Optical constants of monoclinic anisotropic crystals: Orthoclase

Speclrochimica Acta, Vol. 42A, No. Z/3, pp. 187-190, Printed inGreatBritain.

0584%539/86S3.00 + 0.00 0 1986PergamonPress Ltd.

1986.

Optical constants of monoclinic Arthur D.

anisotropic

crystals: orthoclase

JAMES R. ARONSON Little, Inc., Acorn Park, Cambridge, Massachusetts

02140, U.S.A.

(Received 30 May 1985) Abstract-The optical been derived in the i.r. and for the a-c plane simulate the spectrum

constants of the monoclinic crystal orthoclase [ideal composition 4(KAlSi, Os)] have region of the spectrum by the use of dispersion theory. Values for the El/b orientation have been used, together with a theory of the emittance of particulate materials, to of orthoclase powder.

I. INTRODUCTION

family of minerals has considerable importance, and we felt that obtaining a rigorous set of optical constants for a family member would be quite useful. We therefore carried out an analysis of an orthoclase sample reputed to have originated in Madagascar that had come into our possession. Orthoclase, ideal composition 4(KAlSi30,), is a monoclinic crystal having space group C2/m with a = 8.562A, b = 12.996A, c = 7.193A and /I = 116.02”[8].

The optical constants, the real and imaginary parts of the complex refractive index of any substance, are useful in modeling the optical properties of that material. For biaxial crystals there are three sets of optical constants which may be observed at various directions in the crystal. For the monoclinic and triclinic crystal systems the optical axes of the crystal wander with frequency[l] so that experiments to determine the optical constants have hitherto had to be made at different orientations for each frequency of interest. In the i.r. spectral region where the optical constants are subject to large spectral variations, a modification of classical dispersion theory has been developed [2-51 to simultaneously determine the principal indices from a set of reflectance measurements of the crystal. The feldspars, with the exception of orthoclase and saninine, are rarely obtainable in the form of the large ( - 1 cm on a side) single crystals required for the dispersion theory analysis. Therefore, modeling experiments previously carried out with respect to feldspars in the i.r. region of the spectrum have had to rely on pseudo optical constants [6, 71. This prominent

500

800

1000

II. LORENTZ

spectrum

OF ORTHOCLASE

Our method of obtaining the optical constants of anisotropic monoclinic crystals is described in Ref. [4]. We measured the reflectance of i.r. radiation having its electric vector parallel to the crystallographic b axis using a wire grid polarizer and a Fourier transform spectrometer (Digilab FTS 1X) at normal incidence. The reduction of these data are straightforward[9] with good convergence. The fit of the dispersion theory parameter theoretical spectrum to the experimental spectrum is shown in Fig. 1 and the dispersion theory parameters are given in Table 1. The data obtained for this orientation of the crystal were similar to those obtained by BOILLET [lo], although our measure-

1200

1400

WAVENUMBERS, Fig. 1. Reflectance

LINE PARAMETERS

of orthoclase 187

-

Dato, E II b

---_

Fit

1600

2000

1800

cm-l

(Ellb) fitted with seven Lorentz

lines.

JAMESR. ARONXIN

188 Table 1. Lore&

line parameters for ortboclase E)(b. Range of validity is 5OOcm-’
s, = 1.9528 u(E,) = 0.0291 k

vt(cm-‘)

1 2 3 4 5 6 7

1107.38 1015.70 986.79 762.07 729.30 608.56 541.51

s,

dSk)

Yt

dud

0.02137 0.05979 0.49618 0.05881 0.02909 0.02883 0.05041

0.00306 0.02257 0.02541 0.0164% 0.01463 0.00699 0.00648

0.06207 0.02411 0.02721 0.04007 0.02546 0.01615 0.01194

0.00602 0.00447 0.00245 0.01232 0.01362 0.00561 0.00246

a(vk)(cm-‘) 1.58 1.86 0.83 3.01 2.98 1.21 0.47

The us are the variances in the parameters as described in Ref. [4].

ments did not extend to low enough frequencies to include his last observed spectral band (435 cm- ‘). Three reflectance spectra were obtained from the monoclinic (a-c) plane and the data reduced according to the method described in Ref. [4]. Once again the data are similar to that of BOILLET.The fit is shown in Fig. 2 and the dispersion theory parameters in Table 2. An interesting result of our analysis is that if we use two low frequency resonances that we obtained and plot them on a diagram such as that given by HAFFNER and LAVES[ 1l] we find that our sample is an ordinary orthoclase, as we suspected, but had not been able to prove m. We were told [12] it could have been a sanidine, and very careful optical measurements would have been required to distinguish the two. The usual HAEFNER and LAWS method works with i.r. transmission spectra of powders and is quite easy to implement. For single crystals that are opaque our method allows the &me &hnique to be &l&d.

1.0 E

---

III. OPTICAL CONSTANTS OF ORTHOCLASE

In Fig. 3 we show the three principal absorption indices (imaginary part of the complex refractive indices) for orthoclase obtained in this work. These were obtained from the dispersion formulae [4,9] e(v)=m2(v)=ciE,+

:

k=ll+iyk

Sk

00 ;

Dot0

c

E

b

Fit

9o"

l.O-

EC

&__Q

1350 0

,

I 05ciI

2

(1)

;

Here v,, S,, ykare the frequency, strength and damping for each of the N resonances k and s, is the high frequency dielectric constant. For the monoclinic case:

a

0.5-

-

1000 WAVENUMBERS,

I 1500

2000

cm”

Fig. 2. Reflectance spectra of orthoclase (monoclinic plane) fitted with 11 Lore&

lines.

Optical constants of orthoclase

189

Table 2. Lorentz line parameters for orthoclase, monoclinic plane. Range of validity is 5OOcn-’ < v < 2OOOcm-’ k 1 2 3 4 5 6 7 8 9 10 11

vk(cm-‘)

dvi)(cm-‘)

0.41 0.97 0.67 3.02 1.95 9.98 5.01 2.52 1.35 2.39 0.46

1126.58 1108.37 1034.23 1034.16 1011.38 742.14 720.50 641.20 640.64 605.43 571.15

4%)

Sk

0.05674 0.17706 0.46177 0.20767 0.20861 0.00636 0.01314 0.03 194 0.09101 0.01283 0.41492

0.00276 0.00990 0.03087 0.05319 0.06441 0.01179 0.01013 0.02105 0.02028 0.00884 0.01971

Yt

dYk)

&t?

0.02474 0.02585 0.02310 0.04016 0.02966 0.02023 0.02521 0.02699 0.03580 0.02355 0.00935

0.00078 0.00123 0.00088 0.00448 0.00637 0.04143 0.02184 0.00978 0.00561 0.01554 0.00105

51.53 -26.23 83.56 - 13.91 23.27 102.31 61.24 158.89 48.96 54.73 - 38.12

ew)

2.55 0.80 2.62 8.93 7.01 60.21 21.41 41.61 16.55 6.74 0.47

= 2.0871, u(e;J = 0.0392, &,g= 0.0035, a(&:) = 0.0383, &,q= 2.2415, ~(6:) = 0.0313.

WAVENUMBERS,

cm-1

WAVENUMBER.

cm-1

Fig. 3. Spectral absorption indices of orthoclase.

u xxk

=

u

= sin’ (0, - 4)

zzk

cd (0, - &, Uxrk =

cos (0, - 4) sin (0, - 4)

and

2’

the optical constants in a small table such as those given in this paper and to generate the optical constants when needed at any frequency.

(4) IV. USE OF THE OPTICAL

8k is the azimuth of the oscillator with respect to the a axis of the crystal and 4 is the orientation of the a axis of the crystal with respect to the X axis. For the El/b orientation the spectral complex index is m = n - ik. For the monoclinic plane, the other two principal complex refractive indices at any frequency may be obtained by

It is helpful for modeling purposes

to store the data on

CONSTANTS

POWDER

FOR MODELING

DATA

The optical constants obtained in this work were used to model the powder spectrum of orthoclase as shown in Fig. 4. The theoretical simulation of a powder spectrum has been described in previous work by ARONSONand EMSLIE [ 131, but this is the first time that a feldspar spectrum has been simulated with real optical constants as opposed to pseudo ones such as those obtainable from a polycrystalline sample [ 143. The sample for which the powder spectrum was run was obtained from CARL FRANCIS, the Curator of the

JAMESR. ARON~ON

190

‘*O* ti 20.5

1400

Experiment f =0.54

I

I

I

I

I

I

I

1300

1200

1100

1000

900

800

700

600

Theory f=0.54 o%OO I

J=172pm

I

1300 I

1200 I

1100 I

1000 I

900 I

800 I

(1:l:l) 700 I

c 500

d= 170pm I

1

600

500

WAVENUMBERS, cm-l Fig. 4. Emittance spectrum of orthoclase powder.

Harvard University collection. He indicated that our single crystal was undoubtedly from Madagascar and chemically likely to be quite similar to the sample he provided. An X-ray fluorescence analysis confirmed the latter with regard to cation ratios. The spectra shown in Fig. 4 indicate a reasonably good simulation as to general signature and emittance level. The two principal discrepancies are a shift of the experimental 6OOcm-’ feature by about 2Ocm-’ in the simulation and a somewhat more gradual increase in emittance at high frequencies than is observed experimentally. The parameters used for the simulation were chosen by examination of the characteristics of the powder sample. We presumed the powder to consist of randomly oriented particles and therefore used a 1: 1: 1 ratio for the three principal complex refractive indices. A number of computer experiments were run to examine whether preferred orientation might have accounted for the discrepancies noted. Increased amounts of the complex refractive index from the El/b orientation increase the similarity of the theoretical spectrum to the experimental spectrum at high frequencies, but only at the expense of reducing the intensity similarity in the 6OOcm-’ feature. Despite these discrepancies the comparison of

the experimental data with the theoretical simulation shows a good overall similarity and is much like the fits we have obtained in the past [13] using the optical constants of minerals belonging to simpler crystal systems. V. CONCLUSION

The optical constants of orthoclaas have been derived for E [lb and for the monoclinic (u-c) plane by dispersion theory analysis of measurements of reflec-

tance spectra in the i.r. region. These optical constants were shown to be effective in simulating the emittance spectrum of orthoclase powder using a previously developed theory of the emittance of particulate materials. Acknowledgements-1

wish to thank CARL FRANCISfor helpful discussions and for providing the orthcclase sample used for the powder spectrum, ED PETERSfor X-ray fluorescence analysis and EMMETTSMITH,ELLENMISEOand LOUISEGUILMET~E for experimental measurements. This work was supported by the U.S. Army Research Office. VI. REFERENCES

[i] M. BORNand E. WOLF,Principles of Optics, p. 676. MacMillan. New York I19641 [Z] V. F. PAVIN~Hand M. V:BEL&JSOV,Opt. Spectrosc. 45, 881 (1978). [3] A. G. EMSLIEand J. R. ARONSON,J. Opt. Sot. Am. 73, 916 (1983). [4] J. R. ARONSON, A. G. EM~LIE, E. V. MISEO,E. M. SMITH and P. F. STRONO,Appl. Opt. 22,4093 (1983). [s] J. R. ARONSON,A. G. EMSLIE and P. F. STRONO,Appl. Opt. 24, 1200 (1985). [6] J. R. ARONSON and A. G. EMSLIE, J. Geophys. Res. SO, 4925 (1975). [7] J. R. ARONSON and E. M. SMITH,Proc. 9th Pm. Lunar Planet. Sci. Con&,p. 2911 (1978). [8] L. BRAGG,G. F. CLARINGBULL and W. H. TAYLOR, Crystal Structure OfMinerals, p. 307. Cornell University Press, Ithaca (1965). [9] J. R. ARON~~Nand P. F. STRONG,Appl. Opt. 14,2914 (1975).

[lo [ll 3 [12] [13]

P. BOILLET, Cub. Phys. 149, 1 (1962). ST. HAFNERand F. LAVE~,2. Kristai 109,204 (1957). C. S. HURL~KJT, JR., Private communication. J. R. ARONK~N and A. G. EMSLIE, in h&wed and Ramun Spectroscopy

of Lunar and Terrestrial

Minerals, P. 143

(edited by-C. RARR,JR.). Academic Press, New-York (1975). [14] J. R. ARONSON and A. G. EMSLIE,Appl. Opt. 19,412s (1980).