Analysis of interlaboratory measurements on the vapor pressure of cadmium and silver

Abstract

Detailed statistical analyses have been made of results obtained from a series ofinterlaboratory measurements on the vapor pressures ofcadmium and silver. Standard Reference Materials 746 (cadmium) and 748 (silver) which were used for the measurements have been certified over the respective pressure ranges 10-11 -10-4 atm and 10-12 -10-3 atm. The temperature ranges corresponding to these pressures are 350-594 K for cadmium and 800-1600 K for silver. The heats of sublimation at 298 K and the associated two standard error Iimits for cadmium and silver are 26660 ± 150 caljmol and 68010 ± 300 caljmol, respectively. Estimates of uncertainty have been calculated for the certified temperature/pressure values as weil as for the uncertainties expected from a typical single laboratory's measurements. The statistical analysis has also been made for both the second and third law methods, and for the withinand between-laboratory components of error. The uncertainty Iimits are observed as functions of both the heat of Sublimation and the temperature.At the XXVIth Council Meeting ofiUPAC in Washington, DC, on 21 and 23 J uly 1971, the use of metallic cadmium and silver as standards for testing apparatus and procedures for vapor pressure measurement, proposed by the Commission on High Temperatures and Refractory Materials, was approved. of the Task Force on Vapor Pressure of the Commission on High Temperatures and Refractory Materials. The materials cadmium, silver, gold, platinum and tungsten are being certified by the US National Bureau of Standards for vapor pressures as a function of temperature. The certifications cover the 10~ 12 -10-3 atm range; for the complete series ofmaterials, the temperatures corresponding to these pressures will vary from 350 to 3 000 K. Gold has previously been certified over the temperature range 1300--2100 K 1 • This report describes the current certification of cadmium (350--594 K), and of silver (800--1600 K)*.These vapor pressure standard reference materials will allow workers in the field to detect systematic errors and to evaluate their results quantitatively. The materials should be most useful for checking low vapor pressure measurement methods, such as the Knudsen, torque Knudsen, Langmuir, and mass spectrometric methods.Experience in vapor pressure measurements, particularly at high temperatures, has shown that large systematic errors are common, even among experienced investigators. This report gives estimates of the uncertainties of the certified temperature/pressure values as weil as estimates of the uncertainties of a 'typicar single laboratory's measurements.The current certification of cadmium and silver, when taken in conjunction with the prior certification of gold, gives an indication of the temperature dependence of the uncertainties of vapor pressure measurements. These uncertainties are statistical in nature and reflect results for typical experienced investigators. The use of vapor pressure standard reference materials should aid in the detection and elimination of errors a...

Estimating common parameters in heterogeneous random effects models

“…In the silver vapor pressure study (Paule and Mandel, 1971) several laboratories performed via different technique measurements of silver vapor pressure as a function of the absolute temperature T in the (individual for each laboratory) range from 800 to 1600 K. After removal of dubious results of one laboratory, there are a total of 298 different temperature points T ij , i ¼ 1, . .…”

“…. ,n i ,n 1 þ Á Á Á þn 8 ¼ 298 given in Table 4 in Paule and Mandel (1971) which employs 1/T10 4 in K À 1 units.…”

“…Our motivation is collaborative studies of meta-analysis, in particular arising in metrology applications. As a first motivating example, we use a study by Paule and Mandel (1971) in which several laboratories performed (via different techniques) measurements of silver vapor pressure P as a function of the absolute temperature T. According to the heat law, the logarithm of pressure, Y ¼ logP, is a linear function of 1/T. After removal of obvious outliers there are 298 different temperature points provided by p ¼8 laboratories as given in Table 4, Paule and Mandel (1971).…”

“…Silver vapor pressure data.Here are the estimates of the intercept y 0 and the slope y 1 with the (restricted) maximum likelihood estimator b X found from the R-language function lme, Numerical evaluation of b X would not be possible without the removal of the mentioned outliers, as with the full data, an error message in lme function indicated false convergence.The estimated between lab variance X Quantification of heterogeneity effect in interlaboratory studies is quite important Paule and Mandel (1971). (who were unaware of the size of X) write ''..a typical laboratory's ability to reproduce its own vapor pressure measurements exceeds its ability to reproduce other laboratories' measurements''.The almost unbiased estimator(16)of Varð e X Þ of e X (1/T10 in K À 1 unitsThe covariance matrix of b x of the restricted maximum likelihood estimator reported by the lme procedure is much smaller,…”

Mass spectrometric study of the vaporization and thermodynamic properties of components in the BaO-TiO2-SiO2 system

“…The temperature was measured using an EOP-66 optical pyrometer with an error of no more than ± 10 K in the temperature range 1700-2200 K. The measured temperature was corrected for absorption in the glass window of the vacuum system of the mass spectrometer. The experimental equipment was preliminary calibrated against the vapor partial pressures of gold [2] and CaF 2 [3].…”