Diffraction studies in non crystalline systems

Elements of refinement - BackgroundSmoothInelastic and resonantStructuredThermal Disorder Scatteringnj2 n0 r0m0KtjIj2 2MI f (1 e )TDS•Acoustic phonons peaks at Braggreflections•Optical and multiphonon processeshave a smooth variationIn Debye modelITDSIhkl2MalnRgm Rhkl24 Jan 2006 Refresher course 5

Powder Diffraction - AdvantagesSingle Crystal•Determine Crystal Structure•Fundamental physical propertiesPowder•Wider investigation ofphysical, chemical &mechanical properties•Easier to make in largequantity•Applications

Structure factorF N f exp[ 2i(hx ky lz )]exp[ M]KjjjjjjjMj 28u2sSin222usis the root-mean square thermal displacement1/24/2012 7Discussion meeting on synchrotronutilization

Rietveld method- Calculate Intensityyci s L F (2 2) P Akkk2ikkyBackgroundbiAbsorption factorScale factorPreferred orientation functionStructure factorReflection profile functionLorentz, polarization, and multiplicity factor1/24/2012 8Discussion meeting on synchrotronutilization

Nd 0.5 Sr 0.5 MnO 3Effect of reducing the particle size800 nm40 nm

The structure factor in the case of crystalline materialsSG jfjexp( iG rj)S f exp[ i2( hxky lz)]Gjj1/24/2012 10Discussion meeting on synchrotronutilization

In the absence of long range order -Non crystalline solids – Glass, liquids….Short range orderRadial distribution function - paircorrelation function# of atoms in a spherical shell ofunit thickness at a distance r froma reference atomDiffraction diffuse in natureG(r) = 4πrρ o [ρ(r)/ρ o -1]ρ(r) and ρ 0 are the local andaverage atomic densities1/24/2012 11Discussion meeting on synchrotronutilization

Reciprocal lattice vector G replaced by arbitrary scattering vectors, Δk=k’-kS( k) f mexp( ikrm)mISSmnfmfnexp[ ik(rm rn)]( I f f sin Kr ) /mnmnmnKrmn1/24/2012 12Discussion meeting on synchrotronutilization

S (K) = I/Nf 2Liquid structure factorN - # of atoms, f – Atomic form factorRadial distribution function, g(r)g(r)112 2 r0dK[S(K)1]K sinKr1/24/2012 13Discussion meeting on synchrotronutilization

I(q)q = 4π sinθ/λÅ -1G(r) 2 / qmaxq0q[S(q)1]sin(qr)dq1/24/2012 14Discussion meeting on synchrotronutilization

1/24/2012 15Discussion meeting on synchrotronutilization

G(r) 2 / qmaxq0q[S(q)1]sin(qr)dqq max should be at least 20 Å -1 possible only with synchrotron or MoRemove air background, sample holder, correct for absorption effects, ifanyCorrect data for Compton scattering1/24/2012 16Discussion meeting on synchrotronutilization

•RAD•PDFX•RMCPOW1/24/2012 17Discussion meeting on synchrotronutilization

1/24/2012 18Discussion meeting on synchrotronutilization

Neutron Scattering - Elemantary• Neutron interacts with nuclei• It has a magnetic moment

Experimental facilities in Dhruva24 Jan 2006 Refresher course 20

The measure of the isotropic size effectsize(gaussian) 180 Zin Angstromssize(lorentzian)360 2YAnisotropic broadening of size – only lorentzian component is considered andvarious models are chosen through the parameter F24 Jan 2006 Refresher course 21