1 / 58

Rattling Atoms in Group IV Clathrate Materials

Rattling Atoms in Group IV Clathrate Materials. Charles W. Myles Professor, Department of Physics Texas Tech University Charley.Myles@ttu.edu http://www.phys.ttu.edu/~cmyles Colloquium, Auburn U., Friday, April 4, 2003.

jarrod-morrow
Download Presentation

Rattling Atoms in Group IV Clathrate Materials

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Rattling Atoms in Group IV Clathrate Materials Charles W. Myles Professor, Department of Physics Texas Tech University Charley.Myles@ttu.edu http://www.phys.ttu.edu/~cmyles Colloquium, Auburn U., Friday, April 4, 2003

  2. “Tech” is NOT an abbreviation for “Technological” or “Technical”!It is part of the official name! Multi-purpose, multi-faceted university. 27,000 students, including 3,500 graduate students. Texas Tech University • Nine Colleges:Agriculture, Architecture, Arts & Sciences, Business, Education, Engineering, Human Sciences, Law, Visual & Performing Arts. • PLUS:Health Sciences Center:Schools of Allied Health, Medicine, Nursing, Pharmacy.

  3. Bob Knight Texas Tech’s most famous staff member! Texas Tech University

  4. 21 Faculty Research:Astrophysics, Atomic & Molecular Physics, Biophysics, Forensic Physics, Particle Physics, Physics Education, Pulsed Power Physics, Materials Physics. Theory & Experiment. Basic & Applied. Ave. Faculty Age 45. External Funding  $3.5M/year Department of Physics • 40 Graduate Students:MS & PhD Programs inPhysics & Applied Physics. Includes MSi Program. • 75 Undergraduate Students:BS Programs inPhysics & Engineering Physics.ABET Accreditationfor Engineering Physics.

  5. Population 200,000.Named by Money Magazine as one of the top places to live in the US! Location:Southern High Plains. Elevation 3,250 feet.FLAT!!!!!Southern Panhandle of Texas. Climate:Semi-arid. 15-18 inches of rain/year. Hot, dry summers, mild winters. Main Industry:Agriculture (Cotton). Lubbock Lubbock, Texas • Geography:100 miles South of Amarillo, 320 miles West (& North) of DFW, 320 miles South (& East) of Albuquerque, 400 miles South (& East) of Denver. • Most famous “Native Son”: Buddy Holly!

  6. Collaborators • Otto F. Sankey: Arizona State University • J.J. Dong: Auburn University • Was Otto Sankey’s post-doc at Arizona State • George S. Nolas: University of South Florida • Materials synthesis & electrical characterization • Chris Kendziora: Naval Research Labs • Experimentalist: Raman spectroscopy • Jan Gryko: Jacksonville State U. (Alabama) • Experimentalist: Materials synthesis

  7. Outline • Introduction to clathrates Crystal structures. Contrast to diamond structure • Brief discussion of computational method • Sn clathrates (Type I) • Equations of state (Etotvs. volume) • Electronic bandstructures (Ek) • Vibrational (phonon) properties (k) • Raman spectra & comparison with experiment • Si, Ge, & Sn clathrates (Type II) • Vibrational (phonon) properties (k) • Raman spectra & comparison with experiment

  8. Group IV Elements  • Valence electron configuration: ns2 np2 [n=2, C; n=3, Si; n=4, Ge; n=5, Sn] 

  9. Group IV Crystals • Si, Ge, Sn: Ground state crystalline structure = Diamond Structure. • Each atom tetrahedrally (4-fold) coordinated (4 nearest-neighbors) with sp3 covalent bonding • Bond angles:Perfect, tetrahedral = 109.5º • Si, Ge: Semiconductors. • Sn: (-tin or gray tin) - Semimetal

  10. Carbon Crystals • C: Graphite & Diamond Structures • Diamond  Insulator or wide bandgap semiconductor • Graphite  Planar structure sp2 bonding  2d metal (in plane) • Ground state (lowest energy configuration) is graphiteat zero temperature & atmospheric pressure. Graphite-diamond total energy difference is VERY small!

  11. Other Group IV Crystal Structures(Higher Energy) • C: “Buckyballs” (C60)  “Buckytubes” (nanotubes), other fullerenes 

  12. Sn: (-tin or white tin) - body centered tetragonal lattice, 2 atoms per unit cell. Metallic. • Si, Ge, Sn: The clathrates.

  13. Clathrates • Crystalline Phases of Group IV elements: Si, Ge, Sn (not C yet!)“New” materials, but known (for Si) since 1965! • J. Kasper, P. Hagenmuller, M. Pouchard, C. Cros, Science 150, 1713 (1965) • As in diamond structure, all Group IV atoms are 4-fold coordinated insp3 bonding configurations. • Bond angles:Distorted tetrahedra Distribution of angles instead of perfect tetrahedral 109.5º • Lattice contains hexagonal & pentagonal rings, fused together with sp3 bonds to form large “cages”.

  14. Pure materials: Metastable, expanded volume phases of Si, Ge, Sn • Few pure elemental phases yet. Compounds with Group I & II atoms (Na, K, Cs, Ba). • Possible application: Thermoelectrics. • Open, cage-like structures, with large “cages” of Si, Ge, or Sn atoms. “Buckyball -like” cages of 20, 24, & 28 atoms. • Two varieties: Type I (X46) & Type II (X136) X = Si, Ge,or Sn

  15. Why “clathrate”? Same crystal structure as clathrate hydrates (ice).

  16. Si46, Ge46, Sn46: (Type I Clathrates) 20 atom (dodecahedron) cages & 24 atom (tetrakaidecahedron) cages, fused together through 5 atom rings. Crystal structure = simple cubic, 46 atoms per cubic unit cell. • Si136, Ge136, Sn136: (Type II Clathrates) 20 atom (dodecahedron) cages & 28 atom (hexakaidecahedron) cages, fused together through 5 atom rings. Crystal structure = face centered cubic, 136 atoms per cubic unit cell.

  17. Clathrate Building Blocks • 24 Atom Cage:  • 20 Atom Cage:  • 28 Atom Cage: 

  18. Clathrate Structures 24 atom cages Type I Clathrate Si46, Ge46, Sn46 simple cubic 20 atom cages Type II Clathrate Si136, Ge136, Sn136 face centered cubic 28 atom cages

  19. Clathrate Lattices Type I Clathrate  Si46, Ge46, Sn46 simple cubic [100] direction Type II Clathrate  Si136, Ge136, Sn136 face centered cubic [100] direction

  20. Group IV Clathrates • Not found in nature. Synthesized in the lab. • Not normally in pure form, but with impurities (“guests”) encapsulated inside the cages. Guests “Rattlers” • Guests: Group I (alkali) atoms (Li, Na, K, Cs, Rb) or Group II (alkaline earth) atoms (Be, Mg, Ca, Sr, Ba) • Synthesis: NaxSi46 (A theorists view!) • Start with Zintl phase NaSi compound. • Ionic compound containing Na+ and (Si4)-4 ions • Heat to thermally decompose. Some Na vacuum. • Si atoms reform into clathrate framework around Na. • Cages contain Na guests

  21. Type I Clathrate(with guest “rattlers”) 20 atom cage with guest atom  [100] direction + 24 atom cage with guest atom  [010] direction

  22. Clathrates • Pure materials: Semiconductors. • Guest-containing materials: • Some are superconducting materials (Ba8Si46) from sp3bonded, Group IV atoms! • Guests weakly bonded in cages: Minimal effect on electronic transport • Host valence electrons taken up in sp3bonds • Guest valence electrons go to conduction band of host ( heavy doping density). • Guests vibrate with low frequency (“rattler”) modes Strong effect on vibrational properties Guest Modes  Rattler Modes

  23. Possible use as thermoelectric materials. Good thermoelectrics should have low thermal conductivity! • Guest Modes  Rattler Modes: A focus of experiments. Heat transport theory: Low frequency rattler modes can scatter efficiently with acoustic modes of host  Lowers thermal conductivity  Good thermoelectric! • Among materials of experimental interest are tin (Sn) clathrates. Mainly Type I. Much of my work. • Also, Si and Ge, Type II. Most recent work.

  24. Calculations • Computational package: VASP- Vienna Austria Simulation Package. First principles! Many electron effects: LocalDensityApproximation (LDA). Exchange-correlation: Ceperley-Adler Functional Ultrasoft pseudopotentials Planewave basis • Extensively tested on a wide variety of systems • We’ve computed equilibrium geometries, equations of state, bandstructures & phonon spectra.

  25. Start with lattice geometry from expt or guessed (interatomic distances & bond angles). • Supercell approximation • Interatomic forces act to relax lattice to equilibrium configuration (distances, angles). • Schrdinger Eq. for interacting electrons. Newton’s 2nd Law for atomic motion.

  26. Equations of State • Total binding energy minimized in the LDA by optimizing internal coordinates at a given volume. • Repeat calculation for several volumes. • Gives minimum energy configuration. LDA binding energy vs. volume curve. • To save computational effort, fit this to empirical equation of state (four parameters): “Birch-Murnaghan” equation of state.

  27. Birch-Murnaghan Eqtn of State Fit LDA total binding energy vs. volume curve to E(V) = E0 + (9/8)K0V0[(V0/V) -1]2 {1 + (4-K)[1- (V0/V)]} 4 Parameters: E0 Minimum binding energy V0 Volume at minimum energy K0 Equilibrium bulk modulus K dK0/dP Pressure derivative of K0

  28. Equations of State for Sn SolidsBirch-Murnhagan fits to LDA E vs.V curves Sn Clathrates: expanded volume, high energy, metastable Sn phases Compared to -Sn: Sn46 V: 12% larger E: 41 meV higher Sn136 V: 14% larger E: 38 meV higher  Clathrates: “Negative pressure” phases!

  29. Equation of State ParametersBirch-Murnhagan fits to LDA E vs.V curves Sn Clathrates: Expanded volume, high energy, “soft”Sn phases Compared to -Sn: Sn46 -- V: 12% larger,E: 41 meV higher, K0: 13% “softer” Sn136 -- V: 14% larger,E: 38 meV higher, K0: 13% “softer”

  30. Ground State Properties • Once equilibrium lattice geometry is obtained, all ground state properties can be obtained (at minimum energy volume) • Electronic bandstructures • Vibrational dispersion relations Bandstructures • At relaxed lattice configuration (“optimized geometry”) use one electron Hamiltonian + LDA many electron corrections to solve Schrdinger Eq. for bandstructures Ek.

  31. Bandstructures • NB= # of valence bands Ne = # valence electrons / atom NA= # atoms per cell  NB = Ne x NA • Diamond Structure &Clathrates:Ne = 4 Diamond:NA = 2  NB = 8 Clathrates: X46: NA = 46  NB = 184 X136: NA = 136  NB = 544

  32. Diamond Structure Sn BandsM.L Cohen & J. Chelikowsky, Electronic Structure and Optical Properties of Semiconductors, (Springer) Solid State Science, 75 (1989). Diamond Structure Sn(-Sn): A semimetal (Eg = 0) *

  33. Sn46 & Sn136 BandstructuresC.W. Myles, J. Dong, O. Sankey, Phys. Rev. B64, 165202 (2001). The LDAUNDER-estimates bandgaps! Sn46 Sn136   LDA gap Eg 0.86 eVLDA gap Eg 0.46 eV Semiconductors of pure tin!!!! (Hypothetical materials. Indirect band gaps)

  34. Compensation • Guest-containing clathrates: Valence electrons from guests go to conduction band of host (heavy doping). Change material from semiconducting to metallic. For thermoelectric applications, want semiconductors!! • COMPENSATEfor this by replacing some host atoms in the framework by Group III or Group II atoms (charge compensates). Gets semiconductor back! • Sn46:Semiconducting. Cs8Sn46: Metallic. Cs8Ga8Sn38& Cs8Zn4Sn42: Semiconducting • Later: Si136,Ge136, Sn136: Semiconducting. Na16Cs8Si136, Na16Cs8Ge136, Cs24Sn136: Metallic

  35. For EACH guest-containing clathrate, including those with compensating atoms in framework: • ENTIRELDA procedure is repeated: • LDA total energy vs. volume curve  Equation of State • Birch-Murnhagan Eqtn fit to LDA results. • At minimum energy volume, compute bandstructures & lattice vibrations. • Compensated materials: ASSUME an ordered structure.

  36. Cs8Ga8Sn38 & Cs8Zn4Sn42 BandsC.W. Myles, J. Dong, O. Sankey, Phys. Rev. B64, 165202 (2001). The LDAUNDER-estimates bandgaps! Cs8Ga8Sn38 Cs8Zn4Sn42   LDA gap Eg 0.61 eVLDA gap Eg 0.57 eV Semiconductors (Materials which have been synthesized. Indirect band gaps)

  37. Lattice Vibrations (Phonons) • At optimized LDA geometry:Calculate total ground state energy:Ee(R1,R2,R3, …..RN) • Harmonic Approx.:“Force constant” matrix: (i,i)  (2Ee/Ui Ui) Ui= atomic displacements from equilibrium. Instead of directly computing derivatives, we use • Finite displacement method:Compute Eefor many different (small; harmonic approx.) Ui Compute forces  Ui. • Dividing forces by Ui gives (i,i) & thusdynamical matrix Dii(q).

  38. Phonons • Group theory limits number & symmetry of Uirequired. (Materials have high symmetry). • Positive & negative Uifor each symmetry: Cancels out 3rd order anharmonicity (beyond harmonic approximation). • Once have all unique (i,i), do lattice dynamics. • Lattice dynamics in the harmonic approximation:  classical eigenvalue (normal mode) problem det[Dii(q) - 2 ii] = 0 Dynamical matrix Dii(q) obtained from force constant matrix  in usual way. First principles force constants! NO FITS TO DATA!

  39. Eigenvalues: Squares of vibrational frequencies 2(q)(phonon dispersion relations) NB= # of branches (modes) in (q) NA= # of atoms / unit cell  NB = 3 x NA • Diamond Structure:NA = 2  NB = 6 Clathrates: X46: NA = 46  NB = 138 X136: NA = 136  NB = 408 • 3 Acoustic branches, NB - 3 Optic branches

  40. Diamond Structure Sn PhononsW. Weber, Phys. Rev. B15, 4789 (1977). 3 Acoustic branches 3 Optic branches

  41. Sn46 & Sn136 PhononsC.W. Myles, J. Dong, O. Sankey, C. Kendziora, G. Nolas,Phys. Rev. B 65, 235208 (2002) Sn46 Sn136 Flat optic bands! Large unit cell  Small Brillouin Zone reminiscent of “zone folding”

  42. Guest-Containing Clathrates as Thermoelectrics • Guest atoms:Weakly bound to clathrate framework. • Framework: Fully sp3 tetrahedrally bonded. Guest atom e- don’t participate in bonding or affect electronic transport very strongly. • Guests have low energy (“rattling”) phonon modes (guest atoms vibrating in cages, small force constants). Will see this explicitly later in talk.  These strongly affect vibrational properties & thus phonon-phonon scattering & thermal conductivity.

  43. Good thermoelectrics should have low thermal conductivity. • Guest Modes  Rattler Modes: A focus of experiments Heat transport theory: Low frequency rattler modes can scatter efficiently with acoustic modes of the host  Lowers the thermal conductivity  Good thermoelectric!  Many experiments (e.g., Raman scattering) have focussed on the rattler modes of the guests. Our calculations have also done so.

  44. Cs8Ga8Sn38 PhononsC. Myles, J. Dong, O. Sankey, C. Kendziora, G. Nolas,Phys. Rev. B 65, 235208 (2002)  Ga modes Compare to Sn46 results.  Cs guest “rattler” modes (~25 - 40cm-1) “Rattler” modes:Cs motion in large & small cages

  45. Raman Spectra • Do group theory necessary to determine Raman active modes. • Raman spectroscopy probes only modes at zone center (q = 0). • Frequenciescalculated from first principles as described. • Estimate Raman scattering intensities using an empirical (two parameter) bond polarization model.

  46. C.W. Myles, J. Dong, O. • Sankey, C. Kendziora, G. Nolas, Phys. Rev. B 65, 235208 (2002). • Experimental & • theoretical rattler (& other!) modes in good agreement! • UNAMBIGUOUS • IDENTIFICATION of low (25-40 cm-1) frequency rattler modes of Cs guests.Not shown: Detailed identification offrequencies & symmetries of several observed Raman modes by comparison with theory.

  47. Type II Clathrate PhononsWith “rattling”atoms • Current experiments: Focus on rattling modes in Type II clathrates (thermoelectric applications). Theory:Given success with Cs8Ga8Sn38: Look at phonons & rattling modes in Type II clathrates Search for trends in rattling modes as host changes from Si  Ge  Sn • Na16Cs8Si136 : Have Raman data & predictions • Na16Cs8Ge136 : Have Raman data & predictions • Cs24Sn136: Have predictions, NEED DATA! • Note: These materials are metallic!

  48. PhononsC. Myles, J. Dong, O. Sankey, submitted, Phys. Status Solidi B Na16Cs8Si136 Na16Cs8Ge136 Narattlers(20-atom cages)Narattlers(20-atom cages) ~ 118 -121 cm-1 ~ 89 - 94 cm-1 Csrattlers(28-atom cages)Cs rattlers(28-atom cages) ~ 65 - 67 cm-1 ~ 21 - 23 cm-1

  49. Si136, Na16Cs8Si136 Na16Cs8Ge136 Raman Spectra 1st principles frequencies. G. Nolas, C. Kendziora, J. Gryko, A. Poddar, J. Dong, C. Myles, O. Sankey J. Appl. Phys. 92, 7225 (2002). Experimental & theoretical rattler(& other) modes in very good agreement! Not shown: Detailed identification of frequencies & symmetries of observed Raman modes by comparison with theory.

  50. Reasonable agreement of theory & experiment for Raman spectra, especially “rattling” modes (of Cs in large cages) in Type II Si & Ge clathrates.  UNAMBIGUOUS IDENTIFICATION of low frequency “rattling” modes of Cs in Na16Cs8Si136(~ 65 - 67 cm-1) Na16Cs8Ge136 (~ 21 - 23 cm-1)

More Related