Understanding and possible prediction of material physical properties depends upon the knowledge of the local atomic arrangement and crystal structure. Study of nanocrystalline or amorphous materials can be performed with techniques like Pair Distribution Function (PDF) that is used to solve local atomic arrangement by using X-Ray, neutron or electron diffraction (ED) sources. ED related PDF (e-PDF) in Transmission Electron Microscope (TEM) has the advantage over X- Ray PDF technique that allows studying ordering of nanocrystalline materials at very small local scale (nm scale instead of mm ) by collecting (ED) patterns in very short time (ms instead of hours with conventional X-Ray Au or Mo sources). e-PDF has been recently applied to study nanoparticles and amorphous materials and has been established that e-PDF patterns match well equivalent X-Ray PDF patterns. However, local structure information quality based on e-PDF analysis, may be affected by dynamical effects present in ED that affect e-PDF peaks height. In this work we apply e-PDF analysis to study local order on various amorphous and crystalline materials ; in particular we study the influence of Precession Electron Diffraction (PED) to obtain reliable e-PDF local order analysis by lowering dynamical electron diffraction effects.
Electron pair distribution function(e-PDF) with TEM
Use of Pair Distribution Function (PDF) analysis enables to understand local atomic order in nanocrystalline & amorphous materials , using X-Ray , Neutron or Electron Difffaction in TEM microscope.
In our work we have used Libra (120 kv) TEM microscope (IIT Pisa) to generate good quality ED patterns registered on 2kx 2k CCD camera. PED device (Digistar) from NanoMEGAS was attached to the microscope.
Principle of the PDF. Inter-atomic distances r cause maxima in the PDF G(r). The area below the peaks correspond to the number of neighbors, scaled by the scattering power of the respective atoms
Advantages of using e-PDF for local structure studies
(Top) e-PDF pattern of polycrystalline material showing various interatomic distances (peak heights) over long range order
(bottom) e-PDF pattern of an amorphous material showing local order vanishes at about 5 Å
PED Digistar from NanoMEGAS and (top right) Electron Diffraction PDF of nanocrystalline gold thin film and (bottom right) X-ray PDF of same material. e-PDF and X-Ray PDF are very similar.
e-PDF in TEM has the advantage over X- Ray PDF that allows studying ordering of nanocrystalline materials at very small local scale (nm instead of mm) and allows collecting ED patterns in very short time (ms instead of hours with conventional X-Ray Au or Mo sources).
e-PDF with TEM to study local order of amorphous materials
Opal mineral can be nanocrystalline or amorphous and consists of random stackings of SiO2 (cristobalite and tridymite) over very short range scale. ED pattern (top left) of an opal crystal taken with 120 kv TEM and its corresponding e-PDF pattern showing no long range order beyong 7 Å (blue arrow). Red arrows correspond to 1.535 Å (Si-O), 2.589 Å (O-O) 4.153 Å (Si-O/O-O) and 4.736 Å (O-O/Si-O/Si-Si) interatomic distances.
e-PDF for phase identification analysis
In order to identify the presence of cubic or hexagonal phase on NaYF4 nanoparticles, we applied e-PDF analysis on powder NaYF4 pollycrystalline ED pattern ; after comparison of e-PDF peaks with calculated interatomic postitions of both cubic and hexagonal phases, e-PDF correlation analysis shows the studied phase is mostly hexagonal. Our results have been confirmed independently with ASTAR orientation /phase mapping technique 
e-PDF with Precession Electron Diffraction
(a) Amorphous Opal ED pattern (no precession applied) and (b) with 2º precession angle (c) Opal ED line scans without and with various precession angles (d) corresponding Opal e-PDF patterns without and with various PED angles; there is no any difference observed at e-PDF patterns with 2º PED angle in relation with 0o PED
Dynamical effects present in ED although affect the height of e-PDF peaks do not affect their positions that correpond to accurate interatomic distances 
We have used Precession Electron Diffraction (PED)  that is known to diminish dynamical interactions to evaluate its influence on the e-PDF peak height.
(a) NaYF4 nanoparticles ED pattern (no precession applied) and (b) with 2º precession angle (c) NaYF4 ED pattern line scans without and with various precession angles (d) corresponding e-PDF patterns without and with various PED angles; although PED does not visibly affect ED patterns, e-PDF with 2º PED angle shows an important increase of all e-PDF peak heights in relation with 0º PED
Case study: reliable local order (coordination number) with e-PDF Precession Difraction
In order to quantify precisely the PED influence on NaYF4 e-PDF patterns we compared the experimentally obtained total area (obtained with and without precession) around the e-PDF peak at 2.36 Å (Na/Y- F bonding). Results shown on corresponding table are very promising as show that use of Precession Electron Diffraction leads to very reliable information on the number of neighbours (coordination number) extracted from e-PDF peaks.
(left) e-PDF obtained from ED pattern (with and without PED), arrow show peak at 2.36 Å. Table shows experimental (with and without PED) Versus theoretical coordination number
Our results show that e-PDF (electron Pair Distribution Function) analysis with TEM can be very effective technique to study local crystal order (eg for nanoparticles and amorphous materials) and help to indentify nanocrystalline phases. The presence of dynamical diffraction affects ED intensities and e-PDF peak height but does not affect e-PDF positions that corresond to interatomic distances. Our work shows that PED application affects significantly e-PDF peak height (case NaYF4 nanocrystals) and leads to very reliable information on local coordination number. Such results may encourage a more general use in TEM of Precession Electron Diffraction and e-PDF combination for nanoparticles and disordered materials study.