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THERMODYNAMIC and TRANSPORT PROPERTIES of URANIUM DIOXIDE and RELATED PHASES the Following States Are Members of the International Atomic Energy Agency

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THERMODYNAMIC and TRANSPORT PROPERTIES of URANIUM DIOXIDE and RELATED PHASES the Following States Are Members of the International Atomic Energy Agency TECHNICAL REPORTS SERIES No. 39 Thermodynamic and Transport Properties i of Uranium Dioxide i • ¡i and Related Phases INTERNATIONAL ATOMIC ENERGY AGENCY,VIENNA, 1965 THERMODYNAMIC AND TRANSPORT PROPERTIES OF URANIUM DIOXIDE AND RELATED PHASES The following States are Members of the International Atomic Energy Agency: AFGHANISTAN ITALY ALBANIA IVORY COAST ALGERIA JAPAN ARGENTINA REPUBLIC OF KOREA AUSTRALIA LEBANON AUSTRIA LIBERIA BELGIUM LIBYA BOLIVIA LUXEMBOURG BRAZIL MALI BULGARIA MEXICO BURMA MONACO BYELORUSSIAN SOVIET SOCIALIST MOROCCO REPUBLIC NETHERLANDS CAMBODIA NEW ZEALAND CAMEROUN NICARAGUA CANADA NIGERIA CEYLON NORWAY CHILE PAKISTAN CHINA PARAGUAY COLOMBIA PERU CONGO (LÊOPOLDVILLE) PHILIPPINES CUBA POLAND CZECHOSLOVAK SOCIALIST REPUBLIC PORTUGAL DENMARK ROMANIA DOMINICAN REPUBLIC SAUDI ARABIA ECUADOR SENEGAL EL SALVADOR SOUTH AFRICA ETHIOPIA SPAIN FINLAND SUDAN FRANCE SWEDEN FEDERAL REPUBLIC OF GERMANY SWITZERLAND GABON SYRIA GHANA THAILAND GREECE. TUNISIA GUATEMALA TURKEY HAITI UKRAINIAN SOVIET SOCIALIST REPUBLIC HOLY SEE UNION OF SOVIET SOCIALIST REPUBLICS HONDURAS UNITED ARAB REPUBLIC HUNGARY UNITED KINGDOM OF GREAT BRITAIN ICELAND AND NORTHERN IRELAND INDIA UNITED STATES OF AMERICA INDONESIA URUGUAY IRAN VENEZUELA IRAQ VIET-NAM ISRAEL YUGOSLAVIA The Agency's Statute was approved on 23 October 1956 by the Conference on the Statute of the IAEA held at United Nations Headquarters, New York; it entered into force on 29 July 1957. The Headquarters of the Agency are situated in Vienna. Its principal objective is "to accelerate and enlarge the contribution of atomic energy to peace, health and prosperity throughout the world". © IAEA. 1965 Permission to reproduce or translate the information contained in this publication may be obtained by writing to the International Atomic Energy Agency, Kärntner Ring 11, Vienna I, Austria. Printed by the IAEA in Austria January 1965 TECHNICAL REPORTS SERIES No. 39 THERMODYNAMIC AND TRANSPORT PROPERTIES OF URANIUM DIOXIDE AND RELATED PHASES REPORT OF THE PANEL ON THERMODYNAMIC AND TRANSPORT PROPERTIES OF URANIUM DIOXIDE AND RELATED PHASES HELD IN VIENNA 16 -20 March 1964 INTERNATIONAL ATOMIC ENERGY AGENCY VIENNA,. 1965 International Atomic Energy Agency. Thermodynamic and transport properties of uranium dioxide and related phases. Report of the Panel on Thermodynamic .. ., held in Vienna, 16- 20 March 1964. Vienna, the Agency, 1965. 105 p. (IAEA, Technical reports series no. 39) 541.11 546. 791. 4-31 621. 039. 543.4 THERMODYNAMIC AND TRANSPORT PROPERTIES OF URANIUM DIOXIDE AND RELATED PHASES, IAEA, VIENNA, 1965 STl/DOC/10/39 FOREWORD Because of the growing importance of thermodynamics to nuclear tech- nology, the International Atomic Energy Agency has initiated a project to assist in assessing and disseminating data on important nuclear materials. As a beginning, it organized a Symposium on the Thermodynamics of Nuclear Materials which was held in Vienna in May 1962. This was followed by a Panel on the Thermodynamic Properties of the Uranium-Carbon and Plutonium-Carbon Systems, held in Vienna in October 1962. The present Report is the result of a further Panel in this series, convened from 16 - 20 March 1964 to assess the thermodynamic and transport properties of the uranium dioxide phase and related uranium oxide phases. This Panel made a critical evaluation of the available data, bearing in mind the practical aspects of the use of uranium dioxide as a nuclear fuel. The findings of the Panel are presented by the Agency in this issue of the Technical Re- ports Series in the belief that they will prove to be of value for nuclear technology. The Report was compiled and edited by Dr. Charles Holley of the Division of Research and Laboratories. CONTENTS I. INTRODUCTION 1 II. STRUCTURAL WORK 3 1. Stable phases in the U-O system 3 2. UO2 (room temperature) .' 3 2.1. Lattice parameter. Density. 3 2.2. Atomic positions. Temperature factors 3 3. UO2 (high temperature) 5 3.1. Variation of lattice parameter with temperature 5 3.2. Temperature factors. Characteristic temperatures. Breakdown of harmonic approximation 6 4. U02 + x region 7 4.1. Variation of lattice parameter and density with composition 7 4.2. Crystal structure 9 4. 2.1. Atomic positions in statistical cell. Occupation numbers. Temperature factors .... 9 4. 2. 2. Interpretation of results for statistical cell .... 12 5. U409 5.1. Variation of lattice parameter with composition and temperature 15 5.2. Structure 15 5.2.1. X-ray studies 15 5.2.2. Neutron studies 17 6. Tetragonal phases 19 7. Conclusions 20 III. THERMODYNAMICS ... 23 1. Heat capacity measurements 23 1.1. Low temperature heat capacity data 23 1.2. High temperature heat capacity data 24 2. Lattice Dynamics of UO2 , 25 3. Free energy, enthalpy, and entropy measurements 29 3.1. Chemical thermodynamics of the UO2. oo - 2.25 region... 29 3.2. The phase diagram, U02 to U4O9 38 3.3. Hypostoichiometric U02 39 4. Vaporization processes 40 5. Theoretical treatment of U02 + x phase 42 5.1. Statistical thermodynamics of interstitials and vacancies • 42 5.2. Application of defect theory to UO2+ x 44 IV. SURFACE AND OXIDATION PROPERTIES 51 1. Adsorption properties 51 2. Oxidation processes 52 2.1. Low temperatures 52 2.2. High temperatures 53 V. PHYSICAL PROPERTIES 55 1. Thermal conductivity 55 1.1. Low temperature thermal conductivity 55 1.2. High temperature thermal conductivity 55 1.2.1. Lattice conductivity 57 1.2.2. Radiant transfer 58 1.2.3. Electronic transfer 59 2. Electrical properties 60 2.1. Normal electrical properties 60 2. 2. Effect of irradiation on electrical properties 67 3. Optical measurements 69 3.1. Intrinsic absorption edge 69 3.2. Defect absorption 70 3.3. Infra-red absorption 72 4. Magnetic measurements 73 5. Diffusion processes in UO^ 75 5.1. Oxygen diffusion 75 5.2. Uranium self-diffusion 76 5.3. Argon diffusion in calcium fluoride as a model process for fission gas transport in uranium dioxide .. 76 5.4. Fission gas release 78 6. Correlative theory of physical properties 81 6.1. Transport of energy 81 6. 2. Transport of matter 83 VI. PRACTICAL IMPLICATIONS OF THERMODYNAMIC AND TRANSPORT PROPERTIES 85 » 1. Interaction of fuel and can 85 1.1. Thermal cracking 85 1.2. Dimensional changes in UO2 under irradiation 86 2. Thermal conductivity 88 3. Phase equilibria ' 88 4. Material transport processes 89 VII. CONCLUSIONS 93 Appendix: Mathematical treatment of defect absorption 95 References 99 List of participants 103 Reports submitted to the Panel 105 I. INTRODUCTION The high melting point of uranium dioxide and its stability under ir- radiation have led to its use as a fuel in a variety of types of nuclear reac- tors. A wide range of chemical and physical studies has been stimulated by this circumstance and by the complex nature of the uranium dioxide phase itself. The boundaries of this phase widen as the temperature is increased; at 2000°K a single, homogeneous phase exists from U2.27 to a hypostoichio- metric (UO2-X) composition, depending on the oxygen potential of the sur- roundings. Since there is often an incentive to operate a reactor at the maxi- mum practicable heat rating and, therefore, maximum thermal gradient in the fuel, the determination of the physical properties of the U02±xphase becomes a matter of great technological importance. In addition a complex sequence of U-O phases may be formed during the preparation of powder feed material or during the sintering process; these affect the microstruc- ture and properties of the final product and have also received much attention. Uranium dioxide, therefore, provides an important example of a com- pound that exists as a single non-stoichiometric phase at high temperatures and becomes unstable as the temperature is reduced, disproportionating into phases of nearly ideal stoichiometry involving more or less complex ordered structures. Ideally, the thermodynamic stability and physical pro- perties of U02±x should be related to the same atomic and electronic model, and its study should provide an opportunity for the correlation of a number of different properties. The International Atomic Energy Agency (IAEA) therefore called a panel meeting to discuss the thermodynamic and transport properties of the non- stoichiometric uranium dioxide phase, and this Report presents a summary of the data placed before the Panel and of the conclusions reached. A con- siderable amount of data on the main features of the phase diagram and on the composition limits of the various phases exists and X-ray and neutron diffraction evidence indicate some possible structural models. Chemical thermodynamic values are known with some precision for most of the region concerned. Specific discussions were held on (i) the interrelation of vi- brational constants deduced from structural work and heat capacity data; (ii) the correlation of thermal conductivity with electrical conductivity and optical data; and (iii) the calculation of entropy values by the statistical treat- ment of simple models that are consistent with the structural, optical, and electrical properties. The outline of a generalized theory that should allow better correlation of transport and thermodynamic properties in the future was presented. The importance of making all measurements of physical properties on samples of accurately known composition, which are struc- turally well-characterized, was emphasized. 1 II. STRUCTURAL WORK 1. STABLE PHASES IN THE U-O SYSTEM There are as many as 16 well-characterized uranium oxide phases, and the existence of a dozen more has been claimed. A survey of work on the uranium-oxygen phase diagram up to 1961 has been made by ROBERTS [1]. Figure 1 is a reproduction of his phase diagram. The work described in Fig. 1 Portion of U - О phase diagram. Circles denote X-Ray results. (Reproduced by courtesy of L.E.J. Roberts [1]) this chapter is restricted to U02, U02 + x, U4O9 and the tetragonal phases with compositions in the rangfe U02 3 to U02 4 .
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