NIST Measurement Services: . . T

. ^^^^^^^^^^^^^^^^^^^^^^^^^^ Research Information Center

National Institute of Standards and Technology

Gaitbersburg, Maryland 203*)

NIST Leak Calibration

Service

Charles D. Ehrlich and Stuart A. Tison

U.S. Department of Commerce

Technology Administration

National Institute of Standards and Technology

NiST MEASUREMENT SERVICES:

NIST Leak Calibration Service

Charles D. Ehrlich and Stuart A. Tison

Thermophysics Division

Chemical Science and Technology Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

January 1992

U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary

TECHNOLOGY ADMINISTRATION

Robert M. White, Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

John W. Lyons, Director
National Institute of Standards and Technology Special Publication 250-38

Natl. Inst. Stand. Technol. Spec. Publ. 250-38, 89 pages (Jan. 1992)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1992

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
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 different calibrations, measurement 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 measurement 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 (NIST

SP 250- ) on a particular calibration service includes:

o specifications for the service

o design philosophy and theory

o description of the NIST measurement system

o NIST operational procedures

o measurement uncertainty assessment

o 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 250-38, NIST Leak Calibration Service,

by Charles D. Ehrlich and Stuart A. Tison, describes calibration

technology and procedures utilized in connection with NIST Service

Identification Number 30060S listed in the NIST Calibration

iii
Services Users Guide 1989 , pages 49 to 51. Inquiries concerning

the contents of these documents may be directed to the author (s) or

to one of the technical contact persons identified in the Users

Guide . 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 D. Simmons, Chief

Physical Measurement Services Program

iv
TABLE OF CONTENTS

Page

Preface iii

1 . Introduction 1

2. Description of the NIST Leak Calibration Service 2

3. Design Philosophy and Theory 3

Design Philosophy: Introduction 3

Design Philosophy: NIST Primary Leak Standard 3 Flow into Upper Chamber 4

Extension of Low Flow Rate Measurements: Flow into

Lower Chamber 7 Measurement of Upper to Lower Chamber Flow Ratio 7 Flow into Lower Chamber 10

Design Philosophy: Leak Comparator System 11

4. Description of System and Operational Procedures 14

Primary Leak Standard System Description 14

Leak Manifold 14

Main Vacuum Chamber 14

Bellows Flowmeter 15

Calibration of Helium Leaks 15

NIST Leak Comparator System Description 17

Temperature Coefficient Determination 18

5. Assessment of Uncertainties 20

Primary Leak Standard 20

Flowmeters 20

Temperature and Orifice Conductance 22

Pumping Speed 22

Upper Chamber Pressure Indication 23

Flow into Upper Chamber 24

Upper -to -Lower Chamber Flow Ratio 25

Flow into Lower Chamber 26

Summary Analysis: Calibration of Customer Leaks 27

Leak Comparator System 28

Temperature Coefficient Uncertainty 28

Summary Analysis: Calibration of Customer Leaks 28

v
TABLE OF CONTENTS (CONTINUED)

Page

6. Quality Control 30

Control Charts 30

Closed-Reservoir Helium Permeation Leaks 30

Upper-to-Lower Chamber Flow Ratio 31

Comparison of Primary Standards 31

Flowmeter Intercomparisons 31

Domestic Intercomparisons 32

International Intercomparisons 33

7 . Future 34

8 . Acknowledgments 35

9. References 37

10. Bibliography 39

11. Appendices

A. Use and Conversion of Units of Flow Rate and Throughput A-l

B. General Theory of Gas Flow in Vacuum Systems B-l

C. A Note on Flow Rate and Leak Rate Units

(reprint of published article) C-l

* D. Low-Range Flowmeters for use with Vacuum and Leak

Standards (reprint of published article) D-l

* E. Sample Leak Calibration Report E-l

vi
LIST OF TABLES

Page

11 . Conversion of Units for Universal bas Lionscant \&) 4

2. Bellows Flowmeter Uncertainties 21

3. Summary of Uncertainties for Flow into the Upper Chamber 25

4. Summary of Uncertainties for Flow into the Lower Chamber 27

A-l. Leak Rate Conversion Chart A-6

vii
LIST OF FIGURES

Page

1. Simple Schematic of the NIST Primary Leak Standard 40

2. Schematic of the NIST Primary Leak Standard 41

3. Valving Sequence for Leak Calibration Through Upper Chamber 42

4. Valving Sequence for Leak Calibration Through Lower Chamber 43

5 . Valving Sequence for Measurement of Upper to Lower

Chamber Flow Ratio 44

6. Schematic of Leak Comparator System 45

7. Temperature Dependence of Helium Permeation Leak 46

8. Measured vs. Actual Leak Rate Using Leak Comparator System 47

9. Valving Diagram of NIST Primary Leak Standard 48

10. Valving Diagram of Bellows Flowmeter 49

11. Piston Flowmeter Uncertainties 50

12. Bellows Flowmeter Uncertainties 51

13. Leak Control Chart for NBSL22 52

14. Control Chart of Upper to Lower Chamber Flow Ratio 53

15. Linearity of Leak Comparator System 54

16. Schematic Cross Section of NIST Permeation Leak 55

17. Random Uncertainties for Piston and Bellows Flowmeters 56

18. Measured Leak Rate Differences Between Flowmeters 57

19. Comparison Between NIST and Other Laboratories 58

20. Schematic Diagram of simple Gas Flow System: Single Piston 59

21. Schematic Diagram of simple Gas Flow System: Dual Pistons 60

viii
1 . INTRODUCTION

The industrial need for demonstrated accuracy of low-range gas flow rate or leak rate measurements used to calibrate leak detectors and gas analyzers,

traceable to a recognized standards authority, prompted the National Institute

of Standards and Technology (then the National Bureau of Standards) to

initiate a Leak Standards Program in 1984. As helium leak detection has

emerged as the most popular method of detecting even the smallest leaks, the

demand for quantifying small flow rates of gaseous helium was quickly

identified as the area in which to put the initial emphasis. A Special Test

Service for helium permeation (or diffusion) leaks, covering the range of leak

rates 10" 8 to 10" 11 mol/s (2x10" A to 2x10" 7 atm cm3 /s @ 0 °C) at room

temperature, has been offered since the summer of 1986. Helium permeation leak

artifacts sent to the NIST Special Test Service by customers are calibrated

over the temperature range 0 to 50 °C. Presently, estimated total

uncertainties (3a) of the measurements performed on customer artifacts are typically between ±5% and ±15% over the range of the Special Test Service.

There are small additional uncertainties as the equilibrium temperature varies

from the 23 °C reference temperature.

The overall objective of the NIST Leak Standards Program is to provide a Leak Calibration Service to the user community. This first required the

development of a primary leak standard suitable for accurately calibrating a transportable leak artifact (or "transfer leak") over the range of leak rates

and gas species required by the users. It also necessitated the

characterization of the stability and reproducibility of transfer leaks over

the long and short term, under both static and dynamic conditions. All of

these types of studies, in conjunction with a leak calibration service, allow

the transfer of measurements from NIST standards to the users, with estimable

uncertainty levels. In order to help the users make the best use of these

capabilities, NIST staff members also participate in instructional seminars

and workshops, and provide documentation.

This document describes in detail the Primary Leak Standard and Leak

Comparator system (on which the temperature dependence of the leaks is

determined) , deriving the equations that are used to calculate the leak rate

from a leak artifact based on the experimental parameters, and evaluating the

uncertainties associated with the measurements. A discussion of the observed

behavior of helium permeation leak artifacts will also be provided, as will a discussion of the units that are used (and frequently misused) to describe gas

flow rate. It will conclude with a look at outstanding problems in the Leak

Standards Program and Leak Calibration Service.

1
2. DESCRIPTION OF THE NIST LEAK CALIBRATION SERVICE

The Thermophysics Division of the National Institute of Standards and

Technology provides a Calibration Service* for helium permeation leak

artifacts in the range 10" 8 to 10" 11 mol/s (2x10"* to 2x10" 7 atm cc/s @ 0 °C)

A Calibration Report, which presents the measured value of leak rate over a nominal temperature range of 0 to 50 °C is issued for each artifact submitted.

At this time, all leak artifacts submitted for measurement must meet the

following specifications:

1) Nominal value of helium leak rate of the artifact at room

temperature must be between 10" 8 and 10" 11 mol/s (2x10"* and

2x10" 7 atm cc/s (§0 °C) .

2) Construction: all-metal reservoir and tubing, of ultra-high

vacuum type design, ending in a standard 2.75" conflat-type

flange on the vacuum end, and a helium reservoir.

3) The leak element must be of a sealed glass design, permeable to

helium gas, and structurally rugged.

4) An easily observable customer identification number or code must

be engraved on the circumference of the 2.75" flange.

This Calibration Service must be scheduled in advance. To obtain a Test

Authorization Number and shipping instructions, send a request stating name,

organization, mailing address, telephone number, number of leak artifacts to

be calibrated (with nominal leak rates, at room temperature, in mol/s), and

any other pertinent information to:

Mr. Stuart Tison

Leak Program, Special Test Service

Metrology Building/A55

National Institute of Standards and Technology

Gaithersburg, MD 20899

(301) 975-2857

For further information, contact Mr. Stuart Tison (301) 975-2857 or

Dr. Charles Tilford (301) 975-4828.

*This Calibration Service involves measurement or calibration methods which

are continually being perfected. Refer to NBS SP250 for updates on the status

of this Service.

2
3. DESIGN PHILOSOPHY AND THEORY

DESIGN PHILOSOPHY: INTRODUCTION

The Primary Leak Standard that has been developed at NIST is shown

schematically in figure 1 . This type of apparatus was chosen over several

alternatives because it benefits from considerable development work already

completed in the NIST high vacuum standards program [1]. The standard is

divided into three major components: the main vacuum system, the constantpressure flowmeter, and the manifold on which the leak is mounted. In the

first stage of operation, gas is allowed to flow from the leak into the "upper

chamber" of the main vacuum chamber, through an orifice into the "lower

chamber" of the main vacuum chamber, where it is subsequently exhausted by the

pump. When an equilibrium flow rate has been established, the pressure

generated in the upper chamber is recorded. The leak is then valved out of

the vacuum system and a flow is subsequently established from the flowmeter

and adjusted so that the same pressure indication, measured with either an ionization gage or a partial pressure analyzer (tuned to the gas species being

measured), is achieved in the upper chamber. This flow rate is then measured

using the flowmeter, and to a first approximation the leak rate would be set

equal to the measured flow rate. The details that go into providing a more highly refined analysis will be discussed subsequently. In addition, the use

of a flow division technique (also discussed later) , where gas from the

flowmeter is valved into the lower chamber (not indicated in fig. 1), allows

extension of the dynamic range of the system to lower flow rates. To date,

this system has been operated and errors evaluated for flow rates between 10" 6 and 10" 12 mol/s.[2,3] (See Appendix A for a discussion of flow rate units.)

An overview of the general theory of gas flow as it pertains to the flowmeter

and leak geometries can be found in Appendix B.

DESIGN PHILOSOPHY: NIST PRIMARY LEAK STANDARD

The schematic diagram of the NIST Primary Leak Standard presented earlier in

figure 1 is shown in slightly more detail in figure 2, where it can be seen

that gas flow from either the leak to be calibrated or either of two constantpressure flowmeters can be directed into the "upper chamber" or "lower

chamber" of the main vacuum chamber. In a typical calibration sequence, once background pressure indications in the upper chamber are recorded for various

valving configurations with no gas flow, flow from the leak is then directed

into the upper chamber. The gas flow is allowed to stabilize (as monitored by

recording the upper chamber pressure indications on a strip chart recorder)

and equilibrium upper chamber pressure indications and pump speed are then

recorded (as are the temperature of the main vacuum chamber and the leak) . This process is indicated schematically as Step 1 in figures 3 and 4. In Step

2, the leak is valved out and gas is introduced into one of the two flowmeters

(see Appendices B and D and the next section on Description of System for

details on design and operation of the flowmeters) , which admits gas into

either the upper chamber (fig. 3) or the lower chamber (fig. 4) of the main

chamber via a variable leak valve.

3
Flow into Upper Chamber

After Step 2 of the calibration process the system is allowed time to

equilibrate, at which point the valving in the flowmeter is configured and the

flowmeter electronics are activated so that the flow rate of the gas emanating

from the variable leak valve is measured. This measurement is accomplished by

measuring the rate of change of the volume (dV/dt) of the working reservoir

required to maintain a constant pressure (Pw ) in the working reservoir, which

is at temperature Tw (indicated schematically in Step 3 of fig. 3). The leak

rate from the leak can then be calculated according to:

Pw3 (dV/dt) To 3 h

Si Co3 + S 3 R • tw3 _ ^U3 _

• _ Tol _

• _ s 3 Col + Si _

where the subscripts (1 or 3) refer to the Step Number in figure 3, P0 is the

pressure indication in the upper chamber, TQ is the temperature of the main

vacuum chamber (and orifice) , S is the pumping speed of the combination of the

turbomolecular pump and entrance plumbing, CQ is the conductance of the

orifice, and R is the universal gas constant (see table 1).

Table 1. Conversion of Units for Universal Gas Constant (R)

R = 8.31441 Joule mol" 1 K" 1

= 8.31441 Pa m

3 mol" 1 K" 1

= 8.31441 xlO3 Pa i mol-1

K" 1

= 8.31441 xlO6 Pa cm3 mol-1

K" 1

= 62.3634 Torr i mol-1 K" 1

= 62.3634 xlO3 Torr cm3 mol" 1 K" 1

= 82.05685 atm cm3 mol" 1 K" 1

Equation (1) can be derived by using the principles developed in Appendix B

as follows. Beginning with figure 3, Step 1, once steady state flow is

achieved, the conservation of total number of molecules requires that the flow

rate of gas leaving the leak (N^ ) be the same as the flow rate of gas passing

through the orifice (Nol ), which from eq (B5) in Appendix B is:

4
(]?U1 - PL1 ) . Col

Ni = Noi = (2)

R • To 1

where PL1 is the pressure in the lower chamber. But this must also equal the

flow rate of gas through the pump, which from eq (B12) is

Nsl =

*L1 ' S l R • To 1

(3)

Equating Nj with Ns

then gives

Pui = PL •['*M°ol

(4)

Combining eqs (2) and (4) then gives

^ = Pu:

Si • Col

Col + Si

/ (R Tol ) (5)

Turning now to Step 3 of figure 3, arguments similar to those used to derive

eq (4) yield

JU3 = PL 3 ' [

1 + — ] Co 3

(6)

Also, the flow rate through the orifice:

No3 =

( PU 3 PL 3 ) * Co 3 (7)

R • To3

must be equal to the flow rate as measured by the flowmeter

N

Pr3 (AV/At)

FM (8)

R • T,w3

5
When comparing eq (8) and the corresponding parameters in eq (1), note that

Pr

replaces Pw3 and that AV/At replaces dV/dt. This is due to the fact that

in the flowmeter, it is the reference volume pressure (Pr

) and not the

working volume pressure (Pw ) that is measured experimentally, and the

instantaneous volume rate of change of the working volume (dV/dt) is actually

determined experimentally as the change in volume AV over a measured time

interval At. The temperature of the working volume (Tw ) is equal to the

temperature of the reservoir volume (Tr

) . The implications are discussed in

the section on Assessment of Uncertainties. Equating the right hand sides of

eqs (7) and (8) , solving the resulting equation for PL3 , and substituting PL3

into eq (6) results in

U3

Co3 + S 3

Co3 " S 3 J

Pr3 • (AV/At) • (To3 /Tr3 ) (9)

Dividing eq (5) by eq (9) then gives equation (10), where the functional

dependence of the conductance (C0

) on temperature (C0

oc JTQ

) for conditions of

molecular flow has been incorporated, as have the experimentally derivable

quantities Pr and AV/At:

NL -

Pr3 (AV/At) Pui To 3 h

Si Co3 + S 3

R • Tr3 _ *U3 _

• _ To1 _• _ s 3 Col + s x _

(10)

There are several points worth noting about eq (10). First, only the

pressure ratio Pui/?u3 ^ s involved, so that it is not necessary to know the

absolute pressures in the upper chamber. What is required is a gage that is

stable during the course of the measurement process (typically 6 to 8 h) , and

that is linear over the relatively small 1% or less of reading that separates

Pul and Pu3 . If the gage is of the total pressure type, then it is also

important that any differential impurities in the gas flows be accounted for.

Mass spectra are routinely taken using a quadrupole residual gas analyzer at

each stage of the measurement process to monitor for this eventuality. One

total pressure ionization gage and two residual gas analyzers tuned to the mass species being measured are typically used to record Py . Another

noteworthy point is that the orifice conductance in the NIST Primary Leak

Standard (CQ

) is on the order of 40 i/s for helium, while the pumping speed is

roughly 2500 i/s, so that the last term in eq (10) is very nearly equal to 1 for any reasonable fluctuation in pumping speed and is usually ignored (note

that a similar term is not ignored in the next section, however!). As an

example, if the pumping speed differs by 1% between the two measurements, so that S 3 = 2488 i/s and S^^ = 2512 i/s, the last factor in brackets in eq (10)

is equal to 1.0002. While the temperature ratio factor is also very nearly

6
equal to 1 for the slight variations in room temperature, it is routinely

retained in the data analysis routine. A difference of 1 °C in the chamber

temperature results in a correction factor of 1.002 in eq (10). Further

discussion concerning sources of uncertainties associated with this equation

is in the Assessment of Uncertainties section.

Another important point concerning eq (10) is that it is an equation

representing the measured value of the leak rate for the leak at temperature

TL

, as indicated in Step 1 of figure 3. The data analysis routine

subsequently determines what the leak rate would have been if the leak had

been measured at 23 °C, using the previously determined temperature dependence

of the leak (see section on Leak Comparator)

Extension of Low Flow Rate Measurements:

Flow into Lower Chamber

At flow rates of about 10" 12 mol/s, the uncertainties associated with the

flowmeters approach the 10% level. To extend the measurement capabilities of

the system to lower flow rates while keeping uncertainties at a reasonable

level, it is necessary to utilize a flow division technique, as illustrated in

figure 4. The principle behind the flow division technique is that, for

constant orifice conductance and pumping speed, the ratio of [the flow rate

into the upper chamber that gives any upper chamber pressure (that results in

molecular flow through the orifice)] to [the flow rate into the lower chamber

that results in the same upper chamber pressure] is a constant. This constant

can be measured using relatively high flow rates into both chambers, where the

uncertainties associated with the flowmeters will be low, and then used at

lower flow rates. There are of course additional uncertainties associated with

measuring these flow ratios, as will be discussed subsequently.

Measurement of Upper to Lower Chamber Flow Ratio

Figure 5 illustrates the two main steps involved in measuring the ratio of

flows (Ru/ L

) that give the same upper chamber pressure indication. In Step 1,

gas at pressure Pr 1 is admitted into the flowmeter and valved into the upper

chamber (resulting in an upper chamber pressure of and a lower chamber

pressure of PL1 ), the system is allowed to equilibrate, and the flow rate of

the gas is measured using the flowmeter. In Step 2, gas is again admitted

into the flowmeter but now valved into the lower chamber. The gas admitted to

the flowmeter is at a pressure Pr2 such that the upper chamber pressure PU2 is

very nearly equal to the upper chamber pressure PV1 from Step 1. Since ?V1

and PU2 are seldom exactly equal, nor are the chamber temperatures or pumping

speeds in the two steps usually equal, it is necessary to derive an expression

for the ratio Ru/L that corrects for these differences and so refers to a single temperature (TQ

) and pumping speed (S). In principle (as will be

shown), for a given gas specie and orifice geometry, Ru/L is a function of TQ and S only.

7
From Step 1, conservation of flow rate (Nx

) at the flowmeter, orifice and

pump gives

Pl i

' S i Nx = (11)

and

Si

Pui = Pli ' ( 1 + ) • (12)

Col

In Step 2, under equilibrium conditions, there can be no net flow across the

orifice, so that

PU2 = PL2 (13)

and conservation of flow rate (N2

) from the flowmeter to the pump gives

Pl2 ' S2 N, = (14)

Substituting PL 1 from eq (12) into eq (11), and PL2 from eq (13) into eq

(14), and dividing the two resulting equations gives

PU2 * S 2• Tol S x RL /u = (Nz/Ni) = • ( 1 + ). (15)

pui ' s !

• To2 Col

Note that if Fu

, S and TQ were not to change from Step 1 to Step 2, then eq

(15) would collapse to the last factor in parentheses, which depends only on S

and CQ (which is proportional to Jt~0

) . It is the last factor, 1 + (S 1 /Col ),

that represents the true ratio (RL. 0 ) t being sought. However, the pumping

speed and orifice conductance are not known, so that eq (15) cannot be used to

calculate this ratio. Instead, the experimentally determined ratio comes from

the two flowmeter measurements

8
Pr2 . (AV/At) 2

• Trl

<Rl/u>» = < 16 > Prl • (AV/At), • Tr2

where the subscript "m" refers to the measured quantity. Substituting eq (16)

into eq (15) and solving for (RL /u) t ( re ferenced to S x and TQ x ) gives:

Pr2 • (AV/At) 2

• Trl Pux • S, • To2

(RL/u )t(Si,Tol ) = • • (17)

Prl • (AV/At) x

• Tr2 PU2 • S 2

• Toi

Equation (17) represents an individual measurement of lower chamber to upper

chamber flow ratio for a specific set of conditions, namely the chamber

temperature Tol and the pumping speed S x

. Experimentally, several such

measurements are typically performed over a 1 to 2 week period. Since the

pumping speeds and chamber temperatures vary over this time period, it is in

principle necessary to reference each measurement to a common set of Tr f and

S ref . This is most easily accomplished by using the 'definition' of (Ri/u)t :

[ 1 + (S ref /Cref ) ] (RL/u ) t (S ref ,Tref ) = • (RL/u ) t (S 1> Tol ) (18)

[ 1 + (Si/Col ) ]

" S ref

" co1

• _ S

l _ _ cref _

• (RL/H ) t (S 1 ,Tol ) (19)

S r e f T0 i

• _ Si _ _ Tref

—I h

(RL , u )t(S 1 ,Tol ). (20)

As will also be discussed in section V, the turbomolecular pump speed S has

been found to vary linearly with the pump rotational frequency, so the ratio

Sref/Sj can be replace by fref /flf where f is the measured frequency.

Although the frequency has varied by as much as 5% in the past, with

regulation of the pump controller input voltage the frequency now varies by

less than 0.1% during the course of a day.

The average value (denoted RL/U (S,T0 )) of the set of measured values from

eq (17) or (20) is then referred to as the lower- to-upper flow ratio, and its

inverse will be denoted as RU/L (S,T0 ). In practice, TQ is 298.15 K (or 25

°C), and fref is 577 Hz. Typical fluctuations in the measured flow ratio of

helium are as large as 2% from day to day. A typical control chart showing

the measured values is presented in the section on quality control (see

fig. 13).

9
Flow into Lower Chamber

With the upper- to- lower chamber flow ratio now determined, it is possible to use the technique shown in figure 4 to measure flow rates below 10" 12 mol/s

with the flowmeter, or to measure higher flow rates with smaller uncertainties

than can be obtained using the direct flow technique of figure 3. Step 1 of

figure 4 shows the leak valved into the upper chamber of the main vacuum

chamber. After equilibration, the various parameters are recorded. In Step 2,

gas is introduced into the flowmeter, and the valving is such that the gas

flows into the lower chamber. The reference reservoir pressure (Pr2 ) is such

that the upper chamber pressure (Pu2) ^ s verY nearly equal to the upper

chamber pressure when gas from the leak flows into the system (Pui)- Once the

system has equilibrated, the flowmeter is used to measure the flow rate into

the lower chamber (N3 )

, as indicated in Step 3.

To derive an expression for the leak rate (NL

) in terms of the measured

parameters, we proceed as in the previous sections. From Step 1, conservation

of flow rate at the leak, orifice and pump gives:

*L1 ' S l NL = (21)

and

Si

PD1 = PL1 • ( 1 + ) . (22)

Col

In Step 3, under equilibrium conditions, there can be no net flow across the

orifice, so that

PU3 = PL3 (23)

and conservation of flow rate (N3

) from the flowmeter to the pump gives

N3 = (24)

R ' To3

Substituting PL 1 from eq (22) into eq (21), PL3 from eq (23) into eq (24),

and dividing the two resulting equations by each other gives

10
. . PU3 * S 3 * Tol S l N3 /NL = • ( 1 + ). (25)

PU1 * S l ' To3 Col

From the discussion in the previous section, the last factor on the right in

eq (25), 1 4- S 1 /Col , is the theoretical flow rate ratio (RL/U ) t for pump

speed S x and orifice conductance Col . Its average value is denoted by

RL i u (S t

, C0 1) , and its inverse as Rv , L (S x

, C0 1) , so that eq (25) can be

rewritten as

rui " °i o

NL = Ru/L (S 1 ,Tol )

• N3

• (26)

PU3 * S 3 • Tol

Pr3 • (AV/At) 3 ?V1 • S, • To3 = Ru/l(Si,To1 )

• ' • (27)

R ' Tr3 PU3 • S 3• Tol

Equation (27) is then the basis for measurement of the leak rate from a leak

using the flow division technique, where the upper- to- lower flow ratio (Ru/L ) is measured at relatively high flow rates using the method of the previous

section. As noted earlier in reference to eq (10), this expression for the

leak rate is for the leak at temperature TL

.

DESIGN PHILOSOPHY: LEAK COMPARATOR SYSTEM

Once the leak rate from one leak undertest has been measured on the Primary

Leak Standard (for the leak referenced to a particular temperature), it is

possible to use this "standard" leak to measure other "unknown" leaks by

direct comparison. This comparison function can be performed on the Leak

Comparator System (LCS) . An additional function of the LCS is to measure the

temperature dependence of the unknown leak, which is accomplished by varying

the temperature of the unknown leak and comparing the resulting leak rate with

the leak rate of the standard leak (which is kept near its reference

temperature) . Both of these functions of the LCS rely on determination of the

LCS linearity, which has been investigated experimentally [4]

The Leak Comparator System is shown schematically in figure 6 (a more

complete discussion of the system is given in the Description of System

section). Basically, a rectangular high vacuum manifold with pneumatically

controlled valves on the corners (designated Vi

, where i = 6 to 9) is

connected to a commercial helium leak detector (along the leg V6 -V7

) . The

leak to be characterized ("unknown" leak) is connected to the manifold in the

V7 -V9 leg, and the leak with which it is to be compared ("standard" leak) is

connected to the manifold in the V6 -V8 leg. A turbomolecular pump (50 2/s) is

connected to the manifold along the V8 -Vg leg. Gas from either the unknown

11
leak or standard leak, or both leaks, can be valved into the leak detector.

When gas from a leak is not routed to the leak detector, then it is routed to

the turbo pump, so that both leaks are continuously pumped. The unknown leak

is encased in a temperature-controlled environment, with a controllable

temperature range from -10 to 60 °C. The standard leak is thermally

insulated, and the temperatures of both leaks are monitored with platinumresistance thermometers (PRTs) . The output voltage from the leak detector

electrometer and PRTs is converted through an analog to digital converter

(ADC) to be read by a computer, which also controls sequencing of the

automated data acquisition system. Data is usually taken at 5 °C increments

from 0 to 50 °C.

The equilibrium temperature dependence of leak rates from leaks depends

strongly on the type of leak element (through which the gas "leaks") inside

the leak. For orifice-type leaks, over a limited but useful temperature

range, the temperature dependence can be represented according to:

L(T) = L .[1 + o.(T-T0 )] (28)

where L(T) is the leak rate for the leak at temperature T, LQ is the leak rate

for the leak at temperature TG

, and a is referred to as the "linear

temperature coefficient" of the leak. For permeation or diffusion leaks,

however, the temperature dependence is exponential [2]:

L(T) = A • T • e" B/T (29)

= L0

• (T/To) • e

" B -( To-T)/(T-To) (3Q)

where B is referred to as the "exponential temperature coefficient" of the

leak, and A has been solved for explicitly in eq (30) in terms of LQ and TD

. Figure 7 shows data (+) , obtained using the LCS , and the fitted curve for a helium permeation leak. The data were fit using eq (29) , and the resulting

curve is arbitrarily normalized to unity at the T = 0 °C leak rate value.

Note that the leak rate increases by a factor of almost seven over the

temperature span used for this leak, not an uncommon result for a permeation

leak. The value of B is typically between 2200 and 3500 K, and for many

commercial helium permeation leaks is close to 3000 K. It is clear from this

figure that the detection system of the LCS must be linear or errors will be

introduced when fitting the data. Figure 8 shows a plot of the measured leak

rate versus the actual leak rate over one decade of operating range of the

LCS, indicating a maximum deviation from linearity of 1% when using

techniques described in Reference [4]

An interesting aspect of the LCS is that it is not necessary to know the

absolute value of the leak rate from the standard leak in order to determine

the temperature coefficient, either linear or exponential, of the unknown

leak. This can be seen more clearly by rewriting eq (28) in the form

12
and eq (30) in the form

a [L(T)/LJ - 1

(T - TQ ) (31)

B =

T • T,

(T - TD )

Jin L(T) • T

(32)

Note that in both eqs (31) and (32) the ratio (L(T)/LQ ) appears, and not LQ alone, so that it is not necessary to know the absolute magnitude of the leak

rate, but only its relative change with temperature, to determine the

respective temperature coefficients. While it would in principle be possible

to calculate B as the average of the individual values of a set of data using

eq (32), what is done in practice is to use eq (29) and fit the data (using

linear regression) according to

in[L(T)/T] = in(A) - (B/T)

(33)

obtaining B as the slope of in[L(T)/T] vs. 1/T. It can also be seen in this

equation that only the relative value of L(T) needs to be known to determine

B, since the term (in(A)), representing the absolute magnitude of the leak

rate, enters only as the y- intercept of the line, and does not effect the

slope ( -B)

13
4. DESCRIPTION OF SYSTEM AND OPERATIONAL PROCEDURES

PRIMARY LEAK STANDARD SYSTEM DESCRIPTION

The NIST Primary Leak Standard (PLS) is composed of three main components;

the main vacuum chamber, the leak manifold, and a flowmeter. The PLS may be

used with either the piston or bellows flowmeter but is primarily used with

the latter. Calibration of a customer leak is performed by [comparing the

partial pressure of the test gas generated in the upper chamber of the vacuum

chamber by the gas flowing from the leak] to [the upper chamber partial

pressure generated by the gas flowing from the flowmeter] . Although this

system is capable of calibrating leaks for a wide variety of gas species, the

calibration service is limited to calibration of helium leaks at the present

time. The following paragraphs detail the salient characteristics of the

Primary Leak Standard and the steps taken to calibrate a helium leak. The

reader should refer to figures 9 and 10 for identification and placement of

components of the PLS referred to hereafter.

Leak Manifold

The primary purpose of the leak manifold is to provide a means of installing

a leak in such a way that the measurement of the leak rate of the leak can be

accomplished in a minimum amount of time and without the introduction of

additional errors to the measurement process due to the installation

configuration. The leak manifold has provisions for installation of up to six

leaks simultaneously. The manifold is composed of stainless steel tubing and

other high vacuum hardware and connected with all-metal seals, which

eliminates outgassing which can occur with elastomer seals. The leak manifold

uses two 50 i/s turbomolecular pumps to achieve a high vacuum and maintain

pumping of the helium gas emitted from the installed leaks. A quadrupole mass spectrometer is connected to the system at port (P6) and is used to monitor

gas purity from the installed leaks as well as other contaminants which can be

emitted from leaks which have been manufactured with substandard materials or have been used in contaminated environments. For open-reservoir leaks three

pressure gages are used to measure reservoir pressures. This is primarily for

research on the conductance properties of leak elements.

Main Vacuum Chamber

The main vacuum chamber is used for measurement of the partial pressure

generated by the flow of gas from either a leak or the flowmeter. The main

vacuum chamber is divided into two sections which are separated by a 1 cm diameter orifice. The volume above the orifice is referred to as the upper

chamber and the volume below the orifice is referred to as the lower chamber.

Pressure measurements in the upper chamber are accomplished using three

quadrupole mass spectrometers, and three "nude" type ionization gages. The

system vacuum pump connected to the chamber with a 10 inch flange is a 2000

i/s turbomolecular pump, which is backed by a mechanical pump for evacuation

of pumped gases. For accurate measurement of the leakage rate from a test leak

the system must be able to achieve, maintain, and measure helium partial

14
pressures ranging from 1 x 10" 4 to 1 x 10" 8 Pa. This requires that the

turbomolecular pump have the capacity and stability over the corresponding

flow rates to achieve pumping speed stabilities of less than 0.1% per hour.

It is also necessary that the quadrupole mass spectrometers have the necessary

sensitivities and stabilities to measure helium partial pressures over this

range with a 3ct random error of less than 1% per hour. Since changes in the

valving configurations also change the background partial pressure, most

notably hydrogen, it is also desirous that the quadrupole mass spectrometers

be insensitive to changes in the hydrogen background pressure. Changes in the

normal hydrogen background pressures encountered while calibrating leaks

result in changes in the helium sensitivity of the quadrupole mass spectrometers of less than 0.2%.

Bellows Flowmeter

The bellows flowmeter is composed of a reference volume, variable volume,

two pistons, piston advance control system and pressure measurement devices as indicated schematically in figure 10. The bellows flowmeter generates and

measures a flow of gas by changing the volume of the variable volume at a measured rate such that the pressure in the variable volume remains constant.

The pressure in the variable volume is determined using capacitance diaphragm

gages (CDGs) in the reference volume to measure the pressure, and a differential CDG is used between the reference and variable volumes to measure

the pressure difference between these two volumes. The reference and variable

volumes are filled to the same pressure and then isolated from each other by

closing valves Bl and B2 . The pressure in the variable volume decreases due

to the gas escaping through the leak valve which produces a change in the

differential CDG (D5) signal. The differential CDG signal activates a servo control system which controls the rate of advance of the piston to maintain a zero differential pressure between the two volumes. The flow from the

flowmeter can then be calculated using the methods of section 3.

CALIBRATION OF HELIUM LEAKS

To calibrate a helium leak, the leak is first installed on the leak manifold

(leak ports P1-P6) using 2 3/4 inch conflat-type fittings which utilize allmetal seals. This is accomplished by first isolating the turbomolecular pumps

(turbo 1 and turbo 2) from the leak manifold by closing valves L9 , L16, L17,

and L18. Argon gas is then introduced at a pressure slightly above

atmospheric by opening valve LA and one of the leak isolation valves (L30-

L35) . A positive flow of argon gas through the system during installation of

the helium leak minimizes the amount of water vapor which enters the system

when exposed to the atmosphere. The leak is then installed on one of the six

leak ports (P1-P6) as stated earlier. The argon gas is then evacuated by an exterior roughing pump through valve L4 after which valve L4 is closed.

Valves L16-L18 are then reopened to the turbomolecular pumps to re-establish a high vacuum. The helium leak is continually pumped on the leak manifold until

its leak rate reaches equilibrium, which usually occurs in 24 h.

The day before a calibration on an unknown leak is performed, the flow from

the leak is diverted from the leak manifold to the main vacuum chamber by

15
closing valve L30 and opening valve L24 if the unknown leak is installed on port Pi. The gas then flows through valves L21 and L36 and enters the upper

chamber of the main vacuum system, and is ultimately evacuated through the

orifice into a turbomolecular pump. When the upper chamber helium partial

pressure reaches equilibrium (usually 30 min) as measured by quadruple mass spectrometers QMS1, QMS2 and QMS3, the mass spectrometer ranges are adjusted

to the proper scales. The composition of the flowing gas is examined using

QMSl to identify if there are significant levels of contaminants which could

compromise the integrity of the measurement. Since quadrupole mass spectrometers are somewhat sensitive to the total pressure and composition of

the measured gas, contaminant gases (gases other than helium flowing from the

leak or elsewhere) may introduce instabilities and changes in the

sensitivities of the mass spectrometers (Reference [5]). If the contaminant

gases do reach a level which may compromise the calibration, the leak will not

be calibrated. The flow from the leak is then diverted back to the leak stand

by reversing the described process.

On the day of the calibration, the partial pressure of helium is measured in

the main vacuum chamber with valve L37 opened and with valves L36 and L38

closed while the flow from the leak is still being evacuated by the leak

manifold. The values obtained for the helium partial pressure are termed the

baseline of the lower chamber. The process is repeated with valves L37 and L38

closed and valve L36 open. The data obtained is termed the baseline of the

upper chamber. This data corresponds to zero data taken for the specific

valving configuration and is later subtracted from the values obtained while

the leak is flowing with the same valving configuration. With valve L36 open

and valve L37 and L38 closed, the flow from the leak is diverted from the leak

manifold into the upper chamber of the main vacuum system. Sufficient time is

then allowed for the helium partial pressure in the upper chamber to reach

equilibrium, after which the helium partial pressure is recorded for mass spectrometers QMS2 and QMS3. QMSl is usually used to examine the gas purity

emitted from the leak and is not tuned to helium but scans from 1 to 100 AMU.

The total pressure in the upper chamber is also recorded using three "nude

type" ionization gages (Nl , N2 and N3) . The flow from the leak is then

diverted back to the leak manifold.

The flowmeter is then set up to generate approximately the same flowrate

into the upper chamber of the main vacuum chamber in the following way. The

capacitance diaphragm gages (D1-D4 in fig. 10) used to measure to the fill

pressure of the reference volume are zeroed while being exposed to a high

vacuum (<10~ 4 Pa) as measured by the ionization gage (II). The ionization

gage is then shut off and the turbomolecular pump is isolated from the

flowmeter by closing valve B17. Helium gas is then introduced with valves Bl

and B2 open into the flowmeter by opening valve B14 until the desired pressure

is attained. Helium then flows through the leak valve to the upper chamber

of the main vacuum system, which generates a partial pressure of helium

proportional to the flowmeter fill pressure. The pressure in the flowmeter is

then adjusted so that the equilibrium flow from the flowmeter gives the same helium partial pressure, to within 0.1%, as that recorded while the leak was flowing into the upper chamber.

16
The flow from the flowmeter is measured in the following manner. The 1 Torr

differential CDG (D5) is zeroed and the variable and reservoir volumes are isolated by closing valves Bl and B2 . The piston is then set in motion by

pushing the enable button on the controller and the advance of the piston is

controlled by the feedback circuitry which maintains a constant pressure in

the variable volume. The time elapsed for the piston to displace consecutive

5% intervals of the total piston volume is recorded by the computer controlled

data acquisition system until the piston reaches its total displaced volume.

After this has been completed the variable and reservoir volumes are valved

back into the flowmeter system by opening valves Bl and B2 . The leak rate of

the leak can then be calculated using the methods described in section III.

The leak rate of the leak can also be measured using a flow division

technique, described previously in section 3, by flowing gas from the

flowmeter into the lower chamber of the main vacuum system. This is

accomplished in the following manner. The flow of gas from the flowmeter is

first diverted from the upper to the lower chamber by closing valve L36 and

opening valve L37. The helium pressure in the flowmeter is adjusted so that

the equilibrium flow from the flowmeter into the lower chamber gives the same helium partial pressure in the upper chamber as that recorded while the leak

was flowing into the upper chamber, to within 0.1%. The steps of the

preceding paragraph are then repeated. The leak rate of the leak can then be

calculated using the methods described in section 3.

NIST LEAK COMPARATOR SYSTEM DESCRIPTION

The Leak Comparator System (LCS) , shown in figure 6, was originally designed

and provided by the Sandia Primary Standards Laboratory and was subsequently

modified at NIST. The LCS is composed of three main components: the leak

detector, the leak manifold, and the control systems. The leak manifold

provides a way of introducing gas flow from two leaks simultaneously or individually, without requiring venting of the system. The control system

operates the valving and controls the temperature of the leak under test. The

leak detector is used to measure the partial pressure of helium generated by

the flow of helium from the leaks on the manifold and is described in more

detail in the following paragraph.

The helium leak detector used in the LCS is a commercially available "tuned"

magnetic-sector mass spectrometer. The term "tuned" in this case means that

the instrument only measures partial pressures of molecules with molecular

weight of 4 AMU. The mass spectrometer consists of an ion source with a thoria coated tungsten filament, a magnet and an ion collector. Gas entering

the mass spectrometer is ionized and then separated by its mass/charge ratio

so that only helium ions strike the collector. The signal originating from

the collector is then converted to a proportional voltage which is measured

using a digital voltmeter. The leak detector has the following

characteristics which are necessary for leak rate measurements over the range

of the NIST calibration service: a response time of 5 s, a minimal detectable

leak rate of 1 x 10" 14 mol/s, and an ion-current drift rate of 1% of full

scale per hour.

17
The LCS control system uses an IBM-compatible computer to control the data

acquisition and analysis of the data. Its main functions include the

following: control of the temperature bath to within 0.02 °C of the set point

temperature, control of the valving of the LCS leak manifold, monitoring of

the temperatures of the standard and unknown leaks installed on the LCS,

collection of the ion signal data from the system digital voltmeter, and least

squares curve fitting to the functional temperature dependence of permeation

leaks given in section 3. The program to accomplish these functions is

written in a Basic language and uses corresponding instrument drivers for

IEEE-488 communications.

TEMPERATURE COEFFICIENT DETERMINATION

The temperature dependence of the leak rate of a helium permeation leak is

determined by measuring the leak rate of the leak at temperatures over a range

of 0 to 50 °C. The temperature coefficient is then determined by performing a least squares curve fit to the functional temperature dependence given by eq

(33) in section 3. The data collection is collected using the following

procedure

A helium permeation leak for which the temperature dependence is to be

measured is installed on the Unknown port of the LCS. A standard leak with

approximately the same leak rate is installed on the Standard port of the LCS.

The leaks are pumped by a turbomolecular pump until the leak rates reach

equilibrium, usually within 24 h. The leak detector is also turned on (according to the manufacturer's procedures) and allowed to warm up for a 24 h

period. The program is then loaded and run, and the user specifies the

sequence and number of temperatures for which the leak rates will be measured

for the unknown leak. The user also specifies the number of data points to be

taken at each individual temperature. It is common practice to take 5 data

points at each of the following temperatures (°C) in the given sequence: 25,

35, 50, 40, 30, 20, 10, 0, 15, 25.

The program then executes the following data control and acquisition

routine. The temperature bath is controlled to obtain a temperature stability

of the unknown leak to within 0.02 °C. Thermal gradients within the unknown

leak are then allowed to stabilize by maintaining this temperature for a 2 h

period before the leak rate measurement is performed. After the stability

time of 2 h has elapsed, the background ion current of the leak detector is

measured 10 times over a 5-min interval and the average and standard

deviations are recorded. The standard leak is then valved into the leak

detector and allowed to stabilize for 60 s before the data is collected. Ion

current data are collected over a 5-min period, and the average and standard

deviations are calculated based upon the 10 collected readings. The standard

leak is then isolated from the leak detector and the unknown leak is valved in

and allowed to stabilize for 60 s. The ion current data is then collected

over a 5-min interval and the average and standard deviation are calculated.

The leak detector is then isolated from both leaks and allowed to stabilize

for 60 s before the background ion current is measured using the same procedure described above. The program then calculates the leak rate of the

unknown leak based upon the ratios of the recorded ion signals corrected for

18
zero drifts. This process is repeated for the data points at each temperature

in the data collection sequence. At the conclusion of the data acquisition

the program performs a least square fit to the data using the functional form

of eq (33) in section 3. The temperature coefficient and the uncertainty in

the temperature coefficient are calculated. The absolute leak rate at 23 °C

is also calculated and compared to the value obtained using the primary leak

standard. The difference between the two techniques has historically been no greater than 1.5%, and well within the uncertainties of the respective

systems

19
5. ASSESSMENT OF UNCERTAINTIES

PRIMARY LEAK STANDARD

Flowmeters

The fundamental equations relating the measured leakage rate of a leak (at a given temperature) to the measured parameters of the Primary Leak Standard

were derived in section 3 (eqs (10), (17) and (27)). At the heart of these

equations are the terms arising from the operation of either of the two

constant-pressure flowmeters. A thorough discussion of the uncertainties

associated with the various flowmeter terms can be found in the article in

Appendix D. A brief review is presented here for convenience.

In its simplest form, a constant pressure flowmeter consists of a container

of gas, a flow element through which the gas can escape, a gage which monitors

the pressure of the gas in the container, and a mechanism for mechanically

varying the volume which the gas occupies in a controlled manner. The volume

which the gas occupies is referred to as the "variable volume," and in

operation the "variable volume" is varied in such fashion as to keep the

pressure of the gas in the variable volume essentially constant. The two

flowmeters employed in this study utilize electronic feedback circuitry to

accomplish this goal.

The 'exact' equation expressing the average flow rate of gas from a constant-pressure flowmeter, over the time interval At, is

[dN/dt] ave = [(Pi Vi )/(RTi

) - (Pf Vf )/(RTf )]/At (34)

where Pi (Pf

) is the pressure in the variable volume, Vi (Vf) is the volume of

the variable volume, and Ti (Tf

) is the temperature of the gas in the variable

volume of the flowmeter at the beginning (end) of the time interval At. This

equation is essentially a definition, since the first group of terms in the

right-hand bracket is the amount of gas in the variable volume at the

beginning of the measurement, and the second group of terms is the amount of

gas remaining in the variable volume at the end of the measurement. Thus eq

(34) represents the net quantity of gas that has left the variable volume in

the time interval At, divided by that time interval. Under ideal conditions

the initial and final pressures would be identical, but deviations occur in

practice and are therefore explicitly taken into account. Defining AT=Tf -Tit

AP=Pf -Pi

, and AV=Mi -V{ , eq (34) can be rewritten as

[dN/dt] ave = [(Pi AV)/(RTi At)]{l - (Vf /AV)[(AP/Pi )-(AT/Ti )]} (35)

to first order in AP/Pi and AT/Tt

. This form of the equation provides a convenient way of assessing the uncertainties, and emphasizes the importance

of keeping the so-called dead volume ratio (Vf /AV) to a minimum.

20
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21
Table 2 gives estimated uncertainties of the individual terms for the

"bellows" flowmeter for flow rates which are lower (10" 12 mol/s) than those

presented in Appendix D for the "piston" flowmeter. This information is

presented graphically in figures 11 and 12.

Temperature and Orifice Conductance

All temperatures, including that of the leak, the main chamber (and

orifice) , and the flowmeter are obtained using platinum resistance

thermometers that are thermally anchored to the individual parts. The

systematic uncertainty associated with the calibration of these instruments is on the order of 10 mK, which at room temperature is .003%. The largest

contribution to random fluctuations (say over the course of an hour) are variations in room temperature. While the room in which the Primary Leak

Standard is located is thermally controlled, variations in room temperature of

up to several degrees during a workday are possible. Thus, correcting for

temperature-related effects, as is done in the above mentioned equations, can

be important. Note, however, that except in the case of the flowmeter

temperature (discussed in Appendix C) and leak temperature, all other

temperatures appear in the equations as ratios, which reduces the overall

uncertainty caused by systematic error (but not random error) . Typical three

sigma values of the temperature fluctuations of the leak and main chamber

(expressed as % of reading) over the individual 20-min data- taking sequences

using the flowmeter are only .01% (for both). While it is possible that a slight systematic difference may exist between the measured temperature of the

leak and the actual temperature of the leak element, which is located inside

the leak housing, insulating procedures should limit this difference to well

under 0.1 °C. This would amount to a 0.3% error in the leak rate of a permeation leak having a typical 'linearized' coefficient of 3%/°C. Note also

that the orifice conductance appearing in eq (10) is proportional to the

square root of the chamber temperature, but contributes less than .02% to the

uncertainty of the flow rate measurement as is described in the example in

Section 3

Pumping Speed

The pumping speed of the turbomolecular pump is quite difficult to measure

directly, so instead we have measured the rotational frequency of the turbine

blades, which is obtained from a signal within the pump controller and

displayed using a frequency counter. The systematic uncertainty associated

with the frequency measurement is entirely insignificant and unimportant, as only ratios of pumping speeds are present in the equations. More important is

the uncertainty associated with the assumption that the pumping speed is

directly proportional to the rotational frequency, since until recently the

rotational frequency would drift and fluctuate uncontrollably. It has been

experimentally verified that the observed frequency fluctuations and drift are correlated with similar variations in the ac line voltage powering the pump

controller. Attempts to regulate the line voltage without otherwise

disturbing operation of the pump proved to be unsuccessful until recently.

Before regulation of the power supply voltage, drifts of 5% or more during the

22
course of a workday, particularly in the afternoon, were not uncommon, so that

corrections certainly needed to be taken into account.

The assumption that the pumping speed is directly proportional to the

rotational frequency is difficult to verify. It can best be determined by

observing the change in the upper chamber pressure indication when a presumably constant flow rate of gas is flowing into the lower chamber. If

the rotational frequency shifts abruptly, then the corresponding change in the

upper chamber pressure indication can be noted, and, assuming linearity of the

upper chamber pressure indicator with upper chamber pressure, the linearity of

pumping speed with rotational frequency can be measured. Unfortunately,

without regulation, the change in the rotational frequency is usually more of

a long-term drift (abrupt changes of less than 1% have been observed, but were

erratic) , so that the natural time constant of this part of the system

(between 10 and 20 min) prevents precise measurement of this effect. However,

measurements that have been obtained recently by controlling the power line

voltage indicate speed/rotational frequency proportionality is within .01% over the 5% or so observed range of rotational frequencies.

During the entire 20 min data- taking sequence using the flowmeter, the pump

rotational frequency is recorded, and an average value is obtained. With

regulation of the pump controller input voltage, three sigma standard

deviations of pump rotational frequency, expressed as % of reading, typically

range between .05% and 0.1%. As will be shown below, the contribution to the

total uncertainty associated with the uncertainty in pumping speed for flow

into the upper chamber is insignificant, while for flow into the lower chamber

it is of the same order of magnitude as the values given here

Upper Chamber Pressure Indication

Measurement of the upper chamber pressure (Pu ) presents several interesting

challenges. Good sensitivity, linearity, repeatibility and low zero drift of

the pressure measuring instrument over a wide range are important. Monitoring

and accounting for gas impurities can be tricky, as different gases move through the vacuum system at different rates, and are not differentiable in

total-pressure gages. Opening and closing various portions of the vacuum

system from the main chamber at different stages of the data- taking cycle

result in varying outgassing rates of hydrogen and other contaminants into the

vacuum system, which must be accounted for with separate zero readings

depending on whether flow is into the upper or lower chamber. Other more

subtle effects, such as the possible slight pumping action of helium by the

getter pump in the upper chamber, must sometimes be considered.

As indicated in previous sections, one well-regulated nude Bayard-Alpert

type ionization gage (total pressure gage), and two quadrupole- type residual

gas analyzers (partial pressure gages) , tuned to helium, are used to measure

the pressure in the upper chamber. In addition, a third quadrupole residual

gas analyzer is used to monitor the background gases . The reason for the

redundancy of gages, besides the obvious advantage of multiple measurements of

presumably the same quantity, is that gage stability and repeatiblity were

23
found to depend strongly on the particular operating range of the quadrupole

instruments, and at the lowest pressures (10~ 7 Pa and below), correcting for

the differential hydrogen outgassing rendered the total pressure gage of

marginal use. It was found that if either of the residual gas analyzers tuned

to helium was also used to scan for background gases, the problems associated

with retuning and restabilization of the gage for upper chamber pressure

measurements were intractable. While none of these gages is calibrated, it is

not necessary to do so since it is the ratio, and not the absolute magnitude,

of upper chamber pressures that enters in all of the equations of importance.

What is important is that the gages be linear over the range of use, stable

over the time of use, and repeatable in going through the cycling process when

gas from the leak and the flowmeters is alternately valved into and out of the

system. If in addition the sensitivity of the gage depends on the level or composition of background gas, this effect must be minimized or accounted for.

Such an effect has been seen recently in the sensitivity of a gage to helium

for varying hydrogen background. For the typical differences in upper chamber

residual hydrogen partial pressures seen during a day, the change in

sensitivity could account for up to 0.3% change in the helium partial pressure

indication.

In order to minimize uncertainties associated with gage linearity, general

operating procedure is to achieve an upper chamber partial pressure indication

of helium for helium gas flowing from the flowmeter (into either the upper or lower chamber) that is well within 1% of the upper chamber partial pressure

indication when helium gas from the leak is flowing into the upper chamber, as recorded by the most stable gage. In order to minimize uncertainties due to

gage instability, the upper chamber partial pressure indication is recorded

and averaged ten times for flow from the leak (with nominal three sigma

deviations between .15% and 0.3% of reading for the residual gas analyzers,

and 0.7% for the nude ionization gage), and 20 times for flow from the

flowmeter (with the same nominal three sigma deviations) . In order to

minimize uncertainties associated with gage repeatability during the course of

the measurement sequence (Steps 1 through 3 in figs. 3 and 4), every effort

is made to keep the upper chamber partial pressure as constant as possible

during the valving and filling operations, or at least to minimize the time

that the upper chamber partial pressure is changing. This presumably minimizes

any 'hysteresis' type of effects that may occur when cycling these gages.

A control chart of the measured leak rate (referenced to 23 °C) versus time

of a check standard is shown in figure 13. This figure illustrates the

relative differences in leak rate measurement using the various upper chamber

pressure measuring instruments. The pronounced systematic offset between the

nude gage data and that taken using the residual gas analyzers is due to

changing hydrogen backgrounds during the measurement process, which the nude

gage cannot compensate for. This effect is more pronounced at lower flow

rates where the hydrogen partial pressure is comparable to the helium partial

pressure, as it is for the data in this figure.

Flow into Upper Chamber

Using the individual uncertainties discussed above, it is now possible to

24
discuss an overall uncertainty associated with an individual measurement of

flow rate by flow into the upper chamber. The equation which describes this

flow rate is reproduced here for convenience:

Pr3 (AV/At) Pul To 3 Si Co3 + S 3

R • Tr3 _ Pu3 _

• _ Tol _• _ s 3 C ol + Si _

The total uncertainties associated with the flowmeter factors are a function

of the actual flow rate, and can be found in Appendix D and table 2. These

total uncertainties are predominantly systematic. The uncertainties

associated with the ratio of upper chamber pressure indications are also a function of flow rate, and are given as three times the standard deviation of

the observed indicated pressures for a specified set of upper chamber gages.

These uncertainties are treated as random. Uncertainty in the chamber

temperature is primarily due to random fluctuations in room temperature, which

results in measured differences in chamber temperature of up to 0.1% during an

8 h period. The rightmost factor in brackets shows that, even though the

pumping speed and temperature are known to drift, the entire factor is so close to unity that these uncertainties are inconsequential. As evidence,

consider a 'worst case' example where 3^2500 i/s , Tol =299 K, Col =40 i/s,

S 3 =2375 i/s, To3 =293 K, Co3 =36.6 £/s. The correction term in brackets is

calculated to be 0.9994, so that the correction is only 0.06%. These

uncertainties are summarized in table 3.

TABLE 3. Summary of Uncertainties for Flow into the Upper Chamber

Flow Rate (mol/s)

10" 6 - -10" 9 10" 1 0 10" 1

10" 12

Bellows Flowmeter (sys) 0 82 2. 0 2 02 9.8

Bellows Flowmeter (ran) 0 02 0. 1 0. 1 1.5

Upper Chamber Pressure (ran) 0 3 0. 3 0 3 0.3

Chamber Temperature (ran) 0 1 0. 1 0. 1 0.1

Pump Speed/Conductance (ran) 0 06 0. 06 0. 06 0.06

Total [(sys) + rss(ran)] 1 30 2. 56 2 58 11.76

Note that, at the lowest flow rates,

uncertainty in this Table is consistent

seen in figure 13. The first two rows table 2.

Upper- to -Lower Chamber Flow Ratio

the sum of the random components of

with the observed random uncertainty

of table 3 are described earlier in

The equation used to calculate individual measurements of upper- to- lower

25
flow ratio is eq (17). A slightly modified form (the reciprocal value) is:

Prl • (AV/At) 1

• Tr2 PU2 • S2• T0l

(Ru/L ) t (Si,Tol ) = — • . (17a)

Pr2 • (AV/At) 2

• Tr x P01 • S x• To2

The first set of factors involving the flowmeter is again a ratio, so that

many of the systematic errors associated with the flowmeter cancel. Typically

the residual systematic uncertainty of the flow ratio should be less than 1%.

Furthermore, both flowmeter runs are usually at relatively high flow rates

(10" 11 mol/s and mid 10" 10 mol/s) , so that the random uncertainty due to the

flowmeters is on the order of 3%. Again, at the higher flow rates the random

uncertainty in upper chamber pressure indication is small, so that a total

uncertainty of 0.3% due to the pressure ratio term is appropriate. From

above, the uncertainty in pumping speed due to fluctuation and linearity

assumptions is 0.1%, so that the uncertainty due to the pumping speed ratio is

estimated at 0.2%. Finally, the uncertainty in the chamber temperature ratio

from above is 0.1%.

The total random uncertainty in each individual measurement of (Ry # L ) t will

be taken as the square root of the sum of the squares of the individual random

uncertainties

5(Ru/ L )t = 7[5 2 (flowmeter) + 5

2 (PU ) + 5

2 (S) + 5

Z (TQ )] , (36)

which for the values above gives 3%. The total uncertainty would then be 4%.

Figure 14 is a control chart of the measured upper -to -lower chamber flow

ratio over a period of 280 d, uncorrected for changes in pumping speed or orifice temperature. Even without these corrections, the three-sigma spread

in the data is only ±2.3%, which is in good agreement with the predicted

random uncertainty. Note in figure 14 that much of the scatter in the data

for a given day is due to the variation in the upper chamber pressure

indication. However, there is an apparent correlation between the average of

the various sets of data and the average turbopump frequency for the day which

could also account for some of the observed differences.

Flow into Lower Chamber

The equation describing leak rate measurement for flow into the lower

chamber is:

Pr3 • (AV/At) 3 P01 • S, • To3

N, = Ru/L (S lf Tol )

• • , (27)

R ' Tr3 PU3 • S 3

• Tol

26
which contains elements similar to those in both of the sections above. The

uncertainties associated with the particular factors are again a function of

the flow rate of the flowmeter and are summarized in table 4.

TABLE 4. Summary of Uncertainties for Flow into the Lower Chamber

Leak Rate (mol/s)

10-6_i 0

-9 10" 1 0 10" 1

10" 1 2 Upper/Lower ratio (sys) 4. 02 4. 02 4. 02

Bellows Flowmeter (sys) 0. 84 2. 10 2. 12

Bellows Flowmeter (ran) 5 5 1. 0

Upper Chamber Pressure (ran) 3 3 3 Chamber Temperature (ran) 1 1 1 Pump Speed (ran) 1 1 1

Total [(sys) + rss(ran)] 5. 46 6. 72 7. 19

Note that the uncertainties given are for leak rate , not flowmeter flow rate,

and reflect the fact that the flowmeter is being operated at a factor of

roughly 67 times higher in flow rate than for the corresponding upper chamber

flowmeter runs. Thus, while there is an additional uncertainty due to the

upper/lower flow ratio for a given measurement of leak rate, this is offset by

a corresponding decrease in the uncertainty of the flowmeter. From figure 13

it can be seen that the random scatter in the lower chamber data is consistent

with the rss random error value of 1.1% derived from table 4.

Summary Analysis: Calibration of Customer Leaks

Calibration of a customer leak on the Primary Leak Standard typically

involves at least five individual measurement sequences (on five separate

days), each sequence including leak rate measurement using the bellows

flowmeter valved into first the upper chamber, and usually then the lower

chamber (for leaks with leak rates below 10" 8 mol/s). Uncertainties

associated with measurements for flow into both chambers are evaluated using

the methods indicated above, and the uncertainty that goes into the

calibration report is the smaller of the two, provided that the two average

values of leak rate for the two 'methods', plus and minus their respective

uncertainties, overlap at the three-sigma level. While there is almost always

overlap, the individual three-sigma values are found to vary from fractions of

a percent to 5% or more, and the magnitude is not found to correlate strongly

with leak rate. In addition, the differences between the average measured

value of leak rate using the two methods is found to vary from fractions of a percent to almost 3% for leak rates between 5x10" 12 and 7x10" 11 mol/s,

although again there is not a strong correlation with leak rate, confirming

that the flow ratio is not a function of the flow rate. A sample calibration

27
report is presented in Appendix E.

LEAK COMPARATOR SYSTEM

As discussed earlier, the exponential temperature coefficient of helium

permeation leaks is determined using the Leak Comparator System (LCS) . This

is done by fitting the relative leak rate vs. temperature data to eq (33) to

obtain parameter B.

in[L(T)/T] = in(A) - (B/T) . (33)

The uncertainties associated with this procedure arise from three sources, the

systematic uncertainty associated with any nonlinearity in the measured leak

rate vs. actual leak rate, the random uncertainties associated with the data

acquisition process and errors associated with the linearized fitting

procedure

Temperature Coefficient Uncertainty

In order to determine the linearity of the system over the normal operating

range, a single leak with a variable backpressure reservoir was calibrated on

the Primary Leak Standard, at several leak rates, between 2x10" 12 mol/s and

1.4x10" 11 mol/s. The leak was then mounted on the LCS in the "unknown"

position, and the 'normalized' leak rate was measured over this range, using a constant-reservoir leak (nominal leak rate 1.5x10" 11 mol/s) in the "standard"

position [4], The results are presented in figure 15, where residuals from

the linear fit of the measured leak rate are plotted against actual leak rate.

The maximum deviation from linearity was 1.5%. Solving eq (33) for B and

differentiating with respect to L gives the systematic uncertainty of B:

6Bsys /B = (T/B)(6L/L). (37)

Using worst-case values of B=2200 K and T=323 K gives SBsys /B=.2%. The random

component of uncertainty in B (denoted 5Bran ) is taken as three times the

standard deviation of the B coefficient obtained by linear regression of the

data to eq (33) .

Summary Analysis: Calibration of Customer Leaks

The systematic and random errors in B discussed above can be combined to

give an overall uncertainty according to:

SB = 5Bsys + 5Bran . (38)

28
This uncertainty in B must then be translated into an uncertainty in leak

rate, which is expressed as an additional uncertainty per °C away from the

23 °C reference temperature at which the leak was measured on the primary leak

standard. Rewriting eq (30) as:

L(T)±5 L=L0

• (T/To) . e

" <B±*B) • (TG -T)/(T.T0 )

> (39)

Dividing through by L(T)

1±«L/L = e WB.(T0 -T)/(T.T0 )

Expansion of the exponential term to first order then gives

SL 5B-|T0 -T| — = . (41)

L T • TQ

The additional uncertainty in leak rate per degree C from the reference

temperature TQ is obtained by dividing equation (41) by |

0

- T j

5L SB

(42)

L • |

0 -T | T • Tc

Equation (42) is used to assign an additional uncertainty to the calibration

of leak rate for calibrations at temperatures T different than the reference

temperature T0 =23°C. What is done in the calibration report is to use the

worst-case example of T=0°C, so that a constant, worst-case uncertainty is

reported (see sample report in Appendix E) . A typical value is 0.1% per °C.

29
6. QUALITY CONTROL

Once the operating characteristics and uncertainties of a primary standard

have been established, subsequent use of the primary standard at the same

level of uncertainty requires periodic verification to ensure that none of the

uncertainties have changed with time. This is accomplished most readily by

using the standard to measure a quantity of interest, in this case leakage

rate from a "reference" leak, which is hopefully stable with time. By

maintaining quality control charts (measured leakage rate vs. time) on multiple reference leaks one can minimize the stability concern. Periodic

verification of specific critical components internal to the standard is also

a good idea to guard against hidden compensating changes which may mask

overall changes in uncertainty. Such verification includes annual calibration

of the pressure and temperature sensors.

Another consideration that frequently falls under the heading 'quality

control' is how well measurements performed using one primary standard compare

with similar measurements using other primary standards, of the same or different design, in the same or other laboratories. Comparisons of this sort

have been performed, and will be discussed below.

CONTROL CHARTS

Closed-Reservoir Helium Permeation Leaks

The leak rate of helium gas coming from a closed-reservoir helium permeation

leak is a function of several parameters, the most important being the

diffusion coefficient and surface area of the glass leak element, the

temperature of the leak and the amount of helium gas in the closed reservoir.

Figure 16 shows a schematic cross section of a leak of NIST design, where a valve is connected to the reservoir to allow for initial filling (and possible

refilling) . While the temperature of the leak can be regulated or monitored,

the density of helium gas in the closed reservoir can usually only be

surmised, based on the initial filling conditions and the thermal history of

the leak. For a leak that is kept at more or less the same temperature after

its initial filling, the leak rate from that leak is not constant in time, but

decays at a rate that depends on the mechanical properties and geometry of the

leak. Without knowing all of these details, it is still possible to calculate

the time constant for decay by knowing the initial quantity of gas in the

reservoir (N(t=0)) and the initial leak rate (N(t=0)), according to

r = [N(t=0)/N(t=0)] . (43)

N(t=0) can be estimated by estimating the reservoir volume, measuring the

initial fill pressure and temperature, and using the ideal gas law (see eq

(Bl)). N(t=0) can be measured after the leak rate equilibrates after initial

filling, which usually takes several days. Note that r is the amount of time

that it takes for the leak rate to decay by a factor of 1/e ( = .368), or 63%.

Many leak manufacturers state a value of decay of leakage rate in terms of

%/year, which is not to be confused with, but can be derived from, the value

of T . 30
As an example, for a leak rate of 10" 9 mol/s, a fill pressure of 145 psi (1

MPa) , and a reservoir volume of 200 cm3

, the time constant r is approximately

3 yr (1 yr = 3.1536xl07 sec). In 1 yr, the leak rate will have decayed by (1-

e" 1/3 ), or 28%. Most leaks sold commercially have yearly decay rates of 10% or less.

Figure 13, referenced earlier, is a control chart for a closed-reservoir

helium permeation leak (NBSL22) of the NIST design, which has been used as a reference standard since the present Primary Leak Standard configuration was first characterized. The leak rate of this leak is in the mid 10" 12 mol/s

range, the reservoir volume is roughly 150 cm3

, and the initial fill pressure

was 73 kPa. The estimated time constant is then approximately 35 yr,

implying a yearly decay rate of roughly 2%/year, which is borne out by the

control chart. The chart also verifies the consistency of performance of the

Primary Leak Standard at the corresponding flow rates for both upper and lower

chamber flow, at least within the scatter of the data.

Upper- to -Lower Chamber Flow Ratio

Another test of the performance constancy of the Primary Leak Standard is

periodic verification of the upper- to- lower chamber flow ratio. This data was presented earlier in the Control Chart in figure 14. For the period

indicated, the flow ratio has remained constant, within the scatter of the

data. Additional data taken over a 3 yr period have yielded similar results.

Lower scatter has been observed after input voltage regulation has been

applied to the turbo pump power supply.

COMPARISON OF PRIMARY STANDARDS

Flowmeter Intercomparisons

The piston flowmeter was first used to perform primary calibrations of

vacuum gages in 1984. When the bellows flowmeter was brought on-line in 1985, an extensive series of intercomparisons between the two flowmeters was performed, using the Primary Leak Standard, over the range 10" 12 to 10" 10

mol/s. Several fixed-reservoir helium permeation leaks and one sintered

silicon carbide leak were used as stable transfer standards for these

intercomparisons

The technique used to compare the flowmeters at a particular flow rate

consisted of first using one flowmeter and then the other on the same day to

measure the leak rate from a particular leak, repeating the process on subsequent days. This procedure was repeated for several different leaks in

order to make the intercomparison at different flow rates . Measurements were

made almost exclusively for flow into the upper chamber. Data from this study

are summarized in figures 17 and 18. In figure 17 the la random uncertainty

in measured leak rate is presented for five different leaks , for measurements

using the bellows flowmeter alone, the piston flowmeter alone, and the data

31
from both flowmeters combined. The NIST serial number for the leak used at a given flow rate is indicated along the top axis of the figure. The measured

random uncertainties are seen to slightly increase with decreasing flow rate.

Figure 18 presents the difference in average measured leak rate using the two

flowmeters, again as a function of flow rate, using each of the individual

upper chamber pressure measuring instruments seperately as well as combined.

Here also the difference between measured flow rate using the two flowmeters

increases with decreasing flow rate. This is most probably due to observed

differences in hydrogen outgassing rates in the variable and reservoir

volumes, which has a significant influence on the measured total leak rate at

the lower flow rates, and points out the need for going to flow into the lower

chamber to measure flow rate at these lower values . Methods for compensating

for hydrogen outgassing are being developed. Above 5x10" 12 mol/s, the

flowmeters agree with each other to better than 1%, providing confidence that

systematic uncertainties such as incorrect piston areas or timing errors do

not exist.

In a separate study, a leak (NBSL11, leak rate 9. 8x10" 12 mol/s) was used to

compare the flowmeters using both pistons cn each flowmeter, and several range

settings of the differential CDG's used to measure the pressure differentials

between the reservoir and variable volumes. This study resulted in a maximum

measured difference of 1.7% between the leak rate values using the two

flowmeters. Other data taken using NBSLll and the bellows flowmeter for flow

into the lower chamber, using both the inch and centimeter diameter pistons,

gives a difference between average measured leak rate of only 0.3%. Similar

small differences were also found in the 10" 8 mol/s range using molecular drag

gages as transfer standards on the piston f lowmeter [ 1 ] .

Domestic Intercomparisons

The NIST leak calibration program began in 1984, with strong collaboration

with the Primary Standards Laboratory at Sandia National Laboratories (SNL)

A comparison of primary leak standards between laboratories, using two

sintered metal leaks as transfer standards, gave agreement at the „ 1% level

using helium, nitrogen and argon over the leak rate range from mid 10" 11 to

mid 10" 9 mol/s [2]. The primary leak standard used by SNL for this

intercomparison was their "PAV" system, which differs in design philosophy

from the NIST standard [6]. This data is designated NBSL1 in figure 19.

An additional intercomparison with SNL, using a helium permeation leak

(NBSL13) with nominal leak rate 1.3x10" 12 mol/s, gave results that differed by

9.3% (SNL value was higher). While this difference is relatively large, at

that low a flow rate the uncertainties asociated with the NIST Primary Leak

Standard are also large, and yet the values agree well within their combined

uncertainties (the SNL uncertainty is also ±10% at this leak rate). This data

is presented in figure 19, which summarizes such intercomparisons.

32
International Intercomparisons

While there have not been any international round robins for NIST to

participate in since the leak program began in 1984, a round robin sponsored

by the Commission of the European Communities, Community Bureau of Reference

(BCR) in 1982 resulted in the calibration by several European national

laboratories of a variety of leaks, including at least two helium permeation

leaks[7]. After the round robin, these leaks were put in safe storage, but

were made available to the participant laboratories for selected

intercomparisons. One of the participant laboratories, which requested

anonymity, made these two permeation leaks available to NIST for purposes of

intercomparison of the measurement capabilities of the two laboratories.

These leaks were assigned NIST identification numbers NBSL20 and NBSL23, and were subsequently calibrated on the NIST Primary Leak Standard. The NIST

data, referenced to 23 °C, was compared to the calibrations by the European

laboratory. The results are presented in figure 19. The European laboratory

calibration of NBSL20, with a nominal leak rate of 3. 3x10" 11 mol/s, differed

from the NIST value by 1.9%, while the calibration of NBSL23, at the lower

nominal leak rate of 4. 2x10" 12 mol/s, differs from the NIST value by 4.0%.

Both of these measured differences are well within the combined estimated

total uncertainties (3a) of the two laboratories (approximately ±10% for each

laboratory)

33
7 . FUTURE

There are several areas in which to concentrate future research activities

associated with the NIST Leak Calibration Service. First, there is

considerable industry interest in having NIST extend the lower end of the

service at least another 4 decades, to 10" 15 mol/s (2x10" 11 std cc/s) or below, at better than the ±10% uncertainty level. At the other end of the

range, there is some outside interest in extending the upper flow rate limit

of 10" 8 mol/s. While the helium permeation leak remains, by far, the type of

leak most requested for calibration, occasional inquiries for services for

leaks emitting other gases warrant consideration. Another area which is

receiving immediate attention is the Leak Comparator System (LCS) , which will

be upgraded with a newer version using a stable residual gas analyzer to

replace the relatively noisy (electronically) helium leak detector.

The highest priority of the research activities discussed above is the

extension of the low flow rate end of the present helium permeation leak

calibration service at improved uncertainty levels. The accepted industry

norm for the uncertainty associated with a commercially available calibrated

leak is ±10%, irrespective of the leak rate. As the uncertainty associated

with the calibration of helium permeation leaks using the present NIST

equipment reaches this level at 10" 12 mol/s, a NIST service offered at this

flow rate would not allow manufacturers to transfer the ±10% uncertainty level

to their customers, due to the increased uncertainties that they would have to

add as part of their calibration process. While the performance limits of the

flowmeters at the lowest flow rates seem to have been reached, it may still be

possible to reduce the lowest leak rate offered in the calibration service

without constructing a new primary standard. This may best be accomplished by

assembling a group of 10 or more helium permeation leaks with leak rates that

are very nearly equal (at the 10" 12 mol/s level), and measuring the leak rate

of the entire assembly of leaks at one time using the Primary Leak Standard

(PLS) , as suggested by Rangan [8]. By separately measuring the ratio of leak

rates from the various leaks to each other, it would then be possible, with a minimum of additional uncertainty, to ascertain their individual absolute leak

rates as the appropriate ratio of the measured total. Such a program is

receiving serious consideration.

Providing calibration services for gases other than helium implies

calibrating other types of leaks besides permeation, which would require

intensive evaluation programs of the stability, repeatability, etc. of these

leak types. Some preliminary investigations of sintered and capillary leaks

have already been performed [2,4], and further studies are planned.

At present, all customer leaks sent in for calibration are first installed

on the LCS to determine the temperature coefficient, and to otherwise check

the suitability of the leak before installing it on the PLS. If the

"standard" leak against which the customer leak is compared on the LCS were

also calibrated, the entire calibration of the customer leak could be

completed on the LCS with minimal additional uncertainty, freeing up the PLS

for other measurements. With the advent of the new LCS, a goal is to

calibrate (on the PLS) either an ensemble of closed-reservoir leaks, or a few

variable backpressure leaks, so that the entire customer leak calibration

34
service can be performed on the new LCS. This will make the process more efficient in several ways, reducing the cost per calibration of an individual

leak.

8 . ACKNOWLEDGMENTS

The authors would like to acknowledge the major contributions of Drs . K.E.

McCulloh and C.R. Tilford in the conception and design of this standard. We

also thank Mr. D.F. Martin and Mr. B. Dove for their efforts in the

manufacture and assembly of many of the components involved, and Mr. F. Long

for his efforts in designing and maintaining the electrical components.

Special thanks are extended to Mr. T. Moss of Sandia National Laboratories for

permission to reprint his conversion table for leak rate units in Appendix A.

35

9 . REFERENCES

[1] S. Dittmann, "High Vacuum Standard and Its Use," U.S. Government

Printing Office, NIST Special Publication 250-34 . 31 (1989)

[2] R.W. Hyland, CD. Ehrlich, C.R. Tilford and S. Thornberg, "Transfer

Leak Studies and Comparisons of Primary Leak Standards at the National

Bureau of Standards and Sandia National Laboratories,"

J.Vac.Sci.Technol. A 4, 334 (1986)

[3] K.E. McCulloh, C.R. Tilford, CD. Ehrlich and F.C Long, "Low-range

Flowmeters for Use with Vacuum and Leak Standards," J.Vac.Sci.Technol.

A 5, 376 (1987)

[4] CD. Ehrlich, S.A. Tison, H.Y. Hsiao and D.B. Ward, "A Study of the

Linearity of Transfer Leak Standards and a Helium Leak Detector,"

J.Vac.Sci.Technol. A 8, 4086 (1990)

[5] L. Lieszkovszky , A.R. Filippelli and C.R. Tilford, "Metrological

Characteristics of a Group of Quadrupole Partial Pressure Analyzers,"

J.Vac.Sci.Technol. A 8, 3838 (1990)

[6] M.V. Iverson and J.L. Hartley, "Methods for Calibration of Standard

Leaks," J. Vac. Sci. Technol. 20, 982 (1982)

[7] D. Gould, "Intercomparison of the Calibration of Helium Leaks for Use

in Leak Detection," Commission of the European Communities EUR 8325 EN,

(1982)

[8] K. Rangan, Lockheed Missiles and Space Company, Presented at the

Standard Leak Calibration Workshop, Gaithersburg, Maryland, 1987

[9] T.A. Moss, "Conversion Tables for Pressure and Leak Rates,"

J.Vac.Sci.Technol. A 5, 2962 (1987)

[10] CD. Ehrlich, "A Note on Flow Rate and Leak Rate Units,"

J.Vac.Sci.Technol. A 4, 2384 (1986)

[11] M. Knudsen, "Die Gesetze der Molekularstromung und der inneren

Reibungsstromung der Gase durch Rohren," Ann. Physik 28, 75 (1909) and

"Die Molekularstromung der Gase durch Offnungen und die Effusion," Ann.

Physik 28, 999 (1909)

[12] M. von Smoluchowski , "Zur kinetischen Theorie der Transpiration und

Diffusion verdunnter Gase," Ann. Physik 33, 1559 (1910)

[13] S. Dushman, "The Production and Measurement of High Vacua," Gen.

Electric Rev. 23, 493 (1920)

[14] 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)

37
[15] J.H. Dymond and E.B. Smith, "The Virial Coefficients of Gases," Oxford

University Press, copyright 1969

[16] J.F. O'Hanlon, "A User's Guide to Vacuum Technology," J. Wiley & Sons,

copyright 1980

38
10. BIBLIOGRAPHY

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

consult the following.

Units

"Standardization and Temperature Correction of Calibrated Leaks," CM.

Soloman, J. Vac. Sci. Technol. A 4, 327 (1986)

Leaks

"The Modeling of Standard Gas Leaks," J.L. Chamberlin, J . Vac . Sci . Technol . A 7,

2408 (1989)

"Diffusion Leak Artifacts as a Secondary Standard for Gas Flow," W. Jitschin,

G . Grosse and D. Wandrey, Vacuum 38, 883 (1988)

Rarefied Gas Flow :

"The Flow of Highly Rarefied Gases," A. Venema, Phillips tech. Rev. 33, 43

(1973)

Texts and Handbooks

"Nondestructive Testing Handbook, Second Edition; Volume 1, Leak Testing,"

R.C. McMaster ed. , published by American Society for Metals, copyright 1982

by American Society for Nondestructive Testing, Inc.

"Vacuum Manual," L. Holland, W. Steckelmacher , J. Yarwood, E.&F.N. Spon Ltd.,

London, copyright 1974

"Scientific Foundations of Vacuum Technique," S. Dushman, John Wiley & Sons,

New York, copyright 1962

"Dictionary of Terms for areas of Science and Technology served by the

American Vacuum Society (second edition)," H.G. Tompkins ed. , published for

the American Vacuum Soiciety by the American Institute of Physics, copyright

1984

"Vacuum Technology ( second , revised edition)," A. Roth, North-Holland

Publishing Company, copyright 1982

"Ultrahigh Vacuum Practice," G.F. Weston, Butterworth & Co. Ltd., copyright

1985

39
Flowmeter

Nfm

Vacuum

Chamber

Upper

Chamber

P,T

Lower

Chamber

Turbo

Pump

Leak Manifold

Leak

, Partial

Lj—Urr Pressure Gage

Orifice

Figure 1. Schematic drawing of the NIST Primary Leak Standard, showing the

major components. The pressure indication (P) in the vacuum chamber (at

temperature T) caused by gas flow (rate NL

) from the leak is matched by flow

(rate NFM ) from the flowmeter. The flow rate NFM is then measured using the

flowmeter

40
41
LEAK CALIBRATION THROUGH UPPER CHAMBER

Z5£ 35

Step 3

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Figure 3. Valving sequence for measuring leak rate of unknown leak by flowing

gas from flowmeter into the upper chamber of the main vacuum chamber.

42
LEAK CALIBRATION THROUGH LOWER CHAMBER

331

Figure 4. Valving sequence for measuring leak rate of unknown leak by flowing

gas from flowmeter into the lower chamber of the main vacuum chamber.

43
Figure 5. Valving sequence for measuring flow rate ratio.

44
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60
11. APPENDICES

APPENDIX A

USE AND CONVERSION OF UNITS OF FLOW RATE AND THROUGHPUT

To discuss the differences between flow rate and throughput units, consider

the simple experimental apparatus in figure 20, where a cylindrical volume is

divided by a plate with a small orifice in it, a tightly-fitting piston is

inserted in one end, and the other end is attached to a vacuum pump. While

this system is quite simple, it can be used to discuss many of the factors

which should be considered when performing gas flow rate measurements. Let an

ideal gas at pressure P and temperature T fill the reservoir side of the

cylinder. As gas effuses through the orifice and is pumped away, let the

piston be moved at a rate that maintains the pressure in the reservoir at P. The equation of state of the gas at each instant of time is

P V = N R T, (Al)

where N is the number of moles of gas contained in the volume V, and R is the

universal gas constant (numerically equal to 8.31441 Joule mol-1 K" 1 or 82.057

atm cm3 mol" 1 K" 1

) . If dN moles of gas are passing through the orifice every

dt seconds, giving the molar flow rate Q,,, = dN/dt, then, to keep P constant,

the piston must be moved at a rate such that the volume change per unit time

is given by

dV/dt = [(R T) / P] (dN/dt) = [ (R T) / P] Qm. (A2)

It is assumed that the process is slow enough and that the heat capacity of

the cylinder walls is great enough that the process is isothermal. Eq (A2) can be rewritten as

Qm

ee dN/dt = [P / (R T)] (dV/dt) = [P (dV/dt)] / (R T)

= Q / (R T) , (A3)

where Q [=P (dV/dt) ] is frequently called the "throughput" of the gas. Thus

while the number of moles of gas passing through the orifice per unit time

(Q,,,) is an explicit function of the gas temperature, the throughput (Q) is

not

For example, if the pressure P is equal to one atmosphere (1 atm) and the

volume rate of change necessary to maintain that pressure is one cubic

centimeter per second (1 cm3 s~

1

)

, then the gas throughput is equal to

A-l
Q = P (dV/dt) = (1 atm) (1 cm3 s" 1

) = 1 atm cm3 s" 1

, (A4)

independent of the temperature of the gas. If the gas temperature is 273.15 K

(0 °C), the molar flow rate of gas can be computed using eq (A3) as

Qm = Q / (R T)

= (1 atm cm3 s" 1 )/ [ (82 . 057 atm cm3 mol" 1 K" 1

) (273.15 K)

= 4.462 x 10" 5 mol s" 1

. (A5)

If the temperature of the gas is 296.15 K (23 °C), then the molar flow rate of

gas can again be computed, using eq (A3) , as

Qm = Q / (R T)

= (1 atm cm3 s" 1 )/ [ (82 . 057 atm cm3 mol-1 K" 1

) (296. 15 K)

= 4.115 x 10" 5 mol s" 1

. (A6)

Thus, while it is frequent practice to interchange the words 11 throughput" and

"flow rate," this example illustrates clearly that, for the same throughput of

1 atm cm3 s" 1

, the actual flow rate of gas will have different values,

depending on the temperature of the gas

If throughput and flow rate are not the same quantity, we may ask if

throughput has any physical significance. From the example above, we see that

the quantity Q called throughput is actually the amount of work per unit time

(or power) that must be done by the piston on the gas to maintain constant

pressure P in the reservoir as gas effuses through the orifice, and that this

quantity is independent of temperature. For isothermal conditions, this

energy is transported across the orifice in the form of kinetic energy of the

gas molecules.

Dual usage of the word throughput, on the one hand defined by Q = d(PV)/dt,

and on the other hand meant to be synonymous with leakage rate, has caused

considerable confusion in the literature over the years, and has led to the use of the words "throughput units" or "PV units" when the word throughput is

meant to be synonymous with gas flow rate. The way that PV units or throughput units are associated with flow rates can be seen using the example

above. For the conditions used to compute the flow rate in eq (A5) , the

throughput is 1 atm cm3 s" 1

, the temperature of the gas is 0 °C, and the flow

rate is 4.462 x 10" 5 mol s" 1

. The PV unit or throughput unit that is

associated with this flow is 1 atm cm3 s" 1 @ 0 °C. Similarly, for the

conditions used to compute the flow rate in eq (A6) , the throughput is still 1 atm era

3 /s , the temperature of the gas is now 23 °C, and the flow rate is now

4.115 x 10" 5 mol/s. The PV unit or throughput unit that is associated with

A-2
this flow is 1 atm cm3 s" 1

(3 23 °C. It is important to note that PV units or throughput units are not really units at all, in the sense that on their own

they do not have clear dimensions: they are merely expressions of convenience

that are, in fact, defined by the flow rates with which they are associated.

Thus, an equivalence relationship can be established

1 atm cm3 s" 1 @ 0 °C = 4.462 x 10-5 mol s~

1

. (A7)

From eqs (A5) and (A6) it can be seen that this definition can be extended to

other PV units or throughput units at arbitrary temperature according to:

1 atm cm3 s" 1 @ Tx (K) = ( 27315/Tl (K) ) • 4 . 462x10" 5 mol s" 1

. (A8)

Generalizing even further, then, to move from one PV unit or throughput unit

to another, eq (or 'equivalence') (A8) can be used to derive the expression

1 atm cm3 s

-

@ T1 (K) = [T2 (K) /T1 (K) ] atm cm3 s" 1 @ T2 (K) . (A9)

Equations (A7) , (A8) , and (A9) then form the basis on which conversions to

other PV units or throughput units, such as Pa m

3 s" 1 @ T3 (K) , atm cm3 s" 1 @

(K) , Torr 1 s" 1 @ T5 (K) , etc., can be performed. Table Al lists conversion

factors for various units[9]. The following example illustrates such a conversion.

Let us say that for the gas flow rate measured under the conditions

corresponding to eq (A5), we would like to know the flow rate in terms of the

PV/throughput unit Pa m

3 s" 1 @ T3 (K) . That is, we would like to find A3 in

A3 {Pa m

3 s" 1 @ T3 (K)} = 1 atm cm3 s" 1 @ 0 °C. (A10)

The first step is to perform the conversion between atm cm3 s" 1 and Pa m

3 s" 1 which, from table Al , is

1 atm cm3 s" 1 = 0.101325 Pa m

3 s" 1

, (All)

Note that table Al must be used with some caution. The units in the top

left quadrant, which is highlighted with a heavy black line, are all

throughput units, and the conversions between them are independent of

temperature. Alternatively, the units outside of the top left quadrant are all flow rate units, but are also independent of temperature (except for "ATM

STP cm3 /s", where the temperature is referred to in the unit). When the

expression "@ 0 °C" is added to the throughput units in the upper left

A-3
quadrant, as the Table Al caption indicates is intended, the throughput units can then be regarded as flow rate units, and conversion of flow rate units

across the heavy black line is then allowed. Substituting eq (All) into eq

(AlO) then gives

A3 {Pa m

3 s" 1 @ T3 (K)} = (0.101325 Pa m3 s -1

) @ 0 °C (A12)

The next step is to convert to the desired temperature T3 (K) on the right hand

side of eq (A12) , using eq (A9) in the more generalized form

Q @ TX (K) = [T2 (K) / T X (K)] Q @ T2 (K) , (A13)

where Q is any throughput unit, such as atm cm3 s" 1

, Pa m

3 s" 1

, etc. We get

A3 (Pa m

3 s' 1 @T3 (K)) = (0 . 101325) •

3 (K)/273 . 15 , (A14)

so that A3 is

A3 = (0.101325) • [T3 (K)/273. 15] . (A15)

This example can then be taken one step further to handle the most general

conversion from QA @ TA to Q3 @ T3

, that is

AA {QA @ TA

) = A3 {Q3 @ T3 }, (A16)

where Q3 and QA are any two throughput units, related by the temperatureindependent conversion factor /x 4 3

Q« = M«,3 Q3

• (A17)

We wish to find A3 in terms of the other known parameters. Following steps

virtually identical to eq (A10) through (A15) , we get

A3 = A4 /v.* T3W / TA (K). (A18)

For example, suppose we wish to convert 1x10" 7 atm cm3 s" 1 @ 0 °C to Torr 1 s _1 @ 23 °C

A-4
1x10" 7 atm cm3 s" 1 @ 0 °C = A3 Torr 1 s" 1 @ 23 °C. (A19)

Then, in eq (A16) , AA = 1x10" 7

, QA = atm cm3 s" 1

, and TA = 0 °C = 273.15 K, Q3 = Torr 1 s" 1

, and T3 = 23 °C = 296.15 K. From Table Al , the conversion factor

in eq (A17) is 1 atm cm3 s" 1 = (0.760) Torr 1 s" 1

, so that 3 = 0.760.

Using eq (A18) we obtain

A3 = lxlO" 7

• (0.76) -296.15/273.15 = 8.24xl0" 8

, (A20)

so that

1x10" 7 atm cm3 s" 1 @ 0 °C = 8. 24x10" 8 Torr 1 s" 1 @ 23 °C. (A21)

From eq (A7) , this is equivalent to 4.462x10" 12 mol s" 1

.

From this discussion it should be clear why a unit such as moles per second

(mol s

_1

) is chosen as the recommended unit for flow rate or leakage rate, as opposed to a throughput unit. Other possibilities, such as kilograms per

second, were also considered, but have the drawback that in comparing flow

rates from leaks emitting different gas species or mixtures, it is necessary

to know the relative molecular weights. Another popular leak rate unit is the

standard atmosphere cm3 s" 1

. However, there is an opportunity for ambiguity

in stating the standard conditions in temperature because of the availability

of more than one accepted standard, with 0°C, 25 °C, 20 °C, etc. in use. Since "standard atmosphere cm3 s" 1 " requires knowledge of the "standard"

temperature, the calibration temperature and the usage temperature, further

confusion is possible [ 10 ] . Therefore, the recommendation of use of the unit

moles per second is further strengthened. This use reduces the problems of

ambiguity and confusion, since the originator of the measurements must

immediately incorporate knowledge of the temperature T into the appropriate

equation in order to express the flow rate in mol s" 1

. Likewise, the user of

a leak, given the temperature dependence of the leakage rate in mol s" 1

, can readily convert data to the applicable units during use knowing the

temperature of the measurement process.

A-5
A-6
APPENDIX B

GENERAL THEORY OF GAS FLOW IN VACUUM SYSTEMS

The flow of highly rarefied gases through various components of a vacuum

apparatus has been a topic of serious interest since the early 1900' s. The

works of Knudsen [11], Smoluchowski [12], Dushman [13] and Clausing [14] on

the flow of such gases through tubes of various lengths and shapes are still

of current interest and use today. Derivation of expressions which adequately

quantify gas flow *rate in the "transition region" between molecular and

viscous flow, based on first principles of the kinetic theory of gases, remain

elusive. The need still exists to make accurate measurements of gas flow

rates in these regions to better define and understand the physical parameters

that are most important in describing this flow.

Fundamental to any understanding or measurement of the flow rate of gases is a clear definition of the system through which the gas will be moving, the

forces (mechanical or otherwise) which cause the gas to move, the equation of

state of the gas under conditions of equilibrium and the energy flow in the

system. A system capable of controlled gas flow is shown schematically in

figure 21, where a cylindrical volume is divided by a plate with a small

orifice in it, and tightly-fitting pistons are inserted into either end.

While this system is quite simple, it can be used to discuss many of the

factors which should be considered when performing gas flow rate measurements.

Consider first the conditions where gas at pressure Pj^ initially fills the

right volume Vx (= Xx

- A, where X1 is the linear distance between the face of

the piston and the plate with the orifice, and A is the cross sectional area

of the cylinder) , the left volume V2 is evacuated, and the entire system is

maintained at temperature T. We wish to determine the net flow rate of gas

through the orifice, as a function of time, when the pistons are first held in

a fixed position. It is frequently the case that the equation of state of the

gas under equilibrium conditions can be represented to sufficient accuracy by

the ideal gas law:

P-V = N-R-T (Bl)

where P is the equilibrium pressure of the gas, V is the volume in which the

gas is contained, N is the number of moles of gas contained in the volume, R

is the universal gas constant (= 8.31441 Joule mol" 1 K" 1

, see table 1 for

conversion to other units) and T is the absolute temperature of the gas and

the walls of the containment volume. For the highest accuracy it is necessary

to replace eq (Bl) with a virial expansion:

P/(kB -T) = n + B2 (T)-n2 + B3 (T)-n3 + ... (B2)

where n (=N-NA /V) is the molecular density of gas, kB is the Boltzmann

constant (=R/NA =1 . 381E-23 Joule K" 1 where NA is Avagadro's number = 6.022E23

B-l
mol" 1 ), and the coefficients Bt are the "virial coefficients", which are available in the literature for many gases (e.g., [15]). As an example, for

helium at room temperature and atmospheric pressure, the correction term

corresponding to the second virial coefficient is on the order of 10 to 100

parts per million. For all of the work done to date in conjunction with the

NIST Leak Service, the accuracy afforded by eq (Bl) is completely adequate,

and virial corrections are ignored.

At time t=0, then, the molar density of gas in volume 1 can be calculated

from the equation of state given in eq (Bl):

Nx (t=0) Pi(t=0)

V1 R-T

(B3)

As time progresses, gas atoms or molecules from volume 1 will pass through the

orifice into volume 2, and some may return from volume 2 into volume 1. A

good measure of the net rate of flow of molecules from volume 1 into volume 2 would then be the rate of change of the molecular (or molar) density of

molecules in volume 1 or volume 2 (assuming insignificant adsorption of

molecules to the walls) . Since the total number of molecules must remain

constant at each instant in time, N t +N2 = N1 (t=0), a measure of the density in

one of the volumes is sufficient to determine the density in the other. The

actual rate at which the gas densities change depends on several factors, such

as the type of gas, the initial pressure (P1 (t=0)), the temperature, and the

size of the orifice. The first three factors determine the mean free path (A)

of the gas

A « l/(n-a) (B4)

where n is the molecular density of the gas and a is the "cross sectional

area" of the atom or molecule. Comparison of A with the diameter of the

orifice (D) gives an indication of the functional dependence of the net rate

at which gas atoms or molecules will move from volume 1 to volume 2 (A/D is

sometimes referred to as the Knudsen number)

1) A/D » 1 molecular flow The net flow rate is found to depend on the

pressure differential across the orifice

according to (dN/dt) = [C/(R-T) ]

• (Pj -P2 )

where C is referred to as the conductance of

the orifice, and is a function of the orifice

geometry but not the gas pressure. For a particular model, such as the kinetic theory

of gases, the value of C can be calculated.

2) A/D « 1 viscous flow The net flow rate is in general a complicated

function of pressure, gas type, etc., so that

the conductance is highly pressure dependent.

Hydrodynamic flow theory, utilizing the

Navier-Stokes equations, is needed. For

B-2
3) A/D ~ 1

certain geometries other than an aperture it

is possible to derive explicit expressions,

such as Poiseuille flow through a 'long' pipe.

transition flow The net flow rate is in general a function of

several parameters, and adequate theories are not well developed.

While no explicit formulas are presented here for viscous or transition flow

(many widely available textbooks discuss such relationships for a variety of

geometries [e.g., 16]), it is almost always the case that net flow rates are greater in these flow regimes than in the molecular flow regime, due to the

higher pressures usually involved, and due to the mechanism of interaction of

the gas molecules. It is worth noting that for purposes of estimation, the

mean free path of many simple gases is on the order of 10" 5 cm at atmospheric

pressure

Returning to our discussion of the system in figure 21, for sake of

calculational simplicity we will assume that the diameter (D) of the orifice

is such that the flow is molecular. Then the equation describing the net flow

rate through the orifice, resulting in a loss of molar density in volume 1 and

an increase in molar density in volume 2 is:

d(Ni)

dt C-CPi-PjjVCR-T) (B5)

and the equation representing the conservation of total number of molecules

is

Nj + N2 = constant = Nx (t=0) (B6)

Substitution of eq (B6) and eq (Bl) into eq (B5) results in the equation: —d(Ni) C (Vj + V2 ) = —2 [Ni (t=0)

- N

* — (B7)

with solution:

Ni(t=0)

t / T (B8)

where r = V1 V2 /[C(V1 +V2 )] (B9)

B-3
The rate at which gas leaves volume 1 (or enters volume 2) is then:

dNj dN2 N^t-0) C - e' t/T

. (BIO) dt dt Vx

These results demonstrate that even for such a very simple gas flow system the

flow rate of the gas through the orifice is constantly changing, making flow

rate measurement generally complicated. However, by designing systems such

that V2 is large compared to V1

, or by measuring only over times that are short compared to the time constant r, it is possible to perform 'pressure

rate of rise' measurements to determine either the 'instantaneous' or 'time

averaged' gas flow rate to a reasonable degree of accuracy.

It is in general much more desirable, both for convenience in measurement

and for achievable accuracy, to establish a steady-state gas flow past a particular region of a vacuum system, and measure the (constant) gas flow rate

a multiple number of times. Returning to the system in figure 21, this can be

accomplished by now allowing the pistons to be moved while maintaining a constant pressure differential across the orifice. Assuming the same initial

conditions as above (dNj^/dt = [N x (t=0) •C/V1 ] ), the piston on the right hand

side must be moved at a rate:

dXx R-T dN x dT = pIS • dF (B11 >

in order to maintain constant pressure P x

. However, as the initial pressure

on the left hand side was zero, the piston on that side would have to move at

'infinite' speed to maintain that condition. Since this is impossible, the

next best solution is to provide a means of exhausting the gas from the region

using a vacuum pump. Since vacuum pumps have finite pumping capabilities and

are naturally limited by the gas dynamics, it is necessary to tolerate a slight pressure (and pressure differential) in the region to the left of the

orifice. For a pumping system with pumping speed S (with units of 1 s~

1

) in

the pressure region of interest, the pressure that will be developed in region

2 is given by:

dNi R-T

p

* Tt—r • (B12)

Note that even if the pressure ? 1 in eq Bll is such that the flow through the

orifice is not molecular, eqs Bll and B12 are still valid, but the conductance

C is then pressure dependent.

B-4
APPENDIX C

A note on flow rate and leak rate units

Charles D. Ehrlich

Centerfor Basic Standards. National Bureau ofStandards. Gaithersburg. Maryland 20899

(Received 31 October 1985; accepted 28 April 1986)

The confusion in the literature and in the laboratory surrounding the terminology and units of gas

flow rates, particularly as applied to calibrated leak artifacts, has prompted this discussion of leak

rate units. Special attention is paid to conflicting usages of the term "throughput," and how this frequently leads to the loss of crucial information about the gas temperature and hence the true gas flow rate. The advantages of expressing leak rates in "mol/s," avoiding the complications of both the explicit mention of temperature in the unit and the need for agreement on "standard"

temperature and pressure, are also discussed.

Upon initiation of a leak standards program at the National Bureau of Standards, we observed that the choice and proper

use of units in which to express the flow of gas from a leak

artifact and through a vacuum system are historically subjects of much confusion, stemming from problems with several of the definitions and usages of units in vacuum technol- ogy in general. While not attempting to cover the broadei

issues, we will discuss the various sources of confusion which

apply to the immediate area of gas flow rate and leak rate

units, and point out how use of the unit moles/second avoids most of the problems with the more commonly used units. We will show how different usages of the term "throughput" and its various associated units are ambiguous, frequently

leading to loss of information about the gas temperature and

hence, the gas flow rate. Other sources of confusion concerning leak rate and gas flow rate units, such as use of "stan- dard" conditions in defining a unit, or the necessity to use multiple temperatures to characterize a leak artifact, will also be discussed. In many instances the errors caused by this confusion are inconsequential, but for high accuracy, high

precision measurements the errors can be quite significant. The NBS Pressure and Vacuum Group intends to use the

unit "mol/s" (moles/second) to report leak rates of cali- brated leak artifacts ( with gas species and temperature of the

leak artifact separately stated), and believes that the rest of

the calibrated leak user community can benefit from using

this unit as well. For calibrated leak artifacts containing gas

mixtures, the unit will be "mol/s" for each of the individual gas species. Looking first at how the common usages of the term "throughput" lead to confusion in the expression of gas flow

rate, consider the definition of "throughput" found in the American Vacuum Society Dictionary of Terms1 (as well as numerous other places in the literature): "throughput—The

quantity of gas in pressure-volume units, at a specified temperature, flowing per unit time across a specified open cross

section." From this definition "throughput" and "gas flow

rate" are inferred by some to be synonomous, and a typical "unit" of "throughput" is "atm cmVs at F, °C." This is

2384 J. Vac. Scl. Technol. A 4 (5), Sep/Oct 1986

most likely the original intent of the word "throughput."

However, the literature also abounds with equations of the type 23 Q = d/dt{PV), (1) where Q is referred to as the "throughput," P is the gas pressure, Vis the containment volume, and (d /dt) indicates the time derivative, but the temperature is not specified. There

are those who argue that it is "understood" that there is an

implicit "at F, °C." Some understand F, to be "room temperature," whatever that may be, others 0 °C. The point here

is that use of the word "throughput," as it is commonly used

to describe gas flow in such an ambiguous fashion, either

results in an ill-defined, implied temperature in the "unit," or encourages the dropping of the temperature from the "unit" altogether, resulting in an incomplete description of

the molar or mass flow rate. That the description is incomplete can be seen from the expression for the molar flow rate

for an ideal gas under isothermal conditions: Qm =Q/(RT), (2)

where Q„ is the molar flow rate, Q '\% defined in Eq. ( 1 ), R is the molar gas constant (R = 8.314 J mol~' K

_l = 82.06 atm cnr mol" 1 K~' = 62.36 Torr 1 mol" 1 K-'),and Fis

the absolute temperature in Kelvins. Loss or misunderstanding of the temperature F subsequently results in either the

inability to calculate or the miscalculation of the molar flow

rate. The use of the unit "mol/s" eliminates this problem,

since the originator of the measurement, who knows the temperature F, must immediately incorporate this knowledge [using Eq. (2) ] to express the flow rate in mol/s. Even when properly used, "units" such as "atm cmVs at F, °C" can be a source of confusion if used to describe leak

artifacts. In addition to the F, in the unit required to calculate mass or molar flow rate, the temperature F2 at which the

leak was calibrated and the temperature F3 at which it is being used must also be known. Under such circumstances it

is very easy for the three different temperatures to become

confused. By expressing the flow rate in mol/s, the possibil2384

C-l
Charles D. Ehrllch: A note on flow rate and leak rate units

ity for confusion is greatly reduced. Another common practice with leak rate units is to ex- press the leak rate in terms of "standard" conditions, such as "standard cm Vs" or "cmVs STP." Unfortunately, there

exist several different usages of "standard conditions." If both the "standard pressure" and "standard temperature"

are not explicitly stated, the units are ambiguous. Occasionally

4 a temperature and/or pressure range will be given for "standard" conditions. The consequences are not trivial for

a helium diffusion leak, where a few degrees change in temperature can result in a few percent shift in the leak rate. Since it is quite unlikely that everyone will suddenly agree on what "standard" conditions are, we suggest that these units be dropped in favor of mol/s, which avoids the problem alto- gether. .To further demonstrate how the term "throughput"

causes widespread confusion, note that the dimensions of

Eq. ( 1 ) are those of [ (force/area) X (volume)/(time) ]. or power, which are not the same dimensions as flow rale di- mensions (mol/time). Accordingly, one occasionally sees in the literature the dimensions of power explicitly ascribed to the word "throughput,"5 illustrating that not everyone au- tomatically infers an implied temperature associated with

Eq. ( 1 ). Strictly speaking, the quantity Q in Eq. ( 1 ) is the power that is required to move a gas at constant flow rate and

temperature across a specified cross section of a vacuum sys- tem, and can be of interest in certain areas of vacuum equip- ment design. ( It is not the additional power that is carried by

the gas across the cross section except in cases of adiabatic

flow.) Thus, for those who use the word "throughput" to mean Q in Eq. ( 1 ) at face value, the dimensions of power are

appropriate. For those who use the word "throughput" to mean Eq. ( 1

) "at a temperature," the dimensions of flow

rate are appropriate. However, it is obviously not appropriate to use the word "throughput" to mean both of these

quantities, since their dimensions are different, a point not

generally recognized. Note that the "unit" "atm cmVs at

r, °C" is an unorthodox unit in the strictest physical and

mathematical sense, since it does not have any well-defined dimensions on its own. It should perhaps be regarded instead

as an expression whose meaning is given by a relationship such as Eq. (2), which has well-defined dimensions of molar

flow rate. Use of mol/s at the outset indicates to the reader

that if the word "throughput" is being used, it is being used

in the sense of a flow rate. Another important consideration is that the unit "mole"

is recognized as the "amount of substance" in the SI system

of units, so that mol/s is the natural SI unit of flow rate. In summary, there are several reasons for preferring the

unit mol/s over several other popular units for leak rate and

gas flow rate. Foremost is that it avoids errors resulting from

the failure to properly specify the temperature in "throughput" units, it also lessens the confusion of multiple temperatures associated with leak artifacts, and it avoids the confusion that sometimes exists with the term "standard"

temperature and pressure. It also clarifies which usage of the word "throughput" is being used. Finally, mol/s is in accor- dance with the SI system of units. Acknowledgments: I would like to thank Richard Hyland

and Charles Tilford for their constructive reading of this note. I would also like to acknowledge the support of the NBS Office of Nondestructive Evaluation.

' Dictionary of Termsfor \ 'acuum Science and Technology, Surface Science, Thin Film Technology. Vacuum Metallurgy, Electronic Materials, edited by Nf. Kaminsky and J. Laflerty (AIP. New York, 1980), p. 69.

"L. Holland. \V. Steckelmacher, and J. Yarwood, Vacuum Manual (E. &

F. N. Spon. London, 1974). P 18. 'A. RoiIi, Vacuum Technology (North-Holland, Amsterdam, 1982), p.67.

J Amcrican Vacuum Society Standards AVS 2.1, 1963 and AVS 2.2. 1968.

'J. F. O'Hanlon. I User's Guide to Vacuum Technology ( Wiley, New York.

1980). p 22.

C-2
APPENDIX I) Low-range flowmeters for use with vacuum and leak standards

K. E. McCulloh, C. R. Tilford, C. D. Ehrlich, and F. G. Long

National Bureau ofStandards. Centerfor Basic Standards. Gaithersburji. Maryland 20X99

(Received 20 October 1986; accepted 28 December 1986) Vacuum pressure standards of the orifice-flow type require known pas flows of 10 '' mol/s (10 ? atm cmVs at 0 °C) and less. Known gas flows can also be used to calibrate "standard" leaks by

comparing the pressures generated when flows from I lie leak and the flowmeter are alternately passed through a constant conductance. Two constant-pressure, piston displacement flowmeters developed at the National Bureau of Standards arc described that can generate flows between 10~ h and 10 " 10 mol/s with an estimated uncertainty of 0.8% to 2%. Comparisons of the flowmeters with alternate calibration techniques, and repeated low-range leak and vacuum gauge

calibrations, have been used to confirm the estimated uncertainty and random errors of the flowmeter.

I. INTRODUCTION

Two areas of vacuum standards require the generation of

very low flows: orifice-flow pressure standards and leak standards. The orifice-flow technique generates a calculable pressure differential by passing a measured flow of gas through a calculated conductance. Reference 1 describes one such standard. The nominal 10 1/s conductance used is typical for this type of device, as is the working range of 10 ' Pa (10 _s Torr) and below. This requires flow measure- ments for different gases with a range starting at 5x 10" 7 mol/s ( 10~ 2 atm em'/s at 0 °C), and extending down three or more decades. Leak measurements cover an even wider

range, and Refs. 2 and 3 describe how the flow from a "stan- dard" leak can be measured by direct comparison with that from a flowmeter. Gas flow rate is defined as the number of molecules or moles of a particular gas species passing through a system

per unit time. A basic gas flow measurement must start with

the equation of state; for the level of accuracy required for these applications the ideal gas law suffices: PV=NRT (1) with the usual convention of fas the pressure, Pas the vol- ume, N the number of moles, R the ideal gas constant, and T

the absolute temperature. As a practical matter, primary

flowmeters are generally realized by varying only the pres- sure or volume, i.e., the molar flow rate is dN/dt= (V/RT)(dP/dt) (2) ordN/dt=(P/RT){dV/dt) . (3) We have chosen to use the latter, "constant pressure" tech- nique as the basis for our design. A constant pressure flow- meter was first used with an orifice-flow pressure standard by Hayward and Jepsen4 and subsequently by several other

experimenters. Their use has been reviewed by Peggs. 5 Basically, constant pressure flowmeters regulate the flow of gas from a small volume through a leak valve into the vacuum

system. The pressure and temperature of the gas in the vol- ume are measured and the gas volume is decreased at a rate

sufficient to maintain a constant pressure. The volume

change is generally accomplished by driving a piston of

376

known cross section into the gas volume through sliding

seals The volume change and flowrate can then be derived from the rate of advance of the piston. A variant of this technique employs a welded bellows as the variable volume

element. We describe here two constant pressure flowmeters. The

first employs a piston with sliding seals and has been in use at the National Bureau of Standards (NBS) for several years over the range from 10""'' to I0~" mol/s (2xlO~ ? -2 X

10 7 aim cmVs at 0 °C). The second uses an all-metal gas system employing a hydraulically driven welded bellows as a variable volume. Its range extends at least two decades lower

than that of the first although its performance at the lowest

flows has not yet been fully analyzed.

II. DESCRIPTION AND OPERATION OF PISTON

FLOWMETER

The piston and sliding seal ("piston") flowmeter is pre- sented schematically in Fig. 1 , and an enlargement of a piston

assembly is shown in Fig. 2. The two pistons of different diameter ( 1 in. and 1 cm) allow for a wider range of flow

rates than a single piston. The pistons are tungsten carbide or chromium plated steel wire gauges, supplied with a dimensional tolerance of 0.0005% along their lengths. They are sealed by Teflon rings with an L-shaped cross section, backed up by rubber O rings, as shown in Fig. 2. All other

seals in the system are metal, including the vacuum valve

closures. The O ring behind the Teflon acts solely as an elastic element to maintain the critical sealing force—the seal must have a minimal leakage but still allow free passage of

the piston. A second ring of the same design, the top one in Fig. 2, serves to maintain the alignment of the piston along

its axis of motion. A bypass channel vents the volume

between rings to the ballast volume. This minimizes the ef- fects of seal leakage by maintaining a guard pressure on the back side of the seal close to the operating pressure of the flowmeter. A clamp at the end of the piston and a coupling

rod, which allows for radial misalignment, connect the pis- ton to an external micrometer screw through a welded bel- lows. The bellows serves to seal the guard pressure. The mi- crometer screw is connected to the linkage by a bearing

J. Vac. Scl. Technol. A 5 (3), May/Jun 1987 0734-2101/87/030376-06501 .00 376

D-l
377 McCulloh el at. : Low-range flowmeters (or use with vacuum and leak standards 377

Fro. 1. Schematic of the constant pressure

piston flowmeter. Two different size pis- tons are included to extend the range. The

turbomolccular pump provides a low ref- erence pressure for the 10-Torr differential capacitance diaphragm gauge.

NBS Gas Piston Flowmeter

which allows free rotation of the screw but maintains a tight

axial coupling.

During operation the micrometer screw for the piston in use is advanced by a stepping motor at a rate that maintains a constant pressure in the flowmeter. A feedback circuit operating on the output of the 10-Torr differential capacitance

To O.M*-wit.*l PieuuH S-nvy

Fig. 2. Detail of the variable volume, including piston seal design and drive mechanism. All seals are metallic except for the sliding seal, lo minimize

leakage past the seal, a guard pressure close to the pressure in the variable volume is maintained on the back side of the seal by the line connected to the

ballast manifold.

J. Vac. Scl. Technol. A, Vol. 5, No. 3, May/Jun 1987

diaphragm gauge (CDG) connected between the reference volume and the variable volumes controls the motor. The

variable volumes, reference volume, and CDG are contained

in a common thermally insulated area to minimize temperature induced pressure changes.

The pressure in the reference volume is measured with 10- and 1000-Torr CDG's calibrated against a primary stan- dard. 6 As discussed below, instabilities in these gauges constitute the largest single source of error. Gas flow to the vacuum chamber is regulated by an all- metal variable leak valve selected for stability and cleanliness. A 8000-cm 1 ballast tank allows a stable flow to be maintained for extended periods so that pressures in the vacuum

chamber can be stabilized to within 0.1% before the flow is measured. After equilibration the pressure drops at a rate of 0.3%/h or less. Gas purity is monitored with a residual gas analyzer in the vacuum chamber. At the highest flowrates

the indicated concentrations of residual gases are less than 0.01% of the test gas. It has not been determined whether

these indicated impurities are in the original gas source or

are generated in the gas analyzer ion source. In either case, they are below the level of concern. At lower flow rates resid- ual gases become more important, presumably because of

outgassing. In particular, at the lowest flows the indicated concentration of hydrogen, probably evolving from stainless-steel components, may exceed that of the test gas. A trapped mechanical rough pump and a 50 1/s turbomolecular pump allow the system to be evacuated before the test gas enters the system. The flowmeter is not baked for fear of damaging the elastomer sliding seals. The turbopump also provides an absolute reference pressure for the 10-Torr CDG and permits the zero setting of the 1000-Torr CDG.

Before each use, the system is pumped with the turbomolecular pump to a pressure < i0~ 4 Pa, measured with a hot

filament ionization gauge. The piston that is not being used is driven fully into the flowmeter to minimize the variable vol- ume. The tut hopump is then valved from the system and gas of the desired species is admitted to the variable volumes.

D-2
378 McCulloh etal. : Low-range flowmeters (or use with vacuum and leak standards 378

ballast tank, and reference volume. The flowmeters have

been operated with hydrogen, helium, neon, nitrogen, and

argon. The system pressure is brought up to the value re- quired to generate the desired flow in the vacuum system. Typical fill pressures vary from 10s Pa for a 10 '' mol/s flow

to 10 Pa for 10" " mol/s. The variable leak valve is preset so

that about 1000 s is required for the piston to advance over

its 2.5-cm range. This procedure is found to give the smoothest operation of the piston drive system. The variable leak valve is typically set at least 5 h before operation to allow any

creep in the valve to settle out. After filling the flowmeter

with gas, the gas flow to the vacuum chamber is maintained

until the pressure in the vacuum chamber and the absorption of gas in the sliding seals have equilibrated. Equilibration times of 30 to 60 min are typical. When equilibrium is achieved, valve A between the refer- ence volume and the ballast tank is carefully shut so that there is negligible pressure differential across the CDG

between the reference volume and the variable volumes. Valve B between the variable volumes and the ballast tank is then shut, and the pressure in the variable volumes starts to drop as gas flows only from this relatively small volume. The

drop in pressure in the variable volumes with respect to the reference pressure is detected by the CDG, whose output

voltage is sent to a proportional motor control unit, which

causes the stepping motor to turn, advancing the piston. The

servo system maintains the differential pressure at less than 0.1% of the reference volume pressure for the lowest flow

rates, and considerably lower at higher flow rates. The mi- crometer screw is allowed to travel 20 revolutions, advancing the piston 2.54 cm, with the elapsed time being logged

after each revolution. After each run the variable volumes

are again connected to the ballast volume, the piston retracted, and the cycle is ready to begin again.

III. DESCRIPTION AND OPERATION OF THE

BELLOWS FLOWMETER

The hydraulically driven bellows ("bellows") flowmeter

is shown schematically in Fig. 3. The basic principle of operation and much of the design are the same as those of the

piston flowmeter. However, in this case the variable volume

is a welded bellows, providing a bakable all-metal gas system

I hat is virtually free of leaks and adsorption effects. Base

pressures after baking are about 10

" 6 Pa. This permits operation at lower fill pressures and correspondingly lower flow

rates. However, the volume change of the bellows is in all likelihood not linear with displacement. This problem is overcome with a technique used at the Electro Technical Laboratory in Japan.

7 The bellows is coupled to a piston by a sealed hydraulic reservoir surrounding the bellows. Care is taken lo eliminate gas from the hydraulic reservoir so that as the piston is advanced through a sliding seal into the reser- voir the volume of the bellows must decrease by a corre- sponding amount. Two pistons are used of the same size and

type as in the other flowmeter. The sliding seals are of the same design but now must only seal oil. The bellows has a nominal cross section of 1 3 cm 2 and stroke of 2 cm. The variable volumes, reference volume, and oil reservoir are contained in a common insulated aluminum block to minimize temperature gradients. The "dead" volumes in both the variable volumes and oil reservoir have been mini- mized. A spinning rotor gauge (SRG) thimble and ball are connected to the variable volumes in anticipation of possible use

for flowmeter control at very low fill pressures. As shown in Fig. 3, the bellows is extended by a variable weight connected to the bellows through a small-diameter

sliding seal. The weight used is such that an oil pressure

NBS OIL/BELLOWS FLOWMETER

Flo 3. Schematic of the constant pressure bel- lows flowmeter. The variable volume is a welded bellows coupled to two different diameter pistons by a sealed oil reservoir. The pis- tons are advanced by a micrometer screw and mechanism similar to that used in the piston flowmeter. All seals in the gas system are metallic.

J. Vac. Scl. Technol. A, Vol. S, No. 3, May/Jun 1987

D-3
379

slightly above atmospheric will be required to compress the

bellows. This will minimize leaks, in particular, leakage of

air into the oil, which would cause significant errors, and

maintain positive contact between the piston and the drive mechanism. Procedures for the use of the bellows flowmeter

are the same as those for the piston flowmeter.

IV. ESTIMATED FLOWMETER UNCERTAINTIES

The piston flowmeter has been in regular use for vacuum

gauge and leak calibrations since 1984 and the bellows flow- meter since late 1985. During this time data have been col- lected on the uncertainties contributed by individual components of the flowmeters as well as on the overall performance. These data can be used to assess the probable

errors of both flowmeters between 10~ 6 and 10~" mol/s. The flowmeters have been operated at lower flows, particularly the bellows flowmeter, but further data are required to

fully assess the uncertainties below 10~" mol/s. The total uncertainty can be estimated by summing component errors. From Eq. ( 1 ), the instantaneous flow rate can be derived

as dN /dt = d/dt[{PV)/(RT)) . (4)

In practice an average flow rate dN /dt over a time Ar is measured: dN/dt = HP,V,)/{RT,) - (P2 V2 )/(RT2 )]/M , (5) where the subscript 1 indicates the respective measurement

at the beginning of the time interval, and the subscript 2 indicates the respective measurement at the end of the time

interval. In the case of the piston flowmeter this equation must be modified to allow for the possibility of gas leakage L

past the sliding seal, and gas absorption or desorption D at the seal: dN/dt = [(P,V,)/(RTI ) - (P2 V2 )/(RT2 ))/ At-L-D. (6) D and L are not known and cannot be corrected for, al- though their magnitude can be estimated and limits placed on the related errors. Defining

AT=1\-T,, (7) AK=K,-F2 , (8)

andAP = P2 -P{

, (9) Eq. (6) can be rewritten, to first order in APand AT, as

'dWTdt = [(P, AV)/(RT, AO){l - ( V,/A V) X [ ( A/VP, ) — ( A7"/r, ) )} —L — D. (10)

In the constant pressure mode the measured flowrate is obtained from the first term of this equation, P, Al'/RT, At. ;md the remaining terms are regarded as sources of error The estimated errors in the first term as well as those due to the other terms are tabulated at different flowrates for the pislon flowmeter in Table I The basis for these estimates is discussed below.

J. Vac. Scl. Technol. A, Vol. 5, No. 3. May/Jun 1987

379

Taiu r I Uncertainties of the piston flowmeter in percent The uncertainties of the bellows flowmeter are the same except at the lowest tabulated

flowrate. where they are marginally smaller Random error? are evaluated

at three times the standard deviations or maximum observed deviations.

Flowrate (mol/s) and piston size

io- 6-io-' io-'° 10""

1 in. I en 1 cm

sr,/p, systematic 0.50 0 50 0.52 random 0.01 0.01 0.10

<5(&I')/A v area systematic 0.001 0.001 0.001

length systematic 0.10 0.10 0.10

<57,/7, systematic 0.003 0003 0.003 random 0.01 0.01 0.01 <5(An/Ar random 001 0.10 0.10

I', SP, b.V P, systematic 0 20 1.30 1.30

V, ST, a v r, systematic 0.006 0.04 0.04

Leakage systematic 0.01 0.06 0.06

Systematic 082 2.00 2.02

( Linear sum

Random 0 02 0 10 0.14 (rms sum)

Total 0 84 2.10 2.16

A. Initial fill pressure: 6/Vi

The systematic uncertainties are due almost entirely to observed long-term instabilities in the calibration of the ca- pacitance diaphragm gauges used to measure the flowmeter

fill pressure. Our experience with gauges used in the flow- meters has been consistent with our experiences with a larger group of gauges." At the lowest flows there is an additional contribution due to a systematic offset in the servo system advancing the piston. The estimated random errors are due

to random reading errors in the CDG's and the inability of the servo loop to maintain zero differential pressure between

the reference and variable volumes. Modification of the ser- vo system may reduce this error.

B. Volume change: 8 (A V)/ V

The uncertainties in piston cross-sectional areas are based on the specifications for the wire gauges. The uncertainties in the linear displacements are based on the maximum nonlincarities in the micrometer screws observed when checked

against a standard length

C. Initial temperature: bT,/Ti

Systematic uncertainties are based on a maximum 10-mK

error in the calibration of the quartz and platinum resistance thermometers used in the flowmeters. The random errors are based on observed temperature changes over 20-30 min

periods, which are indicative of possible temperature differ- ences between the gas and the thermometers.

McCulloh eta/. : Low-range flowmeters for use with vacuum and leak standards

Jt D-4
380 McCulloh elal. : Low-range flowmeters lor use with vacuum and leak standards 380

D. Time interval: 6(A/)/Af

The elapsed time is recorded for each I urn as ihe micro- meter screw advances. Time intervals are calculated from

the differences of successive elapsed limes. The first lew of

these 20 time differences may be excluded from the data

analysis as they may be perturbed by small differential pres- sures generated during the closing of valve A and initial oscillations of the servo system driving the stepping motor. The times per turn exhibit random and systematic variations from turn to turn that depend on the fill pressure, and hence

the flowrate. At higher fill pressures the times do not exhibit a systematic trend but have a random variation due to the

0.1 -s resolution of the timing circuit. As the fill pressures are decreased the instabilities of the differential CDG and servo system become significant and the random variations ia the time increase. The time interval A / is an average of the indi- vidual times. However, with the piston flowmeter a systematic trend in the times becomes evident at 10' " mol/s and becomes larger at lower flows. The times progressively de- crease from the initial values towards an asymptotic value. The magnitude of the initial offset from the asymptotic value

is roughly inversely proportional to the flowrate. This effect

is substantially reduced for the bellows flowmeter. We believe this effect is caused by gas desorbed from the sliding

seal as the piston moves through it. Therefore, we ignore

those time intervals indicating a systematic trend and esti- mate an asymptotic value of the time interval from the re- maining measurements. The probable error in estimating

this asymptotic value is largely determined by the random

variations of the individual times and the decreased number

of "stable" time intervals that can be used in the estimate. Systematic errors in the timing circuitry are negligible.

E. Changes in the pressure during operation:

(IryAtO(WVPi)

We observe unexplained changes in the indicated pressure of the reference volume from the beginning to the end of the piston advancement. Their relative magnitude increases with decreasing fill pressures to a maximum of 0.1% at 10~ 1

mol/s. We do not believe these changes can be due to short-term CDG instabilities or temperature changes. We

treat them as a possible additional error in the measured

pressure of the variable volume. Their effect is multiplied by

the ratio of the final or "dead" volume of the variable vol- umes to the volume change. This factor V2 /LV is 2 for the

larger piston and 1 3 for the smaller. These pressure changes

are almost always a pressure increase, therefore the associat- ed uncertainty has been listed as systematic and evaluated on

the basis of the maximum observed changes.

F. Temperature changes: (l/2 /A P)(67V7V)

Observed maximum 10-mK changes in the measured temperature are treated as possible changes in the gas temperature during the piston advancement. Again, the effect is larg- er for the smaller piston.

G. Leakage: L

Errors due to seal leakage in the piston flowmeter are estiJ. Vac. Scl. Technol. A, Vol. 5, No. 3, May/Jun 1987

mated by deliberately establishing a large pressure differential across the seal and observing the rate of pressure change

in the known variable volume. This observed leakage is scaled down to correspond to the small differential pressures across the sliding seal during operation.

H. Desorption: D

As noted earlier there is evidence at very low flowrates of gas desorption from the sliding seals in the piston flowmeter. Compensation is made for this effect by using asymptotic

values of the time per revolution of the micrometer screw

used to advance the piston. We believe the errors associated with this procedure are included in the increased random

errors in the measurement of the time interval Therefore, no

separate uncertainty contribution for desorption is included

in Table I. From Table I it is apparent that improved accuracies for the flowmeters will largely depend on improvements in the pressure measurements. It is also important to minimize the dead or minimum volume V2 of the variable volume. A large dead volume magnifies the effects of pressure or temperature

instabilities. In this same range the uncertainties of the bellows flow- meter will be substantially the same except that errors due to leakage or desorption have been eliminated. The random errors listed in Table I are based on maxi- mum observed errors. Therefore, the total error is computed

from a linear sum of the systematic uncertainties plus a root sum of the squares of the random errors, with no multiplicative factor for the latter.

V. OBSERVED FLOWMETER PERFORMANCE

The validity of the uncertainty estimates in Table I can be experimentally checked to a certain extent. The estimated random error can be compared with observed random varia- tions in the calibration of vacuum gauges or leak artifacts. Since the only errors common to both flowmeters are minor compared to the total, the errors of the two flowmeters are

essentially independent of one another. Therefore, observed

differences in the calibration of vacuum gauges or leak arti- facts using the two flowmeters should be less than the linear sum of the errors of the two flowmeters. Finally, results obtained with these flowmeters can be compared with those obtained using other standards. In all cases the experimental

data will include the random errors of the rest of the calibra- tion system and the effects of instabilities inherent in the gauge or leak, and therefore, must be considered as an upper bound on the random errors of the flowmeters. This is particularly true of the low-range leak measurements. In these cases the pressures generated by the small helium flows are comparable to changes in the hydrogen background pres- sure in the vacuum chamber. This precludes the use of ion gauges to determine pressure equivalence of the flows from

the leaks and the flowmeter. The quadrupole residual gas analyzers used at the low flows are significantly less stable than the ion gauges, shifts of several percent in sensitivity are

not uncommon, and the random errors of the leak measure- ments are correspondingly higher.

D-5
381

A. Random errors The measured random errors during gauge and leak cali- brations differ with flowrate and type of device calibrated. The pooled standard deviation about the mean for six molecular drag gauges repeatedly calibrated over a two-month pe- riod using the piston flowmeter and flows between 2.2X 10 _9 and 1.3 X 10" 7 mol/sdid not exceed 0.3% for the piston flowmeter. 1 For flows of 10~ 9 mol/s the pooled stan- dard deviation increased to 0.4%, but in this case the results are clearly limited by the imprecision of the molecular drag

gauge. Repeated calibrations of helium diffusion leak at 5 X 10 " " mol/s, using both flowmeters, gave a standard de- viation about the mean of 0.4% for six calibrations with the piston flowmeter and 0.5% for five calibrations with the bel- lows flowmeter. Repeated calibrations of a helium diffusion leak at 5x 10" 12 mol/s had standard deviations about the mean of 1.7% for 10 calibrations with the piston flowmeter and 1.0% for 17 calibrations with the bellows flowmeter. These random errors clearly exceed those listed in Table I, but, as noted, they include instabilities of the leaks and

gauges and random errors due to other parts of the calibra- tion system.

B. Comparisons between flowmeters and with other standards

The means of molecular drag gauge calibrations per- formed with the piston and bellows flowmeter at 2x10 s mol/s differed by 0.7%. The means of leak calibrations per- formed using the two flowmeters at 5 X 10~" and 5 X

10" 13 mol/s differed by less than the standard deviations of

the individual flowmeter measurements so that any differ- ence between flowmeters at this level is masked by the ran- dom errors of the individual flowmeters. The piston flow- meter has been used to calibrate molecular drag gauges lhat were calibrated using a "quantity" meter." The results for four gauges differed by 0.1%, the results for a fifth gauge

differed by 0.5%. This does not indicate a significant differ- ence between calibrations performed using the piston flow- meter and those made using the quantity meter.

381

Calibrations of a sintered metal leak by the NBS and the Sandia National Laboratory Primary Standards Laboratory

differed by no more than 1. 5% between 10 -8 and 10~ A

mol/s. 2 There was evidence of a drift in the transfer leak, but

the differences are, in any case, well within the combined

uncertainties of the leak calibration standards of the two

laboratories.

VI. SUMMARY

Two low-range, constant-pressure, piston displacement

flowmeters have been developed at the NBS. The uncertainlies have been evaluated in the flow range 10~ 6-10~ 11 mo!/

s. and comparisons made with measurements performed on

other systems or using other techniques in this same range. The estimated errors in the flow range 10 _6-10~ 9 mol/s of 0.8%. increasing to about 1 .3% at 10~ " mol/s, appear consistent with the experimental results. Investigations are currently under way to assess the uncertainties at lower flowrates. ACKNOWLEDGMENTS

We would like to acknowledge the support of the NBS

Office of Nondestructive Evaluation, and the Transportation Systems Technology and Analysis Division and the Pri- mary Standards Laboratory of the Sandia National Laboratorv.

'K.E McCulloh. C.R. Tilford. S.D. Wood, and D.F Martin. J. Vac. Sci. Tcch'nol A 4. 362 ( 1<3R6) R Hyland. C D. F.hrlich. C R. Tilford. and S. Thornberg. J Vac. Sci. Technol. A 4. 334 ( 1986).

'C. D Ehrlich, J. Vac. Sci. Techno!. A 5. 125 ( 1987).

'\V Uayward and R Jcpscn. in Transactions of the 9th American Vacuum

Society Vacuum Symposium (American Vacuum Society, New York,

1963). p 4 ^ q 'G.N. Pcggs, Vacuum 26. 321 ( 1976)

"P. V.. M. Heydetnann, C. R Tilford. and R. W. Hybrid, J. Vac. Sci. Tcchnof. 14. 597 (1977).

II Hojo, M Quo, and K Nakayama, in Proceedings ofthe Seventh International I ticuum Congress ( International Union for Vacuum Science, Technique and Applications. Vienna, 1977). p. 117. "R. \V. Hyland and C. R. Tilford. J. Vac. Sci. Tcchnol. A 3, 1731 ( 1986). "K. E. McCulloh. J. Vac. Sci. Technol. A 1, 168 ( 1983).

McCulloh et Bl. : Low-range flowmeters for use with vacuum and leak standards

J. Vac. Sci. Technol. A. Vol. 5. No. 3. Mav/Jun 1987 D-6
UNITED STATES DEPARTMENT OF COMMERCE

National Bureau of Standards

Gaithersburg. Maryland 2QB99

SAMPLE CALIBRATION REPORT

Report Date: February 1, 1988

LEAK ARTIFACT

Submitted by

Name of Company, Inc.

Anywhere, USA

Test performed January 1988

NBS Test Number : L12 / 240840

NBS Leak Identification Number: NBSLC9

Leak Manufacturer: Leak Maunfacturer , Inc

Manufacturer Serial Number: MFG-#

Customer Property Number: S/N CUST0MER#

Leak Type : Fixed reservoir , glass permeation

Gas: Helium

Measured Leak Rate (over temperature range 0-50 °C):

Leak Rate (T) - A T e" B/T mol/s

*

where T is the absolute temperature in kelvins,

A - 4.8708 x 10" 10 mol s"

1 K" 1 and B - 3012.46 K

This equation gives a leak rate of 5.51x10 raol/s when the leak artifact

is equilibrated at 23 °C. 1

See Table I and Measurement Uncertainties

E-l
REPORT OF TEST (continued)

Page 2

PROCEDURES

This leak artifact was calibrated near 23 °C by comparison with

Flowmeter #2 of the NBS Primary Leak Standard, using the upper to lower

chamber flow division technique. The temperature dependence was determined

by varying the temperature of the leak between 0 and 50 °C and comparing its

flow rate with a fixed- temperature leak artifact.

MEASUREMENT UNCERTAINTIES

The present estimate of the total uncertainty in the measured leak rate

of this artifact at 23 °C at the time of test is + 7.9%. This includes a systematic uncertainty of + 3.0% in Flowmeter #2 of the NBS Primary Leak

Standard, + 2.3% random error in the measurement of the upper to lower

chamber flow ratio, and + 2.6% random errors in the measured leak rate of

this artifact. The latter two errors represent three standard deviations.

Between 0 and 50 °C, there is an additional uncertainty of + 0.037% per °C

temperature difference from 23 °C.

Note that under conditions of normal usage and storage at room temperature, the leak rate from an artifact of this type can be expected to decay

by as much as several percent over the course of a year. There is insufficient data provided with this artifact to determine what this decay rate is.

In order to optimize the overall accuracy in the use of this artifact,

it should be stored with any shutoff valve open (a dust cover can be used to

protect the vacuum port), it should be stored at the temperature at which it

will be used for at least 24 hours and pumped for at least 3 hours prior to

use. Sufficient time should also be allowed for the system on which the leak

artifact is to be used to come to equilibrium with the environment. Confidence in the stability of this artifact can be maintained by periodic com- parisons of its leak rate with leak rates of other stable, well-characterized leak artifacts.

COMMENTS

1) THIS ARTIFACT IS FRAGILE, HANDLE WITH CARE

For the Director

National Measurement Laboratory

Arthur 0. McCoubrey, Acting Chief

Temperature and Pressure Division

Center For Basic Standards

National Bureau of Standards

E-2
REPORT OF TEST (continued)

Page 3

"REPORT OF TEST"

NBS Test # L12/240840

Report Date : February 1, 1988 +

LEAK RATE vs. TEMPERATURE

Leak Rate Leak Rate

erap.(°C) mol/s s td cc/s Temp.(°C) mol/sL * std cc/s

0 2 .16E-12 4.84E-08

1 2 .25E-12 5.05E-08 26 6 . 16E-12 1. 38E-07

2 2 . 36E-12 5.28E-08 27 6 •40E-12 1. 43E-07

3 2 .46E-12 5.51E-08 28 6 . 63E-12 1. 49E-07

4 2 .57E-12 5.75E-08 29 6 .88E-12 1.54E-07

5 2 . 68E-12 6 . 01E-08 30 7 . 13E-12 1 . 60E-07

6 2 .80E-12 6.27E-08 31 7 . 39E-12 1. 66E-07

7 2 .92E-12 6.53E-08 32 7 . 66E-12 1.72E-07

8 3 •04E-12 6.81E-08 33 7 . 94E-12 1.78E-07

9 3 .17E-12 7.10E-08 34 8 .23E-12 1.84E-07

10 3 . 30E-12 7 . 40E-08 35 8 . 52E-12 1 . 91E-07

11 3 . 44E-12 7.71E-08 36 8 . 82E-12 1.98E-07

12 3 .58E-12 8.03E-08 37 9 . 13E-12 2.05E-07

13 3 . 73E-12 8.36E-08 38 9 . 45E-12 2 . 12E-07

14 3 . 88E-12 8.71E-08 39 9 . 78E-12 2.19E-07

15 4 . 04E-12 9.06E-08 40 1 . 01E-11 2.27E-07

16 4 . 21E-12 9.43E-08 41 1 . 05E-11 2.35E-07

17 4 . 37E-12 9.80E-08 42 1 . 08E-11 2.43E-07

18 4 . 55E-12 1.02E-07 43 1 . 12E-11 2.51E-07

19 4 .73E-12 1.06E-07 44 1 . 16E-11 2.59E-07

20 4 .91E-12 1.10E-07 45 1 .20E-11 2.68E-07

21 5 . 11E-12 1.14E-07 46 1 . 24E-11 2.77E-07

22 5 . 31E-12 1.19E-07 47 1 . 28E-11 2.86E-07

23 5 . 51E-12 1.24E-07 48 1 . 32E-11 2 .96E-07

24 5 .72E-12 1.28E-07 49 1 . 36E-11 3 . 05E-07

25 5 . 94E-12 1. 33E-07 50 1 . 41E-11 3 . 15E-07

std cc/s refers to conditions of 1 atmosphere (atra) absolute pressure

(101.325 kPa) and 273.15 K (0°C) . 1 std cc/s - 4.46xl0" 5 mol/s.

+As noted on page 2, under normal conditions of storage and use the leak

rate will decay from the values listed here at an undetermined rate.

Table I

* U.S. G .P .0. 1991 -31 1-891/40067 E-3

NIST-114A U.S. DEPARTMENT OF COMMERCE 1. PUBLICATION OR REPORT NUMBER

(REV. 3-90) NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY NIST/SP-250/38

2. PERFORMING ORGANIZATION REPORT NUMBER

BIBLIOGRAPHIC DATA SHEET 3. PUBUCATION DATE January 1992

4. TITLE AND SUBTITLE

NIST Leak Calibration Service

5. AUTHOR(S)

Charles D. Ehrlich

Stuart A. Tison

6. PERFORMING ORGANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

GAITHERSBURG, MD 20899

7. CONTRACT/GRANT NUMBER

8. TYPE OF REPORT AND PERIOD COVERED

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (STREET, CITY, STATE, ZIP)

NIST

10. SUPPLEMENTARY NOTES

11. ABSTRACT (A 200-WORD OR LESS FACTUAL SUMMARY OF MOST SIGNIFICANT INFORMATION. IF DOCUMENT INCLUDES A SIGNIFICANT BIBUOGRAPHY OR

LITERATURE SURVEY, MENTION IT HERE.)

This NIST Special Publication describes the recently offered Leak Calibration Service.

A description of the services provided is followed by a discussion of the design

philosophy and theory, and a description of the total Leak Calibration System. Uncertanties

associated with the Primary Leak Standard and Leak Comparator System are discussed in detail,

Important properties of helium permeation leaks, especially the temperature dependence,

are also discussed. Sections on Quality Control and Future Directions are followed by

appendices discussing general theory of gas flow in vacuum systems, and proper use and

conversion of flow rate units.

12. KEY WORDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITAUZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

Calibrated leak; helium permeation leak; leak; leak calibration; leak calibration service;

leak rate units; leak standards

13. AVAILABILITY UNLIMITED FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE TO NATIONAL TECHNICAL INFORMATION SERVICE (NTIS).

X

ORDER FROM SUPERINTENDENT OF DOCUMENTS, U.S. GOVERNMENT PRINTING OFFICE, WASHINGTON, DC 20402. ORDER FROM NATIONAL TECHNICAL INFORMATION SERVICE (NTIS), SPRINGFIELD, VA 22161.

14. NUMBER OF PRINTED PAGES

89

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and Thermocouple Materials PB89209340

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