Evaluation of truncation methods for accurate centroid lattice parameter determination

Taylor, J.; Mack, M.; Parrish, W.

doi:10.1107/s0365110x64003164

Cited by 18 publications

(8 citation statements)

References 4 publications

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“…To co mple te the de finition of the ce ntroid given by eq (1.1) we mu st s pecify the truncation limits. Taylor, -------Mack , and Parrish [14] have discussed at length several alternative definitions from the viewpoint of crystallographers. They recommended using a specified interval symmetric about the centroid; this interval may be located by s uccessive approximations.…”

Section: S Variance Of Data Pointsmentioning

confidence: 99%

“…It should be noted that crystallographers [14] who have employed the centroid have always assumed an infinite range in the above definition (which is essential in order to apply the convolution theorem for addition of centroids). Experimentally it was, of course, necessary to infer the centroid value by extrapolation from a finite truncated portion of the curve.…”

Section: Profile Features For Wavelength Criteria a The Centroidmentioning

confidence: 99%

“…tical error of the centroid; Parrish [14] and his coworkers studied, both theoretically and experimentally, the use of the centroid for lattice parameter .measurements, including the effect of truncation error. Merrill and DuMond [17 J analyzed the problem of fitting a Lorentzian to the data points by least squares and outlined a method for obtaining the resulting statistical error of the peak.…”

Section: Previous Investigationsmentioning

confidence: 99%

“…To date the peak has been used almost exclusively in x-ray spectroscopy whenever a defining feature was explicitly specified. Some crystallographers [14] and y-ray spectroscopists [15] have employed the centroid and the median in a limited number of cases.…”

Section: Figures In Bracket S Indi Cate the Literature References At mentioning

confidence: 99%

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Effect of statistical counting errors on wavelength criteria for x-ray spectra

Thomsen¹,

Yap²

1968

J. RES. NATL. BUR. STAN. SECT. A.

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Various features of the spectral profil e of an x-ray on e ca n be meas ured with an uncertainty whi ch is onl y a s mall fraction of the observe d line width. With rece nt improve me nts in me asure me nt tech· niqu es, statisti cal errors due to th e ra ndom Au ctuations of th e intensities in counter recordin gs may beco me signifi cant. The prese nt study co nsiders th e effec t of s uch errors on se ver al features of the line profil e whi ch could be used for definition of its wave length. These may be broadly classified into three groups, viz , th e peak, the centroid , and the median. In th e prese nt an alysis the s tatistical eu ors associated with these features are co mpared theore ticall y, with the ass umption of negligible error in angul ar meas ureme nt. Certai n sys temati c errors are also brie Ay exa min ed. The effects of trun cation range, asymmetry, and bac kground intensit y are co ns idered, as well as possibl e optimi z.ation of th e data-taking procedu re.In general, fT , the standa rd dev iation of the wave length , is give n by fT/W = F/(lvn' /2, where IV is the full width at half-maximum intensity, Iv the peak intensit y, T the total countin g ti me, and F a dim ensionless fac tor of the order of unity. Thu s. F may be rega rd ed as a fac tor of me rit for comparing th e various cases, a low valu e of F bein g des irable . Wh en the form of th e on e pro fil e is known a priori , it is usually bes t to make use of thi s kn owl edge; e.g. , a Lore ntzi an ca n be thu s fitted with F "" 0.8 for any of the three wavelength features. Us in g optimize d truncation ranges a nd in cludin g the error in locating end points, one obtain s ap prox im ate ly thi s sa me F for the ce ntroid or medi an even without prior knowl edge of the profil e. In th e latt er case the val ue of F for the pea k usuall y ra nges from abo ut 1.6 to 2. 1. Howeve r, the peak is less subject to c ertain syste mati c errors a nd is prefera ble from th e view point of sim plic ity and hi storical precede nt. It is reco mmen ded that use of the pea k be co ntinued at present; further stud y of th e proble m from the viewpoi nt of atomi c e nergy level interpretation would be desirable.

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Section: S Variance Of Data Pointsmentioning

confidence: 99%

Section: Profile Features For Wavelength Criteria a The Centroidmentioning

confidence: 99%

Section: Previous Investigationsmentioning

confidence: 99%

Section: Figures In Bracket S Indi Cate the Literature References At mentioning

confidence: 99%

See 2 more Smart Citations

Effect of statistical counting errors on wavelength criteria for x-ray spectra

Thomsen¹,

Yap²

1968

J. RES. NATL. BUR. STAN. SECT. A.

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show abstract

“…Crystallographers have frequently employed the centroid of experimentally observed diffraction profiles in the determination of crystal grating constants (Pike & Wilson, 1959;Taylor, Mack & Parrish, 1964). From a mathematical standpoint it would be desirable to deal with the centroid of the entire profile, i.e.…”

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confidence: 99%