BUREAU INTERNATIONAL DES POIDS ET MESURES. Final report

Transcription

1 BUREAU INTERNATIONAL DES POIDS ET MESURES Blateral Comparson of Ω standards (ongong BIPM key comparson BIPM.EM-K.a) between the NIST (USA) and the BIPM. R. Goebel *, R. Elmqst **, N. Fletcher * and M. Stock *. * Brea Internatonal des Pods et Mesres, Sèvres, France. ** Natonal Insttte of Standards and Technology, Gathersbrg, USA. Fnal report December 007 Page

2 Introdcton A comparson of vales assgned to Ω resstance standards was carred ot between the BIPM and the NIST (USA) n the perod Aprl 007 to October 007. Three Ω BIPM travellng standards of CSIRO type were calbrated frst at the BIPM, then at the NIST and agan at the BIPM after ther retrn. The measrement perods are referred to as: 'Before' measrements at the BIPM: Aprl and Jne-Jly 007 NIST measrements: Agst-September 007 'After' measrements at the BIPM: September-October 007 The BIPM calbratons are corrected to the reference temperatre.000 C and the reference pressre 0.5 hpa. Accordng to the protocol, the NIST does not apply pressre and temperatre correctons to ts reslts. The correctons are made by the BIPM, sng the temperatre and pressre coeffcents of the standards together wth the temperatre and pressre measrements provded by the NIST. There s no clear evdence of a sngle lnear drft of each standard over the whole perod of the comparson (three measrement perods, 'Before', 'NIST' and 'After': see Fgres, and ). Drng each perod, the resstance of each standard s therefore assmed to be constant, wth spermposton of a random nose. For each perod, the calbraton vale assgned to each standard s the mean vale of the measrements performed drng ths perod, wth an assocated standard ncertanty. The dfference between the NIST and the BIPM calbratons of a gven standard R can be wrtten as: = R R NIST, BIPM, If three standards are sed, the mean of the dfferences s: NIST BIPM = ( R NIST, = RBIPM, ) () Ths expresson can also be wrtten as: NIST BIPM = R NIST, RBIPM, = = () whch s the dfference of the means. Measrements at the BIPM. BIPM calbratons The BIPM measrements were carred ot by comparson wth a 00 Ω reference resstor (referred to as BI00-) whose vale s known wth respect to the BIPM qantzed Hall resstance (QHR) standard. The comparson s performed sng a DC cryogenc crrent comparator operatng wth a 50 ma crrent n the Ω resstors. In order to mnmze the nterpolaton ncertanty, the 00 Ω reference resstor was calbrated for tmes aganst the QHR n the perod Aprl 007 to October 007. Page

3 The Ω resstors were kept n a temperatre controlled ol bath at a temperatre whch s close (wthn a few mk) to the reference temperatre. The temperatre of the standards s determned by means of a calbrated SPRT, n conjncton wth thermocoples. Drng the frst perod of measrements at the BIPM, the medm-term dsperson was larger than sal (standard devaton n the range 5 to 7 parts n 0-9 nstead of to 4 parts n 0-9 ). Ths cold be attrbted to the pertrbatons prodced by the refrbshment works n other laboratory rooms n the same bldng. The BIPM measrements are smmarzed n Table and the ncertanty bdget n Table. BIPM Relatve dfference from nomnal Ω vale / 0-6 Std. dev. Std. dev. Standard # BEFORE AFTER B A Mean vale of 'Before' and 'After' Standard # mean Dsperson / 0-6 / 0-9 Systematc / Table : Smmary of the BIPM calbratons. The dsperson s estmated by the standard devatons, and 'systematc' refers to the sorces of ncertanty that do not contrbte to the varablty of the reslts. Sorce of ncertanty relatve standard ncertanty Imperfect realsaton of R K-90 x 0-9 Calbraton of the BIPM 00 Ω reference (BI00-) aganst R K-90 x 0-9 Interpolaton / extrapolaton of the vale of BI00- x 0-9 Measrement of the ( Ω / BI00-) rato 8 x 0-9 Temperatre correcton for the Ω standard x 0-9 Pressre correcton for the Ω standard x 0-9 Combned ncertanty 6 x 0-9 Table : BIPM ncertanty bdget for the calbraton of the Ω travellng standards. The vale attrbted to -th standard s the arthmetc mean of the "Before" and "After" vales. R = R + R ) / BIPM, ( Before, After, Page

4 For each standard, the ncertanty assocated wth the dsperson s the qadratc mean of the standard devatons "Before" and "After". = + ) / (, Before, After, s the ncertanty arsng from the combned contrbtons assocated wth the BIPM measrement faclty and the traceablty, as descrbed n Table. Ths component s assmed to be strongly correlated between calbratons performed n the same perod. For a sngle standard, the BIPM ncertanty BIPM, s obtaned from: The, are assmed to be correlated, nlke,. = + BIPM,,, Usng expresson (), when the mean (for three standards) of the NIST-BIPM relatve dfference s calclated, the BIPM contrbton to the ncertanty s: BIPM = =, + () Usng the vales shown n Table, the relatve standard ncertanty BIPM s BIPM = 6. X Uncertanty assocated wth the transfer d s the ncertanty assocated wth the drft (or the step changes) of the travellng standards observed after ther retrn at the BIPM. The fnal resstance vale attrbted by the BIPM (the mean of the 'Before' and 'After' measrements) s n the mddle of the step d: d = ( R After RBefore) As we have no clear knowledge abot the behavor of the standards drng the perod between 'Before' and 'After', t s assmed that the actal resstance cold have had any vale n the range d, wth eqal probablty. Assmng a rectanglar probablty dstrbton, d = d Another sorce of ncertanty assocated wth the transfer s the dfference n the operatng crrents sed by the two laboratores: 50 ma at the BIPM and 00 ma at the NIST. Ths mght nflence the resstance of the standards throgh ther power coeffcents. A seres of measrements were performed at the BIPM to determne these power coeffcents. Unfortnately, or crrent sorce does not allow crrents as large as 00 ma, and smlarly the NIST faclty can not easly be modfed to operate at 50 ma. The BIPM seres of measrements were therefore carred ot sng alternately I = 50 ma and I /, bt no sgnfcant change cold be observed wthn the nose of the measrements, that s abot part n 0 9. A conservatve vale of the relatve standard ncertanty P assocated wth possble power effects n the range 50 ma 00 ma was estmated to be: P = X 0-9. For a sngle standard, the transfer ncertanty T, s obtaned from: T, = d, + P, The P, are assmed to be correlated, nlke d,. Page 4

5 Followng the same reasonng as n expresson (), the ncertanty T assocated wth the transfer (for the mean of three standards) s: T = = d, + P TRANSFER Drft Power Standard # d / 0-9 P / Combned.9 Total T 4.4 Table : Uncertanty assocated wth the drft and the power coeffcent of the standards. Usng the vales of Table, the relatve standard ncertanty T s: T = 4.4 X 0-9 Page 5

6 NIST reslts Seral No. of tem(s): 649, 6400, 6407 Manfactrer: CSIRO Standard ncertanty Dstrbton /method of evalaton Senstvty coeffcent Uncertanty contrbton Degrees of freedom Inflence factor y (y ) Method/(A, B) c (R ) (Ω) ν Scalng / traceablty.00e-08 Normal/B Ω.00E Reference standards 6.50E-09 Normal/B Ω 6.50E-09 Measrng apparats 4.00E-09 Rectanglar/B Ω 4.00E-09 Ambent condtons: Temperatre.00E-0 C Normal/B Pressre.00E-0 kpa Normal/B Standard devaton.90e-09 Normal/A Ω.90E-09 Table 4: NIST ncertanty bdget (typcal vales; the standard devaton vale s gven as an example). Method: The NIST qantm Hall effect standard was compared twce each year to fve 00 Ω standards sng a cryogenc crrent comparator brdge. For tmes each year, these fve standards were compared to two or three Ω standards of the CSIRO desgn, sng a second cryogenc crrent comparator. These CSIRO-type standards were then sed as transfer standards to mantan the mean reference vale of a grop of fve Thomas-type Ω standards n an atomated potentometer measrement system based on a commercal crrent comparator brdge (Gldlne 990). The Ω comparson standards were compared to ths reference grop sng the same potentometrc system. Measrements were repeated on days n the NIST segment of the comparson. All measrements were sed to determne the average resstance vale relatve to the NIST measrement standards. Measrement temperatre control: The reference standards were mantaned n a mneral ol bath mantaned at C as measred by a calbrated SPRT and thermometer brdge (Hart 575). The BIPM comparson standards were measred n a mneral ol bath mantaned at nomnal.00 C as measred by a calbrated thermstor probe (Flke 5640). The thermstor measrements were corrected sng a calbrated SPRT and thermometer brdge (Hart 575). Test crrent: Drect crrent wth reversal, measred at 00 ma. Hmdty: Relatve hmdty n the laboratory averaged 40%. Seral No. of tem: Average measrement date, tme Resstance vale (Ω) Standard devaton vale (Ω) Temperatre Barometrc pressre ncldng mneral ol Ag-007, 0: x C 0.05 kpa Ag-007, 0: x C 0.05 kpa Ag-007, 0: x C 0.05 kpa Table 5: Smmary of the NIST calbratons. The NIST reslts are corrected to the reference temperatre and the reference pressre sng the coeffcents shown n Table 6. Page 6

7 Relatve temperatre coeffcents Relatve pressre coeffcents. Standard # Alpha / (0-6 /K) Beta / (0-6 /K²) / (0-9 /hpa) Table 6: Temperatre and pressre coeffcents of the travellng standards. Reference temperatre =.000 C Reference pressre = 0.5 hpa Relatve correctons appled to the NIST reslts Standard # For temperatre For pressre x x x 0-6. x x x 0-0 Table 7: Correctons for temperatre and pressre appled to the NIST reslts. There s no addtonal ncertanty assocated wth these correctons. The contrbtons arsng from the ncertantes assocated wth the temperatre and pressre measrements at NIST are neglgble de to the very small sze of the correctons. In Table 8, s the ncertanty assocated wth the dsperson (see Table 5, colmn 4) and combnes the other contrbtons (frst three lnes n Table 4). NIST After correctons Resstance / Ω Relatve dfference from Relatve standard ncertantes nomnal. Dsperson Others / 0-6 / 0-9 / Table 8: Smmary of the NIST reslts, after correctons for temperatre and pressre. For a sngle standard, the NIST ncertanty NIST, s obtaned from: NIST, =, +, The, are assmed to be correlated, nlke the,. Usng expresson (), when the mean (for three standards) of the NIST-BIPM relatve dfference s calclated, the NIST contrbton to the ncertanty s:, NIST = + (5) = Usng the vales shown n Table 8, the relatve standard ncertanty NIST s NIST =.7 X 0-9. Page 7

8 4 Comparson NIST BIPM The dfferences between the vales assgned by the NIST at the NIST, R NIST, and those assgned by the BIPM at the BIPM, R BIPM, to each of the three travellng standards drng the perod of the comparson are shown n Table 9. Standard # NIST - BIPM (R NIST R BIPM ) / ( Ω) / mean 0.04 Table 9: Dfferences between the vales assgned by the NIST (R NIST ) and by the BIPM (R BIPM ) to the three travellng standards. The mean dfference between the NIST and the BIPM calbratons s: (R NIST R BIPM ) / ( Ω) = The relatve combned standard ncertanty of the comparson, C, s: = + + C BIPM NIST where BIPM = 6. X 0-9, NIST =.7 X 0-9, T = 4.4 X 0-9 as calclated n sectons and : C = 0.0 X 0-6 T The NIST and the BIPM calbratons are n good agreement, wth a dfference smaller than one standard ncertanty. The fnal reslt of the comparson s presented as the degree of eqvalence D between the NIST and the BIPM for vales assgned to Ω resstance standards, and ts expanded relatve ncertanty (expanson factor k = ), U C D = [(R NIST R BIPM ) / Ω] = U C = Page 8

9 -5.5 Standard # Dfference from nomnal / BIPM 'Before' x NIST BIPM 'After' -5. 5/04/007 5/05/007 4/06/007 4/07/007 /08/007 /09/007 /0/007 Date Fgre : Calbratons at the BIPM (sqares) and at the NIST (crcles) of the travellng standard ref. 649, expressed as the relatve devaton from the nomnal Ω vale Standard # Dfference from nomnal / BIPM 'Before' x NIST BIPM 'After' /04/007 5/05/007 4/06/007 4/07/007 /08/007 /09/007 /0/007 Date Fgre : Calbratons at the BIPM (sqares) and at the NIST (crcles) of the travellng standard ref. 6400, expressed as the relatve devaton from the nomnal Ω vale. Page 9

10 -0.5 Standard # Dfference from nomnal / BIPM 'Before' BIPM 'After' x NIST /04/007 5/05/007 4/06/007 4/07/007 /08/007 /09/007 /0/007 Date Fgre : Calbratons at the BIPM (sqares) and at the NIST (crcles) of the travellng standard ref. 6407, expressed as the relatve devaton from the nomnal Ω vale. Page 0