Phase Transformation Hysteresis in a Plutonium Alloy System: Modeling the Resistivity during the Transformation
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Phase Transformation Hysteresis in a Plutonium Alloy System: Modeling the Resistivity during the Transformation Jeffery J. Haslam, Mark A. Wall, David L. Johnson, David J. Mayhall, and Adam J. Schwartz Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550 ABSTRACT We have induced, measured, and modeled the δ – α’ martensitic transformation in a Pu-Ga alloy by a resistivity technique on a 2.8-mm diameter disk sample. Our measurements of the resistance by a 4-probe technique were consistent with the expected resistance obtained from a finite element analysis of the 4-point measurement of resistivity in our round disk configuration. Analysis by finite element methods of the postulated configuration of α’ particles within model δ grains suggests that a considerable anisotropy in the resistivity may be obtained depending on the arrangement of the α’ lens shaped particles within the grains. The resistivity of these grains departs from the series resistance model and can lead to significant errors in the predicted amount of the α’ phase present in the microstructure. An underestimation of the amount of α’ in the sample by 15%, or more, appears to be possible. INTRODUCTION Plutonium and its alloys have the distinction of producing 6 allotropic phases between room temperature and the liquid state [1]. In pure plutonium the δ phase is stable between 325 and 460°C. However, the δ phase can be stabilized (to a metastable state) at room temperature by additions of various alloying elements. These alloying elements include Al, Ce, Ga, In, Zn and others [1]. In particular, the δ to α’ phase transition is unique in having what is believed to be a martensitic type phase transformation with a nominally 20% change in density resulting from the transformation. This transformation has a large hysteresis in the forward and reverse directions and has been observed to have an isothermal characteristic even though it is believed to be martensitic [2,3]. The large volume change during the transformation probably leads to considerable plastic deformation to accommodate forming particles of the α’ phase. This is thought to make a significant contribution to the rather large hysteresis in the transformation. Dilatometry has been used to characterize the δ to α’ phase transformation [2-4]. The hazards and difficulties associated with working with Pu metal make it necessary and useful to work with very small quantities of the material. The sample size available to this project was a disk, 2.8-mm in diameter and less than 500µm thick (a standard TEM foil size before thinning for electron transparency). Although other dilatometry techniques might be possible, we have chosen resistivity to characterize the martensitic transformation in this plutonium alloy. Resistivity has been used previously to measure phase transformations in plutonium [2,5], and more particularly has been used to follow the δ to α’ phase transformation in alloys of δ-Pu stabilized by the addition of Al or Ga. [6,7]. However, our sample shape did not allow
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