Two-color refractivity measurements are reported for carbon dioxide, oxygen, binary mixtures of nitrogen-oxygen, natural dry air, and water vapor. For the 'dry' gases, the measurements were simultaneously performed at 0.632 9908 μ m and 1.542 383 μ m , and cover temperatures ( 20 < t 90 < 100 °C and pressures p < 0.5 MPa - 1 . For water vapor, the refractivity ratio was studied for six wavelengths 1.52 < λ < 1.57 μ m relative to a simultaneous measurement made at 0.632 9908 μ m . The carbon dioxide and oxygen measurements establish the molar refractivities and second density virial coefficients more accurately than anything done before. A Sellmeier equation is formulated for oxygen which is about 103 times more accurate than extant knowledge dating from 1932. The nitrogen-oxygen measurements are used to derive the second density cross virial coefficient. The natural dry air measurements provide a targeted refinement to the Ciddor formulation for the refractive index of air, because they establish both a reference value for refractivity and the second density virial coefficient. The water vapor measurements ensure an accurate Ciddor formulation at telecom wavelengths, and guide the implementation of the group index.

Realization of the optical pascal has been limited by systematic errors caused by distortion of the optic. In this work, distortion error is circumvented via synchronous measurement of helium refractivity at two optical frequencies. The resultant pressure realization achieves combined standard uncertainty of 5.7 x 10-6p, chiefly limited by ab initio knowledge of helium dispersion. Two-color measurements are also presented for neon, argon, and nitrogen, which enable semiprimary realization of the pascal in a more practical embodiment. For argon dispersion, measurement and ab initio calculation barely agree within mutual expanded uncertainty; experiment is about 16 times more accurate than theory.

A method is described to measure the thermal expansion coefficient of fused quartz glass. The measurement principle is to monitor the change in resonance frequency of a Fabry–Perot cavity as its temperature changes; the Fabry–Perot cavity is made from fused quartz glass. The standard uncertainty in the measurement was less than 0.6 (nm·m^-1)·K^-1 , or 0.15

Recent developments in diameter metrology at NIST have improved the dimensional characterization of piston-cylinder assemblies (PCAs) to unprecedented precision. For the newest generation of PCAs, the standard uncertainty in the measurement of the outer diameter is 12 nm, while uncertainty in the measurement of the inner diameter is 14 nm. With a high-accuracy dimensional dataset in hand, the task of determining the pressure generated by a specific PCA is reduced to converting the diameter (and straightness and roundness) to an effective area (and distortion coefficient). The details on how this was performed for the artifact PCA2062 are described. PCA2062 was dimensioned in 2017 and 2020; the area repeated within 0.2x10-6 & sdot;A0. The calculation produced estimates of fall rate and rotation decay that agreed with experimental observations within 12 %. The fall rate is proportional to the square of the gap width; therefore, the agreement between calculation and measurement validates the dimensional estimate of the gap width within (36 +/- 42) nm, where the 42 nm standard uncertainty is governed by the present state of flow theory. The piston gage model is buttressed by three comparison tests against a laser barometer, which support a view that PCA2062 is linear and reproducible within 0.2 mu Pa Pa-1. Finally, an estimate of uncertainty in the effective area of a dimensioned artifact is provided: as expected, the diameter measurement is the main culprit, but there are open questions regarding the flow model that preclude an accurate evaluation of the distortion coefficient. For the 530 kPa operating range of PCA2062, distortion is not a significant problem, but the effect would be dominant in assemblies operating at 1 MPa and above.

An n(p, T_90) measurement suite is reported for the gases helium, argon, and nitrogen. The methodology is optical refractive-index gas metrology, operating at laser wavelength 633 nm and covering the temperature range (293< T < 433) K and pressures p < 0.5 MPa . The measurement suite produces several things of thermophysical interest. First, the helium dataset deduces the effective compressibility of the apparatus with a relative standard uncertainty of 1.3 × 10^-4 . Next, the argon dataset determines T - T_90 with a relative standard uncertainty of about 3 K·K^-1 . (The implementation is relative primary thermometry; T - T_90 is the difference between thermodynamic temperature and ITS-90.) Finally, the nitrogen dataset estimates the temperature dependence of polarizability within 3.5 % relative standard uncertainty. As a by-product of the nitrogen and argon measurements, values of the second density virial coefficient B_ρ(T) are derived with uncertainties smaller than those of previous experiments. More broadly, the work enables conversion of a measured refractivity at known temperature to optical pressure within 3.5 Pa·Pa^-1 across the stated range, albeit traceable to the diameter of a piston-gage.

A refractive-index gas thermometer has been used to determine T - T-90 in the temperature range (293 < T < 433) K within about 3 mu K/K relative standard uncertainty. The thermometer is based on an optical resonator operating at 633 nm wavelength. The working principle first measured helium refractivity at known pressure and temperature to determine the temperature-dependent compressibility of the resonator. With accurate knowledge of compressibility, the resonator was then run with argon to determine T - T-90 via T approximate to 3A(R) / 2R p/n-1 The molar polarizability A(R) = 4.195735(13) cm(3)/mol of argon was dependent on best-knowledge of thermodynamic temperature at the gallium melting-point; consequently, the implementation is relative primary thermometry, with one key-parameter value tied to T - T90 near 303 K. Notable aspects include a settling-time of 1500 s to reach 0.1 mK gradients, and statistical consistency of 0.5 mu K/K in the multi-isotherm regression.

Single-isotherm n(p, T90) results are reported for the gases Ar, N2, H2O, and D2O at vacuum wavelength $$\lambda = 1542.383(1)$$ λ = 1542.383 ( 1 ) nm. The argon and nitrogen isotherms were measured near 303 K; the water isotherms were measured near 373 K. Combined with the two previous articles of this series, the present results beget several insights via dispersion analyses. The argon result is highly consistent with static measurement plus ab initio calculation of dispersion polarizability. The nitrogen result is nominally consistent with one recent experiment and the dipole oscillator strength distributions, but the present work offers a refined estimate of the molar refractivity at optical wavelengths. For ordinary and heavy water, the dispersion trend is nominally consistent with existing liquid measurements. However, water’s absorption features in the near-infrared preclude a reliable comparison of the present result with literature.

A suite of measurements of refractive index $$n(p,\ T_{90})$$ n ( p , T 90 ) is reported for gas phase ordinary water H$$_2$$ 2 O and heavy water D$$_2$$ 2 O. The methodology is optical refractive index gas metrology, operating at laser wavelength $$633\ \text {nm}$$ 633 nm and covering the range $$(293< T_{90} < 433)\ \text {K}$$ ( 293 < T 90 < 433 ) K and $$p < 2\ \text {kPa}$$ p < 2 kPa . A key output of the work is the determination of molar polarizabilities $$A_{\text {R}} = 3.7466(18) \cdot [1 + 1.5(6) \times 10^{-6} (T/\text {K} - 303) ]\ \text{cm}^3 \cdot \text{mol}^{-1}$$ A R = 3.7466 ( 18 ) · [ 1 + 1.5 ( 6 ) × 10 - 6 ( T / K - 303 ) ] cm 3 · mol - 1 for ordinary water, and $$A_{\text {R}} = 3.7135(18) \cdot [1 + 4.4(10) \times 10^{-6} (T/\text {K} - 303) ]\ \text{cm}^3 \cdot \text{mol}^{-1}$$ A R = 3.7135 ( 18 ) · [ 1 + 4.4 ( 10 ) × 10 - 6 ( T / K - 303 ) ] cm 3 · mol - 1 for heavy water, with the numbers in parentheses expressing standard uncertainty. For heavy water, this work appears to be only the second gas phase measurement to date. For both ordinary and heavy water, this work agrees within $$0.15\ \%$$ 0.15 % with recent ab initio theoretical results for $$A_{\text {R}}$$ A R , but the comparison is affected by imperfect knowledge of dispersion. For ordinary water, the close agreement between the present work and theory suggests problems at the $$2\ \%$$ 2 % level in the low density limit of the reference formulation for refractivity.

Upgrades to the vacuum wavelength calibration service at the National Institute of Standards and Technology are reported. The instrumentation centerpiece is an optical frequency comb stabilized to a GPS-disciplined oscillator, thereby providing direct traceability to the SI second. Historically, the service has covered lasers at the popular interferometry wavelengths red and green. Recently, capability has been added for calibrating wavemeters at multiple telecom wavelengths in the range (1520 < lambda < 1570) nm. For most commercially available wavemeters, the test uncertainty ratio is about 10(4).

From basics of Fabry-Perot (FP) resonator and roundtrip phase, a complete working equation for a FP cavity based optical pressure standard (OPS) is derived and presented which includes corrections of reflection phase-shift, diffraction and pressure-induced distortion.The correction from diffraction, i.e.Gouy phase, is negligible.To operate an OPS as a primary standard, two unknown parameters, i.e. mirror dispersion coefficient and pressure distortion coefficient , in the working equation should be determined independently.Methods to determine and are described and applied to an OPS developed at the National Institute of Metrology (NIM), China.Thermodynamic effect observed in the determination of is also discussed.

A suite of measurements of refractive index n(p, T-90) is reported for gas phase ordinary water H2O and heavy water D2O. The methodology is optical refractive index gas metrology, operating at laser wavelength 633 nm and covering the range (293 < T-90 < 433) K and p < 2 kPa. A key output of the work is the determination of molar polarizabilities A(R) = 3.7466(18) center dot [1 + 1.5(6) x 10(-6) (T/K - 303)] cm(3) . mol(-1) for ordinary water, and A(R) = 3.7135(18) center dot [1 + 4.4(10) x 10(-6)(T/K - 303)] cm(3) . mol(-1) for heavy water, with the numbers in parentheses expressing standard uncertainty. For heavy water, this work appears to be only the second gas phase measurement to date. For both ordinary and heavy water, this work agrees within 0.15 % with recent ab initio theoretical results for A R, but the comparison is affected by imperfect knowledge of dispersion. For ordinary water, the close agreement between the present work and theory suggests problems at the 2 % level in the low density limit of the reference formulation for refractivity.

Thermal expansion sometimes dominates uncertainty in a precision measurement. A cell-based refractometer has been designed at NIST which targets 10−6 relative uncertainty in the measurement of helium refractivity; in terms of absolute refractive index at ambient conditions, the accuracy goal is 3 × 10−11. To achieve this level of accuracy, the length of a 0.5 m gas cell would need to be known within 100 nm. This is achievable when cell length is measured by coordinate-measuring machine at 20 °C. However, the refractometer will operate at the thermodynamically known fixed-points of water and gallium, near 0 °C and 30 °C, respectively. The cell is made from fused quartz glass, which has a nominal thermal expansion coefficient of 0.4 (μm/m)/K. Therefore, to scale the accuracy of the dimensional metrology across 20 °C to the triple-point of water requires that the thermal expansion coefficient of fused quartz glass is known within 10 (nm/m)/K, or 2.5 %. A method is described to measure the thermal expansion coefficient of fused quartz glass. The measurement principle is to monitor the change in resonance frequency of a Fabry–Perot cavity as its temperature changes; the Fabry–Perot cavity is made from fused quartz glass. The standard uncertainty in the measurement was less than 0.6 (nm/m)/K, or 0.15 %. The limit on performance is arguably uncertainty in the reflection phase-shift temperature dependence, because neither thermooptic nor thermal expansion coefficients of thinfilm coatings are reliably known. However, several other uncertainty contributors are at the same level of magnitude, and so any improvement in performance would entail significant effort. Furthermore, measurements of three different samples revealed that material inhomogeneity leads to differences in the effective thermal expansion coefficient of fused quartz; inhomogeneity in thermal expansion among samples is 24 times larger than the measurement uncertainty in a single sample.

An n(p, T-90) measurement suite is reported for the gases helium, argon, and nitrogen. The methodology is optical refractive-index gas metrology, operating at laser wavelength 633 nm and covering the temperature range (293 < T < 433) K and pressures p < 0.5 MPa . The measurement suite produces several things of thermophysical interest. First, the helium dataset deduces the effective compressibility of the apparatus with a relative standard uncertainty of 1.3 x 10(-4 ). Next, the argon dataset determines T - T-90 with a relative standard uncertainty of about 3 KK-1. (The implementation is relative primary thermometry; T - T-90 is the difference between thermodynamic temperature and ITS-90.) Finally, the nitrogen dataset estimates the temperature dependence of polarizability within 3.5 % relative standard uncertainty. As a by-product of the nitrogen and argon measurements, values of the second density virial coefficient B-p(T) are derived with uncertainties smaller than those of previous experiments. More broadly, the work enables conversion of a measured refractivity at known temperature to optical pressure within 3.5 mu PaPa-1 across the stated range, albeit traceable to the diameter of a piston-gage.

A procedure is presented which calibrates a wavelength/refractive-index tracker, so that it can compensate for the absolute refractive index of air within 3 x 10(-8). n. The procedure employs ultrahigh-purity helium and argon as reference gases of known n(p, T) to deduce the two unknown parameters in the working equation of the tracker: gas pathlength and pressure-induced distortion error. The performance of the gas calibration procedure is evaluated by comparing the corrected tracker against a master refractometer based on a Fabry-Perot cavity in nitrogen, a third reference gas of known n(p, T). In nitrogen, the calibrated trackers demonstrate accuracy at the level of 4 x 10(-9) . n. Testing in a fourth reference gas-water vapor-reveals that the working equation of the trackers must include a third unknown parameter: an end-effect caused by a moisture-dependence of the reflection phase-shift. Correcting for this moisture-related error represents the largest contribution to measurement uncertainty, and explains why performance of the calibrated trackers is an order-of-magnitude worse in moist air than in pure gas. In air, the Fabry-Perot cavity-based refractometer performs within 5 x 10(-)(9) . n, but is not a commercially-available device.

Laser refractometers are approaching accuracy levels where gas pressures in the range 1 Pa < p < 1 MPa inferred by measurements of gas refractivity at a known temperature will be competitive with the best existing pressure standards and sensors. Here, the authors develop the relationship between pressure and refractivity p = c 1 ⋅ ( n - 1 ) + c 2 ⋅ ( n - 1 ) 2 + c 3 ⋅ ( n - 1 ) 3 + ⋯ , via measurement at T = 293.1529(13) K and λ = 632.9908(2) nm for p ≤ 500 kPa. The authors give values of the coefficients c 1, c 2, c 3 for six gases: Ne, Ar, Xe, N2, CO2, and N2O. For each gas, the resulting molar polarizability A R ≡ 2 R T 3 c 1 has a standard uncertainty within 16 × 10-6·A R . In these experiments, pressure was realized via measurements of helium refractivity at a known temperature: for He, the relationship between pressure and refractivity is known through calculation much more accurately than it can presently be measured. This feature allowed them to calibrate a pressure transducer in situ with helium and subsequently use the transducer to accurately gage the relationship between pressure and refractivity on an isotherm for other gases of interest.

Dichlorodifluoromethane (R-12) has been widely used as a radiator gas in pressure threshold Cherenkov detectors for high-energy particle physics. However, that compound is becoming unavailable due to the Montreal Protocol. To find a replacement with suitably high refractive index, we use a combination of theory and experiment to examine the polarizability and refractivity of several non-ozone-depleting compounds. Our measurements show that the fourth-generation refrigerants R-1234yf (2,3,3,3-tetrafluoropropene) and R-1234ze(E) (trans-1,3,3,3-tetrafluoropropene) have sufficient refractivity to replace R-12 in this application. If the slight flammability of these compounds is a problem, two nonflammable alternatives are R-218 (octafluoropropane), which has a high Global Warming Potential, and R-13I1 (trifluoroiodomethane), which has low Ozone Depletion Potential and Global Warming Potential but may not be sufficiently inert.

In cell-based laser refractometers, interferometer pathlength uncertainty introduced by deformation and stress in the windows through which the beams pass can be the chief factor limiting measurement accuracy. The fractional contribution of pathlength uncertainty to our recent determination of the Boltzmann constant was 9.8 × 10 -6 , and more than two times larger than the next largest uncertainty component. We briefly describe the error and propose a design in which cell window effects contribute less than 3 × 10 -6 fractional error to the measurement of helium refractivity; performance that would be competitive with state-of-the-art primary thermometry and barometry.

New techniques using refractometry have enabled gas pressure to be measured using laser interferometry. Two key techniques have been studied at NIST which include the Fixed Length Optical Cavity (FLOC) and the Variable Length Optical Cavity (VLOC). The measurement techniques are described and the traceability of these measurements through quantum mechanics that enables them to be primary standards. This technology is critical for gas pressure metrology to move away from artifact based standards (and especially mercury based) and move to quantum based methods for realization of the pascal.