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Cryopumping in the transition and continuum pressure regions
Cryopumping in the transition pressure regions* received G
13 August
Davey,
Cryogenics
and continuum
7975 Laboratory,
University
of Oxford.
Parks
Road,
Oxford,
England
The problems of cryopumping in the pressure region above that in which free molecular flow prevails are considered, and some of the results are reviewed.
Introduction
The literature on cryopumping is now quite extensive and sufficient information is available to allow the design of a wide range of cryopumps. However, almost all the work done so far has been aimed at exploiting the high pumping speed, low ultimate pressure capability of cryopumping and has therefore been carried out at pressuresin the free molecular region. Although it is still true that most cryopumps are required to operate in the high or ultra-high vacuum regions there are some applications for cryopumps where the operating pressure is much higher. These applications include freeze-drying of drugs and foodstuffs, wind tunnels, pumping of reaction products from thruster rockets and possibly the pumping of corrosive or dusty gases in the chemical industry. In these circumstances where collisions between gas molecules becomes important, volumetric pumping speeds are obtained which may be much higher than those in the free molecular region. Because of the pressure and temperature gradients established in the gas within the cryopump, the rapid build up of the condensed phase on the cryopump and the role played by non-condensable impurities, cryopumping in the transition and continuum pressure ranges has its own extensive set of problems which have not yet received sufficient attention. A limited amount of work has been carried out on all these problems and some of the results are reviewed here. Pumping
in the free molecular
flow region
Before we proceed to our main topic it may be useful, for comparison, to briefly consider the main aspects of cryopumping in the free molecular region. Here things are relatively straight forward. A sticking coefficient can be defined as the probability that a molecule incident on a cold surface will stick. This is easy to measure using a small, usually spherical cryopump of carefully defined area in a large vessel. Negligible pressure gradients exist in the vesseland the temperature of the gas is defined by the temperature of the vessel wall since many collisions take place with the wall before a collision with the cryopump occurs and there are not a significant number of collisions between molecules. In these circumstances kinetic theory tells us the rate of incidence of molecules on the cold
surface and therefore the maximum possible volumetric pumping speed V,,,, when the sticking coefficient is one. This can be compared with the measured pumping speed V and the sticking coefficient obtained from
In general the sticking coefficient is a slowly varying function of gas temperature and cryopump temperature and this must be determined experimentally. When necessary,corrections can be made for re-evaporation of molecules from the known vapour pressure of the condensate.’ In a practical cryopump the cold pumping surface is usually not small compared with the size of the chamber and it is shielded by a baffle at a higher temperature. The main design problem is then to calculate the overall pumping speed of the cryopump and baffle array from geometrical considerations and to optimize the geometry against the conflicting constraints of maximum pumping speed and minimum radiant energy reaching the cryopump through the baffle. When pumping at very low pressure some things are clearly not important. If we pump nitrogen gas with a typical cryopump consisting of a 20 K surface protected by a chevron baffle at 80 K, then the time taken to build up a condensed layer 1 mm thick would be around lo4 h at a pressure of lo-’ torr. We are not therefore concerned about the accumulation of condensate on the pump since this does not effect its useful pumping life. Similarly the heat load on the cryopump due to the incidence and condensation of gas is very small and can be ignored. Most of the heat load often comes from radiation emitted by the surrounding shields and although we may wish to minimize this, the thermal absorptive properties of the condensed layer will not normally enter into our considerations. This is for two reasons. Firstly the layer may never be thick enough to have a significant effect and, secondly, because the pump is intended to reach very low pressures it is certain for most gasesto operate at a very low temperature and be shielded by a baffle at a temperature near 80 K. As we shall see, most cryodeposits are almost completely transparent to radiation emitted by such a surface. Pumping
in the transition
and continuum
pressure regions
* Paperpresentedat the colloquium on Cryogenicpumping organized by the Vacuum Group of the Institute of Physicson 13 November 1974at Imperial College,London.
When pumping at higher pressures there are two effects which considerably complicate the situation. The density of the gas is
Vacuum/volume 26/number 1.
Britain
Pergamon
Press
LtdlPrinted
in Great
17
G Davey: much
Cryopumping higher
so that
in the transition the
mass
pumping
and
continuum
speed
increases,
pressure
regions
giving
a rapid accumulation of the cryodeposit. Also collisions between molecules become important and it is this criterion which defines the continuum pressure region in which we are interested. Usually, continuum conditions are said to exist when some characteristic length of the containing vessel is at least 100 times the mean free path of the molecules. If we have a smal! cryopump in the centre of a 500 mm radius vessel at room temperature then this criterion would be met at pressures near 10m2 torr. The region between free molecular condition and continuum conditions where molecular collisions begin to have effect is the transition region. The energy and momentum transfer which results from molecule-molecule collisions produces gas flow and heat transfer mechanisms in the cryopump which are different from those at lower pressures. Under free molecular conditions the gas flows down the pressure gradient by a diffusion mechanism but at higher pressures, collisions force the gas towards the region of lowest pressure so that in a cryopump the gas streams towards the cryosurface at high speed often giving pumping speeds well in excess of the free molecular value. In addition temperature and pressure gradients are established within the pumping vessel,making it difficult to estimate the rate of impingement of molecules on the cryopump surface so that it is usually impossible, even with simple geometrical arrangements, to measure the sticking coefficient. Under continuum conditions the heat load on the cryopump is made up of contributions from radiation, gas conduction down the temperature gradient between vessel wall and cryopump and the heat of sublimation of the condensing gas. In the continuum region the heat load is important. The condensate layer builds up quickly and has a low density and thermal conductivity. The heat flux to its surface produces a temperature gradient in the layer and when the surface temperature is such that the saturated vapour pressureof the condensate approaches the pressure to be maintained in the pumping chamber, the cryopump must he warmed up to remove the deposit. Thus to estimate the useful life of the cryopump before warm up we must know the heat load on the condensed layer, the thermal absorptivity of the layer, its density and thermal conductivity and the thermal resistance between the condensate and the cryopump. The heat load on the cryopump is always going to be much higher than that in the free molecular region mainly due to the contribution from the condensing gas. At a pressureof 5 x IO-’ torr the mass pumping speed for either nitrogkn or water vapour is likely to be near 1 g s-l rns2 for a practical cryopump. Nitrogen has a heat of sublimation of approximately 200 kJ kg-r and water vapour 3000 kJ kg- ’ and so for these two gases which would be pumped in very different temperature ranges this heat source would normally dominate all others. In the continuum region heat conduction through the gas will also he greater than at lower pressures and the condensate deposit on the cryopump will increase the thermal absorptivity and hence increase the amount of radiation absorbed by the cryopump. Where this effect is signiticant the amount of radiation absorbed will increase with time as the layer thickens and this must be taken into account when estimating the amount of refrigeration required and it may also effect the design of temperature control equipment. The effect of non-condensable gasesis more important in the continuum region because of the momentum transfer between condensable gases streaming towards the cryopump and the 18
non-condensable others towards centration of
molecules. the cryopump non-condensable
The
condensable species push the resulting in an increasing congas near the cryopump. This
reduces the pumping speed for condensable gas and in the extreme case the pumping speed is limited to the rate at which gas can
diffuse
through
the
non-condensable
barrier.
Associated with this problem is the phenomenon of cryotrapping. Non-condensable molecules may reside on the surface long enough to be buried and trapped by condensing gas. This gives a finite pumping speed for non-condensable gas which reduces the effect which we have mentioned above and may under some circumstances constitute a practical pumping mechanism. Finally, practical cryopumps are not usually small compared with the vessels which they pump. This makes it difficult to ensure uniform molecular impingement on all the surface. The
effect is particularly pronounced at higher pressures where momentum
transfer
in collisions
causes
the
gas
to
stream
to
certain regions of the cryopump. It is also a serious matter as far as cryopump design is concerned because if the condensed layer builds up preferentially on certain areas of the cryopump the useful life of the cryopump will be reduced. We will now examine some of the available data on these problems which are particularly relevant to cryopumping in the transition and continuum pressure regions. Pumping speed We can best seethe effect of collisions on pumping speed if we look at the volumetric cryopumping speed of a cryopump as a function of pressure for the entire pressure range as shown in Figure 1. In the free molecular region the pumping speed is independent of pressure except at the low pressure end. The fall in pumping speed here is due to the re-evaporation of
Pressure,
torr
Figure 1. Typical pumping speedcurve. molecules from the condensate and clearly the pumping speed must fall to zero when the vacuum chamber pressure is the same as the condensate vapour pressure. This region of the pumping speed curve can be pushed to increasingly lower pressures by lowering the temperature of the cryopump. As the pressure increasesinto the transition region, collisions push the gas at increasing speed towards the cryosurface. Since
G Davey: Cryopumping in the transition and continuum pressureregions the molecular impingement rate with the cryopump increases, if the sticking coefficient does not decrease significantly, the pumping speed will increase. There is however a limit to this process in that the speed of the gas stream will reach the local sonic value at the cryosurface and no further increase in speed is then possible. A region of constant pumping speed will then ensue with the gas reaching the cryopump at the speed of sound. The situation is similar to the phenomenon of choked flow through an orifice. We can imagine the cryosurface area as that of an orifice with the upstream pressure p,, being the actual pressure at the surface and the downstream pressure pd being pu times the reflection coefficient [which is (I - S) where S is the sticking coefficient]. The pressure ratio for the orifice o, is defined by u&=pu(’
-S)=
* -s
PII PY If the pressure ratio is less than a critical value op then flow through the orifice occurs at sonic velocity. The condition for reaching this effect in cryopumping is therefore that (1 - S) < u,
(3)
If we take the case of water vapour at 290 K being pumped by an 80 K surface then S = 0.8 and for water vapour oc = 0.55 so we would expect the pumping speed to be limited by attainment of sonic velocity. The maximum pumping speed can be calculated under these conditions,’ and is given by
sl-nil*=
cc
<+)
A4 F-1 y RT, “*
(4)
where y is the specific heat ratio, R is the gas constant, T, is the gas temperature and M is the molecular weight. oc is given by UC=
2 (5) IIY+l 1 -.
(5)
For water vapour at 290 K this gives a value of 25 I cm-’ s-l. This can be compared with a pumping speed of 12 I cm-* s-i in the free molecular region. In practice it is not easy to demonstrate cryopumping at sonic velocity becauseof the intervention of other effects tending to lower the pumping speed. The typical rapid drop in pumping speed can be seen at the highest pressures in Figure I. It is generally assumed that there are two main reasons for this fall in pumping speed which always occurs when continuum conditions are well established. Firstly, large amounts of heat are transferred to the condensate surface by the mechanisms we have already considered. This may raise the surface temperature high enough to cause a large drop in the sticking coefficient. Secondly, the non-condensable impurities will, as we have seen, reduce the pumping speed in the continuum region. To summarize, in the pressure region in which we are interested, the pumping speed increases in the transition region until it is limited by the speed of sound in the gas. A region of constant pumping speed then follows until continuum conditions are well established when the pumping speed falls rapidly. Figure 2 shows measurements made by Bland’ on the pumping speed of water vapour on a 63.5 mm dia sphere at 80 K in a cylindrical chamber 450 mm dia and 600 mm long. All the
25-
. w
$
l
l ?
w .
.
‘E ” 2o
.
.
15d t ::
. IO.
.-: E” a’
5I 10-3
10-4
I 10-z
I 10-t
Pressure, torr Figure 2. Pumping speedvs pressurefor water vapour. features we have mentioned are clearly shown including the region of constant pumping speed due to the attainment of sonic flow velocity.
Density and thermal conductivity of cryodeposits Cryodeposits are in general polycrystalline solids with mean densities much lower than those of the crystals themselves indicating a very open structure. The details of the structure are a complex function of the conditions under which the cryopumping takes place. A number of measurements have been made of the density of condensed layers produced under cryopumping conditions.3*4 There are rather less measurements of thermal conductivity.4 The results whilst showing some general trends, indicate that growth of crystals from the vapour is a complicated procedure which can be profoundly influenced by small changes in the conditions. The situation is best illustrated by looking at measurements of the density and thermal conductivity of solid nitrogen and carbon dioxide made over a wide range of temperature and deposition ratess These results are shown in Figures 3-6. The thermal conductivity measurements were made in a direction parallel to the cryopump surface so that
I t tIt 1
I
JOO-
:E SW2 i c z 400;
+4
t
I
I
20
t
+
I 50
Moss
flow
+ t
I
tt 4 +
100
I 200
rote,
mg
I 500
m-*
I 1000
I
s-I
Figure 3. The density of nitrogen cryodeposits. 19
G Davey:
Cryopumping in the transition and continuum pressureregions
L i :
~:‘i, +, I, , **I+*,+ ,1 20
50
Mass
100
flow
rate,
200
mg
500
1000
mm2 s-’
Figare 4. The thermal conductivity of nitrogen cryodeposits. any thermal resistance between the condensate and the cryopump surface is not included. Because of the design of the cryopump used in this study, the temperature of the cryopump rose as the deposition rate increased. Thus, when cryopumping nitrogen, the cryopump temperature was 17 K at a mass pumping speed of 0.1 g s-r me2 rising to 32 K at a rate of 1 g s-r me2. The cryopump temperatures for the carbon dioxide measurements were 95 K at the lowest deposition rates rising to over 120 K at 1 g s-r ms2. For cryopumped nitrogen both the density and thermal conductivity rose with increasing values of deposition rate and cryopump temperature to approach the values of 1020 kg me3 and 0.4 Wm-’ K-r for the density and thermal conductivity of nitrogen crystals grown from the liquid. It is not possible to separate the effects of temperature and deposition rate since they were related in the apparatus used. However, at a given deposition rate it was possible to obtain some measurements at cryopump temperatures higher than those used in the main seriesof results and at a given deposition rate both density and thermal conductivity increased as the temperature increased. The situation with carbon dioxide is quite different. Although the density and thermal conductivity also increase at first as the deposition rate increases, both fall very rapidly at a mass flow rate of 0.4 g s-r rns2 corresponding to a cryopump temperature of 106 K. The very low density then achieved is probably due to the growth of whisker type crystals, the interconnecting network of whiskers giving a very large void fraction. With increasing deposition rate and temperature the vapour becomes less supersaturated because the saturated
LOO -
Figare 5. The density of carbon dioxide cryodeposits. 20
Figure 6. The thermal conductivity of carbon dioxide cryodeposits. It should be noted that a large thermal resistance canexist at the internal boundary of the cryopump between the metal and the refrigerant used to cool the pump, particularly if gases with large heats of sublimation are being condensed. It may be necessaryto provide a large area of contact between the cryopump and the refrigerant in order to get sufficient heat transfer.
Thermal ahsorptance of cryodeposits
1000 ‘: E a aoez f 5 6000
MO-
vapour pressure increases very rapidly as the temperature increases. Low values of supersaturation favour the growth of whisker like crystals from the vapour, though impurities may also play an important role. Figure 5 also shows the density measurements made on carbon dioxide by Smith and Irey.3 Although there appears to be a considerable discrepancy this is probably not so since although the deposition rates were the same for both sets of experiments, Smith and Irey condensed their layers at 80 K. Very little information is available on the thermal resistance between the condensate and the metal cryopump surface. Lee” has produced evidence of a significant thermal resistance between cryopumped hydrogen layers and copper pump surfaces at temperatures below 4 K. However attempts to remove cryodeposits from cryopumps by scraping’ suggests that whatever the nature of the bulk of the condensate, a thin layer is always in good mechanical contact with the cryopump. It is therefore unlikely, except at very low temperatures, that the thermal resistance at the external surface of the cryopump is important.
?
We have seen that when pumping at low pressures, changes in the amount of absorbed thermal radiation with time due to the formation of a condensed layer is usually not important. At higher pressures thick layers of condensate are formed which considerably influence and often completely dominate the thermal absorptance properties of the cryopump. When thermal radiation is incident upon a non-opaque solid some of the radiation is reflected at the surface and the rest is transmitted into the solid. It appears that very little radiation is reflected at the surface of cryodeposits since there is no detectable change in absorptivity when a very thin layer is condensed
G Davey:
Cryopumping in the transition and continuum pressureregions
on a clean surface. Some of the transmitted radiation is absorbed as it passes through the layer to the cryopump. Any radiation which is not then absorbed by the cryopump is reflected back through the solid deposit where more of it is absorbed. The condensate has absorption bands for thermal radiation defined by an upper and lower wavelength. All radiation falling within an absorption band suffers some absorption, all other wavelengths being entirely transmitted. As radiation within an absorption band passes through the cryopumped layer it is absorbed so that its intensity is proportional to the distance it has travelled through the layer. A body emits radiation with a spectral distribution governed only by the temperature of the body. In cryopump design we are most likely to be dealing with a situation where the cryopump seeseither 77 K or 290 K surfaces. In the former case the spectral distribution has a maximum at a wavelength of 38 pm and for the latter it occurs at IO pm. The amount of radiation absorbed by a condensed layer therefore depends on its thickness and the position of its absorption bands with respect to the wavelength of maximum emission from its surroundings. If we look first at the case of radiation from a 77 K surface the situation is very simple. Carbon dioxide, oxygen and nitrogen have all been investigated and none have strong absorption bands at wavelengths emitted by 77 K surfaces. Thus Caren, Gilcrest and Ziermana found that starting with a bare cryopump of absorptivity 0.08, this value rose to only 0.1 I after layers of air, nitrogen or carbon dioxide had been deposited with thicknesses greater than I mm. We can thus regard nitrogen, oxygen and carbon dioxide as being transparent to radiation from a 77 K surface. The situation is different for 290 K radiation where the most important gases to investigate are water and carbon dioxide. Figures 7 and 8 show the results ofCaren, Gilcrest andzierman’ for water and carbon dioxide layers receiving 290 K black body
Thickness
of deposit,
I 20
I 40
I 60
Thickness
of
deposit,
I 0
I 00
I 100
I 120
I 0
in x IO3
Figure 8. Absorptance of carbon dioxide cryodeposit for room
temperature black body radiation.
Non-Condensable
impurities
and trapping
We have already described the mechanism by which noncondensable gas forms a barrier at the cryopump surface. Brown” used nitrous oxide of three different purities to investigate the effect of non-condensable gas on pumping speed. His results, shown in Figure 9, show the large fall in pumping speed in the continuum region caused by small amounts of impurity. If non-condensable impurities are present it is necessaryto remove them with an auxiliary pump. Useful studies of cryotrapping in the free molecular region have been carried out* * which indicate that this could in some situations form a viable pumping mechanism, but far less information is available at higher pressures. Some results have been obtained on the trapping of nitrogen and argon by water vapour condensing on a 77 K surface in the pressure region 10-i to IOms torr.i2 The trapping rate was proportional to the water vapour deposition rate up to 1OL8molecules cm-’ s-l.
in x IO3
Figure 7. Absorptance of water cryodeposit for room temperature
black body radiation.
0
Pressure,
radiation. In each case the lower curve is for a cryopump with a low absorptivity surface and the upper one for a pump with high absorptivity. Only a 0.2 mm thick layer of condensed water vapour is necessary to produce a large change in absorptivity whilst a similar effect with carbon dioxide requires a 2 mm thick layer. In both cases the effect can be important in cryopump design. It can be seen that the nature of the cryopump surface always has some effect because radiation outside the absorption bands always reaches the cryopump.
II
10-Z
10-3
torr
Figure 9. Pumping speedvs pressurefor nitrous oxide of three purities
(taken from ref 10).
The trapping rate also depended on the partial pressure of the non-condensable gas. For nitrogen at a pressure of 10-l torr one molecule was trapped for every 100 water molecules condensed, this value falling to one in IO5 near 10Ts torr. Argon was also trapped satisfactorily but neither hydrogen nor helium 21
G Davey:
Cryopumping
in the transition
and
continuum
pressure
regions
suffered any detectable trapping. This is not surprising since to be trapped a molecule must stay on the surface long enough for sufficient molecules of the condensable gas to occupy neighbouring sites and prevent its escape. A long residence time implies significant adsorption on the surface and this does not occur for hydrogen or helium at 77 K. These results do not indicate a promising future for cryotapping as a pumping mechanism but they do give some idea of the type and amount of impurity which can be tolerated before additional pumping effort is required. Concluding remarks There are still many gaps in our knowledge of cryopumping in the transition and continuum pressure regions. Many applications of cryopumping in these pressure regions involve pumping of gas mixtures, some of the gases being non-condensable at the required cryopump temperature, yet there is very little experimental evidence available to guide cryopump designers. The fall in pumping speed at the highest pressures also needs further investigation. It is clear that this phenomenon occurs even for very pure gases and recent results’ indicate that the proposed thermal overload mechanism is probably only partially responsible. An essential stage in the condensation of a solid from its vapour is the formation of a two-dimensional, adsorbed, mobile layer on the surface of the solid. From this two-dimensional phase molecules are either condensed on to the solid or escape back into the vapour. Since the adsorbed layer
22
is essentially a separate phase amounts of heat are produced has a temperature higher than evaporation rate than would sticking coefficient would be temperature of the solid.
and since at high pressures large in this layer it is possible that it that of the solid, giving a higher be expected. Thus the effective lower than expected from the
References ’ J P Dawson and J D Haygood, CrJ~ugefric:r, 5, 1965, 57. 2 M E Bland, Cryogertics. To bc published. 3 H B Smith and R K Irey, Ah Cryo.qen Drgjrg, Vol 15, Plenum, New York (1970). 4 K W Rogers, ‘Experimental Investigations of Solid Nitrogen formed by Cryopumping’. NASA Contractor Report CR-553 (1966). 5 T Cook, Thesis, Oxford University (I 974). h T J Lee, ‘The Condensation and Evaporation of Hydrogen on Liquid Helium Cooled Surfaces’, Proc 3rd It11 Cryogen Engng C’orr/, Berlin (I 970). ’ M E Bland, private communication. 8 R P Caren. A S Gilcrest and C A Zierman, ‘An Experimental Determination of the Absorptances of Cryodeposited Films Using Calorimetric Techniques’, Symposium on Thermal Radiation of Solids. NASA SP 55 (I 965). ‘) R P Caren, A S Gilcrest and C A Zierman, Ah Cryogen Engug, Vol 9, Plenum, New York (I 964). lo R F Brown, ‘Cryopumping of Nitrous Oxide’, AEDC-TDR-63-267 (February 1964). ‘I J D Haygood and R Dawbarn, ‘Helium Pumping by 4.2 K Cryodeposits’, AEDC-TR-66-204 (January 1967). I2 F W Schmidlin, L 0 Heflinger and E L Garwin, ‘Some Investigations of Cryotrapping’, 91/r Na/ SJ~nrp Vuc Tech (1962).
13 August
Davey,
Cryogenics
and continuum
7975 Laboratory,
University
of Oxford.
Parks
Road,
Oxford,
England
The problems of cryopumping in the pressure region above that in which free molecular flow prevails are considered, and some of the results are reviewed.
Introduction
The literature on cryopumping is now quite extensive and sufficient information is available to allow the design of a wide range of cryopumps. However, almost all the work done so far has been aimed at exploiting the high pumping speed, low ultimate pressure capability of cryopumping and has therefore been carried out at pressuresin the free molecular region. Although it is still true that most cryopumps are required to operate in the high or ultra-high vacuum regions there are some applications for cryopumps where the operating pressure is much higher. These applications include freeze-drying of drugs and foodstuffs, wind tunnels, pumping of reaction products from thruster rockets and possibly the pumping of corrosive or dusty gases in the chemical industry. In these circumstances where collisions between gas molecules becomes important, volumetric pumping speeds are obtained which may be much higher than those in the free molecular region. Because of the pressure and temperature gradients established in the gas within the cryopump, the rapid build up of the condensed phase on the cryopump and the role played by non-condensable impurities, cryopumping in the transition and continuum pressure ranges has its own extensive set of problems which have not yet received sufficient attention. A limited amount of work has been carried out on all these problems and some of the results are reviewed here. Pumping
in the free molecular
flow region
Before we proceed to our main topic it may be useful, for comparison, to briefly consider the main aspects of cryopumping in the free molecular region. Here things are relatively straight forward. A sticking coefficient can be defined as the probability that a molecule incident on a cold surface will stick. This is easy to measure using a small, usually spherical cryopump of carefully defined area in a large vessel. Negligible pressure gradients exist in the vesseland the temperature of the gas is defined by the temperature of the vessel wall since many collisions take place with the wall before a collision with the cryopump occurs and there are not a significant number of collisions between molecules. In these circumstances kinetic theory tells us the rate of incidence of molecules on the cold
surface and therefore the maximum possible volumetric pumping speed V,,,, when the sticking coefficient is one. This can be compared with the measured pumping speed V and the sticking coefficient obtained from
In general the sticking coefficient is a slowly varying function of gas temperature and cryopump temperature and this must be determined experimentally. When necessary,corrections can be made for re-evaporation of molecules from the known vapour pressure of the condensate.’ In a practical cryopump the cold pumping surface is usually not small compared with the size of the chamber and it is shielded by a baffle at a higher temperature. The main design problem is then to calculate the overall pumping speed of the cryopump and baffle array from geometrical considerations and to optimize the geometry against the conflicting constraints of maximum pumping speed and minimum radiant energy reaching the cryopump through the baffle. When pumping at very low pressure some things are clearly not important. If we pump nitrogen gas with a typical cryopump consisting of a 20 K surface protected by a chevron baffle at 80 K, then the time taken to build up a condensed layer 1 mm thick would be around lo4 h at a pressure of lo-’ torr. We are not therefore concerned about the accumulation of condensate on the pump since this does not effect its useful pumping life. Similarly the heat load on the cryopump due to the incidence and condensation of gas is very small and can be ignored. Most of the heat load often comes from radiation emitted by the surrounding shields and although we may wish to minimize this, the thermal absorptive properties of the condensed layer will not normally enter into our considerations. This is for two reasons. Firstly the layer may never be thick enough to have a significant effect and, secondly, because the pump is intended to reach very low pressures it is certain for most gasesto operate at a very low temperature and be shielded by a baffle at a temperature near 80 K. As we shall see, most cryodeposits are almost completely transparent to radiation emitted by such a surface. Pumping
in the transition
and continuum
pressure regions
* Paperpresentedat the colloquium on Cryogenicpumping organized by the Vacuum Group of the Institute of Physicson 13 November 1974at Imperial College,London.
When pumping at higher pressures there are two effects which considerably complicate the situation. The density of the gas is
Vacuum/volume 26/number 1.
Britain
Pergamon
Press
LtdlPrinted
in Great
17
G Davey: much
Cryopumping higher
so that
in the transition the
mass
pumping
and
continuum
speed
increases,
pressure
regions
giving
a rapid accumulation of the cryodeposit. Also collisions between molecules become important and it is this criterion which defines the continuum pressure region in which we are interested. Usually, continuum conditions are said to exist when some characteristic length of the containing vessel is at least 100 times the mean free path of the molecules. If we have a smal! cryopump in the centre of a 500 mm radius vessel at room temperature then this criterion would be met at pressures near 10m2 torr. The region between free molecular condition and continuum conditions where molecular collisions begin to have effect is the transition region. The energy and momentum transfer which results from molecule-molecule collisions produces gas flow and heat transfer mechanisms in the cryopump which are different from those at lower pressures. Under free molecular conditions the gas flows down the pressure gradient by a diffusion mechanism but at higher pressures, collisions force the gas towards the region of lowest pressure so that in a cryopump the gas streams towards the cryosurface at high speed often giving pumping speeds well in excess of the free molecular value. In addition temperature and pressure gradients are established within the pumping vessel,making it difficult to estimate the rate of impingement of molecules on the cryopump surface so that it is usually impossible, even with simple geometrical arrangements, to measure the sticking coefficient. Under continuum conditions the heat load on the cryopump is made up of contributions from radiation, gas conduction down the temperature gradient between vessel wall and cryopump and the heat of sublimation of the condensing gas. In the continuum region the heat load is important. The condensate layer builds up quickly and has a low density and thermal conductivity. The heat flux to its surface produces a temperature gradient in the layer and when the surface temperature is such that the saturated vapour pressureof the condensate approaches the pressure to be maintained in the pumping chamber, the cryopump must he warmed up to remove the deposit. Thus to estimate the useful life of the cryopump before warm up we must know the heat load on the condensed layer, the thermal absorptivity of the layer, its density and thermal conductivity and the thermal resistance between the condensate and the cryopump. The heat load on the cryopump is always going to be much higher than that in the free molecular region mainly due to the contribution from the condensing gas. At a pressureof 5 x IO-’ torr the mass pumping speed for either nitrogkn or water vapour is likely to be near 1 g s-l rns2 for a practical cryopump. Nitrogen has a heat of sublimation of approximately 200 kJ kg-r and water vapour 3000 kJ kg- ’ and so for these two gases which would be pumped in very different temperature ranges this heat source would normally dominate all others. In the continuum region heat conduction through the gas will also he greater than at lower pressures and the condensate deposit on the cryopump will increase the thermal absorptivity and hence increase the amount of radiation absorbed by the cryopump. Where this effect is signiticant the amount of radiation absorbed will increase with time as the layer thickens and this must be taken into account when estimating the amount of refrigeration required and it may also effect the design of temperature control equipment. The effect of non-condensable gasesis more important in the continuum region because of the momentum transfer between condensable gases streaming towards the cryopump and the 18
non-condensable others towards centration of
molecules. the cryopump non-condensable
The
condensable species push the resulting in an increasing congas near the cryopump. This
reduces the pumping speed for condensable gas and in the extreme case the pumping speed is limited to the rate at which gas can
diffuse
through
the
non-condensable
barrier.
Associated with this problem is the phenomenon of cryotrapping. Non-condensable molecules may reside on the surface long enough to be buried and trapped by condensing gas. This gives a finite pumping speed for non-condensable gas which reduces the effect which we have mentioned above and may under some circumstances constitute a practical pumping mechanism. Finally, practical cryopumps are not usually small compared with the vessels which they pump. This makes it difficult to ensure uniform molecular impingement on all the surface. The
effect is particularly pronounced at higher pressures where momentum
transfer
in collisions
causes
the
gas
to
stream
to
certain regions of the cryopump. It is also a serious matter as far as cryopump design is concerned because if the condensed layer builds up preferentially on certain areas of the cryopump the useful life of the cryopump will be reduced. We will now examine some of the available data on these problems which are particularly relevant to cryopumping in the transition and continuum pressure regions. Pumping speed We can best seethe effect of collisions on pumping speed if we look at the volumetric cryopumping speed of a cryopump as a function of pressure for the entire pressure range as shown in Figure 1. In the free molecular region the pumping speed is independent of pressure except at the low pressure end. The fall in pumping speed here is due to the re-evaporation of
Pressure,
torr
Figure 1. Typical pumping speedcurve. molecules from the condensate and clearly the pumping speed must fall to zero when the vacuum chamber pressure is the same as the condensate vapour pressure. This region of the pumping speed curve can be pushed to increasingly lower pressures by lowering the temperature of the cryopump. As the pressure increasesinto the transition region, collisions push the gas at increasing speed towards the cryosurface. Since
G Davey: Cryopumping in the transition and continuum pressureregions the molecular impingement rate with the cryopump increases, if the sticking coefficient does not decrease significantly, the pumping speed will increase. There is however a limit to this process in that the speed of the gas stream will reach the local sonic value at the cryosurface and no further increase in speed is then possible. A region of constant pumping speed will then ensue with the gas reaching the cryopump at the speed of sound. The situation is similar to the phenomenon of choked flow through an orifice. We can imagine the cryosurface area as that of an orifice with the upstream pressure p,, being the actual pressure at the surface and the downstream pressure pd being pu times the reflection coefficient [which is (I - S) where S is the sticking coefficient]. The pressure ratio for the orifice o, is defined by u&=pu(’
-S)=
* -s
PII PY If the pressure ratio is less than a critical value op then flow through the orifice occurs at sonic velocity. The condition for reaching this effect in cryopumping is therefore that (1 - S) < u,
(3)
If we take the case of water vapour at 290 K being pumped by an 80 K surface then S = 0.8 and for water vapour oc = 0.55 so we would expect the pumping speed to be limited by attainment of sonic velocity. The maximum pumping speed can be calculated under these conditions,’ and is given by
sl-nil*=
cc
<+)
A4 F-1 y RT, “*
(4)
where y is the specific heat ratio, R is the gas constant, T, is the gas temperature and M is the molecular weight. oc is given by UC=
2 (5) IIY+l 1 -.
(5)
For water vapour at 290 K this gives a value of 25 I cm-’ s-l. This can be compared with a pumping speed of 12 I cm-* s-i in the free molecular region. In practice it is not easy to demonstrate cryopumping at sonic velocity becauseof the intervention of other effects tending to lower the pumping speed. The typical rapid drop in pumping speed can be seen at the highest pressures in Figure I. It is generally assumed that there are two main reasons for this fall in pumping speed which always occurs when continuum conditions are well established. Firstly, large amounts of heat are transferred to the condensate surface by the mechanisms we have already considered. This may raise the surface temperature high enough to cause a large drop in the sticking coefficient. Secondly, the non-condensable impurities will, as we have seen, reduce the pumping speed in the continuum region. To summarize, in the pressure region in which we are interested, the pumping speed increases in the transition region until it is limited by the speed of sound in the gas. A region of constant pumping speed then follows until continuum conditions are well established when the pumping speed falls rapidly. Figure 2 shows measurements made by Bland’ on the pumping speed of water vapour on a 63.5 mm dia sphere at 80 K in a cylindrical chamber 450 mm dia and 600 mm long. All the
25-
. w
$
l
l ?
w .
.
‘E ” 2o
.
.
15d t ::
. IO.
.-: E” a’
5I 10-3
10-4
I 10-z
I 10-t
Pressure, torr Figure 2. Pumping speedvs pressurefor water vapour. features we have mentioned are clearly shown including the region of constant pumping speed due to the attainment of sonic flow velocity.
Density and thermal conductivity of cryodeposits Cryodeposits are in general polycrystalline solids with mean densities much lower than those of the crystals themselves indicating a very open structure. The details of the structure are a complex function of the conditions under which the cryopumping takes place. A number of measurements have been made of the density of condensed layers produced under cryopumping conditions.3*4 There are rather less measurements of thermal conductivity.4 The results whilst showing some general trends, indicate that growth of crystals from the vapour is a complicated procedure which can be profoundly influenced by small changes in the conditions. The situation is best illustrated by looking at measurements of the density and thermal conductivity of solid nitrogen and carbon dioxide made over a wide range of temperature and deposition ratess These results are shown in Figures 3-6. The thermal conductivity measurements were made in a direction parallel to the cryopump surface so that
I t tIt 1
I
JOO-
:E SW2 i c z 400;
+4
t
I
I
20
t
+
I 50
Moss
flow
+ t
I
tt 4 +
100
I 200
rote,
mg
I 500
m-*
I 1000
I
s-I
Figure 3. The density of nitrogen cryodeposits. 19
G Davey:
Cryopumping in the transition and continuum pressureregions
L i :
~:‘i, +, I, , **I+*,+ ,1 20
50
Mass
100
flow
rate,
200
mg
500
1000
mm2 s-’
Figare 4. The thermal conductivity of nitrogen cryodeposits. any thermal resistance between the condensate and the cryopump surface is not included. Because of the design of the cryopump used in this study, the temperature of the cryopump rose as the deposition rate increased. Thus, when cryopumping nitrogen, the cryopump temperature was 17 K at a mass pumping speed of 0.1 g s-r me2 rising to 32 K at a rate of 1 g s-r me2. The cryopump temperatures for the carbon dioxide measurements were 95 K at the lowest deposition rates rising to over 120 K at 1 g s-r ms2. For cryopumped nitrogen both the density and thermal conductivity rose with increasing values of deposition rate and cryopump temperature to approach the values of 1020 kg me3 and 0.4 Wm-’ K-r for the density and thermal conductivity of nitrogen crystals grown from the liquid. It is not possible to separate the effects of temperature and deposition rate since they were related in the apparatus used. However, at a given deposition rate it was possible to obtain some measurements at cryopump temperatures higher than those used in the main seriesof results and at a given deposition rate both density and thermal conductivity increased as the temperature increased. The situation with carbon dioxide is quite different. Although the density and thermal conductivity also increase at first as the deposition rate increases, both fall very rapidly at a mass flow rate of 0.4 g s-r rns2 corresponding to a cryopump temperature of 106 K. The very low density then achieved is probably due to the growth of whisker type crystals, the interconnecting network of whiskers giving a very large void fraction. With increasing deposition rate and temperature the vapour becomes less supersaturated because the saturated
LOO -
Figare 5. The density of carbon dioxide cryodeposits. 20
Figure 6. The thermal conductivity of carbon dioxide cryodeposits. It should be noted that a large thermal resistance canexist at the internal boundary of the cryopump between the metal and the refrigerant used to cool the pump, particularly if gases with large heats of sublimation are being condensed. It may be necessaryto provide a large area of contact between the cryopump and the refrigerant in order to get sufficient heat transfer.
Thermal ahsorptance of cryodeposits
1000 ‘: E a aoez f 5 6000
MO-
vapour pressure increases very rapidly as the temperature increases. Low values of supersaturation favour the growth of whisker like crystals from the vapour, though impurities may also play an important role. Figure 5 also shows the density measurements made on carbon dioxide by Smith and Irey.3 Although there appears to be a considerable discrepancy this is probably not so since although the deposition rates were the same for both sets of experiments, Smith and Irey condensed their layers at 80 K. Very little information is available on the thermal resistance between the condensate and the metal cryopump surface. Lee” has produced evidence of a significant thermal resistance between cryopumped hydrogen layers and copper pump surfaces at temperatures below 4 K. However attempts to remove cryodeposits from cryopumps by scraping’ suggests that whatever the nature of the bulk of the condensate, a thin layer is always in good mechanical contact with the cryopump. It is therefore unlikely, except at very low temperatures, that the thermal resistance at the external surface of the cryopump is important.
?
We have seen that when pumping at low pressures, changes in the amount of absorbed thermal radiation with time due to the formation of a condensed layer is usually not important. At higher pressures thick layers of condensate are formed which considerably influence and often completely dominate the thermal absorptance properties of the cryopump. When thermal radiation is incident upon a non-opaque solid some of the radiation is reflected at the surface and the rest is transmitted into the solid. It appears that very little radiation is reflected at the surface of cryodeposits since there is no detectable change in absorptivity when a very thin layer is condensed
G Davey:
Cryopumping in the transition and continuum pressureregions
on a clean surface. Some of the transmitted radiation is absorbed as it passes through the layer to the cryopump. Any radiation which is not then absorbed by the cryopump is reflected back through the solid deposit where more of it is absorbed. The condensate has absorption bands for thermal radiation defined by an upper and lower wavelength. All radiation falling within an absorption band suffers some absorption, all other wavelengths being entirely transmitted. As radiation within an absorption band passes through the cryopumped layer it is absorbed so that its intensity is proportional to the distance it has travelled through the layer. A body emits radiation with a spectral distribution governed only by the temperature of the body. In cryopump design we are most likely to be dealing with a situation where the cryopump seeseither 77 K or 290 K surfaces. In the former case the spectral distribution has a maximum at a wavelength of 38 pm and for the latter it occurs at IO pm. The amount of radiation absorbed by a condensed layer therefore depends on its thickness and the position of its absorption bands with respect to the wavelength of maximum emission from its surroundings. If we look first at the case of radiation from a 77 K surface the situation is very simple. Carbon dioxide, oxygen and nitrogen have all been investigated and none have strong absorption bands at wavelengths emitted by 77 K surfaces. Thus Caren, Gilcrest and Ziermana found that starting with a bare cryopump of absorptivity 0.08, this value rose to only 0.1 I after layers of air, nitrogen or carbon dioxide had been deposited with thicknesses greater than I mm. We can thus regard nitrogen, oxygen and carbon dioxide as being transparent to radiation from a 77 K surface. The situation is different for 290 K radiation where the most important gases to investigate are water and carbon dioxide. Figures 7 and 8 show the results ofCaren, Gilcrest andzierman’ for water and carbon dioxide layers receiving 290 K black body
Thickness
of deposit,
I 20
I 40
I 60
Thickness
of
deposit,
I 0
I 00
I 100
I 120
I 0
in x IO3
Figure 8. Absorptance of carbon dioxide cryodeposit for room
temperature black body radiation.
Non-Condensable
impurities
and trapping
We have already described the mechanism by which noncondensable gas forms a barrier at the cryopump surface. Brown” used nitrous oxide of three different purities to investigate the effect of non-condensable gas on pumping speed. His results, shown in Figure 9, show the large fall in pumping speed in the continuum region caused by small amounts of impurity. If non-condensable impurities are present it is necessaryto remove them with an auxiliary pump. Useful studies of cryotrapping in the free molecular region have been carried out* * which indicate that this could in some situations form a viable pumping mechanism, but far less information is available at higher pressures. Some results have been obtained on the trapping of nitrogen and argon by water vapour condensing on a 77 K surface in the pressure region 10-i to IOms torr.i2 The trapping rate was proportional to the water vapour deposition rate up to 1OL8molecules cm-’ s-l.
in x IO3
Figure 7. Absorptance of water cryodeposit for room temperature
black body radiation.
0
Pressure,
radiation. In each case the lower curve is for a cryopump with a low absorptivity surface and the upper one for a pump with high absorptivity. Only a 0.2 mm thick layer of condensed water vapour is necessary to produce a large change in absorptivity whilst a similar effect with carbon dioxide requires a 2 mm thick layer. In both cases the effect can be important in cryopump design. It can be seen that the nature of the cryopump surface always has some effect because radiation outside the absorption bands always reaches the cryopump.
II
10-Z
10-3
torr
Figure 9. Pumping speedvs pressurefor nitrous oxide of three purities
(taken from ref 10).
The trapping rate also depended on the partial pressure of the non-condensable gas. For nitrogen at a pressure of 10-l torr one molecule was trapped for every 100 water molecules condensed, this value falling to one in IO5 near 10Ts torr. Argon was also trapped satisfactorily but neither hydrogen nor helium 21
G Davey:
Cryopumping
in the transition
and
continuum
pressure
regions
suffered any detectable trapping. This is not surprising since to be trapped a molecule must stay on the surface long enough for sufficient molecules of the condensable gas to occupy neighbouring sites and prevent its escape. A long residence time implies significant adsorption on the surface and this does not occur for hydrogen or helium at 77 K. These results do not indicate a promising future for cryotapping as a pumping mechanism but they do give some idea of the type and amount of impurity which can be tolerated before additional pumping effort is required. Concluding remarks There are still many gaps in our knowledge of cryopumping in the transition and continuum pressure regions. Many applications of cryopumping in these pressure regions involve pumping of gas mixtures, some of the gases being non-condensable at the required cryopump temperature, yet there is very little experimental evidence available to guide cryopump designers. The fall in pumping speed at the highest pressures also needs further investigation. It is clear that this phenomenon occurs even for very pure gases and recent results’ indicate that the proposed thermal overload mechanism is probably only partially responsible. An essential stage in the condensation of a solid from its vapour is the formation of a two-dimensional, adsorbed, mobile layer on the surface of the solid. From this two-dimensional phase molecules are either condensed on to the solid or escape back into the vapour. Since the adsorbed layer
22
is essentially a separate phase amounts of heat are produced has a temperature higher than evaporation rate than would sticking coefficient would be temperature of the solid.
and since at high pressures large in this layer it is possible that it that of the solid, giving a higher be expected. Thus the effective lower than expected from the
References ’ J P Dawson and J D Haygood, CrJ~ugefric:r, 5, 1965, 57. 2 M E Bland, Cryogertics. To bc published. 3 H B Smith and R K Irey, Ah Cryo.qen Drgjrg, Vol 15, Plenum, New York (1970). 4 K W Rogers, ‘Experimental Investigations of Solid Nitrogen formed by Cryopumping’. NASA Contractor Report CR-553 (1966). 5 T Cook, Thesis, Oxford University (I 974). h T J Lee, ‘The Condensation and Evaporation of Hydrogen on Liquid Helium Cooled Surfaces’, Proc 3rd It11 Cryogen Engng C’orr/, Berlin (I 970). ’ M E Bland, private communication. 8 R P Caren. A S Gilcrest and C A Zierman, ‘An Experimental Determination of the Absorptances of Cryodeposited Films Using Calorimetric Techniques’, Symposium on Thermal Radiation of Solids. NASA SP 55 (I 965). ‘) R P Caren, A S Gilcrest and C A Zierman, Ah Cryogen Engug, Vol 9, Plenum, New York (I 964). lo R F Brown, ‘Cryopumping of Nitrous Oxide’, AEDC-TDR-63-267 (February 1964). ‘I J D Haygood and R Dawbarn, ‘Helium Pumping by 4.2 K Cryodeposits’, AEDC-TR-66-204 (January 1967). I2 F W Schmidlin, L 0 Heflinger and E L Garwin, ‘Some Investigations of Cryotrapping’, 91/r Na/ SJ~nrp Vuc Tech (1962).