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The fundamental rotation-vibration spectrum of HD Bejar Hurtado, Jose Antonio 1972

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E FUNDAMENTAL ROTATION-VIBRATION SPECTRUM OP HD oy JOSE ANTONIO BEJAR HURTADO M.Sc, U n i v e r s i t y o f B r i t i s h Columbia, 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OP THE REQUIREMENTS FOR THE DEGREE OP DOCTOR OP PHILOSOPHY i n the Department o f PHYSICS We accept t h i s t h e s i s as conforming to the r e q u i r e d standard. THE UNIVERSITY OP BRITISH COLUMBIA October, 1972 In present ing t h i s thes is in p a r t i a l f u l f i l m e n t of the requirements fo r an advanced degree at the Un ive rs i t y of B r i t i s h Columbia, I agree that the L ib ra ry sha l l make i t f r e e l y a v a i l a b l e for reference and study. I fu r ther agree that permission for extensive copying of th i s thes i s for s c h o l a r l y purposes may be granted by the Head of my Department or by h is representa t i ves . It is understood that copying or p u b l i c a t i o n of th i s thes i s f o r f i n a n c i a l gain sha l l not be allowed without my wr i t ten permiss ion . Depa rtment The Un ivers i t y of B r i t i s h Columbia Vancouver 8, Canada Date -1-ABSTRACT I s o t o p l c a l l y s u b s t i t u t e d molecules such as HD, u n l i k e o r d i n a r y homonuclear diat o m i c molecules, possess a s m a l l e l e c t r i c d i p o l e moment. This e f f e c t i s a consequence of asymmetric s l i p p a g e of the e l e c t r o n c l o u d w i t h n u c l e a r v i b r a t i o n . The m a t r i x element of the d i p o l e moment f o r the t r a n s i -t i o n v=0 to v=1 i n the ground e l e c t r o n i c s t a t e of HD has been e x p e r i m e n t a l l y determined by u s i n g F o u r i e r Transform s p e c t r o -s c o p i c methods. At p r e s s u r e s below 2 atm the width of the l i n e s due to these t r a n s i t i o n s has been found to be l i m i t e d by pure Doppler broadening w = 0.026 cm" 1, hence no c o l l i s i o n narrowing, as occurs i n H 2 , has been observed. From the r e s o l v e d l i n e s the a b s o l u t e i n t e n s i t i e s were obtained and the matrix element has been found to i n c r e a s e w i t h J from 4.15 x 10~ D debye, f o r -5 J = 0, to 8.42 x 10 debye f o r J = 4. Because of the h i g h r e s o l u t i o n used, new h i g h l y r e l i a b l e f r e q u e n c i e s have been o b t a i n e d . computed. The d i p o l e moment f o r the R-branch i i TABLE OP CONTENTS Abstract i Table of Contents i i Table of Figures i i i L i s t of Tables v Acknowledgement v l Chapter 1 Introduction 1 Chapter 2 Experimental Technique 5 2.1 Introduction 5 2.2 Experimental Arrangement 7 2.3 The Absorption C e l l 9 2.4 The Source 13 2.5 The Interferometer 13 2.6 The Frequency Synthetizer 22 2.7 The Detectors 24 2.8 The Gas Sample and Gas Handling 24 2.9 Data C o l l e c t i o n 26 2.10 Data Analysis 28 2.11 Calculation of Frequencies 32 Chapter 3 Results and Conclusions 39 Bibliography 54 i i i TABLE OF FIGURES FIGURE 1 B l o c k diagram of experimental arrangement. 8 2 Diagram of the c e l l . 10 3 Source and t r a n s f e r o p t i c s between the c e l l and the i n t e r f e r o m e t e r . 12 4 O p t i c a l d e s i g n of the i n t e r f e r o m e t e r . 14 5 Mechanical arrangement of the I n t e r f e r o m e t e r . 15 6 L o c a t i o n of the main experimental components. 17 7 Device f o r the f i n e alignment of the i n t e r f e r o -meter f i x e d m i r r o r . 19 8 I l l u m i n a t i o n of the i n t e r f e r o m e t e r by the l a s e r f o r alignment purposes. 21 9 The frequency s y n t h e t i z e r . 2 3 1 0 , S p e c t r a l windows of r a d i a t i o n f a l l i n g on the d e t e c t o r . 2 5 11 Gas h a n d l i n g diagram. 27 12 Block diagram of data a n a l y s i s . 31 13 S p e c t r a l d i s t r i b u t i o n a r i s i n g d u r i n g v a r i o u s s t e p s of the a n a l y s i s . 3 3 14 T y p i c a l i n t e r p o l a t e d i n t e r f e r o g r a m near the zero path d i f f e r e n c e p o i n t . 34 15 S l i g h t l y asymmetric i n t e r f e r o g r a m . 3 5 1 6 I n t e r f e r o g r a m of F i g u r e 15 w i t h the asymmetry c o r r e c t e d . 36 17 R e p r e s e n t a t i v e a b s o r p t i o n s p e c t r a of the R branch. 4 0 18 A b s o r p t i o n spectrum of the R ( 0 ) l i n e f o r s i x d i f f e r e n t c o n d i t i o n s . 41 19 A b s o r p t i o n spectrum of the R ( 1 ) l i n e f o r s i x d i f f e r e n t c o n d i t i o n s . 42 i v FIGURE 2 0 Absorption, spectrum of the R(3) l i n e f o r s i x d i f f e r e n t c o n d i t i o n s . A 3 21 A b s o r p t i o n spectrum of the R ( 4 ) l i n e f o r s i x d i f f e r e n t c o n d i t i o n s . 4 4 2 2 T y p i c a l a b s o r p t i o n c o e f f i c i e n t . 4 7 2 3 R e l a t i v e i n t e n s i t i e s . 4 9 V LIST OP TABLES TABLE I Experimental c o n d i t i o n s . 39 TABLE I I F r e q u e n c i e s . 4 5 TABLE I I I I n t e g r a t e d a b s o r p t i o n c o e f f i c i e n t s and d i p o l e moment. 51 v i ACKNOWLEDGEMENT I am deeply g r a t e f u l to my s u p e r v i s o r , Dr. H.P. Gush, f o r h i s i n d i s p e n s a b l e help when d e s i g n i n g , b u i l d i n g , running, and a n a l i s i n g the experiment. I would a l s o l i k e to extend my g r a t i t u d e to Dr. H.L. B u i j s f o r h i s h e l p f u l d i s c u s s i o n s , the s t a f f s of the Machine Shop and the Computer Center, Mr. J . Lees and Mr. E. W i l l i a m s f o r the g l a s s work, and Mr. Dickson from the e l e c t r o n i c shop. S p e c i a l thanks go to my w i f e , P l a u r y , f o r "postponing" the b i r t h o f our second c h i l d u n t i l her t y p i n g of t h i s t h e s i s was completed. 1. I n t r o d u c t i o n Diatomic homonuclear molecules such as Hg, 0 9 . ^2* e"t°»» e x h i b i t no o r d i n a r y e l e c t r i c d i p o l e i n f r a r e d spectrum c o r r e s -ponding to molecular v i b r a t i o n or r o t a t i o n . This i s because these molecules possess a h i g h degree of symmetry, incompa-t i b l e w i t h the e x i s t e n c e of an e l e c t r i c d i p o l e moment. I s o -t o p i c a l l y s u b s t i t u t e d molecules such as HD have a lower sym-metry, s i n c e they are not homonuclear, and the presence of an e l e c t r i c d i p o l e moment i s not r i g o r o u s l y f o r b i d d e n because of symmetry. A r o t a t i o n - v i b r a t i o n band of HD was f i r s t ob-s e r v e d by Herzberg ( 1 9 5 0 ) and i d e n t i f i e d as the v= 0 to v=3 t r a n s i t i o n o c c u r r i n g near \ = 9 7 0 0 A. L a t e r , the fundamental and f i r s t overtone bands were i n v e s t i g a t e d i n some d e t a i l by Durie and Herzberg ( 1 9 6 0 ) . The pure r o t a t i o n a l band of HD was f i r s t observed by T r e f l e r and Gush (1-968) i n the h i g h p r e s s u r e gas. Prom the i n v e s t i g a t i o n s of Durie and Herzberg ( i 9 6 0 ) , i t was e v i d e n t t h a t m a t r i x elements of the d i p o l e moment of HD do not v a r y i n the same manner w i t h v i b r a t i o n a l quantum number as f o r a "normal" molecule such as HOI. In the l a t t e r case the f i r s t overtone and second overtone s p e c t r a are much weaker than the fundamental spectrum. However, i n the case o f HD the f i r s t overtone spectrum appeared to be s t r o n g e r than the fundamental. F u r t h e r , from the work o f T r e f l e r and Gush ( 1 9 6 8 ) , i t was apparent t h a t the d i p o l e moment was not -2 constant within a given v i b r a t i o n a l band (in t h e i r case the v=0 to v=0 t r a n s i t i o n ) , because the i n t e n s i t y of the ro t a t i o n -a l l i n e s did not vary i n the usual way with the r o t a t i o n a l quantum number. I t thus appears that the electronic proper-t i e s of HD are quite unusual and a detailed study of the i n -frared spectrum, from which the dipole moment can i n p r i n c i p l e be deduced, i s merited. I t was Wick (1935) who f i r s t predicted that HD should have an i n f r a r e d spectrum and he made an estimate as to i t s i n t e n s i t y based on his calculated value f o r the dipole moment, <V\^ l tf+ i > ~ 1 0 U VV>T i e f y e . This estimate f o r the i n t e n s i t y was confirmed as being rough-l y correct by Herzberg (1950) and Durie and Herzberg (1960). The reason that a dipole moment arises i s roughly as follows. In HD, the centre of mass and the centre of posi-t i v e charge do not coincide, since the former l i e s close to the deuterium nucleus, whereas the l a t t e r l i e s midway between the proton and the deuteron. When the n u c l e i vibrate the centre of mass remains stationary, but the centre of pos i t i v e charge executes o s c i l l a t i o n s about the equilibrium p o s i t i o n . This i s because the amplitude of o s c i l l a t i o n of the proton i s greater than that of the deuteron. Because the centre of negative charge does not follow exactly the centre of pos i t i v e -3-charge, both, a permanent d i p o l e moment and a t r a n s i t i o n d i -p o l e moment a r i s e . A c a l c u l a t i o n o f the d i p o l e moment of HD was c a r r i e d out by B l i n d e r (1960) u s i n g a second order p e r t u r b a t i o n theory treatment, and he obtained f o r the ground v i b r a t i o n a l s t a t e the v a l u e <0lyul0 > = 8.9 x 10~4 Debye. S h o r t l y l a t e r he m o d i f i e d h i s theory s l i g h t l y i n the l i g h t of the e x p e r i -mental r e s u l t s of Durie and Herzberg (1960), and p r e d i c t e d -4 the v a l u e o f 5.67 x 10 Debye f o r the d i p o l e moment i n the ground s t a t e ( B l i n d e r (1960)). This v a l u e was confirmed r e a s o n a b l y c l o s e l y by the experiment o f T r e f l e r and Gush (1968), which y i e l d e d <0\j+\o> = 5.85 x 10 _ Z f Debye. The most g e n e r a l approach to the problem of the d i p o l e moment of HD i s t h a t of Kolos and Wolniewicz (1966), who used a complete n o n r e l a t i v l s t i c f o u r - p a r t i c l e H a m i l t o n i a n , the a n a l y s i s b e i ng c a r r i e d out n u m e r i c a l l y on a l a r g e computer. They o b t a i n e d the v a l u e 1.54 x 10~3 Debye, about three times the experimental v a l u e . Since the p u b l i c a t i o n o f the work of T r e f l e r and Gush (1968) they are r e i n v e s t i g a t i n g t h e i r a n a l y s i s s e a r c h i n g f o r p o s s i b l e e r r o r s . There are no p u b l i s h e d v a l u e s , e i t h e r experimental o r t h e o r e t i c a l , f o r the d i p o l e matrix element HD a p a r t from the one of Wick (1935). Although Durie and Herzberg (1960) measured some i n f r a r e d bands of HD, they were no t a b l e to deduce the a b s o l u t e i n t e n s i t y o f the bands because -4-t h e l r s p e c t r a l r e s o l u t i o n was inadequate. I t would, however, be o f much i n t e r e s t to have t h i s Information to c o n f r o n t w i t h c a l c u l a t i o n s which are being c a r r i e d out a t the pr e s e n t time by P o l l and K a r l (1972). A f u r t h e r reason f o r o b t a i n i n g the d i p o l e moment i s t h a t , s i n c e HD has an i n f r a r e d spectrum i t should be p o s s i b l e to measure i t i n the s p e c t r a of say, d i s t a n t g a l a x i e s . The i n t e n s i t y o f a b s o r p t i o n , combined w i t h a knowledge of the d i p o l e moment, would permit an estimate o f m o l e c u l a r HD content i n the galaxy, and consequently by i n f e r e n c e , the mol e c u l a r hydrogen content. The prime o b j e c t o f t h i s r e s e a r c h was then to measure the a b s o l u t e i n t e n s i t y of the fundamental band of HD from which the d i p o l e moment co u l d be deduced. The major e x p e r i -mental d i f f i c u l t y to overcome was to f u l l y r e s o l v e the r o t a -t i o n - v i b r a t i o n l i n e s so t h a t one c o u l d be sure t h a t the t r u e a b s o r p t i o n I n t e n s i t y was measured. Because of the c o s t of HD o n l y a r e l a t i v e l y s m a l l q u a n t i t y o f the gas c o u l d be used f o r the measurement which e n t a i l s i n i t s t u r n a low p r e s s u r e measurement. The width o f the a b s o r p t i o n l i n e s i s then de-termined by the Doppler e f f e c t and equals about 0.029 cm " 1 f o r the fundamental band. An instrument w i t h a l i m i t o f r e -s o l u t i o n o f approximately 0.01 cm i s hence r e q u i r e d f o r these s t u d i e s . Because the spectrum was s t u d i e d a t h i g h r e s o l u t i o n , f r e q u e n c i e s of h i g h p r e c i s i o n were o b t a i n e d , which w i l l permit the e v a l u a t i o n of improved mole-c u l a r c o n s t a n t s . 2. Experimental Technique 2.1 I n t r o d u c t i o n The h i g h r e s o l u t i o n r e q u i r e d f o r t h i s work makes manda-t o r y the use of an i n t e r f e r e n c e type spectrometer, s i n c e d i f f r a c t i o n g r a t i n g s of s u f f i c i e n t width are not a v a i l a b l e . We have hence made use of a two-beam i n t e r f e r o m e t e r developed i n t h i s l a b o r a t o r y by H. B u i j s (1969), modifying i t substan-t i a l l y f o r use i n the a p p r o p r i a t e wavelength r e g i o n . The advantages of the i n t e r f e r o m e t r i c , or F o u r i e r Transform, technique i n spe c t r o s c o p y are w e l l known, and are d i s c u s s e d i n a l e n g t h y review a r t i c l e by Vanasse and Sakay (1967). I t w i l l s u f f i c e to g i v e a v e r y b r i e f e x p o s i t i o n o f the p r i n c i p l e . In a Ml c h e l s o n i n t e r f e r o m e t e r i l l u m i n a t e d by c o l l i m a t e d l i g h t , the incoming plane wave i s d i v i d e d i n t o two p a r t s (by a beam s p l i t t e r ) which are recombined a f t e r - o n e has been d e l a y -ed w i t h r e s p e c t to the other due to a d i f f e r e n t path. I f the e l e c t r i c f i e l d a t the entrance of the i n t e r f e r o -meter i s E ( t ) the e l e c t r i c f i e l d a t the output can be w r i t t e n : E'(t) = «E(t<-T)+/&E(t+T+tJ where <v and/ 3 are amplitude t r a n s m i s s i o n c o e f f i c i e n t s , T i s the time taken f o r a l i g h t s i g n a l to t r a v e l from the entrance (where E ( t ) i s d e f i n e d ) to the e x i t (where E ' ( t ) i s d e f i n e d ) v i a the f i x e d m i r r o r , and t i s the a d d i t i o n a l time delay - 6 -f o r the s i g n a l p a s s i n g by the moving m i r r o r . The energy a s s o c i a t e d w i t h the outgoing wave i s propor-t i o n a l to The f i r s t two terms of 0 are independent of the time d e l a y and are simply p r o p o r t i o n a l to the i n t e n s i t y of the beams coming from the f i x e d m i r r o r and moving m i r r o r i n d e p e n d e n t l y . However, the t h i r d term (the a u t o c o r r e l a t i o n f u n c t i o n of the r a d i a t i o n f i e l d i n c i d e n t on the i n t e r f e r o m e t e r ) depends c r i -t i c a l l y on the time d e l a y ~C . A d e t e c t o r l o c a t e d a f t e r the i n t e r f e r o m e t e r has an output v o l t a g e p r o p o r t i o n a l to C. The component of t h i s v o l t a g e which v a r i e s as ~C i s v a r i e d i s p r o p o r t i o n a l to the a u t o c o r r e l a t i o n f u n c t i o n a l r e a d y mention-ed. I t i s customary to w r i t e t h i s v a r i a b l e p a r t o f the de-- 7 -t e c t o r s i g n a l ( I n t e r f e r o g r a m ) as l ( 6 ) wh ere c f ~cZ i s the o p t i c a l path d i f f e r e n c e between the two beams i n the i n -t e r f e r o m e t e r . I t i s w e l l known that the c o s i n e F o u r i e r Trans-form of the a u t o c o r r e l a t i o n f u n c t i o n of a s t a t i o n a r y random f u n c t i o n i s i t s power spectrum. Thus i s p r o p o r t i o n a l to the spectrum of r a d i a t i o n e n t e r i n g the i n t e r f e r o m e t e r . <Tz i/X Is the frequency of the r a d i a t i o n i n wavenumbers. The i n t e r f e r o m e t r i c method of s p e c t r o s c o p y c o n s i s t s , thus, of two s t e p s : a) an i n t e r f e r o g r a m of the r a d i a t i o n under study i s r e c o r d e d ; b) the F o u r i e r Transform of the i n t e r f e r o g r a m i s c a l c u l a t e d . 2.2 Experimental Arrangement A b l o c k diagram of the experiment i s shown i n F i g u r e 1 . Continuous r a d i a t i o n from a tungsten f i l a m e n t p r o j e c t i o n lamp i s f o c u s e d w i t h no m a g n i f i c a t i o n i n t o the entrance a p e r t u r e of a White m u l t i r e f l e c t i o n path a b s o r p t i o n c e l l . A f t e r pass-i n g through the gas, the l i g h t f a l l s on a two beam i n t e r f e r o -meter and an o p t i c a l f i l t e r which s e l e c t s bands of r a d i a t i o n i n the v i c i n i t y of the HD a b s o r p t i o n l i n e s under study. At the e x i t of the instrument the l i g h t i s condensed on to a l e a d s u l f i d e photoconductive d e t e c t o r . The o p t i c a l path d i f f e r e n c e i s monitored w i t h the i n t e r -o FIGURE 1 B l o c k diagram of e x p e r i m e n t a l arrangement SOURCE CK IBS. CELL ZPD DETECTOR! STABILAZED HE-NS LASER DOUBLE BEAM MICHELSON INTERFEROMETER LASER DETECTOR f\f\AA) PULSE SHAPER OPTICAL FREQUENCY INFRARED SYNTHETIZER DETECTOR -AND AMPLIFIED WW ILL -fes. ANAL-DIG CONVERTER INTERFACE IBM 3 6 0 / 6 7 AMPEX TM7 2 0 WORDS • DIGITAL BUFFER TAPE MEMORY TRANSPORT SPECTRUM T INTEGRATED ABSORPTION COEFFICIENT - 9 -f e r e n c e f r i n g e s produced by l i g h t from a s t a b l i z e d He-Ne l a s e r which a l s o passes through the i n t e r f e r o m e t e r . These f r i n g e s are used to generate p u l s e s which i n tu r n t r i g g e r an A-D c o n v e r t e r which measures the a m p l i f i e d s i g n a l from the i n f r a r e d d e t e c t o r . The d i g i t i z e d i n t e r f e r o g r a m i s then r e c o r d e d on magnetic tape. An IBM 360/67 computer reads the i n t e r f e r o g r a m , f i l t e r s I t , ev a l u a t e s the F o u r i e r Trans-form, c r e a t e s a background spectrum, produces the a b s o r p t i o n c o e f f i c i e n t as a f u n c t i o n of the frequency, and f i n a l l y c a l -c u l a t e s the area under the a b s o r p t i o n l i n e s . The v a r i o u s p a r t s of the apparatus and the n u m e r i c a l a n a l y s i s are d i s c u s s e d i n t h i s c h a pter. 2.3. The A b s o r p t i o n C e l l The a b s o r p t i o n c e l l was a mu l t i p a s s White c e l l , u s i n g t h r e e s p h e r i c a l concave m i r r o r s w i t h the same r a d i u s o f cur-v a t u r e o f 1.0 meters. The arrangement of the m i r r o r s i s shown i n F i g u r e 2. The c e n t e r s of c u r v a t u r e of A 1 and A2 are on the f r o n t s u r f a c e of B, and the c e n t e r of c u r v a t u r e o f B i s h a l f way between A^ and A 2 . This arrangement e s t a b l i s h e s a system of conjugate f o c i on the r e f l e c t i n g s u r f a c e s of the m i r r o r by means of which a l l the l i g h t l e a v i n g any p o i n t on A^ i s brought to a focus by B a t the cor r e s p o n d i n g p o i n t on A 2 and a l l the l i g h t l e a v i n g t h i s p o i n t on A 2 i s focused back to the o r i g i n a l p o i n t on A^. S i m l l a r i l y , a l l the l i g h t l e a v i n g any p o i n t on B and going to e i t h e r A. or A P i s focused back FIGURE 2 Diagram of the c e l l CELL LOCATION OP IMAGES -11 -to a new p o i n t on B t h a t i s somewhat o f f s e t to one s i d e o f the o r i g i n a l one. I f Aj and A 2 are a d j u s t e d s y m m e t r i c a l l y about B and i t s c e n t e r of c u r v a t u r e , each image on B i s sepa-r a t e d from the one n e a r e s t to i t by the d i s t a n c e between the c e n t e r s o f c u r v a t u r e of A^ and A 2. The r a t i o o f the l e n g t h of B (9.5 cm) to t h i s s e p a r a t i o n determines the number of times the l i g h t passes through the c e l l . The c e l l has been b u i l t so t h a t a l l r e q u i r e d alignments can be done from o u t s i d e , and the s e p a r a t i o n between the cen-t e r s of c u r v a t u r e o f A^ and A 2, hence the number of passes, can be changed by a d j u s t i n g a f i n e micrometer screw. The housings of the goldcoated m i r r o r s are made of aluminum and f u r n i s h e d w i t h c a l c i u m f l u o r i d e windows to permit the en t r y and e x i t of the r a d i a t i o n . The r a d i i of the m i r r o r s are f i v e cm and the diameter of the one meter l o n g pyrex pipe Is 10 cm. Path l e n g t h s of up to 98 m can be ac h i e v e d . For a l o n g e r path, Images o v e r l a p as the astigmatism p r o g r e s s i v e -l y e n l a r g e s the s i z e o f the images. In the f i r s t s e t o f experiments the path l e n g t h used was 70 m, however most of the work has been done a t 18 and 30 m. The c e l l has been f i l l e d w i t h p r e s s u r e s up to 1.5 Atm. The pre s s u r e was mea-sured both w i t h a Bourdon p r e s s u r e gauge and a mercury mano-meter. The r a d i a t i o n from the c e l l i s focused by means of t r a n s -f e r o p t i c s i l l u s t r a t e d i n F i g u r e 3» on the a p e r t u r e of the FIGURE 3 Source and t r a n s f e r o p t i c s between the c e l l and the i n t e r f e r o m e t e r -13-i n t e r f e r o m e t e r . By means of these o p t i c s the c e l l and the I n t e r f e r o m e t e r are o p t i c a l l y matched. 2.4. The Source The spectrum of i n t e r e s t l i e s between 2.43 and 2 . 7 . A tungsten f i l a m e n t lamp of the halogen type ( S y l v a n i a 75 Q/CL) was used because of i t s r e l a t i v e l y h i g h i n t e n s i t y ; and because the q u a r t z envelope of the lamp was devoid of the water a b s o r p t i o n band near 2.7 which i s troublesome i n o t h e r lamps. The lamp, operated i n vacuum, was surrounded by a c l o s e d brass water-cooled housing. An image o f the f i l a ment was f o c u s s e d a t the a p e r t u r e of the c e l l by means of an arrangement of m i r r o r s as shown i n F i g u r e 3. The lamp was operated a t i t s maximum a l l o w a b l e temperature from a r e g u l a t e d d.c. supply. 2.5. The I n t e r f e r o m e t e r The i n t e r f e r o m e t e r c o n s t r u c t e d by H.L. B u i j s and H.P. Gush has been p r e v i o u s l y d e s c r i b e d ( B u i j s and Gush (1967)). However, i n o r d e r to make the e x p o s i t i o n of t h i s work more complete, a s h o r t d e s c r i p t i o n and schematic diagrams of the i n s t r u m e n t are quoted: "The l i g h t f i r s t s t r i k e s the beam s p l i t t i n g s u r f a c e where i t d i v i d e s . The beam which t r a v e l s to the r i g h t ( F i g . 4) passes through the compensating p l a t e (a c o r n e r of which i s shown by a dotted l i n e ) and i s then d e f l e c t e d by a c o r n e r m i r r o r to a p a i r of r e f l e c t i n g prisms; F I G U R E 4 O p t i c a l d e s i g n of the i n t e r f e r o m e t FIGURE 5 M e c h a n i c a l arrangement of i n t e r f e r o m e t e r - 1 6 -t h e l i g h t r e t u r n s to the beam s p l i t t i n g p l a t e v i a the corner m i r r o r and the compensating p l a t e . The r e t u r n i n g beam i s s p a t i a l l y separated from the incoming beam because of the l a t e r a l displacement a t the r e f l e c t i n g prism. The beam which t r a v e l s to the l e f t i s r e f l e c t e d f i r s t from one of a p a i r of f l a t m i r r o r s ; i t i s then r e t u r n e d to the other f l a t m i r r o r by r e f l e c t i o n from the prisms, and recombines w i t h the f i r s t beam a t the beam s p l i t t i n g p l a t e . The path d i f f e r e n c e i s changed by d i s p l a c i n g the prisms p a r a l l e l to the l i g h t path, the I n c r e a s e i n path d i f f e r e n c e b e i n g f o u r times the d i s p l a c e -ment. Small r o t a t i o n s of the prism p a i r have no e f f e c t on the s t a t e of i n t e r f e r e n c e . Two output beams are a c c e s s i b l e f o r d e t e c t i o n , and two i n p u t channels are a v a i l a b l e f o r the so u r c e . " The mechanical d e s i g n o f the i n t e r f e r o m e t e r i s shown i n F i g u r e 5. The instrument was m o d i f i e d f o r the present r e s e a r c h problem i n s e v e r a l r e s p e c t s . The most s u b s t a n t i a l m o d i f i c a -t i o n was t h a t i t was enclosed i n a l a r g e vacuum tank to per-mit o p e r a t i o n i n a s p e c t r a l r e g i o n where the atmosphere i s e s s e n t i a l l y opaque ( F i g u r e 6 ) . The f a c t t h a t the instrument was put i n vacuum meant t h a t the adjustments on many of the m i r r o r s o f the instrument, which f o r m e r l y were manipulated by hand, had to be m o d i f i e d to permit remote c o n t r o l . F u r t h e r -more, the f i n e adjustment scheme of the f i x e d m i r r o r s was completely changed. FIGURE 6 Locat ion of the main experimental components . . l a s e r m o n i t o r i n g f r i n g e s i n t e r f e r o m e t e r f i x e d m i r r o r alignment monochromatojr / i n t e r f e r e - • • • • — • • • • meter t a p e t r a n s p o r t v i b r a ^ , — ( t i o n fool- )';• . y / \ 'v.-l V J n_ j _ i n t e r f a c e memory s y s tern, r e a d - w r i i c o n t r o l , j s a m p l e s j c o u n t e r . Z?D c o u n A - D c o n v . i n f r a r e d a m p l i f i e ; ZPD d e t . a m p l i f i e : l a s e r t u n i n g d i s p l a y a c a n i n g r a i r r o r ; n o t c r c o n t r o l * l a s e r de - : a m n l i f i e i o o l l i m a t ^ emo t e l i n r n m e n t l a s e r p . s . tanlv"presf>. reading s o u r c e r e g u l a t e p . s . - 1 8 -S e v e r a l systems of f i n e adjustment on the f i x e d m i r r o r o f the i n t e r f e r o m e t e r were t r i e d , but the f i n a l one i s essen-t i a l l y h y d r a u l i c i n n a t u r e . The mechanism i s i l l u s t r a t e d i n F i g u r e -7» At the end of the course alignment screws a s t e e l diaphragm which can be h y d r a u l i c a l l y d i s t o r t e d i n a c o n t r o l a b l e and continuous manner from 0 to 20 micrometers has been added. Each of the two f i x e d m i r r o r s has two such adjustment screws. A system of f o u r pressure gauges and e i g h t v a l v e s a l l o w s such a f i n e and smooth alignment t h a t the instrument can be a l i g n e d as i t scans (by l o o k i n g a t the e l e c t r i c a l s i g n a l from the moni-t o r i n g f r i n g e s ) without l o s i n g phase ( F i g u r e s 6 and 7). The d r i v i n g mechanism has a l s o been changed. The nut from a h i g h p r e c i s i o n b a l l b e a r i n g screw, s i m i l a r to those used i n computer p l o t t i n g machines, i s now used to p u l l the c a r r i a g e of the moving m i r r o r . This screw i s turned by h e l l -c o i d a l gear whose p i n i o n i s operated by a v e l o c i t y s e r v o . The speed of the motor can be changed c o n t i n u o u s l y from zero to s e v e r a l thousand rpm. The t y p i c a l speed range i s from 6 to 20 rpm. A f l y b a c k speed i s a l s o p rovided f o r r e t u r n i n g the moving m i r r o r to the s t a r t i n g p o s i t i o n r a p i d l y . The path d i f f e r e n c e i n the i n t e r f e r o m e t e r i s monitored by means of monochromatic f r i n g e s produced by the l i g h t of a h i g h l y s t a b i l i z e d s i n g l e mode He-Ne l a s e r . The f r i n g e s are FIGURE 7 Diagram of the f i n e alignment mechanism of the i n t e r f e r o m e t e r f i x e d m i r r o r . Only-one i s shown. There are f o u r of them (two f o r each f i x e d m i r r o r ) . NOT TO SCALE -20-converted to a t r a i n of pulses which command the A-D conver-t e r used to d i g i t i z e d the i n f r a r e d i n t e r f e r o g r a m . The alignment procedure of the i n t e r f e r o m e t e r has been improved by i n t r o d u c i n g o p t i c s to d i v i d e the l a s e r output i n t o two beams ( F i g u r e 8 ) . One of them enters i n t o the i n t e r -f e r o meter as a c o l l i m a t e d (plane wave) beam. The i n t e r f e r e n c e p a t t e r n produced by t h i s beam a t the plane of the e x i t c o l l i -mator i s used to check the p a r a l l e l n e s s of the wave f r o n t s from the two arms of the i n t e r f e r o m e t e r . The o t h e r beam (the o r i g i n a l narrow beam from the l a s e r ) i s passed through the i n t e r f e r o m e t e r and the i n t e r f e r e n c e p a t t e r n due to t h i s beam a t the plane of the e x i t c o l l i m a t o r i s used to check on the shear between the two arms of the i n t e r f e r o m e t e r . The l o c a t i o n of the zero path d i f f e r e n c e c o n d i t i o n (ZPD) i s important f o r the a n a l y s i s o f the i n t e r f e r o g r a m s . When the spec-t r a l band under study i s narrow, the ZPD p o s i t i o n (peak of the i n t e r f e r o g r a m ) may not be obvious. T h i s problem has been s o l v e d by d e t e c t i n g the i n f r a r e d r a d i a t i o n from the second e x i t of the instrument ( l a s e r e n t r a n c e ) . The i n t e r f e r o g r a m from t h i s e x i t (white l i g h t i n t e r f e r o g r a m ) has a v e r y sharp peak. When ZPD occurs t h i s peak i s used to t r i g g e r and stop a samples counter. U n f o r t u n a t e l y the t r i g g e r i n g system was not f a s t enough and a band pass f i l t e r had to be i n t r o d u c e d to "extend" the ZPD r e g i o n so t h a t our e l e c t r o n i c s see i t . Consequently, the ZPD occurrence was not detected w i t h i n one FIGURE 8 I l l u m i n a t i o n o f t h e i n t e r f e r o m e t e r by t h e l a s e r f o r a l i g n m e n t p u r p o s e s 22 sample as i n p r i n c i p l e i t should be, and oth e r means ( l a t e r e x p l a i n e d ) were used f o r the l o c a t i o n of ZPD. 2.6. The Frequency S y n t h e t l z e r The r a d i a t i o n f a l l i n g on the d e t e c t o r should be r e s t r i c t -ed to s m a l l wavelength bands around the s p e c t r a l f e a t u r e s of i n t e r e s t so t h a t i t i s not loaded with l a r g e s i g n a l s of no i n t e r e s t . I t i s mainly f o r t h i s reason t h a t an o p t i c a l f i l t e r t r a n s m i t t i n g only v e r y narrow bands around the a b s o r p t i o n l i n e s under study i s used. This o p t i c a l f i l t e r t h a t we c a l l frequency s y n t h e t i z e r was used p r e v i o u s l y by H.L. B u i j s (1969) from whom I quote a s m a l l d e s c r i p t i o n and schematic diagrams: "The r a d i a t i o n i s r e s t r i c t e d to narrow bands centered a t the v a r i o u s a b s o r p t i o n f r e q u e n c i e s by means of an o p t i c a l frequency s y n t h e t i z e r which i s shown s c h e m a t i c a l l y i n F i g u r e 9. The ins t r u m e n t c o n s i s t s of a g r a t i n g spectrometer i n which the d i f f r a c t e d rays i n the " e x i t p l a n e " a re s e l e c t i v e l y r e f l e c t e d back to the entrance s l i t by means of a mask and a s e t of s m a l l s p h e r i c a l m i r r o r s . ( M i r r o r s are s p h e r i c a l i n order to image the c o l l i m a t o r each on i t s e l f . ) The incoming and out-g o i n g rays may be separated i n f r o n t of the entrance s l i t w i t h a beam s p l i t t e r , but here i t was more convenient to make an a n g u l a r s e p a r a t i o n of the two l i g h t beams, u s i n g d i f f e r e n t p a r t s of the g r a t i n g f o r the incoming and outgoing r a y s . With a 600 C/m m d i f f r a c t i o n g r a t i n g , 10 cm h i g h x 13 cm wide, and an entrance a p e r t u r e of 3 x 3 ami, the s y n t h e t i z e r has a l i g h t FIGUHB 9 The f r e q u e n c y s y n t h e t i z e r -24-g a t h e r i n g power compatible w i t h the i n t e r f e r o m e t e r . " In our case the s e l e c t e d s p e c t r a l windows are shown i n F i g u r e 10. 2.7. The Detectors The i n f r a r e d d e t e c t o r was a B3 type (area 1 .5 x 1.5 mm2) manufactured by I n f r a r e d I n d u s t r i e s Inc. operated a t room temperature. The b i a s i n g was done as p r e s c r i b e d by the manu-f a c t u r e r f o r an optimum s i g n a l to n o i s e r a t i o and s t a b i l i t y . The e l e c t r i c a l s i g n a l from the d e t e c t o r was a m p l i f i e d by a PAR CR-4 low n o i s e p r e a m p l i f i e r . The frequency of the e l e c -t r i c a l s i g n a l s of the i n t e r f e r o g r a m l i e s around 50 cps, t h e r e -f o r e no l i g h t chopping was r e q u i r e d . The band pass f i l t e r o f the a m p l i f i e r was s e t to a low cut o f f of 1 cps and a h i g h frequency h a l f power p o i n t of 100 cps. Phase s h i f t d i f f e r e n c e s w i t h i n t h i s band were not measurable when l o o k i n g a t the L i s a j o u s f i g u r e g i v e n by an i n p u t s i g n a l and the a m p l i -f i e d output. This i s important i n order to get a c o n s t a n t sampling i n t e r v a l . The r.m.s. n o i s e of the d e t e c t o r p l u s the e l e c t r o n i c s was about 1/4000 times the s i g n a l v a l u e a t ZPD. The l a s e r d e t e c t o r was a p h o t o m u l t i p l i e r and the ampli-f i e r a wideband Hewlett Packard a m p l i f i e r . The ZPD d e t e c t o r was a type T PbS manufactured by I n f r a r e d I n d u s t r i e s and the a m p l i f i e r was a FET O p e r a t i o n a l A m p l i f i e r from Burr-Brown. 2.8. The Gas Sample and Gas Handling FIGURE HO p e c t r a l vfiadows o f r a d i a t i o n f a l l i n g on t h e d e t e c t o r R ( 0 ) RO) R(2) R(3) Rp) 3 7 0 0 38OO 3 9 0 0 4000 4100 1 l -26-The HD gas was purchased from S t o h l e r Isotope Chemicals. The quoted p u r i t y was b e t t e r than 99%- Only 15 l i t e r s of gas (1 Atm) were purchased. This proved to be more than enough f o r our o b s e r v a t i o n s . The HD was t r a n s f e r e d to the c e l l by condensing i t i n t o a s m a l l g l a s s c o n t a i n e r cooled w i t h l i q u i d helium ( F i g u r e 11) and l e t t i n g i t evaporate to the c e l l . This method allowed us to use a l l the gas i n the f l a s k s and a t the same time p u r i f y i t to a h i g h degree by d i s t i l l a t i o n . 2.9. Data C o l l e c t i o n The data c o l l e c t i o n system has a l r e a d y been d i s c u s s e d by H.L. B u i j s (1969) and the d e s c r i p t i o n w i l l not be repeated here. Only a s m a l l p a r t of i t has been m o d i f i e d , t h a t i s the sampling frequency. O r i g i n a l l y there were p r o v i s i o n s f o r a sampling frequency equal to t h a t of the l a s e r or h a l f of i t . I f the f i r s t sampling frequency was chosen, one experiment (100 cm path d i f f e r e n c e ) would have r e q u i r e d c l o s e to 1.6 x 10^ p o i n t s and even the l o n g e s t magnetic tape a v a i l a b l e would not laave been enough to s t o r e a l l the data. (ttote t h a t the l o g i c a l and p h y s i c a l r e c o r d i n the data c o l l e c t i o n system i s o n l y 100 bytes long.) I f the second sampling f r e q u e n c y was chosen, the recovered spectrum from the sampled i n t e r f e r o g r a m would have had o v e r l a p p i n g a l i a s e s ( r e p e t i t i o n of s p e c t r a ) . T h e r e f o r e , to sample every t h r e e l a s e r f r i n g e s was decided to be the most convenient a l t e r n a t i v e . ( I t o n l y r e q u i r e d the a d d i t i o n of another F l i p -FIGURE 1 1 Gas h a n d l i n g diagram TO CELL TO VACUUM SYSTEM i t-c\t i TO MANOMETER LIQUID HELIUM LIQUID NITROGEN LIQUID ED HD GAS - 2 8 -F l o p , a diode and a c a p a c i t o r to the e x i s t i n g c i r c u i t . ) F i g u r e 13 shows the used sampling frequency and the r e l a t i v e p o s i t i o n of the r e a l and r e f l e c t e d spectrum. The s c a n n i n g speed was s e t so t h a t the number of samples per second d i d not exceed 100, a l i m i t imposed by the data a c q u i s i t i o n system. 2.10. Data A n a l y s i s spectrum, r e s p e c t i v e l y , then they are r e l a t e d by the e q u a t i o n : In an experiment, the i n t e r f e r o g r a m i s known onl y to a maxi-mum path d i f f e r e n c e L. Furthermore, i t i s known o n l y a t a and h a f i x e d s t e p . In p r a c t i c e , the spectrum i s hence d e f i n e d by the e x p r e s s i o n I f I( fT ) and B( o~ ) are the i n t e r f erogram and the power CO f i n i t e s e t of e q u i - d i s t a n t p o i n t s , <f = nh, n an i n t e g e r , nz~N n-.i I t may be shown t h a t 3 ( a ) and B ' ( c r ) c o i n c i d e i n the r e g i o n 0^°~^ p r o v i d e d t h a t the st e p h i s l e s s than one h a l f the r e c i p r o c a l of the maximum frequency i n B ( c r ) . -29-To perform the above a n a l y s i s i t i s c l e a r t h a t the sequence o f measured p o i n t s , I(nh) must s t a r t w i t h a p o i n t a t the o r i -g i n o f the i n t e r f e r o g r a m (ZPD). In an a r b i t r a r y experiment t h i s would not happen except by a c c i d e n t . I t i s thus neces-s a r y to f i r s t i n t e r p o l a t e the measured experimental i n t e r f e r o -gram so t h a t a p o i n t f a l l s a t <f = 0 b e f o r e p e r f o r m i n g the above F o u r i e r sum. The i n t e r p o l a t i o n i s e f f e c t e d by a con-v o l u t i o n o f the i n t e r f erogram w i t h a f i l t e r f u n c t i o n , F( <$ ), whose F o u r i e r Transform i s e s s e n t i a l l y u n i t y i n the u s e f u l r e g i o n of 3(cr), and zero o u t s i d e : 1(1')-- flffj F(J'-S)df zk^L l("k+e.)F(S'-Hk-e.) or ](S"*£)^A£. I(nUe)F(S"-nk) n The e q u a l i t y of the two s i d e s of the above eq u a t i o n may be proved by showing t h a t the F o u r i e r Transforms of the two s i d e s a r e e q u a l . I t may be seen t h a t a p o i n t on I a t ZPD can be c a l c u l a t e d even though the o r i g i n a l i n t e r f e r o g r a m does not c o n t a i n t h i s p o i n t . The e r r o r £ between the n e a r e s t sampling l o c a t i o n to - 3 0 -ZPD and the t r u e ZPD i s not known i n advance but must be found i n some way. The way chosen here was to i n t e r p o l a t e the measured i n t e r f e r o g r a m u s i n g the r e l a t i o n above and p l o t i t , l o o k i n g f o r a maximum. This maximum p o i n t would have been assumed to f a l l a t the true ZPD l o c a t i o n except f o r the f a c t t h a t the i n t e r f e r o g r a m s were not p e r f e c t l y symmetric, as a r e s u l t of i m p e r f e c t adjustment of the i n t e r f e r o m e t e r . This asymmetry was p a r t i a l l y removed l n the f i l t e r i n g process as w e l l , through the use of the f i l t e r f u n c t i o n : The parameter f was chosen by t r i a l and e r r o r so t h a t the f i l t e r e d i n t e r f e r o g r a m was as n e a r l y symmetric as p o s s i b l e . A t y p i c a l i n t e r p o l a t e d i n t e r f e r o g r a m i s shown near the ZPD r e g i o n l n F i g u r e 14. I t should be noted t h a t to c o n s t r u c t the graph t h i r t y p o i n t s have been c a l c u l a t e d between every p a i r e x p e r i m e n t a l points. In F i g u r e 15 i s shown an i n t e r p o l a t e d i n t e r f e r o g r a m i n more d e t a i l , showing the asymmetry near ZPD, and i n F i g u r e 16 the same i n t e r f e r o g r a m i s shown w i t h the optimum ch o i c e of the parameter f . F o l l o w i n g the e v a l u a t i o n of the parameters 6 and f , a f i l t e r e d i n t e r f e r o g r a m was c a l c u l a t e d by c o n v o l v i n g the o r i g i n a l w i t h the f i l t e r f u n c t i o n . This f i l t e r e d l n t e r f e r o -gram was sampled, however, wit h a step h 1 equal to 3h, t h i s b e i n g allowed because the f i l t e r i n g f u n c t i o n p r e c i s e l y d e f i n e s FIGURE 12 B l o c k diagram of data a n a l y s i s -31-EXPERIMENT DIGITAL RECORDING OP 550000 MEASUREMENTS VISUAL INSPECTION. STUDY OP SYMMETRY. INTRODUCTIN OF A PHASE CORRECTION. INTERPOLATION ( x 3 0 ) OP 9 POINTS AROUND ZPD. PAST FOURIER TRANSFORM OF 131072 POINTS . PRINTING OF THESE CREATION AND PLOTTING POINTS. OF A BACK-GROUND SPECTRA. EVALUATION OF THE ABSORPTION OOEFF. EVALUATION 0? THE AREAS UNDER THE LINES TAPS READING. TAPS COPYING INTO A 9 TRACK TAPE AT HIGH DENSITY. PRINTING 0? 4340 POINTS AROUND ZPD. COPY 0? THESE POINTS ON A PILE. INTERPOLATED (3Y 30) INTERF. OF 300 POINTS AROUND ZPD. PLOT OF THIS INTERF. EXACT LOCATION OF ZPD BY INTERPOLATION. INTRODUCTION 0? THE FINAL PHASE SHIFT CORREC NUMERICAL REDUCTION OF POINTS RECORDING FILTERING AND OF THE NUMBER BY 1 / 3 . OF FILTERED INTERFEROGRAM ON TAPE. -32-the frequency band. Consequently the new In t e r f e r o g r a m con-A t a l n e d o n l y o n e - t h i r d o f the number of p o i n t s as the o r i g i n a l . A b l o c k diagram showing the sequence of numerical o p e r a t i o n s i s shown i n F i g u r e 12, and i n F i g u r e 13 i s shown the spectrum a t v a r i o u s stages of the a n a l y s i s . Every experiment was performed to the maximum scanning d i s t a n c e (over 1 m) and the whole i n t e r f e r o g r a m was f i l t e r e d . However, only p a r t of i t was transformed. I t was found that a l i m i t of r e s o l u t i o n of 0.0133 cm" 1, corresp o n d i n g to a maximum path l e n g t h of 37.5 cm, was adequate f o r our purposes as an i n c r e a s e d r e s o l u t i o n d i d not make the l i n e s any more i n t e n s e . In o t h e r words, a t t h i s r e s o l u t i o n the l i n e s were r e s o l v e d . The number of f i l t e r e d p o i n t s used was 65536. The F o u r i e r Transform program used (a r e c e n t v e r s i o n of the Tukey-Cooly F a s t F.T.) produced the t r a n s f o r m of a symmetric p e r i o d i c f u n c t i o n , t h e r e f o r e , the i n t e r f e r o g r a m had to be " f o l d e d " w i t h the l a s t p o i n t being the f i r s t one a f t e r ZPD. This o p e r a t i o n doubled the number of p o i n t s to be transformed. The CPU time used f o r the t r a n s f o r m a t i o n of 131072 p o i n t s was about 100 sec. 2.11. C a l c u l a t i o n o f Frequencies The sampling frequency i s d e r i v e d from the f r i n g e s produced by a h i g h l y s t a b i l i z e d s i n g l e mode He-Ne l a s e r (Spec-t r a - P h y s i c s model 119). This frequency becomes the r e f e r e n c e s t a n d a r d . Frequencies are determined from the computer data FIGURE 13 S p e c t r a l d i s t r i b u t i o n a r i s i n g d u r i n g v a r i o u s s t e p s of the a n a l y s R ( 4 ) R ( 3 ) R(2) INFRARED SIGNAL R(1 R ( 0 ) NSW SAMPLING FREQUENCY ^SPECTRUM GIVEN BY THE COMPUTER PROGRAM . r' 1 t ... ' . 1 1 0 0 0 2 0 0 0 3 0 0 0 4000 5 0 0 0 cm FIGURE 14 T y p i c a l i n t e r p o l a t e d i n t e r f e r o g r a m near the zero path d i f f e r e n c e , p o i n t . The l o c a t i o n of the ex-p e r i m e n t a l p o i n t s i s shown by the s e t of arrows on the a b s c i s s a a x i s . FIGURE 15 S l i g h t l y asymmetric i n t e r f e r o g r a m . -35-ZPD ' 1 FIGURE 16 I n t e r f e r o g r a m of F i g u r e 15 w i t h the asymmetry c o r r e c t e d < -36--37-by t a k i n g the r a t i o of the number corresponding to the machine index i n the output a r r a y of s p e c t r a l p o i n t s (from the zero frequency p o i n t ) a t the c e n t e r of the l i n e to the t o t a l number of p o i n t s d e s c r i b i n g the p r i n c i p a l a l i a s e s and then m u l t i p l y -i n g t h i s r a t i o by the sampling frequency. The e f f e c t i v e sampling i n t e r v a l , h, i s not e x a c t l y equal to t h r e e times the l a s e r wavelength. A number of c o r r e c t i o n s must be i n t r o d u c e d due to a) the f i n i t e dimension of the i n f r a r e d entrance a p e r t u r e , b) i n f r a r e d a p e r t u r e and l a s e r e x i t image misalignment, c) p r e s s u r e i n the vacuum tank. When c o r r e c t i o n s f o r these e f f e c t s are i n t r o d u c e d ( B u i j s , 1969) the sampling i n t e r v a l becomes A= 3 \nc,User (l-fy -4*/i-fSt- Sj), \ v a c . l a s e r = l a s e r wavelength i n vacuum r m = r a d i u s of the I n f r a r e d a p e r t u r e = 1 mm f c = f o c a l l e n g t h of the c o l l i m a t o r = 500 mm = r e f r a c t i v i t y of a i r a t the l a s e r wavelength S I R = r e f r a c t i v i t y of a i r a t the I n f r a r e d wavelength. - Sj£ i s d i r e c t l y p r o p o r t i o n a l to the p r e s s u r e w i t h the p r o p o r t i o n a l i t y c o n s t a n t g i v e n by the c o n d i t i o n s i n standard a i r -38-0.001388. 7 •where ( S L - S I R ^ S ~ 366.8 x 1 0~ 8 ( a t the c e n t e r of the s t u d i e d band) and p Is i n t o r r . In h i s a n a l y s i s B u i j s found the f o l l o w i n g u n c e r t a i n t i e s i n the a b s o l u t e v a l u e of the f r e q u e n c i e s when the instrument was operated a t one atmosphere p r e s s u r e : c r IR VAO. - IR MEA3. x 1 ± 3 x IO" 8 t 6 x 10" 8 t 2 0 x 1 0 - 8 due to l a s e r adjustment due to a p e r t u r e alignment due to Index of a i r v a r i a t i o n In t h i s i n v e s t i g a t i o n experiments have been performed a t a p r e s s u r e of 1 t o r r , hence the major u n c e r t a i n t y i n f r e -quency, due to the index of a i r v a r i a t i o n s (changes i n a t -mospheric p r e s s u r e , r e l a t i v e humidity, e t c . ) has been removed. Consequently the f r e q u e n c i e s are b e l i e v e d to be h i g h l y r e l i a b l e . 3. R e s u l t s and Conclu s i o n s A t o t a l of twelve experiments has been an a l y s e d a t h i g h r e s o l u t i o n . Many other low r e s o l u t i o n experiments were a l s o performed f o r the purpose of c a l i b r a t i o n and t e s t i n g but were not used i n the f i n a l r e s u l t s . In Table I i s shown a summary of the experimental c o n d i t i o n s used. Table I. Experimental c o n d i t i o n s . Path l e n g t h (meters) P r e s s u r e (atmospheres) 18 0.5, 1.0, 1.5 30 0.5, 1.0, 1.5 70 0 , 0.7, 1.6 Runs f o r the c o n d i t i o n s of 3 0 m path, 1.5 atm p r e s s u r e , and 18 m path, 1 atm were done twice f o r purposes of a s s e s s i n g the r e p r o d u c i b i l i t y o f the s p e c t r a . The zero p r e s s u r e con-d i t i o n l i s t e d above was used to t e s t the background s p e c t r a f o r the presence of sharp a b s o r p t i o n l i n e s i n the v i c i n i t y o f the HD l i n e s . In F i g u r e s 17 to 21 are shown r e p r e s e n t a -t i v e a b s o r p t i o n s p e c t r a . These f i g u r e s were drawn by the computer p l o t t e r d i r e c t l y from the F o u r i e r Transform output. The frequency s c a l e was e s t a b l i s h e d from the computer p r i n t e r output i n the manner a l r e a d y d e s c r i b e d and the f r e -quency of a g i v e n a b s o r p t i o n peak was taken as the b i s e c t o r of the a b s o r p t i o n p r o f i l e . There was no evidence o f a pr e s s u r e FIGURE 17 R e p r e s e n t a t i v e a b s o r p t i o n s p e c t r a of the R branch FREQUENCY CM" FIGURE 18 A b s o r p t i o n spectrum of the R(0) l i n e f o r s i x d i f f e r e n t c o n d i t i o n s -41-FREQUENCY cm" FIGURE 19 A b s o r p t i o n spectrum of the R(1) l i n e f o r the same c o n d i t i o n s as i n F i g u r e 18 FIGURE 20 A b s o r p t i o n spectrum of the R(3) l i n e r the same c o n d i t i o n s as i n F i g u r e 18 FIGURE 21 A b s o r p t i o n spectrum of the R(4) l i n e f o r the same c o n d i t i o n s as i n F i g u r e 18 - 4 5 -s h i f t i n the l i n e f r e q u e n c i e s over the s m a l l range of pr e s s u r e s used (0.54 to 1.64 Amagat). In the case of H 2» measurements by Pink et a l (1965) and B u i j s and Gush (1971) show t h a t a p r e s s u r e s h i f t of about 0.002 cm"1 would be expected f o r t h i s change i n p r e s s u r e . A s h i f t of t h i s magnitude (r o u g h l y one t e n t h the l i n e width) would have been n o t i c e a b l e i n these experiments had i t been p r e s e n t . Apparently the dependence of frequency on p r e s s u r e i s l e s s marked i n HD than i n H 2. A resume of the f r e q u e n c i e s obtained from the s p e c t r a shorn i n F i g u r e s 17 to 21 i s g i v e n i n Table I I . * Table I I . F r e q u e n c i e s . L i n e T h i s work Durle and Herzberg R(0) 3717.520 3717.527 R ( D 3793.444 3798.471 R(2) 3874.481 3874,374 R(3) 3944.710 3944.718 R(4) 4009.079 4009.096 The f r e q u e n c i e s obtained here agree v e r y w e l l w i t h those of Durie and Herzberg except f o r the R(2) l i n e which i s par-t i a l l y obscured by a v e r y s t r o n g water vapour f e a t u r e . This water vapour i s an i m p u r i t y i n the HD and not water vapour i n the i n t e r f e r o m e t e r (which was evacuated). In t h e i r paper Durie and Herzberg p o i n t out t h a t t h e i r frequency f o r the * 0 n l y the R-branch was s u c c e s s f u l l y measured. I t turned out to be d i f f i c u l t to a d j u s t the frequency s y n t h e t i z e r f o r the P-branch and the s i g n a l was too weak to be u s e f u l i n t h i s f requency r e g i o n . -46-R(2) l i n e i s not v e r y c e r t a i n , because of the presence of the water l i n e . In our case, i n one experiment, the water vapour l i n e was not too s t r o n g and i t was p o s s i b l e to c l e a r l y d i s t i n g u i s h the HD f e a t u r e ( F i g u r e 17). We hence b e l i e v e t h a t the f r e -quency quoted i s r e l i a b l e . The f r e q u e n c i e s quoted above are b e l i e v e d more p r e c i s e than those p r e v i o u s l y obtained and c o u l d be used to improve the m o l e c u l a r c o n s t a n t s . T h i s , however, i s not attempted here, s i n c e to do t h i s i t would be n e c e s s a r y to have f r e q u e n c i e s f o r the overtone s p e c t r a which have not a t t h i s time been remeasured. The a b s o r p t i o n c o e f f i c i e n t has been c a l c u l a t e d from the measured s p e c t r a . T h i s i s d e f i n e d , as u s u a l , by A (<r) = (ft)" lo^ (I «r)/I «rj) where f 3 i s the gas d e n s i t y , & i s the path l e n g t h , / i s the background spectrum and 1M i s the spectrum of the gas. As background spectrum over the r e g i o n of the HD l i n e s a s t r a i g h t l i n e was used which was judged by eye to be a reas o n a b l e c h o i c e . The i n f i n i t e a b s o r p t i o n l i n e i n some cases i was somewhat u n c e r t a i n . T h i s i s because a s l i g h t phase e r r o r i n the F o u r i e r A n a l y s i s , or a s m a l l n o n - l i n e a r i t y i n the e l e c t r o n i c system can s h i f t the p o s i t i o n of the t r u e zero i n t e n s i t y l e v e l i n the f i n a l spectrum. F o r t u n a t e l y , f o r most o f the HD f e a t u r e s t h e r e was a near-by i n t e n s e water vapour FIGURE 22 T y p i c a l a b s o r p t i o n c o e f f i c i e n t -47--48-l i n e the c e n t e r of which c o u l d be taken as f u l l y absorbed. The bottom of the water l i n e s was hence used as the i n f i n i t e a b s o r p t i o n l e v e l . This d i d not d i f f e r s u b s t a n t i a l l y from the zero i n the computed spectrum. T y p i c a l examples of the a b s o r p t i o n c o e f f i c i e n t are shown i n F i g u r e 22. I f the i n t e n s i t i e s of the l i n e s w i t h i n the band were to be s t r i c t l y g i v e n by the thermal d i s t r i b u t i o n of the r o t a t i o n a l l e v e l s , one would have expected an i n t e n -s i t y d i s t r i b u t i o n as i n F i g u r e 23a. The experimental d i s t r i -b u t i o n i s , however, as i n F i g u r e 23b. From these a b s o r p t i o n p r o f i l e s the l i n e width a t h a l f I n t e n s i t y was measured; i t equals 0.025 cm"1 f o r the R(1) l i n e . The o t h e r l i n e s have e s s e n t i a l l y the same width. I t i s i n t e r e s t i n g to note t h a t there was no evidence of a depen-dence of the l i n e width on p r e s s u r e . This dependence i s q u i t e marked i n the case of H 2 » ( B u i j s and Gush, 1971 ) which shows c o l l i s i o n a l l i n e narrowing i n t h i s p r e s s u r e range. The width o f the HD l i n e s i s v e r y n e a r l y equal to the f u l l Doppler width, where m mass of molecule T a b s o l u t e temperature frequency of the l i n e i n cm' -1 For the R ( l ) l i n e , w = 0.026. I t i s c l e a r t h a t i n the case FIGURE 23 Relat ive i n t e n s i t i e s -49--50-of HD c o l l i s i o n a l narrowing does not occur a t l e a s t i n the pr e s s u r e r e g i o n i n v e s t i g a t e d here. The i n t e g r a t e d a b s o r p t i o n c o e f f i c i e n t , <x ~ J A (T) *L<r t f o r each l i n e was evaluated f o r a l l the experiments. In Table I I I i s shown the c o l l e c t e d r e s u l t s . For any g i v e n f e a -t u r e there i s a c o n s i d e r a b l e s c a t t e r In the a b s o r p t i o n co-e f f i c i e n t . However, there does not appear to be any s y s t e -matic dependence on e i t h e r path l e n g t h or p r e s s u r e , and the s c a t t e r i s assumed to a r i s e from n o i s e i n the s p e c t r a l a n a l y s i s . From the i n t e g r a t e d i n t e n s i t y of the a b s o r p t i o n f e a t u r e s the m a t r i x element of the d i p o l e moment of HD can be deduced. The c o n n e c t i o n between the i n t e n s i t y and the d i p o l e moment i s g i v e n i n the f o l l o w i n g formula ( T r e f l e r and Gush, 1968) where (T0 Q U - m a t r i x element of the d i p o l e moment between the / z e r o t h and f i r s t v i b r a t i o n a l s t a t e s . = c e n t e r of the t r a n s i t i o n l i n e = Loschmidt's number = r o t a t i o n a l s t a t e sum - (-ZJ+/)<3 J-The m a t r i x elements of the d i p o l e moment thus deduced are shown i n Table I I I . The s m a l l v a l u e f o r the d i p o l e moment -51-Table I I I . Integrated absorption c o e f f i c i e n t s and dipole moment* LINE PRESSURE mm. Hg PATH m. -1 cm. 120.3 30 1.43x10 - 9 120.3 18 1 .55 76.3 30 0.32 76.3 18 1 .94 33.5 30 1 .05 38.5 18 1 .70 MEAN ex' cm. ~ 1 Debye R(0) 1.49X10-9 4.15x10-5 H(1) 120.3 120.3 76.3 76.3 33.5 38.5 30 18 30 18 30 18 Inf.abs. it 2.69x10-9 6.30 5.01 7.18 5.13X10 - 9 6.63x10-5 R(2) 76.2 70 2.34x10- 1 0 2.84X10" 1 0 1.96xl0" 5 R(3) 120.3 30 2.03x10 120.3 18 1 .33 76.3 30 1 .41 76.3 18 1 .41 33.5 30 0.96 38.5 18 0.45 -9 1.40x10 -9 7.06x10 -5 R(4) 120.3 30 5.22x10 120.3 18 4.62 76.3 30 2.82 76.3 18 5.60 38.5 30 4.03 38.5 18 1.11 4.73x1 O"*10 8.42x10-5 -52-deduced from the R(2) l i n e may be ex p l a i n e d by the f a c t t h a t t h i s l i n e was measured only once, and on the shoulder o f a s t r o n g H 20 f e a t u r e . I t should hence not be taken s e r i o u s l y . I t should be noted t h a t the trend of the d i p o l e moment "to have a h i g h e r v a l u e w i t h h i g h e r J i s j u s t the same as t h a t observed i n the pure r o t a t i o n a l band of H D . ( T r e f l e r and Gush, 1968). Of course, i n a molecule such as HOI which possesses a permanent d i p o l e moment the d i p o l e moment should be e s s e n t i a l -l y independent of J v a l u e . U n t i l r e c e n t l y , a p a r t from Wlch's p r e l i m i n a r y work, there have been no t h e o r e t i c a l p r e d i c t i o n s of the matrix elements o f the d i p o l e moment i n HD between the z e r o t h and f i r s t v i b r a -t i o n a l l e v e l s , a lthough some work has been p u b l i s h e d on the d i p o l e moment i n the ground v i b r a t i o n a l s t a t e ( B l i n d e r , Wol-n l e w i c z ) . However, J.D. P o l l and G. K a r l (unpublished) by a m o d i f i c a t i o n of the theory of B l i n d e r , and by u s i n g machine c a l c u l a t e d wave f u n c t i o n s f o r HD, have estimated the mat r i x element of the d i p o l e moment to be 0.8 x \0~^ debye. This i s i n r e a s o n a b l y good agreement with Wich's p r e d i c t i o n and our new e x p e r i m e n t a l l y measured v a l u e s . I t would thus appear t h a t the simple theory o f B l i n d e r d e s c r i b e s the HD molecule r a t h e r w e l l s i n c e i t p r e d i c t s c o r r e c t l y both the d i p o l e moment i n the ground s t a t e and the f i r s t e x c i t e d v i b r a t i o n a l s t a t e . E x t e n s i o n of t h i s work to Include the overtone bands i s planned and p r e l i m i n a r y measurements of the v=0 to v=2 band -53-have been made. These measurements w i l l permit not o n l y the d i p o l e moment to be evaluated but a l s o more p r e c i s e f r e q u e n c i e s , which w i l l permit a r e - e v a l u a t i o n of the molecular c o n s t a n t s . I t would a l s o be of some i n t e r e s t to examine the spectrum of molecules such as 0 1^0 1^, o c c u r r i n g In n a t u r a l oxygen which sh o u l d e x h i b i t a s i m i l a r type of a b s o r p t i o n . The spectrum i n the frequency r e g i o n of the Q-branch of HD was examined i n two of the l o n g e s t path l e n g t h experiments i n the hope t h a t the quadrupole spectrum would be r e v e a l e d . No d e f i n i t e a b s o r p t i o n f e a t u r e s were found. In the case of hydro-gen, the quadrupole spectrum can be seen a t t h i s path l e n g t h ( B u i j s and Gush, 1971). Since the quadrupole moments of H 2 and HD would be expected to be s i m i l a r , the reason f o r our f a i l u r e to see the HD quadrupole spectrum must be a t t r i b u t e d to the f a c t t h a t the l i n e width i s s u b s t a n t i a l l y g r e a t e r than f o r H«. - 5 4 -BIBLIOGRAPHY BLINDER, Si.M. i 9 6 0 . J . Chem. Phys. 32, 1 0 5 , 582. BUIJ3, H.L. and GUSH, H.P. 1 9 6 7 . J . de Physique, 28, C2 - 1 0 5 - " ~~ BUIJS, H.L. 1969 Ph.D. T h e s i s , U n i v e r s i t y of B r i t i s h Colum-b i a , Vancouver, B r i t i s h Columbia BUIJS, H.L. and GUSH, H.P. 1971. Can. J . Phys. 49, 2 3 6 6 DURIE, R.A. and HERZBERG, G. 1960. Can. J . Phys. ^8, 806 PINK, U., WIGGINS, T.A. and RANK, D.H. 19 6 5 . J . Mol. Spe c t r y . \8, 384 HERZBERG, G. 1950. Nature \66, 5 6 3 K0L03, K. and WOLNISWICZ, L. 1966. J . Chem. Phys. 4J5, 9 4 4 TREPLER, M. and GUSH, H.P. 1968. Phys. Rev. L e t t e r s , 20, 7 0 3 VANAS3E, G.A. and SAKAI, H. 1967. Progress i n O p t i c s , 6, chapter 7 WHITE, J.U. 1948. J . Opt. Soc. Amer. 3 2 , 2 8 5 WICK, G.C. 1935. A t t i Reale Accad. L i n c e i 21, 708 

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