The anomalous wide angle X-ray scattering technique was used to determine
the partial structure factors and then the partial radial distribution
functions for vacuum evaporated Cd—As amorphous films containing 41 and
74% at. As. The experiments were performed using synchrotron radiation
tuned near the As and Cd absorption edges. The obtained structural information
about the individual Cd—Cd, Cd—As and As—As correlations shows
that As and Cd remain almost tetrahedrally coordinated and suggest a certain
degree of chemical disorder of the investigated samples

Burian, Andrzej

Acta Physica Polonica A

English

The anomalous wide angle X-ray scattering technique was used to determine the partial structure factors and then the partial radial distribution functions for vacuum evaporated Cd-As amorphous films containing 41 and 74% at. As. The experiments were performed using synchrotron radiation tuned near the As and Cd absorption edges. The obtained structural information about the individual Cd-Cd, Cd-As and As-As correlations shows that As and Cd remain almost tetrahedrally coordinated and suggest a certain degree of chemical disorder of the investigated samples

Burian, A.

Biblioteka Nauki - repozytorium artykuÅÃ³w

Structure Refinement of Amorphous Cd-As by Analysis of Partial Radial Distribution Functions

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

             Title: Structure refinement of amorphous Cd-As by analysis of partial radial distribution functions    Author: Andrzej Burian   Citation style: Burian Andrzej. (1997). Structure refinement of amorphous Cd-As by analysis of partial radial distribution functions. "Acta Physica Polonica. A" (Vol. 91, nr 5 (1997), s. 917-921).   Vol. 91 (1997)	 ACTA PHYSICA POLONICA A	 No. 5Proceedings of the 3rd ISSSRNS Jaszowiec '96STRUCTURE REFINEMENT OF AMORPHOUSCd—As BY ANALYSIS OF PARTIAL RADIALDISTRIBUTION FUNCTIONSA. BURIANInstitute of Engineering Problems, University of SilesiaŚnieżna 2, 41-200 Sosnowiec, PolandandDepartment of Solid State Physics, Polish Academy of SciencesWandy 3, 41-800 Zabrze, PolandThe anomalous wide angle X-ray scattering technique was used to de-termine the partial structure factors and then the partial radial distributionfunctions for vacuum evaporated Cd—As amorphous films containing 41 and74% at. As. The experiments were performed using synchrotron radiationtuned near the As and Cd absorption edges. The obtained structural infor-mation about the individual Cd—Cd, Cd—As and As—As correlations showsthat As and Cd remain almost tetrahedrally coordinated and suggest a cer-tain degree of chemical disorder of the investigated samples.PACS numbers: 61.43.—j, 61.43.Bn, 61.43.Dq1. IntroductionIn the structural study of non-crystalline materials there is much interestin maximizing the amount of information about such systems. For materials con-taining n atomic species there are n(n -F 1)/2 distinct correlations, which in aconventional scattering experiment are inseparable. The extended X-ray absorp-tion fine structure (EXAFS) and differential anomalous wide angle X-ray scat-tering techniques probe the environment of a selected atomic species, but in thecase of multicomponent materials the different partial contributions, involving thisspecies, may be merged in the near- and next-neighbour coordination spheres be-ing indistinguishable. The resonant changes in the X-ray atomic scattering factorscan be used to vary the weights Wij (K) of the individual partial structure factors(PSFs) Sij (K) to the intensity scattered by a multicomponent material and thento determine PSFs [1, 2]. 	918 	 A. Burianwhere(.0 2 = 	 fi 1 2 , the scattering vector K = 4π sin BSA, 20 is the scattering angle,A is the wavelength and ci is the atomic concentration.Although possibility of application of this method was recognized by Keat-ing (1963) [1], the availability of intense radiation sources as synchrotrons hasrecently made it possible to perform the anomalous wide angle X-ray scattering(AWAXS) experiments. The measurements of the intensities scattered by a non--crystalline sample carried out using the incident beam energies tuned near theabsorption edges of the components can be utilized to construct a system of simul-taneous linear equations (1). However, the changes in the atomic scattering factors,achieved in the AWAXS experiment lead to the relatively weak variations in theWij coefficients. This prevents from a reliable determination of the PSFs using thestandard linear least squares method because the normal equations are very closeto singular. In order to obtain the solution of the system (1) a combined biasedestimator, which utilizes the regularization and truncated singular value decompo-sition methods, has been applied to minimize the effects of ill-conditioning of theproblem [3, 4]. The AWAXS data for the amorphous Cd5yAs41 and Cd26As74 filmswere collected on the wiggler beam line of the DCI storage ring at LURE (Or-say, France). The experiments and the numerical routines are described in detailin [3-6]. It should be pointed out that knowledge of the partial radial distributionfunctions (PRDFs) is the most complete information which can be obtained froma scattering experiment.2. Results and discussionThe PRDFs are computed from the experimentally determined PSFs by theFourier sine transform as follows:and p0 is the average atomic density. The experimental PRDFs are shown in Figs. 1and 2.The structural parameters: the interatomic distances (ri), their standarddeviations (σi) and the coordination numbers (Ni) can be obtained using thecurve-fitting, method which utilizes the Hook—Jeeves type procedure [7], expressingPRDF asStructure Refinement of Amorphous Cd-As ...	 919whereand the sum is taken over all coordination spheres.The experimental PRDFs obtained for the Cd59As41 and Cd 26As74 amor-phous films have been interpreted as described above, basing on Eq. (5). Frominspection of the plots presented in Figs. 1 and 2 it can be seen that the near-neigh-bour coordination sphere for Cd59As41 is predominant by the Cd-As correlations,whereas this r region is mostly influenced by the As-As and Cd-As pairs forCd26As74. This is consistent with an expectation that the occurrence of the con-tributions involving As is more likely for the As-rich composition. It can be alsoperceived that the contributions coming from the minority components, i.e. As-Asfor Cd59As41 and Cd-Cd for Cd59As41, are very weak. Beyond the first peak re-gion of the As-As PRDF for Cd59As41 these minority PRDFs are very close tothe average density functions.First, the near neighbour peak of the PRDFs was analysed. In order to fit theCd-As experimental PRDF for Cd 59 As41 a one-shell model was assumed. The coor-dination number NCd—Cd, the near neighbour interatomic distance rCd_As and itsstandard deviation σCd—As were allowed to vary. The fitting procedure converged tothe structural parameters rCd_As = 2.68 A, σCd_As = 0.09 A and NCd_As = 2.15.The near neighbour region of the Cd-Cd PRDF can be satisfactorily fitted withFig. 1. The experimental (solid line) and modeł (dashed line) PRDFs for Cd59As41.920	 A. BurianFig. 2. The experimental (solid line) and model (dashed line) PRDFs for Cd26As74.two shells. The resulting parameters are: rćd—Cd = 2.67 A, σcd —Cd =0.1 A,N (1)Cd— Cd = 0.8, rCd—Cd = 3.20., σCd_Cd = 0 . 25 A and NCd- Cd = 1.2. The firstattempt to fit the As—As PRDF was made with the one-shell model. This flt ledto the values: rAs_AS = 2.72 A, QAs_As = 0.31 A and NAs_As = 1.64. However,the two-shell model with r("s)—As = 2 .44 A, σAs- As=0.22,NAs_ = 0.4,rAs—As = 2.7G A , ^As_ As = 0.16 and NAs- As = 0.7 matches better the firstpeak of the As—As PRDF. The two-shell model of the Cd—Cd and As—As firstcoordination spheres suggests a certain degree of chemical disorder. Assumingtetrahedral coordination of both atoms and complete chemical disorder (the coor-dination numbers depending on the chemical composition) the near neighbour co-ordination numbers can be calculated [8, 9] being NCd_Cd = 2.36, NCd_As = 1.64and NAs_As = 1.64. The NCd—Cd and NAs_As values, resulting from the chemi-cally disordered model are greater than the experimental coordination numbers,whereas NAs_As is smaller. Taking into account the previous flndings for Cd-richcompositions [6] one can calculate the coordination numbers for Cd59As4 1 startingfrom the model, based on the structure with the 1:1 stoichiometry, in which eachCd is coordinated by 1 Cd and 3 As and each As by 1 As and 3 Cd. Assumingthat the As-positions are statistically occupied by As and Cd, in the proportionsdepending on the chemical concentration, the estimated coordination numbers are:NCd—Cd = 1.54, NCd_A s = 2.46 and NAs_As = 0.46. A comparison of the experi-mental coordination numbers and those estimated from the models also suggestsa certain degree of chemical disorder.Structure Refinement of Amorphous Cd—As ...	 921Similar fitting procedures were performed for Cd26As74 . The obtained struc-tural parameters are: rCd—Cd = 2.8 A, σCd—Cd = 0.37 A, NCd—Cd = 1.1,rCd—As = 2.7 A, σCd—As = 0.15 A, NCd—As = 2.7, rAs—As = 2.47 A, σAs—As =0.056 A and NAs—As = 2.4. However, the Cd—Cd coordination number is un-certain because the first peak in the Cd—Cd PRDF is practically merged in theaverage density function. This indicates that the Cd atoms are almost randomlydistributed in the network formed by the As atoms. The coordination numbers cal-culated for the chemically disordered model are: NCd—Cd = 1.04, NCd—As = 2.96and NAs_As = 2.96. The comparison with the experimental values leads to theconclusion that Cd26As74 is chemically disordered.Beyond the first peak regions the PRDFs were calculated for the models,which are based on the structures of the crystalline polymorphs of the Cd—Assystem CdAs and CdAs 2 . The basic structures are described in detail in [5, 6]. Asit can be seen from Figs. 1 and 2, the experimental and calculated PRDFs are ingood agreement supporting the proposed structural models.4. SummaryThe obtained results demonstrate the ability of the AWAXS technique toprovide structural information which cannot be obtained using other methods.From an analysis of the PRDFs it was found that the Cd and As atoms aretetrahedrally coordinated in both investigated films and their arrangements are toa certain degree chemically disordered.References[1] D.T. Keating, J. Appl. Phys. 34, 923 (1963).[2] Y. Waseda, Novel Application of Anomalous X-ray Scattering for StructuralCharacterization of Disordered Materials, Lecture Notes in Physics, Vol. 204,Springer-Verlag, Berlin 1984.[3] A. Burian, in: Zastosowanie Promieniowania Synchrotronowego, Ed. E. Sobczak,Wyd. im. W. Świętosławskiego, Warszawa 1996, p. 51.[4] A. Burian, to be published.[5] A. Burian, P. Lecante, A. Mosset, J. Galy, J.M. Tonnerre, D. Raoux, J. Non-Cryst.Solids 164-166, 151 (1993).[6] A. Burian, P. Lecante, A. Mosset, J. Galy, J.M. Tonnerre, D. Raoux, submitted toJ. Non-Cryst. Solids.[7] H.P. Kunzi, H.G. Tzschach, C.A. Zehnder, Numerical Methods of MathematicalOptimization with FORTRAN Programs, Academic Press, New York 1971.[8] G.S. Cargill, F. Spaepen, J. Non-Cryst. Solids 43, 91 (1981).[9] S.J. Gurman, J. Non-Cryst. Solids 139, 107 (1992).

Structure refinement of amorphous Cd-As by analysis of partial radial distribution functions

https://rebus.us.edu.pl/bitstream/20.500.12128/8473/1/Burian_Structure_refinement_of_amorphous.pdf

Structure refinement of amorphous Cd-As by analysis of partial radial distribution functions

Abstract

Similar works

Full text

Available Versions

Biblioteka Nauki - repozytorium artykuÅÃ³w

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

Structure refinement of amorphous Cd-As by analysis of partial radial distribution functions

Abstract

Similar works

Full text

Available Versions

Biblioteka Nauki - repozytorium artykuÅÃ³w

Repozytorium Uniwersytetu Śląskiego RE-BUŚ

Biblioteka Nauki - repozytorium artykuÅÃ³w