p-V-T Studies on Molten Alkali Nitrates Part 1 .-Thermal Pressure Coefficients and Compressibilities BY JOHN E. BANNARD*? AND ALLAN F. M. BAR TON^ Department of Chemistry, University of Southampton, Southampton SO9 5NH Received 20th December, 1976 The pV-T relationships of the molten alkali nitrates (Li, Na, K, Rb and Cs) were determined using a gas-pressurised, externally-heated pressure vessel. The cells were the pyknometer type with a long capillary barrier between the pressurising gas and the bulk of the liquid. Data, over a range of temperature from 500 to 800 K and a range of pressure to 1400 bar, were plotted in the form of isochores and used to determine densities and compressibilities of the liquids. The measurement of the conductance of melts at atmospheric pressure is a well established and precise procedure but its extension to conditions of high pressure is not.The case in favour of determining the density-dependence as well as the temperature-dependence of transport processes was argued previously and to obtain significant pressure coefficients requires a range of pressures up to and beyond 1 kilobar.' The analysis of the p and T dependence of conductance requires that the p-V-T relationship of the system also be known over the same range of conditions arid the determination of the isothermal compressibilities of melts becomes necessary. Furthermore, p-V-T data are necessary for an exhaustive study of the liquid state. The externally heated apparatus described earlier was used in the present work on the p-V-T relationships for the molten alkali nitrates.Few other p-V-T measurements at high static pressures have been made. Density measurements at 1 bar are straightforward involving either the Archimedean or the pyknometric methods, but their extension to high pressures involves considerable difficulties. Compressibilities of some alkali nitrates have been reported by Owens,2 a piston- cylinder method being used to 9 kbar and 520°C. Fray used the more elegant pyknometric method to study the nitrates, but, as with his conductance measurements? suffered large uncertainties associated with the solubility of the pressurising gas and with the influence of pressure on the dimensions of his cells. That work has been published together with the preliminary findings of the work reported here. The measurement of the velocity and attenuation of sound waves, however, is a more precise procedure even in molten salts.It gives rise to adiabatic compres- sibilities which can, via known values of Cp or Cv lead to the corresponding isothermal values, because Ps/BT = Cv/C,. Such applications are only feasible at present at 1 bar and both Bockris and Richards and Higgs and Litovitz have evaluated /IT in this way. Their results are in fair agreement and are close to those of Owens. The equilibrium, thermodynamic properties of any system can be described by the density [p = M/v], the thermal expansivity + Present address : Department of Metallurgy and Materials Science, University of Nottingham, NG7 2RD. Present address : Department of Chemistry, Murdoch University, Perth, Australia.153154 MOLTEN ALKALI NITRATES and the isothermal compressibility i av [ P T = -v(ap),l at all real values ofp, T and V. These last two coefficients, the so-called mechanical coefficients, are the experimental quantities normally determined in the studies of liquids; their significance has been discussed in detail by Ro~linson.~ The ratio of the mechanical coefficients is equal to the thermal pressure coefficient : The aim of the present work was to determine the p-V-T relations over a range of pressure and temperature out of contact with the pressurising fluid. The volumes of the salts were measured pyknometrically using a conductance bridge to detect the meniscus of the liquid. Hence constant-volume plots could be obtained at various values of p and T.The externally heated apparatus was used to study the nitrates over a range of temperatures to 52OoC, and pressure to 1400 bar. The practical data were obtained in the form of thermal pressure coefficients, and the data for the molten nitrates of Li, Na, K, Rb and Cs are given. These data are then used to derive densities and compressibilities which are discussed in terms of the possible structure of the melts. EXPERIMENTAL APPARATUS The externally heated pressure vessel, used up to a temperature of 520°C and a pressure of 1500 bar, has been described previous1y.l The vessel was pressurised with argon. The types of cells used are shown in fig. 1. They are all liquid-barrier pyknometers, the capillary presenting a long path to the diffusing gas.Fig. l(a) is a multiprobe cell, 25 cm long, which was used with the sodium and potassium nitrates. Fig. l(6) is a smaller version of this cell, w 14 cm long, with only two probes and was used for the expensive (4 (b) (4 FIG. 1.-The " constant-volume " cells : (a) and (b) Pyrex, (c) quartz.J . E . BANNARD A N D A . F. M. BARTON 155 rubidium and caesium nitrates. As lithium nitrate reacts with glass it was necessary to construct a cell from quartz, fig. l(c). Because of the difficulty in bringing metallic seals through quartz, the probes were introduced from the lip of the cell where they were rigidly held. The position of the meniscus of the melt was determined with the use of a conductance bridge circuit. In the case of the multiprobe cell, contact with a probe would be indicated by a change in the overall resistance; with the other two cells either short circuit or open circuit was identified.The bridge used was of the Wien type. MATERIALS Sodium nitrate and potassium nitrate (B.D.H., AnalaR grade) and rubidium nitrate and caesium nitrate (Johnson Matthey, 99.9 %) were dried at 180°C in an air oven for several days, maintained at just above their melting points for 10-12 h and filtered through sintered glass of porosity 3 before use. Lithium nitrate (Hopkin and Williams, Reagent grade) was recrystallised from distilled water, dried at 180°C for several days and again filtered before use, but this time in silica apparatus. PROCEDURE The alkali nitrates are fairly stable as melts in dry air, so the filling of the cell was made a simple process with the use of a small open furnace.Pure solid salt was placed in the top of the cell which was then lowered into the furnace. Subsequent to the salt melting the cell was alternately cooled and heated, and filling was brought about as a result of this heat-pump effect. The cell, connected to the pressure vessel cap, was then lowered into the hot vessel and removed after the plotting of each isochore in order that a quantity of salt could be added or taken away. Frequent cell failures occurred during this manipulation because freezing of the salt almost invariably led to breakage of the cell. The pressure was raised until the melt made contact with a probe. Time was allowed for thermal equilibrium to be achieved and then gas was allowed to leak out at a rate of one or two bars per min.When open circuit was again reached, the temperature and pressure were recorded. For the multiprobe cells, further rises in pressure allowed the use of another probe and another circuit resistance to identify the position of the meniscus. The duration of a pressure run was limited to -2 h and a similar time was allowed between runs at reduced pressure for the melt to degass. A correction to pressure ; which amounted ACCURACY was applied to the resistance of the platinum resistance thermometer due rT)T = -1.91 x bar-', to mO.7OC per kbar. The temperatures were measured to a tenth of a degree and as every care was taken to allow thermal equilibrium to be reached inside the vessel before the temperature or volume were recorded, the temperature is probably accurate to within k0.2"C.The pressures were recorded to 1 bar. The gauge was calibrated and the pressure will certainly be accurate to + 2 bar. These limits of imprecision are too small to be recorded on the isochores. A possible source of inaccuracy would be brought about by dissolution of the pressurising gas ; however thep-Tpoints always fell on straight lines except when gas was known to have penetrated the bulk of the melt. The effect of decomposition was also considered to be negligible as the experiments were generally carried out at temperatures below the recorded decomposition temperatures and because formation of nitrite was considered to have very little effect on the density and compressibility of the melt.After long periods (several days) at high temperatures, evidence of salt condensation was frequently found around the cell leads in the cooler part of the vessel. However the isochores were not plotted in any specific order and no hysteresis was found on jumpingI56 MOLTEN ALKALI NITRATES from low temperature to high temperature measurements and back again. The effect of salt evaporation was thus considered negligible. The measured slopes of the isochores were corrected for the expansivity and the compressibility of the cell material, Pyrex or quartz. The available values are very old and, as the correction accounted for w10 % of yv, it is possible that an unavoidable error has been introduced, say F 1 % of yv. The correction took the form P C d l + 1 1 %alt - = -(obs.) Yv Yv E s a ~ t + ace11 asalt + ace11 where o! is the volume expansivity of the melt or of the cell material./ ,,/ 0 2 4 6 8 Ib {2 tr pressure/bar x 1 O-’ FIG. 2.-Isochores for molten LiN03. TABLE 1 .-DENSITIES OF FUSED NITRATES a --bx 104 ref. LiN03 2.068 5.46 (lo), (11) NaN03 2.329 k0.017 7.14 (12), (13), (14) KN03 2.315 k0.032 7.29 (14), (10) RbN03 3.099 +0.050 10.10 (12), (14) CSNO~ 3.6206k0.065 11.66 (lo), (15) Calculation of compressibilities from isothermal pressure coefficients (and vice versa) and also from velocity of sound measurements relies greatly on accurate values of expansivity. This quantity is the temperature derivative of density and so any uncertainties in density will give rise to amplified uncertainties in compressibility. Similarly values of y y calculated from ref.( 5 ) and (6) will contain these same uncertainties which are probably _+3 % of a, (see table 1). A total uncertainty of k4.5 % of PT is therefore possible.J . E . BANNARD A N D A . F. M. BARTON 157 Compressibilities were here calculated from the thermal pressure coefficient and cc, from - b / p in the equation p = a+bT. The literature density data on molten salts vary considerably ; those considered the most accurate are given in table 1. RESULTS The raw data in the form of isochores are given in fig. 2-4 for the melts Li, Rb, and Cs nitrates respectively. Those for Na and K nitrates were presented ear lie^.^ Values of the slopes, extrapolated to zero pressure, were corrected for the compres- sibility and expansivity of the cell material as described above, and yv (corrected) was I I 1 I , 1 0 2 4 6 8 10 1 2 1 4 pressure/bar x lo-’ FIG.3.-Isochores for molten RbN03. platted against the temperature of the intercept as given for CsNO, in fig. 5. Also obtainable from the isochores are plots of yv against pressure for various temperatures, and one such family of lines is given for CsNO, in fig. 6. The scatter of the points .~~ ~~-~ _ _ _ _ ____.__ ___ take; from the yv againit T plot, fig. 5. Values of change of compressibility with temperature (fig. 7) may be obtained from plots like fig. 5, and a plot of compressibility against pressure (fig. 8) may be obtained from graphs of the type given in fig. 6. One-atmosphere compressibilities obtained from this work are compared with values obtained by other workers in table 2.158 MOLTEN ALKALI NITRATES The densities calculated at 1000 bar are compared with those of Owens2 in table 3.The atmospheric pressure values in the Gesent work were calculated from the equations given in table 1. Those in Owens' work were taken from ref. (16). The two sets of figures are in good agreement regarding the effect of pressure on density although in some cases different atmospheric pressure values were used. 700 800 12.01 ' - - * ' . - . ' " temperature/K FIG. 5.-yV against temperature for CsN03. Pressure, x , 1 bar ; 0, 1000 bar.salt LiN03 NaN03 KNOj RbNOj CsN03 J . E . BANNARD AND A , F . M. BARTON 0 2 4 6 a 10 pressure/bar x FIG. 6.-yy against pressure for CsN03. TABLE 2.-cOMPRESSIBILITY OF FUSED NITRATES tempPC 300 350 400 500 300 350 400 450 500 300 350 400 450 500 350 400 450 500 400 450 500 106jlT/bar-1 at zero pressure , DISCUSSION ref.(5) 19.6 23.4 28.9 17.8 21.6 26.8 19.3 23.4 29.4 - - - - - - I - - - - ref. (6) 20.3 23.3 27.4 18.1 21.3 26.3 19.3 23.5 28.9 - - - - - - - I - - - - ref. (2) - - 18.5 19.5 - - 21.5 24.5 - - - 20.5 30.5 - - 22.5 24.5 - - - - I59 this work 17.8 19.5 20.8 - 17.9 19.2 20.8 22.5 - - 20.0 22.5 25.7 - 22.4 24.7 27.3 - 28.6 31.7 34.8 The raw isochores (fig. 2-4) and the corrected isochores were all straight lines. The compressibilities of the fused alkali nitrates were determined principally because the thermodynamic analysis of the conductance data, especially the evaluation of the160 MOLTEN ALKALI NITRATES isochoric energies of activation, requires a knowledge of the p- V-T relationship for each of the ~a1ts.l~ Additionally, the data are of interest in their own right and.can be made the basis of an examination of the liquid-state properties of these systems. The corrected data for this study and for the calculation of compressibilities are in the form of values of yv, i.e.(ap/aT),, as a function of the absolute temperature, one of which is shown in fig. 5. These apparently linear plots are general for all liquid^.^ TABLE 3.-DENSITIES COMPARED WITH THE DATA OF OWENS LiN03 1 bar 1000 bar NaN03 lbar 1000 bar KNO, 1 bar 1000 bar RbN03 lbar 1000 bar Owens densities/g cm-3 400°C 500°C 1.700 1.646 1.735 1.682 1.853 1.783 1.892 1.826 1.824 1.753 1.861 1.801 2.395 2.298 2.448 2.352 this work densities/g cm-3 400°C 500°C 1.700 1.646 1.848 1.777 1.886 1.818 1.825 1.752 1.864 1.796 2.420 2.319 2.476 2.381 1.735 - That the relationship cannot be linear over the whole accessible temperature range is evident from the fact that an asymptotic rise in yv is to be expected as the solid or glassy state is approached. Also, as the temperature rises towards T,, yv rapidly approaches zero.The critical temperatures for these materials are not known, nor do we have data in the low temperature (glassy) region, but it may be concluded that the yv against T functions are virtually linear segments of an otherwise curved relationship. I 1 . 1 1 600 700 temperature/K FIG. 7.-Change of isothermal compressibility with temperature for the molten alkali nitrates.It is evident from fig. 7 that the compressibilities rise with temperature. This is to be expected as the gas-like character of the liquid develops and it also follows that with decreasing temperature, the compressibilities would decrease to the low values characteristic of the glassy and solid states. The compressibilities also change significantly with applied pressure (fig. 8) even over the relatively small range of pressures studied here. The values themselves are typically those of other liquidJ . E . BANNARD A N D A . F . M. BARTON 161 systems and it is possibly worth noting that the equilibrium, steady state and non- steady state properties of almost all liquids are very similar even though the melting points differ considerably.This is because the liquid state reflects short range interactions and the solid state long range interactions, Short range van der Waals interactions are similar for most molecular ensembles as are the repulsive interactions. Only if there is extensive structuring in the liquid state are the normal liquid properties significantly changed. * Whilst, therefore, the molten alkali nitrates have typical values of yv and PT, there are systematic differences between the values for the five salts (fig. 7 and 8) which correspond to the variation in cation radius. This does not seem to be a geometric factor because even in crystals there is a corresponding increase in PT. An increase in cation radius attenuates the residual coulombic attraction, and to a lesser degree the van der Waals attraction, without significantly affecting the repulsive interactions and a corresponding increase in compressibility is to be expected.The fact that NaNO, and LiN03 have similar compressibilities and that (fig. 7 and 8) I 1 20 - Li oo 10 pressure/bar x lo-" FIG. S.-Change of isothermal compressibility with pressure for the molten alkali nitrates. their T and p functions intersect arises simply because there is a lower limit of effective cation size at which anion-anion contact limits the further shrinkage of molar volume and at which anion-anion coulombic repulsion begins to attenuate the compres- sibility. The small size of the lithium ion will allow it to find refuge in a position bidentate to the nitrate ion thus hindering rotation and thus producing a large temperature derivative of the rotational degree of freedom.The similar steep rise in PT with temperature for CsNO, indicates a similar phenomenon, but this time low rotational order has probably been retained by virtue of large r++ repulsions rather than large r+- attractions. We thank the S.R.C. for financial support (to J. E. B.) and Prof. G. J. Hills for making laboratory facilities available. A. F. M. Barton, B. Cleaver and G. J. Hills, Trans. Faraday Sac., 1968, 64,208. B. B. Owens, J. Chem. Phys., 1966,44,3918. D. J. Fray, Ph.D. Thesis (London, 1965). A. F. M. Barton, G. J. Hills, D. J. Fray and J. W. Tomlinson, High Temp. H&h Press., 1970, 2,437-452. 1-61 62 MOLTEN ALKALI NITRATES J. O'M. Bockris and N. E. Richards, Proc. Roy. SOC. A, 1957,241,44. R. W. Higgs and T. A. Litovitz, J. Acoust. SOC. Amer., 1960, 32, 1108. C. Duval, Inorganic Thermogravimetric AnaZysis (Elsevier, 1963). G. W. Morey, The Properties of Glass (Rheinhold, 1938). ' J. S. Rowlinson, Liquids and Liquid Mixtures (Butterworths, London, 1959). lo G. J. Janz, Molten Salts Handbook (Academic, 1967). l 1 F. M. Jaeger and B. Kapma, 2. Anorg. Chem., 1920,113,27. l2 B. C. J. Neil, P h B . Thesis (Southampton, 1968). l3 B. de Nooijer, Ph.D. Thesis (Amsterdam, 1964). l4 W. J. McAuley, E. Rhodes and A. R. Ubbelohde, Proc. Roy. SOC. A , 1966,299, 151. l5 I. S . Yaffe and E. R. van Artsdalen, J. Phys. Chem., 1956,60,1125. l6 A. Klemm, in Molten Salt Chemistry, ed. M. Blander (Interscience, 1964). I'J. E. Bamard, A. F. M. Barton and G. J. Hills, High Temp. High Press., 1971, 3, 65-80. S. D. Hamann, Physico-chemical Efects ofPressure (Butterworths, 1957). (PAPER 6/2315)