Rietveld方法原理.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,陈小龙,中国科学院物理研究所,2006.10,杭州,Lecture notes,Rietveld,方法原理,1,Isostructural Compounds,Nd2CuO4 Gd2CuO4,a=0.39419nm a=3.8938nm,c=1.21627nm c=11.8810nm,Z,Nd,=0.353 Z,Gd,=0.349,Nd(Gd),2,XRD patterns of Solid solution,NaSr,4-x,Ba,x,B,3,O,9,(0 x4),:,First cubic borate only with BO,3,Cubic borates are estimated below 1%.,L.Wu,X.L.Chen,et.al.2004,3,Phase transition of BaTiO,3,from tetragonal to cubic at about 132,C,4,YBa,3,B,3,O,9,:Phase transition and structure determination,S.G.:,P6,3,cm,(No.185),a=9.4235(4),c=17.602(1),1100,C,S.G.:,R-3,(No.148),a=13.0441(1),c=9.5291(1),1140,C,X.Z.Li,X.L.Chen,et.al.2004,5,LiAlB,2,O,5:,Search for new SHG materials,B,3,O,7,5-,&AlB,2,O,7,5-,6,Structural Data for LiAlB,2,O,5,7,Final Refinement of New compound of LiAlB,2,O,5,8,Structure vs Temperature:,KCaCO3F,0.8120(3)0.1880(3)0.5 by x-ray data,9,LiSr,4,B,3,O,9:,A comparison between structure determination from single-crystal and powder X-ray diffraction,a=14.9470,S.G:,Ia-3d,(Z,B,/Z,Sr,),2,=(3/38),2,0.6%,Single-crystal:R,int,=0.0745,R,1,(all data)=0.0695,w,R,2,(all data)=0.1887,with weighting scheme:,W=1/,2,(Fo,2,)+(0.0000P),2,+359.71P where P=(Fo,2,+2Fc,2,)/3,SDPD:,R,B,=0.07,R,p,=0.0609,R,wp,=0.0811,R,exp,=0.0314,10,What is a Rietveld Refinement?,-a standard treatment of powder diffraction data to make the final structural model achieve the accepted criterion;,-a best known method that fully makes use of the step-mode scanned data to dig out a lot of structural and other information;,-a procedure for structural solution in nature.,11,What can we get to perform a Rietveld refinement?,Lattice Parameters Quantitative phase Analysis,Atomic Positions Grain size,Atomic Occupancy Incommensurate Structure,Debye Temperatures Structure factors,Crystallinity Phase transitions,Magnetic structures,12,History Review,Rietveld originally introduced the Profile Refinement method(Using step-scanned data rather than integrated Powder peak intensity)(1966,1967),Rietveld developed first computer Program for the analysis of neutron data for Fixed-wavelength diffractometers(1969),Malmos&Thomas first applied the Rietveld refinement method(RR)for analysis of x-ray powder data collected on a Ginier Hagg focusing Camera(1977),Khattack&Cox first applied the RR to x-ray powder data collected on a diffractometer(1977),Conference on Diffraction Profile Anlysis Sponsored by IUCr in Poland,suggested the term“Rietveld Method”(1978),Wiles and Yang developed a general computer program(D.B.W)for both x-ray&neutron diffraction data(fixed wavelength)(1981),Von Dreele,Jorgensen and Windsor extended to the program to the neutron diffraction data(1982),Fitch et al,193 refined parameters,UO2 DAs.4D2O(1982),13,Aminoff Prize,Stockholm,1995,H.M.Rietveld,Acta crystallogr,.,22,151(1967).,H.M.Riveted,J.Appl.Crystallogr,.,2,65(1969).,14,Structural model,Raw data,Rietveld Refinement,Refined model,shift,15,How RM works?,The RM refines a structure by minimizing a quantity through the Newton-Raphson algorithm,where,y,i,is the observed intensity at a certain 2,y,c,i,is the calculated intensity at the same angle,w,i,is a weight,we usually take w,i,=1/y,i,i=1,2,n,=(,1,2,p,),the parameters to be refined.,16,Given a solution,=,opt,(,1,2,p,)that approximately satisfy the above equation.To find a better solution,we begin an iterative process by expanding into a Taylor series,.,17,A,1,=b,1,=,0,+,1,1,is a shift.,18,S,is the scale factor of the phase,L,h,contains the Lorentz,polarisation and multiplicity factors.,F,h,is the structure factor,A,h,is the absorption correction,P,h,is the preferred orientation function is the reflection profile function that models both instrumental and sample effects,19,where,f,i,atomic scattering factor for ith atom,x,i,y,i,and z,i,the fractional coordinates for ith atom,The mean square displacement of the atom in a direction normal to the reflecting planes,20,Where RELAX is relaxtion factors that are used to control the shifts to avoid divergence;,and CC is a multiplier.,21,What we need to perform a RR?,A set of step-mode scanned data,usually 2,=10-120,or more,step,2,=0.02,collecting time is instrument dependent from 1-20s,for laboratory diffractometer;,An initial structural model having roughly accurate lattice,constants,correct space group and approximate atomic positions,22,How we obtain an initial structural model?,-solid solutions usually adopt same structure types of their parent compounds;,NaSr,4-x,Ba,x,B,3,O,9,(0 x4),Compounds with same chemical formula,YBa,2,Cu,3,O,7,and NdBa,2,Cu,3,O,7,but always alert that exceptions are not uncommon,La,2,CuO,4,and Nd,2,CuO,4,Try and error,Ab inito structure determination,23,Is the compound known?Crystallographic Structure Databases,ICSD (Minerals and Inorganics),www.fiz-karlsruhe.de/,Minerals and Inorganic,Over 60000 entries,Cambridge Structure Data Bank,）,www.ccdc.cam.ac.uk,Organics&Organometallics,Over 250000 entries,ICDD diffraction data,http:,&Organic,Over 140000 entries,NIST Crystal Data,www.nist.gov/srd/nist3.htm,Inorganic&Organic,Over 230000 entries,24,A new structural database(2003):,aimed at freely retrieving data,18000 Patterns already!,25,Parameters in PCR file,The parameters in PCR file can be divided into three categories,-,relating only to samples,refinable,such as atomic positions,temperature factors,-relating both to samples and instruments,such as scale factors,FWHM(Full width at half maximum),-user-specified parameters,such as BKPOS,Nba,26,27,Codewords(I),codewords are used to control parameters when to be refined,when to be fixed and when to be constrained and etc.A codeword is formed as,C,=S(10P+CC),Where S stands for the sign mark,P is an ordinal number set by users from 1 to p,the maximum number of parameters,28,Codeword(II),For example,an atom Ca position is(0,0,z)with z to be refined from its initial value 0.1.The codeword in your PCR file looks like the following,Ca1 Ca+2 0.0 0.0 0.1 ,0.0 0.0 120.5,Here,S=1,P=12,and CC=0.5.That means that z of Ca1 is the 12nd parameter to be refined in the iterative process,and x and y of Ca1 occupy special positions not needed to be refined.,29,Codeword(III),Another example:the lattice constants of a tetragonal compound are to be refined.The codeword in your PCR file looks as follows,3.891 3.891 11.732,51.0 51.0 61.0,In this case,constraint is put on,a,and,b,by using the same codeword since,a,=,b,always holds in tetragonal compounds,30,Codeword(IV),One more example:the occupancies of two kinds of atoms at one site are to be refined.Solid solutions are the most common among this kind of refinements.The codewords in your PCR file are set as,Y Y+3 0.8,10.3,Yb Yb+3 0.2,-10.3,Only in this way are the occupancies guaranteed to satisfy,Occ(Y)+Occ(Yb)=1,31,Codeword(V),each parameter usually controlled by one codeword.Be alert that one codeword should be given to two or more parameters that are irrelevant;,-there is no limit to choose ordinal numbers.,But we usually set the first ordinal numbers to global parameters such as zero point,background parameters and the etc.,32,Modeling backgrounds,The background intensity bi at the ith step may be obtained by any of the following three method.,a specified background function,usually a polynomial;,linear interpolation between user-selected points in the pattern,A user-supplied function,33,Control flags,The choice of background type is indicated by a control flag,Comment line(4)Job Npr Nph,Nba,Nex,0 5 1,0,2,Nba:,=0 Refine background with a polynomial,=1 Read background from file COFHIL.bac,=2,3,N linear interpolation between N given,points,34,Where Bm are parameter to be refined,BKPOS is a user-specified parameter,origin of polynomial function,non-refinable.,If 2,=BKPOS,we see b,i,=B,0,Users can look into their data files to set the values of BKPOS,35,Profile functions(I),Gaussian(G),Npr=0,Lorentzian(L)Npr=1,Parameter to be refined:H,k,Full Width at Half Maximum(FWHM),36,H,k,=0.2,37,Profile functions(II),Mod.I Lorentzian,Npr=2,Parameter to be refined:H,k,Mod.I Lorentzian,Npr=3,38,Profile functions(III),Psudo-Voigt,Npr=5,Parameters to be refined:H,k,0,X,0,=shape,39,Pseudo-Voigt functions H,k,=0.2,40,Profile functions(III),Pearson VII,Parameters to be refined:H,k,m,0,X,Y,41,Profile functions(IV),(Mod-TCHZ pV),L(x)and G(x)have different FWHMs H,L,and H,G,Parameters to be refined:H,G,and H,L,42,Full width at half Maximum(FWHM),For Npr=06,H,k,=H,G,For Npr=7,H,L,is required,apart from H,G,43,Typical variations of FWHM vs 2,44,Summary for the parameters to be refined with different profiles,Npr=0,Gaussian:,U,V,W,I,g,3,Npr=5,pv:U,V,W,I,g,0,(Shape),X,5,NPr=6,Pearson VII:,U,V,W,I,g,0,(Shape),X,Y,6,NPr=7,TCHZpv:U,V,W,I,g,X,Y,S,z,6,45,46,Preferred orientations(I),Nor=0,Rietveld-Toraya Model,G,1,and G,2,are refinable parameters,H,is the acute angle between d*,H,and the normal to the crystallites(platy habit),Note:preferred orientation vector Pr1,Pr2 and Pr3 is needed to specify,a priori,by users,47,Preferred orientations(II),Nor=1,modified Marchs Model,G,1,and G,2,are refinable parameters,G,1,1 Needle-like habit,48,49,Systematic line-shift,Bragg-Brentano Geometry,Specimen displacement,Specimen Transparency,SYCOS,SYSIN,:the linear absorption coefficient of the sample,50,WDT,FWHM,WDT5,preferably,10,51,Monochromator polarization correct,Incident angle to a monochromator,CTHM=cos,2,2,=,0.8009 for a graphite monochromator,CuK,52,Asymmetry correction for profiles,P,1,P,2,P,3,and P,4,are parameters to be refined,AsymLim,:peaks below this 2,angle limit,are corrected for asymmetry,53,54,Occupancy,m is the site multiplicity,M is the multiplicity of the general site for a given space group.,For example,KCaFCO3,P-6m2(187),K+1 occupies 1(a)site;O-2 3(k)site;general site 12(o),Occ(K+)=1/12=0.08333,Occ(O-2)=0.25,both atoms chemical occupancy=1.0,55,Agreement Factors(I),Profile Factor,Weighted Profile Factor,Expected Weighted Profile Factor,56,Agreement Factors(II),Goodness of fit indicator,Bragg Factor,Crystallographic R,F,factor,57,Variations of agreement factors and esd.,Hill&Madsen,Powder Diffraction(1987),58,An estimation of S for an ideal refinement,take,S,1 since NP,59,Gaussian,Lorentzian,R.J.Hill and H.D.Flack,J.Appl.Cryst.20(1987)356-361,60,Durbin-Watson statistic parameters,d Q,D,:,positive serial correlation,Q,D,d 4-Q,D,:negative serial correlation,61,Variations of d,eds,R,wp,and R,B,vs cycles,R.J.Hill and H.D.Flack,J.Appl.Cryst.20(1987)356-361,62,Comments on agreement factors,R,F,and R,B,are more indicative of structural model fits,R,p,and R,exp,are more indicative of overall profile fits,R,F,R,B,R,p,and R,exp,are not good indices for the refinements of different patterns,S should be as close as 1,d,is a more sensitive index over R,F,R,B,R,p,and R,exp,At least Rp,Rwp and Rexp should be given when submitting a paper to a journal,63,Quantitative Phase Analysis,where,W,j,is the weight fraction for the jth phase;,S,j,is scale factor for the jth the phase;,Z,j,is the number formula units per cell for the jth phase;,M,j,is the mass of the formula unit;,V,j,is the unit cell volume;,t,j,Brindley coefficient,that comes into effect when the,linear absorption coefficients of phases in powder,differ a lot to each other.,64,KCaFCO,3,CaCO,3,65,Multiphase Rietveld Analysis,66,Result in*.out file,No absorption correction is applied,67,To obtain a satisfactory quantitative phase analysis based on the Rietveld method,we should be cautioned:,-Sample should be carefully prepared:powder is homogeneous in compositions and have a sufficient number of grains with random orientations;,Structures of phases are well known;,Absorption correction is applied whenever the phases differ a lot in their linear absorption coefficients.The Brindley coefficients can be consulted in the,Fullprof Manual,.,68,Calculation of bond length,angle and bond valence sum,69,ESDs,70,Bond valence sum is a good indicator of the structural validity.For details,see,I.D.Brown,Acta Crystallogr.B48,141(1992),71,EPS and Relax factors,Forced termination when shifts10000,Too less sample.Sample should fully cover the sample holder window;,Overflow in low angle region;,Too less angle region 2,120,;,Too large EPS that leads to false minimum;,Improper profile function;,Too less WDT values,.,75,Error messages(I),Hole in Matrix:,the number of parameters to be refined NPR larger than the number of codewords,For example,you set NPR=12,while one codeword 80.5 is missing or 101.0 is mistyped as 11.0,-Negative FWHM:,H,G,2,0,meaningless!Increasing the negative U,V,or W while set smaller Relax values in the ensuing the refinements,76,Error messages (II),-,No scattering factor :atom identifier TYP is not recognizable by Fullprof.,For example,Ca+2 is accepted while Ca2+is not accepted.,Too many reflections:For a given point,there are too many reflections contributing to the intensity that are beyond the softwares capacity.Usually this results from the false FWHM,Invalid integer or Invalid real:Examine the format of parameters,Note:The software does not always give the correct lines where errors occur.Look into the nearby lines!,77,chenhong,MAC MXP18A-HF,FormCon2.0,78,huming,理学,DMAX 2000,79,Refine scale factor S,80,R,wp,=962 138,S=0.5E-2 0.64E-3,81,Refine zero point along with S,82,Rwp=62.8 ZP,0.05,83,Refine background along with S and ZP,84,Rwp=32.9%,85,Refine lattice parameters along with others,86,Rwp=28.9%,87,Refine peak profile along with other parameters,88,Rwp=18.9%,89,Refine asymmetry,90,Rwp=16.8%,91,Refine atomic coordinates:first two atoms Pb and S,the number of parameters to be refined:22,92,Rwp=14.0%,Further refine atomic coordinates of 3 O atoms Rwp=13.1%,93,Refine temperature factors along other parameters,94,Rwp=12.5%,95,R,p,=8.92%,R,wp,=10.8%,R,exp,=6.57%,96,Calculate the bond lengths and bond valences,And the results are stored in*.dis,97,a,b,a,b,c,PbSO,4,98,Fourier synthesis,Set Fou=4 in your Pcr file,PbSO,4,99,R,p,=7.3%-16.6%,5.82%,8.91%,R,wp,=8.2-20.0%,7.83%,10.8%,R,exp,=1.5%-7.0%,4.83%,6.71%,GodF=1.3-7.4,1.6,1.6,Compare with the Rietveld Refinement Round Robin,Total 23 respondents,Background excluded,100,Range mean single crystal this work,a(,)8.4764-8.4859 8.4804(4)8.482(2),8.4818(1),b,()5.3962-5.4024 5.3989(3)5.398(2),5.3997(1),c()6.9568-6.9650 6.9605(4)6.959(2),6.9614(1),Compare with the Rietveld Refinement Round Robin,R.J.Hill,J.Appl.Cryst.25,589(1992),101,Range mean single crystal this work,Pb x 0.1875-0.1883 0.18783(4)0.1879(1),0.18785(7),z 0.1669-0.1683 0.16752(9)0.1667(1),0.16742(10),S x 0.0621-0.0673 0.0642(2)0.0633(6),0.0638(4),z 0.6799-0.6860 0.6838(4)0.6842(7),0.6834(6),O1x 0.902-0.924 0.9083(13)0.908(2),0.9069(11),z 0.585-0.601 0.5945(7)0.596(3),0.5929(14),Compare with the Rietveld Refinement Round Robin,102,Range mean single crystal this work,O2 x 0.177-0.200 0.1850(11)0.194(2),0.1894(11),z 0.523-0.548 0.5398(13)0.543(2),0.5423(14),O3 x 0.071-0.080 0.0778(5)0.082(1),0.0789(6),y 0.018-0.041 0.026(13)0.026(2),0.0214(9),z 0.806-0.819 0.8139(7)0.809(2),