for a better understanding of the present invention , together with other and further objects , advantages and capabilities thereof , reference is made to the following disclosure and appended claims taken in conjunction with the above - described drawing . the partial pressures of gaseous species such as c , co , co 2 , h 2 , ch 4 , c 2 h 2 , can be estimated from ( a ) the thermodynamic equilibrium between carbon and oxygen impurities in the nitrogen gas , ( b ) the outgassing behavior of carbonaceous materials , and ( c ) the decomposition of ch 4 . the equilibrium partial pressure of carbon ( p c ) over graphite is given in table 1 and shown in the figure . the free energy change ( δg 0 ) for reaction ( 1 ) is − 600 kj / mole and − 630 kj / mole at 2000k and 2273k , respectively . inputting into equation ( 2 ) the δg 0 values at 2000k and 2273k , the value for r of 8 . 3 j / mole , the p c values of table 1 , and using a po 2 of 1 ppm for ultra - high purity nitrogen yields a p co of 4 × 10 − 8 atm at 1727 ° c ., and 1 . 4 × 10 − 4 atm at 2000 ° c . the oxidation of co to co 2 is shown in reaction ( 3 ): the ratio of p co / p co2 for reaction ( 3 ) is represented in equation ( 4 ): since p o2 is 1 ppm or 1 . 0 × 10 − 6 atm , p co / p co2 equals 1 × 10 3 . thus , p co2 is 4 × 10 − 11 atm at 1727 ° c ., and 1 . 4 × 10 − 7 atm at 2000 ° c . as seen in fig1 , the partial pressure values of carbon ( p c ) derived from the equilibrium between gaseous and solid carbon range from about 10 − 9 to about 10 − 12 atm between 2000 ° c .- 1700 ° c . this very low p c level is hard to control because ( 1 ) the levels of p co , p co2 , and p c are lower than those calculated ( see below ) due to high - temperature outgassing of graphite furnace components , and ( 2 ) the outgassed species seep through the tiny openings between the sintering crucible and cover ( which are loosely engaged ) to enter into the inside of the crucible so as to dominate the p co , p co2 , and p c calculated solely from the solid carbon . studies have been conducted on the outgassing behavior of graphite and carbon - fiber insulation . see , e . g ., g . wei et al ., “ outgassing behavior of carbon - bonded carbon - fiber thermal insulation ,” proc . conf . carbon , 249 - 250 ( 1979 ); and l . overholser et al ., “ the degassing behavior of commercial graphite ,” proc . conf . carbon , 194 - 204 ( 1961 ). these carbon - or graphite - based furnace materials absorb gases like water vapor and oxygen , which then react with the carbon / graphite to result in the outgassing . in particular , the levels of co , co 2 , and h 2 that can be derived from high - temperature outgassing of graphite / carbon boats , elements , and fibrous insulations will affect the sintering atmosphere since the outgassed species are always in the background of the carbon - element furnaces . graphite boats , carbon heating elements , and carbon - fibrous insulation in the furnace exhibit a weight loss of about 0 . 01 - 0 . 1 % at high temperatures (& gt ; 1800 ° c .). the major outgas species from graphite are co and h 2 with ˜ 38 cc per 100 cc of graphite . as an example , a volume of graphite boat and carbon element in the hot face of the furnace hot zone of ˜ 100 cc releases 38 cc of gases which occupy a volume of ˜ 3000 cc and under a relatively low gas flow speed (˜ 1 m / min ). this corresponds to a total pressure of ˜ 10 − 2 atm with about equal amounts of co ( 5 × 10 − 3 atm ) and h 2 ( 5 × 10 − 3 atm ). outgassing species from carbon fibrous insulation are chiefly co and co 2 . the reported 0 . 01 - 0 . 1 % in weight loss will , for about 10 g carbon fibrous insulation in the hot face , yield ˜ 5 × 10 − 5 mole of co , which is ˜ 10 cc of gas ( 3 × 10 − 3 atm in 3000 cc of volume ) at ˜ 2000k . thus , for example in our furnace , consideration of outgassing of the carbon / graphite components indicates a p co of ˜ 10 3 atm and a p h2 of ˜ 10 − 3 atm at ˜ 2000 ° c . these values are much higher than the expected equilibrium partial pressure of carbon vapor ( p c ) from a solid carbon source . h 2 reacts with carbon to form ch 4 and c 2 h 2 at high temperatures . when p h2 =˜ 10 − 3 atm , the equilibrium partial pressures of ch 4 and c 2 h 2 at 2000 ° c ., are 2 × 10 10 and 4 × 10 − 7 atm , respectively . c . decomposition of ch 4 in a nitrogen - methane sintering atmosphere the figure also shows the curves representing the calculated equilibrium partial pressures of carbon for the following reaction at two methane concentrations in nitrogen : n 2 containing 0 . 5 % ch 4 , and 0 . 005 % ch 4 . as can be seen , the values of the equilibrium partial pressure of carbon are much higher than those derived from solid carbon , and relatively constant with respect to temperature . these are distinct advantages over the use of solid carbon whose values of partial pressure of gaseous carbon are much lower and are a strong function of temperature . the equilibrium partial pressure of hydrogen , p h2 , is two times that of p c in accordance with reaction 5 . in the case of n 2 containing 0 . 5 % ch 4 , the calculated p h2 are much higher than those estimated from outgassing of the carbon insulation , but are closer to each other for the case of n 2 containing 0 . 005 % ch 4 . this means that at 0 . 5 % ch 4 the contribution from the background outgassing of the carbon / graphite furnace components represents a negligible contribution . however , at 0 . 005 % ch 4 , it becomes necessary to include the contribution from the background outgassing . sintering aln tubes under n 2 — ch 4 atmosphere to high transmittance discharge vessel shapes of equivalent to a 70 w pca size were formed from an organic binder and an aln powder doped with 1 - 3 wt % of a cao - based sintering aid . other sintering aids such as y 2 o 3 and rare earth oxides at appropriate levels may also be used . binder removal was completed by prefiring in air at 500 ° c .- 900 ° c . for 1 - 10 hours . prefired aln parts were placed in bn or aln crucibles which were semi - enclosed with a cover . sintering was conducted in a horizontal carbon - element furnace containing fibrous carbon insulation and under one atmosphere of flowing high - purity - grade n 2 gas to which was added a pre - determined amount of ch 4 gas . the gas flow rate in the furnace corresponded to a linear gas speed of about 0 . 02 m / s . the sintering temperatures ( about 1800 ° c . to about 1925 ° c .) were reached by heating at a rate of from about 2 . 5 ° c ./ min to about 30 ° c ./ min . the dwell time at the sintering temperature ranged from about 30 minutes to about 40 hours . the total transmittance measurement was measured by placing a fiber - optical source inside the sintered aln tube and measuring the total amount of diffuse light transmitted and integrated over a sphere . typically , the onset of translucency pertains to the tubes showing a high total transmittance of greater than about 90 %. a more detailed description of the measurement of total transmittance is given in u . s . patent publication no . 2005 / 0258759 , which is incorporated herein by reference . sintering experiments using the n 2 — ch 4 atmosphere produced as - sintered aln arc tubes having a high total transmittance of greater than about 90 %. a preferred level of ch 4 in n 2 is about 0 . 05 to about 0 . 1 %. as shown in tables 2 - 4 , the total transmittance ranged from about 40 - 92 % within the range of 1 %- 0 . 005 % ch 4 content in n 2 . an important finding was the need to use ch 4 during the temperature ramp up to the sintering temperature . a preferred ramp rate is less than about 10 ° c ./ min . runs involving a high ramp rate (˜ 30 ° c ./ min ) resulted in low transmittance ( 57 - 79 %). in addition , the data identified the critical role , in terms of achieving high transmittance , of changing to a relatively pure nitrogen atmosphere for the latter portion of the dwell at the sintering temperature . if the methane is used throughout the sintering cycle , the sintered aln tubes are brownish and dark in color , in contrast with the colorless nature of high - transmittance aln tubes . a total dwell of about 10 to about 25 hours is preferred . it is preferred to stop using ch 4 in the nitrogen gas sintering atmosphere at about 1 hour to about 15 hours after the start of a 20 hour dwell . the role of methane gas in the nitrogen sintering atmosphere is thought to involve production of the gaseous carbon species , which then act to remove the second phases derived from the sintering aids after the sintering aids complete their roles and the body reaches a closed - porosity stage . the absence of the gaseous ch 4 additive in n 2 atmosphere during the second half of the dwell prevents excessive reduction of aln ( i . e . formation of nitrogen vacancies ) and minimizes any incorporation of carbon impurity into the sintered aln . the high - transmittance aln tubes sintered in n 2 — ch 4 atmosphere have the same colorless appearance as those sintered with solid piece of carbon as a charge material . the use of the n 2 — ch 4 atmosphere is judged to be advantageous over the use of a solid piece of carbon charge material due to the uniform distribution of the gas and the ability to better control the partial pressure of carbon during the sintering cycle . while there have been shown and described what are at present considered to be the preferred embodiments of the invention , it will be apparent to those skilled in the art that various changes and modifications can be made herein without departing from the scope of the invention as defined by the appended claims .