final report of key comparison apmp.m.p-k3 … report of key comparison apmp.m.p-k3 absolute...

Final report of key comparison APMP.M.P-K3 absolute pressure

measurements in gas from 3×10-6 Pa to 9×10-4 Pa

H. Yoshida1, K. Arai1, H. Akimichi1, S. S. Hong2, H.W. Song2

1 NMIJ/AIST: The National Metrology Institute of Japan / the National Institute of

Advanced Science and Technology, Japan

2 KRISS: Korea Research Institute of Standards and Science, Republic of Korea

Abstract

The results of a key comparison of ultra-high vacuum standards at two National

Metrology Institutes (NMIJ/AIST and KRISS) are reported. This bilateral comparison

was carried out from May 2010 to October 2010 within the framework of the

Asia-Pacific Metrology Programme (APMP) to determine their degrees of equivalence

at pressures in the range from 3×10-6 Pa to 9×10-4 Pa. The pilot institute was

NMIJ/AIST. Two spinning rotor gauges and two hot cathode ionization gauges were

used as the transfer standards. NMIJ/AIST used two calibration systems; the dynamic

expansion system (NMIJ-DES) and two-stage flow-dividing system (NMIJ-TFS).

KRISS used the dynamic expansion system. The transfer standards were sufficiently

stable to meet the requirements of the comparison compared with those of previous

international comparisons owing to some improvements of the protocol and the transfer

standards. The ultra-high vacuum standards of NMIJ/AIST and KRISS were found to be

equivalent within their claimed uncertainties in the range from 3×10-6 Pa to 9×10-5 Pa.

The NMIJ-DES results, which have smaller uncertainty than NMIJ-TFS, were

transferred to the corresponding CCM key comparison, CCM.P-K3, in the range from

3×10-6 Pa to 9×10-5 Pa and it is shown that the NMIJ values were equivalent to the

CCM KCRV within the claimed uncertainties.

2

1. Introduction

The National Metrology Institute of Japan / the National Institute of Advanced

Science and Technology (NMIJ/AIST), Japan, has developed a high vacuum standard in

the rage form 10-6 Pa to 10-4 Pa using dynamic expansion system (DES). NMIJ/AIST

also developed another calibration system, the two-stage flow-dividing system (TFS),

for routine calibrations of vacuum gauges in the rage from 10-7 Pa to 10-2 Pa. This

system is typically used for calibration of partial pressure analyzers.

The Korea Research Institute of Standards and Science (KRISS) of Korea

successfully participated in the CCM comparison, CCM.P-K3 [1], in the range form

3×10-6 Pa to 9×10-4 Pa using two spinning rotor gauges (SRGs) and several ionization

gauges (IGs) as the transfer standard. A bilateral comparison was planned by the both

laboratories using two SRGs and two IGs.

This bilateral comparison was identified as APMP.M.P-K3 by Asia-Pacific Metrology

Programme (APMP). APMP.M.P-K3 is linked to the CCM key comparison, CCM.P-K3,

which has a same pressure range as APMP.M.P-K3. The results of this comparison will

be submitted to the Key Comparison Database (KCDB) of BIPM following the rules of

CCM and can be used to establish the degree of equivalence of national measurement

standard by National Metrology Institutes (NMIs).

3

Before the comparison, two IGs were tested for the viewpoint of the stability as

transfer standards at TFS in NMIJ/AIST. A protocol was prepared based on results of

the test by NMIJ/AIST in cooperation with KRISS with reference to the protocol of

CCM.P-K3.

2. Participating institutes and their calibration systems

Two NMIs participated into this comparison, which are listed in Table 1.

Table 1 List of participants and the standards used for the calibration. NMI Standard

Dynamic expansion system (DES)

NMIJ / AIST (Pilot institute) Japan

Two-stage flow-dividing system (TFS)

KRISS Korea

Dynamic expansion system

2.1 Dynamic expansion system (DES) at NMIJ/AIST

In a dynamic expansion system at NMIJ/AIST, standard pressures are generated by

producing a gas flow with known flow rate, which passes through an orifice with known

conductance. This high vacuum standard consists of a flowmeter and a vacuum chamber

with an orifice. The full calibration range of the standard is 10-7 Pa to 10-3 Pa. The gas

4

flow generated by the flowmeter is determined from the product of the pressure and the

volume change rate [2]. The vacuum chamber is approximately 286 mm in diameter and

429 mm long. The chamber is evacuated with a turbomolecular pump (TMP). The upper

and lower chambers normally communicate through a 20 mm diameter orifice. The

conductance of the orifice is calculated from the dimension [3]. In addition, the

influence of the effective pumping speed of the TMP and the pressure distribution of the

calibration chamber are estimated and included in the determination of the standard

pressure.

2.2 Two-stage flow-dividing-system (TFS) at NMIJ/AIST

The two-stage flow-dividing system is used for routine calibrations of vacuum gauges

in the pressure range from 10-7 Pa to 10-2 Pa [4]. This system has two advantages: its

simple structure neither does require any flow meter nor a precise measurement of the

geometry of the orifice, and the easy operation due to the computer control for the

generated pressure, although its uncertainty of the generated pressure is a little bit larger

than that of the dynamic expansion systems.

The system consists of four chambers; a first chamber V0, a flow divider V1, a

calibration chamber V2, and an evacuation chamber V3. The calibration chamber V2 is

5

evacuated through an orifice (30 mm in diameter) by the main TMP (550 L/s). The flow

divider V1 is also evacuated by a subsidiary TMP (220 L/s). Chambers V0 and V1,

chambers V1 and V2, and chambers V2 and V3 are connected to each other with a

capillary, a sintered filter, and an orifice, respectively.

The pressure in the first chamber p0 is maintained at a pressure from 103 Pa to 105 Pa

using a pressure controller. Corresponding to stabilizing the p0, both the pressure in the

flow divider p1 and that in the calibration chamber p2 are kept constant from 10-3 Pa to

10 Pa and from 10-6 Pa to 10-2 Pa, respectively. The standard pressure p2 is proportional

to p1 because the conductances of both the sintered filter C2 and the orifice Cmain become

constant by realizing a molecular flow. Therefore, p2 is calculated from p1 using the

constant conductance ratio, C2/(C2 + Cmain) [4].

2.3 Dynamic expansion system at KRISS

The primary standard for the ultra high vacuum (UHV) at KRISS used for this

comparison is an orifice-type dynamic expansion system. It consists of two dynamic

calibration systems: one for high vacuum (HV) from 10-5 Pa to 10-2 Pa, and the other for

UHV from 10-7 Pa to 10-5 Pa. The UHV system is connected to the HV by a porous plug

with a very small conductance (6.36×10-3 L/s in N2 at 23 ºC) and a by-pass line whose

6

conductance is higher than porous plug. During calibration at low pressures, the path

containing the porous plug is used. However, at comparatively high pressures, the

porous plug is isolated and the by-pass line is used. Gas is supplied to the high vacuum

system from a constant pressure-type flowmeter, some of which flows through the

porous plug into the UHV chamber. The HV system is evacuated using a TMP with a

pumping speed for N2 of 345 L/s, and the UHV system is evacuated using a closed loop

helium refrigerator-type cryopump with a pumping speed for N2 of 1500 L/s. Further

details of the systems and a full uncertainty analysis are given in [5].

3. Transfer standards

The transfer standard package consisted of two spinning rotor gauge sensor heads

(SRG-CE6 and SRG-CE8) and two ionization gauges (Stabil-ion gauge (SIG) and

Miniature gauge (MG)). Table 2 lists characteristics of gauges and controllers that were

supplied with the package. Setting parameters of SRGs and IGs, and specifications of

the transfer thermometers are listed in Table 3, Table 4, and Table 5, respectively. The

pressure readings of SRGs were compensated by the chamber temperature at the process

of data analysis after measurements.

7

Table 2 Transfer standards used in APMP.M.P-K3.

Gauge description Gauge Identifier

Pressure range for calibration / Pa

Gauge head Controller Manufacturer

SRG-CE6 9×10-4 Spinning rotor gauge sensor head, 4.50 mm diameter stainless steel rotor

None provided

SRG-CE8 9×10-4 Spinning rotor gauge sensor head, 4.50 mm diameter super invar rotor

None provided

MKS Instruments, Inc.

SIG 3×10-6 to 9×10-4

Metal enclosed Bayard-Alpert ionization gauge (Stabil-Ion gauge)

Model 370 ion gauge controller

Brooks Automation, Inc.

MG 3×10-6 to 9×10-4

Metal enclosed Bayard-Alpert ionization gauge (Miniature gauge)

Miniature gauge controller M-430HG

Canon ANELVA corp.

8

Table 3 Input parameters of SRGs

SRG CE-6 SRG CE-8 Ball density [g/cm3] 7.700

(Stainless steel)

8.200 (Super invar)

Ball diameter [mm]

4.500

Accommodation coefficient

1.000

Molecular weight [u]

39.95

Temperature [K]

295.4

Duration of each measurement [s]

30 (NMIJ), 10 (KRISS)

Table 4 Setting parameters of IGs

SIG MG Filament number

1 1

Gauge scale factor or Sensitivity

1 6

Emission current [mA]

4 1

Cathode (Filament)

+ 30 + 45

Anode (Grid)

+ 180 + 180

Electric potential [V]

Ion corrector

0 0

9

Table 5 Specification of transfer thermometers

Number

2

Manufacturer, model

T and D cooperation, TR-71Ui

Channel

2

Temperature range

− 60 oC to 150 oC

Resolution

0.1 oC

Accuracy

0.5 oC

Five improvements of the protocol and the transfer standards were tried from those of

CCM.P-K3. First, an isolation all-metal valve was attached to each gauge head of the

SRG and the IG to keep the inside of it in vacuum during the transfer from NMIJ/AIST

to KRISS, and vise versa (Fig. 1). In addition, the rotor heads of SRGs did not detach

from their thimbles to keep the rotor stationary by the magnet in the rotor head. These

procedures were performed to decrease the change in sensitivity of these gauges during

the transfer as low as possible. Similar treatments were also applied on the key

comparison Euromet.M.P-K1.b [6] and CCM.P-K14 in progress. Second, stainless steel

rotor and super invar rotor were applied for SRG-CE6 and SRG-CE8, respectively.

10

(a) SRG-CE6

MG

SIG

(b) SRG-CE8

(c) SIG and MG

(a) SRG-CE6

MG

SIG

(b) SRG-CE8

(c) SIG and MG

Fig.1 Photographs of transfer standard packages. The photographs of (a) SRG-CE6, (b) SRG-CE8, and (c) SIG and MG are shown.

Stainless steel has high reliability and high stability for use in vacuum. Super invar has

about 30 times smaller thermal expansion coefficient than that of stainless steel. In our

experience, the stability of the effective accommodation coefficient (σeff) against the

11

change in temperature became better because of smaller change in the diameter of rotor

by thermal expansion. Invar rotor was also applied on the regional key comparison

Euromet.M.P-K1.b [6]. Third, in addition to SIG used at CCM.P-K3, MG was

employed as a transfer standard because it has wide linear response range. Fourth, no

bake-out was allowed for transfer gauges to decrease the change in the characteristics.

The protocol of CCM.P-K14 in progress also requires no bake-out for the transfer SRGs.

Fifth, two simple thermometers were also transferred to check the temperature

differences between the calibration chambers and the gauge heads. Temperature

measurements are important for the comparisons because pressure readings of both

SRGs and IGs depend on the temperatures. Figure 2 shows positions where the

temperature was measured.

Upperchamber

Lowerchamber

Vacuumpump

Flowmeter

TFM

Tchamber1

Troom

SIGMIG

SRG

TSIG

TMIG

Tchamber1

Tchamber2

Own thermometers

Transferred thermometers

Upperchamber

Lowerchamber

Vacuumpump

Flowmeter

TFM

Tchamber1

Troom

SIGMIG

SRG

TSIG

TMIG

Tchamber1

Tchamber2

Own thermometers

Transferred thermometers

Fig.2 Positions where the temperature was measured. SIG, MG and two SRGs were

actually mounted at the same horizontal plane, although this schematic diagram does not show that.

12

4. Results of pretests for two ionization gauges as transfer standards

Before the comparison, the stabilities of SIG and MG were simultaneously tested at

TFS in NMIJ/AIST.

4.1 Fluctuation and drift of pressure reading

Changes in pressure readings of SIG and MG were measured while the pressure in

the calibration chamber maintained using Ar at 3×10-6 Pa, 3×10-5 Pa, and 9×10-4 Pa for

1 hr. No significant fluctuations and drifts over 0.5 % were observed for both SIG and

MG. This result indicates that there is no significant influence on the difference of the

time interval from gas introduction to pressure measurements for calibrations.

4.2 Effect of power supply voltage

The power supply voltages in NMIJ/AIST and KRISS are AC100 V and AC120 V,

respectively. Therefore, the effect of power supply voltage on the pressure readings of

SIG and MG were examined. Changes in pressure readings of SIG and MG were less

than 0.5 % against the change in a power supply voltage from AC100 V to AC120 V at

the pressure of 3×10-6 Pa.

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4.3 Effect of changing in chamber temperature and gauge temperature

An inverse of correction factor, a0, as defined by eq.(1) often used to show the

sensitivity of IGs.

ref

BGreading0 P

PPa

−= , (1)

where Preading and PBG are pressure readings of IG during calibration and at background,

respectively. Pref is the reference pressure, for example, generated by the primary

standard.

The a0 is proportional to the inverse of the chamber temperature because of the

change in the gas density [7,8]. To confirm this characteristic about SIG and MG, 11

calibrations were performed by changing the chamber temperature from 296 K to 303 K.

The results showed that the a0 of SIG and MG were proportional to inverse of chamber

temperature within ±1 %.

The gauge temperature also influences the pressure readings of IGs by thermal

transpiration effect [8,9]. The gauge temperature of MG was changed from 316 K to

290 K by cooling water during keeping the chamber temperature at 302 K ± 1 K. The

results showed that the pressure reading of MG was proportional to the inverse of the

14

square root of the gauge temperature within ±1 %.

4.4 Effect of bake-out, Switching off/on, disconnecting/connecting,

closing/opening each isolation valve, and removing the gauge head from the

vacuum chamber and re-mounting

Figure 3 shows the change in a of SIG and MG depending on a bake-out, switching

off/on, disconnecting/connecting, closing/opening each isolation valve, and removing

the gauge head from the vacuum chamber and re-mounting. a is the temperature

compensated inverse of the correction factor by calculated using eq.(2).

ref

chamber0 T

Taa ⋅= , (2)

where Tchamber and Tref are the chamber temperature and reference temperature (23 oC),

respectively. The results were summarized below.

1) The effect of switching off/on and disconnecting/connecting the cable is negligible

(see (i)).

2) a of SIG increased by a bake-out (see (ii), (iii), and (iv)) and only operating in

ultrahigh vacuum (~10-7 Pa) for several days (see (v) and (ix)). The magnitude of

15

the change in a of SIG was about 6 %.

3) a of MG also increased by a bake-out. But it recovered the original value within

1 % at the second calibration from the bake-out (see (ii), (iii), and (iv)). Although

no influence was observed by operating in ultrahigh vacuum (see (v) and (ix)), a

tended to decrease with the number of calibration. Such a tendency is often

observed for the characteristics of IGs [10-13]. The magnitude of the change in a

of MG was about 1 % ~ 2 %.

4) No influence was observed by closing/opening each isolation valve for both SIG

and MG (see (vi) and (vii)). However, significant decrease of a was observed for

SIG by removing the gauge head with the isolation valve and remounting it (see

(viii)). Although the inside of the gauge heads kept in vacuum by each isolation

valve, a little amount of air in the dead volume between the isolation valve and one

equipped to the calibration chamber was exposed to the inside of the gauge head

when it was remounted. No significant change was observed for MG in spite of the

same condition.

5) These results indicate that a of SIG is sensitive to the surface condition of the

inside of gauge head, but a of MG is insensitive to that. Therefore, MG seemed to

be more suitable to use as a transfer standard than SIG.

16

0.98

1

1.02

1.04

1.06

3x10-6 Pa9x10-6 Pa3x10-5 Pa9x10-5 Pa3x10-4 Pa9x10-4 Pa

(a) SIG

Cha

nge

in a

0.98

1

1.02

1.04

0 2 4 6 8 10 12 14 16 18Number of calibration

(b) MG

(i)(ii)

(iii)(iv)

(v)(vi)

(vii)(viii)

(ix)0.98

1

1.02

1.04

1.06

3x10-6 Pa9x10-6 Pa3x10-5 Pa9x10-5 Pa3x10-4 Pa9x10-4 Pa

(a) SIG

Cha

nge

in a

0.98

1

1.02

1.04

0 2 4 6 8 10 12 14 16 18Number of calibration

(b) MG

(i)(ii)

(iii)(iv)

(v)(vi)

(vii)(viii)

(ix)

- Closing the isolation valve after switching off- Removing the gauge heads with the isolation valves from the calibration chamber- Keeping the gauge heads in a shelf for 2 days- Remounting the gauge head to vacuum chamber- Evacuation for 1 day

(viii)

Evacuation for 3 days(ix)Closing the isolation valve for 1 day after switching off(vi)

Evacuation for 3 days(v)

Closing the isolation valve for 1 day after switching off, which is same as (vi)

Bake-out at 200~220 oC　for 4 hour(iv)

(vii)

Bake-out at 200~250 oC for 4 hour(iii)

Bake-out at 150 oC for 1 hour(ii)

Switching off / onDisconnecting / connecting the cable(i)

- Closing the isolation valve after switching off- Removing the gauge heads with the isolation valves from the calibration chamber- Keeping the gauge heads in a shelf for 2 days- Remounting the gauge head to vacuum chamber- Evacuation for 1 day

(viii)

Evacuation for 3 days(ix)Closing the isolation valve for 1 day after switching off(vi)

Evacuation for 3 days(v)

Closing the isolation valve for 1 day after switching off, which is same as (vi)

Bake-out at 200~220 oC　for 4 hour(iv)

(vii)

Bake-out at 200~250 oC for 4 hour(iii)

Bake-out at 150 oC for 1 hour(ii)

Switching off / onDisconnecting / connecting the cable(i)

Fig.3 Change in a of SIG and MG depending on a bake-out, switching off/on, disconnecting/connecting, closing/opening each isolation valve, and removing the gauge head from the vacuum chamber and re-mounting.

17

5. Chronology of the measurements

Table 6 shows the chronology of the measurements made with the transfer standard

during the comparison loop. The sensor heads (rotor head, thimble, and rotor) of SRGs

and the gauge heads of IGs were hand carried. The controllers of IGs, cables, and the

thermometers were shipped.

Table 6 Chronology of the measurements, gauges, and number of calibrations during the comparison.

Participants Start date End date Number of

calibration runNumber points per run

Number of points Nijm

DES1

25-May-2010 16-Jun-2010 5 11 55 NMIJ /AIST

TFS

28-Jun-2010 2-Jul-2010 8 9 72

KRISS

3-Sep- 2010 8-Sep-2010 3 3 9

NMIJ /AIST

DES2 1-Oct- 2010 27-Oct-2010 5 11 55

6. General calibration procedure

6.1 Preparation for calibration

The two SRGs and two IGs were mounted to the calibration chamber at the same

horizontal plane. Following the installation of vacuum standards, the vacuum chambers

18

were evacuated to a pressure bellow 10-4 Pa, and each isolation valve was fully opened.

The setting parameters of transfer standards were verified or set to the values as shown

in Table 3 and Table 4.

The calibration chambers and the transfer standards did not allow to be baked to

prevent the σ of SRGs and a of IGs change owing to changing the surface condition of

gauge heads. No degassing of IGs also required for the same reason.

6.2 Calibration of the gauges

The IGs were calibrated in argon at six target pressure steps (PT) at the values 3×10-6

Pa, 9×10-6 Pa, 3×10-5 Pa, 9×10-5 Pa, 3×10-4 Pa, and 9×10-4 Pa. The purity of Ar in a

bottle was higher than 99.9999 %. Each pressure was generated a minimum of three

times in the calibration. The SRGs were calibrated at 9×10-4 Pa. The generated pressure

was required to be within 10 % of the target pressure.

7. Analysis of the reported data

7.1 Correction for zero pressure offset

The gauge pressure are first corrected for their “zero” reading with the vacuum

chamber evacuated and at the base pressure:

19

ijmkijmkijmk ppp G0G −= . (3)

Here, pGijmk is the uncorrected gauge reading, pG0ijmk is the zero-pressure gauge reading,

and pijmk is the gauge reading for zero-pressure offset. Meanings of indices for

abbreviated terms are summarized in Table 7.

Table 7 Meanings of indices for abbreviated terms.

Index Meaning i Transfer standard gauges

1 SRG-CE6 2 SRG-CE8 3 SIG

4 MG j Institute and calibration system

1 NMIJ-DES 2 NMIJ-TFS

3 KRISS m Number of calibration cycle k Individual reading of gauges

pG0ijmk for SRGs and IGs corresponds to the offset of SRG (poffset) and the background

pressure of IG (pBG), respectively. Table 8 shows the typical values the standard

deviations of poffset for SRGs and those of pBG for IGs, respectively. Since the duration of

20

10 s was employed for the measurement of SRGs at KRISS, the standard deviations of

SRGs were larger than those of NMIJ/AIST.

Table 8 Typical values of the offset (poffset) for SRGs and of the background pressure (pBG) for IGs measured by each calibration system. Their standard deviations σ are also shown.

SRG-CE6 SRG-CE8 SIG MG

poffset or pBG

/ Pa 2.5053 E-04 3.8354 E-04 9.40 E-08 1.84 E-07 NMIJ-DES1

σ / Pa 6.43 E-07 9.29 E-07 6.17 E-10 1.05 E-09

poffset or pBG

/ Pa 2.9100 E-04 6.6205 E-05 1.73 E-07 2.84 E-07 NMIJ-TFS

σ / Pa 4.87 E-07

1.13 E-06 1.09 E-09 1.65 E-09

poffset or pBG

/ Pa 2.3932 E-04 3.3858 E-04 6.14 E-07 9.55 E-07 KRISS

σ / Pa 7.84E-06

7.33E-06 No change No change

poffset or pBG

/ Pa 5.8898 E-04 2.0130 E-04 9.11 E-08 2.09E- 07 NMIJ-DES2

σ / Pa 7.61E-07 1.02 E-06 5.88E-10 1.21E-09

7.2 Temperature compensations of pressure reading of SRGs and IGs

Pressure readings of SRGs and IGs should be compensated by the chamber

temperature for the precise comparison because these depend on the chamber

21

temperature owing to the change in gas density [7,8]. In addition, pressure readings of

IGs depend on the gauge temperature due to thermal transpiration effect [8,9]. Therefore,

pijmk is compensated by using eq. (4).

),IGs(4,3for'

),SRGs(2,1for'

gref

gauge

cref

chamberTTTC

input

chamberSRG

===

===

−−

iTT

TTpccpp

iT

Tpcpp

ijmkijmkijmk

ijmkijmkijmk

(4)

where pijmk’ is the temperature compensated gauge pressure reading, cSRG is the

correction factor for the SRG, cTC and cTT are the correction factors for IGs owing to the

chamber temperature and the thermal transpiration effect, respectively. Tinput is the input

temperature of SRG (295.4 K (22.25 oC)). Tchamber is the measured chamber temperature,

Tref-c is the reference chamber temperatures of 296.15 K (23 oC), Tgauge and Tref-g are the

measured gauge temperatures of IGs and the reference gauge temperatures of 347.15 K

(74 oC) for SIG and 317.15 K (44 oC) of MG, respectively. Table 9 lists the room

temperature, the chamber temperature, and the gauge temperatures at each calibration

system. No discrepancy was observed between temperatures measured by own

thermometers and the transfer thermometers. The temperature correction factors, cSRG,

cTC, and cTT are also shown. The calibrations of NMIJ-TFS were performed at two

22

Table 9 Summary of the results of temperature measurements at each calibration system. The room temperature, the chamber

temperature, and the gauge temperatures at each calibration system are listed. The temperature correction factors, cSRG, cTC, and cTT are also shown. The calibrations of NMIJ-TFS were performed at two different temperature conditions.

Own thermometers Transfer thermometers Correction factors

Troom / K

Tchamber1 / K

Tchamber2 / K

Tgauge of SIG / K

Tgauge of MG / K

cSRG cTC for IGs

cTG of SIG

cTG of MG

NMIJ-DES1 296.0 296.7 297.0 296.8 345.3 316.6 1.002 1.002 0.997 0.998

Thigh 296.5 300.4 300.2 299.7 346.6 318.2 1.008 1.014 0.999 1.003NMIJ -TFS

Tlow 292.0 295.9 295.8 295.0 341.1 313.0 1.001 0.999 0.991 0.987

KRISS 294.5 294.8 294.8 294.5 335.3 308.2 0.999 0.995 0.983 0.972

NMIJ-DES2 296.0 296.8 297.0 296.8 345.3 316.6 1.002 1.002 0.997 0.998

different temperature conditions.

The magnitudes of corrections were less than 0.1 % for SRGs and 3 % for IGs. The

corrections for IGs are, however, canceled by normalization using the calibration results

of SRG as shown in appendix A.

7.3 Calibration ratio at 9×10-4 Pa based on the SRGs

The SRGs are normally linear devices, and the ratio of the transfer standard pressure

reading to the standard pressure will be independent of the pressure around the target

pressure of 9x10-4 Pa. For SRG i, calibration system j, cycle m, reading k, the average

calibration ratio (commonly referred to as accommodation coefficient for SRGs) is

∑∑==

==ijmijm N

k jmk

ijmk

ijm

N

kijmk

ijmijm P

pN

aN

a11

'11 (5)

i has the value 1 (SRG-CE6) and 2 (SRG-CE8). N1jm = N2jm.

Figure 4 shows the calibration ratio (aijm) for the two SRGs as determined by all the

cycles of all the participants. The x-axis shows the chronological progression in the

comparison. The calibration ratio for SRG-CE8 was higher than that for SRG-CE6 for

all the calibration systems. Maximum relative difference was 2.9 % for between

24

NMIJ-TFS and KRISS. Table 10 shows the shift in the calibration ratio of SRG-CE6

and SRG-CE8 for the two calibration cycles at NMIJ-DES for the estimation of the

uncertainty of the long-term shift

1

1.01

1.02

1.03

1.04

1.05

1.06

NMIJ-DES1 NMIJ-TFS KRISS NMIJ-DES2

a ijm

a1jm (SRG-CE6)

a2jm (SRG-CE8)

1

1.01

1.02

1.03

1.04

1.05

1.06

NMIJ-DES1 NMIJ-TFS KRISS NMIJ-DES2

a ijm

a1jm (SRG-CE6)

a2jm (SRG-CE8)

Fig.4 Calibration ratio (aijm) for the two SRGs as determined by all the cycles of all the participants.

Table 10 Shift in the calibration ratio aijm measured by SRGs at NMIJ-DES at the pressure of 9×10-4 Pa.

NMIJ-DES1 NMIJ-DES2 aij2 − aij1 a1jm (SRG-CE6)

1.0103 1.0150 -0.0047

a2jm (SRG-CE8)

1.0281 1.0287 -0.0006

25

7.4 Calibration ratio at 3×10-6 Pa to 3×10-4 Pa based on the IGs

The average calibration ratio aijm (commonly referred to as inverse of the correction

factor for IGs) is also calculated for SIG and MG by eq. (5). Figure 5 shows aijm of SIG

and MG as determined by all the cycles of all the participants.

1.1

1.15

1.2

1.25

1.3

1.35NMIJ-DES1

NMIJ-TFS

KRISS

NMIJ-DES2

a3jm

(SIG)

4.2%

1.36

1.4

1.44

1.48

1.52

10-6 10-5 10-4 10-3

NMIJ-DES1

NMIJ-TFS

KRISS

NMIJ-DES2

Pressure (Pa)

2.8%

a4jm

(MG)a ijm

1.1

1.15

1.2

1.25

1.3

1.35NMIJ-DES1

NMIJ-TFS

KRISS

NMIJ-DES2

a3jm

(SIG)

4.2%

1.36

1.4

1.44

1.48

1.52

10-6 10-5 10-4 10-3

NMIJ-DES1

NMIJ-TFS

KRISS

NMIJ-DES2

Pressure (Pa)

2.8%

a4jm

(MG)a ijm

Fig.5 Calibration ratio (aijm) of SIG and MG as determined by all the cycles of all the participants.

26

The hot cathode ionization gauges are also normally linear devices. aijm of SIG, however,

increased at the pressure higher than 10-4 Pa, while aijm of MG was almost constant

against the change in pressure. The better linearity of MG should be caused by the

smaller emission current of MG than that of SIG. The increase of aijm of SIG was caused

by space charge effect, which increases with the emission current.

Figure 6 shows the calibration results (aijmk) for SIG and MG reported by each

calibration system. The x-axis shows the chronological progression in the comparison.

The change in ajimk of MG was much smaller than that of SIG as expected from the

results of pretests. aijmk of SIG increased during each calibration cycle and decrease after

the transportation. The magnitude of the change in aijm for SIG was 13.5 % at maximum.

On the other hand, that for MG was 2.6 % at maximum, which observed at NMIJ-TFS.

This fluctuation of data was caused by the change in temperature condition; first three

points and the last one were calibrated at high chamber temperature of 300.3 K (27.2

oC) and the rests were calibrated at low chamber temperature of 295.9 K (22.8 oC).

Although the origin of this difference was unclear, it might be caused by the change in

the temperature distribution of the calibration chamber. aijmk of MG tended to decrease

with the number of calibrations.

27

1.341.361.381.4

1.421.441.461.48

1.5%

MIG1.05

1.1

1.15

1.2

1.251.3

1.35

1.4

3x10-6 Pa9x10-6 Pa

3x10-5 Pa9x10-5 Pa

3x10-4 Pa9x10-4 Pa

4% SIG

NMIJ-DES1 NMIJ-TFS NMIJ-DES2KRISS

Thigh

Tlow

a ijm

k

MG

1.341.361.381.4

1.421.441.461.48

1.5%

MIG1.05

1.1

1.15

1.2

1.251.3

1.35

1.4

3x10-6 Pa9x10-6 Pa

3x10-5 Pa9x10-5 Pa

3x10-4 Pa9x10-4 Pa

4% SIG

NMIJ-DES1 NMIJ-TFS NMIJ-DES2KRISS

Thigh

Tlow

a ijm

k

MG

Fig.6 Calibration results (aijmk) for SIG and MG reported by each calibration system.

Comparisons for the pressure range (3×10-6 Pa to 3×10-4 Pa) are based on the result of

MG only because better linearity of aijm, better stability, and no discrepancy of results

between SIG and MG in practice. Table 11 shows the shift in aijm of MG for the two

calibration cycles at NMIJ-DES to estimate the uncertainty of the long-term shift. As a

reference, those of SIG are also shown. The uncertainty of the long-term shift, uLTS(pij),

are summarized in Table 12.

28

Table 11 Shift in the calibration ratio aijm measured by SIG and MG at NMIJ-DES at

the pressure from 3×10-6 Pa to 9×10-4 Pa. PT / Pa NMIJ-DES1 NMIJ-DES2 aij2 − aij1

3×10-6 1.199 1.168 0.030 9×10-6 1.199 1.170 0.029 3×10-5 1.200 1.172 0.029 9×10-5 1.181 1.157 0.024 3×10-4 1.236 1.217 0.020

a3jm (SIG)

9×10-4 1.307 1.296 0.011 3×10-6 1.427 1.415 0.012 9×10-6 1.419 1.411 0.008 3×10-5 1.423 1.410 0.013 9×10-5 1.420 1.404 0.016 3×10-4 1.417 1.411 0.006

a4jm (MG)

9×10-4 1.420 1.410 0.009

Table 12 Relative uncertainty of the long-term shift, uLTS(pij)/pij, for SRG-CE6, SRG-CE8, and MG.

PT / Pa uLTS(p1j)/p1j

(SRG-CE6) uLTS(p2j)/p2j (SRG-CE8)

uLTS(p4j)/p4j (MG)

3×10-6 - - 0.42 % 9×10-6 - - 0.28 % 3×10-5 - - 0.45 % 9×10-5 - - 0.56% 3×10-4 - - 0.20 % 9×10-4 0.23 % 0.03 % 0.32 %

29

8. Results of the comparison

Three vacuum standards were compared by the same manner of CCM.P-K3 [1]. The

mean gauge pressure reading, pjU, is calculated from the average calibration ratio aijm for

three vacuum standards. The key comparison reference value (KCRV, or the reference

pressure pR) and the degree of equivalence are evaluated from pjU of each vacuum

standard. The calculation procedure is summarized in appendix.

8.1 Results at 9×10-4 Pa using the two SRGs

Results at 9×10-4 Pa using the two SRGs are summarized in Tables 13a and 13b. The

largest component of uc(pijm) is ustd for NMIJ-DES and NMIJ-TFS. However, uoffset is

the largest component for KRISS because of the short sampling time for SRGs. The

mean gauge reading (pjU) and its uncertainty (u(pjU)) calculated from results of two

SRGs are listed in Table 14.

30

Table 13a Results for SRG-CE6 (i=1) for each cycle at each calibration system for 9×10-4 Pa. Listed are calibration ratio (aijm), predicted gauge reading (pijm), relative standard uncertainty contributions to uc(pijm), and the combined standard uncertainty uc(pijm).

Relative standard uncertainty a1jm p1jm

/ Pa

uA ustd uoffset uT uLTS uc

uc(pijm) / Pa

NMIJ -DES1

1.0103 9.0927E-04

0.18 %

0.40 %

0.07 %

0.05 %

0.23 %

0.51% 4.60 E-06

NMIJ -TFS

1.0044 9.0398E-04

0.23 %

1.37 %

0.05 %

0.17 %

0.23 %

1.42 %

1.28 E-05

KRISS 1.0298 9.2684E-04

0.53 %

0.47 %

0.85 %

0.01 %

0.23 %

1.13 %

1.05 E-05

NMIJ -DES2

1.0150 9.1347E-04

0.11 %

0.40 %

0.08 %

0.05 %

0.23 %

0.49 %

4.46 E-06

Table 13b Results for SRG-CE8 (i=2) for each cycle at each calibration system for

9×10-4 Pa. Listed are calibration ratio (aijm), predicted gauge reading (pijm), relative standard uncertainty contributions to uc(pijm), and the combined standard uncertainty uc(pijm).

Relative standard uncertainty a2jm p2jm

/ Pa

uA ustd uoffset uT uLTS uc

uc(p2jm)/ Pa

NMIJ -DES1

1.0281 9.2529E-04

0.13 %

0.40 %

0.10 %

0.05 %

0.03 %

0.44 %

4.07 E-06

NMIJ -TFS

1.0219 9.1972E-04

0.05 %

1.37 %

0.12 %

0.17 %

0.03 %

1.39 %

1.28 E-05

KRISS 1.0514 9.4623E-04

0.47 %

0.47 %

0.77 %

0.01 %

0.03 %

1.02 %

9.66 E-06

NMIJ -DES2

1.0287 9.2584E-04

0.06 %

0.40 %

0.11 %

0.05 %

0.03 %

0.43 %

3.95 E-06

31

Table 14 Summary of results at 9×10-4 Pa target pressure based on calibrations of the SRGs Listed are mean gauge pressure reading (pjU), uncertainty in mean gauge pressure reading (u(pjU)), and its relative uncertainty u(pjU)/ pjU.

PT / Pa Participants pjU / Pa u(pjU) / Pa u(pjU)/ pjU

NMIJ-DES 9.1846E-04 3.87E-06 0.42 % NMIJ-TFS 9.1185 E-04 1.27 E-05 1.39 %

9×10-4

KRISS 9.3654 E-04 7.80 E-06 0.83 %

8.2 Results from 3×10-6 Pa to 3×10-4 Pa using MG

Results from 3×10-6 Pa to 3×10-4 Pa using MG are summarized in Table 15. Ion

gauge calibration ratios Kjm(PT) obtained by participants are shown graphically in Fig 7.

The largest component of uc(pijm) is typically ustd for all calibration system. The mean

gauge reading (pjU) and its uncertainty (u(pjU)) are listed in Table 16.

0.99

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

10-6 10-5 10-4 10-3

NMIJ-DES1NMIJ-TFSKRISSNMIJ-DES2

Ion

gaug

e ca

libra

tion

ratio

, Kjm

Pressure (Pa)

Fig.7 Ion gauge calibration ratios Kjm(PT) obtained by APMP.M.P-K3 participants.

32

Table 15 Results for MG for each cycle at each NMI, as a function of target pressure (PT). Shown are ion gauge inverse correction factor (aijm), and its relative Type A standard uncertainty (u(aijm)/ aijm), calibration ratio (Kjm), predicted gauge reading (pjm), relative standard uncertainty contributions to uc(pjm), and uc(pjm).

Relative standard uncertainty on pjm PT

/ Pa a4jm

u u u u u

u(a4jm)/ aijm

Kjm Pjm / Pa

uA std T uBG SRG LTS c

uc(pjm) / Pa

3×10-6 1.4271 0.27 % 1.0259 3.078

E-06 0.32 % 0.47 % 0.10 % 0.04 % 0.12 % 0.42 % 0.73 % 2.24

E-08

9×10-6 1.4187 0.17 % 1.0198 9.178

E-06 0.25 % 0.41 % 0.10 % 0.01 % 0.12 % 0.28 % 0.58 % 5.33

E-08

3×10-5 1.4225 0.15 % 1.0226 3.068

E-05 0.23 % 0.41 % 0.10 % 0.00 % 0.12 % 0.45 % 0.67 % 2.04

E-07

9×10-5 1.4200 0.10 % 1.0208 9.187

E-05 0.21 % 0.40 % 0.10 % 0.00 % 0.12 % 0.56 % 0.74 % 6.76

E-07

3×10-4 1.4165 0.17 % 1.0183 3.055

E-04 0.25 % 0.40 % 0.10 % 0.00 % 0.12 % 0.20 % 0.54 % 1.64

E-06

NMIJ -DES1

9×10-4 1.4196 0.18 % 1.0205 9.185

E-04 0.18 % 0.40 % 0.10 % 0.00 %

NMIJ -TFS

3×10-6 1.4358 0.37 % 1.0201 3.060 E-06

0.39 % 1.37 % 0.34 % 0.04 % 0.25 % 0.42 % 1.55 % 4.73

E-08

33

9×10-6 1.4288 0.39 % 1.0151 9.136 E-06

0.41 % 1.37 % 0.34 % 0.01 % 0.25 % 0.28 % 1.52 % 1.39

E-07

3×10-5 1.4263 0.27 % 1.0133 3.040 E-05

0.30 % 1.37 % 0.34 % 0.00 % 0.25 % 0.45 % 1.53 % 4.65

E-07

9×10-5 1.4183 0.29 % 1.0077 9.069 E-05

0.31 % 1.37 % 0.34 % 0.00 % 0.25 % 0.56 % 1.57 % 1.42

E-06

3×10-4 1.4248 0.20 % 1.0123 3.037 E-04

0.24 % 1.37 % 0.34 % 0.00 % 0.25 % 0.20 % 1.47 % 4.45

E-06

9×10-4 1.4261 0.13 % 1.0132 9.119 E-04

0.13 % 1.37 % 0.34 % 0.00 %

3×10-6 1.4319 0.49 % 1.0435 3.131 E-06

0.52 % 1.39 % 0.02 % 0.00 % 0.68 % 0.42 % 1.68 % 5.27

E-08

9×10-6 1.4216 0.40 % 1.0361 9.324 E-06

0.44 % 0.96 % 0.02 % 0.00 % 0.68 % 0.28 % 1.29 % 1.20

E-07

3×10-5 1.4077 0.16 % 1.0259 3.078 E-05

0.22 % 1.03 % 0.02 % 0.00 % 0.68 % 0.45 % 1.34 % 4.12

E-07

9×10-5 1.3824 0.26 % 1.0075 9.067 E-05

0.31 % 1.22 % 0.02 % 0.00 % 0.68 % 0.56 % 1.54 % 1.39

E-06

3×10-4 1.4445 0.54 % 1.0527 3.158 E-04

0.57 % 0.45 % 0.02 % 0.00 % 0.68 % 0.20 % 1.02 % 3.21

E-06

KRISS

9×10-4 1.4279 0.16 % 1.0406 9.365 E-04

0.16 % 0.47 % 0.02 % 0.00 %

34

3×10-6 1.4150 0.08 % 1.0238 3.071

E-06 0.12 % 0.47 % 0.10 % 0.04 % 0.12 % 0.42 % 0.66 % 2.04

E-08

9×10-6 1.4106 0.21 % 1.0207 9.186

E-06 0.23 % 0.41 % 0.10 % 0.01 % 0.12 % 0.28 % 0.57 % 5.27

E-08

3×10-5 1.4098 0.09 % 1.0201 3.060

E-05 0.13 % 0.41 % 0.10 % 0.00 % 0.12 % 0.45 % 0.64 % 1.95

E-07

9×10-5 1.4042 0.54 % 1.0160 9.144

E-05 0.55 % 0.40 % 0.10 % 0.00 % 0.12 % 0.56 % 0.89 % 8.18

E-07

3×10-4 1.4109 0.05 % 1.0208 3.062

E-04 0.11 % 0.40 % 0.10 % 0.00 % 0.12 % 0.20 % 0.49 % 1.50

E-06

NMIJ -DES2

9×10-4 1.4104 0.10 % 1.0205 9.185

E-04 0.10 % 0.40 % 0.10 % 0.00 %

35

Table 16 Summary of results at target pressures from 3×10-6 Pa to 3×10-4 Pa based

on calibrations of the MG. Listed are mean gauge pressure reading (pjU), uncertainty in mean gauge pressure reading (u(pjU)), and its relative uncertainty u(pjU)/ pjU.

PT / Pa Participants pjU / Pa u(pjU) / Pa u(pjU) / pjU

NMIJ-DES 3.075E-06 1.80E-08 0.59 % NMIJ-TFS 3.060E-06 4.73E-08 1.55 %

3×10-6

KRISS 3.131E-06 5.27E-08 1.68 % NMIJ-DES 9.182E-06 4.55E-08 0.50 % NMIJ-TFS 9.136E-06 1.39E-07 1.52 %

9×10-6


3×10-5


9×10-5


3×10-4

KRISS 3.158E-04 3.21E-06 1.02 %

8.3 Degree of equivalence

The degree of equivalence of participants to the reference value is summarized in

Table 17. The results are shown graphically in Fig. 8. The pair-wise degree of

equivalence between the participants is summarized in Table 18. Shaded cells indicate

results where there is a lack of equivalence at k=2 level. The vacuum standard of the

three participants were found to be equivalent within the claimed uncertainty in the

36

range from 3×10-6 Pa to 9×10-5 Pa. The lack of equivalence was shown at the pressure

of 3×10-4 Pa and 9×10-4 Pa between NMIJ-DES and KRISS, although the result of

9×10-4 Pa was marginal. The results of NMIJ-DES and NMIJ-TFS show good

equivalence at all pressures in spite of the different method.

Table 17 Summary of results at target pressures from 3×10-6 Pa to 9×10-4 Pa. Listed

are corrected mean gauge reading (pj), difference (dj) between pj and reference pressure (pR), and associated standard uncertainties. U(dj) = 2u(dj). Shaded cells indicate results where |dj|/U(dj) exceeds 1.0.

PT / Pa

Participants pj / Pa

u(pj) / Pa

dj / Pa

u(dj) / Pa

dj / PR dj / U(dj)

NMIJ-DES 2.973E-06 1.74E-08 -2.707E-08 2.69E-08 -0.90 % -0.502NMIJ-TFS 2.959E-06 4.57E-08 -4.097E-08 5.31E-08 -1.37 % -0.386

3×10-6

KRISS 3.027E-06 5.10E-08 2.707E-08 2.69E-08 0.90 % 0.502 NMIJ-DES 8.931E-06 4.43E-08 -6.917E-08 6.26E-08 -0.77 % -0.553NMIJ-TFS 8.886E-06 1.35E-07 -1.138E-07 1.49E-07 -1.26 % -0.383

9×10-6


3×10-5

KRISS 3.007E-05 4.02E-07 6.636E-08 2.17E-07 0.22 % 0.153 NMIJ-DES 9.049E-05 5.79E-07 4.869E-07 7.46E-07 0.54 % 0.326 NMIJ-TFS 8.953E-05 1.40E-06 -4.671E-07 1.59E-06 -0.52 % -0.147

9×10-5

KRISS 8.951E-05 1.37E-06 -4.869E-07 7.46E-07 -0.54 % -0.326NMIJ-DES 2.952E-04 1.34E-06 -4.796E-06 1.69E-06 -1.60 % -1.420NMIJ-TFS 2.931E-04 4.30E-06 -6.906E-06 4.62E-06 -2.30 % -0.748

3×10-4


9×10-4

KRISS 9.088E-04 7.57E-06 8.768E-06 4.22E-06 0.97 % 1.038

37

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

NMIJ-DES NMIJ-TFS KRISS

d j / p R

9x10-6 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


d j / p R

3x10-6 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


d j / p R

9x10-5 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


d j / p R

3x10-5 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


d j / p R

9x10-4 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


d j / p R

3x10-4 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


d j / p R

9x10-6 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


d j / p R

3x10-6 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


d j / p R

9x10-5 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


d j / p R

3x10-5 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


d j / p R

9x10-4 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


d j / p R

3x10-4 Pa

Fig. 8 Degree of equivalence of APMP.M.P-K3 participants to the reference value

from 3×10-6 Pa to 9×10-4 Pa. Plotted is relative difference (dj/pR) of corrected mean gauge pressure reading (pj) from reference value (pR), with expanded (k=2) uncertainty in relative difference shown as error bars.

38

Table 18 Summary of degree of equivalence to reference value (dj, U(dj)) and pair-wise degree of equivalence between the participants (djj, U(djj’)). Expanded uncertainty U given at k=2. Shaded cells indicate results where |dj|/U(dj) exceeds 1.0 or |djj’|/ U(djj’) exceeds 1.0.

NMIJ-DES NMIJ-TFS KRISSPT

/ Pa Partici- pants

dj / Pa

U(dj) / Pa

djj / Pa

U(djj’) / Pa

djj / U(djj’)

djj / Pa

U(djj’) / Pa

djj / U(djj’)

djj / Pa

U(djj’) / Pa

djj / U(djj’)

NMIJ-DES -2.71E-08 5.39E-08 1.39E-08 1.19E-07 0.117 -5.41E-08 7.62E-08 -0.711

NMIJ-TFS -4.10E-08 1.06E-07 -1.39E-08 1.19E-07 -0.117 -6.80E-08 1.19E-07 -0.571

3×10-6

KRISS 2.71E-08 5.39E-08 5.41E-08 7.62E-08 0.711 6.80E-08 1.19E-07 0.571

NMIJ-DES -6.92E-08 1.25E-07 4.47E-08 3.22E-07 0.139 -1.38E-07 1.77E-07 -0.781

NMIJ-TFS -1.14E-07 2.97E-07 -4.47E-08 3.22E-07 -0.139 -1.83E-07 3.22E-07 -0.568

9×10-6

KRISS 6.92E-08 1.25E-07 1.38E-07 1.77E-07 0.781 1.83E-07 3.22E-07 0.568

NMIJ-DES -6.64E-08 4.33E-07 2.35E-07 1.10E-06 0.215 -1.33E-07 6.13E-07 -0.2173×10-5

NMIJ-TFS -3.02E-07 1.01E-06 -2.35E-07 1.10E-06 -0.215 -3.68E-07 1.10E-06 -0.336

39

KRISS 6.64E-08 4.33E-07 1.33E-07 6.13E-07 0.217 3.68E-07 1.10E-06 0.336

NMIJ-DES 4.87E-07 1.49E-06 9.54E-07 3.51E-06 0.272 9.74E-07 2.11E-06 0.462

NMIJ-TFS -4.67E-07 3.18E-06 -9.54E-07 3.51E-06 -0.272 1.99E-08 3.51E-06 0.006

9×10-5

KRISS -4.87E-07 1.49E-06 -9.74E-07 2.11E-06 -0.462 -1.99E-08 3.51E-06 -0.006

NMIJ-DES -4.80E-06 3.38E-06 2.11E-06 9.83E-06 0.215 -9.59E-06 4.78E-06 -2.008

NMIJ-TFS -6.91E-06 9.23E-06 -2.11E-06 9.83E-06 -0.215 -1.17E-05 9.83E-06 -1.190

3×10-4

KRISS 4.80E-06 3.38E-06 9.59E-06 4.78E-06 2.008 1.17E-05 9.83E-06 1.190

NMIJ-DES -1.58E-05 8.55E-06 -7.49E-06 5.62E-05 -0.133 -3.16E-05 2.42E-05 -1.308

NMIJ-TFS -8.32E-06 2.68E-05 7.49E-06 5.62E-05 0.133 -2.41E-05 5.62E-05 -0.429

9×10-4

KRISS 1.58E-05 8.55E-06 3.16E-05 2.42E-05 1.308 2.41E-05 5.62E-05 0.429

40

8.4 Discussion of the lack of equivalence between NMIJ-DES and KRISS at the

pressure of 3×10-4 Pa and 9×10-4 Pa.

The final report of CCM.P-K3 [1] shows that the KRISS results were in good

agreement with other NMIs. In general, KRISS system has no problem because KRISS

used the same system and the same measurement procedures as that of CCM.P-K3.

NMIJ/AIST believes, however, that the NMIJ/AIST results are consistent because the

sensitivity of MG should be almost constant at the pressure of lower than 10-3 Pa from

typical characteristics of hot cathode ionization gauges [14-17]. The ion gauge

calibration factor Kjm in Fig. 7 obtained in NMIJ/AIST shows a linear characteristic. In

addition, the results of CCM.P-K12 show that the flowmeter of NMIJ/AIST, whose

uncertainty is the dominant factor of that of NMIJ-DES, were in good agreement with

other NMIs [18].

It should be noted that the dynamic expansion system of KRISS has two paths of the

gas for high flow rate and low flow rate, and the path was changed between 9×10-5 Pa

and 3×10-4 Pa. It means that equivalent was observed when KRISS used the path for

low gas flow rate and was not achieved after changing the path. This might influence

the results of the comparison. Another possibility of the non-equivalence is owing to the

instability of the effective accommodation coefficient of SRGs or the difference of the

41

condition and/or the procedure for calibrations.

After all, the reason of the lack of the equivalence at the pressure of 3×10-4 Pa and

9×10-4 Pa is unclear. This non-equivalence must be solved in cooperation between

KRISS and NMIJ/AIST in the near future.

9. Linking key comparison APMP.M.P-K3 to key comparison CCM.P-K3

The results of NMIJ-DES, which have smaller uncertainties than that of NMIJ-TFS,

are used as those of NMIJ/AIST, and are linked to the corresponding CCM key

comparison, CCM.P-K3, using the results of KRISS that participated in both

comparisons. The linking were performed in the range from 3×10-6 Pa to 9×10-5 Pa, in

which the calibration results of KRISS show an almost linear characteristics. The

calculation procedures are shown in appendix.

The degree of equivalence of NMIJ/AIST to the reference value of CCM.P-K3 is

summarized in Table 19. The results are shown graphically in Fig. 9. Error bars in this

figure show the relative expanded (k=2) uncertainty U(dj)/pR. When error bars cross

x-axis, there is equivalence to the reference value. The pair-wise degree of equivalence

between the participants of CCM.P-K3 and NMIJ/AIST is summarized in Table 20. The

NMIJ/AIST results were equivalent to the reference values and participants of

42

CCM.P-K3 within the claimed uncertainties.

Table 19 The degree of equivalence of NMIJ/AIST to the reference value of CCM.P-K3 at target pressures from 3×10-6 Pa to 9×10-5 Pa. Listed are the deviations from the difference of CCM.P-K3 to that of APMP.M.P-K3 for KRISS (D3 − d3), the difference of NMIJ/AIST values to the CCM.P-K3 reference value (D1), and associated standard uncertainties. Expanded uncertainty U given at k=2. No cells indicate results where |dj|/U(dj) exceeds 1.0.

Standard uncertainty on D1 / Pa PT /

Pa D3 − d3

/ Pa D1 / Pa

u(p1-APMP) u(pR-CCM) u(p3-CCM) u(D1)

Dj / pR Dj/U(Dj)

3×10-6 -1.878

E-08

-4.585

E-08

5.32

E-08

5.32

E-08

5.96

E-08

6.63

E-08

-1.53 % -0.385

9×10-6 -1.312

E-07

-2.003

E-07

1.15

E-07

1.15

E-07

1.31

E-07

1.46

E-07

-2.23 % -0.765

3×10-5 -3.304

E-07

-3.967

E-07

3.50

E-07

3.50

E-07

4.12

E-07

4.54

E-07

-1.32 % -0.482

9×10-5 -4.561

E-07

3.080

E-08

8.24

E-07

8.24

E-07

1.11

E-06

1.20

E-06

0.03 % 0.014

43

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

NIST PTB NPL NPLI KRISS NMIJ/AIST

Dj /

p R

3x10-6 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


Dj /

p R

9x10-6 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


Dj /

p R

3x10-5 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


Dj /

p R

9x10-5 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


Dj /

p R

3x10-6 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


Dj /

p R

9x10-6 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


Dj /

p R

3x10-5 Pa

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


Dj /

p R

9x10-5 Pa

Fig.9 Degree of equivalence of CCM.P-K3 participants and NMIJ/AIST to the reference value from 3×10-6 Pa to 9×10-5 Pa. Plotted is relative difference (dj/pR) of corrected mean gauge pressure reading (pj) from reference value (pR), with expanded (k=2) uncertainty in relative difference shown as error bars.

44

Table 20 Summary of pair-wise degree of equivalence between NMIJ/AIST and participants of CCM.P-K3. Expanded uncertainty U given at k=2. No cells indicate results where |djj’|/ U(djj’) exceeds 1.0

NMIJ/AIST PT / Pa NMIs

D1j / Pa U(D1j’) / Pa D1j / (D1j’) NIST -1.285E-08 7.66E-08 -0.084 PTB 3.605E-08 8.36E-08 0.216 NPL -8.375E-08 8.51E-08 -0.492 NPLI -3.255E-08 8.58E-08 -0.190

3×10-6

KRISS -5.414E-08 8.50E-08 -0.318 NIST -1.745E-07 1.67E-07 -0.522 PTB 3.766E-08 1.84E-07 0.102 NPL -3.143E-07 1.87E-07 -0.839 NPLI -1.736E-07 1.90E-07 -0.457

9×10-6

KRISS -1.383E-07 1.86E-07 -0.373 NIST -4.294E-07 5.14E-07 -0.418 PTB 3.803E-07 5.65E-07 0.337 NPL -6.537E-07 5.75E-07 -0.568 NPLI -3.707E-07 5.89E-07 -0.315

3×10-5

KRISS -1.327E-07 5.74E-07 -0.116 NIST 1.568E-07 1.32E-06 0.060 PTB 2.571E-06 1.41E-06 0.913 NPL -6.722E-07 1.43E-06 -0.235 NPLI -3.352E-07 1.51E-06 -0.111

9×10-5

KRISS 9.738E-07 1.45E-06 0.335

10. Conclusions

KRISS and NMIJ/AIST participated into this APMP key comparison of ultra-high

45

vacuum pressure standards from 3×10-6 Pa to 9×10-4 Pa. NMIJ/AIST used two

calibration systems; the dynamic expansion system and the two-stage flow-dividing

system. KRISS used the dynamic expansion system.

The transfer standard was sufficiently stable to meet the requirements owing to five

improvements of the protocol and the transfer standards. In other words, the uncertainty

of the vacuum standard ustd became the dominant factor of that of the corrected gauge

pressure reading, pj, typically.

The ultra-high vacuum standards of NMIJ-DES and NMIJ-TFS were found to be

equivalent with KRISS within their claimed uncertainties in the range from 3×10-6 Pa to

9×10-5 Pa and from 3×10-6 Pa to 9×10-4 Pa, respectively. The NMIJ-DES results in the

range from 3×10-6 Pa to 9×10-5 Pa were transferred to the corresponding CCM key

comparison, CCM.P-K3, and it is shown that the NMIJ values were equivalent to the

CCM KCRV within the claimed uncertainties. The lack of equivalence between

NMIJ-DES and KRISS at the pressure of 3×10-4 Pa and 9×10-4 Pa is the problem to be

solved in the near future, although the bias at 9×10-4 Pa was marginal.

Acknowledgements

The invaluable advice from Dr. Woo, the chairperson of the Technical Committee on

Mass and Related Quantities (TCM) of APMP, is gratefully acknowledged.

46

Contributions by several of the staff in the pressure and vacuum standards section at the

NMIJ/AIST, in particular Dr. Kobata, are gratefully acknowledged for their help and

encouragement.

47

Appendix The calculation procedure for the comparison

A.1 Determination of mean gauge pressure reading, pjU

A block diagram to determinate the mean gauge pressure reading, pjU, from the

average calibration ratio aijm is shown in Fig. A1. Details are summarized in below.

Reported calibration results

SRG-CE6 SRG-CE8 SIG MG

Inverse of the correction factor from 3×10-6 Pa to 9×10-4 Pa

Average calibration ratio, aijm

Effective accommodation coefficient at 9×10-4 Pa

Predicted gauge reading, p1jm

p2jm

pjmU

Mean cycle gauge pressure reading, pjmU

Mean gauge pressure reading, pjU, at 9×10-4 Pa

Ion gauge calibration ratio, Kjm

Normalization

pjU from 3×10-6 Pa to 3×10-4 Pa

pjm

Fig. A1 Block diagram for the determination of mean gauge pressure reading, pjU.

48

A.1.1 pjU at 9×10-4 Pa determined from the calibration ratios of two SRGs

The calibration ratio aijm is used to calculate a predicted gauge pressure reading on

SRG i when each vacuum standard of participants j (j=1, 2, and 3 mean NMIJ-DES,

NMIJ-TFS, and KRISS, respectively) at calibration cycle m is set to target pressure, PT.

TPap ijmijm = . (A1)

The predicted gauge reading of eq. (A1) (designated by the inclusion of subscripts j and

m) is not the same as pijmk’; pijm is the actual reading of the SRG when the vacuum

standard is set to pressure PT.

A single gauge “pressure” is useful to compare the pressures of the calibration

systems to a reference pressure and to each other. For each calibration cycle of each

calibration system, a mean cycle gauge pressure reading pjmU was calculated as the

simple arithmetic of the predicted gauge readings of the two SRGs:

221

Ujmjm

jm

ppp

+= , (A2)

49

where the subscript U denotes that the gauge readings are uncorrected to the target

pressure (explanation to follow), and m refers to the cycle of the calibration cycle.

For the NMIJ-DES, a single value pjU was calculated as the arithmetic mean of the

two cycle values:

∑=

=2

1UU 2

1m

jmj pp . (A3)

For NMIJ-TFS and KRISS, the subscript m can be dropped in eq. (A2) to define pjU as

the mean gauge pressure reading, as these calibration systems had only one calibration

cycle.

A.1.2 pjU from 3×10-6 Pa to 3×10-4 Pa determined from the calibration ratios of MG

The calibration ratio of MG from 3×10-6 Pa to 9×10-4 Pa is normalized by that of

SRG at 9×10-4 Pa. This normalization comes from assuming the generated pressure of

the vacuum standard, at 9×10-4 Pa, was the same whether it was being measured with an

IG or an SRG. The ion gauge calibration ratio, Kjm(PT), is defined as

50

( ) ( )( ) R

U4

4

T4T 109 p

pa

PaPK j

jm

jmjm ⋅

×= − , (A4)

where pjU is determined from the SRGs at 9×10-4 Pa, and pR is numerically equal to

9×10-4 Pa. As mentioned before, this normalization cancels the temperature correction

using eq. (4) for pijmk of MG. Figure 7 shows the Kjm(PT) obtained by participants as a

function of the target pressure PT.

The predicted gauge pressure reading for MG is calculated by

( ) TT PPKp jmjm ⋅= . (A5)

Mean gauge pressure readings of pjU from 3×10-6 Pa to 3×10-4 Pa are calculated from

pijm by the similar procedure shown above.

A.2 Estimation of the uncertainty of pjU at 9×10-4 Pa based on the SRGs and from

3×10-6 Pa to 3×10-4 Pa based on the MG.

The standard uncertainty in the mean gauge pressure readings, uc(pjU), at 9×10-4 Pa

51

based on the SRGs are calculated by eq. (A6) for the NMIJ-TFS and the KRISS:

( ) ( ) ( ) ( ) ( ) ( )( )2/12

1

2LTS

2A

2offset

2T

2stdUc 4

1

++++= ∑

=iijijijjjj pupupupupupu . (A6)

For the NMIJ-DES, pjU is the mean of 4 values of pijm (2 gauges, 2 cycle):

( ) ( ) ( ) ( ) ( ) ( )( )2/12

1

2

1

2LTS

2A

2offset

2

1

2T

2stdU 16

141

++++= ∑∑∑

= == m iijijij

mjjjc pupupupupupu .

(A7)

Here, ustd is the uncertainty of the vacuum standard, uT is that of temperature, uoffset is

that of the offset, uA is the Type A uncertainty, in other wards the standard deviation, of

calibration results at the cycle m, and uLTS is the uncertainty owing to the long-term shift

of aijm.

The standard uncertainty in the mean gauge pressure readings, uc(pjU), from 3×10-6 Pa

to 3×10-4 Pa based on the MG are calculated by eq. (A8) for NMIJ-TFS and KRISS:

52

( ) ( ) ( ) ( ) ( ) ( ) ( )( )

( ) ( )( )( )

( )( )( )

2

4

4A

2

T

TA2A

2/12LTS

2A

2BG

2T

2SRG

2stdc

109109

×

×+

=

+++++=

−

−

ij

ij

ij

ij

ij

ij

ijijijjjjjU

SSu

PSPSu

ppu

pupupupupupupu

. (A8)

For NMIJ-DES, pjU is the mean of 2 values of pijm (1 gauge, 2 cycles):

( ) ( ) ( ) ( ) ( ) ( ) ( )( )

( ) ( )( )( )

( )( )( )

2

4

4A

2

T

TA2A

2/12

1

2LTS

2A

2BG

2T

2SRG

2stdUc

109109

41

×

×+

=

+++++=

−

−

=∑

ijm

ijm

ijm

ijm

ijm

ijm

mijmijmijmjjjj

SSu

PSPSu

ppu

pupupupupupupu

.

(A9)

Here, uSRG is the standard uncertainty in the mean gauge pressure from the SRGs at

9×10-4 Pa, which is calculated by eq. (A10):

( ) ( ) ( )jUjUj pupupu 2std

2cSRG −= . (A10)

The uncertainty of the long-term shift, uLTS(pij), is calculated from the difference of

calibration results before and after shipping at NMIJ-DES by eq. (A11):

53

( ) ( )1

1211LTSLTS

21

i

ii

ij

ij

ij

ij

aaa

aau

ppu −

⋅== . (A11)

Table 12 shows the relative uncertainties of long-term shift, uLTS(pij)/pij, for SRG-CE6,

SRG-CE8, and MG. These values of SRGs are comparable or a little smaller than the

previous comparisons [1,8] and the value of MG is smaller than the previous one [1].

A.3 Estimation of the key comparison reference value and the degree of

equivalence

A block diagram to estimate the key comparison reference value (KCRV, or pR) and

the degree of equivalence is summarized in Fig. A2.

The uncorrected reference pressure as pRU is determined by the arithmetic mean

between p1U (NMIJ-DES) and p3U KRISS:

2U3U1

RUppp +

= . (A12)

Here, p2U (NMIJ-TFS) is not included because it has a correlation with p1U

(NMIJ-DES).

54

p1U for NMIJ-DES p2U for NMIJ-TFS p3U for KRISS

Uncorrected reference pressure, pRU

Scaling factor, fc

Corrected mean gauge pressure reading, p1

Difference, d1 Difference, d2 Difference, d3

Degree of equivalence

Expanded uncertainty in the difference, U(d1)

U(d2) U(d3)



Reference pressure, pRU

p1U for NMIJ-DES p2U for NMIJ-TFS p3U for KRISS

Uncorrected reference pressure, pRU

Scaling factor, fc


Difference, d1 Difference, d2 Difference, d3

Degree of equivalence

Expanded uncertainty in the difference, U(d1)

U(d2) U(d3)



Reference pressure, pRU

Fig. A2 Block diagram for the estimation of the key comparison reference value (KCRV, or pR) and the degree of equivalence.

The scaling factor, fc, which sets the reference pressure is numerically equal to the target

pressure, is determined by eq. (A13):

RU

Tc p

Pf = . (A13)

55

The reference pressure and its uncertainty are determined by eq. (A14):

( ) ( ) ( )( ) 2/13

2c1

2cR

U3U1cRUcR

21

2

pupupu

ppfpfp

+=

+=⋅=

. (A14)

The scaling factors and reference pressure uncertainties are listed in Table A1.

Table A1 Uncorrected reference pressure, pRU, scaling factor, fc, reference pressure (KCRV), pR, and standard uncertainty in reference pressure, u(pR) as a function of target pressure.

PT / Pa pRU / Pa fc pR / Pa u(pR) / Pa u(pR) / pR 3×10-6 3.103E-06 0.9669 3.000 E-06 2.69E-08 0.898 % 9×10-6 9.253E-06 0.9726 9.000 E-06 6.26E-08 0.695 % 3×10-5 3.071E-05 0.9769 3.000 E-05 2.17E-07 0.722 % 9×10-5 9.116E-05 0.9872 9.000 E-05 7.46E-07 0.829 % 3×10-4 3.108E-04 0.9651 3.000 E-04 1.69E-06 0.563 % 9×10-4 9.275E-04 0.9703 9.000 E-04 4.22E-06 0.469 %

The corrected mean gauge pressure reading obtained by each participant and its

56

uncertainty can be expressed as:

( ) ( Uc

Uc

jj

jj

pufpu

pfp

⋅=

⋅=

). (A15)

The degree of equivalence is defined as the difference of the laboratory result from

the reference value along with the uncertainty of the difference. The difference, dj, is:

Uppd jj −= , (A16)

and its uncertainty for NMIJ-DES and KRISS is:

( ) ( Rpudu j = )

)

. (A17)

For NMIJ-TFS, the uncertainty is:

( ) ( ) ( )( 2/12

2cR

2 pupudu j += . (A18)

57

Equivalence to the KCRV is evaluated by comparing the difference dj to the expanded

(k=2) uncertainty in the difference 2u(dj). There is equivalence if:

( ) ( ) 0.12

≤=j

j

j

j

du

d

dU

d. (A19)

Degree of equivalence between participants and its uncertainty are given by pair-wise

difference in the deviation from the reference pressure and the associated uncertainty:

( ) ( ) ( )( 2/1'

2c

2c'

'''

jjjj

jjjjjj

pupudu

ppddd

+=

−=−=

) . (A20)

There is equivalence if:

( ) ( ) 0.12 '

'

'

'≤=

jj

jj

jj

jj

du

d

dU

d. (A21)

A.4 Method for linking key comparison APMP.M.P-3 to key comparison

CCM.P-K3

58

The results of NMIJ-DES were used as those of NMIJ-DES. The degrees of

equivalence of NMIJ/AIST can be transferred to CCM.P-K3 comparison using:

1331 ddDD +−= , (A22)

where D1 and d1 are the differences of NMIJ/AIST values from the reference values of

CCM.P-K3 and APMP.M.P-K3, respectively, and D3 and d3 are those of KRISS.

The expansion of eq. (A22) is:

( ) ( ) ( )( )

3CCMAPMP1

APMP3CCM3CCMAPMP1

APMPAPMP1APMPAPMP3CCMCCM31

ppppppp

ppppppD

R

R

RRR

∆+−=−+−=

−+−−−=

−−

−−−−

−−−−−−

, (A23)

where p3-CCM, p3-APMP, and ∆p3 are the corrected mean gauge pressure reading of KRISS

at CCM.P-K3 and at APMP.M.P-K3, and their difference, respectively, p1-APMP is the

corrected mean gauge pressure reading of NMIJ/AIST at APMP.M.P-K3, and pR-CCM

and pR-APMP are the reference pressure of CCM.P-K3 and of APMP.M.P-K3,

respectively.

The D1 is calculated from eq.(A22). The uncertainties of D1 are calculated to be:

59

( ) ( ) ( ) ( ) ( )32

CCMR2

APMP12

11 22 pupupuDuDU ∆++== −− , (A24)

from eq.(A23). Although ∆p3 is the difference between p3-CCM and p3-APMP, it is assumed

that the u(∆p3) is equal to the u(p3-CCM) to avoid double-counting because there is a

correlation between p3-CCM and p3-APMP. u(p3-CCM) is comparable or a little bit larger than

the u(p3-APMP).

The pair wise differences between the participants of CCM.P-K3 and NMIJ/AIST

were also calculated by the similar method shown in the section 3 of the

appendix.

60

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