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Neutron Diffraction Gives Pu Melting-Point Information

The melting point of plutonium is unusually low, given its position in the periodic system. A criterion for the melting points of materials, devised by F. A. Lindemann in 1910, relates the melting point of a material to its vibrational amplitude at the melting point. In this article, we explain how Lindemann's rule can be used with neutron diffraction data on the light actinides to understand why the melting point of plutonium is so low. We find that the temperature dependence of the elastic properties of plutonium must be taken into account in order to give a good description of its high-temperature behavior.

Figure 1. Composite phase diagram for the light actinides. (Used with permission, J. L. Smith and E. A. Kmetko, "Magnetism and bonding: a nearly periodic table of transition elements," J. Less-Common Metals 90 83-88, Elsevier Science, Oxford, UK, 1983.)

Figure 1 is a composite phase diagram of the light actinides. It shows that the unusually low melting point that is characteristic of plutonium appears at exactly the same place in the 5-f series where one finds the complex structures for which the actinides are famous. Understanding the anomalous melting point of plutonium is important for modeling its behavior in applications.

No comprehensive theory for the melting points of materials has ever been proposed. Lindemann was inspired by the recent publication of Einstein's theory on the heat capacity of materials. He wanted to devise a way of estimating the characteristic Einstein temperature, an atomistic measure of lattice stiffness on which the predictions of Einstein's theory are based. Lindemann realized that the amplitudes of the thermal atomic vibrations, which also depend on the Einstein temperature, could not become too large before the material would shake itself apart. The mean-square amplitude of thermal vibration is directly proportional to the absolute temperature and inversely proportional to the square of the Einstein temperature, so Lindemann could use Einstein's theory to estimate the temperature at which the atoms would begin to experience violent collisions with their neighbors. Thus, he was able to devise a simple formula that related the Einstein temperature to the melting temperature. His paper was published just before the invention of the Debye theory in 1914, which is still the basis of the modern theory of heat capacities and atomic vibrations.

The Debye temperature (roughly equivalent to the Einstein temperature) for plutonium is 132 K. Using the Lindemann equation, the melting temperature for Pu is 1700 K-which is too high by a factor of two! Does this discrepancy mean that something is wrong with the Lindemann criterion? No, the problem is that Debye temperature decreases quite strongly with temperature, and it is so large that the Debye temperature is reduced to only 89 K at the melting point. When this lower value of the Debye temperature is used, a value of 779 K is obtained for the melting point, in much better agreement with the experiment. The discrepancy is reduced from 88% to 15%. We conclude that temperature-induced softening of the lattice is responsible for the low melting point of plutonium.

We have used neutron powder diffraction at LANSCE and at the Intense Pulsed Neutron Source at Argonne National Laboratory to measure the temperature dependence of the Debye temperature for all the light actinides. We have data for Th, alpha-U, alpha-Np, alpha-Pu, and delta-Pu alloys. Single crystals are not required for these measurements.

Figure 2. Calculated and observed melting points for the light actinides and for lead. Neutron diffraction showed that the temperature dependence of the elastic properties of plutonium must be taken into account in order to give a good description of its high-temperature behavior.

Polycrystalline Np and Pu samples were prepared in NMT Division from pure electrorefined metal. The neptunium metal was 99.97 wt % neptunium; the highest impurity levels were from calcium and are typically 100 ppm. All other impurity levels were less than 100 ppm. The plutonium metal was 99.85 wt % plutonium with isotopic enrichment to 95% 242Pu. This isotope is required to minimize the absorption of neutrons. Alloys were prepared by arc melting. Rods were cast either in a casting furnace or the hearth of the arc melter and turned to the final dimensions. All samples were heated to 450°C. The samples were doubly encapsulated in thin-walled vanadium tubes for radiological containment during the neutron diffraction experiments.

Figure 2 shows the melting points for the light actinides together with two estimates of the melting point based on the Lindemann rule. The circles show the measured melting points. The triangles shows the Lindemann estimate of the melting point based on the low-temperature value of the Debye temperature uncorrected for its temperature dependence. The squares show the Lindemann estimate with the Debye temperature corrected for its temperature dependence measured with neutron scattering. The corrected data provide a good estimate of the melting point.

For many materials, some temperature dependence of the elastic properties is induced by thermal expansion. This is because the atoms are subjected to weaker forces when they move further apart as the temperature is raised. However, the thermal expansion of delta-phase plutonium is negligible, so the observed lattice softening is an intrinsic effect, arising from the electronic structure or other f-electron physics. Our work shows that these effects must be taken into account in order to predict the behavior of plutonium at high temperatures.

The anomalous temperature dependence of the elastic properties of plutonium can be studied at a more fundamental level by looking at inelastic neutron scattering. Such experiments are planned at LANSCE on both polycrystalline and single-crystal specimens of plutonium.

This article was contributed by A. C. Lawson (MST-8). Other researchers on the project include B. Martinez (NMT-11), R. Martinez (NMT-11), F. Vigil (NMT-5), R. Sheldon (NMT-9), J. A. Roberts (LANSCE-12), B. I. Bennett (NW-SS), and J. W. Richardson, Jr. (IPNS, Argonne National Laboratory).


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