pistons, respectively. The pistons are coupled to stepping motors through
bellows and twenty-turns-per-inch micrometer screws. There is about
one-quarter turn backlash in the piston drive but this has no effect as the
piston is always driven in the same direction during measurements.

The piston seals contain elastomers. In order to reduce gas leakage
across these seals, the fill pressure is brought to both sides of each seal.
Tests have indicated that the leakage across the seals under normal operating

conditions contributes an error of no more than 0.01%.

The Piston Advance System

A stepping motor turns a micrometer screw which drives the piston into
the working reservoir and the rate at which the motor turns is controlled by
the reading of the differential CDG between the working and reference
reservoirs. The length the piston travels in a given number of turns enters
directly into the throughput and pressure calculations as part of the
displaced volume. Therefore, the threads of the screw must be linear and
accurate. Checks of the micrometer screws have indicated that they are linear
to +0.001 inch.

As the piston is driven into the working reservoir, the elapsed time is
measured with a resolution of 0.1 second and is displayed after each turn of

the piston.

Reservoirs

Thermal stability of the reference volume (B) is important so that its
pressure does not change during a flow measurement (20-30 minutes). The
working reservoirs (E) must be small in relation to the piston and both
dimensionally and thermally stable. The nominal volumes of the working
reservoirs are 39 cm’ and 32 cm’ for the 1-in and 1-cm pistons respectively
(the nominal volumes displaced by the 1-in and 1-cm pistons are 13 and 2 cm®).
They are thermally insulated and the temperature is monitored. They are

fabricated from stainless steel.

Thermo rs

One thermometer on the flowmeter measures the temperature of the working
reservoirs. Accuracy is important so a calibrated quartz thermometer is used.
A liquid-in-glass thermometer with a resolution of 0.05 °C is used to monitor

the chamber temperature.

13


of 1-2% in 2 year's time. These particular customers are knowledgeable users
of the gage and we expect that the rotors have been treated carefully between
calibrations.

VII. NEEDS AND PLANS

The major limitations of this system are 1) the presence of elastomer
seals in the gas piston flowmeter, 2) the accuracy with which the pressure in
the reference reservoir can be measured when a low fill pressure is used, and
3) the limitation of an achievable base vacuum to 10°® Pa.

In an effort to address the first limitation, we have constructed the
second flowmeter which is used primarily in the primary leak standard. The
differences between the two are discussed above. Future flowmeters will
undoubtedly be based on the hydraulically-coupled flowmeter design in order to
eliminate outgassing from the elastomer seals and to permit baking the
flowmeter.

The second limitation is a major source of certainty in the flow rate

measurements. We have implemented a system to permit in situ calibrations of

the flowmeter CDGs with the ultrasonic interferometer manometer [15,16].

A new program is underway to develop an ultra-high vacuum standard which
will help us overcome the third limitation. A major part of the work is
directed toward lowering the achievable base vacuum. This has involved high
temperature baking over extended periods (e.g., 500 °C for 200 hours) to
reduce the room temperature hydrogen outgassing rate from the stainless steel
walls of the vacuum chamber. In addition, experimentation with various types
of ultra-high vacuum pumps (e.g., turbomolecular, titanium sublimation, ion,
and cryogenic pumps) is in progress.

The increasing availability of ion gages designed for use under ultra-
high vacuum conditions suggests that the performance of the standard at
pressures below 1x10°® Pa could be investigated using these gages as transfer
standards. Expected limitations in this pressure region include the stability
of the base vacuum and the linearity of the gage sensitivities and the gage
residual currents.

. The primary high vacuum standard is used for both experiments and
calibrations, and the increasing number of calibrations means that it is
becoming increasingly difficult to perform necessary experiments. One means
of increasing the productivity of the system is to automate as many of the

operations as possible. Certain operations lend themselves very readily to

34


VI QUALITY CONTROL

The determination of systematic and random errors in a primary standard
is but the first step in characterizing its performance. By its very nature,
a primary standard is difficult to monitor over long periods of time and
various laboratories have developed several methods of doing this. Some of
these are the maintenance of additional primary standards, interlaboratory
comparisons of primary standards of the same or different designs, and the
maintenance of a bank of check standards, We have adopted all chree of these
methods.

COMPARISONS AGAINST ADDITIONAL NIST PRIMARY STANDARDS

The original primary high vacuum standard in use before 1984 [11] wae
suitable only for the direct calibration of early molecular drag gages. It
was based on the integrating principle of the MDG rotor and the integrating
capabilities of the MDG controller, and was operated by exhausting a known
volume of gas into the chamber ("gas burst" method). The MDGs respond not to
pressure per se but to molecular flux and the deceleration experienced by the
gages was due to the total number of molecules striking the ball surface. The
calibration was. a two step procedure and gave reproducible calibration factors
over time.

Upon completion of the orifice-flow standard, it was compared with the
gas burst method described above using 5 MDGs as transfer standards. The
typical difference between the two methods was 0.1% and the worst difference
was 0.5%. This case occurred using the small (1 cm) piston in the flowmeter.
We have subsequently modified the piston-drive circuit to allow for both
proportional and on-off control. A major advantage of the flowmeter is that
it may be used to calibrate IGs as well as MDGs since the pressure generated
in the chamber is calculated directly and can be kept constant.

A second flowmeter has been constructed which operates on the same
principle as the first [i]. The primary differences between them lie in the
design of the piston seals and improved fill pressure measurement capability
in the second flowmeter. The second flowmeter does not use elastomer seals
but hydraulically translates the piston motion to a bellows which is part of
the working reservoir. This second flowmeter is completely bakeable. The
original flowmeter has only two CDGs for measuring the fill pressure - 1.3 and
133 kPa (10 and 1000 Torr) full-scale. The second flowmeter has three CDGs -
0.13, 1.3 and 133 kPa (1, 10, and 1000 Torr) - and a force-balanced quartz

30


(k)
Gas
Inlet"
Line H =)
Gas
Supply I
Cylinder fe)
F G
NW WE (| LIT
Mo Working }-—& Chamber
Reservoir
Variable
D Leak
MH = Reference Turbo
Volume Pump
B J
Ballast
Volume (c)
A
Figure 1. Schematic of the Primary High Vacuum Standard Including the

Chamber, the Flowmeter and the Orifice. Letters Indicate
Components which are Discussed in the Text.

39


upper side to a depth of 0.61 cm from the center out to a diameter of 8.89 cm,
and a centered 1.12-cm diameter hole was bored through the plate. The
underside of the plate was machined to form a hollow, truncated 80° half-angle
cone, leaving a thickness of 0.74 mm at the edge of the center hole. The
orifice edge region was formed by lapping the hole with a steel ball of
1.587-cm (0.6250 in) diameter to nominally equal depths from above and below.
Upon final lapping with an unworn ball, the two concave spherical surfaces
thus generated met at a sharp circular edge with a measured diameter of 1.1240
em (0.4425 in +0.0003 in) and a computed edge angle of 90.1°. Microscopic
examination revealed a clean, sharp, burr-free edge.

Calculation of the orifice conductance is based on the molecular
transmission probability approach initiated by Clausing [2]. It assumes free
molecular flow and cosine-law scattering at surfaces. A full derivation of
the orifice conductance is given in Appendix C.

From the work in Appendix C and the dimensions of the orifice, we derive

c* = 0.2464-S cms"? (4)
where S is the mean molecular speed in cm s"+. The overall uncertainty in C*
is estimated to be +0.18%, with the largest contribution being 0.14% due to
the uncertainty in the measured value of the radius of the hole.

Knowing the orifice conductance, CG, and the throughput, Q, of gas, we can
obtain the pressure difference across the orifice,

Py - PB, = Q/C, (5)
where Py and P, designate the pressures in the upper and lower chambers.
Because of the finite pumping speed below the orifice, P, is not negligible:
P, is 3.7% of P, for N, in our system. It is difficult to measure P, directly
since this would require a gage calibrated below the range of pressures
generated by the standard. However, if we can measure the ratio, Rp, of the
pressures above, Py, and below, P,, the orifice,

Rp = Py/PL, (6)

then from eqs (5) and (6) we have

Py = QRp/C(Rp-1). (7)
The pressure ratio Rp is measured by a molecular drag gage that, as shown in
figure 2, can be connected through 1 1/2 - in (3.8 cm) bakeable valves to one
of the gage ports in the upper chamber or to a similar port in the lower
chamber. Since the MDG operates at the temperature of the gas and is
reproducible at the 1% or better level above 10°‘ Pa, it can be used to
determine Rp quite precisely in the high vacuum range. The value of Rp/(Rp-1)

is quite insensitive to errors in Rp. A more significant problem is that as


ABPENDIX B

SAMPLE REPORT OF CALIBRATION FOR
MOLECULAR DRAG GAGE

Spinning Rotor Vacuum Gage
Submitted by

CUSTOMER NAME
CITY, STATE ZIP

TPD Reference Number: HV X

NIST Identification of Flange: 654321
Manufacturer's Identification of Flange: 123456
Manufacturer: MANUFACTURER
Model Number: ABC XYZ
Serial Number of Controller: 123456
Serial Number of Suspension Head: 12345
Diameter of Ball: 4.5 mm
Gas: Nitrogen
Previous test record: HV XX

Date Received: MONTH DAY, YEAR Test Completed: MONTH DAY, YEAR

Procedure

This unit was tested on an all-metal vacuum chamber designed to maintain
a low residual gas background and minimize pressure gradients. The chamber was
pumped with a turbomolecular pump to a base pressure of about 10°® Pa. After
being mounted on the chamber, the thimble and ball were baked overnight in
argon at 250 °C at a pressure of 10°74 Pa and then cooled slowly. After the
thimble had cooled, the suspension head was installed and the ball was spun
up.

During the calibration, known pressures of about 5x10°? Pa were generated
in the chamber. Prior to the calibration, the residual drag of the ball was
measured at a base pressure of about 10°® Pa and was subtracted from
subsequent readings. This correction must be redetermined at the time of use,
as noted below.

Before calibration, the signal strength and timing uncertainty of the
unit were examined. Errors of the timing circuitry were evaluated by applying
a stable 200 uV p-p, 414 Hz signal to the input of the electronics unit. The
signal scatter (SSC) with this synthetic signal was X.Y usec. Visual

inspection of the ball indicated that the surface was smooth and shiny.


Pa. Using calibrated molecular drag gages, the estimated uncertainty in the
generated pressure between 10°* and 10°! Pa is 1.6% + 2x10°® Pa.

The gage tube was mounted on the calibration chamber and evacuated and
baked overnight at 250 °C. It was degassed by being operated during the
bakeout.

Results

The tube designated XXX was calibrated with the controller designated in
this report from MONTH DAY to DAY, YEAR. The tube was operated with a
measured emission current of 5.4 mA as established by the controller. All
gage readings were obtained from the front panel display. The data presented
below were obtained after overnight pumpdown to pressures below 5x10°® Pa.
The generated pressures are pressure increases above base vacuum and within
each day were generated starting with the lowest and proceeding sequentially
to the highest each day. The corrected controller readings were obtained by
subtracting the controller reading at base conditions just prior to a
calibration series from all subsequent readings. The controller readings at
base conditions are due to the system base pressure and the gage residual
currents. ‘The calibration factor is the ratio of the generated pressure in

Torr to the corrected controller reading.

Generated N, Pressure Controller Reading Corrected Calibration
Pascal Torr Torr Reading, Torr Factor
(1 Torr=133.32 Pa)

9.19x10"7 6. 89x107° 1.2x107® 0.8x107® 0.56
3.77x10°& = 2.83x1078 5.2x1078 1.4x1078 0.54
1.41x10°5 106x107? 2.0x1077 2.0x10°7 0.54
4,28x10°5 -3..21x1077 5.8x1077 5.8x10°7 0.56
1.34x10°4 ==. 1, 00x10 1,8x10°® 1.8x10°§ 0.56
3.79x10"* 2. 85x10"® 5.3x107® 5.3x107® 0.54
3.80x10°* = 2.85x107§ 5.3x107& 5.3x107§ 0.54
4.13x10"* 3.101076 5.7x107® 5.7x10°& 0.54
1.28x10°3 959x107 1.7x10°5 1.7x10°5 0.56
1.33x10°$ —-9.99x10" 1.8x1075 1.8x1075 0.56
4.20x10°3 —-3.15x1075 5.9x10°5 5.9x1075 0.53
5.28x10° —3.96x10"> 7.5x1075 7.5x10"5 0.53
1.22x10°2-9.16x10"5 1.7x10"4 1.7x10"4 0.54
4.10x10°23.07x10"4 6.6x10°4 6.6x10°4 0.46
6.39x10°2 4. 79x10"4 10.0x10"* 10.0x10"* 0.48


Gallagher, who reported a value 2ry = 0.4425 in +0.00003 in, where Yo is the
radius. Each of the spherical segments terminates at an axial distance
b = 0.0150 in 40.0005 in from the plane of the throat. Transition to the full
thickness of the orifice plate is made above by a cylindrical step 0.240 in
high at a diameter of 3.50 in, and below by a truncated cone 0.230-in high
with an apex half-angle of 80°.

Microscopic examination gave no evidence for burrs or significant
irregularities at the throat edge. The edge angle computed from the above
dimensions is 90.1°, in close agreement with the nominal design value of 90°,

which was chosen specifically for the purpose of minimizing burr formation.

Calculation of the Molecular Flow Conductance

Rectangular coordinate axes Oxyz are chosen with the origin in the center
of the throat and the axis Oz in the axis of rotational symmetry. The axial
coordinate z increases downward, in the direction of flow. Symbols are listed
in Appendix C-I. The plarie of the throat is assumed to be a plane of symmetry
for the central duct. Any error from this assumption is absorbed within the
error bounds assigned to dimension b. The cross sections in the planes Z = -b
and Z = b, where the surfaces A and B terminate, will be referred to as
entrance and exit apertures, respectively. Centers of curvature for surfaces
A and B are at the points (0,0,-a) and (0,0,a), respectively, where
a® = R? - xo?,

Following Poulter [17], the molecular conductance L can be adequately
approximated in the form

L = nr,2WK,K,¢/4, (¢1)
where r, is the entrance aperture radius. The molecular transmission
probability W of the central duct is to be calculated by neglecting the
cylindrical step above the plane z = -b and the conical transition below the
plane z= b. This neglect requires the introduction of two correction
factors: K, for the effect of the step and K, for that of the cone. The
symbol c represents the mean molecular speed in a Maxwellian distribution.

No adequate basis for estimating K, has been found in the literature.
Indeed, the draft international standard ISO/DIS 3570/I for dynamic expanders
requires no correction for a step having the dimensions given above. Although
a complete analysis of this subject is beyond the scope of this report, simple
estimates based on a generalization of Clausing’s theory [2] provides the

bounds

c-2


Gas Conductance (L/s)

H, 43.52
He 30.89

N, 11.675
ar 9.777

The effect of deviations from the cosine law of scattering is beyond the
scope of this report. A simple model, based on the assumption that a small
fraction of molecules undergoes specular reflection, suggests that the small
difference 1-K is roughly proportional to the fraction of molecules undergoing
cosine law scattering.

The correction for finite Knudsen number in the transition region near
the limit of free molecular flew will require an empirical approach. The
theoretical treatment by Willis applies to an ideal infinitely thin orifice

with zero pressure on the downstream side [19]

onc lusioy

The orifice in the NIST dynamic-expander satisfies the three conditions
stated in the Introduction. The simple form of eq (C12) and the ability to
impose narrow bounds on the transmission probability are consequences of the
spherical geometry and the symmetry of the central duct with respect to the
place of the throat. Application of more precise dimensional metrology would

decrease the uncertainty in the calculated conductance.

C-6


N
7

80°
Figure 7.

'
Z

Detail of the Central Duct Through the Orifice Plate. The
Surfaces Marked A and B are Spherical Segments Lapped to
Radius of Curvature R, and Their Centers. of Curvature are
Marked with Coordinates (0,0,-a) and (0,0,a), Respectively.
Throat and Entrance Apertures have Radii rp) and r,, Respec-
tively. Planes of the Throat, Entrance Aperture, and Exit
Aperture are z = 0, z = -b, and z = b. Approximate Dimensions
in Inches are R = 0.312, ry = 0.221, r, = 0.235, a = 0.221,
and b = 0.015. The Direction of Gas Flow is Downward.

45


because the inlet line is grounded at the flowmeter and at the chamber. The
inlet line should sizzle when water is dropped on it. In addition, the heater
on the turbomolecular pump should be started.

The oven should remain at temperature for at least 8 hours. Then, the
controller may be set to decrease the temperature slowly. The inlet line
should be cooled slowly and the turbomolecular pump heater switched off. The
goal is keep the temperatures of all components as uniform as possible so that
impurities do not condense in cold spots.

After the external oven walls are cool, the argon flow is stopped and the
oven may be removed. When the MDG thimbles have cooled to room temperature,
the suspension heads may be attached, and the balls levitated and accelerated.
The pick-up signals of the MDGs should be checked and the signal scatters
monitored. If needed, the suspension head may be removed after the ball is
braked to a stop and the ball remagnetized to improve the pick-up signal
strength. This completes the baking procedure.

Degassing

The IGs are normally degassed by operating them during the baking of the
chamber. This has served very well. On some occasions, it may be desirable
to further degas a specific IG after baking by wrapping it in glass wool
building insulation and operating it overnight. Electron bombardment or

resistance heating of the grid is not used.

THE DAY PRIOR TO THE CALIBRATION

Preparations for calibration against the NIST Primary High Vacuum
Standard begin the day before the actual calibration. Several procedures must
be completed in preparation - the MDGs must be spun up, the IG voltages and
currents should be checked, the flowmeter pistons must be positioned, and the
leak valve must be set for the proper flow rate.

The MDG balls must be spun up if they are to be used. This is done the
day before in order that they may dissipate the heat produced by the accelera-
tion process. If the ball has been at rest, one must wait several hours (5-7)
before the effect of the cooling is less than the equivalent of 1x10°® Pa, so
it is essential that this be done the day before calibrations.

If IGs are to be used, the filament and grid biases of those gages on
NIST-built controllers should be adjusted as should the emission currents.

This is straightforward. The emission currents of customers’ gages should be

17


automation, among those being the recoraing or tne piston arive information,
the recording of CDG and temperature information, and the recording of MDG
transfer standard readings. Those IGs which are tested on NIST-designed
controllers may also be read automatically. However, we do not foresee at
this time the automatic reading of customer gages owing to the large variety
of instruments that are submitted for calibration.

It is hoped that automatic data acquisition will not only lead to
increased productivity but will allow us to more easily document system
behavior as data are collected. Both the orifice-flow standard and MDGs are
relatively new and our understanding of their operation and capabilities will
be expanding as new results are available. Having those results in a form
amenable to ready analysis will promote optimum performance.

A second means of improving productivity is to install a larger chamber
which would allow the calibration and testing of more gages at one time.

There are fundamental limitations to this system which are not amenable
to treatment with equipment or technique. At the highest pressures, we have
overcome the inherent limitations of the orifice by using MDGs as transfer
standards. However, they become increasingly nonlinear and we have no way of
calibrating them because NIST currently has no vacuum standard to cover the
pressure range 10°? to 0.5 Pa. The orifice-flow standard and ultrasonic
interferometer manometer cover the low and high pressure ends of this range
but there is no provision for direct comparison. This is in part because of
the mercury vapor in the manometer. One appropriate step would be to put
several calibrated MDG balls on the manometer with some protection against
direct mercury exposure. However, the problem of sensitivity to the molecular
weight of the test gas remains for the MDGs.

We anticipate that the working range of the NIST primary high vacuum
standard will remain 10°® to 10°? Pa for the foreseeable future. Our task at
this time is to improve performance within this range with technique and
equipment until our ultra-high vacuum program is well established and until a
new primary standard is designed and built which will bridge the gap between

the ultrasonic interferometer manometer and the flowmeter-orifice standard.

VIIL, ACKNOWLEDGMENTS

We gratefully acknowledge the major contributions of Drs. K.E. McCulloh
and C.R. Tilford in the conception and design of this standard and their work

in the early phases of characterizing the standard. We also thank Mr. D.F.

35


II.

IIl.

Iv.

VI.

VII.

VIIL.

Ix.

‘ABLE OF CONTENTS

Preface
Introduction

Description of the NIST Vacuum Calibration Service

Theory, Design Philosophy and Description of the Calibration

System

The Chamber

The Flowmeter

The Orifice

Extension to Lower Pressures
Calibrations at Higher Pressures
Component Selection Criteria

Operational Procedures for Calibration Using the NIST High

Vacuum Standard

Installation and Preparation of Gages
The Day Prior to the Calibration

The Morning of the Calibration
Measured Flow to Upper Chamber
Measured Flow to Lower Chamber
Steady Flow Generator

Shutting Down

Venting the System

Data Analysis

Assessment of Uncertainties
Systematic Errors
Random Errors

Summary of Errors

Quality Control

Comparisons Against Additional NIST Primary Standards
International Comparisons

Continuous, Repeated Calibrations of Vacuum Gages
Additional Checks

Needs and Plans

Acknowledgments

References

Bibliography

i

Rom anrw

15
16
18
19
20
20
21

yal

35

36

37


A more realistic assessment of the random errors can be obtained from
calibrations repeated on different days. For flow into the upper chamber we
expect that errors at the lowest pressures will be dominated by random
flowmeter errors. The data in figure 4a) are typical of that for ion gages
calibrated in this manner, indicating random variations equivalent to +5x10°°
Pa. This is consistent with the random errors shown for a different gage,
again calibrated with the flow into the upper chamber, shown in figure 4d).
Where calibrations of the same gages have been performed-with flow into the
lower chamber, and repeated flow into the upper chamber, the results agree to
within 1 - 2%. Examples of such data are.shown in figures 4b) and 4c). These
data indicate an upper bound on the random errors of 2% down to pressures
where the flowmeter random errors will again dominate. For flow into the
lower chamber we expect that these errors will exceed 2% at 1x10°7 Pa.

An additional estimate of the random errors at low pressures is obtained
by examining the results of calibrating sixteen ion gages over the pressure
range 3x10-® to 4x10°3 Pa by flowing gas into the lower chamber [10].
Repeated calibrations for most of the gages differed by less than +2.5% and
linear fits of these calibration data had standard deviation of the residuals
between 0.26 and 3.5% with an average standard deviation of 1.95%.

Based on the data above, we have, adopted +2.5% as the upper bound on

random errors of the standard with flow into the lower chamber to 10°© Pa.

SUMMARY OF ERRORS

The component errors previously discussed are summarized in table IV for
nitrogen at four different pressures. The uncertainties at the highest
pressure designated "molecular scattering" are due to the high pressure
nonlinearities in the conductance of the orifice. The effects due to pressure
gradients in the upper chamber and orifice mounting have been left out as
negligible. Errors at the lowest pressure have been assessed on the basis of
flow into the lower chamber. The flow ratio contribution includes random
errors and a systematic contribution for the additional flowmeter measurement
needed. The uncertainty due to changes in the assumed pumping speed is based
on the observed bounds of systematic changes in measured gage sensitivities.
This uncertainty is not applicable at higher pressures because with flow into
the upper chamber the effects of changing pump speed are greatly reduced. The
uncertainty for temperature errors has been somewhat arbitrarily doubled from

the minimum expected value.

28


The flowmeter is thermally insulated but not temperature-controlled. It
is insulated with polystyrene to protect it from short-term temperature
fluctuations and insure internal uniformity. A second quartz thermometer is
located inside the polystyrene at a different location from the first. The
difference between the two temperatures is usually tens of millidegrees. The
actual temperatures of the flowmeter and chamber are not important when the
flowmeter is used simply as a pressure generator but they must be known when
used in the primary standard configuration. Changes in the temperature dif-
ference between the reference and working reservoirs will cause spurious

differential pressure changes.

ible Leak Valve

The gas from the working reservoir flows into the chamber through a
commercially available, all-metal, variable leak valve (G). This valve
enables us to have a large fill pressure, P,,, and still introduce only a very
small amount of gas into the chamber to achieve a given pressure. Large fill
pressures can be more easily measured because of the characteristics of the
CDGs and their calibrations, and they minimize the effects of outgassing.

This valve must be dimensionally stable for stable flow and it is set the day
before a calibration to stabilize mechanical drift which may change the

conductance of this type of valve by as much as 10% overnight.

Vacuum Pumps

A small (0.05 m’s"!) turbomolecular pump backed with a mechanical pump is
used to evacuate the flowmeter reservoirs and to provide a reference vacuum
for the 1.3-kPa CDG on the reference reservoir. A second mechanical pump
serves as a roughing pump for the ballast volume and flowmeter reservoirs. A
larger turbomolecular pump (J) exhausts the chamber. Its speed must be
constant over long periods of time in order to make meaningful measurements.
The pump speed must also be high enough to ensure a large pressure ratio
across the orifice and a very low base vacuum (two orders of magnitude below
the lowest calibration pressure for both MDGs and IGs if possible). The pump
in use has a nominal pumping speed of 0.5 m’s"? for N, gas. The
turbomolecular pump is backed by a molecular-sieve trapped mechanical pump.
An additional requirement is that the pump be free from mechanical vibration

in order that the stability of the MDG readings not be compromised. We have

14


final reading should be slightly positive. Once the valve is closed, the
pressure in the working reservoir will start to fall because gas is flowing
out of the reservoir into the chamber. Any time before the differential
pressure reading becomes negative, piston travel should be enabled. The
piston only travels when the reading is negative and overshoots slightly on
each step. There is provision to choose between proportional and on-off
control of the piston advance.

The elapsed time for each turn of the piston is monitored and displayed.
This display is locked for one-half of each turn to enable the operator to
note both it and the reservoir temperature as read by the quartz thermometer.
The mid-point of all gage readings should occur half way through the piston
travel (turn number 10). The IGs are read once before turn 10 and again in
reverse order after turn 10 in order to average the effects of any pressure
drift. The MDG readings should be started at times appropriate to the timing
algorithm of the controller so that the mid-point of the readings occurs at
the tenth turn.

.After 1-in of piston travel (20 turns), piston travel is stopped and the
working reservoir is reconnected to the ballast volume and the fill pressure
is read as are the chamber and reservoir temperatures. Then the piston is
driven out, the reference reservoir valve is opened, and the system is either
pumped out or adjusted for the next series of measurements. If a new pressure
is established, the operator must wait another 45 minutes for gas sorbtion in

the elastomer seals to equilibrate.

MEASURED FLOW TO LOWER CHAMBER

To calibrate ion gages between 10°* aud 10°75 Pa, the gas flow is directed
into the lower chamber. The operation of the flowmeter is as outlined above.
The 1-cm piston is normally used in this pressure region. Data are taken as
above, the only difference being in the data analysis. The ratio of flow in
the lower chamber to that in the upper chamber, R,, for a given pressure must

be determined and eq (8) used instead of eq (7).

STEADY FLOW GENERATOR

For the calibration of IGs above 1x10" Pa, the flowmeter is used only to
generate a steady flow. In this case, the piston is not used. Gas is
admitted into the ballast volume until the desired calibration pressure is
reached. Gas from the ballast volume is allowed to leak into the upper

20


INSTALLATION AND PREPARATION OF GAGES
Bake-Out

Each venting of the system must be followed by a complete baking of the
chamber and inlet lines. The chamber is designed to be baked at temperatures
up to 250 °C. The gas pison flowmeter may not be baked because of the use of
elastomer seals for the pistons but as much of the gas line to the chamber as
possible should be baked. At present, only the chamber and the inlet line
between the variable leak valve and the chamber are baked. The flowmeter
upstream from the variable leak valve is maintained at high enough pressures
to ensure viscous flow so outgassing and backstreaming during the bake are not
so critical.

The MDG balls are cleaned in alcohol and acetone and dried in a stream of
pure nitrogen gas. The thimbles should be degreased if they have been exposed
to contaminants.

Once the gages have been installed on the chamber with metal-gasketed
seals, high temperature leads are attached between all IGs and ion gage
controllers. The IGs are operated during the bake-out. Suspension heads must
be removed from the MDGs. The turbomolecular pump and its mechanical roughing
pump are started and the system is checked for leaks: Once it has been
ascertained that the system is leak-tight, the chamber is evacuated with the
roughing and turbomolecular pumps and the ion gages are turned on. The IGs
should be set for the biases and emission currents at which they will be
calibrated. The oven is carefully lowered over the entire chamber and the
oven controller, safety switch and thermocouple connected. A flow of argon
gas generating about 10°‘ Pa (10°® Torr) as monitored by an IG in the chamber
is established through the inlet line into the chamber. Because of the small
conductance of the inlet line, this will maintain viscous flow in the inlet
line and across the variable leak valve to prevent backstreaming of
contaminants.

The oven controller may now be turned on to increase the temperature
slowly. It should take at least a day to reach 250 °C. Slow heating is
needed because the temperature must remain uniform so that the upper and lower
chamber flanges do not differentially expand with respect to the center plate
between them. The temperature may be monitored with the thermocouple. When
the chamber is at maximum temperature, the inlet line is heated by a bank of
low-voltage transformers passing equal currents of approximately 60 A from the

center of the inlet line through each half. This configuration is used

16


The tabulated random errors are upper bounds based on repeated MDG
calibrations with nitrogen and argon. These included the random errors of the
standard, flowmeter and gages. The value at 10°‘ Pa is based on three times
the short-term deviations observed in ion gage calibrations at this pressure.
We expect that longer term random changes, due to orifice plate sealing and
flowmeter seals leakage, are probably no different from those included in the
higher pressure MDG data. .

Random errors are not tabulated at 10° Pa because they are included in
the determination of the pump speed uncertainty.

Assessment of errors in some cases is hampered by the limited data
available. Therefore, we must regard these results as tentative at this time.
As we gain more data and experience with the operation of this system, we
expect the uncertainties to change. In particular, we expect to reduce the
uncertainties due to the flowmeter by maintaining tighter calibration control

over the CDGs.

TABLE IV. Uncertainties of the NIST High Vacuum Standard with Nitrogen

Pressure, Pa

107+ 10°2 1074 10°
Systematic Contributions 0.18 01.8 0.18 0.18
Orifice Conductance (%) 0.18 0.18 0.18 0.18
Molecular Scattering (%) 1.2 0.12 - 7
Flow Rate (%) 0.82 0.82 0.82 2.00
Pressure Ratio (%) 0.04 0.04 0.04 0.04
Flow Ratio (%) - - - 0.90
Assumed Pump Speed (%) - - - 2.5
Temperature (%) 0.1 0.1 0.1 0.1
Total Systematic (%) 2.34 1.26 1.14 5.72
Random Errors (3 S.D., %) 0.21 0.30 0.30 -
Total (%) 2.6 1.6 1.4. 5.7

We have chosen to linearly sum the systematic errors and three times the
random errors as a worst-case estimate. If the individual systematic errors
were combined using the square root of the sum of the squares and three times
the random errors were linearly added, the results would be 1.68% at 107+ Pa,
1.15% at 1072 Pa, 1.15% at 1074 Pa, and 3.33% at 10°© Pa.

29


COMPONENT SELECTION CRITERIA

Each part of the calibration system must meet certain performance
criteria to insure that the system is operating under optimum conditions. The
chamber and orifice criteria are discussed above. The three remaining parts
of the system are the molecular drag gages, the flowmeter, and the vacuum
pumps. The criteria that have determined the design and selection of

components are discussed below.

Molecular Drag Gages

Molecular drag gages are used as transfer standards to perform
calibrations between 10°‘ and 10°! Pa. Important characteristics of a
transfer standard are long and short-term stability, ruggedness, and
predictability. The molecular drag gage combines all of these
characteristics. While there may be small effects on ball performance due to
the vacuum thimble containing the ball and due to the controller, the major
predictor of performance is the ball itself. The ball must contain some
magnetic material and must be slightly aspherical in order that the spin and
magnetic axes not align when the ball is rotating. It is the horizontal
component of the magnetic field which produces the signal for the controller.
However, if this asphericity is too large, the residual drag will have a large
frequency dependence. This can be taken into account mathematically but may
reduce accuracy at the lower pressures. In practice, commercially available
steel ball bearings of diameter 4.5 - 4.76 mm may be used as rotors. These
may be either shiny or etched and made of either normal steel or 400 series
stainless steel.

The MDG performance is limited at the lowest pressures by the stability
of the residual drag and its measurement (the offset correction) [8]. Factors
affecting it are slow temperature changes, vibration, signal strength and
timing circuitry errors. The factor having the largest impact on system
design is the necessity to minimize vibrations. Temperature changes affect
MDC performance as the dimensions of the ball change. The fact that the ball
is contained in a vacuum helps to reduce the rate of temperature change.

The residual drag is equivalent to an apparent pressure reading of
10°‘ Pa or more and its stability is important. Every effort is made to keep
random errors no larger than 10°® Pa. At this level of stability, the MDG is

capable of performance at the 1% level at pressures as low as 10°* Pa.

11


b
1-We | h(z)p(z)dz, (C2)
where p(z), translating its verbal definition into mathematical form, is the

solution of the inhomogeneous Fredholm integral equation of the second kind

b
pz) = po(z) +f glz,upp(uyau. (c3)

These two equations provide the basis for the conductance calculation.

The probabilities and probability densities appearing in these equations
depend only on geometric parameters, not on any particular distribution of
molecular flux. Hence they must hold at equilibrium, where conditions for
detailed balance lead to the reciprocal relations

mr,7h(z) = 2aR p,(z) (C4)

and

e(z,u) = g(u,z). (C5)
The factor 2mR occurs in eq (C4) and the kernel g(z,u) is symmetric because
the differential 2nRdz is an element of wall area. Also, because the plane
z= 0 is a plane of symmetry for the central duct, w(z) = p(-z). Since
p(z) + w(z) = 1,

p(z) + p(-z) = 1 (C6)
No further use of the forward escape probability w(z) is required.

From eqs (C2) and (C4).

b
x,2(1-W) = 2R | Py (z)p(z)dz. (C7)
This form is useful because expressions for p,(z) can be conveniently
formulated.
From Clausing's auxiliary theorems, [2]
2Rp(z) =R+a-b; -b<2z<0,
and equating two expressions for the probability that a molecule scattered
from the wall will next pass through the throat,
0
Py (z) + J g(z,u)du = (R-a)/(2R); O<z<b.
-b
Further, if z and u are both positive or both negative,
2Rg(z,u) = 1.

c-4


THE CHAMBER

The design of the vacuum chamber, illustrated in figure 2, is largely
determined by the need to maintain a low background pressure, to provide room
to mount the gages to be calibrated, and to maintain a geometry where the
orifice conductance calculations will be valid and the necessary degree of
pressure uniformity can be assured. The chamber is in two. cylindrical halves,
each 27 cm in diameter and 34 cm long, separated by a central wall with the
orifice in the center. This size chamber permits the incorporation of eight
3.5-cm i.d. mounting ports on the upper half 13.3 cm above the plane of the
orifice. A circular baffle 5 cm below the top of the upper chamber insures
that gas molecules entering through the top of the chamber from the flowmeter
will experience several collisions with the chamber walls before entering a
gage or passing through the orifice at the bottom. These collisions are
essential to insure the random distribution of molecular velocities, which is
necessary for pressure uniformity and which is assumed in the conductance
calculation.

As discussed below, the uniform distribution of molecular flux will be
perturbed by the molecules entering the chamber from the inlet line and by
those escaping through the orifice. These perturbations can be kept within
acceptable bounds by using an orifice whose area is a small fraction of the
surface area of the chamber. At the same time, the orifice conductance must
be large enough to maintain a low background partial pressure and ensure a
high enough flow that gage pumping and outgassing are minor perturbations. In
our system, the compromise used is a nominal 1.1-cm diameter orifice,
described in detail below, with a nitrogen conductance of about 12x10°? m*s"?
and an area of 0.03% of the chamber surface.

Because of the finite pumping speed available at the lower chamber, some
fraction of the molecules passing through the orifice from the upper chamber
will return back through the orifice. This is a second order perturbation
that can be readily accounted for if these returning molecules originate from
a uniform flux distribution. This is achieved by making the lower chamber an
almost symmetric duplicate of the upper chamber, with a baffle 12 cm above the
inlet of the nominal 0.5 msec’! turbomolecular pump attached to the bottom of
the chamber. The chamber is not perfectly symmetrical as the baffle is
located 24 cm below the orifice (the top baffle is 29 cm above the orifice).
The effective rate of exhaust from the lower chamber has been measured to be

0.3 ms"! for nitrogen. The pump speed is somewhat limited by the baffle in


pressures assumes that pump speed does not change with decreasing pressure.
Any change in the pump speed will cause errors in the calculated pressure,
with corresponding errors in the sensitivity of any gage calibrated. In
particular, a decrease in pump speed, with decreasing pressure, will cause an
apparent increase in gage sensitivity. This will be particularly true for
measurements made with gas flow into the lower chamber since the pressures
calculated from eq (8) depend directly on R,, which depends directly on the
pump speed. A constant measured gage sensitivity implies that either the gage
sensitivity and pump speed are both constant, or that both change with
pressure in a manner such that the changes exactly cancel. Neither case can
be proven, but it is unlikely that different gages will have the same
nonlinearities, particularly if the gages are of different designs, so, as
more gages are found to have constant measured sensitivities, the second
possibility becomes increasingly unlikely.

The low pressure ion gage sensitivities presented in figure 4 for
different gages calibrated over a year’s time can be used to establish an
upper bound on possible pump speed changes. The results include random
uncertainties in both the gages and the standard. The data in figure 4b) and
4c) were for gages calibrated with flow into the lower changer and their
sensitivities show a maximum change ‘(in all cases a decrease) of 2% in going
from 10° to 10°® Pa. In a second experiment, data were taken on four
different type of ion gages at pressures from 3x10°® to 10°‘ Pa using flow
into both the upper and lower chambers. The difference in the sensitivities
determined by the two methods over a period of up to 5 days was between -1 and
+18.

Another method of assessing pump speed changes is to look for trends in
ion gage calibration data. Sixteen ion gages were calibrated by directing the
flowmeter into the lower chamber at pressures between 3x10°® and 4x10°> Pa and
the resulting data were fit to an equation of the form S = A+B(logP), where S
is the gage sensitivity and P is the generated pressure [10]. The slopes (B)
of these 16 equations varied from -2.5 to 3.9% per decade. If the individual
coefficient are weighted by their inverse variances, the average value of B
for the 16 gages is less than 1% per decade.

Any assessment of the pump speed will, of necessity, involve random
errors due to the gages involved. Based on these data and the discussion of
random errors below, we have set the error due to pump speed variation at 2.5%

per decade below 10°> Pa.

26


I, = IfE (13)
S= (I, - 1,6)/(1.P) (14)
where R, is a resistor specific to the controller and the emission current
range, V, is the voltage drop across R,, I, is the emission current, Ij is the
measured collector current, E is a range factor for the electrometer and P is
the generated pressure. The subscript "o" refers to readings at base vacuum.
MDG readings are the average of 10 readings taken about the tenth turn of
the piston. The calibration coefficient is determined by dividing the
generated pressure by the MDG reading. The effective accommodation
coefficient is determined by dividing the MDG reading by the generated

pressure.

V.__ASSESSMENT OF UNCERTAINTIES

SYSTEMATIC ERRORS

In addition to the errors already discussed in Appendix C regarding the
conductance calculation and the measurement of the pressure and flow ratios,

Rp and R,, several other possible sources of error must be taken into account.

Pressure Gradients

A high degree of pressure uniformity from port to port in the upper
chamber has been demonstrated by establishing a nitrogen flow to generate a
pressure of about 10°? Pa in the upper chamber. The pressure was measured by
four ion gages which were well distributed about the upper chamber. After
recording the gage readings, the orifice plate was raised and the flow was
increased by a factor of about 15 to establish the same pressure. The
relative gage readings with the orifice plate raised agreed to within 0.1%
with the reading obtained with the orifice plate lowered. Since nonuniformity
due to axial asymmetry of the flow would be proportional to the flow rate
required to generate a specified pressure, the results indicated any such
nonuniformity to be less than 0.01% im normal operation with the orifice plate
lowered.

The upper chamber pressure will have a vertical perturbation due to the
net flow of molecules between the gas inlet and the orifice. This will have
two contributions, one due to the molecules exiting through the orifice and
not being scattered back, and the second due to the molecules entering from

the inlet. The first contribution is reasonably straightforward to calculate

23


Il.

Til.

Iv.

v

VI.

1.
2.
3.

4.

6.

7.

Summary of the vacuum calibration service

Primary standard configurations used for calibrations
Primary standard nonlinearities

Uncertainties of the NIST high vacuum standard with nitrogen
. Results of first international intercomparison

Ion gage sensitivities, nitrogen gas

LIST OF FIGURES
Schematic of the primary high vacuum standard
Schematic of the vacuum chamber
-Axial section of the orifice plate

Representative measured low-pressure nitrogen sensitivities for
different ion gages

Deviations from initial value for calibrations of five molecular
drag gages

Ion gage sensitivity in nitrogen for two ultra-high vacuum
ionization gages

Detail of central duct through orifice plate

vil

15

25

29

31

33

39

40

41

42

43

44

45


xI.

Appendices

A. Sample Report of Calibration for Ionization Gage

B. Sample Report of Calibration for Molecular Drag Gage

C. Dimensions and Conductance of the Orifice in the NIST
Dynamic Expander

vi


The performance of these gages is discussed in the section on errors.
With careful use, the calibration of the gage will change no more than 2% over.

a 2-year period.

The Flowmeter

All letter references in this section are to figure 1.

The Gases

Because the orifice conductance, the MDG constant K, and the IG
sensitivity are all dependent on the molecular mass of the calibration gas,
gas purity is important. The gas composition in the chamber is routinely
monitored with a residual gas analyzer to check for impurities. The
calibration gases are used as purchased with no further purification and the

purity levels have been more than adequate.

Capacitance Diaphragm Gages

The pressure in the reference reservoir is measured with capacitance
diaphragm gages (C). Two, with different ranges, are used. Accuracy and
long- term stability are the most important criteria. One of the CDGs is a
1.3 kPa full-scale differential unit which uses the vacuum created by a small
turbomolecular pump as its reference pressure. The other is a 133 kPa
absolute gage. The CDGs are calibrated against the NIST ultrasonic
interferometer manometer which has an accuracy of 15 ppm + 1.3x10°? Pa.

A third CDG (D) is used to measure the pressure difference between the
reference and working reservoirs. Short-term stability (20-30 minutes) is the
most important criterion. . This unit is only used to measure small pressure

differences and is not calibrated.

The Pistons

The volume of the piston which moves into the working reservoir appears
in eq (1) as dV. Thereforc, dimensional stability and charactcrization are
very important. We are using "wire gages" as pistons. These are readily
available, well characterized, and carefully constructed cylinders of tungsten
carbide. One of the pistons has a nominal diameter of 1 inch (2.540 cm +
40 ppm, -O ppm) and the other has a nominal diameter of 1 cm
(1.0000 cm + 51 ppm). They will be referred to as the inch and centimeter

12


TABLE I, Summary of the Vacuum Calibration Service

Calibration
Sensor Range Standard Uncertainty
Pa percent:
MDG 5x107° Primary high 1.4-1.6
vacuum
Ig 1o-* - 1072 Calibrated MDG 1.4-2.6
I¢ 10-§ - 1074 Primary high 1.4-5.2
vacuum

If calibration of a gage other than a hot cathode ionization gage or a
molecular drag gage is desired, contact the Temperature and Pressure Division
at the address below.

The Report of Calibration for an MDG gives the effective accommodation
coefficient or calibration coefficient of the rotor, and a discussion of the
care and use of the gage for best results. The Report of Calibration for an
ionization gage gives the correction factor for the gage's indicated pressure
as determined as a function of pressure and the characteristics of the con-
troller (grid and filament biases and electrometer performance if applicable),
and provides a discussion of the treatment and use of the gage for best
results. See Appendices A and B for sample reports.

For information concerning these services or to schedule a calibration,
please contact Temperature and Pressure Division, Bldg. 220, Room A55,

National Institute of Standards and Technology, Gaithersburg, MD 20899.

Ill. THEORY, DESIGN PHILOSOPHY AND DESCRIPTION OF THE CALIBRATION SYSTEM

High vacuum calibrations are performed at the National Institute of
Standards and Technolgoy (NIST) with the Primary High Vacuum Standard - an
orifice-flow system (see fig. 1) - between 10°® and 10°? Pa and against a
group of calibrated molecular drag gages (also called spinning rotor gages)
between 10°* and 10+ Pa. ‘he three main components in the primary standard
are the vacuum chamber, the flowmeter and the erifice. Pressures are
generated by producing a known flow of gas which passes through an orifice of
known conductance, thereby producing a known pressure drop across the orifice.
This pressure drop is calculated from first principles and constitutes a

primary standard. The details of the system are discussed below.


checked and adjusted if necessary and the zeros of the electrometers should be
set by mechanical adjustment on a high-range scale and electrical adjustment
at low-range scale readings after removing the collector lead.

For pressures at the low end of the range (<10TM* Pa), the 1-cm diameter
piston will be used. The 1-in diameter piston covers the higher end (>107‘
Pa) (see table II). The piston not in use should be left at the end of its
travel to make the volume of the working reservoir as small as possible. The
piston to be used should be placed‘at the top of its travel and then advanced
slightly to eliminate backlash.

The leak valve must be set the night before a calibration to stabilize
mechanical drift. The flowmeter performs most reliably when the piston takes
about 1000 seconds to travel 1-in. All leak valve adjustments should be made
in the direction of increasing conductance as the valve has substantial
backlash.

In general, the system should be left overnight with the flowmeter and
chamber evacuated and the orifice plate up. If very low pressures are to be
generated (near or even below 1x10°§ Pa), it may be advisable to leave the

orifice plate down overnight for maximum stability in the base vacuum.

THE MORNING OF THE CALIBRATION

The first order of business is to check the base readings of the IGs to
be sure that the system is at an appropriate base pressure. If so, the
orifice plate should be gently lowered if it is up and the time noted. Then,
the IG voltages and currents should be rechecked. The chamber temperature
should be noted and the MDGs set up for the day. This will involve entering
the date, run number, gas and ball parameters (molecular weight, viscosity,
diameter, density and temperature of 298.15 K for a second generation gage),
an effective accommodation coefficient (1 for any second generation gage to be
calibrated), timing interval of 30 in the sécond generation units, etc., as
appropriate.

After the gage readings have stabilized (about 45 min after lowering the
orifice plate), the base readings of the IGs and MDGs should be checked for
stability. The MDG readings should be stable to better than +1x10°® Pa.
Offsets should be read for the MDGs and the base readings for the IGs should
be taken. These offsets should be entered into the MDG controllers and the

resulting MDG readings should be observed to be sure that they vary about zero

18


NIST MEASUREMENT SERVICES:
High Vacuum Standard and Its Use

Sharrill Dittmann

Center for Basic Standards

National Measurement Laboratory

National Institute of Standards and Technology
Gaithersburg, MD 20899

March 1989

NOTE: As of 23 August 1988, the National Bureau of
Standards (NBS) became the National Institute of
Standards and Technology (NIST) when President
Reagan signed into law the Omnibus Trade and
Competitiveness Act.

U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary
Ernest Ambler, Acting Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

Raymond G. Kammer, Acting Director


a 3.50” aa

0.50 : = ”
K go° K

Figure 3. Axial Section of the Orifice Plate, with Dimensions in Inches.

Details of the Central Duct are Shown in figure 7. This Plate
can be Raised to Provide a Large Conductance Between the Upper
and Lower Chambers of the Dynamic Expander During Evacuation.
For Generating Calculable Pressures by Flow Through the Orifice,

the Knife Edge K is Lowered into a Groove Gilled with Gallium to
Provide a Gas-tight Seal.

41


after a sufficiently long time following establishment of a steady gas flow.
Second, stable pressures are readily generated for long periods: of time.
Third, the only dimensions which need to be characterized are those of the
orifice and the volume of the piston, and these are not dependent on the
position of valves. A detailed examination of the flowmeter is found in
Ref.1.

Before examining the flowmeter, we briefly review the equations used to
calculate the flow rate of the gas and the pressure drop across the orifice.
The equations used are:

for the throughput Q,

Q = Peg l (AV) /(dt) ] (Ten /Tem) in Pa ms"? qd)
for the orifice conductance C,
CG = C*(T,,/298.15 K)t/2 in ms"? (2)

for the pressure at the upstream side of the orifice,

P = (Q/C)Rp/(Rp - 1) in Pa Q@)
where Q is the throughput of the gas, C” is the conductance of the orifice, (I
in fig. 1) at 298.15 K for the gas in question, P is the pressure on the
upstream side of the orifice, and Rp is the ratio of the pressures in the
upper and lower chambers. The superscript "*" refers to quantities calculated
at 298.15 K, the subscript "fm" refers to quantities measured in the flowmeter
and the subscript "ch" refers to quantities measured in the chamber.

All letter references in the following discussion are those indicated in
fig. 1.

Q is generated as follows. Initially, two interconnected reservoirs (B
and E) are filled to the same pressure from a ballast volume (A). Gas flows
from the ballast volume into the reference reservoir (B) and through the
working resérvoir (E) into the chamber (H). The rate of flow into the vacuum
chamber is regulated by an all-metal leak valve (G). To initiate a calibra-
tion, the reference reservoir (B) is isolated. At this time, Py, is measured
in the reference reservoir with a capacitance diaphragm gage (CDG) (C). Pry
is between 0.07 and 133 kPa and is within the range where the CDGs have
adequate accuracy. After the reference reservoir is sealed, the flow trom the
ballast volume continues into the chamber through the working reservoir (E).
Gas purity is continuously monitored with a residual gas analyzer. No special
precautions are taken once the gas leaves the high-pressure supply cylinder,
but for some gases, it has been found necessary to purchase high purity

samples.


the lower chamber and by the 15-cm i.d. connection between the lower chamber
and the pump. The turbomolecular pump was chosen for its stable high pumping
speed, low base pressure, and compatibility with all gases.

Ultra-high vacuum construction practices are employed throughout the
chamber; the chamber material is type 304 stainless steel, only all-metal
seals are used, and the chamber and all gages are baked at, about 250 °C after
each venting to air. However, the small orifice clearly would restrict the
attainment of a low base pressure in the upper chamber. Therefore, the
orifice is contained in a plate that seals into a gallium-filled groove
located in the central wall as illustrated in figure 2. During pump-down or
bakeout the orifice plate can be lifted through a bellows at the top of the
chamber, opening a 12.7-cm hole between the upper and lower chambers. For the
gallium to form a seal when the orifice plate is lowered, it must remain
supercooled for prolonged periods below its 302.95 K melting temperature.
Should the gallium freeze, the edge of the orifice plate would fail to make an
integral seal with the central wall. Leaks of 10 cm’s"1 or larger will have a
significant effect on our measurements. In 4 years of operation we have never
observed any erratic calibration data for our check standards which would
indicate unreproducible sealing or failure of the seal. Nor have we seen any
evidence of gallium vapor in the chamber, which is consistent with gallium's
predicted vapor pressure of 10°28 Pa at room temperature.

This system routinely attains base pressures of about 10°® Pa, the
residual gas being almost entirely hydrogen. The base pressure in the upper
chamber increases by about a factor of two when the orifice plate is lowered

and sealed in the gallium groove.

THE FLOWMETER

The flowmeter is used to generate a known flow of gas through the orifice
which produces a pressure drop across the orifice. The differential pressure
thus produced plus the pressure below the orifice is measured by the gage
under test. The flow is produced by a P(dV/dT) method in which gas is allowed
to leak out of a reservoir which is maintained at a constant pressure by
changing its volume through the advance of a piston. The time taken for the
piston to advance a known distance is measured and the flow is thus known.
This use of the orifice-flowmeter system offers three distinct advantages over
a static expansion system. First, because this is a steady flow system,

transient behavior associated with adsorbtion and desorbtion become negligible


0.99995 < K, < 0.99997.

A carefully designed conical transition in place of an abrupt step would
require a correction factor much closer to unity. Unfortunately, design and
fabrication preceded recognition of this point.

From the computed results and uncertainty estimates published by
Iczkowski et al. [18] for conical orifices

0.9999 < K, < 1.0000.
On the basis of these inequalities a nominal value of 0.9999 for the

product K,K, is employed in the subsequent computations.

The transmission probability W remains to be calculated. It is assumed
that molecules from a solid angle 2x of a Maxwellian distribution enter the
central duct through the entrance aperture and that the wall, consisting of
surfaces A and B, scatters impacting molecules according to the cosine law.
Clausing’s treatment of this law [2] provides a basis for calculating several
probabilities required for the conductance calculation. These probabilities,
which depend only upon axial coordinates because of rotational symmetry, are
defined as follows:

h(z): Points of initial impact on the wall by molecules entering the duct
through the entrance aperture are distributed with respect to z with
probability density h(z).

g(u,z): If the axial coordinate has the value u at a scattering point P on
the wall, points of next impact n the wall by molecules scattered
from P are distributed with respect to z with probability density
g(u,z).

Po (2): Molecules scattered from the wall at (x,y,z) make direct
line-of-sight escape back through the entrance aperture with
probability p,(z).

p(z): Molecules scattered from the wall at (x,y,z) made eventual escape
(direct plus indirect) back through the entrance aperture with
probability p(z), which equals p,(z) plus the probability of escape
after again striking the wall one or more times.

w(z): Molecules scattered from the wall at (x,y,) make eventual forward
escape through the exit aperture with probability w(z). As the
walls are assumed not to capture molecules, p(z) + w(z) = 1.

If W is the molecular transmission probability of the orifice, the

complementary probability 1-W is given by the integral

C-3


[15] P. L. M. Heydemann, CG. R. Tilford, and R. W. Hyland, "Ultrasonic
Manometers for Low and Medium Vacua under Development at the National
Bureau of Standards," J. Vac. Sci. and Technol. 14, 597 (1977).

[16] R. W. Hyland, "NIST Measurement Services: Calibration at the National
Institute of Standards and Technology over the Low Vacuum Range from 1 to
1.5x10° Pascal," to be published as NIST Special Publication SP 250-35.

[17] K. F. Poulter, "The Calibration of Vacuum Gauges," J. Phys. E 10, 112
(1977).

[18] R. P. Iczkowski, J. L. Margrave, and S. M. Robinson, "Effusion of Gases
through Conical Orifices," J. Phys. Chem. 67, 229 (1963).

[19] D. R. Willis, "Mass Flow through a Circular Orifice and a Two-Dimensional
Slit at High Knudsen Numbers," J. Fluid Mech. 21, 21 (1965).

X.__ BIBLIOGRAPHY

In addition to the references cited above, the interested reader may wish

to consult the following.

Intercomparisons:

"Intercomparisons of Vacuum Standards of. Countries within the European
Community in the Range 8x10°5 to 8x10"? Pa," K. F. Poulter, A.
Calcatelli, P. S. Choumoff, B. Iapteff, G. Messer, G. Grosse, J. Vac.
Sci. Technol. 17, 679 (1980).

“Intercomparison of the National Low Pressure Standards in the LNE and PTB,"
G. Messer and L. Rubet, Proceedings of the Eighth International Vacuum
Congress, Cannes, France, 1980 J. P. Langeron and L. Maurice Eds., V. II,
259 (1980).

Standards:

"The Measurement of Gas Throughput in Range 10°* to 10°19 Pa m’s"1," G. N.
Peggs, Vacuum 26, 321 (1976).

"Summary Abstract: Long-Term Stability of Low-Pressure: Standards in the
German Calibration Service Deutscher Kalibrierdienst," G. Grosse and G.

Messer, J. Vac. Sci. Technol. A 5, 2463 (1987).

37


results are based on the readings of 12 MDGs taken over a period of 4 days and
are summarized in table III below. Total deviations are expressed as the mean
difference between the pressure indicated by the MDGs and pressure generated
by the high vacuum standard + three times the standard deviation of the MDG

readings.
Table III. Primary Standard Nonlinearities
Nitrogen Total
Pressure, Deviation MDG Nonlinearity
Pa percent percent
1x10°2 0.0740.2 0
7x10"? 0.7 40.3 0.2 (11 MDGs)
1x1072. 1.7 40.6 0.3
Temperature

The average temperature of the gas molecules is determined by the average
temperature of the chamber walls, which is known with an uncertainty of 0.3 K
in the absence of heat sources, notably ion gages. The normal temperature is
296 to 298 K. Ion gages are heat sources and, depending on the number of
gages and whether they are tubulated or immersed in the chamber, this
uncertainty in the chamber temperature could be as much as an order of
magnitude larger in extreme cases. This will contribute an uncertainty to the
pressure varying from 0.05 to 0.5%. This does not include uncertainties in

the thermal transpiration corrections for ion gages being calibrated.

Flow Rate Errors

The uncertainty of the flowmeter [1] is dominated by the uncertainty of
the capacitance diaphragm gages (CDGs) used to measure pressures. The
uncertainty of the CDGs is based on observed calibration shifts of the CDGs
used in the flowmeter and our experience with the long-term stability of a
larger group of CDGs [9]. The estimated total systematic uncertainties of the
flowmeter are listed in table IV.

Changes in Pump Speed

As discussed earlier, the pressure and flow ratios can be reliably

measured only at higher pressures and their use in eqs [7] and [8] at lower

25


30

e I T T
e
Cr ° -o—
30 ® a) 4
Ff 5 =
EB ot -& x—* *
2
= 5E b) +
G 5+
n ° “]
o —
2 0 x x x » 6 °
& 5p c) 4
@
© sf a
bd e
; phn ey
e
5 |
1 ! _l q)
7 6 5 4 -3
Log Pressure, Pa
Figure 4, Representative Measured Low-Pressure Nitrogen Sensitivities for

Different Ion Gages. Sensitivities for Each Gage are Relative to
its Value at 10°’ Pa. The +'s Indicate Flow into the Lower
Chamber, the 0's are into the Upper Chamber. The Data in a) are
for a Nude Gage with an Electrode Structure Commonly Found in
Tubulated BA Gages. The + 20 - 30% Variation at the Lowest
Pressure is Typical of Results for Other Gages Calibrated at the
Same Time.

42


since the orifice is an ideal sink. This contribution will decrease the
pressure at the gage ports from that given in eq (7) by a factor of 0.99956.
The second contribution is more difficult to calculate because the
scattering of the inlet flow produces a diffuse source and it will take
several collisions before the effects of the initial nonuniformity are
negligible. However, this contribution is somewhat smaller than the first, but
of the opposite sign. The sum of these two contributions results in a
condition in which the pressure at the gage ports is slightly less than at the
orifice so that the net flow of gas is from a region of lower pressure to one

of higher pressure, an entirely possible result in the molecular flow regime.

Mounting of the Orifice Plate

Another small error is the perturbation of the calculated conductance
caused by the mounting of the orifice plate. The orifice plate is mounted in
the wall between the two chambers with a short duct, 12.7 cm in diameter and
1.27 cm long, between it and the lower chamber. The probability of
transmission to the lower chamber of molecules exiting the. orifice is
estimated to be 0.9997 + 0.0001. This effectively increases the pressure in
the upper chamber by the factor of 1.0003, offsetting the effect at the gage
port of the small vertical pressure gradient previously discussed.

We estimate that 0.003% is a generous upper bound on the uncertainties
caused by the combined upper chamber pressure gradients and the mounting

configuration of the orifice plate.

High Pressure Nonlinearities

The calculation of the orifice conductance assumes an absence of
molecule-molecule collisions. The number of such collisions increases with
pressure, with a corresponding increase in the error of the conductance
calculation. We have chosen at this time not to attempt to correct for this
effect but rather to restrict the upper pressure limit of the standard to keep
this error within reasonable hounds. The error due to non-molecular flow
conditions amounts to 0.1% at about 8.5x10°? Pa for N,, and at about 2.5x107?
Pa for He, and increases linearly with pressure.

The orifice-flow standard was operated above the molecular flow range to
assess the total nonlinearity of the system at "high" pressures. MDGs were
used as the standards in this case as their nonlinearity is known and is

smaller than the nonlinearity in the orifice conductance (Appendix C). The

24


1 INTRODUCTION

Vacuum measurements are an important tool for many segments of the
American economy and for American defense efforts. The accuracy of these
measurements affects a large variety of industries ranging from space simula-
tion to semiconductor processing. The National Institute of Standards and
Technology provides calibrations for a variety of vacuum gages over a broad
range of pressures - from atmospheric pressure (about 10° pascal) to high
vacuum (about 10°® pascal).

This document presents an in-depth discussion of the NIST primary high
vacuum standard, used between 10°® and 10°? Pa. Included are discussions of
the theory, design, and construction of the standard. In addition, the sys-
tematic and random errors in the standard and the methods used to check the
accuracy of the standard are presented.

Also included is a brief discussion of the molecular drag gage and its

performance as a transfer standard between 10°‘ and 107! Pa.

IL, DESCRIPTION OF THE NIST VACUUM CALIBRATION SERVICE

The National Institute of Standards and Technology provides calibrations
of suitable high vacuum gages over the range 10°® to 1071 Pa (pascal) (107® to
10-8 Torr) using gases compatible with the standard. Gages must be stable and
capable of precision at the level of a few percent to be considered suitable
for calibration. Molecular drag gages (MDGs) are calibrated against the NIST
primary high vacuum standard at 5x10? Pa (4x10°5 Torr). Hot cathode
ionization gages (IGs) are calibrated against calibrated molecular drag gages
over the range 10°‘ to 10°! Pa. They are calibrated against the NIST primary
high vacuum’ standard over the range 10°® to 10°* Pa (10°® to 10°® Torr).

These services are summarized below:


found turbomolecular pumps to be satisfactory if the MDGs are mounted with

care.

IV. OPERATIONAL PROCEDURES FOR CALIBRATION USING
THE NIST HIGH VACUUM STANDARD

This section describes in some detail the operation of the orifice-flow
standard, Users are referred to Ref. 6 for MDG operating procedures.

There are two flowmeters of similar design at NIST and either may be used
with the orifice-flow standard. It is also possible to use either flowmeter
with the primary leak standard. However, there is only one vacuum calibration
chamber with an‘orifice of the design described above. The chamber has eight
ports of which one is part of a by-pass manifold between chamber halves and
one is occupied by a residual gas analyzer. This leaves six ports for gages
under test and transfer standards. Care must be taken that ion gages sharing
ports do not interact by having ions generated in one gage collected at the
other. This is generally accomplished by avoiding line of sight connections
between ionization gages. Within these limitations, the number of gages that
may be calibrated at one time is limited only by gage geometry and operator
preference.

As discussed earlier, the IG calibrations fall naturally into three

groups:

Table Il. Primary Standard Configuration Used for Calibrations

Flow in Which Piston
Pressure Chamber Diameter
Pa
10°® to 107° Lower One Centimeter
1075 to 1074 Upper One Centimeter
>1074 Upper One Inch or MDGs

MDGs are calibrated with the flow into the upper chamber using the 1-in
diameter piston. These calibrations are procedurally like the IG calibrations
between 10°> and 10°‘ Pa. The calibration is performed at only one pressure
(5x10° Pa) which represents a compromise between the upper limits of the
orifice conductance linearity and the lower limit of acceptable MDG perfor-
mance. The MDGs remain linear between 10°* and 1071 Pa but the random scatter
in the residual drag becomes a problem near 10°* Pa if performance at the 1%

level is desired.

15


APPENDIX G

DIMENSIONS AND CONDUCTANCE OF THE ORIFICE
IN THE NIST DYNAMIC EXPANDER*

Introduction

The orifice in the NIST dynamic expansion apparatus was designed and
fabricated in 1980 to satisfy three conditions:

1. Sufficient thickness to ensure dimensional stability,

2. A molecular flow conductance differing by less than 1% from that of
an infinitely thin orifice having the same diameter, and

3. A geometric form to facilitate accurate calculation of this
conductance by the integral equation method introduced by Clausing [2].

An orifice with a sharp circular edge in the plane of minimum cross section
best satisfies these conditions. Spherical geometry was chosen for the
surfaces meeting at this edge in order to facilitate the conductance
calculations. In addition, these surfaces could be generated by lapping.

A generalization of Clausing’s theory is required because of the
departure from cylindrical geometry. Although the present formulation
emphasizes probabilities for retrograde escape from the orifice duct, while
Clausing's is based on forward escape probabilities, the two are equivalent.
Either formulation can be derived from the other or directly from first

principles.

Structure and Dimensional Details

An axial section of the orifice plate as designed and fabricated of
stainless steel is shown in figure 3, and details of the central duct appear
in figure 7. The two surfaces A and B in figure 7 are spherical segments
generated by lapping to a radius of curvature R = 0.3125 in. The diameter of
the throat where these surfaces meet at a sharp edge was measured at NIST by

R. Veal and W.

*A Technical Report submitted by The Catholic University of America to the
Temperature and Pressure Division of the National Institute of Standards and
Technology in Compliance with the Terms of Grant NB82NAHA3005, K E. McCulloh,
Principal Investigator.

c-1


APPENDIX C-II

The Integral A and the Transmission Probability K

The integral A and the transmission probability K have been narrowly
bounded without solving integral eq (C8). First the integrals

b
I(z) = ar f g(z,u)du; -b<x<0
0

and

0
a= J. I(z)dz

were evaluated by numerical quadrature. Although a suitable analytical
expression for g(z,u) has not been found, arguments based on the spherical
geometry and Clausing'’s first auxiliary theorem {2] identify the product
2nRI(z) with a particular area on the (mathematical) sphere of which surface A
(fig. 7) is a segment. This is the area traversed by molecules scattered from
a point (x,y,z) on surface A and next striking surface B.

The quadratures were performed in BASIC on a minicomputer by Simpson's
rule. Several hours of running time on the otherwise idle computer were
required. The grid was sufficiently fine to compute I(z) at 101 points with
ati uncertainty less than 0.001 b. The integral J was computed with an
uncertainty less than 0.001 b?.

Absolute bounds based on generous overestimates of uncertainty yield the
inequalities

I, = 0.63-b < I(z) < 0.79-b = I); -b<z<9O,
and
J, = 0.69-b? < J < 0.71-b? = JQ.
Then if p,, pz, A,, and A, are absolute bounds such that
Py < p(z) < Pa; 0<z<b,
and

A, <A<Ay,

one obtains from eqs (C8) and (C9) the system
Pps = eT be
2Rp, = R-at+ A, - TiPi,
(2R-b)A, = b(R-a) - Jnp2,
(2R-b)A, = b(R-a) - Jyp,-

C-II-1


A second set of four balls was sent to NIST in 1986 in a continuation of
the round robin. Preliminary results indicate that the mean of the four NIST
values for argon was within 0:5% of the pilot laboratory's value. The results
for nine laboratories (representing five different types of primary standard)
were within +2% of the pilot laboratory at argon pressures between 10°? and
10°71 Pa with the exception of two laboratories whose values were within +3%
(13].

Several additional informal intercomparisons are underway at standards
labortories. Rotors calibrated at NIST are now in use at Istituto di
Metrologia "G. Colonnetti", Turin, Italy -and Korea Standards Research
Institute, Seoul, Korea and two calibrated MDG rotors have been sent to the
National Physics Laboratory, New Dehli, India.

Intercomparisons have been carried out with other primary standards
laboratories at very low flow rates using calibrated leaks as transfer
artifacts [14]. Early results showed differences increasing to 10% at flow
rates of 10°12 mol s~+ which correspond to a nitrogen pressure of about 10°?
Pa in the upper chamber. ‘It is expected that improvements since these data

were taken should decrease the differences.

CONTINUOUS, REPEATED CALIBRATIONS OF VACUUM GAGES
Repeat MDG Calibrations

Many NIST-owned MDG balls have had multiple calibrations. Systematic
calibrations were begun in 1983 using the gas burst method and continued with
the orifice-flow standard. One rotor in particular has been calibrated
repeatedly between February, 1983 and April, 1987. A total of 106
calibrations in nitrogen have been performed. The range in the effective
accommodation coefficient is from 0.99 to 1.02. These results are indicated
by the dashed line in figure 5. Results of repeated calibrations for four
additional balls are also shown in figure 5. The data shown have been
clarified by plotting deviations from the initial calibration expressed as a
percent of that initial value and by averaging points taken within a few days
of each other. There is some evidence of an increase in the effective
accommodation coefficient which is expected. Large abrupt changes in the
calibrations of any of the rotors have always been traced to problems with the
primary high vacuum standard (such as the presence of foreign gases in the
chamber, the use of unbaked rotors or failure of the turbomolecular pump) and

not with the rotor surface.

32


Ion Gage Comparisons

Ion gages are not as stable as MDGs and we do not expect to gain as much
information about system performance from our ion gage data. However, because
of the broad pressure range covered by these gages, we can use them to look
for systematic errors in the high vacuum standard performance depending on
whether the flow is directed into the upper or lower chamber and depending on
which piston is used in measuring the flow. To date, we have not seen any
systematic differences at the 2% level.

Figure 6 shows data for two ion gages. Two extensive sets of
calibrations were performed on each gage between 10°? and 1071 Pa. The two
sets were performed 3 months apart. The gage in figure 6a) is designed for
use between 10°19 and 10°? Pa and showed no shift in sensitivity as a function
of calibration method. Four different configurations of the flowmeter were
used as well as a bank of calibrated MDGs. The gage in figure 6b) is designed
for use between 10°® and 10°! Pa and showed a definite shift in sensitivity
between the two sets of calibrations but exhibited excellent short-term
stability. Again, we see no systematic differences between results using the
various calibration methods. Table VI gives means and standard deviations for
these two gages at 10°‘ Pa for two frequently used calibration methods. It
should be noted that each method of determining the pressure has a range of
pressures over which it functions best. For example, we would expect more
scatter in data taken at or below 10°‘ Pa with an MDG than at higher

pressures.

TABLE VI. Ion Gage Sensitivities, Nitrogen Gas 107? PaTM*

Gage 6a Gage 6b
Method Mean Standard Mean Standard Date
Deviation, Deviation, %
Flow to upper chamber, 6.63 1.4 5.12 0.2 9/85
1 em piston 6.63 0.6 4.09 0.8 1/86
Molecular drag gages 6.79 0.8 5.17 0,4 9/85
6.64 2.3 4.25 2.4 1/86

ADDITIONAL CHECKS

Eight MDGs have been returned by customers for recalibration at this
time. The changes in the calibration factors varied from -2.3% in 2 year’s

time to +2.7% in 1.7 year’s time. All of these are within our expected change

33


The operating parameters of the electrometer were independently checked
and are noted below.for your information. The controller required

approximately 24 hours after being turned on to reach a stable indication.

Current at Collector Indicated Pressure,
Input, Amps Torr, No
8.337x107 1° 1.0x107®
2.634x10"® 10.0x10°®
2.601x10"9 1.0x10°7
2.074x107® 10.0x1077
2.074x10°® 1.0x10°®

. 2.043x10°7 10.0x10"
2.043x10°7 1.0x107>
2.216x10°& 10.0x1075
2.216x10°® 1.0x107*
3.916x10"> 10.0x10"4

Changing emission current or bias voltages can cause changes in the gage
tube sensitivity and therefore the calibration factor.

In order to obtain optimum stability from this tube, we recommend that it
not be operated with significant pressures of air or oxygen, that long periods
of outgassing be avoided, that after outgassing it be allowed to equilibrate
for eight or more hours, and that after exposure to atmospheric air or opera-
tion with other gases it be baked out at a high temperature or wrapped in
fiberglass insulation and operated for 8 hours or more in a high vacuum. An
overnight equilibration period should be allowed after bakeout. Operation
with 10°? Pa N, for 1 or 2 hours followed by baking may help to stabilize
subsequent N, readings. When a sequence of pressures is to measured, the gage
will perform most reliably when an increasing sequence is used. Preferably,
the gage should be stabilized by operation for several hours at a pressure at

least a factor of 10 below the lowest pressure to be measured.


chamber and the gages are monitored until the readings are steady. At this
time the gages are read: MDG readings are started, the IGs are read once, and
then the IGs are read in reverse order. The analysis of the gage readings is
described below with the exception that a group of MDGs is used to measure the
chamber pressure. MDGs which are used as transfer standards should have the

appropriate calibration parameters entered before the offset data are taken.

SHUTTING DOWN

After the last run of the day, the flowmeter should be evacuated with the
mechanical pump and the small turbomolecular pump. The MDG readings at base
vacuum should be checked with the orifice in place to evaluate errors caused
by possible drifts in the residual drag. Then, the orifice plate should be

raised,

VENTING THE SYSTEM

Several precautions should be taken before the system is vented to remove
customers’ gages or for any other reason. All IG and residual gas anaylzers
must be turned off. The MDG drive must be disabled. The suspension heads may
be left on or not until they must be removed for baking. If they are to be
removed, the balls must first be stopped using the controllers (and an
oscilloscope or spectrum anaylzer to monitor their rotational frequencies if
necessary) and lowered into their thimbles. The residual gas analyzer must be
isolated behind a closed valve. The turbomolecular pump is stopped and its
mechanical pump vented.

The system pressure is increased to slightly above one atmosphere with

argon or dry. nitrogen. The system is then vented.

DATA ANALYSIS

Three types of data may be gathered in the course of a calibration. The
first are the data pertaining to the flowmeter which will be used to calculate
the pressure in the upper chamber. The second are the MDG readings and the
third are the IG readings. The way in which the system is being used and the
instruments being calibrated will determine which types of data are recorded.

Concerning the first (the flowmeter), the operator should have the
following numbers available:

The fill pressure before and after the run, P,,.

The chamber temperature before and after the run, T,,.

21


The effective accommodation coefficient given for the ball applies only
for nitrogen.

Before the gage is used, the chamber temperature, in kelvins, must be
entered from the front panel of the controller as a parameter. Temperature
corrections must be made for the viscosity, and the residual drag must be
determined for the temperature of use.

Care must be exercised in using a spinning rotor gage to achieve optimum
performance. For use at the lowest pressure, the ball and thimble should be
baked with the vacuum system. Mechanical or chemical damage to the surface of
the ball should be avoided and the ball should always be stopped before it is
lowered in the thimble. External magnetic fields (time dependent fields in
particular) will have an unpredictable effect on the behavior of the unit. To
obtain the optimum rotational timing signal, it may be necessary to
periodically remagnetize the ball, particularly after it has been baked.

Since the magnitude of the residual drag can change, it must be
redetermined each time the ball is suspended, and preferably before each
series of low pressure measurements. The residual drag should be determined
by monitoring the indicated pressure at "zero" pressure. The most accurate
values will not be obtained until 5 to 7 hours after spinning up the ball from
rest. This allows for dissipation of the ball’s induced heat. The frequency
dependence of the residual drag can change as well when the ball is
resuspended, and therefore should be checked.

The error of a measurement made with this gage, assuming pure nitrogen
and appropriate parameters, will include the 1.5% uncertainty of the NIST
standard, random reading errors of the gage, and any shift in the effective
accommodation coefficient as a function of time because of changing ball
surface conditions. Random reading errors will depend on the strength of the
rotational timing signal, the measurement time and local temperature and
vibrational instabilities. They should be evaluated by the user by observing
repeated measurements at a stable pressure. This is most easily accomplished
by making repeated observations of the indicated zero or residual drag at low
(<10°® Pa) pressure. Operating the ball in a different thimble from the one in
which it was calibrated may change the calibration by up to 1%. The
mechanisms contributing to this change are not well understood. Experience to
date indicates that if the ball is not mechanically scuffed or exposed to
aggressive gases, changes in the effective accommodation coefficient should be

less than 2% over 1 or 2 year's time.


Assigning nominal values to the orifice dimensions and solving this system for
the bounds,

0.14763 < p(z) < 0.14822; O0<z<b
and
0.14792-b <A < 0.14801-b.
From eq (C12) and these bounds on A,
0.991672 < K < 0.991677.
Hence K = 0.99167 to five decimal places, with an uncertainty of 0.03% due to

dimensional imprecision.

C-II-2


documents may be directed to the author or to one of the technical contact
persons identified in the Users Guide (SP - 250).

Suggestions for improving the effectiveness and usefulness of the new series
would be very much appreciated at NIST. Likewise, suggestions concerning the
need for new calibration services, special tests and measurement assurance
programs are always welcome.

Joe Simmons, Chief
Office of Physical Measurement Services

Katharine Gebbie, Director
Center for Basic Standards

iv


Bakeabie
Valve

Gas
Inlet

Orifice Plate Lifting
Mechanism

Baffle

Orifice
Plate

~%)

DE - PZ

Bakeable
Valve \
en)

Figure 2.

a)

Baffle

x)

| Turbopump [

Schematic of the Vacuum Chamber Showing the Lifting

Mechanism and Sealing Method of the Orifice Plate.
Shown is the Arrangement of Valves and Gages Permitting the
Measurement of the Upper to Lower Chamber Pressure and Flow

Ratios.

40

Bakeable
Valve

Spinning
Rotor
Gage

Bakeable
Vaive

Also


Vacuum Gage Galibra

on:

"Calibration of Spinning Rotor Gas Friction Gauge Against a Fundamental Vacuum
Pressure Standard," G. Comsa, J. K. Fremerey, and B. Lindenau (KFA) and
G. Mésser and P. Rohl (PTB), J. Vac. Sci. Technol. 17, 642 (1980).

“The Calibration of Vacuum Gauges," W. Steckelmacher, Vacuum 37, 651. (1987).

Vacuum Gages:

"Molecular Drag on Freely Rotating Balls and Vanes," G. Comsa, J. K. Fremerey
and B. E. Lindenau, Proceedings of the Eighth International Vacuum
Congress, Cannes, France, 1980 J. P. Langeron and L. Maurice eds, V. II,
218 (1980).

"Long Term Stability of Various Reference Gauges over a Three Years Period,"
G. Messer, Proceedings of the Eighth International Vacuum Congress,
Cannes, France, 1980 J. P. Langeron and L. Maurice eds, V. II, 191
(1980) .

"Long Term Behaviour of Ionization Gauges," K. F. Poulter and C. M. Sutton,
Vacuum 31, 147 (1981).

“Spinning Rotor Vacuum Gauges," J. K. Fremerey, Vacuum 32, 685 (1982).

“Reliability of High Vacuum Measurements," C. R. Tilford, J. Vac. Sci.
Technol. A 1, 152 (1983).

"Long-term Stability of Two Types of Hot Cathode Ionization Gauges," S. D.
Wood and C. R. Tilford, J. Vac. Sci. Technol. A 3, 542 (1985).

“Sensitivity of Hot Cathode lonization Gages," C. R. Tilford, J. Vac. Sci.
Technol. A 3, 546 (1985).

"an Electrostatically-Suspended Spinning-Rotor Vacuum Gauge: A Feasibility
Study," J. D. Nuttall and D. C. Witt, Vacuum 37, 347 (1987).

"Total Pressure Gauges," R. K. Fitch, Vacuum 37, 637 (1987).

"The Use of Hot Filament Ionization Gauges," P. Nash, Vacuum 37, 643 (1987).

38


the pressure is reduced, the random error of the MDG, typically 10° Pa or
greater, precludes its use for a direct determination of Rp. Rp will be a
function only of the orifice conductance and the pump speed, and in the
molecular flow range, the only variable can be the turbomolecular pump speed.
As detailed below, we have indirectly found the pump speed, and therefore Rp,
to be constant to within a few percent down to a lower chamber pressure of

3x10°® Pa.

EXTENSION TO LOWER PRESSURES

The lowest usable pressure generated with an orifice-flow standard is
determined by the lower limit of acceptable performance of the flowmeter and
the base pressure of the vacuum chamber. In the case of the NIST system, this
limit is determined by the behavior of the flowmeter.

The base pressure is normally 10-8 Pa and, were it possible, the useful
range of the standard could be extended down to 10°® Pa with the residual gas
pressure constituting no more than 1% of the calibration pressure. This has
effectively been done by injecting the gas flow into the lower half of the
vacuum chamber, which permits using a higher gas flow to generate a given
pressure. As a result, the usable range of calibration pressures has been
extended two decades lower at the cost of slightly increased uncertainties in
the generated pressure. The pressure gradients in the lower chamber preclude
the direct calculation of the resultant pressure in the upper chamber.
However, we can experimentally determine the ratio of the flows, Rp, into the
two chambers required to generate the same pressure in the upper chamber. A
pressure is established by a measured flow, Q,, from the flowmeter into the
upper chamber. Using the valves identified as K in figure 1, the flow is then
redirected from the upper chamber to the lower chamber; the flow is then
increased to a value Q, until the same pressure as before is established in
the upper chamber. This measured flow is used to derive Rp = Q/Qy. Equation
7 is then modified to give

Py = QRp/[RpC(Rp-1)]. (8)
Molecular drag and ion gages in the upper chamber are used to determine Rp.
There is a random error in the determination of R, of the order of 0.1%. More
importantly, there is an additional systematic uncertainty due to the two
flowmeter measurements required. This effectively doubles the contribution of

the flowmeter error in eq (8). In the NIST standard, R, differs from Rp by


At the time of test, the pickup signal from the ball, the residual drag
and the frequency dependence of the residual drag were all monitored. All of
these factors may change during use and must’ be redetermined at the time of
use. The ball was remagnetized until its signal strength exceeded 100 mV.
The frequency dependence of the residual drag was checked and the residual
drag was found to change from Xx10°* Pa at 415 Hz to Ax107 at 405 Hz.

Corrections for frequency dependence were made in the calibration data.

Results

Any number of calibrations were performed against the primary vacuum
standard between MONTH DAY and MONTH DAY, YEAR. The parameters used were
28.0134 for the molecular weight of nitrogen gas, 175.7 upoice (at 298.15 K)
for the viscosity of nitrogen gas, 4.5 mm for the diameter of the ball, and
7.78 g em for the density of the ball. From these calibrations, the ball
was found to have an average effective accommodation coefficient of

1.00
in nitrogen gas for pressures less than 10°1 Pa. The residual standard
deviation of the measured effective accommodation coefficients was 0.X%. The
estimated total uncertainty of the NIST primary standard used for this
calibration is 1.5%. Nonlinearities in the gage, not included in the above
effective accommodation coefficient will increase with pressure and amount to
about 0.1% at 0.05 Pa and 1% at about 0.5 Pa. Corrections are made for this
nonlinearity by the controller using the viscosity data entered by the user.
The uncertainty in this correction had not been quantified.

Please note that the parameters for this ball and gas constitute an
integral part of the calibration. For the proper use of this calibration, the
operating temperature and the appropriate viscosity must be entered and the

other parameters must remain unchanged.

Discussion

This ball was calibrated as part of a system consisting of the ball, the
thimble, the suspension head and the controller. We expect that the effective
accommodation coefficient will depend primarily on the properties of the ball
and the ball's surface. However, we cannot predict the effect on the
effective accommodation coefficient of changing the other components of the

system.


Because of eq (C6) it suffices to expand the integral eq (C3) only in the

range of positive z. After some manipulation the result becomes
b
2Rp(z) = R-atA-2R f g(-z,u)p(u)du; 0 <2<b,
0

where

b
A= f 3 p(u)du.

Integrating eq (C8),
(2R-b)A = b(R-a) - B, (c9)
where

0 b
B=2R J dz f g(z,u)p(u)du.
-b 0
Substituting for p,(z) in, eq (C7) and introducing an effective transmission
probability K based on throat area mr,?, where
ro2K = r,2W, (C10)
X,2(1-K) = b(R-a) - (2a- ? )A-B (¢c11)
Eliminating the double integral B from eqs (C9) and (C11) yields the
unexpectedly simple result
K = 1-2A/(Rta), (C12)
while eq (C1) becomes
L = mx, ?KKyK,c/4. (C13)
Fquation (@13) is preferable to eq (C1) for assigning uncertainties hecause
the uncertainty of 0.14% in the area factor mr,” is dominant, while that in
the factor K is only about 0.03%, and that in the product K,K, is estimated to
be about 0.01%. The uncertainty in K is due almost entirely to the assigned
imprecision in the dimension b. Hence with K = 0.99167 from Appendix B and
kz = 0.9999, the final result becomes
= 0.9916-nr,2¢/4,
with an uncertainty of 0.04% for the formula and an additional 0.14% when the
measured value is assigned to the throat diameter.
The molecular flow conductance is proportional to the square root of the
absolute temperature through the factor . Values for several gases at 298.25

K are tabulated below, with an estimated uncertainty of 0.18%.


MDG performance at pressures above 107! Pa is limited by nonlinearities
arising from interactions between the gas surrounding the ball and the walls
of the steel thimble which contains the ball in the vacuum chamber. The
resulting changes may be empirically treated but NIST currently has no
facility for evaluating this effect.

Comsa, et al. [7], have investigated the linearity of the MDG at
pressures as high as 2.0 Pa using the primary vacuum standard (a static
expansion system) at the Physikalisch-Technische Bundesanstalt (PTB). Their
results show nonlinearities in the MDGs of 0.3% at 10° Pa. The resulting
errors in pressure are much smaller than those generated by the nonlinearities
in the orifice conductance at these pressures, hence the use of the MDGs as
transfer standards. As a general practice, we do not calibrate vacuum gages
above 10°! Pa using either the primary high vacuum standard or MDGs. The
ultrasonic interferometer manometer is used at these higher pressures.

Of greater concern is the increasing random noise in the residual drag of
the MDC as the pressure is decreased toward 1074 Pa. We have investigated the
errors in this range by calibrating IGs with both the orifice-flow system and
with MDGs at pressures near 10°‘ Pa. Differences are less than 2% for IG
measurements.

When using the MDGs as transfer standards, the flowmeter is simply
treated as a gas source used to establish a steady flow of gas into the
chamber. It is not important to know the flow rate, only that it is stable.
The pressure in the chamber is measured by the MDGs, and the orifice serves to
ensure a uniform pressure in the calibration chamber. The upper to lower
chamber pressure ratio is computationally unimportant although a change would
imply some degradation of the calibration system. The stability of the flow
over the course of the measurement and a low base pressure are the most
important qualities of the system in this configuration.

With a stable flow, the pressure is measured by the MDGs and readings are
taken on the customer's ion gage. Because the MDG is a differential gage, the
customer's gage reading must be corrected to reflect the fact that it reads
total pressure while the MDG reads only the pressure above the base vacuum.
This is accomplished by subtracting the base vacuum reading of the ion gage
from the reading at the calibration pressure before the correction factor is

computed.

10


PREFACE

Calibrations and related measurement services of the National Institute of
Standards and Technology provide the means for makers and users of measuring
tools to achieve levels of measurement accuracy that are necessary to attain
quality, productivity and competitiveness. These requirements include the
highest levels of accuracy that. are possible on the basis of the most modern
advances in science and technology as well as the levels of accuracy that are
necessary in the routine production of goods and services. More than 300
ditferent calibrations, measurcment assurance services and special tests are
available from NIST to support the.activities of public and private
organizations. These services enable users to link their measurements to the
reference standards maintained by NIST and, thereby, to the medsurement
systems of other countries throughout the world. NIST Special Publication
250, NIST Calibration Services Users Guide, describes the calibrations and
related services that are offered, provides essential information for placing
orders for these services and identifies expert persons to be contacted for

technical assistance.

NIST Special Publication 250 has recently been expanded by the addition of
supplementary publications that provide detailed technical descriptions of
specific NIST calibration services and, together with the NIST Calibration
Services Users Guide, they constitute a topical series. Each technical
supplement on a particular calibration service includes:

¢ specifications for the service
« design philosophy and theory

* description of the NIST measurement system
* NIST operational procedures

© measurement uncertainty assessment

error budget
systematic errors
fandom errors

¢ NIST internal quality control procedures

The new publications will present more technical detail than the information
that can be included in NIST Reports of Calibration. In general they will
also provide more detail than past publications in the scientific and
technical literature; such publications, when they exist, tend to focus upon
a particular element of the topic and other elements may have been published
in different places at different times. The new series will integrate the
description of NIST calibration technologies in a form that is more readily
accessible and more useful to the technical user.

The present publication, SP 250-34, NIST Measurement Services: The National
Institute of Standards and Technology High Vacuum Standard and Its Use, is one
of approximately 20 documents in the new series published or in preparation by
the Center for Basic Standards. It describes calibration technology and
Procedures utilized in connection with NIST Service Identification Numbers
from 30030 to 30050S listed in the NIST Calibration Services Users Guide
1986-88/Revised (pages 45-46). Inquiries concerning the contents of these

M
m
tm


Bourdon gage. Some initial work has been done to compare the two flowmeters
using both standard leaks and MDGs as transfer standards. The leak work has
been done at low flow rates while the MDG work has of necessity been done at
much higher flow rates. Eleven MDGs were calibrated on both flowmeters
between 1074 and 10°! Pa over a 10-day period. The differences in the
calibrations on the two flowmeters ranged from 0 to 0.5%. For eight of the
gages, the differences were within three standard deviations of zero. The

leak data showed differences of <1% at flow rates above 10711 mol sTM!

INTERNATIONAL COMPARISONS

Two calibrated MDG balls were sent to the Physikalisch-Technische
Bundesanstalt (PTB) and the National Physical Laboratory in England (NPL) for
comparison against the static expansion standards at those facilities. The
success of these comparisons was limited by instabilities in the balls. The
first ball gave very promising results - the results from all three
laboratories were within 1% of each other and the first and last calibrations,
done at NIST, differed by less than 1%. The second ball was very unstable.
The results are given in table V below. The instability was traced to changes
in the residual drag, not to ball surface changes. Subsequent calibrations at

NIST have indicated that neither ball was particularly stable.

TABLE V. Results of First International Intercomparison

Laboratory Difference from
—— NIST, %
Ball 1 Ball 2
NIST - -
NPL -0.3 +1
PTB 41.6 +2
NIST -0.2 +4
NIST (17 months later) 41

A second intercomparison was undertaken when PTB sent four balls as part
of an international round robin under the auspices of the International Bureau
of Weights and Measures (BIPM) [12]. The effective accommodation coefficients
of the balls were measured according to the circulated protocol at pressures
between 1074 and 10°? Pa in nitrogen, argon, and hydrogen. Several NIST and
customer balls were calibrated at the same time. Unfortunately, the four
balls were damaged in transit and the shifts between calibrations performed at

PTB before and after the measurements at NIST were as large as 8% in hydrogen.

31


Pa. Then, gas may be introduced into the appropriate half of the chamber from

the flowmeter.
Depending on the calibrations to be done, the flowmeter may be used to

generate a known flow of gas or it may be used simply to establish a steady

flow. The second case is a subset of the first and will be discussed later.

MEASURED FLOW TO UPPER CHAMBER
Order of Pressure Generation

Pressures to be measured should be established sequentially from the
lowest to the highest for each gas. This ensures that the elastomer seals and
any IGs on the system will not absorb gas at higher pressures and desorb at
subsequent lower pressures. This may not always be possible from day to day
but in no case should a higher pressure be run before a lower one within a
day. The only exception is to evacuate the chamber in order to check the

residual drag of an MDG.

Establishing a Pressure

The gas flow is directed into the upper chamber for the calibration of
all MDGs and the calibration of IGs at pressure above 10°> Pa. Gas is intro-
duced from the compressed gas cylinder into the ballast volume and reservoirs
while the test or monitoring gages are observed. When the desired calibration
pressure has been reached, the inflow is halted. The ballast volume now
serves as the source of gas. The fill pressure may be adjusted to achieve the
calibration pressure. At this point, the gas should be allowed to flow for
about 45 minutes while the elastomer seals in the working reservoir absorb
gas.

During this time, the operator should check that the necessary parameters
have been entered into the MDG controllers and check the IG operating
parameters.

Flowmeter operation is initiated by closing the valve which isolates the
reference reservoir. The valve should be closed slowly because there is the
possibility that gas will be driven into the reference reservoir by the valve,
raising the pressure. Once the valve is closed, the fill pressure is read
with the appropriate CDG and recorded. At the same time, the chamber and
working reservoir temperatures are read and recorded.

Next, the valve is closed which removes the ballast volume from the
system. The differential CDG is monitored while this valve is closed and the

19


Library of Congress Catalog Card Number: 88-600605

National Institute of Standards and Technology Special Publication 250-34
Natl. Inst. Stand. Technol. Spec. Publ. 250-34, 68 pages (March 1989)
CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE
WASHINGTON: 1989

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325


3 T T T
2 4
2 1 4
<
2
s ? 7
>
®
Qa
-1 >
21 4
3 i | i i I
0 10 20 30 40 50 60
Months Since January, 1983
Figure 5. Deviations from the Initial Value of the Effective Accommodation

Coefficient of Five Molecular Drag Gage Rotors as Determined by
Calibrations Against the NIST Primary High Vacuum Standard. All
Data were Taken Using Nitrogen Gas. Values have been Smoothed
for Clarity by Averaging Points Taken within a Few Days of Each
Other.

43


RANDOM ERRORS

Upper bounds on the random errors can be set by evaluating the variation
of repeated gage calibrations. These numbers will, of course, include the
random errors of the gages as well as those of the standard.

A measure of the short-term repeatability at higher pressures can be
obtained from four repeated calibrations of six different MDGs with N, at
4.9x10°3 Pa. In this case, the calibrations were made over a period of 8
hours. The pooled standard deviation of the effective accommodation
coefficients of the six gages was 0.00026 (the nominal effective accommodation
coefficient is 1.0) with no significant difference in the random errors
associated with any gage.

A second experiment was performed to check longer-term performance of the
system. Twelve MDGs were mounted on the system and were calibrated in
nitrogen at pressures ranging from 10°* to 10°! Pa. Each MDG was calibrated
two to six times at each pressure over a 5-day period. The pooled standard
deviations of the effective accommodation coefficients were 0.0011 at 5x10TM°
Pa and 0.0017 at 1x10°‘ Pa.

Similar results were obtained when repeated calibrations of 10 MDGs were
done with argon at pressures ranging from 5x10°* Pa to 3x10"? Pa. In this
case, three to five different calibration series were performed at each
pressure, each series taking place on a different day and involving a complete
calibration cycle, starting with the vacuum chamber and flowmeter at base
vacuum and the orifice plate raised above the gallium-filled groove. The data
from two of the MDGs were eliminated because of clearly excessive random
errors in the gages. The pooled standard deviations of the remaining eight
gages were 0.0010 at 3x10"? Pa, 0.0008 at 7x10" Pa, 0.0012 at 3x107% Pa, and
0.0041 at 5x10TM* Pa. .

At the lowest pressures the above results are probably dominated by the
short-term random errors of the MDGs, and MDG data at yet lower pressures will
not be useful in assessing random errors of the standard, Therefore, we must
rely on ion gage data at lower pressures.

As a measure of the random errors at low pressure, short-term
repeatability data were obtained with three calibrations for a tubulated,
tungsten-filament Bayard-Alpert gage made over a period of several hours. In
this case separate flowmeter measurements were made for each calibration. At
2x10°4 Pa the calibrations differed by a maximum of 0.1%, and at 2x10°> Pa by
0.02%.

27


Martin for his efforts in the manufacture and assembly of the many components

involved.

(1]

(2]

(3]

[4]

[5]

[6]

(7]

[8]

(9]

[10]

(11]

[12]

REFERENCES,

K. E. McCulloh, C. R. Tilford, C. D. Ehrlich, and F. G. Long, "“Low-Range
Flowmeters for Use with Vacuum and Leak Standards," J. Vac. Sci. Technol.
A 5, 376 (1987).

P. Clausing, Ann. Physik 12, 961 (1932); English translation appears in
“The Flow of Highly Rarefied Gases through Tubes of Arbitrary Length," J.
Vac. Sci. Technol. 8, 636 (1971).

J. K. Fremerey, "The Spinning Rotor Gauge," J. Vac. Sci. Technol. A 3,
1715 (1985).

J. K. Fremerey, "Spinning Rotor Vacuum Gauges," Vacuum 32, 685 (1982).

M. Hirata, H. Isogai, M. Ono, "Effect of Measuring Conditions on the
Accuracy of a Spinning Rotor Gauge," J. Vac. Sci. Technol. A 4, 1724
(1986).

S. D. Wood and C. R. Tilford, "Vacuum Calibrations Using the Molecular
Drag Gage," material accompanying a course given at the National
Institute of Standards and Technology, Gaithersburg, Maryland.

G. Comsa, J. K. Fremerey, B. Lindenau, G. Messer, and P. J. Rohl,
“Calibration of a Spinning Rotor Gas Friction Gauge against a Fundamental
Vacuum Pressure Standard," J. Vac. Sci. Technol. 17, 642 (1980).

K, E. McCulloh, S. D. Wood, and C. R. Tilford, "Zero Stability of

1738 (1985).

R. W. Hyland, C. R. Tilford, "Zero Stability and Calibration Results for

1731

Spinning Rotor Vacuum Gages," J. Vac. Sci. Technol. A 3,
a Group of Capacitance Diaphragm Gages," J. Vac. Sci. Technol. A 3,
(1985).

C. R. Tilford, S. Dittmann, K. E. McCulloh, "The NIST Primary High Vacuum
Standard," J. Vac. Sci. Technol. A 6, 2853 (1988).

K. E. McCulloh, "Calibration of Molecular Drag Vacuum Gages,” J. Vac.
Sci. Technol. A 1, 168 (1983).

CG. Messer, P. Rohl, G. Grosse, W. Jitechin, "High Vacuum Measured by the

- Spinning Rotor Gauge: Status Report of the Bureau International des Poids

[13]
[14]

et Measures Intercomparison," J. Vac. Sci. Technol. A 5, 2440 (1987).
W. Jitschin, PTB, Private communication.

Cc. D. Ehrlich, NIST, Private communication.

36


The reference reservoir temperature before and after the run, T,,.

When the flow is into the upper chamber, the formula used to calculate the

pressure is

Py = (Q/C) (Rp) /(Rp-1) (3)
where Q is the throughput into the upper chamber given by
Q = Peg (dV/dt) (To, /Tem) (1)
and C is the conductance of the orifice given by
C = C*(T,,/298.15 K)t/2. (2)

Pre, is the average fill pressure which is measured in terms of the output of
the CDG (i.e., in volts). The NIST calibration coefficents of the CDG are
used to convert the average of the before and after readings into Torr and
this is converted to pascals using the factor 1 Torr = 133.322 Pa. dV is the
volume of the piston which was driven into the working reservoir. The values
are 1.9949 cm? for the 1-cm piston and 12.870 cm® for the 1-in piston. ‘dt is
the total time elapsed for the piston travel (the first reading minus the
twenty-first reading). C is the temperature-corrected value of the conduc-
tance of the orifice and C* is the value of the conductance at 298.15 K
(Appendix C). Rp is determined experimentally and checked periodically. ts
value depends on the gas in use and the performance of the turbomolecular
pump.

When the flowmeter is used with the flow into the lower chamber, Q" is
calculated as above and then divided by R,, the lower to upper chamber flow
ratio. This gives the effective throughput that would be required to generate
the calibration pressure with the flow into the upper chamber. The final form
of the equation for the throughput becomes

Q = Pm (dV/dt) (Tan /Ton)/Re - (10)

For ion gages read with commercial or customer controllers, the generated
pressure should be divided by the-IG reading minus the IG reading at base
vacuum to obtain a calibration factor:

Cal. Factor = Pressure drop/(IG reading - IG reading at base vacuum) (11)
Attention should be paid that all readings are in the same units of pressure
(usually Torr).

Ion gage readings taken on NIST-built controllers require more work to
reduce them to gage sensitivies. The data acquired at each pressure consist
of the collector current and the voltage drop across a known resistor due to
the emission current. Comparable data are also taken at base vacuum. The
following equations are used to calculate gage sensitivity, S:

I, = V./R, (12)

22


The next step is to isolate the working reservoir (E) from the ballast
volume so that flow is out of the working reservoir alone into the chamber.
This flow of gas will tend to reduce the pressure in the working reservoir but
constant pressure is maintained by advancing a piston (F) to displace volume
in the working reservoir. The piston enters the working volume through an
elastomer and PTFE sliding seal. A differential CDG (D) reads the pressure
difference between the two reservoirs and the piston is advanced by a stepping
motor in such a manner as to keep the reading of that CDG at zero.

For optimum sensitivity and control, the volume of the piston should be a
large fraction of the volume of the working reservoir. This has been achieved
without sacrificing a wide range of available flow rates by constructing two
working reservoirs in series. Each reservoir has its own piston and the
piston areas are 0.8 cm* and 5.1 cm*. The piston not in use during a
measurement is driven into its working reservoir in order to minimize dead
volume in the flowmeter. We shall refer to a single working reservoir and
piston in this document with the understanding that there are actually two.

The piston is allowed to travel 2.54 cm as measured by a micrometer
screw, at which time the measurement is terminated. The time needed for the
piston to complete its travel is monitored and displayed after each turn of
the micrometer screw.

The temperatures of the working reservoir, T,,, and the chamber, T,,, are
recorded before and after the calibration as is the pressure in the reference

reservoir, Pea.

THE ORIFICE

C in eqs (2) and (3) is the conductance of the orifice (I in fig..1).
From theory and dimensional measurements, the conductance of the orifice
corresponding to the chamber temperature is calculated for each gas, as
indicated in eq (2).

The orifice was designed so that its conductance could be easily
calculated In addition, it was desirable that its area be a emall fraction
of the vacuum chamber area and that the desired pressures in the vacuum
chamber correspond to the accurate range of the flowmeter.

The orifice, is a sharp-edged hole at the center of a 15.2-cm diameter,
1.27-cm thick, stainless steel plate (fig. 3). The outer edge of the plate
includes a lip (K in fig. 3) that fits into the gallium-filled groove in the

wall between the chamber halves. The plate was fabricated by machining the


Xot

a:

ty:
L:

e:

APPENDIX C-I

List of Symbols

radius of curvature of surfaces A and B (fig. 7).

radius of the throat.

distance from the center of the throat to the center of curvature of
surface A or surface B. a? = R? - r,?

distance from the center of the entrance aperture to the center of the
throat; also from the center of the throat to the center of the exit
aperture.

radius of the entrance (exit) aperture. r,? = R? - (a-b)?

molecular flow conductance of the orifice.

mean molecular speed. ¢? = 8kT/(xm)

W, K, h(z), g(z,u), Po(z), p(z), w(z): probabilities defined in text.

CG-I-1


0.10 Tr 7 T
. é 1
° 4
. x ryt a Bat .
ite , |
‘
L .
iF a) ° |
0 L 1 1 i L 1 !
8 7 6 5 a 3 2 A 0
Log Pressure, Pa
T
0.06 + +
< res 4 +
% 9.05+ _ . 4
c=
2 L . : 4
a xx @ i go on
& 0.04 * 4 ani ba* wee |
L 4
0.03 - 71
5)
i 1 1 1 1 1 1

8 7 6 S 4 3 2 A 0
Log Pressure, Pa

Figure 6. a) and b) Ion Gage Sensitivity in Nitrogen for Two Different
Ultra High Vacuum Ionization Gages’ as Determined by
Calibrations Against the NIST Primary High Vacuum Standard and
Against Calibrated Molecular Drag Gages.-4 ~ Flow into Upper
Chamber, 1-cm Piston; + - Upper Chamber, 1-in Piston; X - Lower
Chamber, 1-cm Piston; = - Lower chamber, 1-in Piston;

« - Molecular Drag Gages. Gage 6a is Designed for Use Between
10°1° and 10°? Pa and Gage 6b is Designed for Use Between 10°&
and 10°! Pa.

44


XI. APPENDICES
APPENDIX A

SAMPLE REPORT OF CALIBRATION FOR
IONIZATION GAGE

Ion Gage Tube and Controller
Submitted by

CUSTOMER NAME
CITY, STATE ZIP

TPD Calibration Number: HV XX
NIST Identification of Gage: XXX
Supplier of Gage: SUPPLIER
Gage Model: AB123
Manufacturer of Controller: MANUFACTURER
Controller Model: 123
Controller Serial Number: 456
Gas: Nitrogen

Date received: MONTH DAY, YEAR Test completed: MONTH DAY, YEAR

Procedures

This calibration is for a thoria-coated filament ion gage and the
associated controller. The gage was calibrated with the electrode axis
vertical and the collector pin up. The ambient temperature was 24 °C with
free but not forced air circulation about the gage tube.

The calibration data presented in this report were obtained with the
controller and gage tube operated as a unit. Operating with an emission
current of 5.4 mA as determined by the controller, the dc filament bias was
30.9 V and the grid bias was 132.3 V.

The calibration was performed on a turbomolecular-pumped, all metal
chamber designed to minimize pressure gradients and maintain gas purity. The
generated pressures, which are pressure increases above base vacuum, were
measured with the primary vaccum standard from 10°® to 10°* Pa (10°® to 107°
Torr) and with calibrated molecular drag gages from 10°‘ to 1071 Pa (10°® to
10°° Torr). Estimated uncertainties in the generated pressures using the NIST

primary vacuum standard were 1% above 1x10°5 Pa increasing to + 5% at 1x10°®


less than 1% although this may be fortuitous since flux and pressure gradients
of several percent are known to exist in the lower chamber.

The flow ratio cannot be directly measured for pressures lower than those
that can be reliably generated by a measured flow into the upper chamber,
which is 1075 Pa for a 0.8% random uncertainty. However, since the system is
clearly in the molecular flow regime at these lower pressures, Ry will be
constant with decreasing pressure if the turbomolecular pump speed does not
change with pressure. As described below we have indirect evidence that the
pump speed does not change significantly down to 3x10"® Pa. On one occasion
we found that the turbomolecular pump speed had decreased over a period of
weeks as the bearings deteriorated, causing a noticeable decrease in the pump

rotor speed and in Rp.

CALIBRATIONS AT HIGHER PRESSURES

Because of the increasing deviations from conditions of molecular flow at
pressures above 10°? Pa, calibrations in this range are performed against
molecular drag gages which have been calibrated against the primary standard.
Molecular drag gages are used because of their linearity, reproducibility, and
precision in this pressure range. In brief, the molecular drag gage consists
of a magnetically levitated rotor inside the vacuum chamber which is
accelerated to about 400 Hz. It is then allowed to rotate freely and the
pressure is indicated by the deceleration of the rotor as gas molecules strike
its surface (the molecular drag). There is an additional slowing due to eddy
currents induced in the rotor by the magnets in the monitoring and suspension
circuitry which is referred to as the residual drag.

Pressure is computed from the deceleration rate according to the
following formula:

P = (K/o)(-w/w - R.D.) (9)
where w is the rotational frequency of the ball, w/w is the relative
deceleration, R. D. is the residual drag, and K is a constant which is a
function of the ball density and diameter, the gas in use, and the
temperature. The effective accommodation coefficient, o, is determined when
the MDG is calibrated. The orifice conductance and MDG are both sensitive to
the molecular weight of the calibration gas. A thorough discussion of the
theory of MDGs may be found in Refs. 3 and 4. A discussion of techniques for
using the MDG may be found in Refs. 5 and 6.