Acuerdos bilaterales suscritos por México para el combate al lavado de dinero

to diffusion pump Penning gauge to gas cylinders

to rotary pump \ J cold trap baratron toN2 cylinder to rotary pump pressure balance _w

inlet tube cold trap

cylindrical resonator spherical resonator

were thoroughly flushed with the sample gas before being re-evacuated to a pressure not exceeding 10 mPa. The Baratron zero was set and the system was then fille d

w ith the sample gas to the initial maximum pressure For the measurements on

argon and xenon, was the largest pressure achievable using the available gas

cylinder (about 750 kPa for argon and 540 kPa for xenon), except fo r the xenon

isotherm near 189 K , where p^^ was restricted to about 300 kPa to avoid

condensation w ithin the resonator. The maximum pressure for the measurements on nitrogen and the mixture {0.5 A r + 0.5 N j} was chosen to be approximately the same as that used for the argon isotherms. After fillin g w ith sample gas, the apparatus was le ft overnight to reach thermal and hydrostatic equilibrium.

Measurements were taken for the five modes T M ll, TM12, TM 13, TM21 and TM31, always in that order; modes T M ll, T M l2 and T M l3 were the three lowest frequency triply-degenerate TM modes (the lowest order o f degeneracy for modes o f the sphere), and TM21 and TM31 were the lowest frequency TM modes w ith five­ fold and seven-fold degeneracies, respectively. For each mode, the quarter-power- point frequency range (the frequency range over which the power transmitted through the cavity was greater than, or equal to, one quarter o f the maximum

transmitted power for that resonance) was found by manual adjustment o f the microwave synthesiser, w ith the sensitivity scale o f the lock-in am plifier and output power o f the synthesiser being set as described in section (6.4). The in itia l temperature and pressure were recorded immediately before the microwave measurements began.

Under computer control, the power transmitted through the sphere was measured at 31 discrete, equally-spaced frequencies over the quarter-power-point range o f a resonance, w ith a delay o f 0.4 s (four time constants) allowed after each frequency change for equilibrium to be established. The sweep was then reversed and the transmitted power was re-measured at each frequency. The powers measured at each frequency were averaged to take account o f any small changes in conditions (e.g., temperature d rift) during the scan. The average o f the squared differences between the up and down-sweep powers at each frequency was used as an estimate o f the variance o f the data for the reduced chi-squared statistic employed in the analysis o f each resonance [see section (6.7)]. Once measurements for all five modes had been completed, the final temperature and pressure were immediately taken and the averages o f the in itia l and final values were assigned to the set o f microwave measurements; i f the temperature or pressure had changed significantly during the measurements then all five modes were scanned again.

The gas pressure was reduced by about (Pmax/10) and the sphere was electrically heated, i f required, to help recover the initial temperature - the expansion o f sample gas into the vacuum line, used to reduce the pressure, took place almost adiabatically. The apparatus was le ft for about 25 min, in order that equilibrium could be established (the resonance frequencies were usually w ithin about 1 ppm o f their final, equilibrium values after only 5 mins), and then microwave measurements were taken again. This procedure was repeated until measurements had been made at, usually,

10 pressures, from;?^,^ to

A set o f measurements was also taken at a pressure o f about iPjnJ2Qi) for all isotherms, and at pressures o f about (Pmax/40) and (p^^^/SO) for the xenon isotherms at 273 and 300 K , to more thoroughly investigate the behaviour at low pressures. Finally, the resonator and external pipework were evacuated to a pressure not exceeding 10 mPa and the last o f the microwave measurements were taken. The

final Baratron output potential was noted, during the vacuum measurements, to ascertain whether there had been any drift in its zero setting over the course o f the isotherm.

The cylindrical resonator

The procedure for the isothermal measurements in the cylinder was very sim ilar to that followed for the sphere and so only a brief account is given here.

Following the in itia l evacuation o f the cylinder and external pipework to 1 mPa, the thermostatted bath was set to control at the desired temperature; the system was then thoroughly flushed w ith nitrogen and re-evacuated to 10 mPa. The resonator

and pipework were fille d to the maximum pressure , which was about 4.015 MPa

fo r all o f the isotherms, and then the apparatus was le ft overnight to attain equilibrium.

Measurements were taken for the three modes TMOlO, T M O ll and T M l 10, always in that order; modes TMOlO and TMOl 1 were the two lowest frequency non­ degenerate TM modes and T M l 10 was the lowest frequency doubly-degenerate TM mode. The resonances were swept exactly as described for the sphere measurements, w ith a lock-in time constant o f 0.1 s and delay times o f 0.4 s (four time constants) being allowed for all three modes. The initial and final temperatures and pressures were recorded and averaged as before.

The gas pressure was determined using the pressure balance which was floated w hilst the resonances were scanned. Microwave measurements were usually taken at pressures near 4.015, 3.504, 3.001, 2.501, 2.000, 1.500, 1.200, 0.800, 0.400, 0.200 and 0.079 MPa, and under vacuum (p < 10 mPa), w ith a 30 m in period being allowed for the system to return to equilibrium following each pressure reduction (the resonance frequencies were usually within 1 ppm o f their final, equilibrium values after 7 mins).

6.6 Materials

A ll the gas samples were supplied by B.O.C. Gases Ltd. and were used without further purification.

The ‘zero-grade’ argon and nitrogen, previously used for speed o f sound measurements [35], from 80 to 373 K, in the same spherical cavity adapted for speed o f light measurements in this work, were o f a certified minimum 0.99998 purity. Data provided by the suppliers indicated that the gases each contained less than 3 ppm o f oxygen, less than 2 ppm o f water, and less than 1 ppm o f each o f carbon monoxide, carbon dioxide, hydrogen and hydrocarbons; the ‘zero-grade’ argon also contained up to 6 ppm o f nitrogen. It is estimated that the stated impurities would alter the refractive index o f argon, at 215 K and 724 kPa, by less than 0.1 ppm, and that o f nitrogen, at 243 K and 4.015 MPa, by less than 0.3^ ppm.

The argon and nitrogen gas mixture was prepared by the suppliers, from pure components o f the same ‘zero-grade’ specification, to a nominal composition o f {0.5 A r + 0.5 N j}. The mole fraction o f nitrogen was accurately determined to be (0.50178 ± 0.00006), from measurements o f the speed o f sound in the mixture, at temperatures from 90 to 373 K, using the same spherical cavity used in this work [83].

The ‘research-grade’ xenon had a certified minimum purity o f 0.99995. The suppliers stated that the gas contained up to 40 ppm o f krypton, less than 5 ppm o f nitrogen, and less than 1 ppm o f each o f argon, oxygen, hydrogen, water, carbon dioxide and hydrocarbons, all o f which impurities would alter the refractive index o f xenon, at 189 K and 294 kPa, by less than 0.15 ppm.

6.7 Resonance analysis

As described in section (6.5), the resonance frequencies and halfwidths o f the modes o f the spherical and cylindrical resonators were determined by measuring the transmitted power over the quarter-power-point frequency range o f the resonances.

The power P transmitted through the spherical or cylindrical resonator was assumed

to be proportional to the potential measured at the diode, and was, therefore, fitted to the theoretically-predicted function [24, 132]

P(J)=

(6.7.1)

+ f ( / - A ) .

using non-linear least-squares regression, where / is the microwave drive frequency and f y , gj\i a n d /i// are the resonance frequency, halfwidth and complex amplitude, respectively, o f a component, denoted by the subscript N = Inm for a sphere mode and N = p q s for a cylinder mode. The expression in parentheses {• • •} is a Lorentzian function, and B and C f are the first two terms o f a complex Taylor series used to take account o f any background which may include the ‘tails’ o f other, nearby resonances, and the effects o f electronic cross-talk.