Experimentally determined effect of throughput and time on the cryopumping of argon, carbon dioxide, and nitrogen

The influence of throughput on the experimentally determined capture coefficients in the cryopumping of argon, carbon dioxide, and nitrogen is reported. A model and its electronic analogue computer circuit for determining relative effects of system parameters is presented. The variation of capture coefficient with time ('bare surface effect') was also investigated.

EXPERIMENTALLY DETERMINED EFFECT OF THROUGHPUT AND TIME ON THE CRYOPUMPING OF ARGON, CARBON DIOXIDE, AND NITROGEN P. F. PUCCl, J. A. BEVAN, D. R. BRECKENRIDGE, V. R. EVERLY, and L. C. TEDESCHI

THE NEED for the simulation of outer space environments has led to the development of low temperature and ultra high vacuum environmental chambers. One method of attaining ultra high vacuum is by cryopumping. After an initial evacuation of the chamber by conventional vacuum pumping equipment, the temperature of an interior surface is lowered by cryogenic cooling to below the solidification temperatures of the gases remaining in the environmental chamber. Upon collision with the cryogenically cooled surface (cryosurface), the gas freezes out and adheres to the cryosurface, reducing the pressure to the vapour pressure corresponding to the cryosurface temperature. This vacuum producing technique is called cryopumping.1 A measure of cryopumping performance is the capture or sticking coefficient which is generally defined as the probability that a gas molecule will condense on the cryosurface on its first collision with that surface. 2 A complete understanding of the interaction of the gas and the condensate molecules at the solid-gas interface is not yet available, although considerable insight into the problem has been made.3,a,s It is the purpose of this paper to present the experimentally determined influence of gas throughput and time on the capture coefficient for three gases in a particular cryopumping facility. The definition of capture coefficient used in this paper follows that of Dawson and Haygood,6 that is, the ratio of the actual rate of molecules condensed by a cryosurface to the theoretical maximum rate of condensation. Represent!ng the experimentally determined pump!ng speed as Vexp, and the theoretical pumping speed as Vth, thecapture coefficientf = l?exo/l?th.In the free molecular regime of the gases in a high vacuum environment, the theoretical pumping speed is obtained by the application of the Maxwell-Boltzmann molecular velocity distribution, the perfect gas law, and thermal transpiration

PFP is at the Department of Mechanical Engineering, Naval Postgraduate School, Monterey, California, USA. JAB, DRB, VRE, and LCT are with the United States Navy. Received 14 May 1969. CRYOGENICS • OCTOBER 1969

NOMENCLATURE

A f fg fs k rn M P Q R t T V I2

Surface area Capture coefficient Condensation coefficient Evaporation coefficient Boltzmann constant Molecular mass Molecular weight Molecular flow rate Pressure Throughput Universal gas constant Time Temperature Volume Volumetric flow rate

Subscripts

a c d g i L o r s

Gas addition volume Cryosurface Diffusion pump Gas Inner volume Gas addition Outer volume Leakage and outgassing Cryosurface

yielding

FRTgq where As is the cryosurface area, R the universal gas constant, To the gas temperature, and M the gas molecular weight. The experimental pumping speed is obtained by applying the continuity equation to the environmental system. The net rate of gas flow into the system is equal to the rate of gas condensed plus the rate of increase of gas

within the system. Utilizing the perfect gas law, this becomes

PC i,v TL = -~8 + - ~ s where the subscript L refers to the gas entering .the system. For chamber pressure equilibrium at Pc, P is zero. Defining the throughput rate, QL = PLIYL, the experimental pumping rate becomes

= PgAs[2~mk Tg]-i

OzTa I/L = f'exp-~ PeTL

Of these incident molecules, a fraction .fg will condense and the remainder will be reflected. In addition, molecules of the condensate will evaporate. By definingfs such that the rate of evaporation of the condensate is represented

and the capture coefficient becomes

e:, [2~M] ' PeTLA, [R TaJ

f-

It is helpful to relate the capture coefficient to two similar parameters, namely, the condensation coefficient, fg, and the evaporation coefficient, fs. Consider the case of a pure condensed gas in an isothermal enclosure. The vapour and solid phases will be in equilibrium at the vapour pressure corresponding to the equilibrium temperature. The rate of gas molecules incident upon the solid is obtained from (1) by introducing the perfect gas law and Boltzmann's constant, that is,

. . . (2)

by

Nevap = fsPsAs[2zcmk Tel- t Fill. and vent tines

r;IH

then at equilibrium, with no net mass transfer,

Jk

~/'eond = N.va,

and faea fse. T~ - T~

...

(3)

For a system into which a stream of gas is admitted while a cryosurface is pumping, steady state may also be achieved at some chamber pressure Pc. The net capture rate of molecules on the cryosurface is the difference between the condensation and evaporation rates, that is,

IllI

Gas add i l i o n line

,

N.et = [2 .[gP, A J'~P,A n m k Tg] t - ~[2rcmk Ts] ~ Dividing by the theoretical incident flux yields

Cryogenic trap

'J

pump

]

~

¢]

/~rnet "f -

Diffusion pump

~l

Ps[Ta] ½ - f g - f e -ff-e -~s

Substitutingfi in terms offg from (3) Figure 1. Schema of system

.[,

To vacuum chamber

,4,

Also

t

, (Pc - Ps) Qt, To [2nM] t f = Jg P-e - PeAsTL [R TaJ Calibration volume

I

To

auxiliary pumping

Figure 2. Gas addition and flow measurement system 344

(5)

Experimental facility

[__

Test gas

[2.M],

--~s)AsrL [ ~ g J

...

1 Variable leak val.ve

o r, fg = (P,

The environmental chamber used is shown schematically in Figure 1. The vacuum chamber is a 102 cm diameter by 147 cm long cylindrical stainless steel tank with a chamber volume of 994 1. The chamber has within it a 83-8 cm diameter by 91.4 cm long cylindrical double walled shroud, and two 91.4 cm diameter disc double walled shrouds. The shrouds are singly embossed on the outer surfaces, and are manufactured from type 304 stainless steel and electropolished. Each shroud has its fill and vent piping, and the volumetric capacity of the shrouds is 33 1. The cryosurface used is also a singly embossed type 304 stainless steel electropolished panel, rectangular, 30.5 cm by 50.8 cm, with fill and vent lines. The surface area of the cryosurface is 3 300 cm 2. C R Y O G E N I C S • OCTOBER 1969

The vacuum pumping system consists of a 47.2 1/s single stage mechanical forepump and a 15 cm diameter, four stage fractionating diffusion pump with a liquid nitrogen cold trap. The gas addition and flow measurement system is shown in schematic in Figure 2. The flow rate was set at an approximate value, indicated by the counter on the metering valve, and calibrated by the pressure rise method 5 prior to each run. Pressure measurements were made using a conventional Bayard-Alpert ionization gauge and a cold cathode triggered discharge gauge mounted on the chamber wall, and a nude Bayard-Alpert gauge mounted within the shroud envelope. Temperatures were measured with calibrated copperconstantan thermocouples. Four thermocouples were mounted on the cylindrical shroud, four on each end disc shroud, and six were mounted on the cryosurface. A baffle, placed at the gas addition line discharge into the chamber, prevented streaming, and thus permitted the assumption that the gas temperature was the same as the shroud temperature. The cryosurface temperature was maintained by either a helium gas refrigeration system for the lower temperatures, (20-40 K), or by liquid nitrogen for the higher temperatures, (80-90 K).

The leakage and outgassing rates, Nr~, Nro, and A~ra, are assumed to be constant and expressable in the following form = k~

The molecular flow rate of the controlled addition gas is given by kL - P L ~ _ kTL

Q~ kTL

The intervolume molecular flow rates depend on the conductances between the volumes, and are expressed in the form

NS* = PsAsk[27~mk TS]- ~ - P1cAks[2nmk Tk]- ½ Thus Na* = Ca[PaTa- ~ - P~Ti- t]

where Ca = Aal[2nmk] -~

and fifo = Ct[P~T~ - ~' -- PoTo -+]

Model

A model of the system consists of three volumes, as shown schematically in Figure 3. The cylindrical and end disc shrouds separate the chamber into two regions: an inner volume, V~, and an outer volume, Vo, between the shrouds and the chamber walls. The conductance between the two volumes consists of two circular viewing ports in the centre of the end disc shrouds, and a clearance between the end disc shrouds and the cylindrical shroud. The gas addition volume, Va, consists of the piping from the controlled gas supply to the inner volume. The figure also denotes the corresponding pressures and temperatures associated with these volumes, and the individual molecular flow rates. A mass balance on each of the three volumes yields for the net molecular flow rate into the inner volume, 1Qi = )Vrt + ~fa, -- ]Qc -- Nio

where G = Alo[27rmk]-

The diffusion pump pumping speed, I?d, can be assumed to be constant over the pressure range of interest and its molecular rate can be represented by

r~ Pal where a is a factor which includes the effect of the limited conductance of the cryogenic trap. Substitution into (6), (7), and (8) yields the following equations for the rate of change of pressure in each volume.

Q,.,

=-VT+L

ko = k,o + k r o - f,~

...

[

.~face inner volume Ni Pi Vi Ti Nc--.'-

~Nio

I~Id

_I

pump]

~r. I Ncli / Y Addition h ] L / volume I1~ . I~L iN.p" Vo Tel[ Tesl gQs Figure 3. Model

CRYOGENICS

•

OCTOBER 1969

rc ,
_P"+L~J

+ L @ /

i,o Q,o f C,~To1

o

:

C~k(TD~ fgA.i kT~\ q

+ -~

fia

Qra

QLTa

+ ~t~)

jn

p,v~ C,k(To)q~,o

= --Co + IVo(T,)q p~ - I-Co +

=

J

,< )l

i-~-~,

Cak(T~)~

(7)

and for the net molecular flow rate into the piping volume, . . . (8) Na ]QL-l- ]Qra-- ]Vai

Outer volume No Po Vo To

v,

. . . (6)

for the net molecular flow rate into the outer volume,

t

= kT

[CakTa]

=~+v~+[~JP'-t

Voo

J

[ C a k ( T a ) ~]

vo jPa

These equations may be rewritten as fi~ = al + azPo + a3Pa -- a4Pl

.

. . (9)

1;o = as + a6Pi - (a7 + as)Po

. . . (10)

1;a = ( a 9 + a l o ) + a l l P / - a ~ 2 P a

. . . (11)

where the coefficients an are given in Table 1. In this form the equations are adaptable to the electronic analogue computer. 7 The circuit developed is shown in Figure 4. It is useful in determining the relative magnitude of the effects of the variation in the system parameters. 34S

[

Outer votume, Vo

Results

Inner votume~ Vi

The experimental technique used is based on the pressure drop method described in the model analysis section, and shown in Figures 3 and 6, which results in the expressions for the condensation and capture coefficients in (4) and (5). After initial evacuation of the chamber, the cryosurface is cooled by gaseous helium or liquid nitrogen, which reduces the chamber pressure to approximately 1-5 × 10-8 la. The rate of controlled gas addition is set and calibrated. After steady state is achieved, the diffusion pump is isolated from the system. The gas addition is

J.

I

(/~t

I--~'~

J Addition votume, Va

vatve

oos

addition ~ vatve

]iJ/"

I TABLE 1. MODEL EQUATION COEFFICIENTS

f,A,T,P,(k~

Q.

Figure 4. Analogue circuit for model

a, = - ~ + ~ C~ kT~ Vl(To)O. s

a=

C , kT~ a 3 - V=(Ta)O.~

Cak(TO °'5

a,

I AP

Pf

0"~

\2nmT,]

v~

fgAs { kT~ ~o.5

+ ~

ffE~!

C,k(TOO.5

+

v~

Q,-o

x

ft...

]

.

111

[

a6

a(/ a a, = -~o

a8

C~ kTo Vo(TOO.5 C~ k( To)°'5

Vo

Q,.a

I ['1

a5 = ~

a, = T =

tZ

ta

Ca kTa V.(TOO. 5

an-

Time

alo =

Q~T. V~,T*

an

Ca k(T,) °'5 V,~

Figure 5, Chamber pressure versus time

Consider the following sequence of events. At time t~, gas is being admitted to the chamber, a steady state pressure having been established at PI with both the diffusion pump and the cryosurface pumping. This is shown as regime I in Figure 5. At time t2, the chamber is isolated from the diffusion pump and the pressure rises to a new steady state pressure, Pe (regime II in Figure 5). At time l'3, the inflow of admitted gas is abruptly halted and the pressure drops to a new steady state pressure, Pg (regime III in Figure 5). If, in addition to the controlled admitted gas, other condensable and noncondensable gases are present, due to impurities in the admitted gas, inleakage of the local atmosphere through the chamber walls and seals, and outgassing of components of the system, a slight pressure rise will occur in time regimes II and III, as indicated in Figure 6. The solutions of (9), (10), and (11) yield for the pressure drop in the inner volume between time regimes II and III

P~(II) - P~(III) =

a3 a s

t_

I ]

I

II

Ill

l

[ ta

t~ Time

Figure 6. Chamber pressure versus time 1'0

Argon

0.8 •~0.6 u ,e-

a~o

a4 a8 a l 2 - - a2 ao a12 - - a3 a s

o u

QII

•

0.4 ®

o.

Ig-A--~sTLl RTd

O

O

C)

O r,

'

0.2"

(9

O

O

O®

fg = [P,(II) --P--~-II)]A.TL [-R-~.] ...

(12)

This is the same result as that given in (5), since T~ = Tg, P~(II) = Pe, and P~(III) = Pg.

0 0.01

I 0.05

I 0.1 Throughput, T, I/s

0.S

Figure 7. Capture coefficient versus throughput for argon CRYOGENICS - OCTOBER 1969

abruptly halted and the resulting chamber pressure drop, AP, determined from the recorded pressure. Three high purity, laboratory gases were used--argon, carbon dioxide, and nitrogen, and two separate effects were investigated on each. Experiments were performed to determine the influence of the gas addition throughput on capture coefficient,S, 9 and the influence of time (bare surface effect) on capture coefficient.1° T A B L E 2. C O M P A R I S O N OF REPORTED D A T A ARGON Throughput Ix I/s not reported not reported not reported 0.00332 0-021 0.1236 0.150

AP, 10 -~ r

Ts, K

Tg, K

0.10 1.55 13.4 14.1

10 20 20 19 26.6 25 25.6

300 300 300 297 294 297 295

FOR

Capture coemcient Reference 0.68 0.65 0"66 0.68 0.355 0.25 0.28

12 12 6 * * * *

* this work

T A B L E 3. C O M P A R I S O N OF REPORTED D A T A C A R B O N DIOXIDE Throughput, Ix I/s

AP, 10-e r

0.00356 0.060 0.158 0.208 0.219 0.244 not reported not reported not reported not reported not reported variable not reported not reported 0.027 0.0798 0.103 0.185 0.226 0.399

0.128 2.60 8.69 13.5 15.0 17.9

1.11 5.62 11.8 11.2

Ts, K

Tg, K

19.0 27.9 28.8 28.3 24.0 37.5 10.0 10.0 20.0 20.0 20.0 86.0 77.0 77.0 89.4 77.0 93.6 90.2 82.0 77.0

297 296 296 296 294 291 300 300 300 300 300 300 300 300 295 300 294 299 297 300

The capture coefficients obtained for gas throughputs less than 0.05 ~t l/s agree well with published data, see Tables 2, 3, and 4. For higher throughputs, the capture coefficient decreases rapidly for the three gases investigated, which may indicate that the cryopumping becomes insensitive to vapour pressure and depends on partial pressure, see Figures 7, 8, and 9. The bare surface effect was first reported by Wang. z Since that time, various investigators have reported the phenomenon for different gases under different conditions. One group of investigators reported that the effect did not exist, while others recognizing that the effect may exist, condensed test gas on the cryosurface until a coating was visible prior to measuring the capture coefficient. Mullen and Hiza 17 observed an 'activation' phenomenon for carbon dioxide in which no cryopumping was observed until a definite partial pressure of the carbon dioxide was reached corresponding to a given cryosurface temperature. At temperatures above 80 K, activation began when the partial pressure was raised to the corresponding vapour pressure at that temperature. Below 80 K, they observed activation partial pressures to be higher than the corresponding vapour pressures.

FOR 1-0

Capture coe~cient Reference 0.65 0.559 0.464 0.408 0.39 0.368 0.77 0.75 0.62 0.63 0.64 0.68 0.63 0.62 0.589 0.60 0.467 0.411 0.51 0.42

* * * * * * 12 6 12 6 13 * 6 14 * 2 * * * 2

Carbon d i o x i d e

,~ 0'8

~ o

U

0.6

B B

P

0

O oOO O

3 O.

u 0.6,

o

13

0-2

O Ts~27K _ 47 a

B? -9/+

0 0.01

I

I

0-05

0.1

0.5

Throughput,; t/s

* this work

T A B L E 4, C O M P A R I S O N OF REPORTED D A T A NITROGEN Throughput, Ix I/s

AP, 10-e t

0.00226 0.00383 0.0098 0.05 0.102 0.104 0.158 0.164 0.204 0.216 0,218 0.425 0.433 not reported not reported not reported

0.068 0.116 0.284 1.77 3,86 3.81 6-93 7.51 7.85 9.48 12.6 34.6 40.6

Ts, K

Tg, K

25.0 20.0 25.0 27,7 34.9 25,0 25.0 34,6 24,0 25.0 33.7 25.0 30.0 10.0 20.0 20.0

300 298 300 293 293 300 300 292 299 300 292 300 295 300 300 300

* this work C R Y O G E N I C S • O C T O B E R 1909

Figure 8. Capture coefficient versus t h r o u g h p u t for carbon dioxide

FOR

Capture coe~cient Reference 0.62 0.63 0,64 0.552 0.52 0.54 0.47 0,447 0.52 0.44 0.369 0.28 0.241 0.66 0.61 0.60

* * * * * * * * * * * * * 12 12 6

1"0 Nitrogen

0.8 ® o

O @ @OOOo

:~ 0.6

@

~0'4

~°o2 0

=

0"0005 0"001

I I I I 0-005 0'01 0.05 0.1 Throughput~ x [/s

I 0"5

1-0

Figure 9. Capture coefficient versus t h r o u g h p u t for nitrogen 347

Additionally, they observed a gradually increasing capture coefficient as the monolayers of surface deposit increased. Table 5 is a compilation of other reported bare surface effects and includes the results of this investigation. No bare surface effect was observed for argon (see Figure 10). For nitrogen, a bare surface effect was observed for two different throughputs (see Figure 11). For carbon dioxide, no bare surface effect was observed

'or 0'8

~'~-c:Po,i~ ~o ~%o~e~°o°o°°°o

T A B L E 5. REPORTED O B S E R V A T I O N S OF THE BARE SURFACE EFFECT

Gas CO= CO= CO= CO= CO2 Nz N= N= H= A A

T~, K

Tg, K

Bare sur[ace effect observed?

77 77 82 24 19 18 24 20 3 25 19

300 300 297 294 297 79 299 298 300 297 297

yes no yes no no yes yes yes yes no no

Throughput, I.t I/s

Reference

0.5 not reported 0.226 0.219 0.00356 not reported 0.2042 0.00383 not reported 0.1236 0.00332

2 4 * * * 15 * * 16 * *

* this w o r k

.~_ 0"G u

"I ¢u

Argon

3o-~,

~

Figure 10. Capture coefficient versus time for a r g o n

for two throughputs at a cryosurface temperature of 19-24 K. However, one high throughput run at a higher cryosurface temperature, 82 K, did indicate an effect, which is consistent with Mullen and Hiza 17 (see Figure 12). An uncertainty analysis, using the method of Kline and McClintock, 11 of the six measured quantities used in the determination of the capture coefficient, yielded a maximum uncertainty of 12~.

1"0

The support of the Office of Naval Research, Naval Postgraduate School Foundation Research Programme is gratefully acknowledged.

0"8

REFERENCES

~

Ts~ K

QL,

......,

x

0'2

t/s

e 0.00332 m 0.1236

0

I

I

50

100

19

25

150

Time, rain.

:~ 0"6 .e_

tara --BBB Uee e

BB ~ea0~(~oOdical~oe

.u o

E1

El

m

B

BB

[]

80.~

Nitrogen Ts,K o° 0 . 2

B 0-0O383 O 0'2042 0

L

t

10

20

I

I

30 rain.

Time,

2O 24

40

,50

Figure 11. Capture coefficient versus t i m e f o r nitrogen

1"00

~0"75

~

e oeJDeDee

0.50 -

e

ee

e

o

o eeee

•

e <~o B m m Bfal.Bflm

ct m m

toni

1=4

OL

o00.25

El

Carbon dioxide QL, Ts, l/s K e ff00356

1

10

I

20 l i m e , rain.

e

00.226

19 86

130.219

24

I

30

40

Figure 12. Capture coefficient versus time for carbon dioxide

I. BAILEY, B. M., and CHUAN, R. L. 1958 Vacuum Symposium Transactions, p. 262 (Pergamon Press, 1959) 2. WANG, E. S. J., COLLINS,J. A., and HAYGOOD,J. D. Advances in Cryogenic Engineering 7, 44 (1962) 3. LENNARD-JONES,J. E., and DEVONSHIRE,A. F. Proc. Roy. Soc. A156, p. 887 (London, 1936) 4. BUFEHA~, B. A., HENAULT, P. B., and FL1NN, R. A. 1962 Vacuum Symposium Transactions, p. 205 (Pergamon Press, 1963) 5. DAWSON, J. P., and HAYGOOD,J. D. 'Temperature effects on the capture coefficient of CO2', AEDC-TDR-63-251 (1964) 6. DAWSON,J. P., and HAYGOOD,J. D. Cryogenics 5, 57 (1965) 7. TEDESCHI,LOUISC. 'Capture coefficients of carbon dioxide and nitrogen gas on a cryogenic cooled surface', MS thesis, Naval Postgraduate School, 1966 8. BEVAN,J. A. 'Capture coefficients of nitrogen on a cryogenically cooled panel', MS thesis, Naval Postgraduate School, 1967 9. BRECKENRIDGE,D. R. 'A study of the capture coefficients of nitrogen and carbon dioxide', MS thesis, Naval Postgraduate School, 1968 10. EVERLY,V. R. 'The bare surface effect in cryogenic pumping', MS thesis, Naval Postgraduate School, 1967 11. KLINE, S. J., and MCCLINTOCK,F. A. Mechanical Engineering (January 1953) 12. DAWSON, J. P. 'Capture coefficients of six common gases', AED C- TD R-64-68, (1964) 13. DAWSON,J. P., HAYGOOD,J. D., and COLLINS,J. A. Advances in Cryogenic Engineering 9, 443 (1964) 14. BROWN, R. F., and WANG, E. S. J. Advances in Cryogenic Engineering 10, 283 (1965) 15. ROGERS, K. W. 'Experimental investigations of solid nitrogen formed by cryopumping', NASA CR-553 (1966) 16. CHUBB,J. N., GOWLAND,L., and POLLARD,I. E. 1966 Vacuum Symposium Abstracts (Herbick and Held Printing Co., Pittsburg, 1966) 17. MULLEN,L. O., and HIZA, M. J. Journalof Vacuum Science and Technology 4, 219 (1967) CRYOGENICS

• OCTOBER

1969