Structural transformations in nanomaterials


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Structural transformations in nanomaterials

  1. 1. Structural transformations in nanomaterials Deepak Varandani
  2. 2. Nanomaterials <ul><li>Materials with structural elements which have at least one dimension less than 100 nm </li></ul><ul><li>Polycrystals with finest grains and extremely high fraction of boundaries </li></ul><ul><li>Quantum confinement of charge carriers </li></ul><ul><li>Larger fraction of surface atoms </li></ul><ul><ul><li>Lead to significantly altered properties </li></ul></ul>Characteristic features Definition
  3. 3. Boundary/Interface volume fraction d= 5 nm V.F.= 50 % d= 12 nm V.F.= 50 % d Δ
  4. 4. Structure of boundaries <ul><li>Adjacent misoriented crystallites separated by grain boundaries </li></ul><ul><li>Boundaries carry the crystallite geometric mismatch </li></ul><ul><ul><li>Dislocations, Vacancies </li></ul></ul><ul><li>Coarse grained polycrystals </li></ul><ul><li>Volume fraction extremely low (<1%) </li></ul><ul><li>Low angle, high angle, non-equilibrium, amorphous </li></ul>
  5. 5. Structure of….. <ul><li>Nanocrystals </li></ul><ul><li>Volume fraction high. Triple junctions important </li></ul><ul><li>Conflicting reports </li></ul><ul><ul><li>Long-range stresses, frozen-gas like behaviour, reduced density, high energy </li></ul></ul><ul><ul><li>Well ordered, low energy, small excess volumes </li></ul></ul><ul><ul><ul><li>Structure mostly non-equilibrium </li></ul></ul></ul><ul><li>Boundary structure crucially depends on synthesis conditions </li></ul><ul><li>Affects the structure of the crystallites they surround </li></ul>
  6. 6. Structural transformations <ul><li>Solids exist in different structural phases depending on temperature, pressure and other ambient conditions </li></ul><ul><li>In nanomaterials size is an additional variable controlling structure </li></ul>amorphization Nanomaterials allotropic transformations lattice distortion metastable phases crystallites/grains
  7. 7. Lattice distortion The variation in Pd (111) peak with the nanoparticle size, showing the size induced lattice contraction Variation of Debye Waller parameter with grain size in Se <ul><ul><li>Unit cell dimensions </li></ul></ul><ul><ul><li>Debye-Waller parameter </li></ul></ul><ul><ul><li>Debye temperature </li></ul></ul>Pd nanoparticle layers Se nanoparticle layers Zhang 1997 Aruna 2005 <ul><ul><li>Lattice expansion or contraction </li></ul></ul>
  8. 8. Metastable phase stabilization Normalized unit cell volume (N.U.C.V.) as a function of particle size for different phases of Al 2 O 3 Mole percentage of tetragonal phase in BaTiO 3 as a function average particle size Lattice expansion along with structural transformation in Al 2 O 3 nanoparticles Cubic metastable phase in BaTiO 3 Kwon 2006 Ayyub 1995
  9. 9. Theoretical considerations <ul><li>Interface driven structural transformations </li></ul><ul><ul><li>Nanocrystallites enveloped by highly non-equilibrium grain boundaries </li></ul></ul><ul><ul><ul><li>reduced density or excess volume </li></ul></ul></ul><ul><ul><ul><li>vacancies, vacancy clusters, extrinsic dislocations </li></ul></ul></ul><ul><ul><li>Defects generate stress fields </li></ul></ul><ul><ul><li>Atoms displaced from equilibrium positions due to stresses </li></ul></ul>
  10. 10. Interface driven….. <ul><li>Square shaped grains with orthogonal boundaries </li></ul><ul><li>Stress due to vacancy and vacancy clusters  x -3 , . x is the distance from the defect center </li></ul>a 0 = perfect lattice interatomic separation ξ = mean grain boundary width Δ V= excess grain boundary volume d=crystallite diameter <ul><li>Lattice distortion depends on a 0 and microstructure </li></ul><ul><li>Distortion mainly in thin layer near boundary </li></ul>Qin 1992
  11. 11. Thermodynamic treatment <ul><li>G=U-TS+PV…………….Volumetric free energy </li></ul><ul><li>G=U-TS+(P+ Δ P)V+ γ A …….. Size independent </li></ul><ul><li>γ A= Surface free energy </li></ul>U=internal energy T=temperature, P=pressure, V=volume, A=area Δ P=excess internal pressure due to surface stress γ =surface energy density <ul><li>Free energy G decides which phase is stable </li></ul><ul><li>G is modified for small particles </li></ul>Gilbert 2003
  12. 12. Thermodynamic…… <ul><li>At small sizes metastable phases may have low total G due to low γ </li></ul><ul><li>Thus phase inversion at nanodimensions is possible </li></ul>Size-dependence of structure in Co nanoparticles Ram 2001 Structure Size Surface energy density (J/m 2 ) hcp (bulk stable) fcc (metastable) bcc (metastabe) 10-20 nm 2-5 nm 2.79 2.73 2.73
  13. 13. Thermodynamic …….. <ul><li>Co nanoparticles </li></ul><ul><li>Thus lower surface energy ensures that below a critical size fcc or bcc phase is stabilized in preference to hcp phase </li></ul>Sample Lattice parameters (nm) Lattice area (10 −2 nm 2 ) Lattice volume (10 −3 nm 3 ) Lattice surface energy (10 −20 J) Bulk hcp structure fcc structure a=0.2507 c=0.4070 a= 0.3545 93.90 75.40 66.50 44.55 261.98 205.85 bcc structure fcc structure a =0.2840 a=0.3540 48.39 75.19 22.91 44.36 132.11 205.27 fcc structure a=0.3535 74.98 44.17 204.70
  14. 14. Amorphization <ul><li>G c <G A +G D </li></ul><ul><li>G c =Free energy of crystalline phase </li></ul><ul><li>G A =Free energy of amorphous phase </li></ul><ul><li>G D =energy increase due to defects </li></ul><ul><li>In nanomaterials the anti-site disorder & anti-phase boundaries increase G d , resulting in amorphization </li></ul>
  15. 15. Universal thermodynamic approach <ul><li>P l -P o =2 γ /r </li></ul>P l =pressure inside P o =pressure outside γ =surface tension/energy r=radius <ul><li>As size decreases metastable phase region is driven into its strongly unstable region due to the shift in the phase boundary line </li></ul><ul><li>In fine particles internal pressure increases due to Laplace-Young effect </li></ul>Wang 2005 P(r,T)=a+bT-2 γ /r
  16. 16. Bond-OLS correlation mechanism <ul><li>Atoms at surface suffer bond order loss </li></ul><ul><li>Spontaneous relaxation of rest of bonds: Contraction or expansion </li></ul><ul><li>Reduced binding energy and increase in bond strength </li></ul><ul><li>In nanomaterials effect is significant </li></ul>c i = contraction (<1) or expansion (>1) factor for the ith layer (i≤3) b i , E B (b i ) are respectively the bond length and the binding energy of the ith atomic layer of atoms b, E B (b) are respectively the bond length and the binding energy of the bulk atoms z i = coordination number of the ith layer m = a parameter which varies with the nature of the bond, being equal to 1 for elemental solids and 4 for compounds and alloys. Sun 2002
  17. 17. Bond-OLS …….. Δ b= lattice distortion  i = N i /N= weighting factor The bond-OLS correlation mechanism as applied to the case of lattice contraction in Ni, Cu and Ag. Agreement is reached by taking z 1 =4 (c 1 =0.88, 0.9), z 2 =6 (c 2 =0.96, 0.97) and m=1 (Sun 2002).
  18. 18. Conclusions <ul><li>Boundary component critically influences structure </li></ul><ul><li>Boundary defects generate stress fields, leading to static distortion of lattice </li></ul><ul><li>Metastable phases stabilized below a critical crystallite size: Explained using free energy considerations </li></ul><ul><li>UTA and BOLS mechanism commonly invoked to explain structural transformations </li></ul><ul><li>Need to recognize the role of synthesis conditions </li></ul><ul><li>Size calculated using different techniques. Unambiguous comparison difficult </li></ul>
  19. 19. References <ul><li>H. S. Kim, Y. Estrin and M. Bush, Acta Mater. 48 , 493 (2000) </li></ul><ul><li>I. Aruna, B. R. Mehta and L. K. Malhotra, Applied Physics Letters 87 , 103101 (2005) </li></ul><ul><li>Y. H. Zhao, K. Zhang, and K. Lu*, Phys. Rev. B 56 , 14322 (1997). </li></ul><ul><li>Pushan Ayub, V. R. Palkar, Soma Chattopadhyay and Manu Multani, Physical Review B 51 (9) , 6135 (1995) </li></ul><ul><li>Soon-Gyu Kwon, Kyoon Choi, Byung-Ik Kim, Materials Letters 60 , 979 (2006) </li></ul><ul><li>W. Qin, Z. H. Chen, P. Y. Huang and Y. H. Zhuang, Jl. Alloys and Comp. 292 , 230 (1999) </li></ul><ul><li>Benjamin Gilbert, Hengzhong Zhang, Feng Huang, Michael P. Finnegan, Glenn A. Waychunas and Jillian F. Banfield, Geochem. Trans. 4 , 20 (2003) </li></ul><ul><li>S. Ram, Materials Science and Engineering A 204-306 , 923 (2001) </li></ul><ul><li>C. X. Wang, G. W. Yang, Materials Science and Engineering R 49 , 157 (2005) </li></ul><ul><li>Chang Q Sun, B. K. Tay, X. T. Zeng, S. Li, T. P. chen, Ji Zhou, H. L. Bai and E. Y. Jiang, J. Phys. Condens. Matter 14 , 7781 (2002). </li></ul>