () [9] ()
3
2
1
293 333 . , , () , .
[3] 3 -
=-4( - 1822). (17)
-, , 3 = 8 3%0 3 = -^40 . (17) , .
, 8 ( << E ) Ps , ( 320321 ) = 322 (.1). (17). , . 3 , , 322 (. 1).
> , 3 . 3 , , .
. 3 , [10]. . 393 . 3. = 393 , 278 3 ,
4. 393 , 18 / 2 26 /2 . 278 , . -343 -363 . [10].
. 2 3
3
= .
\{ - ) 2
(18)
- , - , .
, (18) 3, . , , ,
. 8(2)2 [11]. = 7,65 , = 8,53 , = 5,52 ( V). 202 180 ( IV). 180 176 ( III) = 2,5-10-9 /2. 176 169 ( II) 169 ( I) , = 3-10-6 /2 [11].
, . 3 - () .3. . 180 176 , -
0,35
0,3
0,25
0,2

3
0,15
0,1 -
0,05
ї


',
^



300 320 340 360
()
380
400
. 2. 3 3 () (18) ()
4 3,5 3 2,5 2 1,5 1
0,5
80
0,043 0,038 0,033 0,028
3
- 0,023 ^ 0,018 0,013 0,008
....."
hi
0,003
100
120
140 160 ()
180
200
220
. 3. 8(2)2 () () [11] ()
III. , I, I. , , - SC(NH2)2.
.
(PbZrO3) , [12] . PbZrO3 , 503 .
0
0
, - 1,6-105 463 . 23 , 503 , . , - , -. [13-15] , 503 10-25 . 23. .
. 4 , . () , 503-489 , -
. 503-489 , , [13-15]. , , 3 .

. , , 300 /, 3 470-475 . , , . . 4 () - .
5.
, , , , . () P -
3
0,06
0,05
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0,01
440
60 -50 -40 -30 -20 -10 -0
460
480 ()
500
520
. 4. 3 203 100 / (1), 200 / (2) 400 / (3). 100
0
. - PbZrO3 , , - . .
- ( 2014/424).

1. Wei X., Yao X. Reversible dielectric nonlinearity and mechanism of electrical tunability for ferroelectric ceramics // Int. J. Mod. Phys. B. 2006. V20. . 2977-2998.
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4. Non-Linear Dielectric Response of Ferroelectrics, Relaxors and Dipolar Glasses / S. Miga, J. Dec, W. Kleemann // Ferroelectrics. Characterization and
Modeling. 2011. V.53. . 181-202.
5. - / .. , .. , .. , .. // . 1999. .70. . 9. . 625-631.
6. .. - ( ) // . -2001. .171. 10. . 1091-1097.
7. .. . . .: , 2002. 638 .
8. KNO3 -41 / .. , .. , .. , .. // , 2013. .55. 12. .2439-2442.
9. ., . [ .. ]. .: , 1965. 555 .
10. / .. , .. , .. , .. , .. , .. . .: , 1971. 476 .
11. G. J. Goldsmith and J. G. White. // J. Chem. Phys. 31, 1175 (1959).
12. Antiferroelectric structure of lead zirconate / E. Sawaguchi, H. Maniva, S. Hoshino // Phys. Rev. 1951. V.83. P. 1078.
13. Tennery V.J. High-temperature phase transition in PbZrO3 // Journ. Amer. Ceram. Soc. 1966. V.49. P. 483-486.
14. . // . 1966. .8. . 2469-2477.
15. Scott B.A., Burns G. Crystal growth and observation of the ferroelectric phase of PbZrO3 // Journ. Amer. Ceram. Soc. 1972. V.55. P. 331-333.
THE METHOD OF NONLINEAR DIELECTRIC SPECTROSCOPY FOR THE STUDY OF FERROELECTRICS IN STRONG FIELDS
2014 A.Yu. Milinskiy, Yu.A. Shatskaya, A.A. Antonov, S.V. Baryshnikov
Blagoveshchensk State Pedagogical University
In this paper the theory of the nonlinear dielectric spectroscopy method in weak and strong fields is considered. It is theoretically and experimentally shown, that in case when fields are more coercive, the nonlinear dielectric spectroscopy method allows to obtain the dependence Ps(T) for ferroelectrics of the first and second order transition.
Keywords: nonlinear dielectric spectroscopy, ferroelectric, phase transition, spontaneous polarization, harmonic distortion
Alexei Milinskiy, Candidate of Physics and Mathematics, Associate Professor at the Physics Department. E-mail: a.milinskiy@mail.ru
Julia Shatskaya, Candidate of Physics and Mathematics, Associate Professor at the Computer Science Department. E-mail: shack4@mail.ru
Anton Antonov, Graduate Student at the Physics Department. E-mail: piligrim.a3@gmail.com
Sergey Baryshnikov, Doctor of Physical and Mathematical Sciences, Professor at the Physics Department. E-mail: svbar2003@list.ru