MIT Amorphous Materials

Transcription

1 MIT Aorphous Materials 14: Characterizing the Aorphous State Juejun (JJ) Hu 1

2 After-class reading list X-ray diffraction X-ray diffraction, Raan spectroscopy, and calorietry 2

3 Structure Glass cheistry Technique X-ray/electron/ neutron diffraction X-ray absorption spectroscopy (XAS) Raan spectroscopy Nuclear agnetic resonance (NMR) Atoic eission spectroscopy (AES) Energy-dispersive X-ray spectroscopy (EDX) Infrared spectroscopy X-ray photoelectron spectroscopy (XPS) Inforation Crystallinity, pair distribution function, ediu range order Local structure, electronic state Phonon spectra, structural clusters Local atoic configurations Eleental coposition Eleental coposition Cheical bonding, ipurity concentration, optical absorption Valence state of constituents, electron density of states 3

4 Theral analysis Electrical properties Technique Differential theral analysis (DTA) Differential scanning calorietry (DSC) Therogravietric analysis (TGA) Theroechanical analysis (TMA) Teperature-dependent electrical conductivity easureent Ipedance spectroscopy (AC conductivity) Electron paraagnetic resonance (EPR) Inforation Glass transition teperature (T g ), crystallization (T x ) Glass transition teperature (T g ), crystallization (T x ) Cheical decoposition Theral expansion, softening point, glass transition (T g ) Conduction echanis, activation energy, density of states at Feri level (for VRH) Conductivity, dielectric constant Defects (e.g. dangling bonds) 4

5 Mechanical and rheological behavior Optical properties Technique Indentation Ultrasonic wave propagation Fracture toughness test 3/4-point bending test Viscoetry UV-Vis spectroscopy Ellipsoetry Pris coupling Optical fiber/waveguide transission Photoluinescence Inforation Hardness Elastic odulus Fracture toughness Elastic odulus, flexural stress Viscosity Optical attenuation & absorption (100 db/c or higher), Tauc gap Refractive index dispersion Refractive index (bulk and thin fil), optical attenuation Optical attenuation (< 100 db/c) Defect states 5

6 Diffraction techniques Three diensional visualization of diffraction intensities reoved due to copyright restrictions. See Figure 2: "Serial Fetosecond Crystallography." CFEL Science, DESY. Full 3-D x-ray structure factors of Photosyste I, a protein coplex Iage courtesy: Thoas White, CFEL 6

7 X-ray diffraction (XRD) Figure of XRD line scan of aorphous and annealed Metglas foils reoved due to copyright restrictions. See Figure 1: Li, M. et al. "Giant Magnetoelectric Effect in Self-biased Lainates Under Zero Magnetic Field." Appl. Phys. Lett. 102, no (2013): 1-3. Crystals: Strong scattering Localized, intense peaks Glass: Weak scattering Broad scattering background across the entire reciprocal space Appl. Phys. Lett. 102, (2013) 7

8 X-ray diffraction in solids Incident wave r Diffracted wave Saple r : position vector of ato Assuptions: Approxiate incident and diffracted X-ray as onochroatic plane waves Elastic scattering: wavelength of X-ray reains the sae after scattering Neglect X-ray attenuation in the solid saple 8

9 X-ray diffraction by a single ato Incident wave r Saple E : field aplitude of incident X-ray k i : wave vector of incident X-ray k s : wave vector of scattered X-ray f : scattering factor of ato Q = k s - k i : scattering vector Diffracted wave Coplex aplitude of incident wave: i expi E r = E k r Field aplitude of the incident wave at r : i r = expi E E k r Coplex aplitude of wave scattered by ato : s i i expikir iks r r exp iq r E r E exp f 9

10 X-ray diffraction in solids Incident wave r Diffracted wave Saple S (Q) : (static) structure factor N : total nuber of atos in the saple Total scattered aplitude fro the saple : Total scattered intensity: I f exp iq r f exp iq r n f f exp * n exp iq r iq r S Q N f n

11 X-ray diffraction in crystals The condition for a Bragg peak to appear is: 2d sin or: Q ks ki Ghkl The Bragg peak intensity scales with: j i fe Qr j j 2 where the su is over all atos in a unit cell Unit cell: the repeating unit of a crystal T. Proffen, Characterization of Materials using the PDF 11

12 Quantitative description of glass structure Structural descriptions of aorphous aterials are always statistical in nature Pair distribution function (PDF): g(r) Consider an aorphous aterial with an average nuber density of ato given by: NV N : nuber of atos V : aterial volue The nuber density of atos at a distance r fro an origin ato is given by gr () When When r r 0, g 0, g 1 12

13 PDFs of ideal (hard sphere) crystals vs. glasses g(r) 1 st coordination shell 2 nd coordination shell r g(r) 1 0 r 13

14 Matheatical description of PDF Probability density for finding an ato at r : N 1 r r r Hoogeneous solid Probability density for finding an ato pair at r and r : 2 r, r ' Pair distribution function: N N r rn n 2 r r' r g r 2 1 V 2 2 N 2 2 r r ' r r ' r ' Hoogeneous, isotropic solid 14

15 Structure factor of isotropic aorphous solids N N 1 S 2 f i fn i N f n * Q exp Q r exp Q r N N 1 exp N n i Q r expiq r N N 1 1 exp iq ' ' n d d ' N r r r r r r r r n exp iq ', ' d d ' N r r r r r r Q r 1 exp i g r d r where n r rr' n In isotropic solids structure factor is related to the Fourier transfor of PDF 15

16 Debye scattering equation Isotropic aorphous edia: Q 1 exp Q r 2 sin Qr 1 4 r g r dr S i g r d r 0 Qr The inverse transfor: where 1 sin Qr g r S d 2 Qr Q =Q 2 1 Q 1 Q Q sin XRD spectra can be used to infer PDF of isotropic aorphous solids 16

17 Solving PDF fro experiental XRD spectra Raw XRD data Data correction Structure factor noralization Transfor to real space Data fro T. C. Hufnagel, Johns Hopkins University 17

18 Solving PDF fro experiental XRD spectra Raw XRD data Data correction Structure factor noralization Transfor to real space Data fro T. C. Hufnagel, Johns Hopkins University 18

19 Solving PDF fro experiental XRD spectra Raw XRD data Data correction Structure factor noralization Transfor to real space N f 2 Scattered intensity oscillates around the coherent independent scattering at large Q values I S Q N f 2 Data fro T. C. Hufnagel, Johns Hopkins University 19

20 Solving PDF fro experiental XRD spectra Raw XRD data Data correction Structure factor noralization Transfor to real space Structure factor oscillates around unity at large Q values When Q I S Q N f N f S Q Data fro T. C. Hufnagel, Johns Hopkins University 20

21 Solving PDF fro experiental XRD spectra Raw XRD data Data correction Structure factor noralization Transfor to real space 1 Q sin Qr g r S 2 d 2 0 Qr ax 2 1 Q 1 Q Q r, g 1 Data fro T. C. Hufnagel, Johns Hopkins University 21

22 Solving PDF fro experiental XRD spectra Sources of error S(Q) data truncation error X-ray photon shot noise Finite resolution Mitigation strategies Use Mo ( Ka = 0.71 Å) or Ag ( Ka = 0.56 Å) sources instead of Cu source ( Ka = 1.54 Å) Increase collection tie Deterination of Pair Distribution Functions (PDF) fro Bruker PDFGetX2 hoepage J. Appl. Cryst. 37, 678 (2004) 22

23 Electron and neutron diffraction Electron diffraction Much saller wavelength (e.g. ~ 2 p for 300 kev electrons) Sall spot size (e.g. in the case of SAED) Neutron diffraction Interacts with nuclei rather than electrons Can discriinate neighboring eleents or isotopes Can detect light eleents Aorphous Ta 2 O 5 Crystalline Ta 2 O 5 Electron diffraction patterns Courtesy of INSPIRE HEP. License: CC0. Class. Quantu Grav. 27, (2010) 23

24 Raan spectroscopy When asked about his inspiration behind the Nobel Prize winning optical theory, Raan said he was inspired by the "wonderful blue opalescence of the Mediterranean Sea" while he was going to Europe in Iage is in the public doain. Source: Wikiedia Coons. 24

25 Raan spectroscopy Raan scattering: inelastic and nonlinear interaction of photons with phonons Photon phonon = Stokes line Photon + phonon = anti-stokes line laser-detect.co/technology-ethods/ 25

26 Raan spectra of aorphous aterials Aorphous aterials typically have broad Raan peaks Dispersion of local structures and phonon energy Raan spectru of c-si Raan spectru of As 2 S 3 glass 26

27 Exaple: Raan analysis of TeO 2 -Bi 2 O 3 -ZnO glass Raan band (c -1 ) Assignent Bending ode of Te-O-Te linkage in TeO 3 network backbone Bending ode of O-Te O linkages in TeO 4 network backbone 576 Soda-lie glass substrate contribution Vibration of the Te-O bonds in TeO 4 trigonal bipyraid with bridging oxygen Stretching of Te-O or Te=O which contain non-bridging oxygen (NBO) in TeO 3+1 or TeO 3 J. A. Cera. Soc. 98, 1731 (2015) 27

28 Calorietry (theral analysis) Apparatus for easuring anial heat Pierre Louis Dulong, Annales de chiie et de physique (1841) Courtesy of Gallica. Source: Dulong, "Méoire sure la chaleur aniale." Annales de chiie et de physique SER3, T1 (1841): (plate p. iii). 28

29 Differential Scanning Calorietry (DSC) Differential Theral Analysis (DTA) Both techniques involve a saple and an inert reference with known heat capacity both undergoing controlled heating or cooling Heating rate is kept constant for both the saple and the reference, and heat flow to the saple inus heat flow to the reference is recorded Both the saple and the reference undergo identical theral cycle and teperature difference between saple and reference is recorded Saple Reference Saple Reference Heater Heater Heater Coputer control to ensure identical heating rate Theral couples record teperature difference 29

30 Differential scanning calorietry of glass aterials Endotheric Exotheric Differential heat flow dh S R dh CS CR dt dt dt dt Steady state Glass transition Crystallization Melting Area under a DSC peak is proportional to the heat released or absorbed during a phase change Teperature 30

31 Glass transition regie behavior in DSC Cooling rate: 10 C/s Varying reheating rate 1 C/s 0.1 C/s 10 C/s 10 C/s 1 C/s 0.1 C/s Shape of DSC curve at the glass transition regie depends on heating rate and the saple s theral history 31

32 Differential theral analysis of glass aterials Exotheric Endotheric Teperature difference dh S dt K TF T S dt dt 1 dt T T C C dh R dt K dt K TF T R dt dt Glass transition Crystallization Teperature K : theral conductance S R R S Steady state Melting 32

33 Evaluation of glass foring ability FOM for glass stability: Tx Tg T Tx Figure reoved due to copyright restrictions. See Figure 1: Hrubý, A. "Evaluation of glass-foring tendency by eans of DTA." Czech. J. Phys. B 22 (1972): Hruby coefficient Addition of Si increases glass elt viscosity and iproves glass foring ability Czech. J. Phys. B 22, 1187 (1972) 33

34 Suary Diffraction Debye diffraction equation: relation between structure factor and PDF in hoogeneous, isotropic aorphous solids Solving PDF fro experientally easured XRD spectra: corrections and noralization X-ray, electron, and neutron diffraction Raan spectroscopy Broad Raan peaks: phonon energy dispersion Theral analysis DSC vs. DTA: data interpretation Glass transition regie behavior 34

35 MIT OpenCourseWare Aorphous Materials Fall 2015 For inforation about citing these aterials or our Ters of Use, visit: