20 The "Mass" Effect of Electron Multipliers in High Temperature Mass Spectrometric Applications
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KARL A. GINGERICH Battelle Memorial Institute, Columbus Laboratories, Columbus, Ohio
The
electron
Pr , and U +
+
constant high
multiplier
have been measured
results
best described from
the
dependence able
of
P,
P, +
the
relative
as being independent
usually
applied
literature
data
and
Sb ,
With
multiplier square of
+
applied
the
this
in
exception
gains
of mass. The
results
Co ,
+
to that of Ag+ at
can
be
deviations
root
gains are discussed
the
Bi ,
+
commonly
"inverse
of the multiplier
+
relative
mass spectrometry.
for
As ,
+
ion energy under conditions
temperature
of the
gains
of
mass"
using
avail-
investigation.
' T p h e a p p l i c a t i o n of mass s p e c t r o m e t r y to h i g h t e m p e r a t u r e c h e m i s t r y has d e v e l o p e d d u r i n g the past d e c a d e i n t o one of the most i m p o r t a n t research techniques for s t u d y i n g the c o m p o s i t i o n of vapors f r o m d e n s e d phases a n d the c o r r e s p o n d i n g h o m o g e n e o u s a n d c h e m i c a l reactions i n v o l v i n g the v a p o r components F o r most of
con-
heterogeneous
(12).
the t h e r m o c h e m i c a l c a l c u l a t i o n s , the i o n intensities
r e c o r d e d b y the mass spectrometer m u s t b e c o r r e l a t e d w i t h the r e s p e c t i v e absolute p a r t i a l pressures.
F o r this p u r p o s e i t is necessary to c a l i b r a t e
the mass spectrometer to d e t e r m i n e the p r o p o r t i o n a l i t y constant t h a t relates the m e a s u r e d i o n c u r r e n t intensities to the c o r r e s p o n d i n g p a r t i a l pressures.
A c o m m o n l y u s e d m e t h o d for c a l i b r a t i o n is to v a p o r i z e a
k n o w n a m o u n t of a s t a n d a r d material—e.g., s i l v e r (6,
13)
that is not
r e a c t i v e w i t h the s a m p l e u n d e r i n v e s t i g a t i o n or w i t h the container a n d effusion c e l l m a t e r i a l . I n s u c h a n e x p e r i m e n t the c a l i b r a t i o n constant fc = {
(YT) /P , i
i
w h i c h relates effective p a r t i a l Pi pressure i n s i d e the K n u d s e n
c e l l a n d the m e a s u r e d i o n i n t e n s i t y U at the e x p e r i m e n t a l t e m p e r a t u r e +
T
i9
is d e t e r m i n e d b y i n t e g r a t i n g the i o n c u r r e n t w i t h t i m e i n the u s u a l
way.
T h i s m e t h o d r e q u i r e s k n o w l e d g e of the r e l a t i v e i o n i z a t i o n cross 291
In Mass Spectrometry in Inorganic Chemistry; Margrave, J.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
292
MASS S P E C T R O M E T R Y
IN INORGANIC C H E M I S T R Y
sections a n d of the r e l a t i v e g a i n of the s e c o n d a r y e l e c t r o n m u l t i p l i e r t h a t is c o m m o n l y u s e d as a detector for the r e s o l v e d i o n b e a m . T h e r e l a t i o n b e t w e e n the k n o w n p a r t i a l pressure Pi o f the c a l i b r a t i n g substance i a n d the p a r t i a l pressure P of the v a p o r species χ m e a s u r e d x
is g i v e n b y (13) Ρ,
=
F,
(ZT) +
(nay).
t
(Ζ Γ)
m
(ησγ),
χ
* '
w h e r e Γ is the m e a s u r e d i o n c u r r e n t , Τ the absolute t e m p e r a t u r e , η t h e
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i s o t o p i c a b u n d a n c e c o r r e c t i o n factor, σ t h e r e l a t i v e i o n i z a t i o n cross sec t i o n , a n d γ the r e l a t i v e m u l t i p l i e r g a i n f o r the mass n u m b e r of the i o n i c species m e a s u r e d . T h i s r e l a t i o n shows t h a t a n u n c e r t a i n t y i n the k n o w l edge o f the r e l a t i v e i o n i z a t i o n cross section o r m u l t i p l i e r efficiency results i n a p r o p o r t i o n a t e u n c e r t a i n t y o f the c o r r e s p o n d i n g p a r t i a l pressure. A set o f c a l c u l a t e d r e l a t i v e i o n i z a t i o n cross sections at 7 5 e.v. has b e e n g i v e n b y O t v o s a n d Stevenson ( 1 9 ) f o r most of t h e elements. I n a c c o u n t i n g f o r r e l a t i v e m u l t i p l i e r gains o f m o n a t o m i c ions, the v a r i a t i o n w i t h the mass o f the p r i m a r y i o n at the e x p e r i m e n t a l a c c e l e r a t i o n v o l t a g e is f r e q u e n t l y e s t i m a t e d a c c o r d i n g to t h e suggestions g i v e n b y I n g h r a m a n d co-workers (14, 15), w h i c h w e r e b a s e d o n e x p e r i m e n t a l d a t a f r o m a l k a l i ions. T h e d a t a suggests that at constant i o n e n e r g y the m u l t i p l i e r g a i n is i n v e r s e l y p r o p o r t i o n a l to t h e square root of mass o f t h e isotope i n v e s t i g a t e d . T h i s r e l a t i o n appears to h o l d s p e c i f i c a l l y f o r h i g h e r masses (>
100 a.m.u.) a n d l o w e r i o n energies (2000-3000 e . v . ) , w h e r e the g a i n
is a l i n e a r f u n c t i o n o f t h e i o n energy.
H i g a t s b e r g e r et al. (11)
found
t h a t for the n o b l e gas ions, except h e l i u m , t h e s e c o n d a r y e l e c t r o n e m i s s i o n b y i m p a c t of ions, w h i c h is p r o p o r t i o n a l to t h e e l e c t r o n m u l t i p l i e r g a i n , also v a r i e d a p p r o x i m a t e l y w i t h the inverse square root o f mass over t h e i o n e n e r g y of 2 0 0 0 - 6 0 0 0 e.v. s t u d i e d . P l o c h ( 2 0 ) , as w e l l as P l o c h a n d W a l c h e r (21) h a v e s h o w n e x p e r i m e n t a l l y that f o r t h e isotopic pairs L i - L i , n
7
1 > 0
N e - - N e a n d ™K- K t h e 2
;
s e c o n d a r y e l e c t r o n e m i s s i o n a t i o n energies b e t w e e n 6 0 0 - 6 0 0 0
41
e.v. is
w i t h i n 1 % p r o p o r t i o n a l to t h e velocities o f the isotopic ions—i.e., i n versely p r o p o r t i o n a l to t h e square root o f mass at constant i o n energy. H i g a t s b e r g e r et al. (11) f o u n d a n inverse square root o f mass d e p e n d e n c e at constant i o n energy f o r t h e - ° N e - - N e p a i r a n d t h e i s o t o p i c 2
3 0
Ar- Ar.
pair
T h e d a t a f o r t h e k r y p t o n , x e n o n , a n d m e r c u r y isotopes b y
4 0
H i g a t s b e r g e r et al. also suggest the v a l i d i t y of the inverse square root o f mass r e l a t i o n . io7
A g
.KM)
A g j
I n a s t u d y of t h e m u l t i p l i e r gains o f t h e isotopic pairs
i«.->
R e
.i87
R e ?
a
n
d
l ' o ^ p o r q ^ M c K i n n e y (18) also finds that
at i o n energies of 7000 e.v. t h e inverse s q u a r e root o f mass d e p e n d e n c e a p p l i e s w i t h i n the e x p e r i m e n t a l error.
In Mass Spectrometry in Inorganic Chemistry; Margrave, J.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
20.
Electron
GiNGERiCH
293
Multipliers
I n c o n n e c t i o n w i t h h i g h t e m p e r a t u r e mass s p e c t r o m e t r i c a p p l i c a t i o n s A c k e r m a n et ai. (1,2)
h a v e m e a s u r e d the r e l a t i v e m u l t i p l i e r gains for N e , +
Ar , K r , C u , A g , and A u +
+
+
+
+
at i o n energies of 4500 e.v.
T h e results for
these ions agree f a i r l y w e l l w i t h the suggested inverse square root of mass d e p e n d e n c e .
F r o m these results t h e y c o n s t r u c t e d
a calibration
c u r v e for the "mass d e p e n d e n c e " of the m u l t i p l i e r g a i n . I n subsequent p u b l i c a t i o n s , D r o w a r t a n d co-workers h a v e used this c a l i b r a t i o n c u r v e extensively to estimate the m u l t i p l i e r gains of m o n a t o m i c ions for w h i c h the g a i n w a s not
measured.
De
M a r i a , Goldfinger, Malaspina,
and
P i a c e n t e ( 7 ) m e a s u r e d the r e l a t i v e m u l t i p l i e r gains for the ions Z n , C d , +
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+
A g , T e , H g , a n d P b a n d f o u n d t h e m to b e n e a r l y constant. +
+
+
+
T h e present i n v e s t i g a t i o n is c o n c e r n e d w i t h the c o m b i n e d mass effect a n d effect of e l e c t r o n i c configuration ( often s i m p l y r e f e r r e d to as " m a s s " effect)
o n the m u l t i p l i e r g a i n for several s i n g l y c h a r g e d
monatomic
species.
T h e measurements w e r e m a d e r e l a t i v e to
energy.
T h e e x p e r i m e n t a l results are c o m p a r e d w i t h m e a s u r e d a n d p r e -
1 0 7
A g at constant i o n
d i c t e d literature d a t a . T h e p r i n c i p a l p u r p o s e of this c o n t r i b u t i o n is to d r a w , b y u s i n g the l i m i t e d d a t a a v a i l a b l e , a t t e n t i o n to the fact that the " m a s s " effect i n m u l t i p l i e r g a i n p h e n o m e n a is not r e a l l y u n d e r s t o o d a n d to s t i m u l a t e f u r t h e r w o r k o n this matter. Experimental
Method and Results
T h e mass spectrometers u s e d w e r e 60° sector, 1 2 - i n c h r a d i u s , d i r e c t i o n a l f o c u s i n g instruments b u i l t b y N u c l i d e A n a l y s i s Associates t h a t are s i m i l a r to the one d e s c r i b e d b y I n g h r a m a n d co-workers (6, 2 2 ) . T h e measurements c o r r e s p o n d to c o n d i t i o n s g e n e r a l l y e m p l o y e d i n h i g h t e m p e r a t u r e mass s p e c t r o m e t r i c investigations i n w h i c h E q u a t i o n 1 is a p p l i e d . T h e g r i d c o l l e c t o r a n d F a r a d a y c u p collector, r e s p e c t i v e l y , i n the t w o instruments u s e d for the m u l t i p l i e r g a i n measurements, as w e l l as the angle of i n c i d e n c e of the i o n b e a m o n the first d y n o d e of the e l e c t r o n m u l t i p l i e r w e r e u s e d as s u p p l i e d b y the m a n u f a c t u r e r . N o attempt w a s m a d e to s t u d y the m a n y factors that enter the m u l t i p l i e r g a i n p h e n o m e n a (14,15). B y k e e p i n g a l l e x p e r i m e n t a l c o n d i t i o n s constant a n d b y r e l a t i n g the m u l t i p l i e r g a i n m e a s u r e d for a c e r t a i n i o n d i r e c t l y to that of the Ag i o n m e a s u r e d i n the same e x p e r i m e n t , a l l these factors p r e v i o u s l y d i s cussed (14, 15) except the c o n t r i b u t i o n of the c o m b i n e d mass-effect a n d effect of electronic configuration are a s s u m e d to c a n c e l out. T h e m u l t i p l i e r gains w e r e m e a s u r e d i n c o n n e c t i o n w i t h the s t u d y of the v a p o r i z a t i o n b e h a v i o r of solids. T h e silver a n d the s o l i d to b e s t u d i e d w e r e c o n t a i n e d i n a K n u d s e n effusion c e l l . T h e s i l v e r was e v a p o r a t e d at the b e g i n n i n g of a n e x p e r i m e n t a l series, f o l l o w e d b y the v a p o r i z a t i o n of the s o l i d . E x p e r i m e n t a l details not p e r t i n e n t to the m e a s u r e m e n t of the m u l t i p l i e r g a i n w e r e s i m i l a r to those p r e v i o u s l y d e s c r i b e d (10). Each series for w h i c h m u l t i p l i e r gains are p r e s e n t e d w a s t a k e n over a t i m e p e r i o d of n o m o r e t h a n three days. B o t h instruments w e r e e q u i p p e d w i t h a 16-stage p i e - t y p e e l e c t r o n m u l t i p l i e r that is m a g n e t i c a l l y s h i e l d e d 1 0 7
In Mass Spectrometry in Inorganic Chemistry; Margrave, J.; Advances in Chemistry; American Chemical Society: Washington, DC, 1968.
+
294
MASS S P E C T R O M E T R Y IN INORGANIC C H E M I S T R Y
( 16,17). It is s i m i l a r to the one u s e d b y I n g h r a m a n d co-workers (14,15) b u t has C u - B e dynodes w i t h a p p r o x i m a t e l y 2 % B e i n s t e a d of A g - M g d y n o d e s w i t h 1.7% M g . I n one i n s t r u m e n t used, the r e l a t i v e m u l t i p l i e r g a i n w a s m e a s u r e d w i t h a g r i d - t y p e d u a l collector s i m i l a r to t h a t d e s c r i b e d b y Stevens a n d I n g h r a m (23, 24). A d v a n t a g e s of this m e t h o d are that g r i d a n d m u l t i p l i e r signals are r e c o r d e d s i m u l t a n e o u s l y , thus a v o i d i n g corrections f o r a d r i f t i n the i o n intensity, a n d that a l a r g e n u m b e r of measurements c a n b e m a d e c o n v e n i e n t l y . M u l t i p l i e r g a i n measurements i n K n u d s e n c e l l mass s p e c t r o m e t r i c a p p l i c a t i o n s , u s i n g a g r i d collector, h a v e b e e n d e s c r i b e d p r e v i o u s l y b y B e r k o w i t z a n d C h u p k a (3). Table I.
Multiplier Gains at Ion Energies of 7.0 k v . for P , A s , Sb , B i , and LP Relative to A g Using a G r i d Collector +
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+
+
+
+
Deviation Factor Substance Studied A g + PrSB
Ag + TaP
Ag + UP +
A g + PrAs
A g + PrBi
Ion Meas ured
No. of Measure ments
Average Gain γ X 10
Ag Sb
2 10
9.95 9.93
0.18 1.26
1.00
1.06
5 7
9.02 13.10
0.33 0.95
1.45
0.78
7 22 7
9.11 12.70 9.13
0.48 0.62 0.27
1.39 1.00
0.75 1.49
Ag As^
6 17
9.06 10.35
0.46 0.88
1.14
0.95
Ag Bi
9 23
8.55 7.49
0.12 0.27
0.88
1.22
Ag P U0
2
Ag P u
+
+
+
+
+
+
+
+
+
+
5
S.D.
yi/ 7A , yA
