Cook, V.

Cork, B.

Hoang, T.F.

Keefe, D.

Kerth, L.T.

Wenzel, W.A.

Zipf, T.F.

eScholarship - University of California

Lawrence Berkeley National LaboratoryRecent WorkTitleTHE K- PROTON AND NEUTRON INTERACTION FROM 0.6 Bev TO 3.5 BevPermalinkhttps://escholarship.org/uc/item/4bc3v0m6AuthorsCook, V.Cork, B.Hoang, T.F.et al.Publication Date1960-08-01eScholarship.org Powered by the California Digital LibraryUniversity of California~ . ' ' . J UNIVERSITY OF CALIFORNIA [rnf8t0£awrence UCRL 8736 C<j:L FREE ENERGY FUNCTIONS FOR SOME M02 OXIDES .. I BERKELEY. CALIFORNIA DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California. 0 ·. . " .. UNIVERSITY OF CALIFORNIA Lawrence Radiation Laboratory Berkeley, California Contract No. W-7405-eng-48 ...... UCRL-.8736 Chemistry Distribut,ion FREE ENERGY F~CTIONS FOR SOME M02 OXIDES M. s. Chandrasekharaiah and L. Brewer April 1959 Printed for the u.s. Atomic Energy Commission Printed 1n USA. Price 50 cents. Available from the Offi~e of Technical Services. U .. S .. Department of Commerc'e Washington 2 5, D._ C. ,-' I "'' .y -2-FREE ENERGY FUNCTIONS FOR SOME M02 OXIDES M. s. Chandrasekharaiah and L. Brewer Lawrence Radiation Laboratory and College of Chemistry University of California, Berkeley 4, California April 1959 ABSTRACT UCRL-8736 The free energy functions for nine transition metal dioxides have been est.imated by considering them as linear symmetrical molepules. . l, 2 th f t . d t Unlike the diatomic oxide case, ere are very ew spec roscop~c a a available for the gaseous triatomic oxides of metals. Hence in calculating the thermodynamic functions for these dioxides, almost all of the necessary molecular constants have to be estimated. In the first instance, the free energy functions (fef) for nine transition metal oxides are calculated on the l basis of Ia linear symmetrical mole.cular approximation. (1) Electronic Free Energy Functions ) . . Since the experimentally observed electronic states for any of these molecules are not known, an ion:i,c model similar to one assumed in the calculating of fef for monoxides, 3 is assumed. Thus, the molecular ele;tronic states are equated to the energy l~vels of M+4 ions as given by Moore. 4 Employing these energy levels of ions, the electronic free ene~gy functions were calculated. +4 However, no M ion energy levels for Hf, Ta or W are available and the electronic free energy functions for them have bee:t;l obtained by extrapola:tfi;ng the values of other molecules in the corresponding periodic groups •. (2) Rotational and Vibrational Free Energy Functions In c~mputing the rotational contribution to the fef, the interatomic distances of oxygen atom to central metal atom were approximated to the inter-nuclear distance of the corresponding monoxides. This ·approximation implies that the bond o~der ~n the two ctass~s of oxides are ~he s~e which may not -3- UCRL-8736 strictly be true. But the difference in the bond orders in these two classes introduces fairly-small-changes-in...:the-r-values .-However-,-this-approximation-e . of assuming the same bond distances in both dioXides and monoXides introduces a small correction in fef which is much smaller thar{ the other uncertainties in calculating fef. Moreover, our knowledge of internuclear distances in the monoxides is not accurate to warrant any corrections. Walsh5 has concluded that triatomic molecules with a total of 18 valence electrons would be bent as is observed for dioxides of the sulfur family. However, we have assumed that this would not be true with some of the electrons in d orbitals. One of the biggest uncertainties introduced in calculating the fef for M02 oxides is in estimating the bending frequencies of vibration. These frequencies are generally small and are doubly degenerate. Hence the contribution of bending vibrational mode of.molecule to fef is considerable and any estimation of this frequency introduces a large uncertainty. In our calculation, we have assumed that the stretching force constants of dioxides are the same as the force constants of the corresponding monb.xides. . . . Bending force constants are thus calculated assuming a constant rat.io for the bending force constant to stretching force constant and this ratio VIas considered the same for all molecules as for co2 • Thus all the three fundamental frequencies of vibrations were evaluated using valence force method. The total free energy functions and the estimated frequencies of vibration for gaseous Ti02 , vo2 , Cro2, Zr02 , Nb02, Mo02 , Hf02, Ta02 and W02 ~re given .in Tab:Le 1. .. \ \/' -4- UCRL-8736 Table 1 s Fo - H o Vibrational frequencies and - ( T 0 ) for M02 molecules ,. l -1 -1 -1 298 1000 1500 2000 2500 3000 ru1 em ru2cm ru3cm Ti02 873 292 1125 60.5 65·5 69·3 72o3 74·9 \!'02 882 291 1125 64.2 69.4 73·0 76.4 79·0 Cr02 785 259 996 66.0 71.4 75·4 78.6 81.2 Zr02 863 260 1000 62.4 67.5 71.2 74.3' 76.8 Nb02 870 262 1009 65.3 70.6 74·5 77·8 8o.4 Mo02 776 232 895 66.8 72·3 76.4 79·7 82.4 HfO * 2 860 244 935 64.3 69.4 73o2 76.2 78.8 TaO*· 2 864 244 935 67.4 72o5 76.3 79·4 81.9 wo * 2 675 216 835 62.7 74.0 78.0 80.9 83.4 *electrdnic contributions are extrapolated values from values of other members of the same group. -5- UCRL-8736 REFERENCES G• Herzberg, Spectra of diatomic m9~ectil~s, Van Nostrand, New York, 1950. 2. / . . ; B. Rosen, Donnees Spectroscopiques Con.cernant Les Molecules Diatomiques (Hermann and Cie, Paris, 1951). 3.. L. Brewer and M. S •· Chandrasekharaiah, Free energy functions . for gaseous moriox.ides, University of California Radiation Laboratory Report UCRL-8713, April,-1959• 4. c. Moore, Atomic Energy Levels, National Bureau of Standards Circular 467, Vols I, II, and III. 1949-58. 5. A. D;• Walsh, J. Chem. Soc. 1953, 2266 • This report was prepared as an account of Government sponsored work. Neither the United States, nor the Com-m1ss1on, nor any person acting on behalf of·the Commission: A. Makes any warranty or representation, expressed or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information, appa-ratus, method, or process disclosed in this report may not infringe privately owned rights; or B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any infor-mation, apparatus, method, or process disclosed in this report. As used in the above, "person acting on behalf of the Commission" includes ~ny employee or contractor of the Com-mission, or employee of such contractor, to the extent that such employee or contractor of the Commission, or employee of such contractor prepares, disseminates, or provides access to, any information pursuant to his employment or contract with the Commission, or his employment with such contractor. 

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THE K- PROTON AND NEUTRON INTERACTION FROM 0.6 Bev TO 3.5 Bev

THE K- PROTON AND NEUTRON INTERACTION FROM 0.6 Bev TO 3.5 Bev

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