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VNU_ JOURNAL OF SCIENCE, Nat Sc¡, tXVII, EVALUATION OF INFLUENCE Faculty of Physics, Abstract n)3 - 2001 XAFS OF SPECTRA WITH ANHARMONICITY Nguyen Van Hung University of Natural Sciences, Tr this work the X-ray Absorption Fine VNUIL Structure (XAFS) spectra with influcnce of anharmonicity have been evaluated to get correct structural information The temperature above which the anharmonic effects must be included is identified with Finstemn temperature correclated Binsteim model and as the third cumulant calculated by anharmonic Debye-Waller factor and XAFS spectra of Cu calculated by present procedure are different from those calculated by harmonic model and agree very well with experimental values Using this agreement several important physical parameters are extracted from by other methods extracted experiment, They agree very well with theoretical or results, I Introduction and important ‘The most meaningful task of XAFS is to describe and technique interpret the XAFS spectra and then is to extract physical parameters by comparison between theoretical and experimental results [t was discovered and that the XAFS spec tra are different at different high temperatures, so that they provide different structural information |1, 2] Some recent works {2, 3] are successful in describing the changes of amplitude and phase of XAPS spectra in terms of anharmonic contributions as the temperature 7’ increases where the anharmonic effect is taken into account by an anharmonic factor But in these considerations the temperature above which the anharmonicity must be included is only a fitting parameter and the third cumulant was taken from sxperiment ‘This work is devoted to calculation of the third cumulant {4] and the temperature Ty basing on the anharmonic - correlated Einstein model [5] where Tp is identified with Kinstein temperature ‘They are applied to calculation of Debye-Waller factors and XAFS spectra including anharmonic “yw are compared contributions of atomic with experimental values vibration ‘The numerical results of ‘Thanks to their very good agreement dhysical parameters are extracted from the experiment several UL Formalism In the single-shell model the XAFS function, providing structural information through ts Fourier transform magnitude, is given by |3, 3] x(#) ~ F(Ä) cxp ( =) exp [—2k? (oj, + 04)| sin(2QkR + d(k) a(k)), (1) vhere & is wave vector, #'(k) is scattering amplitude, /? is shell radius, À is electron meanrec-path, đ?y is harmamie contribution to Debye-Waller factor (DWE) and é(k) is total ohase shift ‘Typeset by Ay4S-TEX x Nguyen The anharmonic contribution to SWE Van Hung is given by OUR) = 3(RT)OF (RT) in which the anharmonicity is taken into consideration by the anharmonic (R.T) = l3 2” onl To)| £ a7 (1) the phase change due to anharmonicity oak.) = 2k fART) : ` kyl? is given „a4 D anda Now eo are the Morse potential ture 7), and the cumulants 2ay2a = ĐŸ19091) and 9¢; Einstein ab hs Shap > > exp(-@)/1), 2p 10Da? — DarA and @, are the tem pera- cumulant and thermal : (7) (Ñ) É)ụ (I (10)0 Einstein frequeney and temperature Ay = Bpat (1 le 0, Parameter to calenlate + 0000% OF where V+e gu is Gruneisen hay (hay t8) „ (6) 1+ 4ODal~ ge To No third a exapusion coefficient ay are given by [4] (5) dka(T =~ To) model The first o!), second a, SN 3kpn(T ~ AR(T) parameters we ase the anharmonic-corretated (iy by Ao*(T) = a7, (1) + 74(T) -— 07) (To): where (3) a To) R 2da? ; (+ 3) Hợp factor [(Ða)?£ + 240a£”+ 3€”] (8Day* ont) and (2) h [5 ral ia 8N” see) 207) ặ (10) aN 3) (ly Here gis reduced mass of absorbing and backscattering atoms It is easy from eqs (7-9) to get the following relation Tat (1/2)(1 + oe ee ols) ( 2)(1 + 10z+ which approaches aprlatjo monicity must = from the fheftap to the constant 1/2 in classical limit be included [1] ie (12) 24) value 1/2 Moreover at high temperatures, Therefore, the temperature in eqs (3-6) where the relation the anhar- is identified with Evaluation of XAFS spectra with influence the insted temperatnre calentated DÝ eq, in e0, (2-0) are calcuded by eqs (8 ~ 9) IH Compe ison between Experiment of anharmonicity (1), and the second and th and Extraction ch of physical đan1s nsed parameters Nese we use the formas presented in previous section to calculate SWE and other pannineters as well as NAPS spectra with influence of anharmonicity of atomic vibration That meats at any temperatures Fig la shows the values of DWE of Cu calculated by present procedure valine [Ol at in hartouie 295K Pig Lb aud anharmonic presents the model in comparison with an experimental Fourier transtorm magnitude of XAPS spectrin trom the first shellof Cu ar 2051 calenlated by present auharnionic procedire in comparison with those calenlated by harmonic model and with the result: measured recently in the HASYLAB at DESY [2] Tn both figures the values caleulated by present anharmonic procednre agree very well with experimental result and are different from those caleulated by harmonic model 002 „ 0.50 $ oo Foo E 0.30 001 Ề Ệ + 0.20 0005 © 0.10 100 200 300 1K) 400 500 600 700 0.00 0.0 ~ 20 hy ` Rial - 4.0 60 Fig la DWE of Cu calculated by present anharmonic procedure (solid) in comparison with those calculated by harmonic model (dashed) and those of experiment |6} (E)) Hig 1b Fourier transform magnitude of SAFS spectrum of Cu calculated by present anharmonic procedure (dashed) in comparison with those calculated by harmomic model solid) and those of experiment (dots) [2] Thanks to this agreement several physical parameters of Cu are extracted They we presented in Table The values of a, D and y¢; agree very well with those obtained using experimental values for the energy of sublimation, the compressibility and the lattice constant [7] The values of ky gp and @¢ agree very well with theoretical results of ref land @)) agrees very well with the one of ref to Nguyen a(A') D(eV)- _1359 0.343 Ku(Nm) 2.108 60" 50.748 A) Van O(K) 0.131 Hung OK) 236 315 Table The values of a, Doo).0) effective spring constant ky, and Debye temperature #, of Cu extracted from experiment by present procedure In conclusion, present anharmonic procedure can serve as an effective procedure not only for calculation of DWE and XAFS spectra with anharmonic contributions of atoniic vibration providing structural information at any temperatures but also for extraction of several physical parameters from the experiment This work is in part supported by the fundamental science research project: provided by the MOSTE.” References “A Stern P Livins and Zhe Zhang V Hung R Phys Frahm and H Kamitsubo Rev B43( 1991) p 8850 Journal of Phys Soc Japan, 65( 1996) 3571 Hung J de Physique IV, ©2(1997) p 279 „ Hàng and J.J Rehr Phys Rev., B56(1997), p 43 ‘VY Yokoyama, ‘Tl Susnkawa and T Ohta Jpn J Appl Phys., L G Girifalco and V G Weiser Phys Rev 114(1959), p GST ~ ROM Niclow, G Gilat H Phys Rev., 164( 1967) p ! Smith, E J Ranbenheimer 28(1989), and M p 1905 WK Wikinson TAP CHI KHOA HOC DHQGHN, KHTN, t XVII, n”3 - 2001 DANH GIA CAC PHO XAPS VOLANH Nguyễn Khoa Vat Iv Đại học Nhoa HUONG Văn CUA DAO BONG PHI DIEU Hùng học Tìr nhiền - ĐHQG Hà Nội “Trong phố cấu trúc tình tế hấp thụ tía X (XAES) đạo động phi điều hoà HOA với ảnh hưởng, đánh giá để nhận thơng tín xác cẩu trúc vật thể Nhiệt độ mà ứng đạo động phí điều hoà phải bố sung đồng với nhiệt độ Einstein enmnlant bậc bà tính theo mỏ bình Einstein tương quan phi điều hồ Hệ số Debye-Waller phố XAES Cu tính phương pháp khác với phố tính theo mỏ hình điều hoà trùng tốt với kết thực nghiệm từ thực nghiệm Chúng phương pháp khác Nhờ trùng hợp mà số tham số vật lý trùng tốt với kết lý thuyết hay thực nghiệm rút rút ... is identified with Evaluation of XAFS spectra with influence the insted temperatnre calentated DÝ eq, in e0, (2-0) are calcuded by eqs (8 ~ 9) IH Compe ison between Experiment of anharmonicity... Extraction ch of physical đan1s nsed parameters Nese we use the formas presented in previous section to calculate SWE and other pannineters as well as NAPS spectra with influence of anharmonicity of atomic... only for calculation of DWE and XAFS spectra with anharmonic contributions of atoniic vibration providing structural information at any temperatures but also for extraction of several physical