Comparison of non-linear optical susceptibilities of KNbO3 and LiNbO3

PII: SOO22-36!37(97)00020-6

Pergamon

COMPARISON

J. Phy. Chem So/ids Vol 58. No. 9. pp. 1399-1402. 1997 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0022-3697i97 117.00 + 0.00

0

OF NON-LINEAR OPTICAL SUSCEPTIBILITIES KNb03 AND LiNb03 DONGFENG

XUE

OF

and SIYUAN ZHANG*

Laboratory of Rare Earth Chemistry and Physics, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022, Jilin, Peoples Republic of China (Received 26 November 1996; accepted 6 January 1997)

Abstract-From the chemical bond viewpoint, second-order non-linear optical (NLO) tensor coefficients of KNb03 and LiNbOs crystals have been calculated. By using the bond-valence theory of complex crystals and the modified bond-charge model, we were able to determine contributions of each type of constituent chemical bond to the total second-order NLO susceptibility. The tensor values thus calculated are in good agreement with experimental data. From the comparison of NLO tensor coefficients of these two crystals, we found that the major NLO contributors are KO rzgroups and Li06 octahedra, not the distorted Nb06 octahedra. The difference between their NLO properties arises from their different structural characters, and the high coordination number of constituent elements in KNbO, makes its valence electrons become more delocalised compared with those of LiNbOJ. 0 1997 Elsevier Science Ltd. All rights reserved Keywork A. inorganic compounds, A. optical materials, D. dielectric properties, D. optical properties

1. INTRODUCTION

finally would lead to different

Potassium niobate (KNbOs) is a perovskite ferroelectric with the simplest electrics.

structure of oxygen octahedra

It is a promising

non-linear

material because of its high NLO coefficients; at the same time, its elastic, electro-optic, acoustic and acoustooptic properties

of the con-

In this paper, from the chemical bond viewpoint we calculate the linear as well as non-linear optical properties and chemical bond parameters of each type of constituent chemical bond in the two crystals, KNb03 and LiNbOs, by using the bond-valence theory of complex crystals [7] and the modified bond-charge model [8]. By comparison of their chemical bond properties, we can reveal the origin of the difference in their NLO properties.

ferro-

(NLO)

optical

properties

stituent chemical bonds in the two crystals.

have made this crystal one of the most

widely studied [ 1, 21. Lithium niobate (LiNb03) is used extensively in integrated and electro-optics; being one of the most popular NLO materials, it has also been investigated thoroughly with respect to its NLO properties and

2. THEORY

applications. It is interesting that both crystals with Nb06 octahedra in their structures have large NLO coefficients, and at room temperature orthorhombic coefficients efficiency

KNb03

single crystals

phase have higher phase-matchable and second

harmonic

than those of LiNb03

that consideration

generation

Chemical bond non-linearities have been evaluated on the basis of linear results by means of the bond-charge model of Levine [9]. The corresponding macroscopic property is the SHG coefficient dijk and the complete expression for the total non-linear susceptibility, diik, is written as

with NLO (SHG)

[3-61. It is obvious

of Nb06 octahedra alone cannot give

dvk.= Ed,:, P

a reasonable explanation for the large difference, and K0i2 groups and LiOs octahedra should be taken into

In known inorganic NLO crystals, KNbO3 and LiNbOj including

only two groups, KO rz and Nb06 groups in KNb03 and Li06 and NbO6 groups in LiNb03. Starting from their crystal structures,

F”d$(C) =

we find that all constituent elements

have their own coordination environments,

(1)

where d& is the total macroscopic non-linear contribution of constituent chemical bonds of type p. F” is the fraction of bonds of type ~1composing the crystal, d&(C) is the ionic fraction of the non-linear optical coefficient, and d&(Eh) is the covalent fraction,

account. However, to date, there has been no work offering a quantitative explanation for this difference. are the members with the simplest constituents

= z Fp~;k(C)+d;k(E,,)] P

and this

G$N~(14.4)bp exp( -k:$)

[(Zi)’ +“(z:)*]

(x~)‘CP

(Es)2V’)2q” (2)

*To whom all correspondence should he addressed. I399

D.XUE and% ZHANG

1400

CP = 14.4V exp( - kt.4) [(l/n).(Zi)*/$

-~(Z~)*/$]

(n< 1)

(8)

(3) where qk is the geometrical contribution of the bonds of type cc,which can simply be calculated from

in which the sum on X is over all n: bonds of type /1 in the unit cell, and $(A) is the direction cosine with respect to the ith coordinate axis of the Xth bond of type fl in this cell. N: is the number of bonds of type p per cubic centimetre. Levine found @’= p(Nc)p, and that the actual value for index p depends on the given crystal structure [9]. In our calculation of NLO crystals, it is found that the value of bP decreases with increasing value of NC. In crystals with H-O bonds, the coordination number of the H atom is always less than three, so the the average coordination number NC is less than three, and the value for p is three [IO]. In KNbOs the much higher coordination number of the K+ cation leads to a relatively higher coordination number of the oxygen, which makes KNbOs different from other NLO materials including LiNbOS. In NLO complex crystals the common expression for b” is that P = /3(Nc)2 when 3.0 < NC < 5.33, V = p(N~)‘.82s when NC = 6, and b” = /3(N[)‘.2 when NC > 7.67. /3 can be deduced from the index of refraction for the crystal: here for KNb03, Ra = 2.2576 [ 111,and for LiNb03, no = 2.23 [12], at 1.064 pm. N; = N&l( 1 + n) + n-N&/( I+ n)

(5)

In eqn (2) exp( - e.4) is the Thomas-Fermi screening factor, (2:)’ and (g)’ are the effective valence electrons of A and B ions, respectively [7]. n is the ratio of the number of atoms of element B to that of element A in the subformula, and $ is the susceptibility of a single bond of type ~1.If a crystal is composed of different types of chemical bonds (labelled a) then the total x can be resolved into contributions x” from the various types of bond ,=(~~-1)/4r=~F~x’=~N~XI: P

P

(6)

in which x” = (4~) - ’ 4,%~/E~)2is the total macroscopic susceptibility of a crystal composed entirely of bonds of type p (including local-field effects), and DPis the plasma frequency. C” and Ei are the heteropolar and homopolar parts of the average energy gap between the bonding and the antibonding states, respectively, and (Q2 = (E;)2 + (r?Y2. r? = 14.4P exp( -e$) (n-= 1)

[(Zi)‘/{

- (ZL)*/4] (7)

E”h = 39 . 74/(dp)2.48

(9)

4 = 612 is the average radius of elements A and B in A, and the core radius is P$= 0.35$. The fractional covalency fl of the individual bonds is calculated from fc” = (E;)2/(E;)2. The difference in the atomic sizes is given by pP = (6 - $)/(4 + 4;). where { and 4 are the covalent radii of atoms A and B, their values being taken from ]131. In eqns (2) and (3), q” is the bond charge of the pth bond [8, 101 ~=(n:)*[ll(x~+l)+K~]e

(10)

K is a function of the average covalency F, of all kinds of

bonds in a complex crystal and of the coordination number N,,, of its central cation. We can determine its value by using the following equation [8]: K= (2Fc - 1.1)/N,,

(11)

where F, is defined as

From the viewpoint of chemical bonds, complex (or multibond) crystals can be decomposed into a sum of constituent subformulae [7]. When the detailed crystal structure is known, the subformula of any kind of chemical bond A-B in the complex crystal AoBbDdGg.. . (crystal molecular formula) can be written as follows [N(B - A).a/Ncn] .A [N(A - ~).b/~cs] .B

(13)

in which A,B,D,G,. . . are different chemical elements or different symmetry positions of the same element in the crystal formula, and n,b,d,g,. . . are numbers of the corresponding element, N(I - J) is the coordination number of I ion by J ion, and Nc&ca,. . . are the nearest-neighbour coordination numbers of each element in the crystal. Once the subformula equation of a complex crystal is determined, the chemical bond parameters of bonds of type p in eqns (2) and (3) can be calculated by using the bond-valence theory of complex crystals [7], and then these calculated parameters can be used to evaluate the NLO tensor coefficient dvk of the crystal.

3. RESULTS AND DISCUSSION

At room temperature, KNbOs crystallises in the space group Bmm2 (point group mm2), with cell dimensions a = 5.697 A, b= 3.971 Aandc =5.722 A [14];LiNbOJ is rhombohedral with space group R3c (point group 3m), its

Comparison of non-linear optical susceptibilities of KNbOj and LiNbOJ

1401

cell constants being a = 5.14829 w and c = 13.8631 A

octahedra,

1151. Both crystals have the distorted Nb06 octahedral

acters of these constituent groups, i.e. geometrical

structure. The restrictions

and coordination environment. In KNbOj, oxygen atoms are linked with four potassium atoms and two niobium

imposed by the crystal sym-

metry and the Kleinman symmetry conditions [ 161 on NLO tensor coefficients result in both crystals having the three tensor coefficients djl, dj2 and dj3, and, for LiNb03, d3, = d32. According valence

which is due to the different structural char-

atoms, niobium atoms compared with potassium atoms have relatively more valence electrons, a lower coordination number and a stronger ability to offer these valence

to their crystal structure data, the bond-

equation

(subformula

equation)

for the two

KNb03 = 1/12KO(l),

electrons,

Thus Nb-0

+ 1/12KO(l’)r

have

less linear

+ 1/6KO(l”),

two niobium

+ 1/3Nb0(2) + 113Nb0(2’)

In LiNbO,,

(14)

atoms,

(15) lead to different

of valence electrons in each kind of consti-

atoms

Therefore,

lower value of fractional

LiNb03 = l/2LiO(1)3,2 + 1/2LiO(s),,, + 1/2NbO(1)s,2 + 1/2NbO(s)s,2

niobium

compared

with

lithium atoms have relatively more valence electrons, the same coordination number and a stronger ability to offer these electrons.

environments

contribution.

oxygen atoms are linked with two lithium atoms and

+ l/3KO(2)2 + 1/3K0(2’)r + 1/3NbO( 1)

The different coordination

bonds have the lower value of

fractional covalency f/ compared with K-O bonds and therefore

crystals is written as

distributions

factor

Nb-0

bonds have a

covalency f,” and can have

closer linear contributions when the same coordination environment is under consideration. The structural change in KNbO, makes K-O bonds the major contributor to the total linearity, surpassing the contribution

of

tuent chemical bond. For KNbOj, in K-O bonds, Zi = 1

Nb-0

and & = 1.5; in Nb-0

small, which finally lead to smaller d3, and dj2 compared

bonds, Z&, = 5 and G = 15. On

bonds in value. The values of G[;, and Gg3 are quite

the other hand, for LiNb03, in Li-0 bonds, Zti = 1 and & = 2.0; in Nb-0 bonds, Zzb = 5 and & = 10. From the

with djj. The signs of Gt are opposite in KOt2 groups or

refractive indices of KNb03 and LiNb03, we can calcu-

cancellation

late the detailed

values of GE lead to a strong cancellation, and this is KNbozis smaller than that of the reason why the value of dj3

bond parameters,

linearity

and non-

linearity of individual bonds, which are listed in Table 1 and Table 2. The final calculated NLO tensor coefficients of the two crystals are listed in Table 3. The discrepancy

Li06 octahedra

dLiNbO, 33

and in NbOh octahedra,

among

ds values;

,

the amount of electronic delocalisation

calculated

obviously

mental data; therefore,

with the experi-

these reasonable

reveal the origin of the difference

parameters

between

can

these two

NLO materials. From Tables 1 and 2 we can see the NLO behaviour in

absolute

The calculated results also show there is an increase in

results from the dispersion of its three principal of dy refractive indices, and it can be seen from Table 3 that the results agree satisfactorily

leading to a

the similar

value of the fractional KNb03

lower

covalency

in KNbO,. The

f,” in KNbOj

than that in LiNb03,

that the valance

electrons

weakly than those in LiNb03.

is

we find in

are bonded

This agrees

more

with the

conclusions obtained from the optical spectroscopy

[ 171.

KNbOj and LiNbOj is dominated by the distorted KOlr

In conclusion, the difference between the NLO properties of KNb03 and LiNbO,, both of which have NbOh

groups

octahedra in their crystal structures, is a consequence

and Lion

octahedra,

not the distorted

NbOh

of

Table I. Chemical bond parameters, linear and non-linear properties of each type of bonds in KNbOl and their contributions to the total linearity and non-linearity K-0(1’)

K-0( I) d” (A, EE (ev) CP (eV) R 4%X1 x;h q’le GP 31 d:,t d?’ GF $, d” 17

2.8671 2.9929 3.1767 0.4703 4.975 1 1.4231 0.0579 0.0000 0.0000 0.0000 -1.0000 187.6603

2.8829 2.8764 3.0633 0.4686 5.1197 1.4644 0.0566 0.0000 0.0000 0.0000

0.0000

1.0000 - 199.0666

tdr (10-9esu). $l’he value approaches 0.

K-0( 1”)

K-0(2)

2.8486 2.963 1 3.1473 0.4699 5.0112 1.4334 0.0576 0.0080 -3.0619 0.0000 0.0000 --oYk

2.7923 3.1135 3.2917 0.4722 4.8363 1.3834 0.0592 -0.1276 90.4087 -0.2403 170.2315 -0.1074 76.0973

K-0(2’)

Nb-O( I)

2.8734 2.9001 3.0863 0.4689 5.0895 1.4558 0.0568 0.1269 -99.8365 0.2547 -200.377 1 0.1520 - 119.5297

1.9891 7.2204 27.7035 0.0636 2.2473 0.6428 I .0322 0.0000 0.0000 0.0602 0.1025 0.0002 0.0004

Nb-O(2) 2.1798 5.7538 2 1.8875 0.0646 2.7498 0.7866 0.8947 0.3296 0.8765 O.OOOiI 0.0000 0.4 185 I.1131

Nb-O(2’) 1.8645 8.4768 32.595 1 0.0633 I .9635 0.5616 1.1305 -0.3727 -0.4726 0.0000 0.0000 -0.2871 -0.3641

D. XUE and S. WANG

1402

Table 2. Linear and non-linear properties and chemical bond parameters of each type of bond in LiNbGl and their contributions to the total linearity and non-linearity LiNbGJ Li-O(1)

Li-O(s) d” (A)

EC (eV) C (eV)

f:

4rti X: 4/e G:, d$ ( 1Od9esu)

r& 4, (10e9 esu)

2.0683 6.5540 4.6324 0.6669 2.7134 0.9543 0.1795 -0.1521 22.7847 -0.0412 6.1714

Nb-O(s)

Nb-O(l)

2.2385 5.3868 3.9379 0.6517 3.1129 I .0948 0.1621 0.1753 -34.2479 0.3625 -70.8352

2.1123 6.2206

11.6706 0.2212 5.5288 1.9445 0.5106 -0.1848 2.9738 -0.2997 4.8237

I .8886 8.2111 15.1450 0.2272 4.5365 I .5955 0.6021 0.1839 -2.2004 0.1071 -1.2814

Table 3. Comparisons between theoretical values and experimental data on non-linear tensor coefficients of KNbO j and LiNbG3 crystals, at 1.064 pm KNbO, Expt. -37.72$ 27.05.288 -43.69$ 30.6$,32Il -65.41$ 46.6$,48.8(

LiNbG3 talc.

Expt.

talc.

- 12.0858

- 10.311

- 10.6898

-30.043 1

-10.311

-10.6898

-54.08%

-64.511

-61.1214

tThe units of d, are 10m9esu. ssee [31. $The recommended absolute values of [6]. lIThe absolute data from [4]. ]iSee 15.61.

the different behaviours of their valence electrons, i.e. the higher amount of electronic delocalisation in KNb03 than in LiNbOs. The latter can be attributed to their different crystal structures, which lead to different values of the geometrical contributions of constituent chemical bonds and different coordination environments of the constituent elements. All of these differences can be found from the chemical bond parameters, the linear and non-linear properties of each type of constituent bond. This is why we start from a chemical bond search for the relationship between crystal structure and nonlinear optical properties. Acknowledgements-This work was supported by the State-Key Program of Basic Research of China. REFERENCES I. Zgnoik, M., Schlesser, R., Biaggio, L., Voit, E., Scheny, J. and Gtinter, P.. J. Appl. Phys., 1993.74. 1287. 2. Zgnoik, M., Nakagawa, K. and Gtinter, P., J. Opr. Sot. Am.,

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