Mass Spectrometry in Inorganic Chemistry

6 Shock Tube Study of a D -Ne Mixture 2

From 900°-2300°K. I. D . GAY and R. D .

KERN

1

2

Downloaded by UNIV LAVAL on June 12, 2014 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0072.ch006

Gibbs C h e m i c a l Laboratory, H a r v a r d University, Cambridge, Mass.

A theoretical by electron lated. pling

prediction impact

This prediction a shock

tube

was studied

over

the

data were represented were analyzed posed of a D

+

tron impact bution

2

pressure

dependent

It is shown

experimentally mass

to D ,

D +,

900-2300°K.

and

2

D /D +

by a plot of log

+

that the

2

D

+

vs.

energy reactions

which and

D+ 3

by

had a Boltzmann a D

occurring

that the latter contribution

+

contribution in the is

were The

1/T

peak was

from the fragmentation

molecules

cou-

spectrometer.

range

+

formuby

attributed

by considering

of D

deuterium is

temperature

contribution

of vibrational

of

of temperature

to a time-of-flight

The mass peak heights measured

of the fragmentation

as a function

ion

and comelecdistrifrom

source.

dominant.

T n v i e w of recent interest i n the r o l e of v i b r a t i o n a l l y e x c i t e d species i n h i g h t e m p e r a t u r e gas reactions ( I , 6 ) , i t w o u l d b e d e s i r a b l e t o h a v e a means of m o n i t o r i n g v i b r a t i o n a l e x c i t a t i o n d u r i n g s u c h reactions.

Since

a flexible a p p a r a t u s for h i g h t e m p e r a t u r e k i n e t i c studies is the shock t u b e c o u p l e d to a time-of-flight mass spectrometer

( 5 ) , a n a t t e m p t has b e e n

m a d e to d e t e r m i n e w h e t h e r v i b r a t i o n a l e x c i t a t i o n c a n b e o b s e r v e d w i t h this a p p a r a t u s . It is w e l l k n o w n that the mass s p e c t r o m e t r i c i o n f r a g m e n t a t i o n p a t t e r n of m o l e c u l e s varies w i t h t e m p e r a t u r e , a n d at least p a r t of this v a r i a i o n is a t t r i b u t a b l e to v i b r a t i o n a l e x c i t a t i o n . I n the s i m p l e case of H

2

and

its isotopes, the f r a g m e n t a t i o n p a t t e r n has b e e n successfully p r e d i c t e d b y a s s u m i n g the i o n i z a t i o n process ( for e l e c t r o n energies less t h a n 30 volts ) to b e a s i m p l e F r a n c k - C o n d o n t r a n s i t i o n f r o m t h e g r o u n d state of H Present address: Simon Fraser University, Burnaby, British Columbia, Canada. -'Present address: Louisiana State University in New Orleans, New Orelans, L a . 1

83

In Mass Spectrometry in Inorganic Chemistry; Margrave, J.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

2

to

84

MASS SPECTROMETRY I N INORGANIC

the g r o u n d state of H

(12).

+

2

CHEMISTRY

These calculations have been i m p r o v e d b y

C a s h i o n (2) w h o has also c a l c u l a t e d t h e f r a g m e n t a t i o n p a t t e r n e x p e c t e d f r o m t h e h y d r o g e n isotopes i n v i b r a t i o n a l states other t h a n ν exists a t h e o r e t i c a l p r e d i c t i o n of t h e v a r i a n c e of H / H +

+

2

0. T h e r e

as a f u n c t i o n of

t e m p e r a t u r e w h i c h m a y b e tested e x p e r i m e n t a l l y . W e chose t o d o t h e experiments u s i n g D

rather t h a n H

2

2

since t h e

o b s e r v a t i o n o f masses 2 a n d 4 w a s easier t h a n masses 1 a n d 2. W h i l e t h e c a l c u l a t e d f r a g m e n t a t i o n r a t i o is s m a l l (6.96 X 1 0 " at 3 0 0 ° K . a n d 1.29 3

Χ 1 0 " at 2 4 0 0 ° K . ) , i t increases b y a factor of 1.77 over t h e t e m p e r a t u r e 2

range 1000° to 2400°K., a n d i t w a s t h o u g h t that this change w o u l d b e detectable.

T h e r e is n o interest i n w o r k i n g b e l o w


p o p u l a t i o n o f v i b r a t i o n a l levels greater t h a n ν =

1000°K. since t h e

0 is too s m a l l to cause

a significant c h a n g e i n f r a g m e n t a t i o n r a t i o . It is d e s i r a b l e t o w o r k b e l o w 2400°K. i n o r d e r t o p r e v e n t a n y c o n t r i b u t i o n f r o m t h e t h e r m a l d e c o m p o s i t i o n of D

a n d subsequent i o n i z a t i o n of D atoms.

2

P o s s i b l e effects o f

v i b r a t i o n a l r e l a x a t i o n of D w i l l b e discussed. 2

Theory O n e of t h e e a r l y p r e d i c t i o n s of t h e F r a n c k - C o n d o n p r i n c i p l e w a s that t h e r a t i o of H / H +

2

s h o u l d b e greater t h a n D / D

+

+

ions arise e x c l u s i v e l y f r o m d i s s o c i a t i o n of t h e X 2

+

g

2

+

w h e n the atomic

state o f H

2

+

. This pre

d i c t i o n has b e e n c o n f i r m e d e x p e r i m e n t a l l y , a n d t h e t h e o r e t i c a l m a g n i t u d e of t h e ratios has b e e n c a l c u l a t e d a n d c o m p a r e d f a v o r a b l y w i t h e x p e r i m e n t (2, 14).

A t r o o m t e m p e r a t u r e , t h e f r a c t i o n of H is c a l c u l a t e d f r o m +

the e q u a t i o n Γ

(

t^(r)

v

=

dr

(1)

Q

%t 0

where

r

c

=

finite

i n t e r n u c l e a r d i s t a n c e at w h i c h d i s s o c i a t i o n of H

2

+

i n t o H a n d Η occurs +

φ(τ)

= t =

radial wave function for H m u l t i p l i e d b y r 2

t r a n s i t i o n p r o b a b i l i t y operator w h i c h is l i n e a r l y r e l a t e d t o the excess energy of t h e i o n i z i n g electrons

T o c a l c u l a t e t h e a m o u n t of H

+

(12).

p r o d u c e d f r o m h i g h e r v i b r a t i o n a l levels,

w e use t h e e q u a t i o n

fu

+

= J ] / „ = * yj i= ο

where

i = fv

=

= i dr

t * (r) 2

v

(2)

°

vibrational quantum number

i — B o l t z m a n n population of the i

th

l e v e l at t e m p e r a t u r e T.



6.

GAY A N D K E R N

Shock Tube

2I

1

1

3

5

7

1 9

3000

Study

85

1

1

1

1

1

1

I

I

I

I

I

11

13

15

17

19

21

23

25

27

29

31

1000

500 \

X

I 33

300

10

4

'5

Figure 1. (a)—Theoretical D /D ratio without excess energy correction, (b)—Curve a corrected for 30 e.v. ionizing energy, (c)—Curve b displaced in order to pass through room tempera ture experimental ratios. Δ—Experimental ratios obtained under shock conditions using a 4-mil diameter nozzle. Ο—Same as A except use of a 6-mil diameter nozzle. (d),(e)—Curve c displaced in order to pass through the zero thermal effect points of the 4- and 6-mil data, respectively +

T h e f r a c t i o n of H

2

+

2

is o b t a i n e d b y s u b t r a c t i n g the r i g h t h a n d side of

+

E q u a t i o n 2 f r o m u n i t y . T h e r a t i o of H

+

to H

2

+

is t h e n f o r m e d , a n d it is

a f u n c t i o n of t e m p e r a t u r e o n l y , p r o v i d i n g the e l e c t r o n e n e r g y is h e l d constant.

The D / D +

2

+

r a t i o is c a l c u l a t e d i n exactly the same w a y u s i n g

the a p p r o p r i a t e w a v e f u n c t i o n a n d m o l e c u l a r parameters. E q u a t i o n 2 w a s e v a l u a t e d ( 2 ) u s i n g the eigenfunctions o b t a i n e d b y n u m e r i c a l s o l u t i o n of the r a d i a l w a v e e q u a t i o n u s i n g the a c c u r a t e a d i a b a t i c h y d r o g e n p o t e n t i a l of K o l o s a n d W o l n o w i e c z ( 9 ) .

T h e assumptions

i n v o l v e d i n this c a l c u l a t i o n are that F r a n c k - C o n d o n t y p e transitions t a k e


86


place from D ( % ) 2

to D

+

2

+

(% ), +

t

n

a

t

D

+

arises o n l y f r o m those

m o l e c u l e s w h o s e i n t e r n u c l e a r distance is less t h a n r f r o m h i g h e r e l e c t r o n i c states of D

2

+

CHEMISTRY

D

2

a n d that dissociation

0

is n e g l i g i b l e w h e n the i o n i z i n g elec-

t r o n energy does not exceed 30 e. v. T h e results of t h e c a l c u l a t i o n for v a r i o u s temperatures are s h o w n b y curves a a n d b of F i g u r e 1. C u r v e a was

calculated from

E q u a t i o n 2 w i t h o u t the

transition probability

o p e r a t o r t. C u r v e b shows the effect of i n c l u d i n g t for 30 e. v. electrons. C a l c u l a t i o n s of the D / D +

2

+

r a t i o w e r e m a d e also as a f u n c t i o n of the

e n e r g y of t h e i o n i z i n g electrons.

T h e results of these c a l c u l a t i o n s s h o w

that a n e l e c t r o n e n e r g y s p r e a d of 2 e. v. affects the r a t i o b y o n l y

1.5%.


Experimental E x p e r i m e n t s w e r e d o n e o n a 1 0 % m i x t u r e of D i n N e . B o t h gases w e r e o b t a i n e d f r o m the M a t h i e s o n C o . , the n e o n b e i n g research grade a n d t h e d e u t e r i u m C P . grade. 2

MASS SPECTROMETER SHOCK TUBE VELOCITY GAUGE

V I AMPLIFIER I

SPECTRUM

TRIGGER

9

Q

JDELAYl

RAMP GENERATOR

MONOSTABLE MULTI

RAMP

MULTI

1

(GÂTÉ}-

h h TO THIRD

AND

FOURTH SCOPES

L_t CA

531 A

Figure 2.

CA

531 A

Data collection

system

T h e experiments w e r e p e r f o r m e d w i t h the i m p r o v e d a p p a r a t u s d e s c r i b e d b y G a y et al ( 6 ) . A m o d i f i c a t i o n of the d a t a r e c o r d i n g m e t h o d w a s necessary because of the s m a l l size of the D peak. T h e d a t a w e r e r e c o r d e d o n t w o p a i r s of oscilloscopes, e a c h p a i r h a v i n g a g a i n r a t i o of 10 o r 20. T h e scopes of e a c h p a i r w e r e c o n n e c t e d i n p a r a l l e l , the D p e a k b e i n g m e a s u r e d o n the h i g h e r g a i n m e m b e r of e a c h p a i r , a n d the D p e a k o n the l o w e r g a i n scopes. S e v e n spectra w e r e r e c o r d e d o n e a c h p a i r of scopes, at i n t e r v a l s of 30 /Asec, thus c o v e r i n g a test t i m e of a b o u t +

+

2

+


6.

GAY A N D K E R N

87

Shock Tube Study

420 /xsec. T h e d a t a r e c o r d i n g system is s h o w n d i a g r a m m a t i c a l l y i n F i g u r e 2. S p e c t r a f r o m the first t w o scopes are p r e s e n t e d i n F i g u r e 3; the presence of D i n a n a m o u n t a b o u t e q u a l to D w a s s o m e w h a t s u r p r i s i n g . T h e p e a k at mass 3 is the H D i m p u r i t y present i n the d e u t e r i u m used.


3

+

+

I n i t i a l l y , t w o sets of experiments w e r e p e r f o r m e d . O n e set u t i l i z e d a 6 - m i l d i a m e t e r h o l e i n the n o z z l e , a + 1 . 5 v o l t bias o n a g r i d 1 m m . f r o m the n o z z l e , a n d + 7 . 5 v o l t bias o n the i o n - a c c e l e r a t i n g g r i d . T h e s e c o n d set of experiments u s e d a 4 - m i l d i a m e t e r n o z z l e , the a f o r e m e n t i o n e d grids at g r o u n d p o t e n t i a l , a n d a n a d d i t i o n a l g r i d b i a s e d at —700 volts w h i c h w a s p l a c e d b e t w e e n the i o n - a c c e l e r a t i n g g r i d a n d the d r i f t t u b e entrance g r i d . M o l y b d e n u m w a s i n s t a l l e d as the g r i d m a t e r i a l for the s e c o n d set, r e s u l t i n g i n i n c r e a s e d s e n s i t i v i t y a n d decreased statistical fluctuations. T h e s h o c k e d gas flowed t h r o u g h a d i v e r g e n t n o z z l e i n t o the i o n i z a t i o n r e g i o n , a distance of some 3 m m . w i t h a transit t i m e o n the order of 3 ftsec. A n i o n i z i n g electron energy of 30 volts was used. T h e p e a k heights of D , Ό \ a n d D . w e r e m e a s u r e d f r o m the P o l a r o i d p i c t u r e s . T h e D/ peak was r e a s o n a b l y constant d u r i n g a n e x p e r i m e n t , w h i l e the D a n d D . peaks w e r e subject to c o n s i d e r a b l e statistical fluctuation. A v e r a g e values of the D V D / a n d Ό /Ό ratios w e r e m e a s u r e d as a f u n c t i o n of t e m p e r a t u r e , w h i c h was d e t e r m i n e d f r o m measurements of the i n c i d e n t shock v e l o c i t y . T h e e x p e r i m e n t a l D / D » ratios are p l o t t e d i n F i g u r e 1. T h e reflected shock z o n e t e m p e r a t u r e a n d pressure range c o v e r e d was 65 torr a n d 900 °K. to 300 torr a n d 2330°K. U n d e r s u c h c o n d i t i o n s the d i s s o c i a t i o n of Ό w a s n e g l i g i b l e , a n d the v i b r a t i o n a l r e l a x a t i o n t i m e of D » i n N e , estimated f r o m l i t e r a t u r e values ( 8,10 ), +

+

{

2

{

+

+

+

Λ

+

2

+

2

L


L

+

88


w a s greater t h a n the transit t i m e t h r o u g h the n o z z l e at the h i g h e r t e m peratures, a n d less t h a n the o b s e r v a t i o n t i m e at temperatures a b o v e 1200°K. T h e p r e d i c t e d c h a n g e i n the D / D ratio from E q u a t i o n 2 from r o o m t e m p e r a t u r e to 1200°K. is s m a l l e n o u g h (0.0007) to b e w i t h i n e x p e r i m e n t a l error. The D / D ratio was measured using the B e n d i x analog output at r o o m t e m p e r a t u r e at a t o t a l reservoir pressure of 5 t o r r a n d a n i o n i z i n g e n e r g y of 30 e. v. O p t i m i z a t i o n of the c o l l i m a t i n g a n d c o m p e n s a t i n g magnets p r o d u c e d a n e x p e r i m e n t a l p e a k h e i g h t r a t i o of 0.0045, c o m p a r e d w i t h the c a l c u l a t e d r a t i o of 0.0060. T h i s d i s c r e p a n c y is not serious since the same i n s t r u m e n t a l factor a p p l i e s to a l l experiments. H e n c e , c u r v e c is m e r e l y c u r v e b s h i f t e d to pass t h r o u g h the r o o m t e m p e r a t u r e p o i n t s . The D / D ratios p r e d i c t e d b y E q u a t i o n 2 s h o u l d f a l l o n c u r v e c. T h e first series of shock experiments at a series of temperatures w e r e p e r f o r m e d b y filling the shock t u b e to a constant i n i t i a l pressure of 5 torr. T h e D / D ratios so o b t a i n e d are p l o t t e d i n F i g u r e 1 ( r e p r e s e n t e d b y o p e n circles ). It is c l e a r t h a t the e x p e r i m e n t a l ratios are m u c h h i g h e r t h a n t h e t h e o r e t i c a l ratios. T h e most l i k e l y e x p l a n a t i o n seems to b e that D arises f r o m some other source t h a n f r a g m e n t a t i o n of D , for e x a m p l e , i o n m o l e c u l e reactions. T h i s conjecture is s u p p o r t e d b y the a p p e a r a n c e of m/e = 6 i n the mass spectra w h i c h is c l e a r l y D/ f o r m e d b y t h e w e l l known reaction: +

+

+


CHEMISTRY

2

2

+

+

2

+

+

2

+

+

2

D

2

+

+ D

2

—» D

3

+

+ D

(3)

F u r t h e r s u p p o r t w a s o b t a i n e d b y m e a s u r i n g the D / D r a t i o as a f u n c t i o n of reservoir pressure at r o o m t e m p e r a t u r e . A t a pressure of 50 torr the r a t i o almost d o u b l e d , c o m p a r e d w i t h the r a t i o at 5 torr. It w a s o b v i ous t h a t the D / D r a t i o consisted of t w o c o m p o n e n t s — o n e d e p e n d i n g o n t e m p e r a t u r e as p r e d i c t e d b y E q u a t i o n 2 a n d the s e c o n d d e p e n d i n g o n the i o n source gas density. T h e p o s s i b i l i t y of a pressure-dependent source of D w a s f u r t h e r tested b y r e p l a c i n g the o r i g i n a l 6 - m i l d i a m e t e r n o z z l e w i t h a 4 - m i l d i a m e t e r n o z z l e . T h i s r e d u c e d the a m o u n t of gas e n t e r i n g the mass spectrometer b y a p p r o x i m a t e l y a factor of 2 a n d p r o d u c e d another series of D / D ratios w h i c h are also s h o w n i n F i g u r e 1 ( d e n o t e d b y triangles ). It is c l e a r t h a t there is i n d e e d a pressure-dependent c o n t r i b u t i o n to the D peak height. T h e f o l l o w i n g p r o c e d u r e w a s a d o p t e d to assess t h e c o n t r i b u t i o n to D f r o m sources other t h a n E q u a t i o n 2. S e v e r a l measurements of D / D r a t i o w e r e m a d e near 900°K., a n d the constant p a r t of the t h e o r e t i c a l c u r v e c ( 3 0 0 ° - 9 0 0 ° K . ) w a s r a i s e d to pass t h r o u g h these p o i n t s , thus e s t a b l i s h i n g a zero p o i n t for the t h e r m a l effect. T h e p r e d i c t e d h i g h t e m p e r a t u r e curves d a n d e w e r e t h e n c o n s t r u c t e d b y a d d i n g the increase in D / D f r o m E q u a t i o n 2 to the zero points. I n a d d i t i o n to g i v i n g too h i g h a D s i g n a l , t h e u n k n o w n pressure d e p e n d e n t reactions c a n also e x p l a i n the u n e x p e c t e d l y l a r g e increase of the D s i g n a l w i t h t e m p e r a t u r e . T h i s is a t t r i b u t e d to the fact that w h e n a shock t u b e is o p e r a t e d w i t h constant i n i t i a l pressure, t h e reflected shock d e n s i t y increases s h a r p l y w i t h t e m p e r a t u r e . H e n c e , a n increase of i o n source pressure w i t h t e m p e r a t u r e o c c u r r e d i n the a b o v e experiments, +

+

2

2

+

+

+

+

2

+

+

+

+

+

2

+

+

+


2

+

6.

GAY A N D K E R N

Shock Tube

89

Study

l e a d i n g to a n increase i n the a m o u n t of D p r o d u c e d b y the pressure dependent reaction. S i n c e i t is n o t p r a c t i c a l w i t h this a p p a r a t u s to decrease t h e n o z z l e o p e n i n g b e l o w 4 m i l s , w e d e c i d e d to d o a set of experiments at different temperatures b u t at constant i o n source pressure. U n f o r t u n a t e l y , this is n o t a n easy r e q u i r e m e n t since i t is not possible to measure the i o n source pressure o n the t i m e scale of a shock e x p e r i m e n t , a n d i t is n o t c l e a r w h a t r e l a t i o n s h i p exists b e t w e e n shock t u b e pressure a n d i o n source pressure.


+

Figure 4.

Plot of D /D +

s

vs.

+

2

P

(T /TJ^ 5

F o r t u n a t e l y , the presence of D i n the mass s p e c t r u m gives a n i n d i c a t i o n of the pressure i n the i o n source. S i n c e D is o n l y a f e w p e r cent of D , it is clear f r o m R e a c t i o n 3 t h a t the D / D ratio w i l l vary linearly w i t h i o n source gas density. T h i s r a t i o w a s therefore p l o t t e d against v a r i o u s shock w a v e parameters i n search of a l i n e a r r e l a t i o n s h i p . T h e best l i n e a r i t y w a s f o u n d i n a p l o t of D / D vs. / ο ( Τ / Τ ι ) w h e r e p> a n d T are the d e n s i t y a n d t e m p e r a t u r e of the reflected shock z o n e a n d Τχ is r o o m t e m p e r a t u r e . T h i s p l o t is s h o w n i n F i g u r e 4. T h e scatter i n this p l o t arises f r o m the fact that D is a r a t h e r s m a l l peak, a n d therefore subject to statistical fluctuation. Nevertheless, a l i n e m a y b e d r a w n t h r o u g h the d a t a a n d the o r i g i n w i t h a slope of 90 l i t e r s / m o l e . T a k i n g 3

+

+

3

2

+

3

3

+

+

2

2

+

+

5

5

Ι Λ

5

3

+


r

90


CHEMISTRY

the residence t i m e i n the i o n source as 200 nanoseconds a n d a rate c o n stant f o r R e a c t i o n 3 of 86.8 Χ 1 0 l i t e r / m o l e / s e c . ( 1 5 ) , leads t o a n i o n source d e n s i t y of 0 . 0 5 % of the shock t u b e density. T h i s percentage is i n reasonable agreement w i t h the results of D i e s e n (4), w h o a r r i v e d at t h i s figure f r o m a c o n s i d e r a t i o n of the gas flow i n t o a mass spectrometer d u r i n g a shock experiment. T h e residence t i m e estimate is b a s e d o n the l e n g t h of the i o n i z i n g p u l s e a n d the rise t i m e of the i o n - a c c e l e r a t i n g p u l s e (250 a n d 100 nanoseconds, r e s p e c t i v e l y ) . A test of the s u i t a b i l i t y of the expression ρ^Τ^/Τχ)^ to represent the pressure-dependent processes w a s m a d e i n the f o l l o w i n g w a y . T h e 1 0 % D - 9 0 % N e m i x t u r e w a s s h o c k e d at v a r i o u s temperatures w i t h i n i t i a l pressures a d j u s t e d so t h a t p^(TJTx) w a s constant, a n d t h e D /D r a t i o w a s m e a s u r e d . A n i o n i z i n g energy of 22.5 e. v. w a s u s e d , w h i c h m a d e the N e p e a k o n l y 1.5 times the h e i g h t of the D peak. T h e 4 - m i l d i a m e t e r n o z z l e w a s u s e d . T h e results of these experiments are shown i n F i g u r e 5 along w i t h the D / D ratios that w e r e o b t a i n e d w h e n the i n i t i a l shock t u b e pressure w a s h e l d constant. T h e t h e o r e t i c a l l i n e is c u r v e d of F i g u r e 1 w h i c h has b e e n adjusted to the zero p o i n t for t h e r m a l effects b y a n e x p e r i m e n t a l p o i n t o b t a i n e d at 900°K. I f o n e assumes that the pressure-dependent c o n t r i b u t i o n to D is n o w r e a s o n a b l y constant, t h e agreement of the e x p e r i m e n t a l points w i t h the p r e d i c t e d t h e r m a l effect of E q u a t i o n 2 is g o o d . 1()

2

V2

+

2

+


+

2

+

2

+

+

+

S e v e r a l experiments w e r e p e r f o r m e d w i t h a m i x t u r e of 5 % N a n d 1 % A r i n N e at a n i n i t i a l pressure of 5 t o r r i n the t e m p e r a t u r e r a n g e 1 5 0 0 ° - 3 1 0 0 ° K . , u s i n g a n i o n i z i n g energy of 30 e. v. A c a l c u l a t i o n of N /N w a s m a d e u s i n g a M o r s e p o t e n t i a l for N . A v a l u e of r . w a s o b t a i n e d b y r e q u i r i n g the r a t i o to b e 0.067 at r o o m t e m p e r a t u r e ( 1 3 ) . T h i s is a n unsatisfactory m e t h o d of c a l c u l a t i o n since there are at least five p o t e n t i a l curves of N w h i c h c a n g i v e N w i t h d i f f e r i n g values of r a n d w h i c h are p r e s u m a b l y p o p u l a t e d to different extents b y the i o n i z a t i o n of N ( 7 ) . N e v e r t h e l e s s , u s i n g this v a l u e of r,., the increase of N / N w i t h t e m p e r a t u r e w a s c a l c u l a t e d . A t temperatures a b o v e 2100 °K., t h e e x p e r i m e n t a l p o i n t s agree w i t h t h i s c r u d e c a l c u l a t i o n w i t h i n 1 0 % . B e l o w 2500°K., the N / N r a t i o grows w i t h t i m e , w h i c h w e i n t e r p r e t as b e i n g c a u s e d b y the f a i r l y s l o w v i b r a t i o n a l r e l a x a t i o n of N at these t e m p e r a tures ( 1 0 ) . T h i s effect m a k e s a c c u r a t e r a t i o measurements u n c e r t a i n i n the N system a n d results i n c o n s i d e r a b l e scatter b e l o w 2100 °K. 2

+

2

+

(

2

2

+

+

c

+

2

+

2

2

+

+

2

2

Discussion W h e n the effect of pressure-dependent constant, it is d e m o n s t r a t e d t h a t o u r D / D +

i o n source reactions is h e l d 2

l a t e d values r a t h e r w e l l w i t h i n i n e v i t a b l e s m a l l concentrations.

+

ratios r e p r o d u c e t h e c a l c u fluctuations

Kiefer and L u t z s data (8)

associated

r e l a x a t i o n i n the shock t u b e s h o u l d b e c o m p l e t e u n d e r our at temperatures a b o v e 1200°K.

with

shows t h a t v i b r a t i o n a l conditions

S i n c e l i t t l e p o p u l a t i o n of h i g h e r v i b r a

t i o n a l levels w o u l d b e e x p e c t e d b e l o w t h i s t e m p e r a t u r e , o u r results are n o t seriously affected.

A l t h o u g h the t r a n s l a t i o n a l t e m p e r a t u r e of the gas


6.

GAY A N D K E R N

Shock Tube

91

Study

decreases s h a r p l y o n l e a v i n g t h e shock t u b e (4),

the concurrent expan

s i o n of the gas l o w e r s the c o l l i s i o n a l f r e q u e n c y , a n d there is n e g l i g i b l e v i b r a t i o n a l r e l a x a t i o n i n the 2 - 3 psec. transit t i m e b e t w e e n t h e shock t u b e a n d e l e c t r o n b e a m . W e therefore c o n c l u d e t h a t o u r D / D +

2

ratios

+

u n d e r constant i o n source pressure c o n d i t i o n s are i n fact a measure of t h e


v i b r a t i o n a l state of D

D

2

i n the shock t u b e .

.03h

°

+

2

800

1000

1200

1400

1600 T*

1800

2000

2200

2400

2600

°K

Figure 5. Plot of D /D vs. T . Solid curve—theoretical ratios at 22.5 e.v. ionizing energy. X—Experimental ratios obtained with constant ion source gas density, 22.5 e.v. Δ—Experimental ratios obtained with con stant initial shock tube pressure of 10 torr, 30 e.v. +

+

2

5

A l t h o u g h the thermally i n d u c e d change i n the D / D +

2

+

r a t i o is s m a l l ,

i t is c l e a r f r o m t h e results of C a s h i o n ( 2 ) that a n y s u b s t a n t i a l p o p u l a t i o n of a specific v i b r a t i o n a l l e v e l other t h a n ν = o n t h e ratio.

0 w o u l d h a v e a s t r o n g eifect

T h e shock tube-mass spectrometer m e t h o d seems

quite

c a p a b l e of d e t e c t i n g a b n o r m a l v i b r a t i o n a l energy d i s t r i b u t i o n s i n t h e p r o d u c t s of c h e m i c a l r e a c t i o n p r o v i d i n g t h e source of sources other t h a n e l e c t r o n i m p a c t f r a g m e n t a t i o n of D

2

+

D

+

ions

from

can be eliminated

or h e l d constant.



92

T h e origin of the pressure-dependent D

CHEMISTRY

s i g n a l o b s e r v e d i n these

+

experiments is n o t c e r t a i n . I t c o u l d arise f r o m t h e d i s s o c i a t i v e charge transfer r e a c t i o n N e + D -> Ne + D + D +

(4)

+

2

w h i c h a l t h o u g h e x o t h e r m i c b y 3.3 e.v., has a cross section w h i c h is too l o w (11)

t o e x p l a i n o u r results. A n o t h e r source of D

i n d u c e d d i s s o c i a t i o n of D D

+

2

+

+

is t h e c o l l i s i o n

( 3 ) . A p r o p e r assignment of t h e sources of

f r o m n o n - t h e r m a l o r i g i n s is b e y o n d

t h e a c c u r a c y of t h e d a t a f o r

experiments p e r f o r m e d at constant i n i t i a l shock t u b e pressures.


case since D

+

is a l w a y s a s m a l l f r a c t i o n of D

2

+

the d a t a w i l l b e correct as l o n g as t h e pressure-dependent D a collision between D

2

or D

2

+

In any

, o u r m e t h o d of t r e a t i n g +

arises f r o m

a n d one other species i n t h e i o n source.

It is difficult t o c o n c e i v e of t h e D a r i s i n g i n a n y other w a y . +

It is i n t e r e s t i n g to note that t h e p e a k shape of mass 2 shows some d e f o c u s s i n g u n d e r shock c o n d i t i o n s , as c a n b e seen i n F i g u r e 3. T h i s effect is a t t r i b u t a b l e to greater t h a n t h e r m a l k i n e t i c energy possessed b y the D

+

ions. T h i s k i n e t i c energy is d e r i v e d f r o m t w o sources: those D

2

m o l e c u l e s w h o s e i n t e r n u c l e a r d i s t a n c e is less t h a n r dissociate i n t o D c

a n d D w h i c h h a v e k i n e t i c energy, a n d D

+

produced from

+

+

exothermic

p r e s s u r e - d e p e n d e n t reactions.

Acknowledgments T h e authors w i s h to t h a n k t h e N a t i o n a l Science F o u n d a t i o n f o r t h e f u n d s w h i c h m a d e this w o r k possible.

T h e y also w i s h t o t h a n k G . B .

K i s t i a k o w s k y a n d J . K . C a s h i o n f o r t h e i r h e l p f u l discussions.

Literature

Cited

(1) Bauer, S. H., Ossa, E.,J.Chem. Phys. 45, 434 (1966). (2) Cashion, J. K.,J.Chem. Phys. 45, 1663 (1966). (3) Champion, R. L., Doverspike, L. D., Bailey, T. L.,J.Chem. Phys. 45, 4377 (1966). (4) Diesen, R. W.,J.Chem. Phys. 44, 3662 (1966). (5) Dove, J. E., Moulton, D. McL., Proc. Roy. Soc. A283, 216 (1965). (6) Gay, I. D., Kern, R. D., Kistiakowsky, G. B., Niki, H.,J.Chem. Phys. 45, 2371 (1966). (7) Gilmore, F. R., Memorandum RM-4034-PR, The Rand Corporation, June, 1964. (8) Kiefer, J. H., Lutz, R. W.,J.Chem. Phys. 44, 658 (1966). (9) Kolos, W., Wolnowiecz, L., J. Chem. Phys. 41, 3663 (1964). (10) Millikan, R.C.,White, D. R.,J.Chem. Phys. 39, 3209 (1963). (11) Moran, T. F., Friedman, L., J. Chem. Phys. 42, 2624 (1965). (12) Schaeffer, O.A.,Hastings, J. M., J. Chem. Phys. 18, 1048 (1950).


6.

G A Y AND KERN Shock Tube Study

(13) Schaeffer, Ο. Α.,J.Chem. Phys. 18, 1501 (1950). (14) Stevenson, D. P., J. Chem. Phys. 15, 409 (1947). (15) Stevenson, D. P., Schissler,D.O.,J.Chem. Phys. 23, 1353 (1955).


RECEIVED October 11, 1966.


Mass Spectrometry in Inorganic Chemistry

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