Density of Liquid Niobium and Tungsten and the Estimation of Critical Point Data
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I.
INTRODUCTION
THE knowledge of a metal’s density as a function of temperature is frequently crucial for many scientific considerations and technological applications. It is used as an input parameter in simulations that model thermal natural convection phenomena in furnaces and ladles, to calculate mass balance in refining operations or understand and model solidification processes, to name a few.[1,2] Density as a function of temperature is also needed for the calculation of thermal conductivity from thermal diffusivity and vice versa, or in the measurement of surface tension and viscosity. In fact, various models show a relatively strong sensitivity on input density data compared to other input-properties.[3] Density data of liquid transition metals, however, are often either scarcely available or are very inconsistent with each other. This is also a consequence of the high temperatures that are involved when dealing with liquid metals. These temperatures are typically above several thousand K for transition metals, which leads to a number of technical challenges. It is for this reason that a complementary revisit on liquid density data appears to be appropriate for several transition metals, such as niobium and tungsten. The density of liquid metals is not only of direct technology-related interest, but also of fundamental scientific interest. Measuring a material’s density as a function of temperature means that a part of this
M. LEITNER and G. POTTLACHER are with the Institute of Experimental Physics, Graz University of Technology, NAWI Graz, Petersgasse 16, 8010 Graz, Austria. Contact e-mail: matthias.leitner@ tugraz.at Manuscript submitted November 30, 2018. Article published online May 20, 2019 3646—VOLUME 50A, AUGUST 2019
material’s phase diagram is mapped in the temperature–density projection. Extending the measured density to higher temperatures leads the way to the material’s critical point. For high melting metals, this unique point can be at extremely high temperatures well above 10,000 K and at extreme pressures of several hundred MPa. For this reason, the critical point of these metals can be reached experimentally only with great effort, if at all. However, measuring the liquid density at lower temperatures, e.g., via ohmic pulse-heating, still allows extrapolating of the measured data points according to simplified theoretical models.[4] By this means one can give an estimation of the critical density, critical temperature and the material’s phase diagram in the temperature–density projection. Critical point data of high-melting metals might even be useful one day in future ultra-high temperature technologies, such as for aerospace and energy applications. This paper is organized as follows: Section II provides details on the experimental procedure and the ohmic pulse-heating setup is briefly explained. Section III presents and discusses the obtained temperature–resolved density data and gives the estimated phase diagrams of niobium and tungsten together with their critical point. In Section IV, unce
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