High-pressure melting behavior of tin up to 105 GPa

Abstract

The melting curve of Sn initially rises steeply as a function of pressure but exhibits a decrease in slope (dT m /dP ) above 40 GPa to become nearly flat above 50 GPa. Previous studies have argued that a body-centered tetragonal (bct) to cubic (bcc) phase transition occurs in this range at room temperature. However, our investigations have shown that the phase behavior is more complex in this region with orthorhombic (bco) splitting of reflections occurring in the x-ray diffraction pattern above 32 GPa and coexisting diffraction signatures of bco and bcc structures are observed between 40 and 70 GPa. Here we have documented the simultaneous presence of bco and bcc reflections up to the melting point, negating the possibility that their coexistence might indicate a kinetically hindered first-order phase transformation. In this paper we have extended the observation of Sn melting relations into the megabar (P > 100 GPa) range using the appearance of liquid diffuse scattering in x-ray diffraction patterns and discontinuities during thermal signal processing to diagnose the occurrence of melting. Both techniques yield consistent results that indicate the melting line maintains the same low slope up to the highest pressure examined and does not flatten. The results below approximately 40 GPa agree well with the melting relations produced recently using a multiphase equation of state fitted to available or assumed data. Above this pressure the experimental melting points lie increasingly below the predicted crystal-liquid phase boundary, but above the flat melting from past studies, indicating that the thermodynamic properties of the body-centered "γ "-Sn structure remain to be clarified.

Using density functional theory to construct multiphase equations of state: tin as an example

“…In addition to this, the experimental melt data available for tin is very scattered (see Fig. 4.7), with results from many different types of experiments [51,52,53,57,58,59,60,61,62,63,64,65,66,67,68], making it difficult to decide where to place the melt curve.…”

MIRRORS: A MATLAB® GUI for temperature measurement by multispectral imaging radiometry

“…where the subscripts p and c denote the previous and current maps, respectively, and I x,y,c is taken from the current intensity map. This procedure was first described in the supplementary information of Briggs et al 6 where changes in δ, correlated with sudden drops in peak temperature, were ascribed to percolation of liquid Sn during high pressure melting experiments.…”

“…A similar comparison can be seen in the work of Lord et al 4 These sudden changes in the shape of the temperature field are clear from the sudden increases in the value of the image difference metric that coincide with sudden drops in peak temperature, as observed for Sn. 6…”

“…Recently, new methods have been employed that provide 2D temperature maps of hot DAC samples, circumventing these limitations and providing richer information about the dynamic changes occurring at high temperatures. 6 In the peakscaling method, 5,7,8 a pseudo-Planck curve is measured using a spectrometer with a wide entrance slit that averages the light from the entire ROI. This pseudo-Planck curve is then corrected to determine a peak temperature which is used to scale a monochromatic image of the sample collected simultaneously on a CCD, resulting in a temperature map.…”

Response of the mode Grüneisen parameters with anisotropic compression: A pressure and temperature dependent Raman study of β -Sn

“…Upon further compression, a number of polymorphs with a body-centered and closed-packed lattice are revealed [9][10][11]. The melt line of Sn plateaus above 40 GPa, matching a discontinuous increase in the coordination number of liquid Sn [12,13]. Around 10-30 GPa and up to 1800 K, dynamic shock experiments across the β-Sn to γ -Sn transition have traversed the phase boundary with increases in reflectivity from 5% to 15% [14] and using time-resolved x-ray diffraction [15].…”