Mass Spectrometry in Inorganic Chemistry

5 Direct Mass Spectrometric Sampling of

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High Pressure Systems THOMAS A.

MILNE

and

FRANK

T.

GREENE

Midwest Research Institute, Kansas C i t y , M o .

The

extension

inorganic

of

systems

direct

mass spectrometric

at higher

pressures

the type of species and reactions method

involves

subsequently

nucleation.

including

A three-stage,

observation behavior

of clusters of Hg

preliminary species

Ar

2

and CsCl

indicates

beam. and

differentially and

in Ar and

that collisions

energies and densities

princi-

homogeneous sampling

of flames, to

to the N

2

study

carrier

the

of

the

gases.

of growth

between are

the

pumped

of the kinetics

is

Knowledge

to predict

to the sampling in argon,

consideration

low thermal

is sufficient

mass separation

system has been applied

One

as a free jet, which

into a molecular

of such free-jet expansions pal phenomena,

to in

that can be studied.

an initial expansion

collimated

sampling

offers advantages

A

of

the

molecules

at

important.

" \ T a s s s p e c t r o m e t r y has p r o v e d to be a n extremely versatile detector i n the s t u d y of i n o r g a n i c gaseous systems, as the papers i n this s y m p o s i u m i n d i c a t e . M o s t of the systems s t u d i e d b y d i r e c t line-of-sight s a m p l i n g of r e a c t i v e species, h o w e v e r , h a v e b e e n at r e l a t i v e l y l o w pressures. T h e r e are several reasons for w i s h i n g to extend d i r e c t mass spect r o m e t r i c s a m p l i n g to systems at h i g h e r pressure. B r e w e r ( 5 ) has p o i n t e d out t h a t the c o m p l e x i t y of the v a p o r i n e q u i l i b r i u m w i t h a

condensed

phase f r e q u e n t l y increases w i t h i n c r e a s i n g t e m p e r a t u r e a n d h e n c e i n c r e a s i n g pressure. T h u s , one m a y find, a n d b e a b l e to study, m a n y n e w species at h i g h e r pressures.

A n e x a m p l e is f u r n i s h e d b y the class of

w e a k l y b o u n d v a n der W a a l s ' d i m e r s w h i c h exist i n a l l gases, w i t h the possible exception of H e . F u r t h e r m o r e , b o t h h o m o g e n e o u s a n d heterogeneous e q u i l i b r i a often m u s t b e d r i v e n b y a h i g h p a r t i a l pressure of r e a c t i n g gas to o b t a i n a p p r e c i a b l e concentrations of a p a r t i c u l a r species. T h e case of steam over N a C l ( c ) g i v i n g a p o s t u l a t e d N a C l * 7 H 0 gaseous 2

68

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

5.

M I L N E A N D GREENE

High Pressure

69

Systems

m o l e c u l e ( 7 ) is a n e x a m p l e . A n o t h e r process of some interest is t h a t of h o m o g e n e o u s n u c l e a t i o n of b o t h l o w a n d h i g h t e m p e r a t u r e species, w h i c h is observable i n its earliest m o l e c u l a r stages i n the e x p a n s i o n i n t o a v a c u u m t h a t occurs i n d i r e c t h i g h pressure s a m p l i n g .

Finally,

many

p r a c t i c a l c h e m i c a l processes o c c u r i n h i g h pressure e n v i r o n m e n t s . A s a n e x a m p l e , i t is c u r r e n t l y a m a t t e r of some c o n c e r n w h e t h e r the species w h i c h h a v e b e e n s h o w n to b e i m p o r t a n t i n the l o w pressure o x i d a t i o n of Downloaded by UNIV OF CALIFORNIA SAN DIEGO on December 25, 2016 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0072.ch005

m e t a l s , t h e l o w pressure d e c o m p o s i t i o n

a n d c o m b u s t i o n of s o l i d p r o -

pellants, a n d the l o w pressure e q u i l i b r i a of l i g h t m e t a l c o m p o u n d s , s t i l l the i m p o r t a n t species

at the h i g h e r pressures a n d

are

temperatures

i n v o l v e d i n p r a c t i c a l c o m b u s t i o n systems. I n the f o l l o w i n g sections w e discuss m o l e c u l a r b e a m f o r m a t i o n f r o m a h i g h pressure gas. H i g h pressure here refers to a n y s a m p l i n g c o n d i t i o n i n w h i c h the m e a n free p a t h of the gas, λ, is s u b s t a n t i a l l y s m a l l e r t h a n t h e s a m p l i n g orifice d i a m e t e r , d—i.e.,

the K n u d s e n n u m b e r , K„ =

λ/d,

is m u c h less t h a n 1. O n l y the s a m p l i n g of n e u t r a l gases w i l l b e c o n s i d e r e d . S o m e of the p h e n o m e n a discussed h a v e a b e a r i n g o n the d i r e c t s a m p l i n g of ions, b u t the s p e c i a l p r o b l e m s of i o n e x t r a c t i o n w i l l not b e discussed.

Beam Formation Process Free-Jets. I n c o n v e r t i n g a h i g h pressure gas i n t o a m o l e c u l a r b e a m w h i c h c a n b e i n t r o d u c e d i n t o the i o n source of a mass spectrometer, t h e c r u c i a l changes i n c o m p o s i t i o n or state o c c u r d u r i n g t h e i n i t i a l c o n t i n u u m e x p a n s i o n w h i c h occurs s a m p l i n g orifice.

downstream

(and slightly upstream)

of

the

If the pressure d o w n s t r e a m f r o m the orifice is k e p t

q u i t e l o w , t y p i c a l l y 10" or 10" of the pressure of the gas b e i n g s a m p l e d , r>

fi

one obtains a free-jet

Free-jets are r e c e i v i n g m u c h

study

c u r r e n t l y because of t h e i r p e r t i n e n c e to the K a n t r o w i t z - G r e y (14)

expansion.

type

of supersonic beams for p r o d u c i n g h i g h energy, h i g h i n t e n s i t y m o l e c u l a r fluxes

and

because t h e y c a n p r o v i d e a supersonic flow field of k n o w n

properties for v a r i o u s a e r o d y n a m i c tests. T h e p r o b l e m of h i g h pressure s a m p l i n g , of course, p r o v i d e s a t h i r d m o t i v a t i o n for u n d e r s t a n d i n g freejets. T h e details of free-jet s t r u c t u r e a n d properties are g i v e n i n m a n y recent papers, p a r t i c u l a r l y those i n the p r o c e e d i n g s of the R a r e f i e d G a s D y n a m i c s S y m p o s i a (6). p e r t i n e n t (2, 3, 8,15).

I n a d d i t i o n , s e v e r a l recent r e v i e w articles are

O n l y those aspects of i m m e d i a t e c o n c e r n to d i r e c t

s a m p l i n g w i l l b e discussed here. A s a basis for u n d e r s t a n d i n g the s a m p l i n g process, it is reasonable to a p p r o x i m a t e the c e n t e r - l i n e flow of gas f r o m a k n i f e - e d g e d orifice as c o n s i s t i n g of a c o n t i n u u m a d i a b a t i c i s e n t r o p i c e x p a n s i o n u p to a t r a n s i t i o n p o i n t at w h i c h it a b r u p t l y enters a n essentially collisionless r e g i o n . C l e a r l y , this is not accurate since the a c t u a l t r a n s i t i o n is g r a d u a l , yet t h e


70

MASS SPECTROMETRY

I N INORGANIC

CHEMISTRY

s i m p l e m o d e l has p r o v e d u s e f u l i n c o r r e l a t i n g free-jet d a t a . D i r e c t e x p e r i m e n t a l d a t a f o r s m a l l orifices a n d m o n a t o m i c gases g i v e t h e M a c h n u m b e r of t h e gas as a r e s u l t of t h e c o n t i n u u m e x p a n s i o n a n d c a n b e fit t o a n effective t e r m i n a l M a c h n u m b e r a t w h i c h c o l l i s i o n s essentially cease ( I , 25).

O v e r t h e c o n t i n u u m p o r t i o n of t h e e x p a n s i o n , A s h k e n a s a n d S h e r

man

( 6 ) g i v e t h e c a l c u l a t e d M a c h n u m b e r as a f u n c t i o n of d i s t a n c e


downstream as: M w h e r e y is t h e r a t i o of specific heats, d is t h e orifice d i a m e t e r , a n d χ is t h e d i s t a n c e d o w n s t r e a m f r o m t h e orifice. A a n d x h a v e t h e f o l l o w i n g v a l u e s 0

for different y's: y

A

x /d

5/3 7/5 9/7

3.26 3.65 3.96

0.075 0.40 0.85

A t l a r g e distances M

P

/

P

o

=

w h i c h for γ =

(

1 +

0

A(xfd)^'

1

7-ZJLM»)

«

W

( ^ ) "

1

/

7

l

A - 2 / T - i ( x / d ) - 2

5 / 3 reduces t o :

p / p 0

=

( 2 )

9

w h e r e p is t h e source d e n s i t y a n d ρ is t h e d e n s i t y a t a d i s t a n c e χ f r o m 0

the orifice of d i a m e t e r d. diameters.)

( N o t e t h a t t h e e x p a n s i o n is s c a l e d i n orifice

S t a n d a r d expressions

for isentropic expansion i n

flowing

systems relate t h e M a c h n u m b e r o r d e n s i t y t o t h e l o c a l pressure, t e m p e r a t u r e , a n d v e l o c i t y . I t is i n t e r e s t i n g t h a t t h e flow is s o u r c e l i k e a n d differs r e l a t i v e l y l i t t l e i n t h e rate of d e n s i t y decrease f r o m t h e rate g i v e n b y t h e K n u d s e n effusion expression ( 2 8 ) w e r e t h i s r e l a t i o n s h i p to a p p l y o v e r t h e same source c o n d i t i o n s . _

0.0625

\P/Po) Knudsen — J^Jfiyai

'

^ '

P r e d i c t i o n of t h e t h e o r e t i c a l b e a m i n t e n s i t y at a l a r g e d i s t a n c e f r o m t h e orifice, w i t h

i n t e r v e n i n g slits, r e q u i r e s

consideration

of the terminal

M a c h n u m b e r a n d t h e g e o m e t r y of t h e s e c o n d slit. W i t h a sufficiently l a r g e s e c o n d slit, o r s k i m m e r , A n d e r s o n a n d F e n n (4) A s h k e n a s a n d S h e r m a n ' s source-flow

expression

have argued that

(Equation 2) can be

a p p l i e d at a n y d i s t a n c e , e v e n i n t o t h e essentially collisionless r e g i m e .


5.


High

Pressure

71

Systems

T h u s , a n u p p e r l i m i t to a t t a i n a b l e b e a m intensities is p r o v i d e d i f d e p a r tures f r o m i d e a l i t y a n d scattering are n e g l i g i b l e . A n d e r s o n , A n d r e s , a n d F e n n (3)

give a n expression for i n t e n s i t y i n the case of a v e r y s m a l l

skimmer and a terminal M a c h number, M . Likewise, Anderson and T

F e n n (4)

g i v e a n expression for large s k i m m e r s .

T h e most d e f i n i t i v e

d i s c u s s i o n of b e a m intensities appears to b e that of H a g e n a a n d M o r t o n (23).

Experimental beam

intensities o b t a i n e d i n o u r system w i l l

be


c o m p a r e d w i t h those c a l c u l a t e d f r o m E q u a t i o n 2 i n the next section. F o r m o n a t o m i c gases, the e x p a n s i o n is r e l a t i v e l y s i m p l e ; o n l y t r a n s l a t i o n a l degrees of f r e e d o m exist, a n d n o t w i t h s t a n d i n g s u c h refinements as c o n s i d e r a t i o n of n o n i s e n t r o p i c flow a n d a n i s o t r o p i c a n d n o n - M a x w e l l i a n v e l o c i t y d i s t r i b u t i o n s ( 1 3 ) , the s i m p l e p i c t u r e a b o v e s h o u l d g i v e a u s e f u l d e s c r i p t i o n of the h i s t o r y of the s a m p l e d gas.

It is a s s u m e d , of

course,

that n o h o m o g e n e o u s n u c l e a t i o n is o c c u r r i n g d u r i n g e x p a n s i o n

(dis-

cussed l a t e r ) . W i t h p o l y a t o m i c gases one m u s t c o n s i d e r the r e l a x a t i o n of the v a r i o u s i n t e r n a l degrees of f r e e d o m d u r i n g the e x p a n s i o n .

Direct

e x p e r i m e n t a l d a t a o n the t r a n s l a t i o n a l ( I , 2 5 ) a n d r o t a t i o n a l states 24)

(18,

d u r i n g expansion have been obtained b y velocity distribution mea-

surements a n d b y o p t i c a l spectroscopy.

T h e v i b r a t i o n a l b e h a v i o r has b e e n

i n f e r r e d f r o m the a p p a r e n t y w h i c h describes the m e a s u r e d free-jet p r o p erties.

A s a first a p p r o x i m a t i o n one c a n p r e d i c t c o m p l e t e t r a n s l a t i o n a l

r e l a x a t i o n to the t e r m i n a l M a c h n u m b e r c o n d i t i o n ( a m a t t e r of d e f i n i tion).

Rotational relaxation w i l l be

temperatures

considerable, but

final

rotational

are s u b s t a n t i a l l y h i g h e r t h a n t r a n s l a t i o n a l temperatures.

V i b r a t i o n a l r e l a x a t i o n w i l l u s u a l l y be m i n i m a l .

F o r excited

electronic

states, r a d i a t i v e processes w i l l p r o b a b l y d o m i n a t e over c o l l i s i o n a l d e excitation.

W h e n collisions h a v e essentially s t o p p e d , t h e state of

the

m o l e c u l e s w i l l r e m a i n f r o z e n w i t h the possible e x c e p t i o n of u n i m o l e c u l a r reactions s u c h as those p o s t u l a t e d b y R o b b i n s a n d L e c k e n b y ( 1 6 ) , i n w h i c h w e a k l y b o u n d p o l y a t o m i c clusters essentially rotate

themselves

a p a r t i n the absence of collisions. T h e a c t u a l course of the free-jet e x p a n s i o n is s h o w n i n F i g u r e 1 f o r three gases, A r , N , a n d C H , i n i t i a l l y at 1 a t m . a n d 3 0 0 ° K . T h e curves 2

4

l a b e l e d "free-jet" s h o w the pressure-temperature c o n d i t i o n s of i s e n t r o p i c e x p a n s i o n . T h e t e r m i n a l M a c h n u m b e r for a r g o n c a n b e p r e d i c t e d f r o m Anderson and Fenn's criterion

(4). (4)

T h e three n e a r l y straight lines s h o w the e q u i l i b r i u m v a p o r pressure of the c o n d e n s e d phases of the three gases. T h e significance of these curves w i l l b e c o m e a p p a r e n t i n the d i s c u s s i o n of n u c l e a t i o n . D o u b l i n g of the orifice size, for a g i v e n pressure, w o u l d h a v e t w o effects.

F i r s t , the t e r m i n a l


72

MASS SPECTROMETRY I N INORGANIC

CHEMISTRY

M a c h n u m b e r w o u l d increase a c c o r d i n g to E x p r e s s i o n 4. S e c o n d , the t i m e r e q u i r e d to r e a c h a g i v e n T-P

p o i n t o n the curves, c o r r e s p o n d i n g to a

given M a c h number, w o u l d double.

T i m e s of the o r d e r of

microseconds

are i n v o l v e d over the ranges s h o w n i n the figure w i t h orifice sizes of a few mils. It s h o u l d b e e m p h a s i z e d a g a i n that a l l the a b o v e d i s c u s s i o n assumes a n i d e a l e x p a n s i o n a n d the absence of shock effects, either i n the free-jet Downloaded by UNIV OF CALIFORNIA SAN DIEGO on December 25, 2016 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0072.ch005

or as a result of the presence of the s k i m m e r i n the flow field of the orifice. T h e v a l i d i t y of these assumptions i n o u r s a m p l e r is d i s c u s s e d

elsewhere

(9,10). ι ο

ARGON

•

N

Δ

CH

2

4

FREE JET EXPANSION VAPOR PRESSURE OF CONDENSED PHASE

X= /3 5

y = /£ 7

8 2\ x 10 ) °κ

('/τ

JL

10

12

14

Figure 1. A comparison of calculated free-jet expansion history with saturated vapor pressures for Ar, N„ and CH, initially at 1 aim. and 300 K. t

S


5.


High Pressure

73

Systems

Sampling Effects Accompanying Free-Jet Expansion. T h e r e are a n u m b e r of i m p o r t a n t consequences of d i r e c t free-jet s a m p l i n g . F i r s t , i n s a m p l i n g m i x t u r e s of gases, a w e l l d e v e l o p e d c o n t i n u u m expansion w i l l result i n a n e a r l y u n c h a n g e d c o m p o s i t i o n of gas at the t r a n s i t i o n r e g i o n (26)

w i t h a l l molecules m o v i n g a l o n g the b e a m axis w i t h essentially the

same v e l o c i t y .

T h e m o l e c u l e s of different m o l e c u l a r w e i g h t w i l l

have

d i f f e r i n g r a n d o m t h e r m a l velocities, h o w e v e r , a n d as a w e l l c o l l i m a t e d Downloaded by UNIV OF CALIFORNIA SAN DIEGO on December 25, 2016 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0072.ch005

m o l e c u l a r b e a m is f o r m e d , the l i g h t e r m o l e c u l e s w i l l s p r e a d m o r e r a p i d l y t h a n the heavier. T h e c o n s e q u e n c e , as first p o i n t e d out b y S t e r n , W a t e r man, and Sinclair (27)

a n d verified b y Green, Brewer, a n d M i l n e

is t h a t the m o l e c u l a r b e a m r e a c h i n g the mass-spectrometer

ion

(JO) source

w i l l b e d e p l e t e d i n l i g h t e r molecules i n p r o p o r t i o n to the first p o w e r of t h e i r m o l e c u l a r w e i g h t . T h a t the different m o l e c u l e s w i l l h a v e essentially the same m e a n a x i a l v e l o c i t y has b e e n v e r i f i e d for m i x t u r e s of gases b y a c h o p p e d b e a m , time-of-flight m e t h o d ( 1 2 ) .

F o r example, i n a H e - A r

m i x t u r e s a m p l e d at 1 a t m o s p h e r e t h r o u g h a 0.002 i n c h d i a m e t e r orifice, the A r a n d H e velocities d i f f e r e d b y o n l y a f e w One

percent.

i n t e r e s t i n g c o n s e q u e n c e of the a b o v e v e l o c i t y

phenomenon,

w h i c h has b e e n p o i n t e d out b y A n d e r s o n , A n d r e s , a n d F e n n ( 2 ) , i n terms of

argon-90%

H e m i x t u r e , t h e final b e a m c o m p o s i t i o n w i l l b e a b o u t 5 0 %

argon.

beam-surface

reaction

studies.

For a

has

significance

10%

M o r e i m p o r t a n t , time-of-flight d a t a s h o w that the a r g o n has a

most p r o b a b l e v e l o c i t y e q u i v a l e n t to a n effusive b e a m w i t h a t e m p e r a t u r e 2300°K., e v e n t h o u g h the source t e m p e r a t u r e is 3 0 0 ° K . A l a r g e n u m b e r of m i x t u r e s h a v e b e e n d i r e c t l y s t u d i e d b y A b u a f et al. (1)

illustrating

this feature. A second effect w h i c h occurs i n h i g h pressure s a m p l i n g is r e a l l y just a n e x a m p l e of a f a i l u r e to preserve the concentrations of species o r i g i n a l l y present.

A s F i g u r e 1 shows, e v e n gases w h i c h w e r e o r i g i n a l l y h i g h l y

u n s a t u r a t e d m a y b e c o m e e n o r m o u s l y s u p e r s a t u r a t e d i n the free-jet a n d h o m o g e n e o u s n u c l e a t i o n w i l l result (11, 21).

I n the case of s a m p l i n g of

gases w h i c h are i n i t i a l l y s a t u r a t e d w i t h respect to a c o n d e n s e d phase of s o m e c o m p o n e n t , this p h e n o m e n o n w i l l b e exaggerated.

Such condensa-

t i o n is a n u i s a n c e i n s a m p l i n g a n d m u s t b e suspected i n a n y h i g h pressure s t u d y . O n e w a y to detect this effect w i l l b e m e n t i o n e d later. O f

more

i m p o r t a n c e , h o w e v e r , is the fact that the free-jet presents s u c h a t i m e t e m p e r a t u r e - c o l l i s i o n h i s t o r y that r a p i d c o n d e n s a t i o n processes c a n

be

s t u d i e d i n t h e i r e a r l y , m o l e c u l a r stages. A final p o i n t a b o u t d i r e c t mass spectrometric observations of species f r o m a free-jet is that the i n t e r n a l e n e r g y states of the m o l e c u l e w i l l n o t be precisely k n o w n .

Consequently, w h e n dealing w i t h molecules

from

h i g h t e m p e r a t u r e sources, the f a i l u r e of the v i b r a t i o n a l degrees of f r e e d o m t o r e l a x m a y give rise to f r a g m e n t a t i o n patterns t y p i c a l of h i g h l y e x c i t e d


74


molecules.

CHEMISTRY

S u c h effects h a v e a p p a r e n t l y b e e n o b s e r v e d i n the s a m p l i n g

of flames ( 2 0 ) .

A r e l a t e d p r o b l e m is that w i t h the g e n e r a l a b i l i t y to

s a m p l e r e a c t i v e species, c a l i b r a t i o n s for mass spectrometer s e n s i t i v i t y w i l l often not b e a v a i l a b l e a n d one m u s t resort to estimates of sections a n d f r a g m e n t a t i o n b e h a v i o r J

cross

(21). V


Hi = =

MASS SPECTROMETER

Γ L— GAS INLET

Figure 2. Schematic of a three-stage, high pressure, molecular beam sampling system using a Bendix time-offlight mass spectrometer as a detector

Apparatus

and

Performance

T h e s a m p l i n g a p p a r a t u s t h a t w e h a v e d e v e l o p e d f o r h i g h pressure studies of i n o r g a n i c systems is s h o w n i n F i g u r e 2. T h i s system has b e e n i m p r o v e d f r o m t h a t d e s c r i b e d i n o u r e a r l i e r w o r k (10), b u t uses t h e same c o m p l e m e n t of p u m p s . T h e orifice-to-electron b e a m distance has b e e n r e d u c e d f r o m 16 to 8 inches, a n d i m p r o v e d p u m p i n g i n e a c h stage has r e s u l t e d i n less b e a m scattering. T y p i c a l o p e r a t i n g c o n d i t i o n s are l i s t e d i n T a b l e I. T h i s system is not u n l i k e other h i g h pressure b e a m a n d s a m p l i n g systems a l t h o u g h of modest p u m p i n g c a p a c i t y . F i g u r e 2 shows a m o t o r - d r i v e n c h o p p e r i n stage t w o , w h i c h has p r o v e d to b e a n essential p a r t of o u r system. T h e advantages, p r o b l e m s , a n d results of u s i n g m o d u l a t e d beams f o r b o t h noise a n d b a c k g r o u n d - i o n d i s c r i m i n a t i o n , as w e l l as time-of-flight v e l o c i t y d e t e r m i n a t i o n s , h a v e b e e n d i s c u s s e d (12). A g r a p h i c i n d i c a t i o n of one of these advantages is g i v e n i n T a b l e I I . H e r e the r a t i o of a n o n c o n d e n s i b l e species, A r , to a v e r y u n s t a b l e species, A r , 2



5.

M I L N E AND GREENE

High Pressure

75

Systems

is t a b u l a t e d as a f u n c t i o n of c h o p p i n g f r e q u e n c y . I t is seen t h a t e v e n w i t h a w e l l - c o l l i m a t e d m o l e c u l a r b e a m e n t e r i n g t h e B e n d i x M o d e l 12 i o n i z a t i o n source, d a t a t a k e n w i t h a m a n u a l shutter w o u l d b e i n e r r o r b y a f a c t o r of a b o u t t w o a n d t h a t c h o p p i n g f r e q u e n c i e s of at least 15 c p . s . are n e e d e d to d i s c r i m i n a t e a d e q u a t e l y against b e a m gases scattered i n the i o n source. A n o t h e r a d v a n t a g e of m o d u l a t i o n is t h a t h i g h f r e q u e n c y time-of-flight measurements ( 1 2 ) c a n b e u s e d to d e t e r m i n e the m o s t p r o b a b l e velocities of the b e a m components. V a l u a b l e i n f o r m a t i o n c a n b e d e d u c e d a b o u t t h e extent of the free-jet e x p a n s i o n i n the case of h i g h pressure b e a m f o r m a t i o n a n d a b o u t the m o l e c u l a r w e i g h t of n e u t r a l precursors o f o b s e r v e d ions i n K n u d s e n effusion studies.

Table I.

T y p i c a l Operating Conditions of Molecular Beam Sampling System Exit Slit Dimensions, in.

Pressure, torr Source Stage One Stage T w o Stage Three Ion Source of Bendix M o d e l 12

760 1 3 8 < 1

Typical Scattering Loss, %

8 7-3/4 6-1/2 2-1/8 0

25 15 10

0.002 diam. 0.020 diam. 0.10 X 0.024 0.50 X 0.030

X 10-3 Χ ΙΟ" X 10" Χ ΙΟ"

Table II.

Distance from Ion Source Electron Beam, in.

5

6

6

T h e Dependence of the Observed Ratio A r ^ / A r on Chopping Frequency

Frequency 0 2 8 15 50 100 160

(H ) z

80 /36 +

+

1.45 2.42 2.54 2.64 2.64 2.60 2.62

O u r system has b e e n c a l i b r a t e d to o b t a i n absolute, b e a m fluxes at the i o n source b y c o m p a r i n g the i n t e n s i t y of A r , f r o m a r g o n effusing t h r o u g h a system w i t h k n o w n g e o m e t r y u n d e r K n u d s e n c o n d i t i o n s , w i t h the i n t e n s i t y o b s e r v e d for a s u p e r s o n i c b e a m . I n this w a y b e a m fluxes 8 inches a w a y f r o m the source orifice of a b o u t 5 Χ 1 0 m o l e c u l e s / s q . c m . sec. h a v e b e e n d e m o n s t r a t e d f o r a 0.002 i n c h d i a m e t e r orifice a n d 1 a t m . a r g o n . T h e i n t e n s i t y p r e d i c t e d f r o m E q u a t i o n 2 is 1.3 X 1 0 mole c u l e s / s q . c m . sec. W h e n s c a t t e r i n g corrections of a b o u t 6 0 % are a p p l i e d to the e x p e r i m e n t a l v a l u e , the system approaches to w i t h i n a factor of +

1 5

1 6


76


CHEMISTRY

t w o the t h e o r e t i c a l l y p r e d i c t e d m a x i m u m intensity. D y n a m i c ranges of s t u d y of 1 0 h a v e b e e n o b t a i n e d i n the absence of b a c k g r o u n d peaks. I n o u r p r a c t i c a l studies w e are l i m i t e d b y fluctuations of the s i g n a l f r o m the b a c k g r o u n d h y d r o c a r b o n s r a t h e r t h a n e l e c t r o n i c noise. T h e r e is n o o b v i o u s u p p e r l i m i t to the pressure w h i c h c a n b e s a m p l e d p r o v i d e d the c h o i c e of orifice sizes, distances, a n d p u m p i n g speed a l l o w s g o o d free-jet e x p a n s i o n w i t h o u t excessive scattering. W e h a v e f o r m e d beams f r o m 7 a t m . of a r g o n , w h i l e L e c k e n b y et al. (17) h a v e f o r m e d b e a m s f r o m gases at pressures as h i g h as 40 a t m . O n e c o u l d c o n c e i v a b l y s a m p l e fluid systems a b o v e the c r i t i c a l c o n d i t i o n s . T h e most p r o b a b l e l i m i t a t i o n to the c h a r a c t e r i z a t i o n of the a c t u a l m o l e c u l a r species present i n t h e fluid w i l l b e a m b i g u i t i e s b r o u g h t o n b y n u c l e a t i o n p h e n o m e n a . T h e a b i l i t y of a free-jet expansion to q u e n c h c h e m i c a l reactions w i t h p o s i t i v e a c t i v a t i o n energies s h o u l d b e n e a r l y o p t i m a l o w i n g to the ext r e m e l y r a p i d c o o l i n g rates. L i k e w i s e , reactions s u c h as t h a t of c o n d e n sation, w h i c h h a v e a negative t e m p e r a t u r e coefficient, s h o u l d b e q u e n c h e d w i t h m a x i m u m efficiency since, for a g i v e n orifice size, the free-jet e x p a n s i o n results i n the m i n i m u m n u m b e r of collisions d u r i n g the t r a n s i t i o n to m o l e c u l a r flow.


7

Application

to Inorganic Systems

T h e r e are m a n y a p p l i c a t i o n s of h i g h pressure s a m p l i n g w h i c h w i l l o c c u r to i n o r g a n i c chemists.

W e d e s c r i b e here o n l y those areas w h i c h

are c u r r e n t l y b e i n g p u r s u e d i n o u r l a b o r a t o r y . Flames. O u r w o r k w i t h the d i r e c t s a m p l i n g of flames is representative of a class of s a m p l i n g studies i n w h i c h the s a m p l i n g orifice is not i n t h e r m a l e q u i l i b r i u m w i t h the gaseous system b e i n g s t u d i e d . W e

began

o u r h i g h pressure s a m p l i n g w o r k w i t h the g o a l of s t u d y i n g the t h e r m o d y n a m i c s of gaseous m e t a l - c o n t a i n i n g species at e x t r e m e l y h i g h t e m p e r a tures a n d h i g h p a r t i a l pressures of 0

2

and H 0 .

r e a d i l y a t t a i n a b l e i n the b u r n t gas r e g i o n of

2

S u c h c o n d i t i o n s are

flames.

I n a d d i t i o n , the

a b i l i t y to f o l l o w d i r e c t l y f r e e - r a d i c a l a n d other species t h r o u g h t h e r e a c t i o n z o n e w a s of interest i n terms of the k i n e t i c s t u d y of flame reactions. T h e e q u i l i b r i u m 1-atm. d e t a i l p r e v i o u s l y (20, 22). m a r i z e d as f o l l o w s .

flame

w o r k has b e e n

presented

i n some

T h e present status of this w o r k c a n b e s u m -

It appears that 1-atm. flames as h o t as 4000°K. c a n

b e p r o b e d a n d t h a t f r e e - r a d i c a l a n d other n o n c o n d e n s i b l e species c a n b e q u a n t i t a t i v e l y s a m p l e d . H o w e v e r , w e h a v e b e e n u n a b l e to s a m p l e h i g h l y condensible

species w i t h r e l a t i v e l y c o l d s a m p l i n g orifices.

Isothermal

f u r n a c e studies m e n t i o n e d b e l o w i n d i c a t e that a e r o d y n a m i c effects c a u s e d b y the c o l d orifice a n d o x i d e b u i l d - u p , a n d not the i n h e r e n t h o m o g e n e o u s n u c l e a t i o n or other e q u i l i b r i u m shifts i n v o l v e d i n free-jet expansion, are responsible for this l i m i t a t i o n . A p r o m i s i n g area for f u r t h e r flame w o r k is i n d i c a t e d i n o u r s t u d y of species profiles i n r e a c t i o n zones b y means of the d i r e c t s a m p l i n g of


5.


l o w pressure

flames.

High Pressure

77

Systems

T h e l o w pressure serves m a i n l y t o s p r e a d out t h e

r e a c t i o n zone t o a l l o w a d e q u a t e s a m p l i n g r e s o l u t i o n . V e r y s l o w b u r n i n g flames

c o u l d b e s t u d i e d a t o n e atmosphere.

I n a n apparatus described

elsewhere ( 1 9 ) , w e h a v e o b t a i n e d a n u m b e r o f profiles t h r o u g h a l / 2 0 t h atmosphere, l e a n C H - 0 4

2

flame w i t h C H B r a d d e d . 3

T y p i c a l results a r e

s h o w n i n F i g u r e s 3 a n d 4. A b s o l u t e intensities s h o u l d not b e c o m p a r e d between

species, as s e n s i t i v i t y corrections h a v e n o t b e e n m a d e . T h e


significance o f these d a t a lies i n t h e g e n e r a l agreement b e t w e e n t h e F i g u r e 3 results a n d p r e v i o u s l y p u b l i s h e d q u a r t z m i c r o p r o b e studies ( 2 9 ) for the stable species, c o m b i n e d w i t h o u r a b i l i t y as s h o w n i n F i g u r e 4 t o f o l l o w the concentrations o f H B r a n d B r . T h e s e latter species h a v e n o t p r e v i o u s l y b e e n s t u d i e d successfully b y i n d i r e c t s a m p l i n g t e c h n i q u e s .

BURNER SCREEN TO

ORIFICE DISTANCE IN CM

Figure 3. Stable species profiles obtained by direct molecular sampling of a l/20th-atm., lean, CH, 0 flame. Flame composition: 89.6% 0 , 10.4% CH r

2

Isothermal Transpiration Cells.

2

H i g h pressures of gas h a v e

h

been

e q u i l i b r a t e d w i t h the c o n d e n s e d phases o f m a n y m a t e r i a l s , i n t h e c o n v e n t i o n a l t r a n s p i r a t i o n e x p e r i m e n t , to p e r m i t t h e s t u d y often o f q u i t e m i n o r v a p o r species. B e c a u s e the i d e n t i f i c a t i o n o f s u c h species is i n d i r e c t , a n d serious c o m p l i c a t i o n s arise i f several gaseous species are present, i t w o u l d b e most d e s i r a b l e t o s a m p l e t h e eifluent d i r e c t l y w i t h a mass spectrometer.

W e a r e d o i n g this b y p l a c i n g a resistance h e a t e d N i

t r a n s p i r a t i o n c e l l i n stage o n e , just b e l o w

t h e s k i m m e r , as s h o w n i n


78


CHEMISTRY

F i g u r e 2. O u r present c e l l w h i c h uses orifice d i a m e t e r s of 0.0005 t o 0.004 i n c h w i l l h a n d l e gas pressures u p to 5 a t m . G a s flows are d e t e r m i n e d b y t h e orifice size, for a g i v e n pressure, so several orifice sizes m a y h a v e to b e u s e d to e s t a b l i s h that e q u i l i b r i u m exists. W i t h this system w e are c u r r e n t l y s t u d y i n g the e q u i l i b r i u m L i ( g ) 1/2H

2

+

- » L i H ( g ) , w i t h the i n t e n t i o n of g o i n g o n to o t h e r systems s u c h

as A l +

H

2

w h e r e h i g h e r h y d r i d e s m a y b e present a n d h i g h pressures


m a y b e m o r e advantageous i n d e t e c t i n g species of interest. T h e s t u d y of s u c h h i g h pressure e q u i l i b r i a w i l l a l w a y s i n v o l v e the d a n g e r of

free-jet

n u c l e a t i o n , a n d a p p r o p r i a t e tests, s u c h as the one d i s c u s s e d i n the next section, m u s t b e c a r r i e d out.

Figure 4. Profiles of bromine species in a l/20th-atm., lean, CH -0 containing about 1% CH Br. Flame composition: 89.6% 0 , 10.4% h

a

2

2

flame CH, t

Nucleation and the Thermodynamics of Weakly Bound Clusters. W h e n e v e r a c o n t i n u u m e x p a n s i o n is i n v o l v e d i n the s a m p l i n g process, the d a n g e r of s u p e r s a t u r a t i n g a species exists a n d n u c l e a t i o n m a y occur. S u c h n u c l e a t i o n w i l l b e v e r y sensitive to i n i t i a l t e m p e r a t u r e , pressure, a n d to s a m p l i n g orifice size. T h e b e h a v i o r of a r g o n has b e e n s t u d i e d i n some d e t a i l (21).

A p a r t f r o m the c o m p l i c a t i o n s w h i c h n u c l e a t i o n poses

for s a m p l i n g , the mass s p e c t r o m e t r i c s t u d y of free-jet c o m p o s i t i o n

pro-

v i d e s a u n i q u e a p p r o a c h to e l u c i d a t i n g the earliest stages of h o m o g e n e o u s nucleation.

I n fact, the first step i n s u c h c o n d e n s a t i o n , the

r e c o m b i n a t i o n to f o r m a d i m e r species, c a n b e f o l l o w e d .

three-body

Studies of t h i s


5.


High Pressure

79

Systems

t y p e are not l i m i t e d to gases s u c h as a r g o n , a n d w e are n o w e x a m i n i n g h i g h e r t e m p e r a t u r e species as w e l l . O n e of the approaches to the i n t e r p r e t a t i o n of t h e A r

2

concentrations

o b s e r v e d i n s a m p l i n g p u r e a r g o n is s h o w n i n F i g u r e 5, w h e r e the o b s e r v e d Ar

2

+

intensities ( a t t r i b u t e d solely to s i m p l e i o n i z a t i o n of A r ) are p l o t t e d 2

against orifice size at fixed pressure.

N o t e the r a t h e r h i g h e x t r a p o l a t e d

c o n c e n t r a t i o n at z e r o orifice d i a m e t e r , w h i c h w e i n t e r p r e t as t h e e q u i Downloaded by UNIV OF CALIFORNIA SAN DIEGO on December 25, 2016 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0072.ch005

l i b r i u m c o n c e n t r a t i o n of A r

i n the static gas

2

(21).

T h e exponential

g r o w t h w i t h orifice size is g o v e r n e d b y n u c l e a t i o n k i n e t i c s d u r i n g the i n c r e a s i n g t i m e a n d d e c r e a s i n g temperatures i n v o l v e d i n e x p a n s i o n f r o m l a r g e r orifices. T h i s d e p e n d e n c e of o b s e r v e d species o n orifice size p r o m ises to b e a n i n d i s p e n s a b l e t e c h n i q u e i n d e t e c t i n g the presence of n u c l e a t i o n effects i n s a m p l i n g . 4,000

"0 1 2 3 4 5 6 ORIFICE DIAMETER IN MILS Figure 5. Ar intensities observed after expansion of argon from 5 atm. and 300°K. through several size orifices +

2

W e are not yet p r e p a r e d to discuss the k i n e t i c significance of t h e e x p o n e n t i a l rise of A r c o n c e n t r a t i o n w i t h orifice size, b u t it is of interest 2

to c o n s i d e r the n a t u r e of the c o l l i s i o n a l - t e m p e r a t u r e h i s t o r y of t h e gas d u r i n g the free-jet expansion.

T a b l e I I I shows the effect of orifice size

o n the t e r m i n a l M a c h n u m b e r , t e r m i n a l t e m p e r a t u r e , a n d n u m b e r

of

t e r n a r y collisions, as c a l c u l a t e d f r o m a s i m p l e k i n e t i c m o d e l b y u s i n g


80


temperature-dependent

CHEMISTRY

c o l l i s i o n cross sections a n d a s s u m i n g A n d e r s o n

a n d F e n n ' s c r i t e r i o n of f r e e z i n g for a l l o u r e x p e r i m e n t a l c o n d i t i o n s . f o u r t h c o l u m n lists t h e t o t a l n u m b e r of t e r n a r y collisions p e r

The

molecule

f r o m M a c h 0.50 to the t e r m i n a l M a c h n u m b e r . T h e last c o l u m n lists t h e o b s e r v e d m o l e fractions of A r

2

i n excess of the zero orifice

diameter

e x t r a p o l a t e d values. W i t h o u t d i s c u s s i n g the assumptions m a d e , it is clear that w e are d e a l i n g w i t h collisions b e t w e e n molecules of v e r y l o w r e l a t i v e Downloaded by UNIV OF CALIFORNIA SAN DIEGO on December 25, 2016 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0072.ch005

energy.

F o r e x a m p l e , observe that the n u m b e r of collisions m o r e t h a n

d o u b l e s i n g o i n g f r o m a 0.002 to 0.004 i n c h d i a m e t e r orifice.

I n this

m o d e l , the increase b e y o n d a f a c t o r of t w o is c a u s e d b y the extension of the c o n t i n u u m p a r t of the e x p a n s i o n b y the l a r g e r orifice, as reflected i n the l a r g e r t e r m i n a l M a c h n u m b e r a n d l o w e r t e m p e r a t u r e .

The experi-

m e n t a l A r m o l e fractions also m o r e t h a n d o u b l e f r o m the 0.002 to 0.004 2

i n c h case.

It seems reasonable, t h e n , to relate this excess d i m e r to t h e

collisions w h i c h o c c u r at v e r y l o w temperatures. T h e c o l l i s i o n a l b e h a v i o r i n this r e g i o n is not u n d e r s t o o d at present. A l t h o u g h interpretations m a y b e c o m p l i c a t e d b y s u c h p h e n o m e n a as l o n g - l i v e d o r b i t i n g pairs a n d l a c k of

information

about

the

transition region,

it

seems

well

worth

investigating.

Table III. Calculated Ideal Free-Jet Nucleation History for A r g o n Initially at 3 0 0 ° K . and 5 Atmospheres Orifice Diameter, mils

Terminal Mach No.

Terminal Temp.

Total Ternary Collisions

Observed Excess Mole Fraction of Ar

0.5 1 2 3 4

18.4 24.2 31.9 37.6 42.2

2.6 1.5 0.88 0.64 0.51

71.70 143.58 287.56 431.46 575.48

0.0009 0.0027 0.0075 0.0157 0.0310

2

T h e a b o v e t y p e of c o r r e l a t i o n represents o n l y one of t h e w a y s free-jet n u c l e a t i o n d a t a m a y b e treated.

D i l u t i o n experiments, c o m p a r i s o n

of

expansions s t a r t i n g w i t h different temperatures a n d pressures b u t e n d i n g w i t h the same t e r m i n a l M a c h n u m b e r , a n d other v a r i a t i o n s of the i n i t i a l a n d final states w i l l h e l p i l l u m i n a t e the i m p o r t a n t process of h o m o g e n e o u s n u c l e a t i o n over v a r i o u s t e m p e r a t u r e ranges.

It also seems possible

to

e x t e n d the s t u d y to h i g h e r clusters. T h e n u c l e a t i o n b e h a v i o r of several h i g h e r - t e m p e r a t u r e systems has b e e n e x a m i n e d thus far. A r a n d N

2

h a v e b e e n passed o v e r H 0 , C H O H , 2


3

5.

MILNE

AND GREENE

High

Pressure

81

Systems

L i , H g , a n d C s C l at pressures u p to 2 a t m . I n these studies the species A r , A r · H g and H g 2

2

h a v e b e e n o b s e r v e d i n one a t m o s p h e r e of a r g o n

o v e r H g at 500°K. T h e s e d a t a represent c o n t r i b u t i o n s f r o m b o t h e q u i l i b r i u m species a n d those f o r m e d d u r i n g expansion. A c a r e f u l m e a s u r e m e n t of the orifice size d e p e n d e n c e of concentrations s h o u l d a l l o w b o t h a d e t e r m i n a t i o n of the free energy of the d i m e r s a n d a n i n d i c a t i o n of t h e i r k i n e t i c s of f o r m a t i o n . I n t h e case of A r o v e r C s C l , b o t h the m o n o m e r Downloaded by UNIV OF CALIFORNIA SAN DIEGO on December 25, 2016 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0072.ch005

a n d the d i m e r of the salt w e r e d e t e c t e d Knudsen work. In N

2

i n the r a t i o e x p e c t e d

from

the d i m e r w a s r e d u c e d b y a f a c t o r of a b o u t f o u r ;

this u n e x p e c t e d b e h a v i o r is r e c e i v i n g f u r t h e r s t u d y . It s h o u l d b e possible to o b t a i n d i r e c t l y the free energies of a n u m b e r of m i x e d d i m e r s of t h e t y p e A r * C s , C s * H g , etc. M a n y clusters w e r e o b s e r v e d i n the H 0 a n d 2

C H O H systems. T h e case of p o l y a t o m i c m o l e c u l e s m a y b e m o r e c o m p l i 3

c a t e d because of the possible m e t a s t a b i l i t y of the d i m e r s (16).

F o r ex-

a m p l e , w e see several orders of m a g n i t u d e less d i m e r i n N , 0 , a n d N O 2

t h a n one w o u l d at first expect (12).

2

N e v e r t h e l e s s , d i r e c t mass spectro-

m e t r i c v e r i f i c a t i o n of s u c h p o s t u l a t e d species as the H F h e x a m e r a n d t h e m e t h a n o l tetramer m a y b e feasible. F i n a l l y , d i r e c t second l a w heat determ i n a t i o n s of w e a k l y b o u n d d i m e r s also a p p e a r p r a c t i c a b l e .

Summary D i r e c t mass s p e c t r o m e t r i c s a m p l i n g of h i g h - p r e s s u r e systems is p o s s i b l e i n m a n y cases, w i t h a t o l e r a b l e m i n i m u m of c o m p o s i t i o n d i s t u r b a n c e . T h e s t u d y of flames a n d heterogeneous r e a c t i o n systems has s h o w n p r o m ise. A l s o a large class of e q u i l i b r i u m reactions c a n b e e l u c i d a t e d f u r t h e r b y c o m b i n i n g the t r a n s p i r a t i o n e x p e r i m e n t w i t h d i r e c t mass s p e c t r o m e t r i c s a m p l i n g . T h e s t u d y of gases a n d gas m i x t u r e s w i l l g i v e t h e r m o d y n a m i c i n f o r m a t i o n a b o u t v a n d e r W a a l s ' , charge-transfer, a n d h y d r o g e n - b o n d e d species.

F i n a l l y , n u c l e a t i o n , w h i c h is one of the i n h e r e n t p r o b l e m s i n

h i g h pressure s a m p l i n g , c a n b e t u r n e d to a d v a n t a g e b y a l l o w i n g a d e t a i l e d s t u d y of the c o n d e n s a t i o n process o n the m o l e c u l a r scale.

Acknowledgments T h i s w o r k w a s sponsored b y the C h e m i s t r y Office of the A d v a n c e d R e s e a r c h Projects A g e n c y a n d the P o w e r B r a n c h of the Office of N a v a l Research. T h e authors w i s h to a c k n o w l e d g e the h e l p of J a c o b B e a c h e y a n d D o u g l a s D a y i n c a r r y i n g out the e x p e r i m e n t a l p r o g r a m a n d the h e l p of G o r d o n G r o s s i n i n t e r p r e t i n g the results.

G e n e V a n d e g r i f t has

p r i m a r i l y r e s p o n s i b l e for the free-jet, c o l l i s i o n a l - h i s t o r y c a l c u l a t i o n s .


been

82

MASS SPECTROMETRY IN INORGANIC CHEMISTRY


Literature Cited (1) Abuaf, N., Anderson, J. B., Andres, R. P., Fenn, J. B., Miller, D. R., "Rarefied Gas Dynamics," Vol. 2, p. 1317, C. L. Brundin, ed., Academic Press, New York, 1967. (2) Anderson, J. B., Andres, R. P., Fenn, J. B., "Advances in Atomic and Molecular Physics," P. R. Bates, I. Estermann, eds., Vol. I., p. 345, Academic Press, New York, 1965. (3) Anderson, J. B., Andres, R. P., Fenn, J. B., p. 281, "Advances in Chemical Physics," Vol. X, J. Ross, ed., Interscience Publishers, New York, 1966. (4) Anderson, J. B., Fenn, J. B., Phys. of Fluids, 8, 780 (1965). (5) Brewer, L., "Chemistry and Metallurgy of Miscellaneous Materials: Ther modynamics," p. 261, Natl. Nucl. Energy Ser. IV—19B, L. Quill, ed., McGraw-Hill, New York, 1950. (6) de Leeuw, J. H., "Advances in Applied Mechanics Series," Supplement 1 (1961), Supplement 2 (1963), Supplement 3 (1965), Supplement 4 (1967), "Rarefied Gas Dynamics," Academic Press, New York. (7) Elliott, Guy R. B., "Gaseous Hydrated Oxides, Hydroxides, and Other Hydrated Molecules," UCRL-1831, June 1952. (8) French, J. Β., AIAA J. 3, 993 (1965). (9) Greene, F. T., Milne, Τ. Α., "Advances in Mass Spectrometry," Vol. 3, p. 841, The Institute of Petroleum, London, 1966. (10) Greene, F. T., Brewer, J., Milne, Τ. Α.,J.Chem. Phys. 40, 1488 (1964). (11) Greene, F. T., Milne, Τ. Α., J. Chem. Phys. 39, 3150 (1963). (12) Greene, F. T., Milne, Τ. Α., 22nd Quart. Tech. Rept, Contract Nonr3599(00), May 1967. (13) Hamel, B., Willis, D. R., Phys. of Fluids 9, 829 (1966). (14) Kantrowitz, Α., Grey, J., Rev. Sci. Instr. 22, 328 (1951). (15) Knuth, E. L., Appl. Mech. Rev. 17, 751 (1964). (16) Leckenby, R. E., Robbins, E. J., Proc. Roy. Soc. 291, 389 (1966). (17) Leckenby, R. E., Robbins, E. J., Trevalion, P. Α., Proc. Roy. Soc. (Lon don) 280A, 409 (1964). (18) Marrone, V., Univ. Toronto, Inst. Aerospace Studies Rept. No. 113, (1966). (19) Milne, Τ. Α., Midwest Res. Inst. Rept. FS-127-P (1966). (20) Milne, Τ. Α., Greene, F. T.,J.Chem. Phys. 44, 2444 (1966). (21) Milne, Τ. Α., Greene, F. T., J. Chem. Phys., 47, 4095 (1967). (22) Milne, Τ. Α., Greene, F. T., Symp. Combust., 10th, p. 153, The Com bustion Institute, 1965. (23) Morton, H. S., Jr., Hagena, O. F., "Analysis of Intensity and Speed Dis tribution of a Molecular Beam from a Nozzle Source," Tech. Rept. UVA11-P, Contract No. Nonr 3623(00), October 1966. (24) Robben, F., Talbot, L., Phys. of Fluids 9, 644 (1966). (25) Scott, J., Phipps, J. Α., "Rarefied Gas Dynamics," Vol. 2, p. 1337, C. L. Brundin, ed., Academic Press, New York, 1967. (26) Sherman, F. S., Phys. of Fluids 8, 773 (1965). (27) Stern, S. Α., Waterman, P. C., Sinclair, T. F., J. Chem. Phys. 33, 805 (1960). (28) Taylor, W. J.,J.Chem. Phys. 38, 779 (1963). (29) Wilson, W. E., Jr., Symp. Combust., 10th, p. 47 (1965). RECEIVED November 2, 1966.


Mass Spectrometry in Inorganic Chemistry

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