Accurate measurements of water vapor transmission through high-performance barrier layers
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1 REVIEW OF SCIENTIFIC INSTRUMENTS 83, (2012) Accurate measurements of water vapor transmission through high-performance barrier layers P. J. Brewer, a) B. A. Goody, Y. Kumar, and M. J. T. Milton National Physical Laboratory, Analytical Science Division, Hampton Road, Teddington, Middlesex, TW11 0LW, United Kingdom (Received 3 April 2012; accepted 9 July 2012; published online 31 July 2012) We report a new approach to measuring very low rates of water vapor transmission through highperformance barrier layers, based on detection of the water vapor by cavity ring-down infrared spectroscopy. It provides accurate and traceable measurements with a detection limit for water vapor transmission significantly below g/m 2 /day. The system is underpinned by dynamic reference standards of water vapor generated between 5 and 2000 nmol/mol with an estimated relative expanded uncertainty of ±2%. It has been compared with other methods and demonstrates good comparability American Institute of Physics. [ I. INTRODUCTION Organic semiconductors provide a promising technology that could sustain the growth of the semiconductor industry. 1, 2 They possess the processing and performance advantages needed for low-cost large-area applications with similar electronic and optical properties to inorganic semiconductors. Consequently, there is great scientific and commercial interest in their application to optoelectronic devices such as organic light emitting diodes (OLEDs), thin film transistors, and solar cells. 3 A major obstacle to introducing flexible organic devices into the commercial market is their limited lifetime when exposed to water vapor or oxygen. Water ingress poses a particular problem for flexible displays, since the polymeric substrates from which they are constructed such as polyethylene-terephthalate (PET) and polyethylenenaphthalate (PEN) are highly permeable to water. Studies suggest that a barrier layer with a water vapor transmission rate (WVTR) of less than 10 5 g/m 2 /day is required to achieve an OLED shelf lifetime of more than h. 4 In order to reduce ingress of water vapor, thin coatings of inorganic materials, such as a 10 nm layer of a metallic oxide, can be applied to the flexible polymeric substrates. However, single-layer barriers of this nature fall some way short of meeting the target for encapsulation integrity because of the presence of defects in their manufacture. Depositing additional layers or increasing the layer thickness does not generally improve barrier performance since the defects from the initial layer will be repeated in subsequent layers. In order to meet the requirements for high performance, multilayer structures with organic interlayers have been used to decouple the defects in multiple inorganic coatings. 5 7 The first was reported in 1994 by Shaw and Langlois. 8 These alternating multilayer coatings set up a torturous path for the water vapor and significantly improve the barrier performance. 9 An alternative solution, involves the preparation of single or multilayer barriers by atomic layer deposition Both promise a) Author to whom correspondence should be addressed. Electronic mail: paul.brewer@npl.co.uk. to meet the target transmission rate for water vapor for organic devices. 14 The transport of water vapor into the operational parts of the device is quantified by the water vapor transmission rate (WVTR) defined as the mass transfer rate of water vapor per unit area of barrier and is normally expressed in g/m 2 /day as follows: W R = q A, (1) where q is the mass transfer rate of water vapor (g/day) and A is the area of the barrier (m 2 ). Various methods have been developed to measure WVTR. The most widely used is the calcium test which works by measuring the increase in the optical transmittance of a thin film of calcium as it oxidises following reaction with water. This method can be used to determine the amount, distribution, and permeability of local defects in the barrier coating. However, the calcium test, relies on a high performance material to seal the device under test. Any water permeation through the sealant will compromise the accuracy of the measured WVTR. Moreover, it does not discriminate between oxygen and water. An alternative means of detecting the change in the calcium test is by measuring the change in conductance during the degradation process. Other methods, include coulometric methods (e.g., according to ASTM F1249) 19 and mass spectrometry. 20 The limit of detection of coulometric techniques is often high. For example, the test according to ASTM F1249 has a sensitivity of g/m 2 /day. Alternatively, radioactive tracer methods can be used to implement the same concept as ASTM F1249 but using tritiated water as the permeant and a detector to measure radioactivity. 21, 22 They provide a high sensitivity, but require radioactive substances and substantial experimental efforts. Advances in barrier quality continue to challenge the sensitivity of currently available methods and there is an increasing requirement for standardisation. With the industry goal for barrier layers moving towards 10 6 g/m 2 /day and, with recent reports of flexible barriers achieving 10 7 g/m 2 /day, the measurement of water permeation at such ultra-low levels is /2012/83(7)/075118/6/$ , American Institute of Physics
2 Brewer et al. Rev. Sci. Instrum. 83, (2012) critical. There are no standards that cover such measurements and there has been no validation of the methods in use. This has led to a lack of comparability between published results and no agreed baseline against which to justify claims. In order for products such as OLEDs and solar cells that depend on these high-performance barrier materials to be viable, there is a requirement for a method to provide accurate and reliable measurements of WVTR at these low permeation rates. We report a new approach to measuring WVTR directly, based on cavity ring-down infrared spectroscopy (CRDS). The system operates with a dry chamber separated from two wet chambers of known temperature and relative humidity by the barrier material under test. Water vapor permeating through the film is collected by a flow of dry nitrogen and measured. A major source of error in methods used to measure ultra-low levels of water vapor transport is leakage around the perimeter of the sample under test where it is clamped into the measurement system. The measurement cell described here uses a novel design to minimise leakage through the seal and hence to eliminate water ingress to the dry chamber. This approach is a significant advance beyond existing methods and provides accuracy and traceability with a detection limit below g/m 2 /day. This method is underpinned by a unique facility at NPL for generating reference standards of water vapor in nitrogen between 5 and 2000 nmol/mol with an estimated relative expanded uncertainty of ±2% This facility is capable of stable and repeatable operation with an estimated relative expanded uncertainty of approximately ±2% for measurements above g/m 2 /day. In this paper, we describe the design of the system and show how the measurement uncertainty has been estimated. We then provide examples of its operation and the validation of its performance in a comparison with systems based on different principles. II. PRINCIPLE OF OPERATION AND CALIBRATION A schematic of the system is shown in Figure 1. The system is designed to be symmetrical around a single dry chamber separated from two wet chambers by two samples of the barrier material under test. The two cm samples of barrier material are attached to a central stainless steel support with a thin layer (approximately 1cm from the perimeter) of ultra-high vacuum grease (Fomblin). The barrier layers are sandwiched between two stainless steel outer discs and the central support. The whole assembly is held firmly in place with a G-clamp. Two circular grooves about 1 cm apart and close to the outer circumference of each of the discs each hold an O-ring. When the structure is assembled and clamped, the two rings sit either side of the perimeter of each barrier layer and form a guard chamber. The guard chamber is continuously purged with dry nitrogen to eliminate ingress of water to the dry chamber. The symmetrical design with two pieces of sample material, allows for improved measurement sensitivity by increasing the area through which water vapor can permeate into the dry chamber. Ultra-high purity nitrogen is supplied from cylinders (Air Products, BIP) and is passed through a purifier system (SAES Getter Monotorr). The amount fraction of water in this gas FIG. 1. Schematic of the system. The flow path of nitrogen through the guard and wet chambers is shown with grey solid arrows. The flow path through the dry chamber to the CRDS is shown with grey dotted arrows. stream after purification has been measured to be less than 1 nmol/mol. The output from the purifier passes directly to a pressure regulator (LNI Schmidlin SA) which maintains a constant input pressure to the dry chamber (grey dotted arrows in Figure 1). It also provides the same constant pressure to the wet chamber via the guard chamber and a water bubbler (grey solid arrows in Figure 1). Following the grey solid arrows in Figure 1, dry nitrogen first enters the guard chamber ensuring that the seal around each barrier film perimeter is purged continuously. This acts as a further measure to prevent water passing directly from the wet to the dry chamber via the seal. The nitrogen then flows to a water bubbler when the two way valve is set to wet. Nitrogen containing water vapor is then passed to the wet chamber. The gas then exits the chamber and the humidity is measured using a calibrated impedance meter (Michell MDM 300). A needle valve can be adjusted to dilute the gas stream with dry nitrogen and adjust the relative humidity. With the two way valve set to dry, the dry nitrogen by-passes the bubbler and enters the wet chamber. This setting is used initially to dry the system down prior to the start of each measurement. Following the grey dotted arrows in Figure 1, dry nitrogen passes to the inner (dry) chamber. Any water permeating through the film is collected by the stream of dry nitrogen in the inner chamber and passed to output which is connected to a CRDS with a detection limit of 0.2 nmol/mol (Tiger Optics Lasertrace 6000). The spectrometer is calibrated with trace water vapor standards generated using a unique capability at NPL described in a previous publication. 23 The CRDS analyser detects water vapor by tuning a laser source to an absorption line of water. By measuring the time it takes light to ring-down in a highly-reflecting cavity, it is possible to calculate the absorbance. Conversion of the decay time of the cavity, with and without target gas, enables the concentration of the target gas to be calculated.
3 Brewer et al. Rev. Sci. Instrum. 83, (2012) The input pressure to the system is set to about 1.5 bar (absolute) in order to meet the sampling requirements of the CRDS. Two pressure transducers are used to measure the absolute pressure on each side of the barrier under test. The system is designed to ensure that the differential pressure is negligible. This is essential to avoid applying any stress to the barrier layer or to affect the measurement by changing the driving force. The temperature of the wet and dry chambers and the bubbler is controlled and can be set from ambient temperature up to a maximum of 40 C. The temperatures are measured with an accuracy of ±0.2 C. The temperature of the bubbler is fixed at 2 C below the wet and dry chambers to prevent water condensing in the wet chamber. All surfaces contacted by the gas are metal (tubing is electropolished seamless stainless steel with clean-room welded face-seal fittings). WVTR through a barrier material is described by Fick s first law of diffusion according to the expression W R = D(c 2 c 1 ), (2) l where D is the diffusion coefficient, c 1 and c 2 are the concentrations of water vapor either side of the barrier material and l is the barrier thickness. In our system, it is calculated using W R = (x w x z ) M w Q A, (3) V m A where x w is the amount fraction of water measured from the flow through the dry chamber (mol/mol), x z is the amount fraction of water in the dry nitrogen (mol/mol), M w is the molecular weight of water, V m is the molar volume of an ideal gas at standard temperature and pressure (STP), A is the area of the barrier film exposed to water vapor (m 2 ), and Q A is the flow through the dry chamber (l/day). The flow through the dry chamber is measured at STP using a high accuracy Dry-Cal Flow Calibrator (ML-800, Bios International Corporation) under controlled conditions. III. LIMIT OF DETECTION AND REPEATABILITY In order to determine the lowest value of W R that can be detected in our system, two stainless-steel blanking plates (100 µm, 305 temper, Brown Metals Company) were mounted in the testing device in the position of the barrier layers under test. During this process the wet and dry chambers of the system were exposed to laboratory air. The device was then sealed and the two-way valve was set to dry down the system. The response from the CRDS was recorded and is shown in Figure 2 as a function of time. The data shows a sharp decline in detected water vapor after time zero. The gradient of the response becomes shallower as the system approaches equilibrium, until after approximately 40 h, where a sudden change in gradient is observed. This arises from a change in the averaging process used by the on-board software on the CDRS. After 50 h, at the point where the detector had reached the noise floor, the two way valve was switched over to introduce water vapor (68% relative humidity, 22 C) into the wet chamber. The unperturbed response after 50 h FIG. 2. Response of the CRDS plotted against time. The 2-way valve is set to dry at the start of the experiment. After 50 h a humid atmosphere is introduced into the wet chamber by setting the 2-way valve to wet. The y-axis is shown on a log scale. demonstrates that the seal between the chambers is adequate. The horizontal dotted line shows a detector response equivalent to a WVTR of g/m 2 /day using the area of the blanking plates and the flow through the inner chamber. Hence, we can assume that the uncertainty contributed from water passing to the inner chamber via the seal is negligible, even for measurements below g/m 2 /day. This also shows that the system can achieve measurements of W R with a limit of detection significantly below g/m 2 /day. Figure 3 presents measurements of barrier layers to study the repeatability of the system. In the first instance, a reference barrier developed at NPL was tested. The reference barrier was prepared from a sheet of stainless steel (100 µm, 305 temper, Brown Metals Company) which was cut to size in order to fit the measurement cell. A circle of material of approximately 7 mm diameter was removed from the centre of the stainless steel and a piece of PET (125 µm Melinex R 506, Dupont Teijin Films), just larger than the circle, was bonded around the circumference using an adhesive with a negligible W R compared to the barrier produced. The reference barrier was mounted on one side of the measurement cell. A stainless-steel blanking plate was mounted on the other. The system was dried down for approximately 12 h before water vapor was introduced into the wet chamber. The results in Figure 3(a) show the transient response of the system to four repeat measurement cycles. The water vapor was introduced at time zero. The mean of x w was calculated for each film from the last 30 minutes of data in each plot. W R was calculated for each film from the corresponding x w using equation (3). The mean W R of the batch was g/m 2 /day with a standard deviation of g/m 2 /day. The repeatability of 0.7% is very good at these levels. Figure 3(b) shows the transient response measured from a batch of commercial barrier layers, all prepared with the same materials and using the same process. In this experiment, a dry down period was not employed with water vapor being introduced into the wet chambers at the start of the measurement.
4 Brewer et al. Rev. Sci. Instrum. 83, (2012) FIG. 3. (a) Repeat measurements of an NPL reference film prepared with stainless steel and PET. Water vapor was introduced into the chamber at time zero. (b) Repeat measurements of commercial single barrier layers of Al 2 O 3. Water was introduced into the chamber at the start of the dry down process. In each case an atmosphere of (65 ± 2.0)% relative humidity, (22 ± 0.2) C was generated. The measured value of x w for each barrier appears to reach an equilibrium after around 60 h. From the data a mean W R of g/m 2 /day was calculated for the three barriers with a standard deviation of g/m 2 /day. This result demonstrates excellent performance since it includes contributions from both the repeatability of the measurement and the variability in the barrier films themselves. IV. UNCERTAINTY ANALYSIS The uncertainty in W R has been calculated using equation (3) by applying the principle of the Guide to the Expression of Uncertainty in Measurement, 26 u(w R ) ( ) MW Q 2 A =W R (u W R V m A 2 (x w )+u 2 (x z ))+u 2 r (Q A)+u 2 r (A), where subscript r indicates relative uncertainties. The uncertainties in M w and V m have been omitted as they are extremely small. A conservative estimate for the standard uncertainty of A is 0.5% relative. The standard uncertainty for Q A is estimated from previous work 23 to be 0.2% relative. This includes a contribution from any changes in temperature and pressure when converting from STP to laboratory conditions. As the system is temperature controlled these changes are small. The uncertainty in x W and x Z depends on the estimated uncertainty for the calibration of the CRDS. This has been taken from a calculation from a previous publication. 23 Several values of u(w R ) have been calculated spanning the detection range of the system. The calculation is based on mounting two barrier layers in the measurement chamber with a flow of 600 cc/min through the CRDS. These estimated standard uncertainties are shown in Figure 4 with (4) FIG. 4. Relative standard uncertainty of a generated mixture as a function of W R. The total uncertainty is shown with the open triangles. The four main contributors to the uncertainty budget are u(x w ), u(x z ), u(q A ), and u(a) and are represented by black squares, grey squares, grey circles, and black circles respectively. open triangles. Values for u(x W ), u (x Z ), u (Q A ), and u(a) are also shown and are represented by black squares, grey squares, grey circles and black circles respectively. It can be seen that u(w R ) is approximately 1% for measurements above g/m 2 /day and increases considerably for lower values of W R. This arises due to the increasing contribution from u(x W ) and u(x Z ). Both quantities have a direct correlation with the estimated uncertainty incurred from calibrating the CRDS. The estimated uncertainty of the dynamic reference standards used in the calibration rise significantly at low amount fractions. This is described in a previous publication. 23 The relative contribution from u(q A ) and u(a) do not change with the magnitude of W R. The estimated uncertainties for generating test conditions in the wet chamber of the measurement cell are not included in the calculation presented in Figure 4. The expanded uncertainties for relative humidity and temperature are ±2.0% and ±0.2 C respectively and these measurements are quoted separately to W R. V. VALIDATION WITH REFERENCE FILMS Four stainless steel/pet reference barriers were prepared using the procedure described earlier. The area of PET used was chosen to provide barriers with W R covering the detection range of the system. Figure 5 shows the transient measurements of each barrier after the system was dried down. Each transient plot changes by <1 nmol/mol in the last 3 h of measurement with the exception of the top trace which progresses towards steady state more slowly. This is likely to result from the larger surface area of PET used in the reference film which provides more active surface for water absorption/desorption in the dry chamber of the device. The drift observed in this transient has been considered when determining the uncertainty. Since the area of each film is constant, values of q (determined from data in Figure 5) are plotted against the area of the PET barrier under test in Figure 6. The expanded uncertainty of each value is shown with bars. A linear least-squares
5 Brewer et al. Rev. Sci. Instrum. 83, (2012) FIG. 5. x w of four reference films plotted as a function of time. At the start of each measurement, the inner chamber has been dried down to the noise level of the detector. In each case an atmosphere of (65 ± 2.0)% relative humidity, (22 ± 0.2) C was generated. FIG. 7. The influence of relative humidity in the wet chambers on x w for a reference barrier layer developed at NPL. (a) shows several step changes in relative humidity in the wet chambers (grey line, right axis) and the measured change in x w (black line, left axis). (b) shows a linear relationship when W R is plotted against relative humidity. fit to the data, passing through the origin, demonstrates the expected relationship between q and area of PET and provides validation for the system. The influence of relative humidity on W R was measured to further validate the method. A stainless steel / PET reference barrier, with a diameter of approximately 7 mm, was mounted on one side of the measurement cell. A stainlesssteel blanking plate was mounted on the other. A series of different water vapor concentrations were introduced into the wet chamber. During the experiment, the temperature of the measurement cell was maintained at (22.0 ± 0.2) C. Figure 7(a) shows the step changes in relative humidity in the wet chambers as a function of time (grey line, right axis). The measured x w from the dry chamber is also shown (black line, left axis). An indication of the lag-time from each step change in relative humidity is presented from the overlay of both plots. Under steady state conditions, the relationship between W R and the concentration gradient is governed by Fick s first law of diffusion. 27 Figure 7(b) shows the calculated values for W R at equilibrium versus the relative humidity in the wet chamber. The linear least-squares analysis, fixed to pass through the origin, provides a very good fit to the data and satisfies the theoretical expectation. The slight deviation from linearity is attributed to several factors. The most dominant is the variance in wait time required to achieve steady state when humidity is altered. As the relative humidity is decreased (and the resultant W R ), a longer time is required. The period of the experiment was limited to 100 h in order to ensure that the value of x z did not drift appreciably from start to finish. Therefore in instances of low relative humidity, step changes may have been applied before steady state had been achieved. FIG. 6. Mass transfer rate of water vapor (q) of the reference barriers (shown in Figure 5) plotted against area of PET in each reference barrier. VI. VALIDATION AGAINST ALTERNATIVE METHODS The performance of the system was compared to other methods based on different principles operated by five other laboratories. A multi-layer reference barrier (Fraunhofer POLO (Refs. 28 and 29) was sent to each participating laboratory. Each participant made a series of repeat measurements of W R at 20 C and 50% relative humidity. Figure 8 shows the mean of several measurements submitted by each laboratory together with the standard deviation of the measurements indicated by an error bar. Results from laboratories using the calcium test are displayed with open circles. Filled circles represent alternative methods. Our result (laboratory 4) presents the mean and standard deviation of measurements from three different reference films cut from the same sheet of reference material using the system described here. This accounts for the larger standard deviation from the NPL results compared to those reported by other laboratories. Further work is required to compare the precision of different methods. The reference barrier was also measured by one laboratory with
6 Brewer et al. Rev. Sci. Instrum. 83, (2012) and the European Union. The authors would like to thank the members of the Organic Electronics Association encapsulation working group for organising the comparison and Fraunhofer POLO for supplying the reference barrier. The authors are also grateful to Dr. Craig Murphy and Dr. Fernando Castro (National Physical Laboratory) for many useful discussions and Dr. Steve Wakeham and Hayley Brown (Plasma Quest Limited) for supplying single-layer barrier films. FIG. 8. Comparative measurements of a multi-layer reference film (several laboratories) at 50% RH and room temperature (20 ± 2) C. Open circles represent the reported result from laboratories using the calcium test. Filled circles show results from laboratories using other isostatic methods. Bars indicate one standard deviation of the measurements from each laboratory. a MOCON Aquatran. However W R for this sample was below its limit of detection and is therefore not shown. With the exception of laboratory 6, the NPL results are shown to agree with the other laboratories to within k = 2, and almost k = 1. Given the field of barrier layer measurement is relatively immature with little standardisation, the comparability between laboratories in this exercise brings confidence for valid and accurate measurement. Results from this comparison further demonstrate the validity of the system described here. VII. CONCLUSIONS We have developed a novel system for providing traceable measurements of WVTR with a limit of detection significantly below g/m 2 /day. Measurements can be performed over a broad range of temperature and relative humidity. A relative expanded uncertainty of approximately ±2% has been achieved for measurements above g/m 2 /day. A comparison of measurements of WVTR with methods based on different principles confirms the validity of the system described here. This system provides a much needed infrastructure for disseminating traceability to support the development of high performance barrier layers required by the rapidly developing field of organic electronics. ACKNOWLEDGMENTS This work was funded by the UK BIS National Measurement System s Chemistry Biology measurement programme 1 Y. Shirota, J. Mater. Chem 10, 1 (2000). 2 I. D. W. Samuel, Philos. T. R. Soc. A 358, 193 (2000). 3 R. H. Friend, R. W. Gymer, A. B. Holmes J. H. Burroughes, R. N. Marks, C. Taliani, D. D. C. Bradley, D. A. D. Santos, J. L. Brédas, M. Lögdlund, and W. R. Salaneck, Nature (London) 397, 121 (1999). 4 P. E. Burrows, G. L. Graff, M. E. Gross, P. M. Martin, M. K. Shi, M. Hall, E. Mast, C. Bonham, W. Bennett, and M. B. Sullivan, Displays 22, 65 (2001). 5 T. W. Kim, M. Yan, A. G. Erlat, P. McConnelee, and M. Pellow, J Vac. Sci. Technol. A 23, 971 (2005). 6 G. L. Graff, R. E. Williford, and P. E. Burrows, J. Appl. Phys 96, 1840 (2004). 7 J. S. Lewis and M. S. Weaver, IEEE J. Sel. Top. Quantum Electron. 10, 45 (2004). 8 D. G. Shaw and M. G. Langlois, 37th Ann. Tech. Conf. Proc (Society of Vacuum Coaters, Quimper, France, 1994), p J. Greener, K. C. Ng, K. M. Vaeth, and T. M. Smith, J Appl. Poly. Sci. 106, 3534 (2007). 10 P. F. Carcia, R. S. McLean, M. H. Reilly, M. D. Groner, and S. M. George, Appl. Phys. Lett. 89, (2006). 11 P. F. Carcia, R. S. McLean, M. D. Groner, A. A. Dameron, and S. M. George, J. Appl. Phys. 106, (2009). 12 A. A. Dameron, S. D. Davidson, B. B. Burton, P. F. Carcia, R. S. McLean, and S. M. George, J. Phys. Chem. 112, 4573 (2008). 13 M. D. Groner, S. M. George, R. S. McLean, and P. F. Carcia, Appl. Phys. Lett. 88, (2006). 14 S. Cros, R. De Bettiginies, S. Berson, S. Bailly, P. Maisse, N. Lemaitre, and S. Guillerez, Sol. Ener. Mat. Sol. Cells. 95, S65 (2011). 15 G. Nisato, P. C. P. Bouten, P. J. Slikkerveer, W. D. Bennett, G. L. Graff, N. Rutherford, and L. Wiese, Proc. Asia Display, 8 th IDW (Soc. Inform Display, San Jose, CA, 2001), R. Paetzold, A. Winnacker, D. Henseler, V. Cesari, and K. Heuser, Rev. Sci. Instrum. 74, 5147 (2003). 17 J. H. Choi, Y. M. Kim, Y. W. Park, J. W. Huh, and B. K. Ju, Rev. Sci. Instrum. 78, (2007). 18 S. Schubert, H. Klumbies, L. Müller-Meskamp, and K. Leo, Rev. Sci. Instrum. 82, (2011). 19 ASTM standard (2006). 20 T. Shimada, Y. Takahashi, and T. Kanno, Appl. Phys. Exp. 3, (2010). 21 B. I. Choi, H. S. Nham, S. B. Woo, and J. C. Kim, J. Kor. Phys. Soc. 53, 2179 (2008). 22 R. Dunkel, R. Bujas, A. Klein, and V. Horndt, Proc. IEEE 93, 1478 (2005). 23 P. J. Brewer, B. A. Goody, P. T. Woods, and M. J. T. Milton, Rev. Sci. Instrum. 82, (2011). 24 G. A. Leggett, B. A. Goody, T. D. Gardiner, and M. J. T. Milton, Meas. Control 40/9, 278 (2007). 25 P. J. Brewer, B. A. Goody, T. Gillam, R. J. C. Brown, and M. J. T. Milton, Meas. Sci. Technol. 21, (2010). 26 Guide to the Expression of Uncertainty in Measurement (GUM) (Geneva: ISO, 1995). 27 K. Lahtinen and J. 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