Supplemental Material for High-Pressure Synthesis and Characterization of Incompressible Titanium Pernitride

Transcription

1 Supplemental Material for High-Pressure Synthesis and Characterization of Incompressible Titanium Pernitride Venkata S. Bhadram*, Duck Young Kim and Timothy A. Strobel* Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015, USA *Corresponding author Experimental Details: High-pressure experiments were performed using symmetric diamond anvil cells utilizing µm anvil culets. Rhenium gaskets were pre-indented to 30 µm thickness, and a 90 µm diameter sample chamber was drilled. TiN powders (99.5% pure) were precompressed to thickness of 10 µm and a small flake (20 µm x 10 µm) was picked and loaded in the sample chamber along with two small ruby crystals (see inset of Fig.1a in the main text). Here, ruby fluorescence is measured in situ to estimate the pressure. The sample chamber is filled with compressed N 2 gas (99.999% pure) which acts as a pressure transmitting medium and reactant. Samples were compressed up to ~73GPa (and up to 72GPa in another run) and then heated to ~2400K using double-sided laser heating set up. The formation of TiN 2 has been observed in both the runs. The complete details of the laser heating set up and temperature measurement can be found elsewhere. 1 During decompression run, the uncertainties in the pressure measurement are considered as 5% of the actual pressure estimated using ruby line. The pressure estimation during decompression run has been independently checked with the equation of state of TiN and Raman line of diamond culet which are in the same heating position. We have deliberately chosen a large uncertainty in pressure as 5% of the pressure determined from ruby line. This was justified by estimating the pressure values from the equation of state of TiN and the diamond Raman line at each point, which both fall within the 5% uncertainty value (the average absolute deviation between pressure from Ruby and TiN was ~2%). We have also attempted the synthesis using elemental Ti (in N 2 pressure transmitting medium) as the starting material. In this experiment, we have performed laser heating up to 1900K at 62GPa which yielded only TiN. Synchrotron x-ray diffraction measurements were carried out at HPCAT (beamline 16- IDB) of the Advanced Photon Source, Argonne National Laboratory. A monochromatic beam ( 5 5 μm 2 ) was focused on the sample, and data were recorded on a MAR CCD. Diffraction data were processed using the FIT2D 2 and DIOPTAS 3 data analysis programs. The diffraction pattern of the recovered sample was fitted using the Le Bail method in FullProf program. 4 The

2 lattice parameters of TiN 2 at higher pressures are estimated from the positions of 6 peaks which are individually fitted with pseudo-voigt functions using the Origin program. The electron imaging and EDS analysis are performed using JEOL (JSM-6500F) field emission scanning electron microscope. While performing EDS analysis on the recovered sample, we took precautions to avoid the errors in the elemental analysis due to the overlap of N-K edge with Ti-L edge. We first confirmed that there are no other elements present in the sample other than Ti and N. We measured the ratio of Ti K-line intensity relative to pure titanium (standard) with good precision using high beam energies (15 kev). The approximate N concentration was then inferred as the difference between the measured Ti and 100%. Raman spectra were collected using a Princeton Instruments spectrograph SP2750 (Trenton, NJ) coupled with a liquid nitrogen cooled charge coupled device (CCD) detector. A 532 nm diode laser was used as an excitation source and was focused on the sample using a 20 long working distance objective lens. The laser power was adjusted to optimize the power density on the sample and an exposure time of 60s was used for data acquisition. 2. Computational Details: Calculations were conducted based on density functional theory, as implemented in VASP software. 5 The generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) 6, 7 was used for the exchange correlation functional. We also tested Local Density Approximation (LDA) and PBEsol 8 functionals for comparison. Pseudopotentials with 2s 2 2p 3 and 3s 2 3p 6 4s 2 3d 2 configurations were used to for N and Ti, respectively. Total energy convergence was achieved with a plane-wave basis set cutoff energy of 600 ev and a k-point mesh 16x16x16 in Monkhorst-Pack scheme. 9 We conducted chemical bonding analysis using LOBSTER software, which calculates projected crystal orbital Hamilton population (pcohp) of Ti-Ti, Ti- N and N-N pairs to visualize bonding and antibonding characteristics. 3. Explanation for Low Value of : It is to be noted that the refined value for K (1.45(18)) from 3 rd order EOS fit is lower than that obtained for most materials. While there is no fundamental requirement for a larger value for K, there could be two possibilities for the low value of K observed here if it is not intrinsic: 1) poor choice of the EoS, 2) deviatoric stress due to non-hydrostatic pressure medium. The 2 nd order EoS fit to the data using K =4 (canonical value) results in K =318(9). However, the normalized stress-strain (F-f) plot (see Fig.S3b), which gives a visual indication for the appropriate EoS truncation and value of K, suggests that the 2 nd order EoS fit is not suitable for the present data. Thus, we conclude that the lower value of K could possibly be related to

3 deviatoric stress at high pressures even though its effect on the sample volume is minimal and depends on the anisotropic compressibility of the sample Supporting Figures: Figure. S1: (a) XRD patterns of the sample at 73GPa before laser heating (black line), while heating at 2400K (red line) and after quenched to 300K (blue line). (b) Le Bail fit of the diffraction pattern at 0GPa using tetragonal I4/mcm structure model with a=4.334 Å, c=5.294 Å. The black dotted line shows the calculated diffraction intensities based on the DFT structural model.

4 Figure. S2: The XRD (cake) image of (a) laser heated sample at 73GPa (b) recovered sample at ambient conditions. The red, green and blue bars indicate the reflections from TiN 2, TiN and Re respectively. The white labels are the miller indices of the indexed tetragonal I4/mcm phase.

5 Figure. S3: (a) Plot of the correlated values of and to different confidence levels when taking their covariance into account. 1σ, 2σ and 3σ represent the confidence levels of 68.3%, 95.4% and 99.73% respectively. 13 The common centre of the ellipses with error bars represents the refined and values with the estimated standard deviations obtained from the EoS fit. (b)an F-f plot 13 based on Birch Murnaghan EoS which is a visualization tool for the correct order of the EoS to be used for the experimental data.

6 Figure. S4: Raman spectrum of TiN 2 collected using two different laser power densities. The observed modes in the spectrum collected using high laser power (pink curve) can be assigned to the Raman modes of TiO 2 15,16 which indicates the oxidation of the sample after local heating at high laser power density.

7 Table S1: Lattice parameters (1 atm), isothermal bulk modulus (K ) and its pressured derivative (K ) derived from the first principle calculations for TiN 2 (I4/mcm, no. 140). Corresponding experimental values are shown for comparison. Method a or b (Å) c (Å) V(Å 3 ) Atomic Positions (GPa) Ti (4a) N (8h) LDA x=0.000 y=0.000 z=0.250 PBE x=0.000 y=0.000 z=0.250 PBEsol x=0.000 y=0.000 z=0.250 x= y= z= x= y= z= x= y= z= Expt (1) 5.294(2) (7) 1.45(18) Supporting References: 1. Meng, Y.; Hrubiak, R.; Rod,E.; Boehler,R.; Shen, G., New developments in laser-heated diamond anvil cell with in situ synchrotron x-ray diffraction at High Pressure Collaborative Access Team. Rev. Sci. Instru., 2015, 86, Hammersley, A. P.; Svensson, S. O.; Hanfland, M.; Fitch, A. N.; Hausermann, D., Two-dimensional detector software: From real detector to idealised image or two-theta scan. High Pressure Res. 1996, 14, Prescher, C.; Prakapenka, V. B., DIOPTAS: a program for reduction of two-dimensional X-ray diffraction data and data exploration. High Pressure Res. 2015, 35, Rodríguez-Carvajal, J., Recent advances in magnetic structure determination by neutron powder diffraction. Physica B: Condensed Matter 1993, 192, Kresse, G.; Hafner, J., Ab initio molecular-dynamics simulation of the liquid-metal-amorphoussemiconductor transition in germanium. Phys. Rev. B 1994, 49, Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C., Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 1992, 46, Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K., Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100, Monkhorst, H. J.; Pack, J. D., Special points for Brillouin-zone integrations. Phys. Rev. B 1976, 13, Deringer, V. L.; Tchougréeff, A. L.; Dronskowski, R., Crystal Orbital Hamilton Population (COHP) Analysis As Projected from Plane-Wave Basis Sets. J. Phys. Chem. A 2011, 115,

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