SU1749784A1 - Method of measuring optical anisotropic parameters of crystals - Google Patents

Abstract

Application: crystallography. The invention is a method for determining anisotropic parameters of crystals and their dispersion, including measuring the intensity of light passing through a polarizer, a crystal, and an analyzer depending on the angle of rotation of the crystal. Processing by this method is carried out by Fourier coefficients. 4 il.

Description

The invention relates to crystal optics, namely the measurement of the optical parameters of materials, and can be used in crystal physics, materials science, and instrument engineering.

In crystals, the important parameters characterizing the optical anisotropy are the birefringence, dichroism, and ellipticity of the natural waves associated with optical activity. For the determination of each of the parameters listed above, a number of methods have been developed in which the optical parameters are determined from different experiments on different devices and different samples, which is inconvenient and sometimes, in principle, impossible.

A method is known for determining the anisotropic optical parameters of crystals from measuring the azimuth of transmitted light as a function of the azimuth of incident light using a spectrophotometer.

The closest technical solution to the proposed one is the method of determining the birefringence and ellipticity of eigenwaves in transparent crystals by measuring the intensity of light at the output of a polarization system with a crystal equipped with a photon counter. The value of the path difference for different wavelengths is found through the ratio of the intensities with crossed and parallel polarizers and at small angles of rotation of the main axis of the plate relative to the polarizer.

However, the known method does not determine the nb and takes into account the dichroism of the plate under study, and the values of the phase difference and ellipticity are determined from the dependence graphs (}), which limits the accuracy of determining the desired optical parameters.

The task of the proposed method for determining the optical anisotropic parameters of a crystal is to simultaneously determine the two-component / magnitude. dichroism and optical activity with the help of a specialist (L

WITH

2

YU

sl

00

Ј

software device to the spectrophotometer.

The aim of the invention is to improve the accuracy and speed of determining anisotropic optical parameters.

This goal is achieved by measuring the functional dependences of the transmitted light intensity I f (a) with a variable a from 0 to 360 ° using a spectrophotometer. When measuring, the crystal plate is set normally to incident linearly polarized light between crossed first and second polarizers. After that, the plate is rotated with the selected pitch around the axis of the instrument angle a, changing from O to 360 °, and each time measuring the transmitted light intensity. Then similar measurements are made by rotating the plate located between the parallel polarizers. . . „- ..

In general, the dependence I f («) is obtained when solving the problem of the passage of light through a plate of a birefringent absorbing optically active crystal. For intensity, the dependence I f (a) is written in the form:

one

a + bicos2a +

4 (1 + k2) 2 + b2Sin2o: + cicos4a + C2Sin4ct, (1) e a, B1, B2, ci and C2 are the Fourier coefficients; a 1 (1 -t k2) 2 + 4k2 cos A cos2 y + + 1 - k2) 2 cos2 y; + 2 (t + k2) 2ch 5 + 4k (1 + k2) sin Asln2y bi 2 (1 -k4) sh (5 (1 + cos2 y); b2 2 (1 -k4) sh 5sln2y; ci (1 - k2 ) 2 (ch d - cos A) cos 2 y; ca (1 - k2) 2 (ch d - cos A) sin2 y;

Nl, 2 P1.2 + l K 1,2

in- (2ld / l) (kg + K1U, 6 (27rd / A) (/ c2-K1);

A (2jrd / AXn2-m); N1,2 - complex crystal refractive indices;

D pe (n2 - ni) - elliptical birefunction;

A / SC - () elliptical dichroism;

d is the sample thickness;

A is the wavelength;

k is the ellipticity of the natural waves in a crystal, which is determined by the optical activity;

y is the angle between the directions of oscillations in the polarizer and the analyzer:

a is the angle between the main direction of the polarizer and the crystal.

This expression for intensity is valid for all uniaxial crystals and for some directions of biaxial crystals. If the crystal is inactive (k 0), then it is valid for any crystals. In order not to take into account the initial position of the crystal relative to the polarizer, the values

25

b2 bi2 + b22; c2 ci2 + c22.

With crossed polarizers (90 from (1), having determined the coefficients of 30 Fourier a and c, from the ratio c / a, calculate k2:

1.2. (A1 + ZSL-2U2s1 (a + cl).

35

a, -c,

(2)

, 2 (3

Knowing k2, determine cos Do and I, measured a, b and c when the plate is rotated through an angle a; located between parallel flooring machines (at 0):

cb5d) -gk2 (a, l + c ,.). 0 (a c + k -e Cou-Sc.) J 28 au "-kg) bft (.. Qfkg) (31

e) 2-bll ak) fc, ((k744kzj

If the crystal is inactive (k 0), then

expressions for cos AO and I can also be obtained from (1) at an arbitrary angle y between polarizers;

BUT . 0-c (2 + cosey).

C ° 5 ° L 1a + Cco52 - L2so5gu; d acchino & fcosgy (4)

 a-bco% y - (- co5au Total phase difference A ± De + 2 t, with t and the sign of y Do can be determined by measuring on thin plates or on two plates of different thickness. Having determined Haid, we calculate two

refraction and dichroism of the studied plate. By calculating k and Dpe, one can estimate the optical activity of the crystal, linear and circular birefringence. For this, the following relations are used: D l j – j, DP

yie kk2 lpe

(five)

Dpe2 Dpl2 Dpts2,

where d pa. D p and D pl - elliptical, circular, and linear birefringence of the crystal;

n (n0 + ne) / 2 is the average refractive index of the crystal, while

DPC S / n,

where G is the scalar parameter of gyration

From here it is possible to calculate the specific rotation p, which the crystal would possess if there is no birefringence, from the formula:

n G 2 rk Ape n I (1 + k2)

The orientation of the optical axis in the plate under study can be determined from these measurements if the main values of the refractive indices n0 and Pe are known.

Using the normal equations for the refractive indices of uniaxial crystals without activity:

22

pg o: P2

What

Ео + (Је Јо) COS tp

get the ratio for the angle p.

, t ii i, 2 1

. 2 5t C

Pe /

/ zj 2 (-k2 / k VP

(€ -n.).; + An, -e (2be + An9i7 jj

sin2y

where (p - the angle between the optical axis and the wave normal.

If the value of birefringence is small, then it becomes simpler:

-Atse. (9)

Pe-P0 1 + K2

and when k - 0 it goes into a known relation,

In the known method, it was not proposed to rotate the sample with a certain step, therefore it was not possible to take into account the absorption and dichroism of the plate under study, moreover, the calculation was birefringent

Neither activity was performed graphically; therefore, the accuracy of determining optical parameters is low, and dichroism is determined from another experiment. 5 In the proposed method of finding

Optical parameters of crystals according to the above formulas. The main experimental complexity consists in determining the Fourier coefficients a, b, and c. Therefore, 10 although the dependence I f (a) can be measured on any spectrophotometer with a polarization attachment, the method can be implemented only on an automated device using a computer. The installation should contain holders of polarizers and a crystal with the possibility of rotation around the optical axis of the device, a photometric system, a monbchromator and provide the following functions1 setting the angle between the sample and the system first polarizer - second polarizer by rotating the sample or by synchronous rotation polarizers, measuring the intensity of the transmitted light, and

25 data entry in a computer to determine the Fourier amplitudes

The Fourier amplitude definition by numerical integration using the Fourier formulas of the experimental dependence I f (a

30 or by linear regression analysis is equivalent in this case. In view of the orthogonality of the basis functions, it is possible to decompose only into those of them that are necessary in

35 of this particular case (for example, by

sin2 a, cos2 a functions to determine

dichroism). The gain in accuracy of the Fourier amplitudes is about

М360 / Yes where Yes is the step of measuring the dependence of 1 (“). One of the used installations was created on the basis of a KSVU serial spectrometer (Fig. 1). The light from the incandescent lamp through the capacitor and polarizer hits the sample and then through the polarizer and the second condenser in monochromator MDR-12 and registration system. The microcomputer removes information from the photomultiplier and sends control pulses to the monochromator motor and the ratchet rings of the polarizer water. Two schemes are used: either the sample is placed on the drive and the polarizers are stationary, or when the sample is stationary, the polarizers turn in synchronism to two Identical ones.

55 drives. The accuracy of the angle setting is about 0.5 °, the pitch of the rotation is 10 °, the error of photometry is less than 0.5%. The accuracy of determining the Fourier coefficients is not less than 10, while the accuracy of determining

k. , D, DKMO 7. The computer performs multiple spectral scannings at different angles and with data stored in RAM, then the Fourier analysis is performed during the experiment, the parameters k, L and d are calculated, and then the desired parameters of the optical anisotropy of the crystals D pe, Lkz and G. The results are given to the printer in text or graphic form. All control of the experiment, processing of results and their issuance in textual and graphical form in the measurement process is performed automatically using a special program for the control microcomputer.

Example. Examine the crystals of the proposed method on the installation KSVU. Measurements of an optically active absorbing quartz crystal stained with an iron impurity in brown are measured. FIG. Figure 2 shows the characteristic functional dependences of the transmitted light intensity I on the angle of rotation of the plate d of a sample with a thickness of 2.48 mm for 0.55 µm at two polarizer positions. The following Fourier coefficients are obtained: with crossed polarizers, ax 0.777, GX 0.422; with parallel polarizers a 0.668, b 0.27. s, 0.241,

From these data, the optical parameters are calculated using formulas (2), (3), and (8): k = 0.296; D -98,68 ° + 360 °; d 0,256; p 6.963 °.

Then, the parameters of the optical anisotropy of the crystal under investigation are determined: Dpe 1.61 DK 9.03 G 1.35810 4. Similar values for quartz were obtained in the wavelength range from 0.4 to 0.75 microns. The dispersion of anisotropic parameters is shown in FIG. 3

Crystals of fianites Sr02-V20z with an AUz impurity, which are cubic, optically inactive and should not have anisotropic optical properties, are examined. The optical perfection of these crystals and the change in their optical properties when doping with various elements is investigated. When examined in crossed polarizers, the samples are light and colored, hence they are two-refractors. Since the crystals are birefringent, one can estimate the magnitude of the birefringence in them, as well as the amount of dichroism possibly arising in crystals with impurities.

The proposed method conducts the study of these crystals. Dependence of optical parameters of cubic zirconias on length

waves are shown in FIG. 4. The introduction of the L / Oz impurity increases the value of birefringence, but the values of D p of a pure crystal and a sample of a LuS 0.5% are quite close, while

time as the birefringence value of D p 3, for a sample of L / Oz of 0.1 May%, almost three times greater than LUZ 0.5 wt.% and pure. An increase in the concentration of LUZ to 1 wt.% Reduces the value of the birefringence, which indicates a decrease in the induced anisotropy, i.e., an improvement in the degree of cubicity. In addition, the anomalous course of the dichroism value in all samples was investigated: at a concentration of W03

5 0.1 wt.% Optical properties detect an anomaly, which is associated with a change in the crystal structure when an implant solid solution is formed.

The proposed method for determining the optic anisotropic parameters of crystals by a spectrophotometric method differs from that known for transparent crystals in that the method allows simultaneously by determining the Fourier composi

5 of the I f (() water experiment with high accuracy determine absorption, birefringence, dichroism, ellipticity of natural waves associated with optical activity, orientation of the optical axis by measuring the dependence of the intensity I of the transmitted light on the rotation of the plate with a certain step. In addition, the proposed device makes it possible to automatically determine the optical parameters of a crystal using a special program for the control microcomputer.

F o rm ula of the invention. A method for determining the optical anisotropic parameters of crystals, which consists in measuring the intensity of radiation transmitted successively through the first polarizer, crystal and second polarizer when the length is changed.

5 radiation waves, and determining from the obtained dependences of the birefringence, ellipticity of eigenwaves k, the scalar gyration parameter G and their dispersion, characterized in that

0 increasing the accuracy and speed of determination, as well as expanding the range of measured parameters, additionally change the angle of the crystal relative to the polarizer in the direction of propagation of radiation, determine the ellipticity of the natural waves with crossed polarizers by the formula

k2 fa.tf3 (V 2 42СJos cj a, -C,

o

determine the birefringence D pe and the dichroism D / se with parallel polarizers from the ratios

COSA i: - sc k4) -gKe (ontcB). (au + sih ig yi-zs.);

25 ou (elg bji-k) 4c..i: (uk) 6) 2-Mi-kVc, ((T + 4k2j

where hell, Cj are the Fourier coefficients obtained from measurements with crossed polarizers;

a „, b„, с, Р - Fourier coefficients obtained from measurements with parallel polarizers:

D (2tgs1 / AHp2-P1); J (27rd / A) (2-Ki):

W, 2 is the refractive index of the crystal along and across the optical axis; Dpe P2 - ni - birefringence;

"G 12 is the absorption coefficient of the crystal in the direction along and across the optical axis;

DK K2 - # 1 - dichroism; d is the thickness of the crystal;

A-wavelength radiation, determine the scalar parameter of the gyration by the ratio

0. 2k

0 DPP

1 + k2

i

where n (n0 + pv) / 2 is the average refractive index of the crystal;

Po, Pe are the refractive indices of ordinary and extraordinary rays in a crystal,

and the orientation angle of the optical axis p is determined from the ratio

g, i i / 2i

0

5t% (k / J k

(

/ g i -K4L -p p

{e-no} ho + un9- - 2he un9-- J

Fig-i

V

L f. "Te eu

I1 (

r

four

0 -5

four

an, f0

14

.

four

/

Fig.Z

0, "

0.6

L., micron

Ohno

0.6

V

Claims (1)

Claim The method for determining the optical anisotropic parameters of crystals, which consists in measuring the intensity of radiation transmitted sequentially through the first polarizer, the crystal and the second polarizer when the radiation wavelength is changed, and determining from the obtained dependences of birefringence, ellipticity of eigenwaves k, scalar gyration parameter G and their dispersions, which differs the fact that, in order to increase the accuracy and speed of determination, as well as expand the range of measured parameters, they additionally change the angle crystal relative to the polarizer in the direction of radiation propagation, determine the magnitude of the ellipticity of eigenmodes for the crossed polarizers by formula determine birefringence Δ n _e and dichroism Dke with polarizers parallel relation in so5D = - 25 _ ^a n ( ^< ~ ^{l <g} ) ^{2 <} -bu (lk ⁴ ) 4cl | [(Uk ^g ) ¹ 4 4k ² J. k ⁴ ) <- c (| [(1k ' ¹ ) ¹ + 4k ² J where a _g C / are the Fourier coefficients obtained from measurements with crossed polarizers; a _and b. c _p are the Fourier coefficients obtained from measurements with parallel polarizers; Δ = (2πΰ / Λχπ2 - ni); <5 = (2πά / λ) (k ₂ ^- * ι): πί, 2 is the refractive index of the crystal along and across the optical axis; ΔPe = ig - ni - birefringence; K 12 is the absorption coefficient of the crystal in the direction along and across the optical axis; Δ / c ~ k ₂ - k y - dichroism; d is the crystal thickness: A-wavelength of radiation, determine the scalar gyration parameter by the ratio 1 + k ² 'where ή' = (by + n _e ) / 2 is the average refractive index j5 of the crystal; Po, n _e are the refractive indices of the ordinary and extraordinary rays in the crystal, and the orientation angle of the optical axis φ is determined from the relation