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Metodo Rietved
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Roberto R. de Avillez 2004 1
Mtodo de Rietveld-Quantitativo
tempoVMZ
mS
ppp
pp ..
pkpkpi*kpkp
kkp
ppbici A.P)22(F.F.Lsyy +=
Intensidade Calculada de um material contendo muitas fases:Howard e Hill, Howard e Bish.
Fator de Escala proporcional massa
de cada fase e ao tempo
Roberto R. de Avillez 2004 2
CeO2 + ZrO2
Sonia Letichevsky, Marco A. Fraga, Lucia G. Appel e M. Isabel Pais da Silva
Coprecipitation of mixed oxides and solid solutions from Ce(NO3)3 e (NH4)2Ce(NO3)6
XDR: CuK, 40kV, 30mA, graphite monochromator, Bragg-Brentano geometry.
Roberto R. de Avillez 2004 3
CeO2+ZrO2+MgO* (internal standard)
Roberto R. de Avillez 2004 4
CeO2*+ZrO2+MgO*
Roberto R. de Avillez 2004 5
CeO2*(cs)+ZrO2+MgO*
Roberto R. de Avillez 2004 6
CeO2*(cs)+ZrO2*(cs)+MgO*
Roberto R. de Avillez 2004 7
CeO2*(cs)+ZrO2*(cs)+MgO*
Roberto R. de Avillez 2004 8
Results: CeO2+ZrO2
Rwp= 31,30
25,5
74,5
%Mass
GOF= 1,10Rexp= 28,46Absorption= 499,9
6,15,259ZrO2
15,15,412CeO2
Crystallite size (nm)
Lattice Parameter (Angstron)
Phase
Roberto R. de Avillez 2004 9
(Ce,Zr)O2 + MgO
Roberto R. de Avillez 2004 10
Resultados do Ajuste: (Ce,Zr)O2
GOF= 1,10Rwp= 30,49Rexp= 27,59Absoro= 498,7
-0-ZrO2
6,81005,349(Ce,Zr)O2
Tamanho do Cristalito
(nm)
%MassaParmetro da rede
cristalina (Angstron)
Fase
Ce sublattice occupation: 0,74 Ce + 0,26 Zr
Roberto R. de Avillez 2004 11
Quantitative analysis of amorphous phase
Rafael Cardoso, Maria Cecilia de S. Nobrega
Porcelains for dental prostheses
XDR: CuK, 40 kV, 30 mA, graphite monochromator
Roberto R. de Avillez 2004 12
Rietveld Method-Internal standard
mmm ps =+
1=+ ca ww
( )( )pp
cc
s
pc ZMVS
ZMVSmm
w =
Sample with amorphous + crystalline materials
Initial mass of the sample: ms
Internal standard mass, mp
Roberto R. de Avillez 2004 13
Dental porcelain
Roberto R. de Avillez 2004 14
Quantitative analysis of leucite and amorphous
(73,7)0,1445Original sample
(amorphous)
26,340,95LeuciteK2O.Al2O3.4SiO2
59,050,0263Al2O3
%mass, in the original sample
%mass, determined
by XDR
Mass, gPhase
Roberto R. de Avillez 2004 15
Lattice parameter changes of Zeolites
Bojan Marinkovic, Paula M. Jardim, Fernando C. Rizzo Assuno, Alvaro Saavedra, Lam Y. Lau, Michael Knapp e Carsten Bhtz.
The influence of the temperature on the crystal lattice of ZSM-5 zeolite.
DRX: Luz Sincrotron, HAZYLAB, = 0.9088 A, Debye-Scherrer.
Roberto R. de Avillez 2004 16
Zeolite Structure
Roberto R. de Avillez 2004 17
c
a
b
Estrutura cristalina da ZSM-5
ZSM-5 Crystalline Structure
Roberto R. de Avillez 2004 18
ZSM-5 Results
Roberto R. de Avillez 2004 19
4.4 4.6 4.8 5.0 5.2 5.4 5.610000
20000
30000
40000
50000
Cou
nts
2
ZSM-5
40oC 80oC 120oC 160oC 320oC
13.0 13.2 13.4 13.6 13.8 14.0 14.2 14.4 14.6 14.8 15.010000
20000
Cou
nts
2
ZSM-5
40oC 80oC 120oC 160oC 320oC
1 23
45
6
ZSM-5: XRD as a function of the temperature
Roberto R. de Avillez 2004 20
Negative thermal expansion
0 200 400 600 800 10005260
5280
5300
5320
5340
5360
5380
5400
aps o resfriamento
volu
me
da c
lul
a un
itria
(A3 )
Temperatura (oC)
Unit cell volume as a function of temperature
Roberto R. de Avillez 2004 21
Crystallite size distribution
Bojan Marinkovic, Alvaro Saavedra, Fernando C. Rizzo Assuno
Crystallite size distribution in a mixture of Bohemite, prepared by CENPES-PETROBRAS.
Materials Research-Revista Ibero Americana de Materiais, So Carlos, 4, 1-6 (2001).
XDR: CuK, graphite monochromator, Bragg-Brentano geometry
Roberto R. de Avillez 2004 23
Warren-Averbach method
Advantages Separation of the contributions from the
crystallite size and deformation (distortion) Determination of the crystallite size
distribution Difficulties
Decomposition of the peak in Fourier series Requires the deconvolution of the equipment
and sample effects Requires a standard sample
Roberto R. de Avillez 2004 28
Results for the Crystallite Size Distributions
Warren-Averbach Balzar Enzo et al.Sample Dv Ds 1/2 Dv Ds 1/2 Dv Ds 1/2 80 53 43 0.0011 61 63 0.0165 61 51 0.0018 200 143 103 0.0005 242 125 0.0017 245 125 0.0002Mixture 106 64 0.0008 129 64 0.0035 128 78 0.0005
Mixture is a 50 w% of each nominal sample.Crystalite sizes are in ngstrons.
1/2 is calculated at Dv/2.
Roberto R. de Avillez 2004 29
Geometria associada ao feixe de Raios-X
Colimador de Raios-X