1. 1 Structural Heterogeneity in Twinned Yb 2-x (Fe,Ga) 17+2x Polytypes Yaroslav Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference

2. 2 H. Birkedal 2,3 M. Hostettler 2 1 Laboratory of Crystallography, University of Geneva 2 Institute of Crystallography, University of Lausanne 3 Department of Chem. and Biochem., Univer. of California 4 Department of Inorganic Chemistry, University of L'viv Y. Filinchuk 1 R. Cerny 1 K. Yvon 1 O. Bodak 4 T. Yanson 4 Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference

3. 3 Is of interest as a ferromagnetic material Is a substitution derivative of R 2 Fe 17 str. types (R = Rare earth) in which R atoms are partially substituted by Fe 2 dumbbells, Fe atoms - by Ga atoms, respectively. According to previous work Yb-Fe-Ga alloys crystallize with the hexagonal LuFe 9.5 type (1, P6 3 /mmc) and/or rhombohedral PrFe 7 type (2, R-3m) structure. 1 and 2 (AB and ABC stacking sequences) can be considered as polytypes with maximum degree of order (MDO polytypes). They have the cell parameter relationships a(1) = a(2) and 3c(1) = 2c(2). Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference Yb 12 Fe 64 Ga 24 alloy

4. 4 Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference H R ordered disordered

5. 5 In this work we show that both polytypes can occur within a In this work we show that both polytypes can occur within a coherently twinned crystal Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference plane of ab plane of «large» hex cell

6. 6 Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference Crystals of the cast sample showed peculiar non- space group absences and cell metrics a(1) = a(2) = 8.615 and 3c(1) = 2c(2) = 25.215 A Diffraction patterns: image plate detector synchrotron radiation (SNBL at ESRF)

7. 7 [1] H. Birkedal, M. Hostettler, W. Paciorek, D. Schwarzenbach, Bulletin of the Czech and Slovak Crystallographic Association. Bulletin of the Czech and Slovak Crystallographic Association. Special issue B, ECM-18. 5 (1998), 200 (Abstract A4-P17). Special issue B, ECM-18. 5 (1998), 200 (Abstract A4-P17). Modelled by superposing three sorts of domains: one hexagonal (1) and two rhombohedral (2, 3 - twinned by reticular merohedry). Interference terms arising from possible stacking-faults were neglected. Structure refinement was performed by a newly developed computer program [1] that allows to refine several structures on a single data set. [1] H. Birkedal, M. Hostettler, W. Paciorek, D. Schwarzenbach, Bulletin of the Czech and Slovak Crystallographic Association. Bulletin of the Czech and Slovak Crystallographic Association. Special issue B, ECM-18. 5 (1998), 200 (Abstract A4-P17). Special issue B, ECM-18. 5 (1998), 200 (Abstract A4-P17). Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference

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10. 10 Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference

11. 11 Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference

12. 12 Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference

13. 13 1 and 2(3) displayed different structure features:   1 showed a higher rate of Yb substitution by Fe 2 dumbbells than 2(3);   2(3) showed partial substitution of Fe by Ga. Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference STRUCTURAL HETEROGENEITY IN A SINGLE CRYSTAL

14. 14 Two-phase region as a single crystal !!! Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference Consequences Twinned polytype (called “syntactic coalescence” by polytype scientists) is a link between two classical formalisms:   description of two-phase region composed of related structures by a simple mixture of two phases (often impossible to resolve them by X-rays…)   description of two-phase region composed of related structures by a single phase (solid solution) with variable stacking sequences (“just stacking”…)

15. 15 Diffuse intensity its amount in the streaks along c* enabled us to find out the average domain size along c axis evaluated qualitatively at the level of a few tens of unit cell dimensions Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference

16. 16 A crystal from an Yb 12 Fe 65 Al 23 alloy has the same structural features but shows an extra scattering (H´), with diffuse streaks in the basal plane. It suggests short-range order in the basal plane. Diffuse streaks for the reflections from R (2 and 3) domains indicate frequent stacking faults along c. Yb-Fe-Al system Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference

17. 17 Yb-Fe-Al system Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference

18. 18 Yb-Fe-Al system Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference

19. Yb-Fe-Al system frequent stacking faults along c local R-atom ordering in the basal plane different from that observed in Th 2 Ni 17 and Th 2 Zn 17 type structures

20. 20 Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference Related topics: 1. 1.What is a real TbCu 7 structure? Isn’t it a highly disordered stacking of the layers that have a strong tendency to ordering in the basal plane? 2. 2.D.S. Yufit et al. (2002). Acta Cryst., B58, 673-676 - two polytypes of organic substance in a coherently twinned crystal 3. 3.H. Katzke. (2002). Z. Kristallogr., 217, 127-130 - variations of peak profiles for 2H&3R twinned polytypes of NbS 2 4. 4.D.L. Smith et al. (1981). Acta Cryst., B37, 1807-1812 - 2H&3R coherently twinned polytypes of CuNCS were refined CrystSun1.unige.ch

21. 21 Another story – how to estimate the average domain size along c-direction? Y. Filinchuk L’viv, 25-28 Sept 2002 VIII Intl’ IMC Conference Calculated X-ray diffraction pattern as a function of the stacking fault probability P NbS 2