Pressure-Volume-Temperature Relations in Liquid and Solid Tritium

PVT relations in liquid and solid T2 near the melting curve were measured over 20.5 K–22.1 K and 0 MPa–7 MPa (0 bar–70 bar) with a cell that used diaphragms for pressure and volume variation and measurement. Because of ortho-para self conversion, the melting pressure Pm and the liquid molar volume Vlm increased with time. The rates were consistent with a second order reaction similar to that for c the J = odd concentration: dc/dt=−k1c2+k2c(1−c),where k1 = 6−9×l0−2h−1. By extrapolation, the ortho and para forms differed by ΔPm~6 bar and ΔVlm~0.5%. Measurements of the volume change on melting and the thermal expansion and compressibility for liquid T2 were consistent with those for H2 and D2. Impurities such as H2, HT, DT, and 3He were removed by a technique using an adsorption column of cold activated alumina. Corrections for 3He growth during an experiment were adequate except near the triple point.


Introduction
Basic interest in the hydrogens H2, D2, and T2 is notably enhanced by the existence of significant zero-point energy, large relative mass differences, and different ortho-para characteristics. In addition, D2 and T2 in the condensed phases are prime candidates as fuels for controlled nuclear fusion.
Although the discoveries of D2 in 1931 [1] and T2 in 1934 [2] were close together in time, the pressure-volume-temperature {PVT) measurements on T2 have lagged far behind those on D2. Essentially they were the 1951 measurements of vapor pressure [3] and liquid density [4] up to 3 bar' and 29 ' The bar (= lO^Pa) is used in this paper rather than the pascal in order to facilitate the comparison of the results of this work with the results of previous and similar work. It should be noted that the International Committee for Weights and Measures allows the use of the bar temporarily with the International System of Units.
K and the 1956 melting curve determination up to 3100 bar and 60 K [5]. Contributing to the sluggishness of research efforts have been the high cost of T2 and the difficulties that arise from its radioactivity (2.8 Ci/cm' STP gas). Health and environment concerns require great care in containing T2 and definite provisions for accidental release. The continual creation of ^He from nuclear decay automatically adds a significant impurity. Self-heating demands proper equipment design and/or data corrections. The exchange of tritium with hydrogen in equipment causes physical breakdown of plastics and contamination of the tritium with hydrogen. These problems have affected the accuracy and completeness of the data reported here.

Apparatus and Procedures
The apparatus and procedures were basically those used for similar studies on ^He [6], ''He [7], D2 [8], and H2 [9]. The experimental cell consisted of three BeCu diaphragms welded at their circumferences and separated by 0.3 mm gaps. The lower gap, connected to a room-temperature He gas handling system via a capillary tube, had its pressure adjusted and measured directly. The upper gap was the T2 experimental chamber and was connected to the room-temperature T2 handling system via a low-temperature valve and a capillary tube. The sample pressure was determined from the deflection of the Upper diaphragm, measured by electric capacitance. The experimental volume was determined from the pressures in the two gaps, using the calibrations described in Ref. [8].
The T2 system is shown schematically in Fig. i. Four stainless steel tanks, each of 1500 cm^ volume, were used to hold T2, either for storage or for transfer to various parts of the system. The T2 was pumped at low pressure with a rotary vane pump and compressed to 70 bar with a diaphragm compressor. The uranium bed (U), Pd diffuser (Pd), and AI2O3 adsorption tube (AI2O3) were used for T2 purification. T2 gas samples were collected in sample tubes and analyzed by mass spectrometer. Calibration of capacitance versus cell pressure was done with the cell valve (V20) open and the T2 separated from the oil piston gauge by a differential pressure indicator (DPI). To prevent excessive pressure in the cell upon loss of cooling when V20 was closed, a thermocouple on the cell signaled a motor to open V20, which allowed venting to a tank via a pressure relief valve (PRV). The plastic material in the cell valve tip and in the stem seals of the manipulative valves was the polyimide Vespel SP 211, which resisted the destructive action of T2 quite well.

Purification
A significant problem in T2 experiments is the growth of ^He from radioactive decay at the rate of 0.031% per day. It was anticipated that a ^He-T2 mbcture would behave like a ''He-H2 mixture in solubility and effect on PVT measurements. The ^He growth during an experiment (at most 76 h long) was not expected to exceed solubility limits. Thus it was felt that the PVT measurements could be adequately corrected for ^He growth during an experiment but it was mandatory that the experiment start with ^He-free T2. Several methods of removing ^He were used. Exposure to U at 300 K binds T2 as UT3 and allows the unabsorbed ^He to be pumped away but good removal requires several cycles. A Pd tube diffuser retains all gases except the hydrogens. But these methods are slow and do not remove hydrogen and deuterium, which are initially present or appear in the gas when most materials are exposed to T2. Therefore the final process used was desorption from AI2O3, following basically the method of Depatie and Mills [10] for preparation of 99% 0-H2 or P-D2. About 32 cm^ of 2 mm dia. pellets of AI2O3 was placed in a 21 cm long stainless steel tube ( drawing the gas. Prior to use, the AI2O3 was evacuated at 140 "C for 2 h. The impure gas was added to the AI2O3 tube immersed in liquid H2 until saturation occurred at 87 mbar, after which it was passed through the tube at 87 mbar. The gas entered the top of the AI2O3 column and exited from the bottom until the exiting gas composition was the same as that of the entering gas, at which time flow was stopped. Then the liquid H2 bath was lowered slowly until the effluent gas was almost pure T2, after which the gas was collected separately while the adsorption tube warmed to room temperature. A pre-T2 test on D2 containing 0.61% HD produced 3500 cm' STP D2 with 0.03% HD. For T2 initially containing 0.26% H2, 1.97% ^He, 7.34% HT, and 0.49% DT, Table 1 gives the composition of effluent gas samples taken at various points of withdrawal. Collection of the gas after F=1600 cm' yielded 1600 cm' T2 containing 0.18% H, 0.10% D, and < 0.01% 'He which was enough for a PVT run.

Ortho-Para Considerations
The equilibrium ortho-para composition in T2 for various temperatures was calculated by Jones [11] and Gaines, Tsugawa, and Souers [12] and measured by Frauenfelder, Heinrich, and Olin [13]. The Gaines et al. results (T^ 22.5 K) agreed fairly well with the Jones results, which covered 0 K-175 K. The measurements [13] gave somewhat higher values of c, the/ = odd concentration, which could result from a higher sample temperature than the thermometer reading because of the radioactive heating. The Jones calculation is used as the standard in this paper.
The equilibrium values c (e) versus temperature T for H2, D2, and T2 are shown to 100 K in Fig. 2. The normal (n) values (those at 7 = 300 K) are 0.75 for H2 and T2 and 0.33 for D2. While c(e) for H2 and D2 at 20 K is very small and insensitive to T, c(e) -0.34 for T2 and increases rapidly with increasing T. Furthermore, the o-p conversion in T2 is much faster than in H2 under similar conditions. Therefore, it is important to determine c during the PVT measurements on T2. The variations of c with time t and vapor pressure were measured and partially reported earlier [14]. There, the values of c were derived from gas thermal conductivity measurements on samples from the condensed phase, thus the rapid back conversion, p-^o, in the gas phase decreased reliability somewhat. The best fits of the data were: for the solid, where k and k\ are empirical rate constants and A:2=^ic(e)/(l-c(e)).
The results on o-p conversion are summarized in Table 2 in several useful forms: (a) ro, the conversion rate at zero time; (b) tm, the time to convert 1/2 way to equilibrium; and (c) k,ki, and k2, the rate constants. In solid T2, the observed tm values of 2.0 h, 2.6 h, and 8.1 h at 4.0 K, 15.0 K, and 19.5 K, respectively, are moderately consistent with the NMR results of Gaines et al. [12] and Sater et al. [15] (although the latter found a minimum at 11.4 K) and with 1.5 h at 4 K of Frauenfelder et al. [13] using gas thermal conductivity analysis. However, Albers, Harteck, and Reeves [16]   PVT measurements on a liquid/solid mixture. The value of/TI-SX 10"%"' is eight times the ki for H2 given by Woolley, Scott, and Brickwedde [17]. Vapor pressures of T2 at a certain c value, P(c), and of n-T2 ^(n), were measured simultaneously in a special two-cell system. The differences, AP=P{c)-P{n), are summarized in Table 3. Their behavior follows that of H2 at similar values of P(n), as in Woolley et al. [17]. For example, extrapolation of the /'(n) = 840 mbar data to c=0 gives AP =29 mbar for T2 and 4P = 31 mbar for H2. In the PVT measurements above vapor pressure, gas thermal conductivity could not be used to determine c. Instead, the variations of melting pressure and liquid molar volume with time were used to determine o-p conversion rates. In these measurements, it was assumed that the initial value of c was 0.75 because: (1) the purification process left the T2 sample at c -0.75; and (2) the typical 2 h-5 h storage times at 300 K and 1.1 bar in a 1500 cm^ SS tank before condensation promoted conversion to n-T2.

Results
The PVT measurements typically began 2 h-3 h after condensation and continued for 50 h-76 h. Usually a single loading of the cell at a given T was used to measure compressibility and thermal expansion of liquid and solid, melting pressure, and volume change on melting. The liquid was compressed by a diaphragm until freezing began, which required 2 bar-4 bar overpressure. After the cell pressure stabilized, the compression was slowly continued past completion of freezing, which was indicated by a rapid rise in pressure.

Melting Pressures
The melting pressures Pm discussed here were the first-freeze values, obtained by extrapolation to zero amount of solid. If the compression was delayed, the increase in Pm with time was attributed to o-p conversion and ^He growth. The o-p change seemed to follow Eq. (2) where c=Q.15 -APJq, 15-c), and ki and q are constant at constant T. Measurements of Pm for ''He-H2 mixtures made up in the gas phase showed the regular effects of a slightly soluble gas and agreed fairly well with results of Bereznyak and Sheinina [18]. The mixture Pm increased 3 bar-4 bar per 1% of ''He over the Pm range of 0 bar-70 bar. Since ^He formation in T2 is 1.29 x 10"'% per hour, it was expected that 'He dissolved in condensed T2 would increase Pm by 3.7 mbar-5.0 mbar h"', which would necessitate small corrections. If saturation were exceeded, the 'He would probably act as an ideal gas, i.e., K varies as P~^ Thus, the correction would be 60 mbar h"' at the. lowest Pm (2.4 bar at 20.55 K), and 3.4 mbar h"' at the highest Pm (70 bar). The 'He growth in 76 h (the longest time after purification) is 0.098% whereas the '*He-H2 measurements in this cell and in Ref. [18] gave 0.16% "He as the solubility limit at 2.4 bar and 14 K. It follows that 'He would be expected to stay in solution. However, it apparently had left solution at 20.55 K when Pm and liquid compressibility ^1 were measured. Here the measured "Pm" was 2.4 bar, whereas linear extrapolation from higher T gave Pm = 0. If the excess pressure all came from ideal gas 'He the solubility would be 0.046% 'He. Sherman (R. H. Sherman, personal communication) measured 0.077%, which would result in 0.098-0.077 = 0.021% 'He as gas at 0.97 bar, which would yield 1.4 bar as the real Pm. For this sample, the measured /3i was 10 times "normal," i.e., values for T2 aged 2 h-4 h. Furthermore, T2 with 52 h-70 h ^He growth at 20.60 K and 20.65 K showed /3i to be 4-7 times "normal." These high ^1 values must have been the result of gas in the cell. The '*He-H2 mixtures containing up to 1% "He, but below saturation, never gave /3i values greater than 10% above pure H2 values. This throws suspicion on the high Pm and /3i results for T2.
Taylor [19] summarized some experiments on condensed T2 in which ^He had grown beyond the normal solubility limit. In liquid and solid T2 there was a lack of vapor pressure buildup consistent with the ^He production rate. In another case, analysis of successive aliquots of gas removed from aged liquid T2 showed the last liquid was ^He-rich. Supplementary evidence for ^He not appearing as gas was provided by electrical conductivity and magnetic susceptibility measurements. The formation of free ^He was visually observed by Hoffer (J. K. Hoffer, personal communication), who condensed DT near the triple point in a cylindrical cell with sapphire windows at the ends [20]. After 8 d as a liquid, the DT showed no bubbles. (They could not be hidden in the fill tube, for it entered the bottom of the cell.) After a freeze and a melt, the sample showed a bubble at the top of the cell with a volume that was ~ 1% of the ideal gas volume for 8 d ^He growth. A second freeze and melt produced the same bubble, which persisted for 3 d. Then, within 12 h the bubble grew to 100% of the calculated volume for 12 d 'He growth, taking up 20% of the cell volume. During the next three days no change in the bubble was seen, even after a freeze and a melt. The behavior of 'He grown in condensed T2 seems to be unpredictable.
For this paper, the Pm measurements were corrected as if the 'He -T2 sample formed a solution like '*He-H2. Figure 3 shows APr^=Pr"{t)-Pm(0) at 20.650 K, 21.900 K, and 22.100 K with and without 'He corrections. If the high rate at 20.65 K was caused by 'He growth, it seems that a greater correction is needed. In the fit to Eq. (2), q and the initial APm were varied to get the most consistent ki for each run. The results, summarized in Table 4, show the similarities with the time variation of c in liquid at vapor pressure ( Table 2). The average value q = 6.0 agrees with the H2 values 5.7-6.4 over 14 K-16 K from: /'m(p) by Youngblood [21]; n(n) by Mills and Grilly [5]; and Pm(p) and Pm(n) in the present apparatus.
Regardless of the previous discussion, extrapolation of Pm{t<6h) to t = 0 gave i'm(n).   Table 5, illustrated in Fig. 4 for Pm < 25 bar, and, over 20.
The constant 0.22 is the triple point pressure for n-T2 determined from vapor pressure measurements [3], and it is assumed for e-T2 as well. The linear Pm-T relation corresponds with the H2 and D2 curves. The greater values just above the triple   Table 5, P-Peq is the difference between experimental and equation values of The sole previous Pm measurement in the present range was 56.68 bar at 21.826 K for n-Tz by Mills and Grilly [5], which is 1.48 bar higher than the present result. Of this deviation, 0.76 bar could be from the 0.9% HT impurity in the earlier measurement. Their equation gives values that are lower than the present by 2.5 bar. An equation devised by Goodwin [22] gives values lower than the present by 0.64 bar.

Volume Change with Time
The increase with time seen in liquid volume Vt at constant T and P(~Pm) was also attributed to o-p conversion and ^He growth. The data fit Eq. that o-p conversion almost stops after 30 h and thereafter V) increases mostly from ^He growth. An empirical correction to AVi/V\, -1.0xlO~^h~\ to yield coincidence between the corrected data and the solid equation curve results in ki =8.98X 10"^h~' and s=4.6x 10"l Theki values are similar to the results from Pm (Table 4), but the s values are smaller than the values for H2: 6.5x10'^ by Scott and Brickwedde [23] at vapor pressure; 6.7 x 10"^ by Wallace and Meyer [24] at Pm. Measurements of AV/V vs t on solid T2 at 21.600 K and 53.17 bar were begun after the sample had been liquid for 6 h and solid for 9.5 h. They were added to the 21.000 K liquid value at f = 15.5 h. The results, shown in Fig. 5, follow the liquid curve for 9 h before rising sharply, probably because of breakup of the solid.

Liquid Thermal Expansion and Compressibility
The thermal expansion coefficient, a = V~^ {dVldT)p, and the compressibility coefficient, j3 --V~^{dV/dP)T, of the liquid were measured directly. All a and 2/3 of the )3 measurements were made on essentially e-Tz. The measurements at c = 0.6-0.7 fit in with the others. They would require a -1-1.5% correction, at most, for the volume change from o-p conversion during the 5 min measurement, and this is within the scatter of data. The differences in a and )8 for n-Hi and e-H2 were found to be within 2%. Therefore, it is assumed that the Ta data are independent of c. The a results are given in Fig. 6 as functions of T at various pressures. The dashed curve is through T™ of e-Ta. The p results are shown in Fig. 7 as functions of P at various temperatures, and the dashed curve is through Pm of e-T2. There are no other data on a or j3 for T2. Comparison of a for H2, D2 [8] and T2 is shown in Fig. 8. The three isotopes show similar slopes {dal6T)p and their a values come together with pressure, becoming equal at 57 bar. Figure 9 shows fi for the isotopes tending to merge at high pressures.

Molar Volumes
The molar volume of liquid T2 along the melting curve V\m was calculated from the measurement at the triple point [4], 22.051 cm^mol"' for n-T2, and the measured a and ^ values. This V\m multiplied by the measured AVJV\m yielded AV^, the volume change on melting. Finally, the solid molar volume Fsm was determined from Fim -AVm- Figures 10 and  11 give the results on AVJV[m and AVm, respectively, for T2, H2, and Dz [8]. Essentially, the AVJ V\m curves show a parallel displacement for the isotopes while the AVm curves are fairly close together. The results are given in Table 6. All the smoothed PVT values along the melting curve are summarized in Table 7 which should be self-consistent. Here, the V\m and V^m values are for n-Tz, but the values for e-Tz are only slightly larger. Values of Hra(e-T2) -Kim(n-T2) were calculated from the o-p expansion and the P^ (n-T2)->/'m (e-Tz) contraction, using the s values in Table 4 and the /3 values in Table 7. The two effects largely cancel     [26] calculated values of Km that are 0.05 cm^mol"-0.07 cm^mol"' lower than ours over 20.535 K-22.1 K range.

Solid Thermal Expansion and Compressibility
The measurements of a and ^ for the solid phase gave erratic and probably low values in general.
This behavior can be expected from poor pliability of the solid in the measuring cell, which tends to be worse away from the melting curve [8]. The behavior occurred in all the isotopes, but T2 has other properties that could influence the measurements: ^He production, internal heating, and solid fracturing. Although the measurements were made on e-T2 the results can probably be used for any o-p composition.
For each of H2, D2, and T2, a was measured at several pressures as a function of T, and each time it increased with T. However, a at constant T generally decreases with P. Thus the extrapolations of a to Tm can lead to roughly constant values, which occurs for H2 and D2 [8]. However a increases with Tm for T2. Figure 12 illustrates these behaviors.  Fig, 12. Solid thermal expansion of the hydrogens along the melting curve. MANZ is Manzhelii et al. [27]; UDOV is Udovidchenko et al. [28]; KRUP [29] is Krupskii et al. [29]; KRUP [30] is Krupskii et al. [30]; DRIES is Driessen et al. [26].
along with the overall increase in a from H2 to D2 to T2. The results of Driessen et al. [26] are also shown there. They measured the isochores of P-H2 and 0-D2 up to 2 kbar, between the melting curve and 4.2 K, by use of a cell whose wall deflections were measured with strain gauges. Molar volumes were determined by correlation with data at the melting line and 4.2 K. Isochores were fit by integration of specific heat. The resulting equation of state was used to calculate V, a, and p up to 25 kbar. The derivation of an EOS for P-T2 was "guided by experimental results for H2 and D2." Their a results appear to be in rough agreement with ours for H2 and T2 but for D2 they are about twice as great. Densities were derived from dielectric constant measurements on P-H2 by Manzhelii et al. [27] and on n-D2 by Udovidchenko et al. [28]. Their a results (good to ± 10%), shown in Fig. 12, match the Driessen et al. results for H2 very well and for D2 within 15%. From x-ray studies of lattice parameters, Krupskii et al. [29,30] derived a for P-H2 that is 37% higher than the Driessen et al. result and a for 0-D2 that is 8% lower.
The measurements of /3 as a function of P at several temperatures show a decrease with P. Generally, /3 increases with T, therefore, the extrapolated values of j3 to Pm can be almost constant, as illustrated in Fig. 13. There is also a big decrease in j3 from H2 to D2 to T2. The values for H2, D2 [8], and T2 are about 0.90, 0.55, and 0.77, respectively, of the Driessen et al. [26] results. The measurements of Manzhelii et al. [27] and of Udovidchenko and Manzhelii [31] on j3 of P-H2 are 5%-10% greater than those of Driessen et al. [26] while the values of Udovidchenko et al. [28] for n-Dz are slightly lower. Other measurements on H2 and D2 were made at 4.2 K using various direct and indirect techniques. In general, the values are low. In some cases, values of P were not low enough to allow satisfactory extrapolations.
In spite of these discrepancies in a and /3 results, there is hope for more accurate values for T2. Overall, the Driessen et al. [26] results on H2 and D2 fit in fairly well with others. It follows that their T2 results should be credible. For example, the change in Vs along the melting curve between 20.5  [27,31]; UDOV is Udovidchenko et al. [28]; DRIES is Driessen et al. [26].
K and 22.1 K is calculated from their a and /8 values to be 0.252 cm^mol~', in reasonable agreement with 4K=0.287 in Table 7.
In solid H2 and D2, some anomalies in a and /3 were observed [8] but hardly deserve recognition as phase change effects. There is no point adding to the confusion in this subject [27,28,29,30,32,33]. In T2, no anomaly was recognized, but observation was very limited.

S.6 Thermal Results
The enthalpy change on melting (heat of fusion) calculated from the Clapeyron equation 4^m = T4FmdPJdT, using the present PVT measurements on n-T2, is almost constant at 255 Jmol"^ in the range 20.9 K-22.1 K or 13 bar-70 bar. However, below 20.9 K the rapid decrease in dPm/dT lowers it to 144 Jmol"' at r,p. On the other hand, Mim for H2 and D2 varies linearly with Pm over 0 bar-70 bar from 117 Jmol"' to 130 Jmol"^ for P-H2, according to Dwyer et al. [34], and from 197 to 210 for n-D2 [8], If we wish to focus more on the similarities of the isotopes, perhaps it would be better to compare the behavior of the entropy change ASra = AHJT. This decreases over 13 bar-70 bar by 2% for H2 and D2 and by 4% for T2.

Summary
The PVT relations in liquid and solid T2 were measured near the melting curve over 20.5 K-22.1 K and 0 bar-70 bar. They were compared with measurements on H2 and D2 and with calculations on T2. Comparison of the three isotopes leads to few surprises. The melting pressure variations with temperature and ortho-para composition are consistent. An exception is the strange behavior of Pm for T2 in the 0.3 K interval just above the triple point. The o-p conversion in condensed T2 is faster than in H2 but slow enough to allow observation of its effect on the PVT relations. The liquid and solid molar volumes of the three isotopes are consistent in magnitude and in their variations with o-p composition, pressure, and temperature. Still unresolved is the status of 'He produced in condensed T2.