The Molar Volume (Density) of Solid Oxygen in Equilibrium with Vapor

The molar volume (density) of solid oxygen in equilibrium with vapor

Cite as: Journal of Physical and Chemical Reference Data 7, 949 (1978); https://doi.org/10.1063/1.555582 Published Online: 15 October 2009

H. M. Roder

ARTICLES YOU MAY BE INTERESTED IN

Viscosity of liquid water in the range −8 °C to 150 °C Journal of Physical and Chemical Reference Data 7, 941 (1978); https:// doi.org/10.1063/1.555581

Determination of atomic oxygen density with a nickel catalytic probe Journal of Vacuum Science & Technology A 18, 338 (2000); https://doi.org/10.1116/1.582189

Viscosity of Water Journal of Applied Physics 15, 625 (1944); https://doi.org/10.1063/1.1707481

Journal of Physical and Chemical Reference Data 7, 949 (1978); https://doi.org/10.1063/1.555582 7, 949

H. M. Roder

Center for Mechanical Engineering and Process Technology, National Engineering Laboratory, National Bureau of Standards, Boulder, Colorado 80302 Data from the literature on the molar volume of solid oxygen have -been compiled and critically analyzed. A correlated and thermodynamically consistent set of molar volumes, including the volume changes at the various solid phase transitions, is presented. Evidence for the existence of a 8-solid phase is reviewed. Uncertainties in the data and in the recom mended set of values are discussed.

Key words: Density; molar volume; oxygen; phase transition; solid.

Contents

Page Page 1. Introduction...... -. 949 References. . . . 956 2. Approach, Sources of Data..... 950 3. Phases and Transition Temperatures . 950 List of Tables 4. The Reference Volume-Liquid Density 950 5. Data, and Analysis of the Solid Volumes. . 951 Table 1. Transition Temperatures of Oxygen. 951 5.1. The Volume Change on Fusion, and the Table 2. Values of the Volume Change on o-Solid ..... 951 Fusion Calculated from the Clausius- 5.2. The 'Y-Solid . . . . 952 Clapeyron-Equation ...... 951 5.3~ The p-"{ Transition. . 953 Table 3. Volume Changes for the fi-"{ Transi 5.4. The /3-Solid . . . . 953 tion ...•- .. 953 5.5. The a-tJ Transition. . 954 Table 4. Molar Volumes and Densities of 5.6. The a-Solid 955 Solid Oxygen. . 956 6. Results ..... 955 List of Figures 7. Conclusion . . . 955 8. Acknowledgements. 956 Figure 1. The Molar Volume of Solid Oxygen. 952

1. Introduction ture entropy and enthalpy contributions to establish standard state values at 298.15 K, see for example Liquid oxygen has served as a thermometric fixed [4, 5]. In contrast to entropy, enthalpy, specific heat, point in cryogenics for some time. In the International and the properties of -the ideal gas, the molar volumes Practical Temperature Scale of 1968 (IPTS-68) both of solid oxygen have not been studied extensively. the triple point and the normal- boiling point of It is the purpose of this paper to review the data that oxygen are defined as primary fixed points [1, 2].1 are available from the literature, to critically evaluate Solid oxygen is of considerable theoretical interest the available data, and to present a correlated and because it occurs in at least three, possibly four thermodynamically consistent set of molar volumes different solid modifications and has several isotopic for solid oxygen. cU1IlpOnelltlS. The fourth solid modification, ii, has That tho density (molar volume) of solid oxygen been inve~tigated experimentally [3] but needs to be had not been related to liquid densities became studied further. Details of _the new phase are given evident during .a task performed for NASA [6].. A in section 5.1. compilation of Mullins et al. [71 was completed Considerable experimental effort has gone into the before the proper structures for both a and 'Y oxygen investigation of the solid phase transition tempera had been determined, and could not be used as source tures of oxygen because the transitions might be useful of volumetric data. Discrepancies of 10% indicated as secondary fixed points in thermometry. An appreci in a study by Jahnke [8] had not been removed in a able effort has gone into the evaluation of low tempera- subsequent study by Barrett et al. [9]. We had been asked to assemble thermodynamic properties of I Figures in brackets indicate literature references at the end of tbjs paper. slush oxygen, that is a mixture of solid and liquid. © 1978 by the U.S. -Secretary of Commerce on behalf of the Slush is -being considered as an alternate to liquid United States. This copyright is assigned to the American oxygen in propulsion primarily because the density Institute of Physics and the American Chemical Society. increases in going from liquid to mixtures of liquid

0047-2689/78/3122-0949 $03.00 949 J. Phys. (hem. Ref. Data, Vol. 7, No. 31 1'978 950 H. M. RODER and solid. Thus the density of solid oxygen became simply not defined or achieved sufficiently well to vitally important. permit meaningful comparison. The transition tem peratures are shown to the nearest millikelvin, the orig 2. Approach, Sourc~s of Data inal temperature and temperature scale is indicated The only molar volumes we will consider are those whenever applicable. Qonversions of temperatures to along the saturation boundary of solid-vapor, i.e., at the IPTS-68scale h.ave been made according to the temperatures below the triple point. We specifically paper by Bedford et ala [27]. For this paper we adopt exclude the very few measurements in the single the values given in the last line of table 1. The un phase where ,the solid is under pressure because to certainty for the a-{3 transition is taken from the dis consider them would unduly complicate the paper. persion among the different experiments. The 13-')' and Values for the compressed solid have been measured ,,(-liquid transitions are realized in the national stand [10] and compiled by Mills [11]. The approach will ards laboratories. for calibration purposes to about 0.2 mK on the defined scale [23, 24; 25]. However, it be to work from the triple point toward lower temper~ tures. The density of the liquid at the triple point should be recalled that the IPTS-68 scale as defined is assumed to be known quite accurately and is used may still differ from the ideal thermodynamic scale as a reference or starting value. The volume changes by several mK. For example, the vapor pressure anal for the various phase transitions and each crystal ysis by .Prydz [28) invokes thermodynamic consistency. thermal contraction are considered independently. One of the conclusions that can be drawn from Prydz's They are combined algebraically to form a consistent paper is that' the triple point and the normal boiling set. of molar volumes from the triple point to lower point of oxygen, both defined point::; Ull the IPTB-68, temperatures. Of course, the errors accumulate so should probably be 5 roillikelviIi farther apart than the densities that are least well known are those at they are on the IPTS. In other words, at one point, or very low temperatw-es. perhaps both, the TPTS-68 H,nd t.he ideal thermody The. sources of data that will be considered are namic scale are not yet in exact agreement. those experimental papers that contain information There are several explanations for the disagreement on the transition temperatures, on direct volumetric in temperature among the different experiments. The most logical one involves an error in temperature measurements~ on x-ray, neutron, or electron dif fraction, on dilatometric measurements, on melting measurement. Specifically the thermal link between or transition" curves , and on heats of transition. X-ray sample and thermometer may be inadequate. Low measurements yield both structures and volume thermal conductivity of the solid [29], low vapor values. Melting on transition curve derivatives and pressure, and incomplete conversion from one crystal structure to another all contribute to poor thermal heats of transition are used in-the Clausius-Clapeyron linkage. The result is a' temperature-time trace for equation to obtain volume changes for a given any given transition which'is not flat. As an example, transition. see figure 2 in the paper by Muijlwijk et al. [20], where 3. Phases and Transition Temperatures the authors even used helium gas to improve thermal contact for the a-13 transition. Oxygen occurs in at least three, possibly four solid Another possible explanation is that the transition modifications. Barrett et al. [12] using x-ray dif temperatures, certainly the triple point, are sensitive fraction determined a-oxygen to be monoclinic. The to impurities as shown by Ancsin [30,31]. Differences of structure of l3-oxygen determined by Horl [13] from 2 millikelvin at the triple point can easily be the resul t electron diffraction data is rhombohedral. This struc of some very nominal impurities. Ancsin's results ture has been confirmed by Alikhanov [14, nAllt,ron with helium gns show that the triple point pressure diffraction] and Curzon and Pawlowicz [15, electron is considerably higher with helium present than diffraction]. The structure of 'Y-oxygen was deter without. Therefore, the practice of using helium to mined by Jordan et al. [16] (x-ray) to be cubic. The effect better thermal contact between solid oxygen structure of the ~-solid, if it is verified, is not known. and the thermometer may be a poor experimental The new transition occurs very close to the triple procedure. point. We will consider the ~-liquid and the "(~ trans sitions as if they were one. Thus the transitions of 4. The Reference Volume-Liquid Density interest are a-l3, 13-')', and 'Y-liquid. For the liquid densities and in particular for the Transition temperatures have. been measured by density of the liquid at the triple point we adopt the 3 Roge [17], Orlova [18], Muijlwijk et ala [19, 20], Weber value published by Weber [21], 24.49 2 ±0.02 cm /moL [21], Kemp and Pickup [22], Cowan et al. [23], Kemp For this paper Weber's value is the point of reference, et al. [24] and Compton and Ward [25], The values that is all voluines at lower temperatures will be are collected for comparison in table 1. Values pub referred to it and adjusted as necessary. The uncer lished prior to 1950 by other authors, as given in the tainty of Weber's value becomes crucial to the re reviews by Roge [17] and Orlova [18], a,re not con mainder of the paper and we will, therefore, examine sidered because the earlier temperature scales are it in more detail.

J. Phys. (hem. Ref. Data, Vol. 7, No.3; 1978 THE MOLAR VOLUME OF SOLID OXYGEN 'I!i1

TABLE 1. Transition temperatures of oxygen

Transition Transition Triple point a+----+{3 {34:-~'Y l' or a~liquid

IPT8-68 Orig. scale Ref. IPT8-68 Orig. scale Ref. IPT8-68 Orig. scale Ref.

23.884 23. 886 [17] 43. 806 43.800 [17] 54. 361 54. 363 [17] NB8-39 1950 NB8-39 1950 NBS-39 1950 23.866 23.876 [18] 43.811 43.818 [18] 54. 365 54.368 [18] PRMI-54 ' 1962 PRMI-54 1962 PRMI-54 1962 54. 359 54.350, [191 CCT-64 1966 54. 359 54. 3507 [21] NBS-55 1969 23. 864 23.858 [201 43. 803 43. 794 [20] CCT-64 1969 CCT-64 1969 DAfinf~d [1,2] 54. 361 1969 23.880 43.801 54. 361 [22] 1972 43. 801& £23J 1976 54. 361 [24] 1976 54. 361 [25] 1976 23. 880:!:8:m 43. 801 ± O. 0002 54. 361 ± O. 0002

Weber establishes the liquid triple point density Clapeyron equation using the heat of fusion [38, 39, from the intersection of his high density PVT surface 40, 41, 3] and the melting curve derivative. Except with the Vtt1'vr 1're::ssure curve. The surface is derived for the value ur Ancslu [41] th~ heaL:::; uf fUl:)ion re from some 557 experimental PVT points in the single ported by various authors differ by no more than phase compressed liquid region. The lowest isotherm of 0.4 %, thus the value calculated for the volume experimental points is at 56 K; however measurements change on fusion depends primarily on which melting at lower temperatures along the melting line round curve is used. Weber [21] has compared his own out the set of experimental data. For the region in results to the melting curves published by othet. question Weber indicates an uncertainty of 0.1% in authors as shown in tn.bIe 2. density. This estimate will not be changed appreciably The earliest value obtained by Lisman and Keesom by the 1~5 K extrapolation to the triple point. Chang [42] is seen to fall, quite wide of the more recent ing the temperature scale from the experimental results. Jahnke [8] attributes a value of 0.921 cms/mol NBS-55 to IPT8-68 and challging the vapor pressure to Lisman' and Keesom. The origin of this v-alue is at the triple point to the value currently considered unclear since a recalculation of Lisman and Keesom's the best have negligible effect on the value of the value either through. the melting pressure derivative liquid density at the triple point. or from their published density differences confirms Weber's uncertainty of 0.1% for the liquid triple their value of 1.01 ems/mol. The agreement between point density of oxygen can be verified indirectly Mills and Grilly [43] and Weber [21] is surprisingly t.hrough rp.~111t.s oht.9.1n1=1d on ot.her fluids. Nit.rogem good considering that the former authors obtain all 2 [32], methane [33], and ethane [34] have been meas- of their data at pressures greater than 35 MN1m • -ured in the same PVT system that Weber used for TABLE 2. Values of the volume change on fusion calculated oxygen. Liquid densities for these gases measured by from the Clausius-Clapeyron cquntion Haynes etal. [35, 36, 37] in a totally different apparatus, a magnetic densimeter, differ by no more than 0.1 % Author Calc. volume at temperatures below 120 K. change, em3/mol

s. Data, and Analysis of the Solid Volumes Lisman and Keesom (42J 1. 01 (0. 921 1) a Mills and Grilly [43] 0.93 5.1. The Volume Change on FU$ion, and the 8-Solid Jahnke [8] O. 918::1::0. 02 Weber [21] 0.94 ±0.01 The volume change on fusion has not been measured directly; it must be calculated from the Clausius- a See text. J. Phys. (hem. Ref. Data, Vol. 7, No.3, 1978 952 H. M. RODER

Jahnke [8] pressurized his oxygen samples with helium mental evidence of a new phase has been obtained gas, which may account for his results being slightly very recently by Roder [31. However, additional lower than the others. Weber's [21] melting pressures experiments are needed to confirm the n.ew phase. are· closest in temperature to the triple point. If we Exactly how the a-solid affects the volume changes adopt his calculated value of the volume change on near the triple point remains to be determined. Several fusion with a slightly increased uncertainty to cover possibilities have been indicated by Roder [3]. For this all of the melting curves and the variation in the paper we ignore the a-solid and take the volume change experimental heats of fusion, i.e., 0.94 ±0.02 cm3/mol, in going from the liquid to the 'Y-solid to be O.80±O.03 then the molar volume for the ,),-solid at the triple cm3/mol, i.e., we accept the x-ray determination of point becomes 23.55 ±0.04 cm3/mol. If on the other Barrett et a1. [9] and the liquid values of Weber [21] hand we extrapolate a curve fit of the x-ray measure as representing the best possible values for the molar mentsof Barrett €,t a1. [9] on the ,),-solid to the triple volume of the 'Y-solid and the liquid at the tempera point temperature, then we obtain a value of 23.692 ture of the triple point. Some of Weber's liquid den ±0.05 cms/mo1. sities, the volume change. in going from liquid to -y-solid It is apparent that a systematic difference exists . and the best value for the 'Y-solid at 54.361 K,23.69± between the best x-ray measurements on the ,),-solid 0.05 cm3/mol, are shown in figure 1. on one hand and the liquid densities coupled with the 5.2. The y-Solid volume change on fusion on the other. The size of the discrepancy is 0.14 cm3/mol or about 0.6% in Density data for the 'Y-solid can be obtained from molar volume. The discrepancy has been recognized several sources. Tolkachev and Manzhelii [46] made a as early as 1936 [44] but hag not been resolved. single determination of density; Manzhelii et a1. [47] The individual errors do not overlap. To account for reported thermal expansion measurements made with an error of this size experimentally we would have to a quartz dilatometer; Jordan et a1. [16] reported on postulate an error of 10% in the heat of fusion, un the x-r~y structure determination from which a. likely, an error of 10% in the derivative of the melting· density can be calculated; Cox et al. [48] reported a curve, unlikely, or a systematic error of 2 K in the refinement in structure; and Barrettet a1. [9] made x-ray measurement, also unlikely [45]. A potential x-ray measurements at a number of temperatures explanation of the discrepancy involves the existence from which they determined expansion coefficients as of a new, as yet unrecognized, solid phase for oxygen. well as molar volumes. The published experimental The review of the molar volumes of solid oxygen has data as well as /the results of Schuch and Mills [10J thus ied to a search for a o-solid in oxygen. Experi- are shown in figure 1. The thermal expansion meas-

25r------~------~--

A Dewar (Mooy) '" Keesom & Taconis o Al ikhanov o Barrett et al. o Curzon & Pawl ow; (':7 .. Schuch 8. Mills x Coll ins 24 • Horl • Jordan et al. ~ Cox et al. • To 1kachev & Manzhe 1i i * Calculated From Liquid v M{.;Lelllli1n & Wl1helm === weber (L1qU1d) • Vegard

';; 23 E ",...... E u uS A ::;::: :::::> c! :> 22 a::: c::( ...J 0 ::;:::

liquid

200~------~------~ZO--~-----JLU------~40---L----_~LU---L--~bU TEMPERATURE, K

FIGURE 1. The molar volume of solid oxygen. J. Phys. (hem. Ref. Data, Vol. 7, No.3, 1978 THE MOLAR VOLUME OF SOLID OXYGEN 953 urements of Manzhellii et al. [47] are not plotted TABLE 3. Volume changes for the {j-'Y transition because the method is relative to a known or reference value, however, volume changes obtained from their Author ,Year Method Value cm3/mol results are used in the analysis below. The total volume change for the i'-solid between triple point, And tliA ~-"Y transition is 0.64 cm3/mol Stevenson [49] 1957 Cla'Qsius- 0.759 from the paper of Barrett et al. [9] obtained by extrap Clapeyron el.!. (0.959 1) a olating a linear least squares fit of the published Stewart [50] 1959 Clausius- 1. 16±0. 14 . volume data to the respective temperatures. We note Clapeyron eq. that the expansion coefficient published by Barrett et Extrapolation 1. 18±0. 06 al. [9] for the 'Y-soIid, Af/f=780X 10-6 K-l,must have of.1.V to suffered a digit reversal. A value of 870X 10-6 K-l is zero pressure. probably correct. The value obtained by integrating Jahnke [81 1967 Clausius- 1. 08±0. 05 the thermal expansion values of Mam;helii et a1. [47] Clapeyron eq. is 0.65 cms/mol. The agreement in volume change between the two radically different methods is very Barrett et al. [91 1967 Extrapolation 1. 19 satisfactory. of volumes (x-ray). To obtain a ~urve of recommended values we apply the volume ,change of 0.64±0.Ol ems/mol to the molar volume obtained for the triple point solid in the pre .. See text. vious section. Thus the molar volume of 'Y-solid at the of 175 ~tm/K froni his :figure 6. Using a value of 177.6 i3-'Y transition becomes 23.05±0.06 ems/mol. Values cal/mol [39] for the heat of transition the recalculated at intermediate temperatures are interpolated from value becomes 0.96 ems/mol. We suspect a digital our c~rve :fit to the volumes of Barrett et al. [9]. error in the printing of Stevenson's paper, i.e., 0.759 Experimental precision plotted in figure 1 as error should have been 0.959 ems/mol. bars were obtainod as follows: calculated from the The agreement between the values of Stewart [50] error given for the lattice constant by Jordan et al. and Barrett et al. [9] is excellent. The value contribu (161 and Cox et al. [48J, stated to be ±O.03% in ted by Jahnke (81 is a I~ttle wide, again perhaps be density by Tolkachev and Manzhelii r461, and esti casue of pressurization with helium gas. We adopt the mated to be ± 0.05 ems/mol for the measurements of value of 1.18±O.02 cm3/mol from the values presented Barrett et a1. [9]. The last estimate is calculated from a in table 3. Thus the molar volume of the /3-solid at precision of ±0.005 1 in the lattice constant of a the {j-r transition becomes 21.87 ±0.08 ems/mol. oxygen by Barrett et a1. [12] since the authors did not give an explicit uncertainty in their paper on 'Y-oxygen. 5.4. The ,B-Solid Uncertainties of the recommended values were ob tained by a.dding the error estimate applicable to nAn~ity d9,ta for the ~-solid can be obtained from each separate element. several sources. Horl [131 reported the structure to he 3 We note that the direct determination of density rhombohedral and calculated a density of 1.495 g/cm [46] lies somewhat below the recommendAn vA.hiA~. for a temperature of 28 K. A subsequent paper by wh~reas the values derived from the x-ray experiment Horl [51] has not been used in this compilation. A of Jordan et aI. [16) and the neutron diffraction experi value of 21.32 cms/mol has been calculated from the ment of Cox et a1. [48] fall considerably higher than paper by Curzon and Pawlowicz [15] and assigned a the ones recommended. temperature of 25 K. Mills [11] has calculated a value of 21.05 ems/mol froIn the paper of Collins [52] for a 5.3. The /3-y Transition temperature of 27 K. The papers by Manzhelii et a1. [4.7] a.nd Barrett et 0,1. [0] discussed in the section on The volume change for the /3-'Y transition has been the 'Y-solid also contain 13-~olid data that are used here. measured directly at elevated pressures by Stevenson Experimental values including, the value from Schuch [49] and Stewart [50]. A value of 1.19 cms/mol is and Mills rIO] that can be plotted are· shown in obtained from the measurements of Barrett et a1. figure 1. [9] using the linear curve fit of the previous section The total volume change for the l3-solid between for the 'Y-solid and a parabolic fit for the molar volumes the a-fJ and the i3-"( transitions is found to be 0.94 of the i3-solid. The volume change can also be estab ems/mol from the paper by Barrett et a1. [9]. This lished from heats of fusion [39, 40, 41} and the pressure value wa..'3 obtairied by extrapolating a parabolic least dependence of the 13-"( transition [49, 50,81. The values squares fit of the molar volumes to the respective 1,0 be consideI'ed aTe given in tabl~ 3. temperatures. A parabolic fit is· indicated boco.usc The value published by Stevenson [49] is 0..759 emS! both the molar volumes of Barrett et al. [9] and the mol. Since this value is so very much different from thermal expansion results by Manzhelii et a1. [47] 'the others we checked it in detail. We obtain a slope show tt distm{'.t. t,AmpArn.t.l.lrA nepennence. The total

J. Phys. Chem. Ref. Data; Vol. 7, No.3, 1978 954 H. M.. RODER volume change obtained by integration of the thermal Hollis Hallett [40], Muijlwijk et at [20], Ancsin [41], 3 expansion values of Manzhelii et al. [47] is 0.89 cm / and Dundon [55] when these authors attempt to mol. Again, the agreement between the two different measure a heat of transformation. As mentioned experiments is quite good. The difference probably earlier, the heating curve of Muijlwijk etal. (their arises because the thermal expansion measures the figurQ 2) is not flat. Nevertheless, a distinct heat of property of the bulk material while the calculation transition is indicated by this curve and could hfl,ve of density from the lattice constants assumes a fairly been evaluated by the authors. Thus their conclusion ideal, defect-free crystal. of "no eviq.ence of a latent heat" is· invalid. Fager To obtain a curve of recommended values it is stroem and Hollis Hallet show a A-like transition and appropriate to apply the average of the two total presume a second Qrder transition. Roge is uncertain volume changes, 0.92±0.03 cm3/mol, to the molar about the transformation but places the heat of volume obtained for the ,8-solid at the ,8.." transition. , transition as "about one-fifth the heat of fusion." The Thus the molar volume of the /3-solid at the a-/3 tran reported values for a heat of transition are those of sition becomes 20.95±0.11 cm3/mol. Values atinter Ellcken -17.5 cal/mol, Clusius -21.1 cal/mol, mediate temperatures are interpolated parabolically. Giauque and Johnston -22A2±0.1 cal/mol, and The error bars plotted in figure 1 for the electron Ancsin ~ 103.13 J/mol. A totally different result can diffraction experiments by Horl [13] and Curzon and be obtained from the recent paper of Kemp and Pawlowicz [15] are calculated from the experimental Pickup (221. In contrast to most other authors who precision indicated in these papers, and represent only show the transition as a A-like curve of Osat vs. temper the experimental precision. We have assigned a tem ature, Kemp and Pickup present a temperature perature of 25 K to the value of Curzon and Pawlowicz time trace which is flat (their figure 2). They obtain the because they had to deposit their sample at 25 K to temperature-time trace by using a power input which obtain a definite ring pattern for the ,,-solid. They is constant and appropriato to this transition, i.e., state that they see no change in lattice parameters on very small, 1.6 m W. Their loading is uncertain, around cooling from 25 to 7 K, and therefore calculate their 10 cm3 of liquid, i.e:, approximately 0041 moles. The lattice parameter at 7 K. This paper illustrates clearly heat of transition estimated from this paper is 10 that considerable error in assigning a valid temperature J/mol, nearly a factor of ten smaller than the other to the published lattice parameters is possible. The values! experimental precision for the measurements of Barrett The a-/3 transition has been measured at elevated et al. '[9] is estimated to be ±O.07 cm3/mol from the pressure by both Stevenson [49] and Stewart [50]. uncertainties given by Barrett et al. (12] for the a-solid. Evidence that a volume change does indeed exist is The disagreement between Horl,' Curzon and Pawlo found in figur.e 7 by Stevenson who calculates the wicz, and B~rrett et at is larger than the combined volume change to be 0.117 CIIl3 /11101 from the Clau~iu~ experimental precision for the different experiments. Clapeyron equation using the transition heat from Barrett et al. indicate that Horl's lattice parameters Giauque and· Johnston [39]~ Stewart erroneously fit a temperature of 35 K. This is true for the value of assumed the transition to be second order and did not ao at 36 K, however the 00 values at that temperature present a volume change. However, using the deriva still differ by two part~ in 1,000. In other words, tive of his phase transition curve and the heat of systematic differences between' the three different ex transition from Giauque and Johnston we Can calcu periments remain unaccounted for. late a value of 0.12.; cm3/mol from his paper, which is in excellent agreement with the value by Stevenson. , 5.5. The a-f3 Transition In both cases it would be preferable to extrapolate the measured volume changes to zero pressure. How Considerable confusion as to whether this transition ever, the required values have not been published in is first or second order exis'ts in the literature. Barrett these papers. et al. [9J point out that the transformation cannot be Mau:t;helii e'-' al. [47] tSLaLe Lha'-' '-'he volume change second order for quite general, theoretical reasons. observed in their thermal expansion e:xperiment is on Their' conclusion is that the transition is first order the order of 0.5% even though they are not able to and of a martensitic type, and that "Martensitic trans establish a reproducible vnlue. 'rhA voll1mp, jump formations are sensitive to strain and can easily imitate given by Dundon [55] is 0.135 emS/mol ± 10%. The second-order transformations. Residual strains can aid volume jump can not be established unambiguously or inhibit such a transformation so that the transforma from the x-ray diffraction experiments because the tion of a strained sample does not take place at the a-Oxygen volumes of Barrett et al. (12] and Schuch transition temperature itself, but is spread out over a and Mills (10] differ by 1 %. range of temperatures." 3 A martensitic transformation explains the rather We adopt a value of 0.13 ± 0.11 cm /mol for the , diverse results and interpretations obtained by Eucken volume change of the a-,8 transition as a composite [53], Clusius [38], Giauque and Johnson [39], Hoge of the results of the more recent experiments [10, 41, [171, Borovik-Romanov et al. [34], Fagerstroem and 49, 50, 55]. The uncertainty of the volume change is

J. Phys. Chem. Ref. Data, Vol. 7, No.3, 1978 THE MOLAR VOLUME OF SOLID OXYGEN 955 deliberately estimated as quite large because we feel . the papers of Dewar [56], McLennan and Wilhelm strongly that the heat of transition could be in error [58], Mooy [59], Ruhemann [60], Vegard [61 62] by a factor often. Since the value of the ,8-solid at the Keesom and Taconis [44], Jordan et al. [16], Cox et a-{3 transition had been established at 20.95 ± 0.11 aI.. [48], Horl [13], Curzon and Pawlowicz. [15] and cm3/mol the molar volume of the a-~olid at the a-,8 Ahkhanov [14] should be rejected. The values are transition becomes 20.82 ± 0.22 cm3/mol. We note simply not accurate enough to be included in a criti~ that the uncertainty of 0.22 cm3/mol, nearly 1 % of the cal compilation of the molar volumes of solid oxygen. molar volume, arises in equal parts from the cumula The recommended values are essentially the average tive error in the molar volume and the uncertainty between the thermal expansion results of Manzhelii for the heat of transition for the a-fJ transition. eL al. [47] and Lhe x-ray measurements of Barrett et al. [9, 12J except for the a-solid where the values of 5.6. The a-Solid Manzhelii et al. [47], Collins [52], and Schuch and Mills [10] are preferred. The direct implication is that The .direct density measurement of Dewar [56] nearly all values presently cited in handbooks of made at the boiling point of hydrogel). falls into the physical data need to be revised. temperature riLnge of the a-solid. It is clear from figure Many of the handbook values can be traced to the 1 thaL this value is about 8% wide of the more recent International Critical Tables, 104256 g/cm3 at 20.5 K, measurements. Molar volumes and experimental that is, the value published by Dewar. This value imprecisions derived from the papers of Alikhanov was supposedly confirmed by Mooy [59] with x-rays, [14] Barrett et al. [12J and Schuch and Mills [10] are however we now know Mooy's structural assignment plotted in figure 1. From the neutron diffraction ex to be in error. Dewar's value differs. by nearly 8% periment of Collins [52] we have calculated a value of from the one recommended. This is not surprising; 20.74 cm3/mol at 4.2 K. The uncertainty for this value since he condensed his sam.ples from the vapur ::sLate cannot be calculated, but is taken to be the same as the formation of voids is likely. Similar more recent for that of Alikhanov. The thermal expansion measure experiments with solid nitrogen were shown to con ments of Manzhelii et al. [47] are used to provide a tain up to 30%. voids by measuring the dielectric volume variation down to 18.75 K. At that tempera constant of the condensed material [63]~ Another ture the values extrapolate to zero expansion. At value quite often cited in handbooks is 1.46 g/cm3 at temperatures below 18.75 K the molar volume is assumed to remain contant. Thus the total volume 20.5 K [64, for example]. This value can be traced to the x-ray work of McLennan and Wilhelm [58] whose change for the a-solid becomes 0.06 cm3/mol and the assigned structure we now know to be incorrect. This molar volume at 4.2 K becomes 20.75±0.22 cm3/mol, value is about 6% different from the recommended or very nearly identical to the results of Collins [52]. 3 The uncertainty for the volumes of the a-solid were one. A quite different value, 1.568 g/cm at 0 K is established in the previous section as ± 0.22 cm3/mol. cited in yet another handbook [65]. This value can be traced to the Smithsonian.Tables [66],it is most likely R.n extrR.pols.tlon of Dewar's values for liqqidand 6. Results solid to 0 K. Only by accident is this value close to the recommended values. The results of this study are presented in graphical form in figure 1. Recommended values of molar vol For the {3-crystal Ruhemann [60] was notable to umes and densities are given in table 4. As far as assign a· definite structure, he did, however, state errors are concerned, we have followed the suggestion that McLennan and Wilhelm's structure should not of Rosenfeld [57], that is we assume the errors given be considered final. For the 'Y-crystal Vegard [61,62], in most papers to indicate experimental imprecision, Keespm and Taconis [44] and Jordan et al. [16] all and we establish an actual' uncertainty whenever cite the same structure, cubic. Their lattice param possible from the dispersion among several different eters are identical, 6.83 A, however their published experiments . .By breaking the problem into several densities vary by 2.5%, i.e., 1.30, 1.32, and 1.334 3 parts, each part can be assessed individually and an g/cm • Even the best of thes:e values, Jordan et al. uncertainty for it established. The sum of the parts [16], differs by 2.5% from the work recommended, yields a thermodynamically consistent set of values Barrett et al. [9]. Thus the densities cited by another and a consistent set of uncertainties. The uncertainty compilation of x-ray structures [67] are in error by in recommended values in table 4 increases from about 2.5%. 0.2% nt the triple point to no more than 1.1 % at the The papers rejected do~ however •. yield a clue about very lowest temperature. systematic differences. It appears that structural assignments, temperature control, and temperature 7. Concl usion measurement have improved as time has passed. Two items remain in question: the precise value of One way to state the results of this study is as fol the volume change f()r the ot-,8 transition, and volume lows: The molar volumes obtained, or obtainable from changes from the. 'Y-solid to the liquid, involving as J.Phys. Chern. Ref. Data, Vol. 7, No.3, 1978 956 H. M. RODER TABLE 4. Molar volumes and densities of solid oxygen

Density Temperature K Solid type Molar volume cm3/mol est. error mol/cmil g/cmil ..

4. 2 Alpha 20.75 ±0.22 .04819 1. 542 18.75 20.75 ±0.22 .04819 1.542 20. 20.75 .04819 1.542 22. 20.78 .04812 1. 540 23.880 20.82 ±0.22 .04803 1.537

23. 880 Beta 20.95 ±0.11 .04773 1.527 24. 20.95 .04773 1.527 26. 21.02 .04757 1. 522 28. 21.08 .04744 1.518 30. 21.16 .04726 i.512 32. 21;24 .04708 1. 507 34. 21.33 .04688 1. 500 36. 21. 42 .04669 1.494 38. 21.52 .04647 1.487 40. 21.63 .04623 1.479 42. 21.75 .04598 1.471 43.801 21.87 ±0.08 .04572 1. 463

43.801 Gamma 23.05 ±0.06 .04338 1. 388 44. 23. 06 .04337 1. 388 46. 23.18. .04314 1. 380 48. 23.30 .04292 1. 373 50. 23.43 .04268 1.366 52. 23.55 .04246 1.359 54. 23.67 .04225 1. 352 54.361 . 23.69 ±0.05 .04221 1. 351

54. 361 ;Liquid 24. 493 ± O. 02 .04083 1. 307

B Molecular weight 31.0088 s/moL

they do the a-solid. Both are deserving of further [6] Roder, H. M., The Thermodynamic Properties of Slush careful research. Hydrogen and Oxygen, Nat. Bur. Stand. (U.S.), Internal Rept. No. 77-81)9 (Nov. 1977). [71 Mu1lins, J. C., Ziegler, W. T., and Kirk, B. S., Advances 8. Acknowledgments in Cryogenic Eng. 8, 126 (1962); see also Mu1lins, J. C., Ziegler, W. T., and Kirk, B. S., Georgia Inst. of Techno!. We are very grateful to R. L. Milla of the Loa Tech. Rept. No.2 (Mar. 1962) Contra No .. CBT-7339, Alamos Laboratories both for his interest in this work Proj . No. A-593. and for supplying his results of measurements on [8] Jahnke, J. A., J. Chem. Phys. 47, No.1, 336-7 (1967). ~oli(l oxygp.n. Financial gupport was provided by the [9] Barrett, C. S., Meyer, L., and Wasserman, J., Phys. Rev. 163; No.3, 851-4 (1967). . National Aeronautics and Space Administration [10] Schuch, A., and Mills, R. L., unpublished (1970). Values (Johnson Space Center) with, W. Scott as program near zero pressure and at about 4 kbars for normal monitor. isotopic mixture of O2 and pure 1°02• ll1j MillS, J:t. L., private communication (1977). References [12] Barrett, C. S., Meyer, L., and Wasserman, J., J. Chern. Phys. 47, No.2, 592-7 (1967). [1] International Practical Temperature Scale of 1968, [13] Horl, E. M., Acta Cryst.15, No.9, 845-50 (1962). Metrologia 5, 35 (1969). [14] Alikhanov, R. A., JETP Letters 5, No. 12, 349-52 (1967), [21 The International Practical Temperature Scale. of 1968 Trans!. of Zh. Eksperim. I Teor. Fiz., Pisma V Redakisiyu Amended Edition of 1975, Metrologia 12, 7-17 (1976). 5, No. 12, 430-4 (1967). [3] Roder, H. M., submitted to J. Chern. Phys. [151 Curzon, A. E., and Pawlowicz, A. T., Proc. Phys. Soc. [4] Wagman, D. D., Evans, W. H., Parker, V. B., Halow, I., (London) 85, No. 544, 375-81 (1965). Baily, S. M., and Schumm, R. H., Nat. Bur. Stand. [16] Jordan, T. H., Streib, W.E., Smith, H. W., and Lipscomb, (U.S.), Technical Note 270-3 (Jan. 1968) and also W. H., ACTA Cryst. 17, No.6, 777-78 (1964). Stull, D. R. and Prophet, H., Nat. Bur. Stand. -(U.S.), [17] Roge, H. J., J. Res. Nat. Bur. Stand. (U.S.) 44, 321-45 NSRDS-NBS 37, JANAF Thermochemical Tables, (1950), RP 2081. 2nd Ed. (June 1971). [18] Orlova, M. P., Temperature, Its Measurement and Con [5] CODATA Recommended Key Values for Thermo trol in Science a:nd Industry, Vol 3, Pt. 1, Reinhold dynamics 1975. CODATA Bulletin 17 (Jan. 1976). Publishing Corp., N.Y. (1962), pp. 179-83.

J. Phys. (hem. Ref. Data, Vol. 7, No.3, 1978 THE MOLAR VOLUME OF SOLID OXYGEN 957 [19] Muijlwijk, R., Moussa, M. R., and Van Dijk, H., Physica [43] Mills, R. L., and Grilly, E. R., Phys. Rev. 99, No.2, 480-6 32, 805 (1966). (1955). [20J Muijlwijk, R., Durieux, M., and Van Dijk, H., Physica [44] Keesom, W. H., and Taconis, K. W., Physica 3,141 (1936). 43, No.3, 475-80 (1969). [45] Mauer, F. A., P!ivate communication. [211 Weber, L. A., J. Res. Nat. Bur. Stand. (U.S.) 74A, No; 1, [46] Tolk~chev, A. M., and Manzhelii, V. G., Soviet Phys. 93-129 (Jan.-Feb. 1970). SolId Sta~e 7, No.7, 1711-3 (1966), Transl. Fiz. Tverd. [22] Kemp, W. R. G., and Pickup, C. P., Temperature, Its 'l'elll. 7, No.7, 2125-8 (1965). Measurement and Control in Science and Industry, [471 Manzhelii, V. G., Tolkachev, A. M., and Voitovich, E. I., . Vol 4, Pt. I, Proe. Fifth Symp. on Temperature, Wash Phys. Status Solidi 13, No.2, 351-8 (1966). . ington, D.C., June 21-24, 1971. Instrument Society of [48] Cox, D. E., Samuelson, E. J., and Beckurts, K. H., Phys. America, Pittsburgh, Pa., (1072), pp. 217-24 Rev. 07, No.7, 3102-11 (1973). [23]'Cowan, J. A., Kemp, R. C., and Kemp, W. R. G., Metro [49] Stevenson, R., J. Chern. Phys. 27, No.3, 673-5 (1957). logia 12, 87 (1976). [50] Stewart, J. W., Phys. Chern. Solids 12, 122-29 (1959). [24] Kemp, R. C., Kemp, W. R. G., and Cowan, J. A., Metro- [51]· Horl, E. M., Acta Crystallog. B25, 2515-8 (1969). In this logia 12,93 (1976). . paper thin films are shown to have structures a' and [25] Compton, J. P., and Ward, S. D., Metrologia 12, 101 fJ' different from a and fJ but not otherwise defined. The (1976). present presumption i.:; that the structure of the substrate [261 Orlova, M. P.,Zh. Fiz. Khim. 40, No. 12, 2986-92 (1966). may influence or determine the structure of the [27] Bedford, R. E., Durieux, M., Muijlwijk, R~, and Barber, solidified gas deposited from a vapor phase. C. R., Metrologia 5, No.2, 47-49 (1969). . [52] Collins, M. F., Proc. Phys. Soc. (London) 89, No. 564, [28] Prydz, R., Metrologia 8, No.1, 1-4 (1972). 415-8 (1966). [291 Manzhelli, V. G., and Krupskii, 1. N., Sb. Naueh. Tr. [53] Euckin, A., Verhandl. Deut. Physik. Ges. 18, No.1, 4-17 Fiz.-Tekh. Inst. Nizk. Tomp. Akad. Nauk UKR. SSR (1016). No.2 (1968). [54] Borovik-Romanov, A. S., Orlova, M. P., and Strelkov, [30] Ancsin, J., Temperature, Its Measurement and Control in . P. G., Acad. Nauk. S.S.S.R. Doklady99, 699-702 (1954). Science and Industry, Vol 4, Pt. 1, Proc. Fifth Symp. on [55] Dundon, J. M., Phys. Lett. 61A, 58-60 (1977). . TemperaturQ, Washington, D.C., June 21-24, lQ71. [56] Dewar, J., Proc .. Roy. Soo. (London) A73, 251 61 (1904). Instrument Society of America, Pittsburgh, Pa. (1972), [57J Rosenfeld, A. H., and Stevens, P. R., CODATA, Biennial pp.211-6. International Conf., Proc. 5th (Boulder, Colorado, [31] Ancsin, J., Can. J. Phys. 52, No. 23, 2305-12 (1974). June 28-July 1, 1976), B. Dreyfus, Editor, Pergamon [32] Weber, L. A., J. Chem. Thermodyn. 2, No.6, 839-46 Press, New York (1977) pp. 19-23.. (1970). [58] McLennan, J. C., and Wilhelm, J. 0., Phil. Mag. 3, 383 [33] Goodwin, R. D., and Prydz, R., J. Res. Nat. Bur. Stand. 0927). (U.S.) 76A~ No.2, 81 (1972). [591 Mooy, H. H., Leiden Comm. 20, No. 223 (1932). [34] Straty, G. C., and Tsumura, R., J. Res. Nat. Bur. Stand. [601 Ruhemann, M., Z. Physik 76, 368 (1932). (U.S.) 80A, No.1, 35-39 (Jan-Feb. 1976). [61J Vegard, L., Nature 136, 720 (Nov 1935). [35] Haynes, W. M., Hiza, M. J., and Frederick, N. V., Rev. [62] Vegard, L., Z. Physik. 98, 1 (1935). Sci. Instrum. 47, No. 10, 1237-50 (1976). [63] Roder, H. M., Cryogenics 2,302 (1962). [36J Ha:Yllos, W. M., Rov. Soi. Inotrum. 48, No.1, 3011 (11)77). [64] Lonodalc, K., ct al., Ed., International TablelS fOl' X-Ray [37] Haynes, W. M., and Hiza, M. J., J. Chem. Thermodyn: 9, Crystallography, Kynoch Press, Birmingham, England 179-187 (1977). (1962). [38] Clusius, K., Z. Physik. Chern. (Leipzig) B3,41-79 (1929). [65] Weast, R. C., Ed., Handbook of Chemistry and Physics, [30] Qiauque,· W. F., and Johnato~, H. L., J. Am. Chem. Soc. 56th Ed., Chemical Rubber Oompany Prel5l5 (1975-70), 51, 2300-21 (1929). p. B-120. (40] Fagerstroem, C. H., and Hollis Hallett, A. C., J. Low [66] Forsythe, W. E., Ed., Smithsonian Physical Tables, 9th Temp. Phys. 1, No.1, 3-12 (1969). Ed., Smithsonian Institution (1956), p. 291. [41] Anesin, J., Temperature Measurement 1975, Conference [67] Donnay, J. D. H., and Ondik, H. M., Editors, Crystal Series Number 26, The Institute of Phy::lics (London and Data, Determinative Tables, 3rd Eel. Vol. 2, Inorganic Bristol), B. F. Billing and T. J. Quinn, editors, pp. 57-64. Compounds, U. S. Dept. of Commerce, National Bureau {42] Lisman, J. H. C., and Keesom, W. H., Physica 2, 901~6 of Standards and the J oint Committee on Powder (1935). Diffraction Standards, USA (1973).

J. Phys. Chern. Ref. Data, Vol. 7; No. 3,1978