Generation of Thermal Scattering Laws for YH 2 using Ab Initio Methods
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1 Generation of Thermal Scattering Laws for YH 2 using Ab Initio Methods Michael L. Zerkle Bettis Atomic Power Laboratory WPEC SG42 Meeting May 18, 2015 May 18-19, 2015 WPEC SG42 Slide 1
2 Outline Motivation Yttrium Hydrogen Phase Diagram YH 2 Crystal Structure Ab Initio Approach using MedeA Structure Optimization Lattice Dynamics YH 2 Thermal Scattering Laws Phonon Frequency Distributions Inelastic Scattering Cross Section Incoherent Elastic Scattering Cross Section Conclusions May 18-19, 2015 WPEC SG42 Slide 2
3 Motivation Metal hydrides (ZrH x ) used as high temperature moderator/reflector in nuclear reactors TRIGA SNAP-10 TOPAZ Yttrium hydride (YH x ) has superior hydrogen density (N H ) at elevated temperatures Test improvements to MedeA software, use abinitioapproach to generate TSLs for new moderator materials Hydrogen in metallic Zr, Ce, Y and Ca in equilibrium with 1 atmh 2 at various temperatures. (Source: Metal Hydrides, Academic Press, p. 442, 1968) N H is number of hydrogen atoms/cc x May 18-19, 2015 WPEC SG42 Slide 3
4 Yttrium Hydrogen Phase Diagram H has limited solubility in α-y at low temperatures. H/Y < 2.0 is region of practical interest for nuclear applications Mixture of α-y + δ-yh 2 phases δ-yh 2 phonon frequency distribution needed to develop thermal scattering law (TSL) for YH 2-x (Source: Metal Hydrides, Academic Press, p. 443, 1968) May 18-19, 2015 WPEC SG42 Slide 4
5 YH 2 Crystal Structure YH 2 has a CaF 2 type FCC structure 12 atoms 4 Y atoms (blue) at vertices and faces of cubic unit cell 8 H atoms (grey) located in tetragonal holes between Y atoms Lattice constant a = Å MedeAcalculated lattice constant compares extremelywellwith recent X-ray diffraction measurements by Daou and Vajda [1992] a = (3) Å (90 K) a = (3) Å (295 K) May 18-19, 2015 WPEC SG42 Slide 5
6 Ab Initio Approach Using MedeA MedeA software used to perform the ab initio calculations Informatica tool used to select the initial unit cell structure from the ICSD (crystal structure) database Automated Covergence tool used to optimize unit cell structure Converge k-mesh Converge planewave cutoff energy Converge supercell size Iterative VASP ab initio calculations PHONON tool performs the lattice dynamics calculations on optimized structure Dispersion relations Phonon density of states Thermodynamic properties NJOY/LEAPR used to generate TSL from phonon frequency distribution May 18-19, 2015 WPEC SG42 Slide 6
7 Optimization of the YH 2 Structure VASP calculations Detailed quantum mechanical first principle simulation of crystal lattice using density functional theory Generalized Gradient Approximation (GGA) Projector Augmented Wave (PAW) pseudopotential Optimized structure to a total energy threshold of 0.1 mev Required 42 VASP calculations ev planewave cutoff energy k-spacing of ~0.05 1/Å final k-mesh Optimized lattice constant a = Å Optimized lattice structure then used in PHONON calculations May 18-19, 2015 WPEC SG42 Slide 7
8 YH 2 Dispersion Relations PHONON calculation use supercell (96 atoms) Planewavecutoff energy of 250 ev k-spacing of 0.5/Å (5 5 5 k-mesh) ±0.02 Å displacement Dispersion relations (at right) Well separated acoustical and optical modes (as expected) Lower branches are acoustical modes mainly due to heavy Y atom vibrations Higher branches are optical modes mainly due to light H atom vibrations Frequency (THz) Phonon Dispersion for job 52 W L Γ X W K Brillouin Zone Direction May 18-19, 2015 WPEC SG42 Slide 8
9 May 18-19, 2015 WPEC SG42 Slide 9
10 Udovic(1994) May 18-19, 2015 WPEC SG42 Slide 10
11 Thermodynamic Properties Agree with Measurements May 18-19, 2015 WPEC SG42 Slide 11
12 Thermodynamic Properties Agree with Measurements May 18-19, 2015 WPEC SG42 Slide 12
13 Thermodynamic Properties Agree with Measurements May 18-19, 2015 WPEC SG42 Slide 13
14 LEAPR Models for YH 2 TSLs H-YH 2 and Y-YH 2 TSL generated using LEAPR Phonon frequency distributions from PHONON calculation Incoherent approximation Atomic mass ratios and free atom scattering cross sections from ENDF/B-VII.1 1 H and 89 Y evaluations αand βmesh borrowed from ENDF/B-VII.0 ZrHTSLs 10 temperatures (293.6, 400, 500, 600, 800, 1000, 1200, 1400, 1600 K) May 18-19, 2015 WPEC SG42 Slide 14
15 May 18-19, 2015 WPEC SG42 Slide 15
16 May 18-19, 2015 WPEC SG42 Slide 16
17 May 18-19, 2015 WPEC SG42 Slide 17
18 May 18-19, 2015 WPEC SG42 Slide 18
19 Conclusions abinitiotools like MedeA(VASP, PHONON) have sufficiently matured and can be used to generate TSLs for new moderator materials H-YH 2 and Y-YH 2 TSLs produced using the abinitio 2 2 approach Results consistent with available measurements Currently reviewing α and βmesh to ensure it adequately resolves the S(α,β,T) functions for H-YH 2 and Y-YH 2 Working to submit H-YH 2 and Y-YH 2 evaluations to CSEWG May 18-19, 2015 WPEC SG42 Slide 19
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