Intrinsic Wavelength Standard Absorption Bands in Holmium Oxide

Solution for UVÕvisible Molecular Absorption Spectrophotometry

John C. Travisa...

Chemical Science and Technology Laboratory (CSTL), National Institute of Standards and Technology (NIST), Gaithersburg,

Maryland 20899-8394 ^john.travis@nist.gov&

Joaquin Campos Acosta

Instituto de Fı ́sica Aplicada (IFA), Consejo Superior de Investigaciones Cientı ́ficas (CSIC), Serrano 144, 28006 Madrid, Spain

Gyo ̈rgy Andor

Alapme ́re ́sek I. Fooszta ́ly, Orsza ́gos Me ́re ́su ̈gyi Hivatal (OMH), H-1535 Budapest, Hungary

Jean Bastie

Institut National de Metrologie (BNM-INM), Conservatoire National des Arts et Me ́tiers (CNAM), 75003 Paris, France

Peter Blattner

Length and Optics, Swiss Federal Office of Metrology and Accreditation (METAS), Lindenweg 50, CH-3003 Bern-Wabern, Switzerland

Christopher J. Chunnilall

Optical Radiation Metrology Group, National Physical Laboratory (NPL), Teddington, Middlesex TW11 0LW, United Kingdom

Steven C. Crosson and David L. Duewer

Chemical Science and Technology Laboratory (CSTL), National Institute of Standards and Technology (NIST), Gaithersburg,

Maryland 20899-8394

Edward A. Early

Physics Laboratory (PL), National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899-8441

Franz Hengstberger

Optical Radiometry and Radiation Pyrometry, National Metrology Laboratory, CSIR, 0001 Pretoria, South Africa

Chang-Soon Kim

Photometry & Radiometry Group, Korea Research Institute of Standards and Science (KRISS), Yusong Taejon 305-600,

Republic of Korea

Leif Liedquist

Measurement Technology-Optics and Geometry, SP Swedish National Testing and Research Institute, SE 50115 Bora ̊s, Sweden

Farshid Manoocheri

Department of Electrical and Communications Engineering, Metrology Research Institute, Helsinki University of Technology,

FIN-02150 Espoo, Finland

Flora Mercader

Divisio ́n de Materiales Meta ́licos, Centro Nacional de Metrologı ́a (CENAM), 76900 Quere ́taro, Mexico

0047-2689Õ2005Õ34„1...Õ41Õ16Õ$39.00 J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005 41
L. A. G. Monard

Optical Radiometry and Radiation Pyrometry, National Metrology Laboratory, CSIR, 0001 Pretoria, South Africa

Saulius Nevas

Department of Electrical and Communications Engineering, Metrology Research Institute, Helsinki University of Technology,

FIN-02150 Espoo, Finland

Akihiro Mito

Time and Frequency Division, National Metrology Institute Of Japan (NMIJ), National Institute of Advanced Industrial Science

and Technology (AIST), Ibaraki 305-8563, Japan

Morgan Nilsson

Biomedical Engineering Department C2--67, Karolinska University Hospital, Huddinge, SE-141 86 Stockholm, Sweden

Mario Noe ̈l

Photometry & Radiometry Group, Institute for National Measurement Standards, National Research Council Canada, Ottawa,

Ontario K1A 0R6, Canada

Antonio Corro ́ns Rodriguez

Instituto de Fı ́sica Aplicada (IFA), Consejo Superior de Investigaciones Cientı ́ficas (CSIC), Serrano 144, 28006 Madrid, Spain

Arquı ́medes Ruı ́z

Area de Fisica, Centro Nacional de Metrologı ́a (CENAM), Carretera a los Cue ́s, 76240 Quere ́taro, Mexico

Alfred Schirmacher

Working Group 4.51 Spectrometry, Division 4 Optics, PTB Braunschweig, Bundesallee 100, DE-38116 Braunschweig, Germany

Melody V. Smith

Chemical Science and Technology Laboratory (CSTL), National Institute of Standards and Technology (NIST), Gaithersburg,

Maryland 20899-8394

Guillermo Valencia

Divisio ́n de O ́ ptica y Radiometrı ́a, Centro Nacional de Metrologı ́a (CENAM), 76900 Quere ́taro, Mexico

Natasha van Tonder

Optical Radiometry and Radiation Pyrometry, National Metrology Laboratory, CSIR, 0001 Pretoria, South Africa

Joanne Zwinkels

Photometry & Radiometry Group, Institute for National Measurement Standards, National Research Council Canada, Ottawa,

Ontario K1A 0R6, Canada

~Received 30 June 2003; revised manuscript received 8 December 2003; accepted 29 December 2003; published online 17 March 2005!

42 TRAVIS ET AL.

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
The transmittance minima of 18 absorption bands of a solution of 40 g/L holmium

oxide in 10% ~volume fraction! perchloric acid are certified as intrinsic traceable wavelength standards, by means of a multicenter measurement on material from a single

source coupled with comparisons of a variety of preparations of the material evaluated on

a single instrument. Fit-for-purpose artifact standards for the experimental calibration or

validation of wavelength scales of chemical spectrophotometers can be carefully produced by end users themselves or by commercial standards producers. The intrinsic ~data!

standard confers traceability to the SI unit of length in place of costly transfer artifacts

and repetitive calibration procedures. Certified values are provided for instrumental spectral bandwidths of 0.1–3.0 nm in 0.1 nm intervals, and information values are provided

to a spectral bandwidth of 10 nm at wider intervals. Expanded uncertainties are typically

less than 60.1 nm for certified band positions. © 2005 by the U.S. Secretary of Commerce on behalf of the United States. All rights reserved. @DOI: 10.1063/1.1835331#

Key words: certified wavelengths; holmium oxide solution; intrinsic standards; molecular absorption;

reference materials; spectral convolution; UV/visible spectrophotometry; wavelength standards.

Contents

1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

1.1. Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

1.2. Traceability. . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

1.3. Instrument Dependence. . . . . . . . . . . . . . . . . . . 45

2. Experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.1. Multicenter Value Assignment of Band

Positions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.1.1. Samples. . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.1.2. Measurement Conditions. . . . . . . . . . . . 45

2.2. Supplemental Experiments. . . . . . . . . . . . . . . . 46

2.2.1. Variation Within and Across SRM

2034 Preparations. . . . . . . . . . . . . . . . . . 46

2.2.2. Variation Across Sources. . . . . . . . . . . . 46

2.2.3. Temperature Dependence. . . . . . . . . . . . 46

2.2.4. Concentration Dependence. . . . . . . . . . . 46

3. Results and Discussion. . . . . . . . . . . . . . . . . . . . . . . 47

3.1. Consensus Band Positions. . . . . . . . . . . . . . . . 47

3.2. Deviation from Consensus Values. . . . . . . . . . 48

3.3. Slit Function. . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.4. Band Shape and Location Uncertainty. . . . . . . 49

3.5. Effect of Temperature. . . . . . . . . . . . . . . . . . . . 49

3.6. Variation Across Solution Preparations. . . . . . 49

3.7. Effect of Concentration. . . . . . . . . . . . . . . . . . . 49

3.8. Intrinsic Spectrum. . . . . . . . . . . . . . . . . . . . . . . 49

3.9. Interpolation by Theoretical Slit Function

Convolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5. Disclaimer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

List of Tables

1. Participant instruments and data supplied. . . . . . . . 46

2. Holmium oxide solution preparations other than

NIST SRM 2034. . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3. Measured consensus band positions for three

spectral bandwidths ~SBWs!. . . . . . . . . . . . . . . . . . 47

4. Locations of band minima as a function of SBW. 51

List of Figures

1. The transmittance spectrum of dilute acidic

holmium oxide solution at 0.1 nm SBW . . . . . . . . 44

2. A comparison of the band positions as returned

by a single participating instrument with the

consensus mean values . . . . . . . . . . . . . . . . . . . . . . 48

3. ‘‘Single channel’’ ~emission! spectra of the

deuterium Da line at spectral slit width

settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4. Summary of temperature dependence data at an

SSW of 1.0 nm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5. Concentration dependence of the spectral

position of the minimum of Band 1 . . . . . . . . . . . . 50

6. A portion of the 0.1 nm SBW spectrum and as

broadened by convolution of a triangle function

to 1, 3, 5, and 10 nm SBW values . . . . . . . . . . . . . 50

7. A graphical view of the computed SBW

trajectories and their uncertainties, compared with

the experimental SSW results . . . . . . . . . . . . . . . . . 54

1. Introduction

The present work establishes the transmittance minima of

18 absorption bands of a solution of 40 g/L holmium oxide in

10% ~volume fraction! perchloric acid as intrinsic wavelength standards, by means of an exhaustive multicenter

measurement on material from a single source coupled with

comparisons of a variety of preparations of the material

evaluated on a single instrument. The wavelength location of

each absorption band minimum is a fundamental property of

the ideal absorption spectrum of the solution, in the absence

of instrumental broadening.

1.1. Background

Dilute holmium oxide solutions permanently sealed into

fused silica cuvettes have been widely adopted as reference

a!

Electronic mail: john.travis@nist.gov

© 2005 by the U.S. Secretary of Commerce on behalf of the United States.

All rights reserved.

HOLMIUM OXIDE SOLUTION 43

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
materials for calibration or validation of the wavelength

scale in chemical spectrophotometry.1–5 The methods and

procedures used in the initial development and study of National Bureau of Standards ~NBS! Standard Reference Material ~SRM! 2034 have been described in detail previously by

Weidner et al.1 and in NBS Special Publication 260-102.2

Holmium is postulated to exist as the aquo ion of the general

formula Ho~H2O!n

31 ~or Hoaq31! when Ho2O3 is dissolved in

aqueous perchloric acid.6,7 The expression ‘‘holmium oxide

solution’’ and the spectral band positions reported in this

work refer to this chemical species, known also as ‘‘holmium

perchlorate solution.’’ 4,5 The aqueous perchloric acid solvent

was used from the beginning by NBS ~now the National

Institute of Standards and Technology, or NIST! since the

coordination of the resulting Hoaq

31 is relatively stable to

changes in temperature and concentration.1,8 The 14 certified

bands of SRM 2034 ~and a number of previously uncertified

bands! in the spectral range from 240 to 650 nm are due to

absorption of incident radiation by Hoaq

31 . The spectrum of

the holmium oxide solution is shown in Fig. 1, with the

NIST-certified bands identified by number. A few additional

bands identified by letters are candidates for certification

based on a prior study.9 Term assignments corresponding to

the absorption bands may be found in the literature.10

The true location of the wavelength of a transmittance

band minimum of a holmium oxide solution wavelength

standard of a controlled composition is a spectroscopic property that should remain constant as long as the solution is

chemically stable. If there is a significant change in the

chemical composition of the material, however, Hoaq

31 may

form complexes that have different spectral characteristics.

Absorption bands that show abnormal variations in response

to the environment of rare earth ions are designated as

‘‘hypersensitive.’’ 11 For Hoaq

31 , this designation is applied

particularly to the 5

I8→5G6 , 5F1 absorption band ~Band 10 in

Fig. 1!

11,12 and, to a lesser extent, to the 5

I8→5G5 ~Band 9!

and 5

I8→5F5 ~Band 14! bands.13

Wavelength accuracy requirements for chemical analysis

may be inferred from the Pharmacopeial literature. For calibration with a transmission wavelength standard, the Japanese Pharmacopoeia specifies an accuracy of 60.5 nm.14

The British and European Pharmacopoeias require an accuracy of 61.0 nm in the ultraviolet ~UV! and 63.0 nm in the

visible spectral region.4,5 Other Pharmacopoeias suggest that

analyte band maxima should be found experimentally to be

within 61 nm3 or 62 nm15 of the value specified in the

monograph.

In addition to the holmium oxide solution considered here,

other materials utilized as wavelength standards in transmittance may be found by similar studies to provide intrinsic

wavelength standard absorption bands. Several alternative

wavelength standards provide coverage to both shorter and

longer wavelengths than the holmium oxide solution. The

most widely used artifact wavelength standards in transmittance are based upon various rare earth species in solution or

in glass or crystalline matrices. These include holmium

glass,15,16 didymium glass,3,17 a solution containing holmium

and neodymium,18 a proprietary rare earth solution,19 and

two proprietary rare earth-doped crystals.20 Samples of the

crystalline material known as the ‘‘Nelson standard’’ were

made available to willing participants in the present study,

and the results of that study will be published separately.

1.2. Traceability

Assertion of traceability of a measurement to the meter

~metre! requires ‘‘an unbroken chain of comparisons all having stated uncertainties’’ relating the measurement to ‘‘stated

references.’’ 21 For the certified band positions reported here,

the stated references are atomic spectral lines widely regarded as traceable to the meter, and the evaluation of the

uncertainties is supported by the large number of instruments

and participants employed in the comparison of these references to the holmium oxide solution band positions.

Recent studies9,22,23 suggest the possibility that certain

band positions for holmium oxide solutions meeting carefully prescribed specifications could be assigned intrinsic

values with uncertainties considered fit-for-purpose for many

chemical measurements. The study reported here of solutions

obtained from a variety of sources supports the intrinsic nature of the certified values for a limited range of holmium

oxide concentration.

Artifact standards for the experimental calibration or validation of wavelength scales may thus be carefully produced

FIG. 1. The transmittance spectrum of

dilute acidic holmium oxide solution

at 0.1 nm SBW, identifying the absorption bands evaluated here as intrinsic wavelength standards.

44 TRAVIS ET AL.

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
by end users themselves or by commercial standards producers, with traceability to the Syste`me International d’Unite ́s

~International System of Units, or SI! conferred by the intrinsic ~data! standard reported here in lieu of costly batchcertified transfer artifacts and repetitive traceable calibration

procedures.

1.3. Instrument Dependence

Throughout this discussion, the term ‘‘spectral slit width’’

~SSW! is used to denote the intended full width at half maximum ~FWHM! of the slit function of an instrument ~or the

product of the physical slit width and the reciprocal linear

dispersion!,

24 and the term ‘‘spectral bandwidth’’ ~SBW! is

used to denote the measured realization of the same quantity.

The instrumental SBW is equivalent to the ‘‘resolution’’ as

the term is used in the International Vocabulary of Basic and

General Terms in Metrology ~VIM!.

21

The bands of the holmium oxide solution are unresolved

collections of transitions that form asymmetric features subject to changes in the apparent position of the band minimum

when recorded by an instrument whose SBW is significant

with respect to the spectral width of the absorption band.

Experimental SBW values for this study range from 0.1 nm

~negligible with respect to the narrowest spectral band of the

native spectrum! to the relatively significant value of 3.0 nm.

The native ~intrinsic! spectrum of the solution ~taken to be

revealed by the 0.1 nm spectral acquisitions! is convolved

with an idealized triangular theoretical slit function to interpolate band positions smoothly between measured values.

The resulting band locations given here may thus be used to

calibrate instruments of SBW between 0.1 and 3.0 nm

against certified, traceable values. Information values are

given by theoretical extrapolation for SBWs from 3.0 to 10.0

nm.

2. Experiment

2.1. Multicenter Value Assignment of Band

Positions

2.1.1. Samples

One sample of the 2002 production series of NIST SRM

2034 was sent to each participant. For this series, a new 2 L

solution was prepared by dissolving 80 g Ho2O3 in deionized water and 200 mL high-purity perchloric acid. The

dissolution was facilitated by moderate heat ~below boiling!

on a hot plate. The solution was covered and maintained

overnight at room temperature, and was then diluted to calibrated volume with deionized water. The final aqueous solution contained 40 g/L Ho2O3 in 10% ~volume fraction!

HClO4 .

The 99.99% pure holmium oxide, lot number Ho-0-4-007,

was obtained in a prior year from Research Chemicals, Division of Nucor Corp., Phoenix, AZ. The perchloric acid was

the NIST high-purity solution prepared by sub-boiling

distillation.25 The de-ionized water was from the NIST Advanced Chemical Sciences Laboratory pure water system.

Both the water and acid were checked spectrophotometrically for their UV absorption properties prior to use.

The fused-silica cuvettes of optical quality were tested for

fluorescence with a hand-held source of ultraviolet light. The

square cuvette has a nominal 10 mm pathlength and a fusedsilica tubular end. One pair of opposing faces is transparent

and the other pair of opposing faces is frosted. Cuvettes were

filled using an automatic pipette, with approximately 3.5 mL

per cuvette. Caps to be glued over the sealed-off necks of the

cuvettes were machined from black Delrin in the NIST Fabrication Technology Division, using a numerically controlled

mill. The hinged wooden box made to specifications for storing SRM 2034 contains a routed slot inside with foam and

felt inserts to protect the cuvette.

2.1.2. Measurement Conditions

The nominal measurement protocol followed that of the

earlier studies,9,22 except for the sample identity and allowances made for instrumental idiosyncrasies. Optimal fulfillment of the protocol called for replicate measurements on

separate days of the full spectrum from 230 to 680 nm at a

sampling interval of 0.1 nm, and for SBWs of 0.1, 1.0, and

3.0 nm. Wavelength calibration data were to be furnished by

means of spectral scans of appropriate calibration lamps or

as functional bias correction equations. Acceptable variations

included partial scans covering band tips, final measured values of band positions, and alternative SBWs within the range

of 0.1–3.0 nm. Optimal sample temperature was 25 °C, but

participants were asked to report the actual temperature

rather than attempt to control the temperature, due to the

known low dependence of band position on temperature.1,2

The instruments used and the data furnished are summarized

in Table 1.

Positions were sought for the bands identified in Fig. 1 by

numbers or letters, following the nomenclature of Ref. 1. The

numbered bands have been certified in NIST SRM 2034

since 1985, and the lettered bands represent further possibilities ~with some eliminated by the earlier study9

!. In spite of

the 0.1 nm data interval, band positions were estimated to the

nearest 0.01 nm by peak-location algorithms. Prior study has

revealed the relative robustness of computer peak location

with respect to the details of the algorithm.9 NIST/Chemical

Science and Technology Laboratory ~CSTL! peak locations

represent the minimum of a cubic polynomial fit to the minimum data point of a given band and the two nearest neighbors on each side. Table 1 indicates whether full spectra,

region-of-interest scans ~of the band tips!, or calibrated band

locations were furnished. If spectral scans and band positions

were both furnished, the furnished band positions were used

in the data analysis. If calibrated full or partial spectral scans

were furnished without band position estimates, the NIST/

CSTL five-point cubic peak location algorithm was used.

Two sets of spectra from the earlier study were obtained

on instruments different from those the participants employed in the current study. After demonstrating that there

were no location differences between NIST SRM 2034 SeHOLMIUM OXIDE SOLUTION 45

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
ries 02 and Series 99 materials ~see below!, these data were

added to the current study ~identified as two ‘‘L19’’ instruments in Table 1!.

2.2. Supplemental Experiments

Supplemental studies were performed at NIST to establish

the robustness of the values assigned to a single sample

batch with respect to material properties and to temperature.

The instrument used for all of these studies was the NIST/

CSTL PerkinElmer 900 spectrophotometer. Except for the

temperature dependence experiment, the temperature was

controlled to 2560.2 °C in all cases. In all cases, replicate

spectra were acquired for each sample, with removal and

replacement of the sample in the instrument between runs.

An SSW of 1.0 nm was employed, and band positions were

extracted with the NIST/CSTL five-point cubic algorithm.

2.2.1. Variation Within and Across SRM 2034 Preparations

Eight samples of NIST SRM 2034 ~Series 02! were chosen randomly to determine the variability of band position

within a single material preparation. To study the same variability across different preparations of SRM 2034, spectra

were acquired for at least one sample retained by NIST/

CSTL for each year in which SRM 2034 has been produced

since the introduction of the material in 1985. Samples included all series produced prior to 2002, designated by the

last two digits of the production year with a letter appended

to delineate separate batches: 85a, 85b, 86, 88, 91, 94, 95,

96, 98, 99, and 01. A sample from Series 02 was included as

both a participant and a control for each run required using

the nine-position sample carrousel.

2.2.2. Variation Across Sources

Six samples of dilute, acidic holmium oxide solution were

obtained from sources other than NIST, for comparison with

the NIST SRM 2034 Series 02 sample ~Table 2!. Spectra of

these samples were run following the protocol for all three

bandwidths. Spectra were furnished by NPL for a control

sample containing dilute holmium oxide and an additional

rare earth oxide.

2.2.3. Temperature Dependence

Replicate scans for sample temperatures from 25 to 45 °C

in 5 °C increments were acquired by using two samples of

SRM 2034 ~02! in the temperature-controlled sample carrousel of the NIST/CSTL instrument. The range was limited to

temperatures above ambient by malfunction of the cooling

element. Data were acquired for both 0.1 and 1.0 nm SBWs.

2.2.4. Concentration Dependence

The dependence of band position on holmium oxide concentration was studied using samples of nominal 10, 20, 35,

40, and 60 g/L holmium oxide in solution. Samples at the

TABLE 1. Participant instruments and data supplied

Country Lab Devicea SSW/nm Datai

Canada NRC L900 0.1, 1, 3 S, P

Canada NRC L19 0.1, 1, 3 S, P

Finland HUT L900 0.1, 1, 3, 5 S

France CNAM PBb 0.1 P

Germany PTB PBc 0.1, 1, 3 P

Hungary OMH PBd 0.3, 1, 3 R

Japan NMIJ C500 0.1, 1, 3 S

Japan NMIJ U3410 0.1, 1, 3 S

Mexico CENAM L19 0.1, 1, 3 P

Mexico CENAM C5e 0.1, 1, 3 P

Republic of Korea KRISS C5e 0.1, 1, 3 S, P

South Africa CSIR PBe 2,4 R, P

Spain CSIC L900 0.1, 1, 3 S

Spain CSIC L9 0.1, 1, 3 S

Sweden SP L900 0.1, 1, 3 R, S, P

Sweden KUS C400 0.1, 1, 3, 5 S

Switzerland METAS PBf 1 R, P

United Kingdom NPL C5e 0.1, 1, 3 S

USA CSTL L900 0.1, 1, 3 S

USA CSTL PBg 0.8 R

USA PL C5e 0.1, 1, 3, 5 S

USA PL PBh 1.5, 3.0 R

a

C55Varian Cary 5, C5e5Varian Cary 5e, C4005Varian Cary 400,

C5005Varian Cary 500, L95PerkinElmer Lambda 9, L195PerkinElmer

Lambda 19, L9005PerkinElmer Lambda 900, PB5Purpose built,

U34105Hitachi U3410. b

Reference Spectrophotometer based on 1.5 m f /12 monochromator with

holographic 2000/mm grating.

c

Reference spectrophotometer based on 0.6 m Jobin Yvon HRD1 single-pass

double monochromator.

d

Reference spectrophotometer based on Hillger–Watts double-grating

monochromator.

e

Spectroradiometer based on Jobin von H10D double monochromator.

f

Reference spectrophotometer based on f /5.6 Jobin Yvon HR 640 monochromator.

g

Reference spectrophotometer based on 1 m McPherson 2061 monochromator.

h

Reference spectrophotometer based on 1 m McPherson 2051 monochromator.

i

S5full spectral scan; R5region-of-interest scan about bands; P5band positions.

TABLE 2. Holmium oxide solution preparations other than NIST SRM 2034

Source Designation SSW/nm Date

Perkin-Elmer C005-0403 0.1, 0.25, 0.5, 1, 2, 3 1991

Merck KGaA UV/vis Standard 6 ~1.08166! 0.1, 0.25, 0.5, 1, 2, 3 1996

Starna Cells, Inc. RM-HL 0.1, 0.25, 0.5, 1, 1.5, 2, 3 2002

Slovak Institute of Metrology CRM J01 0.1, 0.2, 0.5, 1, 2, 3, 4, 5, 11 1999

Stranaska, LLC CRM 100 0.1, 0.25, 0.5, 1, 2, 3 2002

CENAM CRM 41-e 0.1, 1, 3 2000

46 TRAVIS ET AL.

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
lowest two mass concentrations were prepared by dilution

from the stock solution for SRM 2034 Series 02. Samples of

nominal 20 and 60 g/L were found among the non-NIST

preparations of holmium oxide solutions, with the mass concentrations inferred from the absorbance values. The 35 g/L

nominal mass concentration sample was one of two batches

of the original Series 85 of SRM 2034.

3. Results and Discussion

3.1. Consensus Band Positions

The measured consensus band positions compiled from

the multicenter measurement are summarized in Table 3 for

the three SBWs of the study. The consensus value is taken as

the unweighted mean, as the data is sparse ~two spectra for

each instrument and SBW! and the repeatability is unrelated

to the bias. Uncertainty intervals 6U95 are 95% confidence

intervals for the true value, computed from the estimated

standard deviation of the mean appropriately expanded for

the number of data sets used.26 Prediction intervals, 6P95 ,

define the range in which a single future determination

would be expected to fall with a level of confidence of

95%.26 The prediction intervals are comparable to the uncertainties of prior studies with fewer participants,9,22 and to the

revised uncertainties for SRM 2034 ~Series 01!. They are

also useful in assigning acceptable performance limits for

testing a single instrument on the basis of a single spectrum.

Determinations of band positions of absorption wavelength standards with a single instrument have required estimates of ‘‘type B’’ uncertainty components, formerly known

as systematic errors, which are not subject to assessment by

statistical methods but require an educated estimate. For

NIST SRM 2034, these included an estimate of the inaccuracy of calibration of the measuring instrument with atomic

pen lamps and an estimate of the inaccuracy of locating peak

minima.1,2 In the present case, the first of these is now confounded into the data experimentally by the use of multiple

research grade instruments with skilled operators. The second is partially confounded by the use of multiple peak location algorithms, and was shown in an earlier study9 to be

negligible in comparison with the first. Temperature effects

were originally found to be negligible over the range from 20

to 30 °C for SRM 2034,1,2 and this finding is further supported below.

The present study supports a further potential source of

calibration bias resulting from a difference in the optical

alignment of the calibration pen lamp and the alignment of

the system continuum lamp~s! to the spectrometer. This uncertainty is also confounded into the final result by the multicenter approach. We therefore assert that the uncertainties

shown in Table 3 represent a complete description of the

uncertainty budget for the intrinsic standard.

TABLE 3. Measured consensus band positions for three spectral bandwidths ~SBWs!

Band

0.1 nm SBW 1.0 nm SBW 3.0 nm SBW

Na lminb 6U95c 6P95d Na lminb 6U95c 6P95d Na lminb 6U95c 6P95d

1 17 240.98 0.04 0.18 17 241.12 0.05 0.21 16 241.03 0.06 0.25

2 17 249.80 0.05 0.22 17 249.87 0.06 0.24 16 250.06 0.09 0.36

d 17 259.98 0.08 0.34 16 260.22 0.07 0.30 16 260.12 0.09 0.36

3 17 278.16 0.04 0.17 18 278.13 0.05 0.20 17 278.04 0.06 0.27

4 17 287.02 0.04 0.19 18 287.19 0.06 0.28 18 287.61 0.07 0.33

i 17 293.34 0.04 0.18 17 293.39 0.05 0.21 17 293.33 0.07 0.30

5 17 333.49 0.04 0.17 18 333.47 0.04 0.19 18 333.48 0.07 0.31

6 17 345.47 0.05 0.21 18 345.39 0.04 0.19 18 345.52 0.07 0.32

7 18 361.29 0.04 0.17 18 361.25 0.03 0.15 19 361.09 0.06 0.29

8 18 385.38 0.04 0.19 18 385.61 0.04 0.19 18 385.99 0.09 0.37

9 18 416.05 0.04 0.17 18 416.26 0.05 0.23 18 416.86 0.08 0.35

10a 18 450.63 0.04 0.17 NAe NAe

10b 18 452.02 0.04 0.17 17 451.40 0.05 0.23 19 451.28 0.05 0.23

11 18 467.78 0.03 0.15 18 467.82 0.03 0.11 18 468.11 0.06 0.22

q 18 473.75 0.05 0.21 18 473.52 0.03 0.12 19 473.53 0.06 0.24

12 18 485.21 0.04 0.17 18 485.23 0.04 0.16 19 485.21 0.06 0.23

13 18 536.43 0.04 0.16 18 536.56 0.04 0.17 19 537.19 0.07 0.29

14 18 640.43 0.03 0.13 18 640.50 0.03 0.12 19 641.11 0.06 0.25

u 18 652.68 0.05 0.21 18 652.69 0.04 0.14 15 653.12 0.18 0.65

a

Number of spectrophotometers providing data for this band at this SBW.

b

The mean ~in nm! of the N values of the band transmittance minimum at this SBW. c

Approximate 95% confidence interval ~Ref. 26! in nm, of the mean value: 6t(0.025,N21)3s/AN, where t(0.025,N21) is the two-sided student’s t for 95%

confidence at N21 degrees of freedom and s is the standard deviation of the N values. The true value for each transmittance minimum at this SBW is

expected, with about 95% confidence, to be within this interval.

d

Approximate 95% prediction interval ~Ref. 26! in nm: 6t(0.025,N21)3s/A(111/N). The next single measurement of the location of this peak at this SBW

made using a measurement system from the same population as those used by the participants in this study is expected, with about 95% confidence, to be

within this interval.

e

There is no transmittance minimum at this SBW.

HOLMIUM OXIDE SOLUTION 47

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
3.2. Deviation from Consensus Values

Wavelength bias as a function of wavelength and SSW is

indicated for each participating instrument by comparison of

the band positions returned by that instrument with the consensus band positions for all participants. Figure 2 shows

such a comparison for one of the participating instruments.

To put the illustrated deviations from consensus in context,

the average ability to calibrate a given participant instrument

based upon the consensus values ~at the 95% confidence

level! is reasonably well indicated by the average of the prediction intervals for a given SBW in Table 3. The similarity

of this value for the 0.1 and 1.0 nm SSW data may carry

either or both of two implications: ~1! the ability to calibrate

the instrument with atomic line pen lamps is roughly equivalent for SSW values below about 1 nm or ~2! the observed

spectrum of holmium oxide solution does not change radically over this range of SSWs.1,2

The example shown in Fig. 2 is typical of most of the

instruments, inasmuch as the average bias ~from the consensus! may exceed the scatter about the fit ~residual standard

deviation! for one or more of the three SSW values studied.

This behavior supports the perhaps radical claim9 that spectrophotometers can be more consistently calibrated with respect to each other by using the holmium oxide solution

standard than by using atomic pen lamps. Given the superior

nature of the atomic emission line profiles, the clear implication is that the absorbing standard accurately represents the

axis defined by the optical train containing the continuum

lamp~s!, whereas the emission standard may not.

With few exceptions, the largest diversions from consensus were for the 3.0 nm bandwidth data as shown. This is

expected since the wider slits permit wider angular alignment excursions and are more difficult to fill uniformly with

the image of the calibration lamp. The results from several

instruments also showed the shift seen here between the data

acquired with the visible lamp and that acquired with the UV

lamp for the 3 nm SBWs, implying that the two lamps do not

share completely a common optical axis or do not illuminate

the entry slit in an equivalent fashion. ~The abrupt transition

at about 315 nm is ameliorated to the eye by the fitted

smooth curve.!

3.3. Slit Function

Nonuniform illumination of the entry slit can result in deviations of the slit function from the triangular ideal, as is

shown in Fig. 3 for the deuterium Da line at 656.1 nm27 on

one of the participating instruments. ~At high resolution, the

residual hydrogen Ha line characteristic of these lamps is

also seen.! In this case, the instrument performs well out to

the 3 nm limit of this study, but demonstrates asymmetry and

shift in the slit function at the extra SSW of 5 nm furnished

by this participant. The digression from consensus at 3 nm

shown in Fig. 2, as well as by several other instruments,

indicates that the onset of nonuniform slit illumination may

occur at lower SSWs for some instruments than for that of

Fig. 3. Significant departures from symmetry and changes in

apparent SBWs and wavelength calibration have been observed on the NIST/CSTL instrument for different pen lamp

alignments.

Slit function symmetry is easiest to achieve with the

smaller entry slits corresponding to 0.1 and 1.0 nm SBWs for

research grade instruments such as these. For many small

instruments used for routine analysis, the slit function may

actually be closer to the ideal at large SBWs than for these

instruments, since the physical slit width would be smaller

than the image of the source lamp.

FIG. 2. A comparison of the band positions as returned by a single participating instrument with the consensus mean values. Symbols shapes indicate

SBWs of 0.1 nm ~circles!, 1.0 nm ~diamonds!, and 3.0 nm ~triangles!. Symbols are filled for bands certified in NIST SRM 2034, and empty otherwise.

FIG. 3. ‘‘Single channel’’ ~emission! spectra of the deuterium Da line at

spectral slit width ~SSW! settings of 0.1 nm ~inside envelope!, 1, 3, and 5

nm ~outside envelope!. The dark traces are experimental and the light traces

are numerical convolutions. The 5 nm result illustrates the effect of nonuniform slit illumination when calibrating and using high-resolution instruments at large slit settings. At 0.1 nm SSW, the residual hydrogen Ha line

can be seen.

48 TRAVIS ET AL.

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
3.4. Band Shape and Location Uncertainty

The two greatest residuals in Fig. 2, for features d and u at

the 3 nm SSW, are not outliers but are illustrative of some of

the larger prediction intervals of Table 3. Comparison of the

band positions found by participant peak location algorithms

with those found by the NIST/CSTL algorithm confirms the

previous finding9 that the algorithm is not responsible for the

relatively large dispersion of results for particular bands.

Rather, the fault lies in the shape and structure of these bands

and on the possibility that false local minima may result

from noise superimposed on relatively flat-tipped bands, as

may be inferred from Fig. 3 of Ref. 9.

3.5. Effect of Temperature

The results of the temperature study at an SBW of 1.0 nm

and over the temperature range of 25– 45 °C are summarized

in Fig. 4. At each wavelength, the data point is the average

departure of the band location at the four other temperatures

~30, 35, 40, and 45 °C! from the band location at 25 °C. The

bars indicate the maximum and minimum deviations from

the 25 °C band location. The dispersion implied by these

bars is generally not distinguishable from the reproducibility

of locating the bands for replicate measurements at the same

temperature on a single instrument. The few maximum or

minimum excursions exceeding 0.05 nm in magnitude are

found to represent apparent wavelength shifts resulting from

temperature-dependent amplitudes of adjacent features. For

this reason it is prudent to restrict the temperature range for

normal use to 2565 °C as originally recommended by

Weidner et al.1,2 for SRM 2034.

3.6. Variation Across Solution Preparations

Example spectra from one sample of SRM 2034 prepared

in each of the 12 batches prepared at NIST revealed minor

differences in the baseline and absorption amplitude. Baseline effects have been attributed to the purity of the holmium

oxide powder,1 to organic impurities in the acid or water

used, or to cuvette-specific effects resulting from local contamination and/or differences in cuvette windows. Amplitude

differences result from minor concentration variations. Shifts

in the apparent positions of the shortest-wavelength certified

bands caused by baseline effects are trivial with respect to

the uncertainties given in Table 3. The prior batches of SRM

2034 were prepared by the same individual using the same

stock of holmium oxide powder, but with several variations

of acid, water, and cuvette manufacturer.

Two of the holmium oxide preparations shown in Table 2

gave experimental evidence of being prepared at mass concentrations other than 40 g/L, and one yielded a significant

baseline effect in the UV portion of the spectrum. In spite of

these differences, band positions obtained from spectra of all

of these samples are well within the stated uncertainties of

those reported here for NIST SRM 2034 ~Series 02!. However, a distinguishable mass concentration effect for certain

bands led to the study reported below.

3.7. Effect of Concentration

Figure 5 illustrates a slight concentration dependence in

the spectral position of the minimum of Band 1. In the lower

plot, data for 10, 20, and 60 g/L concentrations at 1 nm SSW

have been normalized in absorbance space to overlay with

the 40 g/L data to visualize the effect. The absolute wavelength excursion across this concentration range for Bands 1

and 4 is 0.05 nm. The minima for Bands 9, 13, and 14 also

systematically shift with concentration but by less than 0.03

nm. This finding contradicts the original reports1,2 and supports adherence to the nominal 40 g/L solution for the intrinsic standard.

3.8. Intrinsic Spectrum

The intrinsic spectrum is proposed here as a means of

verifying that a preparation of holmium oxide solution is

qualified to convey traceability through the certified band

positions of Table 3.

The spectrum presented in Fig. 1 is wavelength calibrated

to the consensus scale within 60.1 nm for all of the bands

given in Table 3. The spectrum will be made available electronically through the NIST web site28 for overlay with experimental spectra of candidate materials acquired with 0.1

nm SBWs and 0.1 nm data spacing. While the wavelength

axes of these overlaid spectra may not coincide exactly, visual observation should verify that no additional features are

present ~contamination! and that the known features of holmium oxide solution are present in the desired proportions.

Variation in the baseline from about 230 to 275 nm results

from differences in cuvettes or contamination in the cuvette

FIG. 4. Summary of temperature dependence data at an SSW of 1.0 nm.

Each data point represents the average of four shifts of the position of a

single band from the position determined at 25 °C to the position at 30, 35,

40, and 45 °C. The bar represents the range of these four temperature shifts.

The solid symbols represent bands certified in SRM 2034 and the open

symbols represent additional bands reported here.

HOLMIUM OXIDE SOLUTION 49

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
or the solvent ~the acid and/or water!. Although some baseline variation is not critical to the accuracy of the shortwavelength band positions, solutions providing a transmittance value of less than 50% at 230 nm should be rejected

and a fresh solution should be prepared with attention to

avoiding organic contaminants.

3.9. Interpolation by Theoretical Slit Function

Convolution

The effect of instrumental broadening on the highresolution molecular spectrum of Fig. 1 is theoretically modeled by convolving the instrument slit function through the

‘‘single channel’’ spectrum of the light transmitted through

the sample, similarly treating the spectrum of the light incident on the sample, and performing the point-by-point ratio

of the two broadened spectra to compute the resulting broadened transmittance spectrum. As a practical matter, the continuum lamp spectrum is sufficiently featureless to neglect

the effect of the instrument bandwidth on the shape of the

incident spectrum. Further, dividing the broadened transmitted spectrum by the original incident spectrum pointwise is

mathematically equivalent to simply convolving the instrument slit function ~normalized to unit area! through the transmittance spectrum. ~The normalization of the slit function

compensates for not convolving the incident spectrum.! This

latter approach is used here, with the instrumentally broadened transmittance at the ith wavelength channel  ̄

Ti related

to the jth channel of the intrinsic spectrum Tj through the

area-normalized instrument slit function Sk , with a maximum at k50 declining to zero at k56n

 ̄

Ti5 (

k52n

n

SkTi2k , ~1!

where n is the number of data intervals required to span one

half of the SSW. For an ideal grating spectrometer, the slit

function is triangular, representing the image of an entrance

slit ~evenly illuminated with monochromatic light! being

translated across an exit slit of the same size by the rotation

of the grating. For convenience, we define the areanormalized theoretical slit function as

Sk5W2uk/10u

103W2 ,

~2!

k5210W11,210W12, ̄,0, ̄10W22,10W21,

where W is the SBW in nm represented as the FWHM of the

triangular function and the factors of 10 are unique to the 0.1

nm data spacing employed in this study. @The obvious null

end points of the triangle at k5610 W are omitted because

they are inconsequential to the value of Eq. ~1!#. This function may be used to theoretically broaden the intrinsic spectrum to the expected experimental spectrum for any SBW

that is an integral multiple of the 0.1 nm data spacing.

The NIST/CSTL five-point cubic band location algorithm

used for experimental data is also used here to track the

‘‘trajectory’’ of the apparent peak location with theoretical

SBW for discreet convolutions. Figure 6 overlays trajectories

FIG. 5. Concentration dependence of the spectral position of the minimum

of Band 1. The upper section displays the spectral segments of 10 g/L ~1%!,

20 g/L ~2%!, 40 g/L ~4%!, and 60 g/L ~6%! solutions as acquired. The lower

section displays the spectral segments at expanded graphical resolution and

normalized in absorbance space to the 40 g/L spectrum. The band minima

shift to higher wavelengths with increasing mass concentration.

FIG. 6. A portion of the 0.1 nm SBW spectrum and as broadened by convolution of a triangle function to 1, 3, 5, and 10 nm SBW values. The dark

lines denote the peak minima as a function of SBW ‘‘trajectories,’’ computed at every bandwidth from 0.1 to 10 nm at 0.1 nm intervals.

50 TRAVIS ET AL.

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
TABLE 4. Locations of band minima as a function of SBW

SBWa

Band 1 Band 2 Band d Band 3

lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d

0.1 240.97 0.05 0.21 249.78 0.05 0.21 259.99 0.06 0.25 278.15 0.05 0.20

0.2 240.97 0.05 0.21 249.78 0.05 0.21 260.01 0.06 0.23 278.15 0.05 0.20

0.3 240.98 0.05 0.21 249.79 0.05 0.21 260.02 0.06 0.23 278.15 0.05 0.20

0.4 241.00 0.05 0.21 249.80 0.05 0.21 260.03 0.06 0.23 278.15 0.05 0.20

0.5 241.02 0.05 0.21 249.81 0.05 0.21 260.05 0.06 0.23 278.15 0.05 0.20

0.6 241.04 0.05 0.22 249.82 0.05 0.21 260.08 0.06 0.24 278.15 0.05 0.20

0.7 241.07 0.05 0.22 249.84 0.05 0.21 260.11 0.06 0.24 278.15 0.05 0.21

0.8 241.09 0.05 0.23 249.85 0.05 0.22 260.13 0.06 0.25 278.14 0.05 0.21

0.9 241.10 0.05 0.23 249.87 0.05 0.22 260.16 0.06 0.25 278.14 0.05 0.21

1.0 241.12 0.05 0.23 249.89 0.05 0.22 260.18 0.06 0.26 278.13 0.05 0.22

1.1 241.12 0.05 0.24 249.91 0.05 0.22 260.20 0.06 0.27 278.13 0.05 0.22

1.2 241.13 0.05 0.24 249.93 0.05 0.23 260.21 0.06 0.27 278.12 0.05 0.22

1.3 241.13 0.05 0.25 249.95 0.05 0.23 260.23 0.06 0.28 278.12 0.05 0.23

1.4 241.14 0.05 0.25 249.97 0.05 0.24 260.24 0.06 0.28 278.11 0.05 0.23

1.5 241.13 0.05 0.26 249.98 0.05 0.24 260.26 0.06 0.29 278.11 0.05 0.24

1.6 241.13 0.05 0.26 250.00 0.05 0.24 260.26 0.06 0.30 278.11 0.05 0.24

1.7 241.13 0.05 0.27 250.01 0.05 0.25 260.25 0.06 0.30 278.10 0.05 0.25

1.8 241.12 0.05 0.27 250.02 0.05 0.25 260.23 0.06 0.30 278.10 0.05 0.25

1.9 241.12 0.05 0.28 250.03 0.05 0.26 260.21 0.06 0.31 278.10 0.05 0.26

2.0 241.12 0.05 0.29 250.03 0.05 0.27 260.19 0.06 0.31 278.10 0.05 0.27

2.1 241.11 0.05 0.29 250.04 0.05 0.27 260.17 0.06 0.32 278.10 0.05 0.27

2.2 241.10 0.05 0.30 250.05 0.05 0.28 260.16 0.06 0.33 278.09 0.05 0.28

2.3 241.10 0.05 0.31 250.05 0.05 0.29 260.15 0.06 0.33 278.09 0.05 0.29

2.4 241.09 0.05 0.32 250.05 0.05 0.29 260.15 0.06 0.34 278.09 0.05 0.30

2.5 241.08 0.05 0.33 250.06 0.05 0.30 260.15 0.06 0.36 278.08 0.05 0.30

2.6 241.08 0.05 0.34 250.06 0.05 0.31 260.15 0.06 0.37 278.08 0.05 0.31

2.7 241.07 0.05 0.35 250.06 0.05 0.32 260.15 0.06 0.37 278.07 0.05 0.32

2.8 241.06 0.05 0.36 250.06 0.05 0.33 260.15 0.06 0.39 278.06 0.05 0.33

2.9 241.05 0.05 0.37 250.07 0.05 0.33 260.15 0.06 0.40 278.06 0.05 0.34

3.0 241.04 0.05 0.38 250.07 0.05 0.34 260.15 0.06 0.41 278.05 0.05 0.35

4.0 241.00 0.05 f 250.11 0.05 f 260.11 0.06 f 277.98 0.05 f

5.0 240.97 0.05 f 250.15 0.05 f 259.85 0.07 f 277.93 0.05 f

6.0 240.93 0.05 f 250.13 0.05 f 258.89 0.17 f 277.90 0.05 f

7.0 240.87 0.05 f 250.05 0.05 f NAe 277.87 0.05 f

8.0 240.79 0.05 f NAe NAe 277.90 0.05 f

9.0 240.78 0.05 f NAe NAe 278.60 0.05 f

10.0 240.78 0.06 f NAe NAe NAe

SBWa

Band 4 Band i Band 5 Band 6

lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d

0.1 287.03 0.05 0.20 293.32 0.05 0.21 333.48 0.04 0.18 345.46 0.05 0.20

0.2 287.03 0.05 0.20 293.32 0.05 0.19 333.48 0.05 0.18 345.46 0.05 0.19

0.3 287.04 0.05 0.20 293.33 0.05 0.19 333.47 0.05 0.18 345.45 0.05 0.19

0.4 287.06 0.05 0.20 293.33 0.05 0.19 333.47 0.05 0.19 345.44 0.05 0.19

0.5 287.08 0.05 0.20 293.33 0.05 0.19 333.47 0.05 0.19 345.43 0.05 0.19

0.6 287.10 0.05 0.20 293.34 0.05 0.19 333.48 0.05 0.19 345.42 0.05 0.19

0.7 287.13 0.05 0.21 293.34 0.05 0.19 333.48 0.05 0.19 345.41 0.05 0.20

0.8 287.16 0.05 0.21 293.35 0.05 0.19 333.48 0.05 0.20 345.40 0.05 0.20

0.9 287.19 0.05 0.21 293.37 0.05 0.20 333.48 0.05 0.20 345.39 0.05 0.20

1.0 287.22 0.05 0.22 293.38 0.05 0.20 333.48 0.05 0.20 345.38 0.05 0.20

1.1 287.24 0.05 0.22 293.39 0.05 0.21 333.49 0.05 0.21 345.38 0.05 0.21

1.2 287.28 0.05 0.22 293.41 0.05 0.21 333.49 0.05 0.21 345.38 0.05 0.21

1.3 287.31 0.05 0.23 293.42 0.05 0.22 333.49 0.05 0.22 345.38 0.05 0.22

1.4 287.35 0.05 0.23 293.43 0.05 0.22 333.49 0.05 0.22 345.38 0.05 0.22

1.5 287.40 0.05 0.24 293.43 0.05 0.23 333.49 0.05 0.23 345.38 0.05 0.23

1.6 287.44 0.05 0.24 293.44 0.05 0.23 333.48 0.05 0.23 345.39 0.05 0.23

1.7 287.47 0.05 0.25 293.44 0.05 0.24 333.48 0.05 0.24 345.39 0.05 0.23

1.8 287.50 0.05 0.26 293.44 0.05 0.25 333.48 0.05 0.24 345.40 0.05 0.24

1.9 287.51 0.05 0.26 293.44 0.05 0.25 333.47 0.05 0.25 345.41 0.05 0.25

2.0 287.52 0.05 0.27 293.43 0.05 0.26 333.47 0.05 0.26 345.42 0.05 0.25

2.1 287.53 0.05 0.27 293.43 0.05 0.26 333.47 0.05 0.26 345.43 0.05 0.26

2.2 287.54 0.05 0.28 293.42 0.05 0.27 333.47 0.05 0.27 345.44 0.05 0.26

HOLMIUM OXIDE SOLUTION 51

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
TABLE 4. Locations of band minima as a function of SBW—Continued

SBWa

Band 4 Band i Band 5 Band 6

lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d

2.3 287.54 0.05 0.29 293.41 0.05 0.28 333.47 0.05 0.28 345.45 0.05 0.27

2.4 287.54 0.05 0.30 293.40 0.05 0.29 333.47 0.05 0.29 345.47 0.05 0.28

2.5 287.55 0.05 0.30 293.40 0.05 0.29 333.47 0.05 0.29 345.48 0.05 0.29

2.6 287.55 0.05 0.31 293.39 0.05 0.30 333.47 0.05 0.30 345.49 0.05 0.29

2.7 287.55 0.05 0.32 293.38 0.05 0.31 333.47 0.05 0.31 345.50 0.05 0.30

2.8 287.56 0.05 0.33 293.37 0.05 0.32 333.47 0.05 0.32 345.51 0.05 0.31

2.9 287.56 0.05 0.34 293.36 0.05 0.33 333.47 0.05 0.33 345.52 0.05 0.32

3.0 287.57 0.05 0.35 293.36 0.05 0.34 333.47 0.05 0.34 345.53 0.05 0.33

4.0 287.64 0.05 f NAe 333.47 0.05 f 345.57 0.05 f

5.0 287.78 0.05 f NAe 333.47 0.05 f 345.58 0.05 f

6.0 288.01 0.05 f NAe 333.48 0.05 f 345.59 0.05 f

7.0 288.22 0.05 f NAe 333.48 0.05 f 345.59 0.05 f

8.0 288.29 0.05 f NAe 333.49 0.05 f 345.63 0.05 f

9.0 288.14 0.05 f NAe 333.52 0.05 f 345.68 0.05 f

10.0 287.28 0.05 f NAe 333.59 0.05 f 345.68 0.05 f

SBWa

Band 7 Band 8 Band 9 Band 10a

lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d

0.1 361.27 0.05 0.19 385.36 0.05 0.19 416.02 0.05 0.21 450.62 0.05 0.19

0.2 361.27 0.05 0.19 385.37 0.05 0.18 416.03 0.05 0.21 450.63 0.05 0.19

0.3 361.27 0.05 0.19 385.39 0.04 0.18 416.04 0.05 0.20 450.65 0.05 0.19

0.4 361.27 0.05 0.19 385.42 0.04 0.18 416.05 0.05 0.20 450.68 0.05 0.19

0.5 361.27 0.05 0.19 385.45 0.04 0.18 416.07 0.05 0.21 450.72 0.05 0.19

0.6 361.27 0.05 0.20 385.49 0.04 0.18 416.10 0.05 0.21 450.78 0.05 0.20

0.7 361.27 0.05 0.20 385.53 0.04 0.18 416.13 0.05 0.21 450.84 0.05 0.20

0.8 361.26 0.05 0.20 385.56 0.04 0.19 416.17 0.05 0.21 450.96 0.06 0.23

0.9 361.25 0.05 0.21 385.59 0.04 0.19 416.21 0.05 0.21 NAe

1.0 361.25 0.05 0.21 385.61 0.04 0.19 416.25 0.05 0.22 NAe

1.1 361.23 0.05 0.21 385.63 0.04 0.20 416.29 0.05 0.22 NAe

1.2 361.22 0.05 0.22 385.65 0.04 0.20 416.33 0.05 0.23 NAe

1.3 361.21 0.05 0.22 385.67 0.04 0.21 416.36 0.05 0.23 NAe

1.4 361.20 0.05 0.23 385.68 0.04 0.21 416.39 0.05 0.24 NAe

1.5 361.18 0.05 0.23 385.70 0.04 0.21 416.42 0.05 0.24 NAe

1.6 361.17 0.05 0.24 385.72 0.04 0.22 416.45 0.05 0.25 NAe

1.7 361.16 0.05 0.24 385.74 0.04 0.22 416.48 0.05 0.25 NAe

1.8 361.14 0.05 0.25 385.76 0.04 0.23 416.51 0.05 0.26 NAe

1.9 361.13 0.05 0.25 385.78 0.04 0.23 416.54 0.05 0.26 NAe

2.0 361.12 0.05 0.26 385.80 0.04 0.24 416.57 0.05 0.27 NAe

2.1 361.11 0.05 0.26 385.82 0.04 0.25 416.60 0.05 0.28 NAe

2.2 361.11 0.05 0.27 385.84 0.04 0.25 416.64 0.05 0.28 NAe

2.3 361.10 0.05 0.27 385.86 0.04 0.26 416.67 0.05 0.29 NAe

2.4 361.10 0.05 0.28 385.88 0.04 0.27 416.71 0.05 0.30 NAe

2.5 361.09 0.05 0.29 385.90 0.04 0.27 416.74 0.05 0.31 NAe

2.6 361.09 0.05 0.30 385.92 0.04 0.28 416.78 0.05 0.32 NAe

2.7 361.10 0.05 0.30 385.94 0.04 0.29 416.81 0.05 0.32 NAe

2.8 361.10 0.05 0.31 385.96 0.04 0.30 416.84 0.05 0.33 NAe

2.9 361.10 0.05 0.32 385.98 0.04 0.30 416.87 0.05 0.34 NAe

3.0 361.11 0.05 0.33 386.00 0.04 0.31 416.89 0.05 0.35 NAe

4.0 361.14 0.05 f 386.31 0.05 f 417.07 0.05 f NAe

5.0 361.13 0.05 f 386.44 0.05 f 417.32 0.05 f NAe

6.0 361.11 0.05 f 386.60 0.05 f 417.37 0.05 f NAe

7.0 361.09 0.05 f 386.84 0.05 f 417.37 0.05 f NAe

8.0 361.06 0.05 f 387.10 0.05 f 417.36 0.05 f NAe

9.0 361.05 0.05 f 387.32 0.06 f 417.35 0.05 f NAe

10.0 361.04 0.05 f 387.50 0.07 f 417.35 0.05 f NAe

SBWa

Band 10b Band 11 Band q Band 12

lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d

0.1 452.02 0.05 0.19 467.78 0.04 0.15 473.73 0.05 0.19 485.20 0.04 0.17

0.2 452.00 0.05 0.19 467.79 0.04 0.16 473.72 0.05 0.19 485.20 0.04 0.17

52 TRAVIS ET AL.

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
TABLE 4. Locations of band minima as a function of SBW—Continued

SBWa

Band 10b Band 11 Band q Band 12

lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d

0.3 451.98 0.05 0.19 467.79 0.04 0.16 473.71 0.05 0.18 485.21 0.04 0.17

0.4 451.95 0.05 0.19 467.79 0.04 0.16 473.70 0.04 0.18 485.21 0.04 0.17

0.5 451.91 0.05 0.19 467.80 0.04 0.16 473.68 0.04 0.19 485.21 0.04 0.17

0.6 451.86 0.05 0.19 467.80 0.04 0.16 473.66 0.04 0.19 485.21 0.04 0.17

0.7 451.79 0.05 0.20 467.81 0.04 0.16 473.63 0.04 0.19 485.22 0.04 0.18

0.8 451.71 0.05 0.21 467.81 0.04 0.17 473.60 0.04 0.19 485.22 0.04 0.18

0.9 451.59 0.05 0.23 467.82 0.04 0.17 473.57 0.04 0.19 485.23 0.04 0.18

1.0 451.45 0.05 0.24 467.82 0.04 0.17 473.54 0.04 0.20 485.23 0.04 0.19

1.1 451.38 0.05 0.22 467.83 0.04 0.17 473.50 0.04 0.20 485.24 0.04 0.19

1.2 451.35 0.05 0.21 467.83 0.04 0.18 473.48 0.04 0.20 485.24 0.04 0.19

1.3 451.34 0.04 0.21 467.84 0.04 0.18 473.45 0.04 0.20 485.25 0.04 0.20

1.4 451.33 0.04 0.21 467.85 0.04 0.19 473.44 0.04 0.21 485.25 0.04 0.20

1.5 451.33 0.04 0.21 467.86 0.04 0.19 473.44 0.04 0.21 485.26 0.04 0.21

1.6 451.32 0.04 0.21 467.87 0.04 0.20 473.44 0.04 0.22 485.26 0.04 0.21

1.7 451.32 0.04 0.22 467.87 0.04 0.20 473.44 0.04 0.22 485.26 0.04 0.21

1.8 451.32 0.04 0.22 467.88 0.04 0.21 473.45 0.04 0.23 485.26 0.04 0.22

1.9 451.32 0.04 0.23 467.89 0.04 0.21 473.46 0.04 0.23 485.25 0.04 0.23

2.0 451.32 0.04 0.23 467.90 0.04 0.21 473.47 0.04 0.24 485.25 0.04 0.23

2.1 451.32 0.04 0.24 467.92 0.04 0.22 473.48 0.04 0.24 485.24 0.04 0.24

2.2 451.32 0.04 0.24 467.93 0.04 0.23 473.49 0.04 0.25 485.24 0.04 0.24

2.3 451.32 0.04 0.25 467.94 0.04 0.23 473.50 0.04 0.25 485.23 0.04 0.25

2.4 451.33 0.04 0.26 467.96 0.04 0.24 473.50 0.04 0.26 485.22 0.04 0.26

2.5 451.33 0.04 0.26 467.98 0.04 0.25 473.51 0.04 0.27 485.22 0.04 0.26

2.6 451.33 0.04 0.27 468.00 0.04 0.25 473.52 0.04 0.27 485.22 0.04 0.27

2.7 451.34 0.04 0.28 468.02 0.04 0.26 473.52 0.04 0.28 485.21 0.04 0.28

2.8 451.35 0.04 0.29 468.05 0.04 0.27 473.53 0.04 0.29 485.21 0.04 0.29

2.9 451.35 0.04 0.29 468.08 0.04 0.28 473.54 0.04 0.30 485.21 0.04 0.29

3.0 451.36 0.04 0.30 468.11 0.04 0.28 473.54 0.04 0.30 485.21 0.04 0.30

4.0 451.41 0.04 f NAe 473.53 0.04 f 485.26 0.04 f

5.0 451.40 0.04 f NAe 473.35 0.04 f 485.25 0.04 f

6.0 451.42 0.04 f NAe 472.76 0.04 f 485.21 0.04 f

7.0 451.41 0.04 f NAe 472.89 0.04 f 485.14 0.04 f

8.0 451.38 0.04 f NAe 473.15 0.04 f 485.04 0.04 f

9.0 451.36 0.04 f NAe 473.51 0.04 f 484.87 0.04 f

10.0 451.34 0.04 f NAe NAe 484.56 0.04 f

SBWa

Band 13 Band 14 Band u

lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d

0.1 536.42 0.04 0.17 640.41 0.04 0.15 652.69 0.06 0.23

0.2 536.42 0.04 0.17 640.41 0.04 0.15 652.69 0.06 0.22

0.3 536.43 0.04 0.17 640.41 0.04 0.15 652.69 0.05 0.21

0.4 536.44 0.04 0.17 640.42 0.04 0.15 652.69 0.05 0.20

0.5 536.45 0.04 0.17 640.43 0.04 0.15 652.68 0.05 0.19

0.6 536.47 0.04 0.18 640.44 0.04 0.16 652.68 0.04 0.18

0.7 536.48 0.04 0.18 640.45 0.04 0.16 652.68 0.04 0.17

0.8 536.51 0.04 0.18 640.46 0.04 0.16 652.67 0.04 0.17

0.9 536.53 0.04 0.18 640.48 0.04 0.16 652.67 0.04 0.17

1.0 536.56 0.04 0.19 640.50 0.04 0.16 652.67 0.04 0.17

1.1 536.59 0.04 0.19 640.52 0.04 0.16 652.66 0.04 0.17

1.2 536.61 0.04 0.19 640.54 0.04 0.16 652.66 0.04 0.17

1.3 536.64 0.04 0.20 640.56 0.04 0.17 652.66 0.04 0.17

1.4 536.68 0.04 0.20 640.59 0.04 0.17 652.66 0.04 0.18

1.5 536.71 0.04 0.20 640.62 0.04 0.17 652.65 0.04 0.18

1.6 536.74 0.04 0.21 640.65 0.04 0.18 652.65 0.04 0.18

1.7 536.77 0.04 0.22 640.68 0.04 0.18 652.65 0.04 0.18

1.8 536.80 0.04 0.22 640.71 0.04 0.19 652.65 0.04 0.19

1.9 536.83 0.04 0.23 640.75 0.04 0.19 652.65 0.04 0.19

2.0 536.86 0.04 0.23 640.79 0.04 0.20 652.66 0.04 0.20

2.1 536.89 0.04 0.24 640.83 0.04 0.20 652.66 0.04 0.20

2.2 536.93 0.04 0.25 640.86 0.04 0.21 652.67 0.04 0.21

2.3 536.96 0.04 0.25 640.90 0.04 0.21 652.69 0.04 0.21

2.4 536.99 0.04 0.26 640.94 0.04 0.22 652.71 0.04 0.22

HOLMIUM OXIDE SOLUTION 53

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
TABLE 4. Locations of band minima as a function of SBW—Continued

SBWa

Band 13 Band 14 Band u

lmaxb U95c P95d lmaxb U95c P95d lmaxb U95c P95d

2.5 537.03 0.04 0.27 640.98 0.04 0.22 652.74 0.04 0.23

2.6 537.06 0.04 0.28 641.01 0.04 0.23 652.79 0.04 0.23

2.7 537.10 0.04 0.28 641.05 0.04 0.23 652.86 0.04 0.25

2.8 537.14 0.04 0.29 641.08 0.04 0.24 652.96 0.04 0.26

2.9 537.18 0.04 0.30 641.11 0.04 0.25 653.16 0.05 0.34

3.0 537.21 0.04 0.31 641.15 0.04 0.25 653.46 0.11 0.56

4.0 537.58 0.04 f 641.42 0.04 f 653.54 0.05 f

5.0 537.91 0.04 f 641.66 0.04 f NAe

6.0 538.28 0.04 f 641.88 0.04 f NAe

7.0 538.50 0.04 f 642.09 0.04 f NAe

8.0 538.64 0.04 f 642.32 0.04 f NAe

9.0 538.75 0.04 f 642.57 0.04 f NAe

10.0 538.83 0.04 f 642.86 0.04 f NAe

a

Spectral band width ~in nm!. b

The expected location of the transmittance minimum ~in nm! calculated as the mean of 0.1 nm SBW spectra from 13 instruments convolved with an idealized

triangular slit function of width SBW.

c

Approximate 95% confidence interval ~Ref. 26! ~in nm! of the expected transmittance minimum: 6t(0.025,N21)3s/A13, where t(0.025,13-1) is the two-sided

student’s t for 95% confidence at 12 degrees of freedom and s is the standard deviation of the 13 convolved spectra at the given SBW. The true value for each

transmittance minimum at each given SBW is expected, with about 95% confidence, to be within this interval.

d

Approximate 95% prediction interval ~Ref. 26! ~in nm!: 6t(0.025,13-1)3s3MEF/A~111/13!, where MEF is the empirically determined multiplicative expansion

factor 110.0253SBW10.0803SBW2 that accounts for the uncertainty of calibrating real instruments at large SBW. The next single measurement of the

location of this peak at this SBW made using a measurement system from the same population as those used by the participants in this study is expected, with

about 95% confidence, to be within this interval.

e

There is no transmittance minimum at this SBW.

f

Due to the empirical derivation of MEF, P95 cannot be reliably calculated for SBW greater than 3.0 nm.

.for three bands with a portion of the broadened spectrum at

several bandwidths for illustration. The trajectories are computed using every bandwidth from 0.1 to 10 nm at 0.1 nm

intervals, and not just the few shown in the figure.

Table 4 reports the positions of all bands studied here at

SBWs from 0.1 to 3.0 nm in 0.1 nm intervals, with a few

representative values given for larger SBW values. The calculation represented in the table utilized all calibrated full

spectra furnished by participants at an SBW of 0.1 nm (N

513). Each spectrum was convolved to the SBWs shown

and the band locations were extracted for each SBW. The

central value, uncertainty, and prediction interval were comFIG. 7. A graphical view of the computed SBW trajectories ~see Fig. 6!

and their uncertainties, compared with

the experimental SSW results. Meancentered band positions are computed

from theoretically broadened experimental spectra ~Table 4! and are

shown with 95% confidence ~inner

band! and 95% prediction ~outer band!

intervals. The measured SBW values

at 0.1, 1.0, and 3.0 nm reported in

Table 3 are plotted with their approximately 95% confidence interval uncertainties. The open circles represent individual instruments reporting data at

other SBW values.

54 TRAVIS ET AL.

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
puted in the same manner as discussed for Table 3, except for

the use of a multiplicative expansion factor for the prediction

interval. The expansion function used for the prediction interval is a quadratic function with a Y intercept of 1.0, fitted

to the relative U95 values of Table 3 ~normalized to U95 at

0.1 nm SBW for each measured band! and is included to

represent the loss of calibration accuracy in these instruments

at increasing SBW. The calculation of P95 in Table 4 is terminated at a SBW of 3.0 nm, since the experimental data

does not support the estimation of the empirical function

beyond that limit. Minor differences in the 0.1 nm SBW

bandwidth values in Tables 3 and 4 result from the lower

value of N for Table 4, and from the fact that Table 3 uses

band locations extracted from each of two spectra for each

SBW and instrument and Table 4 averages the spectra before

convolution and band position extraction.

The validity of the theoretical convolution used to generate Table 4 may be tested by comparison of the predicted and

measured values at 1.0 and 3.0 nm in Table 3. A graphical

view of the trajectories and comparisons with experimental

values is provided in Fig. 7. Here the data are mean centered

for ease of display, but the figure is useful for observing the

qualitative behavior of the various spectral features with

bandwidth. The central line for each subfigure represents the

mean-centered band shift as a function of SBW. The innermost pair of lines about each trajectory, from 0.1 to 3.0 nm,

is the 95% confidence interval, and the outermost line pair

represents the 95% prediction interval for a single future determination. Vertical bars plotted at 0.1, 1.0, and 3.0 nm represent the U95 for the measured values reported in Table 3.

Additional symbols represent individual instruments reporting data at other SBW values.

For SBWs from 0.1 to 3.0 nm, the values in Table 4 represent certified values as validated by the experimental data

of the multicenter experiment. For SBWs between 3.0 and

10.0 nm, the values are considered to be ‘‘information values’’ for which the uncertainty is less well characterized.

4. Conclusions

The establishment of specified absorption bands of a solution of 40 g/L holmium oxide in 10% ~volume fraction! perchloric acid as certified intrinsic wavelength standards that

are fit-for-purpose for most applications in chemical spectrophotometry is supported by various conclusions:

~1! Realistic uncertainties are furnished by the multicenter

approach, which experimentally confounds calibration

uncertainty into the end result.

~2! Intrinsic band positions as continuous functions of instrumental spectral bandwidth may be supplied by means

of the theoretical broadening of the intrinsic ~narrowband! spectrum as validated through the consensus measurements at discreet spectral bandwidths.

~3! Band positions of different preparations of holmium oxide solution are robust with respect to the origin of materials and to 620% variations in concentration.

We therefore recommend the certified band positions in

Table 4 as intrinsic wavelength standards in the sample temperature range of 2565 °C, applicable to samples of holmium oxide in perchloric acid prepared in the manner described herein and with a high-resolution spectrum shown to

be congruent with the intrinsic spectrum reported here.

5. Disclaimer

Certain commercial equipment, instruments, or materials

are identified in this paper to foster understanding. Such

identification does not imply recommendation or endorsement by the National Institute of Standards and Technology,

nor does it imply that the materials or equipment identified

are necessarily the best available for the purpose.

6. References

1V. R. Weidner, R. Mavrodineanu, K. D. Mielenz, R. A. Velapoldi, K. L.

Eckerle, and B. Adams, J. Res. NBS 90, 115 ~1985!. 2V. R. Weidner, R. Mavrodineanu, K. D. Mielenz, R. A. Velapoldi, K. L.

Eckerle, and B. Adams, NBS Special Publication 260-102, Gaithersburg,

MD, July 1986.

3USP 28-NF23, United States Pharmacopeial Convention, Inc., Rockville

MD, 2004, General Chapter 851.

4British Pharmacopoeia, Vol. II ~The Stationery Office, London, 2002!,

Appendix II B, p. A131.

5European Pharmacopoeia, 4th ed. ~Council of Europe, Strassbourg,

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and Chemistry of Rare Earths, Vol. 3 ~North-Holland, Amsterdam,

1979!. 9 J. C. Travis, J. C. Zwinkels, F. Mercader, A. Ruiz, E. A. Early, M. V.

Smith, M. Noel, M. Maley, G. W. Kramer, K. L. Eckerle, and D. L.

Duewer, Anal. Chem. 74, 3408 ~2002!. 10W. T. Carnall, P. R. Fields, and K. Rajnak, J. Chem. Phys. 49, 4424

~1968!. 11D. G. Karraker, Inorg. Chem. 6, 1863 ~1967!. 12M. T. Devlin, E. M. Stephens, and F. S. Richardson, Inorg. Chem. 27,

1517 ~1988!. 13D. G. Karraker, Inorg. Chem. 3, 473 ~1968!. 14 Society of Japanese Pharmacopoeia, JP XIV ~Yakuji Nippo, Ltd., Tokyo,

2001!, General Test 64, p. 103. 15Pharmacopoeia of the People’s Republic of China, Volume II ~Chemical

Industry Press, Beijing, 2000!, Appendix IV A ~English Edition 2000!. 16Originally produced as Corning 3130 and 3131 glasses. Produced as Kopp

Glass 3131 since the early 1980s. Available from numerous resellers and

from the NIST Calibration Program as ‘‘Wavelength Standard’’ ~38050C!

in 51 mm by 51 mm format or ~38051C! in cuvette format. 17Produced as Kopp Glass 5121 and available through optical filter distributors. 18European Reference Material ERM-FB010a is produced and sold by LGC

Promochem through LGC, Middx TW11 0LY, U. K. It is a mixture of

holmium and neodymium oxides dissolved in dilute perchloric acid. Certified values are provided for the wavelengths of minimum transmittance

of 16 features spanning the range 219–865 nm at spectral bandwidths of

0.5, 1.0, and 2.0 nm. 19 J. Webster, The Application Notebook ~Supplement to Spectroscopy!, February 2004, p. 30. 20The ‘‘McCrone Standard’’ is a monocrystalline Nd-doped YAG crystal

produced by McCrone Scientific Ltd, 155a Leighton Road, London NW5

2RD, U. K. The ‘‘Nelson M-42’’ standard is a monocrystalline erbiumdoped YAG @~Y1.5Er1.5!Al2~AlO4!3# crystal produced by Nelson Gemmological Instruments, 1 Lyndhurst Road, London NW3 5PX, U. K. The

HOLMIUM OXIDE SOLUTION 55

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005
National Physical Laboratory ~NPL!, Middx TW11 0LW, U. K. can also

supply these materials and will calibrate the wavelengths of minimum

transmittance of particular features specified by the customer. 21 International Vocabulary of Basic and General Terms in Metrology, 2nd

ed., BIPM/IEC/IFCC/ISO/IUPAC/IUPAP/OIML ~International Organization for Standardization, Geneva, Switzerland, 1993!. 22 J. C. Travis, M. V. Smith, and D. L. Duewer, Report of the Results of

SIM.QM-P6: UV/Visible Spectrophotometry Wavelength Standard Interlaboratory Comparison, NISTIR 6961, Gaithersburg, MD, January 2003. 23 J. C. Travis and D. L. Duewer, Proc. SPIE 4826, 113 ~2003!. 24Standard Terminology Relating to Molecular Spectroscopy, Standard E

131-02 in Annual Book of ASTM Standards ~ASTM, Philadelpia, PA,

2003!, Vol. 03.06, p. 289. 25 J. R. Moody, C. E. Wissink, and E. S. Beary, Anal. Chem. 61, 823

~1989!. 26R. E Walpole and R. Meyers, Probability and Statistics for Engineers and

Scientists, 5th ed. ~Prentice Hall, Inc., Englewood Cliffs, NJ, 1993!. Also,

see U. Charusombat & A. Sabalowsky. ^http://www.cee.vt.edu/

program–areas/environmental/teach/smprimer/intervals/

interval.html#whatt& 27 J. Reader, Appl. Spectrosc. 58, 1469 ~2004!. 28 ^http://www.cstl.nist.gov/nist839/839.04/molecular–absorption.html&

56 TRAVIS ET AL.

J. Phys. Chem. Ref. Data, Vol. 34, No. 1, 2005