Thermodynamic Properties of Manganese and Molybdenum Cite as: Journal of Physical and Chemical Reference Data 16, 91 (1987); https://doi.org/10.1063/1.555794 Submitted: 28 May 1985 . Published Online: 15 October 2009 P. D. Desai ARTICLES YOU MAY BE INTERESTED IN Thermodynamic Properties of Iron and Silicon Journal of Physical and Chemical Reference Data 15, 967 (1986); https:// doi.org/10.1063/1.555761 Dissociation Energies of Diatomic Molecules of the Transition Elements. II. Titanium, Chromium, Manganese, and Cobalt The Journal of Chemical Physics 41, 3806 (1964); https://doi.org/10.1063/1.1725817 Thermal equation of state and thermodynamic properties of molybdenum at high pressures Journal of Applied Physics 113, 093507 (2013); https://doi.org/10.1063/1.4794127 Journal of Physical and Chemical Reference Data 16, 91 (1987); https://doi.org/10.1063/1.555794 16, 91 © 1987 American Institute of Physics for the National Institute of Standards and Technology. Thermodynamic Properties of Manganese and Molybdenum P. D. Desai Center for Information and Numerical Data Analysis and Synthesis, Purdue University, West Lafayette, Indiana 47906 Received May 28, 1985; revised manuscript received Apri115, 1986 This work reviews and discusses the data on the various thermodynamic properties of manganese and molybdenum available through March 1985. These include heat capacity, enthalpy, enthalpy of transitions and melting, vapor pressure, and enthalpy of vaporiza­ tion. The existing data have been critically evaluated and analyzed. The recommended values for the heat capacity, enthalpy, entropy, and Gibbs energy function from 0.5 to 2400 K for manganese and from 0.4 to 5000 K for molybdenum have been generated, as have heat capacity values for supercooled p-Mn and for y-Mn below 298.15 K. The recommended values for vapor pressure cover the temperature range from 298.15 to 2400 K for manganese and from 298.15 to 5000 K for molybdenum. These values are referred to temperatures based on IPTS-1968. The uncertainties in the recommended values of the heat capacity range from ± 3% to ± 5% for manganese and from ± 1.5% to ± 3% for molybdenum. Key words: critical evaluation; data analysis; enthalpy; enthalpy offusion; enthalpy of vaporization; Gibbs energy function; heat capacity; manganese; molybdenum; recommended values; vapor pres­ sure. Contents 1. Introduction.............. ............... ........ ......... ........... 92 List of Tables 2. Thermodynamic Properties of Manganese .......... 92 1. Structures and transition temperatures of man- 2.2. Low-Temperature Heat Capacity................. 92 ganese ....................................................... ~....... 92 a. a-Manganese ...... .......... ..... ......... .... ..... ...... 92 2. Electronic specific heat coefficitmt of manga- b. p-Manganese·............................................. 92 nese ................................................................... 92 c. r-Manganese ............................................. 93 3. Recommended low-temperature heat capacity 2.3. High-Temperature Heat Capacity (Solid) ... 93 of manganese .............. ................. ....... ......... ..... 93 2.4. High-Temperature Heat Capacity (Liquid). 93 4. Recommended high-temperature thermody- 2.5. Ideal Gas. Properties...................................... 93 namic properties of manganese.. ......... ............. 95 2.6. Vapor Pressure Data ............... .... ........ .......... 93 S. Values for enthalpy of sublimation of manga- 2.7. References ..................................................... 97 nese at 298.15 K ............................................... 97 3. Thermodynamic Properties of Molybdenum....... 98 6. Recommended vapor pressure of manganese .. 97 3.1. Phases and Structures.. ................................. 98 7. Melting point of molybdenum ......................... 98 3.2. Low-Temperature Heat Capacity................. 98 8. Electronic specific heat coefficient and Debye 3.3. High-Temperature Heat Capacity (Solid) ... 100 temperature of molybdenum ............ ................ 98 3.4. High-Tempemture He:lt ~:lpacity (T -iqllirl) . 100 9. Recommended low-temperature heat capacity 3.5. Ideal Gas Properties...................................... 101 of molybdenum ................ .............. .................. 98 3.6. Vapor Pressure Data ..................................... 101 10. Room-temperature thermodynamic constants 3.7. References ..................................................... 104 of molybdenum ...... .......................................... 100 4. Acknowledgments................................................ 107 11. Percentage deviation in heat capacity of molyb- denum .............................................................. 100 12. Percentage deviation in enthalpy for molyb- denum .............................................................. 101 @1987bythe U. S. Secretary of Commerce on behalf of the United States. 13. Values for enthalpy of fusion of molybdenum. 104 This copyright is assigned to the American Institute of Physics and the American Chemical Society. 14. Recommended high-temperature thermody- Reprints available from ACS; see Reprints List at back of issue. namic properties of molybdenum .................... 105 0047-2689/87/010091-18/$06.00 91 J. Phys. Chern. Ref. Data, Vol. 16, No.1, 1987 92 P.D.DESAI 15. Values for enthalpy of sublimation of molyb- 2. Heat capacity of manganese ........ ......................... 96 denum at 298.15 K ........................................... 107 3. Low-temperature heat capacity of molybdenum. 99 16. Recommended vapor pressure ofmolybdenum. 108 4. Percent deviation in y values for molybdenum.... 102 List of Figures 5. Percent deviation in C; values for molybdenum. 103 6. Heat capacity of molybdenum ............................. 106 1. Low-temperature capacity of manganese ............ 94 1. Introduction the recommended values are derived, are listed in Table 2. The principal objective of this work was to critically The recommended heat capacity values below 5 K are based evaluate and analyze all the available data and information on the above measurements except that Gaumer's3 values on the heat capacity, enthalpy, and vapor pressure of manga­ tend to be gradually higher above 1 K to 17% higher at 3 K. 2 nese and molybdenum, and to generate the recommended A small nuClear contribution below 1 K proportional to T- values of these and other thermodynamic properties from .is reported in Refs. 3-8. The recommended C; values above 9 below 1 K to the mehing point and above. 5 K are based on the data of Kelley et al. Co values: ofRooth w· ll p The discussion of the thermodynamic properties and et a.I and of Gunther are, respectively, 10% and 6% low- the details of data analysis are reported in Sec. 2 for manga­ er while those of Braun et al. 12 are 3% lower than the recom­ nese and Sec. 3 for molybdenum. The recommended values mended values. C; values of Elson et al. 13 and of Armstrong cover the temperature range from below 1 to 2400 K for and Grayson-Smith 14 are as much as 20% higher than the manganese and to 5000 K for molybdenum. recommended values; possibly their samples contained The details of the data analysis have been discussed small amounts of/3-Mn. A small anomaly leading to a maxi­ elsewhere. 1 The value of the gas constant used in this paper is mum C; at 98 K was ascribed to an antiferromagnetic Neel 1 1 R = 8.31441 J mol- K- • transformation. Integration of the recommended C; values yields .Ir (298.15 K) - yo (0 K) = 4998 ± 10 J mol- 1 tlnd inte­ 2. Thermodynamic Properties 01 gration of C;/T values yields SO (298.15 K) = 32.221 1 1 Manganese ( ± 0.10) J m01- K- • Manganese is a transition metal with atomic weight 54.938. Four crystalline allotropic forms exist (Table 1): a b. f3-Manganese has a complex bcc (A 12) prototype structure, f3 has a com­ plex cubic (A 13) prototype structure, y has an fcc (A 1 ) The recommended C; values are based on the data of 15 16 structure isotypic with Cu, and 8 has a bcc (A2) structure Shinkoda et al. and of Butera and Craig except that the 15 isotypic with W. Transformation between the a and f3 phase data of Shinkoda et al. above 12 K are up to 20% lower. 10 is rather sluggish. f3- Mn can be preserved at low temperature The data of Booth et al. are about 14% lower than the 15 by quenching; 1/-Mn can be preserved at low temperature recommended values. Shinkoda pt 01. observed a gradual upon quenching only by adding very small amounts of cop­ upturn of Cp IT versus T2 at low temperature which they per or nickel. In the absence of new measurements on var­ described as due to spin fluctuations. It is therefore impossi­ ious transition temperatures, the values listed in Table 1 se­ ble to derive electronic specific heat coefficient. lected by Hultgren et al.41 were adopted after converting The recommended C; values yielded Ir (298.15 1 them to IPTS-68. K) - Ir (0 K) = 5194 ± 10 J mol- and SO (298.15 1 1 K) = 34.905 ± 0.20 J mol- K- • 2.2. Low-Temperature Heat Capacity a. a-Manganese Table 2. Blectronic specific heat coefficient of lIIanlanese There have been numerous measun::menls of the elec­ tronic specific heat coefficient y. Some of them, from which -1 -2 Source y. 111'11101 .X: Franzoslnl et a1.2. 13.72 3 Table 1. Structures and transition temperatnres of lIIan,anese Ga'Ulller 12.10 4 Guthrie 12.55 Martin and BeerS 14.13 6 a-Mu. bee (AU) 980 ± 20 T _ Stetsenk0 15.98 a p 7 Il-M.. o (A13) 1360 .t 10 Tp-y Guthrie et a1. 12.80 8 12.01 y-Mn fcc (Al)