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The effect of vacuum system time constants on thermal desorption spectra
The effect of vacuum system time constants on thermal desorption spectra received 2 April 1977 R P W e b b , S E D o n n e l l y a n d D G A r m o u r , Department of Electrical Engineering, University of Salford, Salford M5 4WT, England
A numerical analysis of the pressure time equation relating to first order single-step gas release has been performed. This has been done for two configurations of vacuum system, each having a volume into which gas release proceeds linked by a conductance C to a detector volume. The differences between the release function and the observed pressure transient have been characterized by observing the manner in which the maximum release rate pm, the temperature for maximum release Tm and the leading and trailing l i e widths We1 and We2 change as a function of the various vacuum system parameters.
Introduction The technique of thermal desorption has been used extensively to study the behaviour of gases adsorbed on to I or implanted into 2 solid surfaces. Briefly, a known quantity of the gas of interest is either allowed to adsorb on to the surface of a solid specimen, or is ionized and energetically injected into the specimen. The rate of evolution of the gas into a vacuum system is subsequently monitored mass spectrometrically as the specimen is subjected .to a controlled annealing schedule. Various schedules have been discussed in the literature, but the most common of these is that in which the temperature increased linearly with time, i.e.
Pumping
speed S Conductance C (o)Experimental configuration ]~
• Conductance C
T=To+at. In the case where the pumping speed of the vacuum system for the gas of interest is either zero or infinite, convenient analytical expressions can be derived relating the evolution rate to the instantaneous pressure or the rate of change of pressure, both for the simple (single volume) vacuum system 3 and for the more realistic complex system comprising two volumes connected by a finite conductance C. 4 However, in reality, many thermal desorption experiments involve release of gas into a complex vacuum system which is pumped with a finite, non-zero pumping speed. Redhead 3 has discussed the perturbations to observed release rates caused by finite pumping speeds for the simple (single volume) system, but to date, the more realistic case of a complex vacuum system pumped with a finite pumping speed has not been disucssed. The object of the present work is to analyse this finite pumping speed case for two common experimental configurations illustrated in Figures l(a) and (b) where V~ is the volume into which the gas is released, 112 is the volume in which the gas is detected, C is the interconnecting conductance and S is the pumping speed. Theoretical considerations
( b ) Experimental configuration ]I Figure 1. The two experimental configurations under consideration.
single-step desorption transient depends on the order of the desorption mechanism. For simplicity, the present work will confine itself to the first order single-step release process, but the trends observed will be true for various other types of release transient. The first order single-step release process can be described by: dNd.__7= - N k o
exp(---~-f,Q)
(1)
where N is the concentration of gas in a trapping site characterized by activation energy Q at any time t and temperature T, ka is rate constant and R is the universal gas constant. For a situation where temperature is varying as T = To + at, equation (a) can be re-written: dN
The mechanism which gives rise to release in a thermal desorption experiment may either be a single-step process, 3 a diffusive process 5 or a combination of the two. 6 Also, the form of the V a c u u m / v o l u m e 2 7 / n u m b e r 9.
Pumping speed S
d---7 =
-Nko
exp [
-Q
"R(ro ~ at
)1
"
(2)
Consideration of the vacuum system state equations for both configurations I and II illustrated in Figure 1 yields the general
PergamonPress/Printed in Great Britain
559
R P Webb, S E Donnelly and D G Armour: The effect of vacuum system time constants on thermal desorption spectra expression relating pressure in the detector D to release rate: d2p
dP
dN
A-d--iT + B-~ + D P = E - ~ ,
(3)
b
where A, B, D and E a r e constants given by: o
A = I~,B= C
V2
CS
+ C+ S,D=--.E=-VI
Vl
C
i
Vi
.~----
for ease I where the detector volunle is directly pumped, and
"2 A = Vz, B = ( C + S ) v t
CS C + C , D = - ~ T , E = V'-'~
for case I1 where evolution proceeds into a directly pumped volume. An approximate solution 7 of equation (I) is given by: dNdt -
k° NO e x p [ -
-r' "I -( ~qb(z')l r ' ) ='
-
(4)
where ~ ( r ' ) = ({)2 ( e - i / r , ) (1 -
2 { + 6r'2),
(4a)
R(To + at) Q '
ko Q Ra ' N O is c o n c e n t r a t i o n at T = 0. Rearrangement of equation (3) and substitution of equation (4) yields: d2P
dP + 2 a - 7 + P = G(r'), dz z o't-
(5)
where:
o
= ~/2 ,,IDA
G(~')
= -~u ,'(r') = ~
B
1
r(r')
~.
(5')
J where r and r ' are related by:
~, = m ' o + r a g x / ( , 4 / D )
(6)
O
E q u a t i o n (5) cannot be solved, to our knowledge, analytically, but numerical analysis is possible by rearrangement of equation (5) and use of a marching techniquefl i.e.
p j + ~ = P j ( 4 a + 4/h - h) - (2/h)(Pj_ 1) + h(Ri + 1 + Rj) (4a + 2/h + h) (7) where h = At, the computing increment. Using this method, numerical analysis of equation (7) has been performed using a c o m p u t e r to generate pressure-time curves for variations in temperatures C, S, I,'1 and V2. These 560
I
~oo
32O
I
340
'~,
360 T~
i
380 Temperolure,
,
I
4O0
,
K
Figure 2. Pressure transients for both experimental configurations. Activation energy Q - 20 kcal mole- t; rate constant ko :- 10 ~3 s- '; ramp rate a - 20 K s-~.(a) S ~ 50 I. s-~, C - 100 I. s-~, Vt I I., Vz = 1 1 . ( b ) S lOI. s-I, C - lOI. s-I, VI :=51., V,=51. (c) Release function R, normalized to unity at maximum for comparison with (a). calculations have been performed for both the experimental configurations illustrated in Figures I(a) and (b). Analysis of the results obtained reveal that, unlike the limiting cases of S = 0 and S--+ w_, the behaviour of the system cannot be characterized conveniently by a single time constant parameter. Consequently, it is not possible to present here a complete analysis of all possible experimental values of S, C, Vj and 11",for a range of values of input function dN/dt. However. the program (in Fortran) is available to readers wishing to characterize their own vacuum system and input functions, on application to the authors. The data illustrated and discussed below are, therefore, intended to exemplify the general behaviour of the observed desorption transient as S, C, V, and V., are altered. To facilitate interpretation of the information presented a set of typical experimental values, i.e. S = 30 1. s-~, C = 100 I. s - ' , V~ = 5 1. and V2 = 1 1. has been chosen for both experimental configurations. Each of the four parameters in turn has then been allowed to vary over a range of values with the other three parameters held constant and the effects on the form of the observed transient recorded. Figure 2 compares the form of the evolution function according to solution of equation (2) with Q = 20 keal m o l e - t and rate constant ko = 10 '3 s -~ with the predicted pressure transients, for (a) a favourable experimental configuration (S = 50 1. s -~, C = 200 1. s-~, P~ = V., = 1 1.) and (b) an unfavourable configuration (S = 51. s -~, C = 5 1. s -~, P~ = 1"2 = 101.). It must be noted that, although there is no real difference between the release peak and the pressure transient for peak (a), the sensitivity (i.e. p,,) is considerably less than in the distorted case. It is interesting to note that when V~ = 1"2 the constants A, B, D and E in equation (3) become identical for both cases so that Figure 2 represents both Cases I and II. It can readily be seen from Figure 2 that, in order to characterize fully the observed transient, four parameters must be considered, namely: the m a x i m u m release rate p,., the temperature for m a x i m u m release rate T,., the leading e-~ width We1, (7"., -- Te~), and the trailing e - t width We2, (Te2 -- T,.).
R P Webb, S E Donnelly and D G Armour." The effect of v a c u u m system time constants on thermal desorption spectra
8 (
°
)
~
eight Pm
ll(b~ercenl°geincre°seintemperaturef°r 4.8J measuredmaximumreleaserote Tm
t, ~q G,
<~ IO0/Vl
~
~ - -
~ _ ~ I O 0 / v ~
1.6--
Soo,v, 0
L ~
I
I0
I
S,C l s-'
20
I
30
I
0
I
-, 20
S, C t s IOO/V~. lOO/V z t -~
IOO/V~, IOO/V2t -~ (c)
I
IO
30
(d)
14 --CS ~\\
12
Percentage mcrease in h%,
I0
Percentage increase
120
=n
o~ tOO
.
#8 c
c
~
g 6
lil~4 2_ -
,oo,
°° ,o
I 0 0 / V z ~ I
I0
I
S,C t s-'
20
20 I
I
I0
30
I
S, C t s-'
20
~ioo/v,
30
lO01V,, lO01V 2 t -L
lO01V,, IO0/V z t -~
Figure 3. Variation in observed release rate maximum pro. Temperature for maximum release 7"=, leading l/e width I,V,q, and trailing l/e width W,.2 as a function of each of the vacuum system parameters S, C, V, and V_~.Case I experimental configuration: activation energy Q = 20 kcal m o l e - t ; rate constant ko = 10 ~3 s - t ; ramp rate a - 20 K s -~. As each vacuum parameter is varied, the other three are kept constant a t a s e t of typical experimental v a l u e s : S - 301. s - t , C = 1001. s - t V~ -- 51., V, = I I.
Inspection of Figures 3(a) and 4(a) reveals that for both experimental configurations, providing C is greater than 5 1. s - t and V, and V2 are less than 20 1., then the behaviour of p,, (i.e. the sensitivity of the detection system) is dependent only upon the pumping speed S through the relation p~, a I/S. In terms of sensitivity this implies that, provided V~ and V2 are fairly small and C is reasonably large for any realistic value of S, the complex system behaves as a simple single-volume system. In practice, of course, the absolute value of p,. is obtained, not from considerations of vacuum system parameters, but by means of a calibration of the mass spectrometric system used for detection. The only empirical requirements for p,,, therefore, are that its magnitude is well within the limits of sensitivity of the detector. A far more important parameter for interpretation of gas release spectra is the temperature for maximum observed release, T,., the behaviour of which, as a function of the four vacuum system parameters, is illustrated in Figures 3(b) and 4(b). It can be seen that both for Case I and Case II all four parameters have an effect on T,., but that this effect, for all realistic values of the parameters is fairly small. It is only when S or C become less than ,~ 2 I. s - I and V~ or 72 become greater than ~ 5 0 1 . that the perturbation becomes considerable.
However, even for a typical experimental configuration, this is liable to give rise to a I-2~o upward shift in the measured T,., which indicates the futility of extremely accurate temperature measurements unless this phenomenon is taken into account. The importance of T,, as an experimental parameter lies in the fact that it is usually easily measured provided that the peaks in the desorption spectra are adequately resolved (see paper by Reed et al. 9 for a full treatment of resolution criteria). K n o w ledge of this value then enables the activation energy for the desorption process to be obtained by means of such relations as
:
exp(-Q)=
a
Q
provided that the kinetics relevant to the peak in question are known. These may be single-step, 3 diffusive s or a combination of the two, 6 and there are a number of ways in which the relevant mechanics may be deduced from the desorption spectra. One of these is by consideration of the form of the release peak itself--first order single-step peaks tend to be relatively narrow with a 'tail' towards low temperatures; single-step second order peaks are slightly broader and roughly symmetrical, and diffusive peaks tend to be broad with a 'tail'
561
R P Webb, S E Donnelly and D G Armour: The effect of vacuum system time constants on thermal desorption spectra
(o)
(b) Percentage increase m temperature for measured maximum release rate Tm
6
8
2.4 2 F-t Vr
OB
I
10
I
20
S,C t s-~ lO0/V,, IO0/V2
30
\lO0/V,
0
I
I
I
IO
20
30
S,C is-' lO0/V,, IOO/Vz l-'
t-'
{c) (d)
14
Percentoge increase in leading I/e width We,
12
_
0~ ~oo
I0
.c
c
trailing I/e width We~
S
¢
8 6
C
Percentage increase in
\
\\\
oo ~ 4o t ~ ~
4
I
I Io°/v,
I0
20
I00/V2
q'" 50
ls-' lO0/V,, lO0/V2 t-'
0
I0
20
30
S,C t s-~
S,C
IO0/V,, IOO/Vz t-'
Figure 4. Variation in observed release rate maximum p,,. Temperature for maximunl release T,,, leading I/e width W,., and trailing I/e width W,z as a function of each of the vacuum system parameters S, C, V, and Vz. Case II experimental configuration: activation energy Q ~ 20 kcal m o l e - ' , rate constant ko = 10 ~3 s - i ramp rate a = 20 K s- '. As each vacuum parameter is varied the other three are kept constant a t a s e t o f t y p i c a l e x p e r i m e n t a l v a l u e s : S = 3 0 1 s - t C = 1001. s - ' . V~ = 51., V2 = I I. towards high temperatures. It is in trying to deduce the mechanics in this manner that the width parameters illustrated in Figures 3(c) and (d) and 4(c) and (d) become extremely important. Figure 2 shows how, in an unfavourable case, a first order release peak can be distorted to the extent that it closely resembles a broad diffusive peak, and Figures 3 and 4 present this information quantitatively, for a range of values of the vacuum parameters. As expected, the leading I/e width We, is essentially independent of experimental parameters. F o r typical experimental values it is liable to be altered by not more than ,-~5 % from its true value. In contrast, however, the trailing l/e width, W~2, is severely perturbed by all the vacuum system parameters and is liable to be ~ 2 0 % wider than the true value even for reasonably optimal values of S, C, l"1 and I"2. It is also interesting to note that on balance the case II experimental configuration, where the release volume is directly pumped by S, causes less perturbation to this parameter than case I. In the analysis presented so far, an activation energy of Q -- 20 kcal m o l e - ' has been chosen. This fairly low value of activation energy gives rise to a narrow release peak at a fairly low temperature. This choice was made to ensure that the results obtained were for a 'worst case' when considering percentage perturbation in peaks where the trapped or adsorbed gas is stable at r o o m temperature. An increased activation 562
energy for detrapping results in a temperature for maximum release at higher temperatures and a broader release peak so that the ratio of transient time constant to effective vacuum system time constant is increased. This results in a smaller percentage perturbation to the observed transient and this fact is illustrated in Figure 5 where the effect of variation in S on the trailing e-1 width is portrayed for a number of different activation energies. In this analysis, a set of typical experimental values was chosen and in turn each of the parameters was varied, whilst the other three were held constant. This 'typical experimental configuration' with S = 30 1. s - 1, C = 100 1. s - ', V, = 5 I. and I/2 = 1 I. corresponds to a small chamber pumped by perhaps a trapped oil diffusion pump and rotary pump with either a magnetic or quadrupole mass spectrometer joined to the chamber by 8 cm of 3.8-cm dia tubing. This type of small U H V gas release apparatus is in regular use in many laboratories.
Conclusions The overall conclusions of the analysis are that, in general, for the type of vacuum system described above, the perturbation to the release spectra arising from vacuum system time constants is liable to be fairly small. The largest effect, providing
R P Webb, S E Donnelly and D G Armour. The effect of v a c u u m system time constants on thermal d e s o r p t i o n spectra
for a trapped diffusion p u m p would give, for xenon, a p u m p i n g speed of only ---8 I. s - ' a n d a similar reduction in the effective c o n d u c t a n c e C. A c c u r a t e experimental data, therefore, on the tempering induced release of heavy gases can only be o b t a i n e d either by careful c o n s i d e r a t i o n of the effects outlined in this c o m m u n i c a t i o n or by using specially designed a p p a r a t u s with high p u m p i n g speeds a n d large conductances.
120
I00
8O
.5 6o g g 4o
g
2O
!1
Q, kcal mole-f 2O
I
0
3
6
9 12 Conductonce
15 18 C, L s
21
24
27
30
Figure 5. Variation in trailing I/e width, H",.2, as a function of conductance, C, for different activation energies, Q. Rate constant k o = JO 13 S - ' , ramp rate a , 20 K s -~, S 30 I. s - ' , V~ = 5 I.,
that tile p u m p i n g speed is r e a s o n a b l y high, is the alteration in 1'1"~2, the trailing l/e width ( ~ 2 0 , % ) . U n f o r t u n a t e l y , in the molecular flow regime which is applicable to such a system, the p u m p i n g speed is p r o p o r t i o n a l to \ ( I / M ) , where M is the mass o f the a t o m or molecule being p u m p e d . This implies that a n o m i n a l 20 I. s - J nitrogen p u m p i n g speed at the c h a m b e r
Acknowledgements We would like to t h a n k Professor G e o r g e Carter for helpful discussion a n d one of us (S E D) would like to acknowledge the U K A E A ( A E R E Harwell) for the provision of financial s u p p o r t d u r i n g the course of this work.
References G Ehrlich, d Chem Phys 34. 1961, 29 and 39. 2 D J Reed, F T Harris, D G Armour and G Carter, Vacuum 24, 1974 4. 3 p A Redhead, Vacutlnl 12, 1962, 225. .t D Edwards, J Vac Sci Te¢hnol 11(6), 1974, 1141. ~ S E Donnelly and D G Armour, Vuctttlm 27, 1977, 21. ~' G Carter, B J Evans and G Farrell, Vacuum 25(5), 1975, 179-199. 7 W A Grant and G Carter, Va('ltlutt 1 5 , 1965, 1. s D R Hartree, Numerical AnalysLr, Oxford University Press, Oxford (1955).
563
A numerical analysis of the pressure time equation relating to first order single-step gas release has been performed. This has been done for two configurations of vacuum system, each having a volume into which gas release proceeds linked by a conductance C to a detector volume. The differences between the release function and the observed pressure transient have been characterized by observing the manner in which the maximum release rate pm, the temperature for maximum release Tm and the leading and trailing l i e widths We1 and We2 change as a function of the various vacuum system parameters.
Introduction The technique of thermal desorption has been used extensively to study the behaviour of gases adsorbed on to I or implanted into 2 solid surfaces. Briefly, a known quantity of the gas of interest is either allowed to adsorb on to the surface of a solid specimen, or is ionized and energetically injected into the specimen. The rate of evolution of the gas into a vacuum system is subsequently monitored mass spectrometrically as the specimen is subjected .to a controlled annealing schedule. Various schedules have been discussed in the literature, but the most common of these is that in which the temperature increased linearly with time, i.e.
Pumping
speed S Conductance C (o)Experimental configuration ]~
• Conductance C
T=To+at. In the case where the pumping speed of the vacuum system for the gas of interest is either zero or infinite, convenient analytical expressions can be derived relating the evolution rate to the instantaneous pressure or the rate of change of pressure, both for the simple (single volume) vacuum system 3 and for the more realistic complex system comprising two volumes connected by a finite conductance C. 4 However, in reality, many thermal desorption experiments involve release of gas into a complex vacuum system which is pumped with a finite, non-zero pumping speed. Redhead 3 has discussed the perturbations to observed release rates caused by finite pumping speeds for the simple (single volume) system, but to date, the more realistic case of a complex vacuum system pumped with a finite pumping speed has not been disucssed. The object of the present work is to analyse this finite pumping speed case for two common experimental configurations illustrated in Figures l(a) and (b) where V~ is the volume into which the gas is released, 112 is the volume in which the gas is detected, C is the interconnecting conductance and S is the pumping speed. Theoretical considerations
( b ) Experimental configuration ]I Figure 1. The two experimental configurations under consideration.
single-step desorption transient depends on the order of the desorption mechanism. For simplicity, the present work will confine itself to the first order single-step release process, but the trends observed will be true for various other types of release transient. The first order single-step release process can be described by: dNd.__7= - N k o
exp(---~-f,Q)
(1)
where N is the concentration of gas in a trapping site characterized by activation energy Q at any time t and temperature T, ka is rate constant and R is the universal gas constant. For a situation where temperature is varying as T = To + at, equation (a) can be re-written: dN
The mechanism which gives rise to release in a thermal desorption experiment may either be a single-step process, 3 a diffusive process 5 or a combination of the two. 6 Also, the form of the V a c u u m / v o l u m e 2 7 / n u m b e r 9.
Pumping speed S
d---7 =
-Nko
exp [
-Q
"R(ro ~ at
)1
"
(2)
Consideration of the vacuum system state equations for both configurations I and II illustrated in Figure 1 yields the general
PergamonPress/Printed in Great Britain
559
R P Webb, S E Donnelly and D G Armour: The effect of vacuum system time constants on thermal desorption spectra expression relating pressure in the detector D to release rate: d2p
dP
dN
A-d--iT + B-~ + D P = E - ~ ,
(3)
b
where A, B, D and E a r e constants given by: o
A = I~,B= C
V2
CS
+ C+ S,D=--.E=-VI
Vl
C
i
Vi
.~----
for ease I where the detector volunle is directly pumped, and
"2 A = Vz, B = ( C + S ) v t
CS C + C , D = - ~ T , E = V'-'~
for case I1 where evolution proceeds into a directly pumped volume. An approximate solution 7 of equation (I) is given by: dNdt -
k° NO e x p [ -
-r' "I -( ~qb(z')l r ' ) ='
-
(4)
where ~ ( r ' ) = ({)2 ( e - i / r , ) (1 -
2 { + 6r'2),
(4a)
R(To + at) Q '
ko Q Ra ' N O is c o n c e n t r a t i o n at T = 0. Rearrangement of equation (3) and substitution of equation (4) yields: d2P
dP + 2 a - 7 + P = G(r'), dz z o't-
(5)
where:
o
= ~/2 ,,IDA
G(~')
= -~u ,'(r') = ~
B
1
r(r')
~.
(5')
J where r and r ' are related by:
~, = m ' o + r a g x / ( , 4 / D )
(6)
O
E q u a t i o n (5) cannot be solved, to our knowledge, analytically, but numerical analysis is possible by rearrangement of equation (5) and use of a marching techniquefl i.e.
p j + ~ = P j ( 4 a + 4/h - h) - (2/h)(Pj_ 1) + h(Ri + 1 + Rj) (4a + 2/h + h) (7) where h = At, the computing increment. Using this method, numerical analysis of equation (7) has been performed using a c o m p u t e r to generate pressure-time curves for variations in temperatures C, S, I,'1 and V2. These 560
I
~oo
32O
I
340
'~,
360 T~
i
380 Temperolure,
,
I
4O0
,
K
Figure 2. Pressure transients for both experimental configurations. Activation energy Q - 20 kcal mole- t; rate constant ko :- 10 ~3 s- '; ramp rate a - 20 K s-~.(a) S ~ 50 I. s-~, C - 100 I. s-~, Vt I I., Vz = 1 1 . ( b ) S lOI. s-I, C - lOI. s-I, VI :=51., V,=51. (c) Release function R, normalized to unity at maximum for comparison with (a). calculations have been performed for both the experimental configurations illustrated in Figures I(a) and (b). Analysis of the results obtained reveal that, unlike the limiting cases of S = 0 and S--+ w_, the behaviour of the system cannot be characterized conveniently by a single time constant parameter. Consequently, it is not possible to present here a complete analysis of all possible experimental values of S, C, Vj and 11",for a range of values of input function dN/dt. However. the program (in Fortran) is available to readers wishing to characterize their own vacuum system and input functions, on application to the authors. The data illustrated and discussed below are, therefore, intended to exemplify the general behaviour of the observed desorption transient as S, C, V, and V., are altered. To facilitate interpretation of the information presented a set of typical experimental values, i.e. S = 30 1. s-~, C = 100 I. s - ' , V~ = 5 1. and V2 = 1 1. has been chosen for both experimental configurations. Each of the four parameters in turn has then been allowed to vary over a range of values with the other three parameters held constant and the effects on the form of the observed transient recorded. Figure 2 compares the form of the evolution function according to solution of equation (2) with Q = 20 keal m o l e - t and rate constant ko = 10 '3 s -~ with the predicted pressure transients, for (a) a favourable experimental configuration (S = 50 1. s -~, C = 200 1. s-~, P~ = V., = 1 1.) and (b) an unfavourable configuration (S = 51. s -~, C = 5 1. s -~, P~ = 1"2 = 101.). It must be noted that, although there is no real difference between the release peak and the pressure transient for peak (a), the sensitivity (i.e. p,,) is considerably less than in the distorted case. It is interesting to note that when V~ = 1"2 the constants A, B, D and E in equation (3) become identical for both cases so that Figure 2 represents both Cases I and II. It can readily be seen from Figure 2 that, in order to characterize fully the observed transient, four parameters must be considered, namely: the m a x i m u m release rate p,., the temperature for m a x i m u m release rate T,., the leading e-~ width We1, (7"., -- Te~), and the trailing e - t width We2, (Te2 -- T,.).
R P Webb, S E Donnelly and D G Armour." The effect of v a c u u m system time constants on thermal desorption spectra
8 (
°
)
~
eight Pm
ll(b~ercenl°geincre°seintemperaturef°r 4.8J measuredmaximumreleaserote Tm
t, ~q G,
<~ IO0/Vl
~
~ - -
~ _ ~ I O 0 / v ~
1.6--
Soo,v, 0
L ~
I
I0
I
S,C l s-'
20
I
30
I
0
I
-, 20
S, C t s IOO/V~. lOO/V z t -~
IOO/V~, IOO/V2t -~ (c)
I
IO
30
(d)
14 --CS ~\\
12
Percentage mcrease in h%,
I0
Percentage increase
120
=n
o~ tOO
.
#8 c
c
~
g 6
lil~4 2_ -
,oo,
°° ,o
I 0 0 / V z ~ I
I0
I
S,C t s-'
20
20 I
I
I0
30
I
S, C t s-'
20
~ioo/v,
30
lO01V,, lO01V 2 t -L
lO01V,, IO0/V z t -~
Figure 3. Variation in observed release rate maximum pro. Temperature for maximum release 7"=, leading l/e width I,V,q, and trailing l/e width W,.2 as a function of each of the vacuum system parameters S, C, V, and V_~.Case I experimental configuration: activation energy Q = 20 kcal m o l e - t ; rate constant ko = 10 ~3 s - t ; ramp rate a - 20 K s -~. As each vacuum parameter is varied, the other three are kept constant a t a s e t of typical experimental v a l u e s : S - 301. s - t , C = 1001. s - t V~ -- 51., V, = I I.
Inspection of Figures 3(a) and 4(a) reveals that for both experimental configurations, providing C is greater than 5 1. s - t and V, and V2 are less than 20 1., then the behaviour of p,, (i.e. the sensitivity of the detection system) is dependent only upon the pumping speed S through the relation p~, a I/S. In terms of sensitivity this implies that, provided V~ and V2 are fairly small and C is reasonably large for any realistic value of S, the complex system behaves as a simple single-volume system. In practice, of course, the absolute value of p,. is obtained, not from considerations of vacuum system parameters, but by means of a calibration of the mass spectrometric system used for detection. The only empirical requirements for p,,, therefore, are that its magnitude is well within the limits of sensitivity of the detector. A far more important parameter for interpretation of gas release spectra is the temperature for maximum observed release, T,., the behaviour of which, as a function of the four vacuum system parameters, is illustrated in Figures 3(b) and 4(b). It can be seen that both for Case I and Case II all four parameters have an effect on T,., but that this effect, for all realistic values of the parameters is fairly small. It is only when S or C become less than ,~ 2 I. s - I and V~ or 72 become greater than ~ 5 0 1 . that the perturbation becomes considerable.
However, even for a typical experimental configuration, this is liable to give rise to a I-2~o upward shift in the measured T,., which indicates the futility of extremely accurate temperature measurements unless this phenomenon is taken into account. The importance of T,, as an experimental parameter lies in the fact that it is usually easily measured provided that the peaks in the desorption spectra are adequately resolved (see paper by Reed et al. 9 for a full treatment of resolution criteria). K n o w ledge of this value then enables the activation energy for the desorption process to be obtained by means of such relations as
:
exp(-Q)=
a
Q
provided that the kinetics relevant to the peak in question are known. These may be single-step, 3 diffusive s or a combination of the two, 6 and there are a number of ways in which the relevant mechanics may be deduced from the desorption spectra. One of these is by consideration of the form of the release peak itself--first order single-step peaks tend to be relatively narrow with a 'tail' towards low temperatures; single-step second order peaks are slightly broader and roughly symmetrical, and diffusive peaks tend to be broad with a 'tail'
561
R P Webb, S E Donnelly and D G Armour: The effect of vacuum system time constants on thermal desorption spectra
(o)
(b) Percentage increase m temperature for measured maximum release rate Tm
6
8
2.4 2 F-t Vr
OB
I
10
I
20
S,C t s-~ lO0/V,, IO0/V2
30
\lO0/V,
0
I
I
I
IO
20
30
S,C is-' lO0/V,, IOO/Vz l-'
t-'
{c) (d)
14
Percentoge increase in leading I/e width We,
12
_
0~ ~oo
I0
.c
c
trailing I/e width We~
S
¢
8 6
C
Percentage increase in
\
\\\
oo ~ 4o t ~ ~
4
I
I Io°/v,
I0
20
I00/V2
q'" 50
ls-' lO0/V,, lO0/V2 t-'
0
I0
20
30
S,C t s-~
S,C
IO0/V,, IOO/Vz t-'
Figure 4. Variation in observed release rate maximum p,,. Temperature for maximunl release T,,, leading I/e width W,., and trailing I/e width W,z as a function of each of the vacuum system parameters S, C, V, and Vz. Case II experimental configuration: activation energy Q ~ 20 kcal m o l e - ' , rate constant ko = 10 ~3 s - i ramp rate a = 20 K s- '. As each vacuum parameter is varied the other three are kept constant a t a s e t o f t y p i c a l e x p e r i m e n t a l v a l u e s : S = 3 0 1 s - t C = 1001. s - ' . V~ = 51., V2 = I I. towards high temperatures. It is in trying to deduce the mechanics in this manner that the width parameters illustrated in Figures 3(c) and (d) and 4(c) and (d) become extremely important. Figure 2 shows how, in an unfavourable case, a first order release peak can be distorted to the extent that it closely resembles a broad diffusive peak, and Figures 3 and 4 present this information quantitatively, for a range of values of the vacuum parameters. As expected, the leading I/e width We, is essentially independent of experimental parameters. F o r typical experimental values it is liable to be altered by not more than ,-~5 % from its true value. In contrast, however, the trailing l/e width, W~2, is severely perturbed by all the vacuum system parameters and is liable to be ~ 2 0 % wider than the true value even for reasonably optimal values of S, C, l"1 and I"2. It is also interesting to note that on balance the case II experimental configuration, where the release volume is directly pumped by S, causes less perturbation to this parameter than case I. In the analysis presented so far, an activation energy of Q -- 20 kcal m o l e - ' has been chosen. This fairly low value of activation energy gives rise to a narrow release peak at a fairly low temperature. This choice was made to ensure that the results obtained were for a 'worst case' when considering percentage perturbation in peaks where the trapped or adsorbed gas is stable at r o o m temperature. An increased activation 562
energy for detrapping results in a temperature for maximum release at higher temperatures and a broader release peak so that the ratio of transient time constant to effective vacuum system time constant is increased. This results in a smaller percentage perturbation to the observed transient and this fact is illustrated in Figure 5 where the effect of variation in S on the trailing e-1 width is portrayed for a number of different activation energies. In this analysis, a set of typical experimental values was chosen and in turn each of the parameters was varied, whilst the other three were held constant. This 'typical experimental configuration' with S = 30 1. s - 1, C = 100 1. s - ', V, = 5 I. and I/2 = 1 I. corresponds to a small chamber pumped by perhaps a trapped oil diffusion pump and rotary pump with either a magnetic or quadrupole mass spectrometer joined to the chamber by 8 cm of 3.8-cm dia tubing. This type of small U H V gas release apparatus is in regular use in many laboratories.
Conclusions The overall conclusions of the analysis are that, in general, for the type of vacuum system described above, the perturbation to the release spectra arising from vacuum system time constants is liable to be fairly small. The largest effect, providing
R P Webb, S E Donnelly and D G Armour. The effect of v a c u u m system time constants on thermal d e s o r p t i o n spectra
for a trapped diffusion p u m p would give, for xenon, a p u m p i n g speed of only ---8 I. s - ' a n d a similar reduction in the effective c o n d u c t a n c e C. A c c u r a t e experimental data, therefore, on the tempering induced release of heavy gases can only be o b t a i n e d either by careful c o n s i d e r a t i o n of the effects outlined in this c o m m u n i c a t i o n or by using specially designed a p p a r a t u s with high p u m p i n g speeds a n d large conductances.
120
I00
8O
.5 6o g g 4o
g
2O
!1
Q, kcal mole-f 2O
I
0
3
6
9 12 Conductonce
15 18 C, L s
21
24
27
30
Figure 5. Variation in trailing I/e width, H",.2, as a function of conductance, C, for different activation energies, Q. Rate constant k o = JO 13 S - ' , ramp rate a , 20 K s -~, S 30 I. s - ' , V~ = 5 I.,
that tile p u m p i n g speed is r e a s o n a b l y high, is the alteration in 1'1"~2, the trailing l/e width ( ~ 2 0 , % ) . U n f o r t u n a t e l y , in the molecular flow regime which is applicable to such a system, the p u m p i n g speed is p r o p o r t i o n a l to \ ( I / M ) , where M is the mass o f the a t o m or molecule being p u m p e d . This implies that a n o m i n a l 20 I. s - J nitrogen p u m p i n g speed at the c h a m b e r
Acknowledgements We would like to t h a n k Professor G e o r g e Carter for helpful discussion a n d one of us (S E D) would like to acknowledge the U K A E A ( A E R E Harwell) for the provision of financial s u p p o r t d u r i n g the course of this work.
References G Ehrlich, d Chem Phys 34. 1961, 29 and 39. 2 D J Reed, F T Harris, D G Armour and G Carter, Vacuum 24, 1974 4. 3 p A Redhead, Vacutlnl 12, 1962, 225. .t D Edwards, J Vac Sci Te¢hnol 11(6), 1974, 1141. ~ S E Donnelly and D G Armour, Vuctttlm 27, 1977, 21. ~' G Carter, B J Evans and G Farrell, Vacuum 25(5), 1975, 179-199. 7 W A Grant and G Carter, Va('ltlutt 1 5 , 1965, 1. s D R Hartree, Numerical AnalysLr, Oxford University Press, Oxford (1955).
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