Phase invariants are important pieces of information about the atomic structures of crystals. There are several mathematical methods in X-ray crystallography to estimate phase invariants. The multi-wave diffraction phenomenon offers a unique opportunity of
FIG.2:(a)Simulatedinstrumentalbroadeninge ectson -scans.SimulationparametersusedintoEq.
(1):δT= 2.6 ,χ=32 ,andp=[0.0012 ,1.0,0.8,0.0,67.683 ,wG]wheretheinstrumentalwidthvalues,wG,areindicatedbyarrows. = 0.(b)TheoreticalaccuracyinphasemeasurementsasafunctionoftheinstrumentalwidthwG,andamplituderatioR.TheE0(δT)curveswereobtainedby ttingthepro lesin(a)withwG=0.001 (opencircles)andwG=0.006 (closedcircles).The ttingshavebeencarriedoutbytheDEAwithintheallowedranges:p=[0.0008 :0.0012 ,R,0.2:1.0,0.0, 0±0.012 ,0.001 :0.007 ]whereR=1.0(blacklines)orR=[0.6:1.4](graylines).De nitiononthe E0/ δT=0positiongivestheaccuracyonδT.
FIG.3:Absolute-meandeviationasafunctionofδT,E0(δT),obtainedfor(a)thesimulatedscansand(b)theexperimentalscansinFig.1.Allcurvesarenormalizedbyitsminimumvalueandaddtoanintegerforbettervisualization.Thecurveswithminimaequalto1,2,3,4,5,and6correspondtothosescanswithχ=8 ,12 ,16 ,20 ,24 ,and32 ,respectively.Allowedrangeisp=[0.0010 :0.0014 ,R,0.0:1.0,0.0:3v2, 0±0.012 ,0.001 :0.006 ]wheretheRvaluesorrangesareshowninthe gureforeachcase,andv2changestheupperlimitofthebrangewiththepolarizationangle;herev2=sin2χ.
-XRD1-1264,FAPESP(proc.No.02/10387-5),andCNPq(proc.No.301617/95-3and150144/03-2).
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