The specific heats below 820°K of potassium, rubidium and caesium By J. D. Filby* and D ouglas L. Martin Division of Pure Physics, National Research Council, Ottawa, Canada ( Communicated by M. Blackman, F.R.S.—Received 28 May 1964) The specific heat of potassium has been measured in the range 0*4 to 26 °K and the specific heats of rubidium and caesium in the range 0*4 to 320 °K. Previously reported specific heat anomalies in the range 100 to 300 °K were not confirmed. The and y values were estimated as 90*6tj!3 °K and 497 + 20/i,cal degK"2 gatom-1 for potassium, as 55-6 + 0-5 °K and 576^ jacal degK-2 gatom-1 for rubidium and as 38*4 + 0*6 °K and 764 + 250/u,cal degK-2 gatom-1 for caesium. A slow release of energy (~ l/xcal s_1 gatom-1), dependent on thermal history, was observed from rubidium and caesium in the region of 4 °K and may correspond to the annealing out of defects introduced by plastic strain on cooling. Positive anharmonic con tributions to the specific heat are evident at high temperatures and an additional contribution to the specific heat, of the form (e~EIRT/T2), becomes apparent from about 50 °K below the melting point and may be identified with the thermal generation of lattice vacancies. The melting point of pure rubidium is estimated as 312*65 + 0*01 °K and the latent heat of fusion as 524*3 + 1*0 cal/gatom. For caesium the melting point is 301*55 + 0*01 °K and, with some assumptions, the latent heat is 498*9 ±0*5 cal/gatom. For both metals the specific heat of the liquid decreases with increasing temperature.
84 J. D. Filby and Douglas L. Martin E xperimental The measurements were made in three different apparatuses. For the temperature range 0-4 to 1-5 °K a helium-3 cryostat was used, the apparatus and techniques having been described by Martin (1961a), the only differences being that the 1962 He-3 temperature scale (Sherman, Sydoriak & Roberts 1962) was used and that the sample was cast into a simple copper calorimeter of the type shown in figure 1 (a).
Specific heats below 320 °K of potassium, rubidium and caesium, 85 The wire through the sample serves to improve thermal contact, no exchange gas having been used inside the calorimeter. (All the calorimeters were made from ca. 0-004 in. thick copper (usually sheet) and assembled with alkali metal resistant hard solder of composition 28-5 wt. % Cu, 71-5 wt. % Ag.) (d) 20 - 320 °K ALKALI METAL CALORIMETER PLATINIUM FILLING THERMOMETER TUBE ' THERMAL ANCHORING OF LEADS •THERMOCOUPLE '"’2-* HEATER Figure 1. (a) 0-4 to 1-5 °K calorimeter vessel. ( ) 3 to 26 °K calorimeter vessel, (c) 20 to 320 °K calorimeter vessel with copper thermometer-heater, (d) 20 to 320 °K calorimeter vessel with capsule type platinum thermometer.
86 J. D. Filby and Douglas L. Martin The alkali metals were all of nominal purity 99-9+ % and were obtained from either Light (Colnbrook, England) or MacKay (New York, U.S.A.). A survey by one of the authors (J. D. F.) showed that no great improvement in purity could be expected from a single distillation and it was therefore decided to use the metals as supplied, but taking great care that no contamination occurred during their transfer to the calorimeter vessels. To this end the stainless-steel apparatus illustrated in figure 2 was constructed. The apparatus was evacuated to a high y *— GLASS PLATE VICE VACUUM SEAL VACUUM LINE AND N CENTRE OF ROTATION OIL BATH CALORIMETER O OVERFLOW TUBE—I WIRE SCREEN TEST SAMPLE TUBES (2) SLUDGE RETAINING LIPS MEASURING POT Figure 2. Apparatus for filling calorimeters with a measured quantity of alkali metal under high vacuum conditions.
Specific heats below 320 °K of potassium, rubidium and caesv $5 00 weight°f sample*(g) 5-11 ±0-01 + 3-220-01 14-86 ±0-01 9-66 ±0-01 ±20-660-01 15-82 ±0-01 13-52 ±0-01 27-36 ±0-01 ^ 1 0 -00 — — — Ag — Mg — Mg 0 < 5 - 0 -------------005-0-000 — — — MgBa MgAg AgSi Mg SiAgCa mpurity.
88 J. D. Filby and Douglas L. Martin Some idea of the purity of the metal in each calorimeter can be obtained from residual resistance measurements on the ‘ test5 tubes filled at the same time as the calorimeter. These are shown in table 1, together with spectrographic analysis results and estimates of purity obtained from melting studies (see later). The residual resistivity ratios are of the same order as those obtained in this laboratory by double distillation (Okumura & Templeton 1962, 1963).
Specific heats below 320 °K of potassium, rubidium and 89 Klucher (1962) and Smith (1963). These are in fair agreement with Mott & Jones’s values. Recent work on thermal expansion has been confined to X-ray data and has been reported by Pearson (1958). The results are not very concordant, possibly because the samples are often east in glass tubes and strained in cooling. The macro scopic data tabulated by Mott & Jones has therefore been considered more reliable. The data used in computing Cv are given in table 2. Owing to the uncertainty of this data it is probable that the derived Cv values are not as accurate as the Cp values. It should be noted that the tabulated Cv values refer to the volume at the tempera ture of measurement. This point has been discussed elsewhere (Martin 1964 a).
90 J. D. Filby and Douglas L. Martin that the abnormality arose from thermal contact problems accentuated by the steady heat leak through the superconducting heat switch. It appears improbable that the present results are affected in this way since thermal equilibrium within the calorimeters was very good and no ‘ overheating ’ was observed in the heating periods.
Specific heats below 320 °K of potassi ,rubidium and caesium 91 cubic in temperature. Possible extreme values of y and 6% were obtained graphically on the assumption that the lattice specific heat was represented by a term cubic in temperature at temperatures below -^6% °K. This assumption is correct within 1 % or so for many metals and appears to be satisfactory for sodium (Filby & Martin 1963). The possible extremes for caesium are very wide and the further, somewhat arbitrary, assumption has been made that the y value is between one and two times the Sommerfeld free electron value. This assumption is supported by the electronic band calculations of Ham (1962). Owing to the relatively enormous lattice specific 0002 S 0-0015 £5 0001 00005 (temperature, °K)2 Figube 3. Plot of (specific heat/temperature) against (temperature)2 for potassium. The line corresponds to Q\ = 90-6 °K and y = 497 /ical degK”2 gatom-1.
92 J. D. Filby and Douglas L. Martin (The correction to constant volume is negligibly small at this temperature.) The results above 0-65 °K have been used in a least squares analysis to obtain the follow ing values: 0% = 90-3 ± 0*7 °K, y = 491 + 18/maldegK~2gatom-1, where the error limits are 95 % confidence limits, all errors being assumed to be random. The values given in table 4 have been obtained graphically and are in reason able agreement with the least-squares results. It will be noted, as discussed above, that Table 3. Smoothed VALUES ATO O 1-5 °K potassium rubidium caesium ______________ A _________ A A T (°K) ' o, de o9 0C ' c9 dc 0-4 (0-00026!) (78-4) (0-000442) (52-0) (0-00090) (36-8) 0-5 (0-000345) (84-4) (0-000648) (54-4) (0-00155) (36-8) 0-6 (0-00045o) (87-1) (0-00096) (54-7) (0-00233) (37-7) 88-8 0-7 0-00057s 0-00135 55-1 0-00335 38-4 0-8 0-000725 89-9 0-00186 55-5 0-00475 38-6 0-9 0-000904 90-5 0-00248 55-6 0-00665 38-4 1-0 0-00111 91-2 0-00328 55-6 0-00905 38-3 1-1 0-0121 0-00136 91-3 0-00427 55-4 38-0 1-2 0-00166 90-9 0-0054* 55-3 0-0159 37-7 0-00202 1-3 90-5 0-00690 55-0 0-0205 37-4 1-4 0-00240 90-9 0-00872 54-4 0-0261 37-1 0-0112 1-5 0-00293 89-5 53-3 0-0331 36-6 Units: C(vcaldegK-1 gatom-1); 6 (°K). J = 4-186. Atomic weights: K, 39-096; Rb, 85-48; Cs, 132-91.