Nanoparticle size distribution estimation by a full-pattern powder diffraction analysis

Cervellino, Antonio; Giannini, Cinzia; Guagliardi, Antonietta; Ladisa, Massimo

doi:10.1103/physrevb.72.035412

Cited by 29 publications

(24 citation statements)

References 40 publications

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“…Their shape has been fitted in detail assuming a size distribution of sharply defined spherical magnetic domains. A magnetic reflection is then represented as the distribution-weighted sum of the peak profiles of domains of different sizes, each of them being convoluted with the instrument resolution function [14]. Two types of distributions, namely, the log-normal and gamma distributions, were used for the fit of the data shown in Fig.…”

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Spin Dynamics and Magnetic Order in Magnetically FrustratedTb2Sn2O7

et al. 2006

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We report a study of the geometrically frustrated magnetic material Tb 2 Sn 2 O 7 by the positive muonspin relaxation technique. No signature of a static magnetically ordered state is detected while neutron magnetic reflections are observed in agreement with a published report. This is explained by the dynamical nature of the ground state of Tb 2 Sn 2 O 7 : the Tb 3 magnetic moment characteristic fluctuation time is ' 10 ÿ10 s. The strong effect of the magnetic field on the muon-spin-lattice relaxation rate at low fields indicates a large field-induced increase of the magnetic density of states of the collective excitations at low energy. DOI: 10.1103/PhysRevLett.96.127202 PACS numbers: 75.40.ÿs, 75.25.+z, 76.75.+i Magnetic materials with antiferromagnetically coupled spins located on triangular motifs exhibit geometrical magnetic frustration because their spatial arrangement is such that it prevents the simultaneous minimization of all the interaction energies [1]. The frustration, which leads to a highly degenerate ground state, forbids magnetic order to occur. Perturbations to the nearest-neighbor exchange interaction, such as exchange interactions extending beyond nearest-neighbor magnetic atoms, dipole coupling, or magnetic anisotropy, are believed to be responsible for the magnetic order observed in some compounds [2]. Typical examples are given by the spinel structure oxide [6]. A prerequisite for understanding the unanticipated behavior of these latter systems is a careful characterization of their dynamical properties.Here we show that positive muon-spin relaxation ( SR) and ND results in the ordered phase of Tb 2 Sn 2 O 7 can be simultaneously accounted for only if the Tb 3 moments are strongly dynamical. An independent and consistent time scale is obtained from a careful analysis of the neutron data. In addition, the initial strong and counterintuitive increase of the muon relaxation rate when a magnetic field is applied indicates an increase of the density of magnetic excitations at very low energy.Tb 2 Sn 2 O 7 crystallizes with the cubic space group Fd 3m. Rietveld refinements of powder x-ray and ND patterns yield the lattice constant a 10:426 A and the free position parameter allowed by the space group for the 48f site occupied by oxygen, x 0:336 [6]. Magnetic measurements point to a magnetic transition at 0.87 K and to strong antiferromagnetic interactions as deduced from the large and negative Curie-Weiss constant CW ÿ12 K [13]. Powder ND indicates a structure with both ferromagnetic and antiferromagnetic components below T sr 1:3 1 K where short-range magnetic correlations which are not liquidlike appear [6]. A steep increase of the Tb 3 magnetic moment Tb and correlation length L c is observed around T lr 0:87 K, where a peak is seen in the temperature dependence of the specific heat C p T . We present below (i) C p T data recorded using a dynamic adiabatic technique, (ii) ND measurements carried out at the cold neutron powder diffractometer DMC of the SINQ facility at the Paul Scherrer I...

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Spin Dynamics and Magnetic Order in Magnetically FrustratedTb2Sn2O7

et al. 2006

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“…This adds small anisotropic contributions on peaks at small diffraction angles. Nanometer-sized fcc-Cu clusters are modeled as in [26], assuming near-spherical clusters with a log-normal diameter distribution, in agreement with TEM results. Diameters ranged from 0.28 to 102 nm with 0.56 nm step.…”

Section: Xrd Data Analysis and Simulationsmentioning

confidence: 95%

Cluster formation, evolution and size distribution in Fe–Cu alloy: Analysis by XAFS, XRD and TEM

Cammelli

Degueldre

Cervellino

et al. 2010

Nuclear Instruments and Methods in Physics Research Section B:

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“…One important issue is that disorder analysis of partially periodic systems needs a statistical description of the defectiveness, while the Debye method is intrinsically deterministic and can be made applicable to stochastically variable atomic structures. At the larger sizes, still in the nanometric range (10-30 nm), shape convolution methods have also proved to be effective [180,181], although with precise limitations [180].…”

Section: X-ray Powder Diffractionmentioning

confidence: 99%