Prof. R. Pynn Prof. Sh. Sinha Prof. M. Bieringer Prof. G. Roth. Hewat V.Yu. Pomjakushin..

Transcription

1 - / : Prof. R. Pynn Prof. Sh. Snha Prof. M. Bernger Prof. G. Roth. 4. A.W. Hewat V.Yu. Pomakushn.. - J. Rodrguez- Carvaal HERCULES Schools: (Hgher European Research Course for Users of Large Expermental. Internatonal Unon of Crystallography (IUCr European Crystallographc Assocaton European Neutron Scatterng Assocaton Integrated Infrastructure Intatve for Neutron Scatterng and Muon Spectroscopy (NMI3. ( (I) (II) R- R

2 1FULLPROF SUITE FullProf 11.. WnPLOTR: FullProf : FullProf FullProfSute FullProf FullProf 1.5. I) FullProf. II) FullProf Studo FullProf II) , FullProf X-RaysRontgenstrahlung Å

3 k k k = / E k k f E f p f (Bragg s Law) k k Q : k, p=k. p q = k f k E = E f E = X- E << E f, E p p f q = k sn(/) n d E E +de : ( a 1a a 3 aa 1a a 3-1 3h,k,l I( l Chadwck, J. Nature

4 ( , ) ) ) ) » 013 n BT/ n/ n ( - -c kev : - coh nc abs coh nc abs 1 H V ~fm). Cd, B, Sm A- H Fe C Co O Cu Al Ar Sm Gd Sm Gd Sm Nd H D Al V Fe Co Shull & Brockhouse Shull & Brockhouse

5 ILL (004) S( (s -1 m - ster - 1 ) (%) (mrad ) (s -1 m - ) :

6 ....),.,.... (-Q- ( : ab nto Q-. ( ), ( ) Q-.. ( (, U,...) ( 1977 CoxYoung. : : -n. : Ta O 7Cl Powder X-ray Dffracton ( = A) L 4 MgReO 6 : powder X-RAY dffracton pattern for L 4 MgReO powder NEUTRON dffracton pattern for L 4 MgReO L 4MgReO 6: - Powder Neutron Dffracton ( = A) Intensty (a.u.) Intensty (a.u.) L 4 MgReO 6 : ( 0 ) ( 0 ) ( 0 ) F N hkl fn( )exp hxn kyn lzn n1 F N hkl bn exp hxn kyn lzn n1 neutrons X-rays b (10-1 m) Z L () Mg (10) Re (69) O (10)

7 LaN 4.5 Sn 0.5 LaN 4.5 Sn 0.5 D (I). 1 3 : (. - = 0:... : ~ (Z-1) Z. (I) (I) 3 (I) 4 (I) 5. (I) 6 (I) 7 (I) 8 (I) 9 ESRF C ESRF C ESRF C ESRF (I) 10 (I) 11 (I) 1 (I) 13

8 C ESRF C ESRF C ESRF C ESRF (I) 14 (I) 15 (I) 16 (I) 17 C ESRF C ESRF ESRF C ESRF (I) 18 (I) 19 (I) 0 (I) 1 (spallaton) (I) (I) 3 (I) 4 (I) 5 (I) 6 (I) 7 (I) 8 (I) 9

9 / -! (I) 30 (I) 31 (I) 3 (I) 33 (FRM II) - ISIS (RAL, UK) ILL - - ILL (I) 34 (I) 35 (I) 36 (I) = 0: (I) 38 (I) 39 (I) 40 (I) = 0: (I) 4 (I) 43 (I) 44 (I) 45

10 (I) 46 (I) 47 (I) 48 (I) 49 (I) 50 (I) 51 (I) 5 (I) 53 (I) 54 (I) 55 (I) 56 (I) 57 (I) 58 (I) 59 (I) 60 (I) 61

11 KAPPA) (I) 6 (I) 63 (I) 64 (I) 65 ID31 ID31 ID31 (I) 66 (I) 67 (I) 68 (I) 69 ID31 ID31 ID31 BM01 (I) 70 (I) 71 (I) 7 (I) 73 - BM01 Pylatus BM01 KAPPA KAPPA (I) 74 (I) 75 (I) 76 (I) 77

12 k ( () k f k f -- k = Q h k f /-h k /h, ( ) ( ).. QE QE (II) 3 (II) 3 (II) 3 3 (II) 4 / =dsn - D0, ILL. - S- «take-ff» 3 (II) 5 3 (II) 6 3 (II) 7 3 (II) 8 const TOF) TOF DRACULA ILL = const 3 He (PSD), det sr D0 (ILL) - 3 (II) 9 3 (II) 10 3 (II) 11 3 (II) TOF- TOF LPS SNS HRFD) (II) 13 3 (II) 14 3 (II) 15 3 (II) 16

13 / TOF- TOF- TOF- TOF HRFD: 0 = 15 0, 7. Å 0 HRPT: 0 = Å, (II) 17 3 (II) 18 3 (II) 19 3 (II) 0 3 (II) 1 3 (II) 3 (II) 3 3 (II) 4 FRM- RESEDA FRM- NSE TOF-TOF KWS KWS 1 PGAA SPHERES (007 MEPHISTO MARIA NREX+ RefSANS SANS-1 KWS 3 DNS MIRA 3 (II) 5 3 (II) 8 48-, - - TOF HRFD) deg detector 8-3 deg detector deg backscatterng detector gude tube 100m sample beam Stop deg detector 3 (II) 3 (II) 30 3 (II) 31 3 (II) 3

14 LMn TeO 6. LMn TeO 6. LMn TeO 6. LMn TeO 6. 3 (II) 33 3 (II) 34 3 (II) 35 3 (II) 36 LMn TeO 6. LMn TeO 6 SINQ/PSI RPT 3 (II) 37 3 (II) (II) 40 (II) RPT / q- / q- SINQ DMC Å 3 (II) 41 3 (II) 3 (II) 43 3 (II) 44 HRPTSINQ HRPTSINQ HRPT D O NEUTRA () 3 (II) 45 3 (II) 46 3 (II) 47 3 (II) 48

15 HRPT Ge hkk Ge hkk 11 hkk) 15 / hhkge- take- take-off 3 (II) 49 3 (II) 50 3 (II) 51 3 (II) 5 HRPT. HRPT : - :6 - ~3~(8-10) 3 (II) 53 3 (II) 54 3 (II) 55 3 (II) 56 - < 3 ) HRPT ILL ILL (II) 57 3 (II) 58 3 (II) 59 3 (II) 60 ILL ILL, DB ILL, DB 3 (II) 61 3 (II) 6 3 (II) 63 3 (II) 64

16 ILL, DB ILL, DB ILL, DB ILL, DB 3 (II) 65 3 (II) 66 3 (II) 67 3 (II) 68 ILL, DB ILL, DB ILL, DB DB DB - (-4) D1A 3 (II) 69 3 (II) 70 3 (II) 71 7 ILL, D0 ILL, D0 ILL, D0 ILL, D0 D0 3 (II) 73 3 (II) 74 3 (II) 75 3 (II) 76 ILL, SALSA ILL, SALSA ISIS, SXD D10 (ILL) 3 (II) 77 3 (II) 78 3 (II) 79 3 (II) 80

17 D9 (ILL) = Å TrCS(PSI) = Å TrCS(PSI) = Å D19 (ILL) = Å 3 (II) 81 3 (II) 3 (II) 83 3 (II) 84 Frst Results from OPAL Rob Robnson, 300 x 50 mm 150 x 50 mm TG3 TG1 Thermal neutron gudes run ~ 40m n bunker CG4 TG4 Performance Acceptance Crtera OPAL measured (RF = reactor face) flux (0 MW equv) (NGH = neutron gude hall) ( n n/cm /sec) Thermal neutron flux at RF for TG4 (E < 100 mev) 4.0 x Thermal neutron flux at RF for TG3 (E < 100 mev) ~.3 x [1] Thermal neutron flux n NGH for TG3 (E < 100 mev).8 x 10 9 Cold neutron flux at RF for CG4 (E < 10 mev).5 x Echdna (HRPD) Quokka (SANS) Platypus (Reflect) Wombat (HIPD) Neutron dffracton Tapan (Trple Axs) Large scale structures Inelastc neutron scatterng Cold neutron flux at RF face for CG3 (E < 10 mev) ~ 1.3 x [] Mrrotron engneers nstallng out-of-ple neutron gudes neutron gude cross-secton Beams vary from mm wde and from mm hgh at ext wndow Cold neutron flux n NGH for CG3 (E < 10 mev) 6.4 x 10 9 [1] estmated wth TG4 spectrum calbraton factor [] estmated wth CG4 spectrum calbraton factor Kowar (Resd. Stress) Koala (QLD) Ska (Cold-Trple Axs) Pelcan (TOF-PAS) 3 (II) 85 3 (II) 86 3 (II) 87 3 (II) (II)

18 V = 64 Å 3 ( = 1.54 Å cubc hexagonal tetragonal orthorhombc monoclnc trclnc ( 0 ) multplctes d (100) = d (-100) = d (010) = d (0-10) = d (001) = d (00-1) d (100) = d (-100) (010) = d (0-10) (001) = d (00-1)

19 CIF n d E E +de

20 D D 1D D D F F ( F ( f(x- au F(u) b(r) / G(r)

21 = const = 0 = const = 0 (H) H (1) Q= k F - k I k F =/ u F k I =/ u I (,,...). (h/)q =(h/)(k F-k I)= h s h=e F-E I (h=0), k F=k I= / Q= Q = (4/) sn, -. : s = Q/. 6. ( ),, - (FT) (SD) (r), -. SD r a (r) R ; SD : : (r)= a (r-r ) : A(s)=FT[(r)] A(s)= exp{sr } a (u) exp{su}d 3 u A(s) = f (s) exp{ sr } I(s) = A(s)A(s) * = f (s) f (s) * exp{ s (R -R )} s, s R =R -R ; Q=ps: I(Q) = f f sn{qr }/(QR ) 6. 4 : (r)= n c (r-r n )= c (r) * n (r-r n )= c (r) * z(r) z(r) z(r)g(r), g(r) g(r)=1 r, g(r)=0 r. G(s)=FT{g(r)}. : A(s)=FT{ f (r)} Z(s) = FT{z(r)} = 1/V c H (s-h) A(s)= FT{ c (r) * z(r)g(r)} = F(s)Z(s) * G(s) = F(s)/V c H G(s-H) : s=h (s=s=sn/, H=1/d hkl ) 6. 5

22 g(r) g(r)=1 r g(r)=0 r G(s)=FT{g(r)}. G (s) : V. (r)= g(u)g(r+u)d 3 u h(r) -,, ", r. (0)=1 r. I(s)=F (s)/v c H G(s-H) H' G * (s-h') NF (s)/(vv c ) H G (s-h) r, I(s) = n( m F mf * m+n) exp{p s R n} F m- p n=f mf * m+n - m. V(R)/Vc I(s) = V/V c n (R n ) F m F * m+n exp{ s R n }= = N n (R n ) p n exp{ s R n } : : F= F =1/N m F m : n =F-F n p n =F + m * m+n = F + n, : I(s) = I Bragg + I Dffuse = N F n (R n ) exp { sr n } + N n (R n ) n exp{ sr n } = N F /(VV c ) H G (s-h) + N n n exp{ sr n }, (R n ) n (R n ). F m =F exp{p s u m }, : m exp{p s u n }=0 : z(r n, s)= exp{ps(u m -u m+n )}. : I(s) = I(s) = N F n h(r n ) z(r n, s) exp{p s R n } s=h+ds : I H (Ds) =N F H n h(r n ) z H (R n ) exp{p Ds R n } F H W x (Ds)

23 stran sze F m =F exp{ s u m }, : m exp{ s u n }=0 : (R n, s)= exp{s(u m -u m+n )}. : I(s) = I(s) = N F n (R n ) (R n, s) exp{ sr n } s=h+s : I H (s) =N F H n (R n ) H (R n ) exp{ s R n } F H x (s) , :,,. : I H (Ds) F H W x (Ds) 3D (), nodes : I {H} (Ds) {H} F H W H (Ds) 1D (I) : y I ( T T ) b c h h h ( xdx ) 1 (FWHM=H) (, m,...) ( x) g( x) f ( x) nstrumental ntrnsc profle (II) y I ( T T ) b I I h h s c h h h ( xh, m) b b. b :,,... X-ray hx ky lz exp B sn F( hkl) f exp / b hx ky lz exp B sn F( hkl) exp / F (hkl) - f - X-ray - b - h,k,l - x,y,z - B I(hkl) - : I( hkl) s p( hkl) L A P( hkl) F s ( hkl) L Lorentz - p - multplcty I( hkl) F( hkl) A P ( = 1,n ), y s I ( T T ) b c, h, h h ( = 1,n), (p=1,n p ) y s I ( T T ) b p p p p p c, h, h h Gx a bx ( ) Gexp( G ) ln 4ln ag bg H H 1 H a ln G LxH (, ) LxH (, ) LxH (, H) GxH (, ) GxH (, ) Gx (, H H ) LxH (, ) GxH (, ) V( xh,, H ) L G L G

24 V( x) Lx ( ) Gx ( ) Lx ( ugudu ) ( ) V( x) V( x, H, H ) V( x,, ) - L G L G pv ( x) L( x) (1 ) G( x) pv ( x) pv ( x,, H ) 1 L V( x) G Reerf x G G x t erf ( x) e dt 0 Mappng: - Thomson-Cox-Hastng ( H, ) F( H, H ) H H 4 HGH 3 HGH HGH HGH H 5 G L 3 L 4 L 5 L ( ) L 3 H H H L L L H H H 1 ( HG, HL) F ( H, ) H L H H G 3 1/ ( ) H G L H ( U (1 ) DST IG )tan V tan W cos G [ Y F( SZ )] HL ( X DST)tan cos ( x) pv ( x) E( x) pv ( x t) E( t) dt - back-to-back : t Et () Ne t0 t Et () Ne t0 N : u v ( x) (1 ) N{ e erfc( y) e erfc( z)} N p q {Im[ ee1( p)] Im[ ee1( q)]} : E 1 erfc : TOF : 1 1 u x v x x x y z px qx : FWHM : T.O.F d- (1) : 7 T Z Dd D d h 0 1 h h dh dh T.O.F d- () T nt (1 n) T T Z D d e t h h h e e e h 0 1 h t t t t A h 0 1 h dh T Z D d 1 1 n erfc{ wcross ( Tcross )} d TOF h T.O.F d- (3) 1 e t 1 e t n (1 n) n (1 n) e e e e e e 0 1dh 0 1dh t t t t 1 t t dh dh () (), F m =F exp{p s u m }, : m exp{p s u n }=0 : z(r n, s)= exp{ps(u m -u m+n )}. : I(s) = I(s) = N F n h(r n ) z(r n, s) exp{p s R n } s=h+ds : I H (Ds) =N F H n h(r n ) z H (R n ) exp{p Ds R n } F H W x (Ds) :,. : I H (s) F H x (s) 3D ( ), : I {H} (s) {H} F H H (s) 1D ( ), : I {H} (s) {H} F H H (s) 1D hkl ( s) n n exp( sndhkl ) n ( s) A S A exp( snd ) D hkl n n hkl n, (-): ( s) A( L)cos( sl) B( L)sn( sl), Lnd hkl hkl L S D A( L) A ( L) A ( L), S D B( L) A ( L) B ( L). -. Mcrostructure Analyss from Dffracton Edted by R. L. Snyder, H. J. Bunge, and J. Fala, Internatonal Unon of Crystallography, ,.. ( sze) D cos ( stran) 4 tan,, :. - - : S 1 D V * Scos S apparent,. apparent : D, V L x y d N 1,... NV h r C column-length p V(L): D L pv ( L) dl V 0 x h L h y

25

26 (/ ) n w ( ) y yc 1 1 w :- " " y, I h LpOACF F. : -(Lp), (O), (A), (C)... h n s F h O f h T exp h S t r r 1 s h h,k,l r 1,,...N r r x, y,z 1,,...n r Fh exp hr h r Fh exp hr h h h. ( ). (). - ( ) F n h O f ht exp hs ts 1 s r - F obs n hr O f Texp hs ts h r 1 h,k,lr r 1,,...N x, y,z 1,,...n r s r r D Q= FWHM Å -1 pd Q ( Å -1 ). : T. : T, y 1,..., n (Q)= / (Q V o ) p D Q multplcty V o Å 3 : y c

27 T:, TOF), T h y : T y -y c, "" R x1 1 1,y,z,x,y,z,...x,y, z N c F h F h, r1 obs r n calc n r n (1) DICVOL, (WnPLOTR) (3) ExPo () (FullProf) (4) ExPo Smulated Annealng (FullProf) or Genetc Algorthms.. Q-:. ( ) Q-. Q-.. (raw data) Q-. Q-,. -.. (raw data)... 3D 1D nm) (I) 9. (I) 9. (I) 3 9. (I) 4 9. (I) 5 9. (I) 6 9. (I) 7

28 . : T. : T h T:, TOF), T, y 1,..., n y : y c - y -y c : T 9. (I) 8 9. (I) 9 9. (I) (I) 11 (/ ) n w ( ) y yc 1 1 w : "" y, Cost n 1 Cost F( y y ( ) ) Cost log( Lkelhood) c : - (1) : 0 yc ( ) 0.,, ( ) A b 0 yc ( 0) yc( 0) Akl w k l yc ( 0) bk w( y yc) k : - () ( k) ( A ) kk N-P+C 9. (I) 1 9. (I) (I) (I) 15 :.. I I y I ( T T ) b c h h {h} h h I ( x, ) h B P :, : b b :,,... y I ( T T ) b c h h {h} {h}.., ( = 1,n ), y s I ( T T ) b c, h, h h ( = 1,n), (p=1,n p ) y s I ( T T ) b p p p p p c, h, h h 9. (I) (I) (I) (I) 19 I y I ( T T ) b c h h {h} S LpOACF h h F. : (S), - (Lp), (O), (A), (C)... n s F h O f h T exp h S t r 1 r s ( x, y, z ) ( 1,,... n) sn T exp( B ) () r O B ( x, y, z ) ( 3n ) ( n-1 ) () ( n ) () + : - (Symmetry adapted ), TLS., -,. 9. (I) 0 9. (I) 1 9. (I) 9. (I) 3

29 n ( ) s F h O f h T g h exp h S t r s 1 s h h T hs k Ss k s 1,,... NG l l s g ( h s ) - DPs DPs Profle Parameters ( xh, P) ( T Th, P) ( x) g( x) f ( x) nstrumental ntrnsc profle ( xdx ) 1 -) ( x) L( x) G( x) V( x) I Fwhm BG Fwhm x 0 x I Gaussan Lorentzan LxH (, ) LxH (, ) LxH (, H) GxH (, ) GxH (, ) Gx (, H H ) LxH (, ) GxH (, ) V( xh,, H ) L G L G 9. (I) 4 9. (I) 5 9. (I) 6 9. (I) 7 (Vogt functon) V( x) V ( x) V ( x) 1 L 1L L G 1G G fl hl gl fg hg gg () FWHM): U, V, W, I G, X, Y IG HG U tan V tan W cos Y HL X tan cos. (- ) TOF + back-to-back Ikeda- Carpenter : ( I fg HhG ( U f (1 f ) DfST ( D))tan H gg cos [ Yf Ff( S)] H ( X D ( ))tan H cos hl f f fst D gl 9. (I) 8 9. (I) 9 9. (I) (I) 31 ) : (stran/sze ): hkl (,, ) ( sze/mcrostran ) (,, ) hkl- :,, : - log-normal gamma sze (Popa et al. J.Appl.Cryst 35, 00, ) NdNO4 CaMnO4 - (3T, LLB) Ca MnO 4. Sze = 0. Sze (hkl),l=n+3. : D0 ILL:! take-off ( M 40º)!) 9. (I) 3 9. (I) (I) (I) 35 hx ky lz exp B sn F( hkl) f exp / b X-ray hx ky lz exp B sn F( hkl) exp / F (hkl) - f - X-ray - b - h,k,l - x,y,z - B I(hkl) - : I( hkl) s p( hkl) L A P( hkl) F s ( hkl) L Lorentz - p - multplcty I( hkl) F( hkl) A P : : - zero pont - atomc postons (); - nstrumental profle - thermal parameters ); ); - ste occupances - profle asymmetry ( ); - lattce parameters - background parameters ); ); - absorpton - scale factor ); ); - preferred orentaton - sample dsplacement ); (); - crystallte sze ); - mcrostran ); - magnetc vectors 9. (I) (I) (I) 37

30 ? : -) : ( ) FFT ( x) FT G( t) F( t) g( x) f( x) 1 ( ) CCSL ISIS FullProf/GSAS TOF : V(x) IK(x) TOPAS :. G(t). Gt () G() tg() tg()... t 1 3 Ft () FtF 1() () tf3()... t ~ (I) (I) (I) (I) (I) 4 9. (I) (I) (II) R- R- (1) yobs, ycalc, Rp 100 yobs, 1/ w yobs, y calc, Rwp 100 w yobs, R-pattern R-weghted pattern 1/ ( N PC) Rexp 100 wy obs, Expected R-weghted pattern R- () wp Rexp R R S R wp exp - R- (3) : R P R WP 10. (II) 10. (II) (II) (II) 5 R- R 100 B R 100 F ' I k k ' F k k ' I obs, k calc, k ' I obs, k obs, k calc, k ' F obs, k ' ' F ' Bragg R-factor Crystallographc R F -factor. '' ( T Tk )( yobs, B) ' I obs, k ' Icalc, k ( y calc, B ) R- ' F obs, k R- ' ' I obs, k Lp ' R F - I obs,k :?? R-? : ndex N. ( ) : -,. : N B : N I=N f : consecutve (resoluton weghted): N eff solvablty : : r = N eff/ N I 10. (II) (II) (II) (II) 9

31 N eff (Q) : (Q) = p /(Q V o) p D Q D Q - FWHM Q-, p Q o N eff 1/(1+N n), N n Q o, verfyng: Q o -p D Q Q n Q o + p D Q N eff: N eff 1 1 N 1, NB 10. (II) (II) (II) (II) 13 structure factors extracton» 10. (II) (II) (II) (II) (II) (II) (II) (II) 1 cutoff 10. (II) 10. (II) (II) (II) 5

32 R (II) (II) (II) (II) (II) (II) (II) (II) 33 FullProf Sute CrysFML/WnPLOTR/FullProf Juan Rodríguez-Carvaal (ILL, France) CrysFML, FullProf, BasIreps, Smbo, Enermag, 1. FullProf Sute.. WnPLOTR: FullProf Sute. 3. : FullProf. Javer González-Platas (ULL, Tenerfe, Span) CrysFML, GUIs, EdPCR, GFourer Therry Rosnel (LCSIM, Rennes, France) WnPLOTR 4. FullProf Sute. 5. FullProf. 6. FullProf. Laurent Chapon (ISIS, U.K.) (ILL, France) CrysFGL, WCrysFGL, FullProf_Studo Carlos Frontera (ICMAB, Barcelona, Span) Polarzed neutrons, Flppng rato data handlng Azz Daoud-Aladne (ISIS, U.K.) Incommensurate crystal structures FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE 4 FullProf Sute WnPLOTR: FullProf Sute FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE 8

33 Fle: wnplotr.set WnPLOTR Demo WnPLOTR WnPLOTR : FullProf New faclty: DICVOL04 : TREOR, ITO : TREOR, ITO : EdPCR, Fp_Studo, DICVOL04, : Pattern decomposton : (CW X-rays & neutrons, Energy dspersve X-rays, TOF neutron dffracton) : smulated annealng FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE 1 FullProf : (.pcr ): PCR-fle, / PCR fle DAT fle(s) FullProf Eventually,, -. DAT fle(s) PCR fle PCR fle: steep learnng curve, Complex to handle : () PCR-,... GUI: EdPCR GUI FullProf: EdPCR FullProf fpk.nf In ths fle new features, as well as dscovered bugs, of FullProf.k are perodcally documented. For detals consult the manual of FullProf. From 10 May 01, comments on the programs consttutng the FullProf sute are also provded. Juan Rodrguez-Carvaal (Insttute Laue Langevn, Grenoble) July An updated verson of FullProf.k s now avalable Some changes have been ntroduced for treatng the background: (1) The polynomal background of 1 coeffcents, for constant wavelength case, has been changed so that the last three coeffcents correspond to nverse powers of theta () Now there s the possblty to nclude several prevously calculated profles as contrbutng, through a lnear combnaton, to the background of a powder dffracton pattern. The ndvdual profles are read n nput fles named "fledat_n.bac". Where "fledat" s the code of the data fle correspondng to a dffracton pattern and the ndex "n" s the number of the contrbutng profle. The addtonal contrbuton to the background s calculated as: FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE 16 FullProf fpk.nf - Reorganzaton of the TOF peak shapes and dervatves. The refnement of the nstrumental parameters s now much more stable The new peak shape INSTR=13 (thanks to Laurent Chapon!) consstng n the convoluton of a pseudo-vogt functon wth the Ikeda-Carpenter functon s now workng. The TOF peak shapes used n FullProf and the meanng of each refnable parameter s now documented n the note: TOF_FullProf.PDF FullProf Sute Open WnPLOTR A button on WnPLOTR gves access to EdPCR Wthn EdPCR you have access to a seres of programs of the FullProf_Sute BasIreps: Irreducble representatons of space groups GFourer: Fourer maps FullProf_Studo: vsualzaton Xtal & Magnetc Structures In constructon: Moment, Smlar, CrystCalc WnPLOTR FullProf handlng - Smulated Annealng FullProf FullProf, Crystallographc Fortran 95 Modules Lbrary (CrysFML) provde. multplcty ste. (: sym) FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE 0 handlng codes FullProf codewords, automatc mode. automatc mode, the manual mode automatc mode.,. handlng codes FullProf automatc mode keywords handlng. keywords - VARY FIX ( ). "name of the phase" column 41. keywords VARY FIX. (),. 'xyz','cell','b' ( ). handlng codes: VARY FIX VARY xyz: VARY xyz 0.1: 0.1., codeword. VARY xyz cell b :,. FIX xyz : ( VARY xyz b FIX b :. 'b, FIX keyword, VARY..,. occupaton (!). FullProf, bond valence sums. Bond_Str FullProf. ds,. dconstr "n".hlp (n PCR FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE 4

34 FullProf Restrans: d(c-c) oxalate= Frst cycle: => Dstance restrants: Dobs Dcalc dff/sgma (C1 - C3 ): (C - C ): Second cycle: (C1 - C3 ): (C - C ): Thrd cycle: (C1 - C3 ): (C - C ): FullProf No restrans => Global user-weghted Ch (Bragg contrb.):.35 => Phase: 1 => Bragg R-factor: 4.1 Vol: 61.68( 0.040) Fract(%): ( 0.91) => Rf-factor=.38 ATZ: Brndley: Restrans: d(c-c) oxalate= => Global user-weghted Ch (Bragg contrb.):.34 => Phase: 1 => Bragg R-factor: 4. Vol: 61.54( 0.040) Fract(%): ( 0.91) => Rf-factor=.43 ATZ: Brndley: FullProf rotators: (Adapted) / s l Q f 4 c Qr b y (, ) f slmp lmp l s s lmp Q s l 4 c Qr b K (, ) sl l l s s l Convergence at cycle 8: (C1 - C3 ): (C - C ): () () sn/, e C 60 (C60) SASH FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE 8 to relax Constant Wavelength Tme of Flght., :, (.,,,, (.). 80. to relax The program expect to read a lst Nspec_ref lnes contanng: h k l nvk D-HG^ Cod_D-HG^ D-HL Cod_D-HL Shft Cod_Shft The lst starts at the end of the profle parameters for a gven pattern. The Gaussan FWHM^ for a specal reflectons s calculated as: FWHM^ = FWHM^(resoluton parameters) + D-HG^ Sgma^= Sgma^(resoluton parameters) + D-HG^ D-HG^ s treated as a free parameter. The Lorentzan FWHM for a specal reflectons s calculated as: FWHM = FWHM(resoluton parameters) + D-HL Gamma = Gamma(resoluton parameters) + D-HL D-HL s treated as a free parameter. (CW) (TOF) (CW) (TOF) The poston of a specal reflectons s calculated as: Theta(degrees) = Theta(cell parameters,zero,etc.) + Shft TOF(mcro-scnds) = TOF(cell parameters,zero,dtt1,dtt,etc.) + Shft Shft s treated as a free parameter. to relax ()! ! Data for PHASE number: 1 ==> Current R_Bragg for Pattern# 1: 1.06! Myphase!!Nat Ds Ang Pr1 Pr Pr3 Jbt Irf Isy Str Furth ATZ Nvk Npr More !!Jv Jd Hel Sol Mom Ter Brnd RMua RMub RMuc Jtyp Nsp_Ref ! P 3 1 c <--Space group symbol ! Pref1 Pref Asy1 Asy Asy3 Asy4 S_L D_L ! Specal reflectons:! h k l nvk D-HG^ Cod_D-HG^ D-HL Cod_D-HL Shft Cod_Shft Na Ca 3Al F 14: shfts of peaks due to complex T.O.F. versus d-spacng FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE 3 Na Ca 3Al F 14: shfts of peaks due to complex T.O.F. versus d-spacng. Effect of relaxng some peak postons FullProf DataRED =============================== DATA REDUCTION PROGRAM: DataRED =============================== DataRED console,.,. FullProf.,..,.,,.. DataRED,. Software ( look before you try ): FullProf Sute and related programs: ftp://ftp.cea.fr/pub/llb/dvers/ FULLPROF SUITE FULLPROF SUITE FULLPROF SUITE (I) fm). N + / : S m = g J J () m = g S S () B - B Q (I) (I) (I) 4

35 FC magnetzaton data ZFC magnetzaton data ESR data Cure-Wess law ft FC magnetzaton data ZFC magnetzaton data ESR data Cure-Wess law ft k I =/ u I kf=/ uf Q= k F - k I ( n, m): 1 Q m Q am Q re f Qm Q 1 Q m Q am Q re f Qm p f Qm Q Q=Q e p= cm 3 f Q m rexp( Qr) d r m m m Q=h () I N N h h * h M h M * h Mh em(h) e M(h) e (em(h)) h h H k e h ml Sk exp krl k : n po f T M exp S s k M h h S Hk t r s ks 1 s (I) (I) (I) (I) 8 ks k ks -. k ks -. S M S exp{ } ks s k ks M s ks k Sk s C nsn( s) n : n po f T exp S s k M h h S Hk t r 1 s k s : s :. S t s k, : n po f T exp S s k M h h S Hk t r s k 1 s n po f TCn sexp k k n s M h h S h r 1 n s Magnetc structure of Tb 14Ag 51 (16 spns of Tb 3+ n the unt cell) from P. Fscher et al., Phys. Rev. B, (I) (I) (I) (I) 1? 1930 M <.... -,,,..: NdFeB, SmCo 5,, -.,. 193 Neel, Landau 1948 Neel 1950 th (canted) Yafet, Kttel, Dzyaloshnsk 1960 th Herpn et al th Brgeneau et al Toulouse 009 Magnetrcty Bramwell et al. 0????? 1931 Lous Néel M = 0 < N canted (I) (I) (I) (I) 16 L 1-x Mn +x TeO 6 (emu/mol) = -91 K LMn TeO 6 (a) T (K) (mol/emu) (emu/mol) = -93 K L 1.0 Mn 1.98 TeO 6 (b) T (K) ZFC FC (mol/emu) 154 Sm 0.3 Pr 0.18 Sr 0.5 MnO 3 : E J S S S 0? (1) J : () E J S S S 0? () J LMn TeO 6 (al 1.0Mn 1.98TeO 6 (b -. : (I) (I) (I) (I) 0

36 ErMnO 3, T N = 4 K (t) = (1 + a sn t) sn 0t 0t + a/ cos ( 0 + )t + a/ cos ( 0 )t () = F[(t)] 0 (t) = F -1 [()] Au Mn, 1961 K [m 1m ] K [m 1m ] S n = S [m 1cos(K t n) p m sn(k t n)], (LSW) K m (TSW) K m S n = S m sn(k t n), T m/t a n. S n [m 1m ], m 1 m = 0, m 1 = m p = 1, p : S n = S 1 exp(k t n) + S 1* exp(-k t n) (t) = (1 + a sn t+ a/ sn t) sn 0t ( 0,, ) (I) (I) (I) (I) 4. : 0(x) = b 0[1 + snt nt) : f() = f 1f, f 1= 0(x) exp)dx k( k/t), T c* Z Y m R n = exp(k n ) m 0, K U K = k propagaton) xa*+k yb*+k zc* b* S T. : (Gerard Toulouse, 1977) f = b 0[1 + (/t)] exp)dx = b 0 [() + /(+1/t) + /(-1/t)]. : X a* 3D : f() = f 1f = b 0 k [( k/t) + / ( k/t + 1/t) + / ( k/t - 1/t)] ( x ) t f ( ) 1/T 1/±1/t (), 1/8V c*. k x, k y, k z 0 1/, 1/3, 1/4. k x/h, k y/k, k z/l, H = ha*+kb*+lc* -. : YMnO 3 N- : 6Cl Kagomé ZnCu 3(OH) Ho T O 7 N = N = 3 N = 4 T x K: a*, b*, c*.. (R.B. Potts, 195) J cos Isng, (I) (I) (I) (I) 8 -: E ab a b/r 3, r E T C 0.1 K 6 T C E 0.1 ev - (r) (r) (r) (r) S a Symm. (r) S a S Antsymm. b : exchange nteracton) : : 4 Dy T O 7 Ho T O 7. two close two n : two far. two out. x = 6... H E I (S as b) - - * * I a (r1 ) b (r )Vab a (r ) b(r1 )dr1dr - Wolfgang Paul Werner Hesenberg Paul Drac John Van Vleck S b 0 1 (,.) (.) :, H E I (S as b) Hesenberg Drac Van Vleck Hamltonan, T (I) (I) (I) (I) 3 exchange nteracton), I ab(s as b) a b/r 3 - (v/c) (l as a) - (superexchange) Mn + - O - Mn + double exchange) Mn 3+ - O - Mn 4+ s-d (f) A sb(s S b) RKKI cos(k 3 FR ab)/r ab - D[S as b] (S as b) Kugel Khomsk couplng t /U (S as b) = - A + B ( ) + C + D [ ] +,,, FullProf. 8.. I II ( III IV : - + n - : ; ; ; (I) (II) (II) (II) 3

37 : (abc) K = (k x k y k z ) (x y z ) = ( x y z ) m Q m Q v' ~ [vr] R v ' b m ~ P(Q) s n S e (S e) e=qq P(Q(x) exp(q x) dv - s n = ½ - : (fm)1 fm=10-13 cm I hkl ~ F hklnuc + M hkl F hklmag Cu: b n = b m = -.65 (S = ½) F hklnuc b exp[(hx +ky +lz )T Mn: b n = -b m = (S = ) F hklmag = S P (Q)exp[(hx +ky +lz )T M hkl =[1 (em) ] = sn hkl. I e=qh mag f e m hkl hkl I mag em m=s P(Q) S n = exp(k L n ) S L 0 - L K L (S L 0) ( K L T n. S n = exp(k n ) S 0 K L = K 1 K L = K 1 S 0 = (0 1 0) T n = (h 0 0): S 0 = (0 1 0) T n = (h 0 0) S h = exp[ 0 = (-1) h S S h = exp[ 0 = (-1) h S 0 0 S k = exp[ 0 = S S k = exp[ 0 = (-1) k S (II) (II) (II) (II) 7 K L K L I. II. NO. ( I T low I T hgh) I + I - ). : AFM NOT N = 53 K FM ferr- K = (½ ½ 0AFM K = (k x k y k z). AFM K K. -k : K = (k x k y k z) K = (k x k y k z) Q = (q x q y q z)... : W. Opechowsk and R. Guccone Magnetc Symmetry E.F.Bertaut Representaton analyss of magnetc structures 1979 ë : (1') (). 1'. 1'... (Acta Cryst. 1968) 1' (II) (II) (II) (II) 11 - m m' A... (C1 ) - (Heesh - G' = g 1': 1651 g: 30 R( ) = g & 1': 30 ( g' = g 1': () T' = T 1' Pnma Pn'maPnm'aPnma'Pn'm'a Pnm'a'Pn'maPn'm'a' (C1') FM CrCl : = lm 1' -Fe = Im3m = Imm'm' R m ' g 1': t' R = : R : 3 1 (3 + 90) M(r) = M(r.. M(r) = 0. : ( ) Pnma: Pn'maPnm'aPnma' m m Pn'm'aPnm'aPn'ma' S S' Pn'm'a' - S S' P P C T' (P cp C) or body centered (P I). P c P I Acta Cryst D.V. Ltvn Tables of crystallographc propertes of magnetc space groups : G : G : : M = g(r) A(S) A(S) (II) (II) (II) (II) 15 I.. II = C C.. H. A. Hauptman Hstory of X-Ray Crystallography (Nobel Prze n Chemstry 1985) Erwn Felx Lewy-Bertaut Head of Laboratore de Dffracton Neutronque (1958) and Laboratore de Crstallographe (1971) n Grenoble. In 007 Erwn Felx Lewy Bertaut Prce of European Crystallographc Assocaton (ECA) and the European Neutron Scatterng Assocaton (ENSA) has been establshed. II. x3 III. - IV. (: () = C () () (II) (II) (II) (II) 19

38 o-18h.grf o-18hf ) y y /m 1 y m y 1 1 y m y y y 1 m y m y m y 1 y m y y : G W : G D(g) g 3 = g 1 g D(g 3) = D(g 1) D(g ) : D(g) g E D: 3D- G - G G a bca= cbc -1. -n 1. 3D. (representatonal) (E.F.Bertaut) S 0 = S S S 0 = S = 0 S(r) K...: II G G'. S n = exp(k n ) S 0 : (II) (II) (II) (II) 3 C1' C -vector: SuperCell [1] C1' C BasIrepsSARAhMODY[3] FullProf [1] (smulated annealng). ). GSAS [4] FPStudo [1] ISOTROPY [5] 1. Juan Rodríguez-. Andrew S. Wlls (UCL) magnetc_structures 4. Bob Von Dreele 5. H.T (II) (II) (II) (II) : F, AF-A AF-CE. F A F I, CE 0000 CE A 1.5K CE F CE AA A F 50K K K I. AF-A 155K N 170 K. AF-CE K K. AF 50K 0 II (deg) Intensty (arb. unts). (GSAS, FullProf) Intensty DMC SINQ : - : d d hkl 3 Å : - : d d hkl (Å) H(=1/d), -1 Intensty HRFD IBR- (La 0.5Pr 0.75) 0.7Ca 0.3MnO : AFM MnO, T N = 118 K Physcal Revew (1949) AFM of MnO Fm3m R-3m ( = 60.7º) T T N A m = a m = b m = c : (II) (II) (II) (II) 31 Sr GaMnO 5+ Sr GaMnO 5+ LPCM-90 LPCM-x T = 00 K G C LPCM-75 LPCM-70 AFM G T = 1.5 K AFM C Nuclear FM AFM-I AFM-II Sr GaMnO 5.5Pmmm C-type AFM Sr GaMnO 5Ima-type AFM Sr GaMnO 5.5Pmmm-type AFM Sr GaMnO 5Ima V.Yu.Pomakushn G-type AFM. - Pnmaa = Åb = Åc = 5.44 Å FM A1 A= 1.96(4) B. LPCM- LPCM-80 (b) LPCM-75 (HRPT & SLS) (II) (II) (II) (II) 35

39 Sr GaMnO 5+ B ) AFM (La 0.Pr 0.8) 0.7Ca 0.3MnO 3 DMC nstrument =.56 Å SINQ (PSI) T N T C at T < 80 K: FM (85%) + AFM CE(15%) (La 0.Pr 0.8) 0.7Ca 0.3MnO 3 DMC nstrument =.56 Å SINQ (PSI) T N T C at T < 80 K: FM (85%) + AFM CE(15%) (La 0.5Pr 0.75) 0.7Ca 0.3MnO 3 DMC =.56 Å SINQ (PSI) T N T C 1 at T < 80 K: FM (85%) + AFM CE(15%) LPCM- 16 O M FM (ac) - LPCM- 18 O AFM FM M AFM (b) - AFM G AFM C G AFM Mn A Mn C C T > T N + T < T C FM + AFM 10 < T < AFM T < AFM T < 1 FM + AFM (II) (II) (II) (II) 39 Sr 3 YCo 4 O ( = ) Sr 3YCo 4O Co1 Co RT HRPT Sr 3YCo 4O 10.5 Co1. T -4. : 14 K DMC Sr K=(0 0 0). 3YCo 4O Sr 3 YCo 4 O ( = ) 1. : I A I B >I AB IR.. : I AB > I A I B IR. Co1 Co1 Co Co Sr 3YCo 4O 10.5 Co1 Co Co D.V.SheptyakovV.Yu.PomakushnO.A.DrozhzhnS.Ya.IstomnE.V.AntpovI.A.Bobrkov Correlaton of chemcal coordnaton and magnetc orderng n Sr 3YCo 4O PRB Sr 3 YCo 4 O ( = ) IR BV Atom m a m b m c BV Atom m a m b m c (BV) k I4/mmm Co1 : : : Co : : : ¾) 8: ¼) Co Co Co U(Pd 0.98 Fe 0.0 ) Ge G4.1 (LLB) (T = 94 K). K z K z= 0.75 T=93 K. (0 ±.5) B. K = K z ) K z. z- z (II) (II) (II) (II) 43 (0,0). FullProf Studo 1 FullProf Studo. : : SuperCell : BasIreps Smulated annealng: FullProf 3. 4 FullProf. Smulated annealng. 5.. y 4 (1,3) (0,0)? (II) (II) (III) (III) S C S s k ks n n n C- n ( ) : k : : n : 1 n : 1 dm ( ) Mag n : ml S k exp krl k m l S - S R l l 1 3 k k - l R r l a l b l c x a y b z c. : : k=1/ H[k = (0,0,0)] m exp kr S n( l) l Sk l k -1 k : :. FST FullProf Studo! Artfcal example for a helcal magnetc structure SPACEG P m m m CELL multple box ATOM HO HO color radus 0.8 ATOM NI NI color { LATTICE P K SYMM x,y,z MSYM u,v,w, 0.0! x y z optons MATOM Ho HO color scale 0.6 GROUP Rx Ry Rz Ix Iy Iz MagPh! K MSY SKP MATOM N NI color GROUP Rx Ry Rz Ix Iy! K MSY Iz MagPh SKP } (III) (III) (III) (III) 6

40 SPACEG P m m m CELL multple box ATOM HO HO color radus 0.8 ATOM NI NI color { LATTICE P K SYMM x,y,z MSYM u,v,w, 0.0 MATOM Ho HO color scale 0.6 GROUP SKP MATOM N NI color GROUP SKP } SPACEG P m m m CELL multple box ATOM HO HO color radus 0.8 ATOM NI NI color { LATTICE P K SYMM x,y,z MSYM u,v,w, 0.0 MATOM Ho HO color scale 0.6 GROUP SKP MATOM N NI color GROUP SKP } k =(0, 0, 0) c b a k=(1/, 0, 0) c b a k=(1/, 0, 1/) c b a k ( -k). S k. m S exp( kr ) S exp( kr ) l k l -k l 1 Sk m u exp( k ) m m u cos ( kr ) l l k (III) (III) (III) (III) 10 k=( , 0.0, 0.0) c a k =( , 0.0, 0.345) c, k. S k a b 1 Sk muu mvv exp( k ) m m u cos ( kr ) m v sn ( kr ) k l u l v l k (III) (III) (III) (III) 14 h = H+k DyMn 6 Ge 6 k=(0,0,0) k= =(0,0,)=(0,0, 0.165) a b b m a = a m b=b m : {k} a m H - k ( k - k= (1/, 1/) k= (0, 0) (III) (III) (III) (III) 18 FullProf : Jbt = +/- 1 n M h po f ht Sk s exp H ks t r s 1 s. S ks k! ! Data for PHASE number: ==> Current R_Bragg for Pattern# 1: 4.09! LaMnO3!!Nat Ds Mom Pr1 Pr Pr3 Jbt Irf Isy Str Furth ATZ Nvk Npr More ! P m m m <--Space group symbol!nsym Cen Laue MagMat ! SYMM x,y,z MSYM u,v,w,0.0 SYMM -x,-y,z+1/ MSYM -u,-v,w,0.0 SYMM -x+1/,y+1/,-z+1/ MSYM u,-v,w,0.0 SYMM x+1/,-y+1/,-z MSYM -u, v,w,0.0!!atom Typ Mag Vek X Y Z Bso Occ Rx Ry Rz! Ix Iy Iz beta11 beta beta33 MagPh Mn1 MMN FullProf : Jbt = +/- 1 Isy=- n k h po f ht Cn Sn sexp h sr k M 1 Irreps ( ). C1, C, C3,. n s S C S s k ks n n n C n LaMnO3!!Nat Ds Mom Pr1 Pr Pr3 Jbt Irf Isy Str Furth ATZ Nvk Npr More ! P m m m <--Space group symbol! Nsym Cen Laue Ireps N_Bas ! Real(0)-Imagnary(1) ndcator for C 0 0 0! SYMM x,y,z BASR BASI SYMM -x+1,-y,z+1/ BASR BASI SYMM -x+1/,y+1/,-z+1/ BASR BASI SYMM x-1/,-y+1/,-z BASR BASI !!Atom Typ Mag Vek X Y Z Bso Occ C1 C C3! C4 C5 C7 C8 C9 MagPh C6 Mn1 MMN (III) (III) (III) (III)

41 LaMnO 3 : 50K 150 K LaMnO 3 : SuperCell ( FullProf Sute WnPLOTR) LaMnO 3 : Extracton : 50K -150K : SuperCell (J. Rodríguez-Carvaal, 1998). " ".,. k=(0,0,0) = (III) (III) (III) (III) 6 SuperCell BasIreps (Sm. Ann.) FullProf k- / GUI BasIreps BasIreps G k m S ls S k exp kr ks k n s C S k n n BasIreps ( k Sn s s l FULLPROF SUITE (III) (III) (III) 9 FullProf : (0,A y,0), FullProf Smulated annealng k=(0,0,0), =1, n=1,,3 =1, =1, s=1,,3,4 S k n s (III) (III) (III) (III) 33 Smulated Annealng: SA -, : Krpatrck, Gelatt and Vecch, Scence 0, (1983). cost, E(),. : - ( Metropols) to mmc, : ( + ). ( ) ( ) Smulated Annealng (SA): SA : J. Panneter, J. Bassas-Alsna, J. Rodríguez-Carvaal and V. Cagnaert, Nature 346, (1990) J.M. Newsam, M.W. Deem and C.M. Freeman, Accuracy n Powder Dffracton II. NIST Specal Publ. No. 846, (199) J. Rodríguez-Carvaal, Physca B 19, (1993) (program MAGSAN) Smulated Annealng : Look drectly : S k, C1, C, C3, C4, C5,... Cm N Rmc G rg r, r1 obs calc Smulated Annealng run of FullProf (III) (III) (III) (III) 37

42 AFM fracton seen by usr Smulated Annealng run of FullProf Smulated Annealng 1.00 LMn O 4 Muon spn spectroscopy) (SR): + e e J-PARC : N = N 0e -t/ [1 + ap(t)cos(t + )] 0.80 Phases (mod Ph_Mna1 Ph_Mna Ph_Mna3 Ph_Mna4 (SR) -Mössbauer effect) /T (NMR) NMR 4 SR (III) (III) (III) (III) 41 La CuO 4+x SR Physca C7 (1996) 77; Phys. Rev. B 58 (1998) 1350 La CuO 4.04 : Pb 1.1 Ba 0.9 Fe O 5 : 57 Fe - NO nm) La T CuO 4.04 c T N lco La CuO 4.04 La CuO 4.0. AFM (100) x = 0.04 x = 0.0. Fe. T N = 65 K K. T > 50 K. NO 1500 nm 100 nm.. (100) peak area T, K AFM SR AFM fracton, % P(t) La CuO 4.0. T=4 K. Pb 1.1Ba 0.9Fe O 5. - AFM T N = 65 K. : G + / G + and G + / G - - T>50 K. 57 Fe - -7 s. I.V. Nkolaev NO 13 nm 138 nm NO (III) (III) (III) (I),, y S Ih( Th T) b h C W S ( ZMV ) D.L.Bsh & S.A.Howard, J.Appl.Cryst. 1, 86 (1988) C W S ( ZMV ) D.L.Bsh & S.A.Howard, J.Appl.Cryst. 1, 86 (1988) constrant 1, : S( ZMV) W S( ZMV) 1,... n S( ZMV) / W S( ZMV) / Brndley 1,... n D.L.Bsh & S.A.Howard, J.Appl.Cryst. 1, 86 (1988) FullProf Brndley: r (: ; r: ). : r < : 0.01 < r < 0.1. : 0.1 < r < 1.0. : r > (I) (I) (I) (I) 5 Brndley Brndley =1, : ( ) r1.46 ( ) r G.W. Brndley, Phlosophcal Magazne. 36, 347 (1945) 0.1 ( ) r 0.1 (Brndley): 0.01 r 0.1 r - - wth S W S ( ZMV). f S ATZ. V N N S.( ZMV). f S ATZ. V 1 1 FullProf () FullProf Brndley( ( -).r FullProf ATZ ZM f FullProf f FullProf FullProf f (Wyckoff mm f=occ. M/mocc. ATZ. ATZ PCR. FullProf 1.: JBT=0 (IRF=0).:.1 hkl hkl F (JLKH=5). g JBT=-3IRF= (Le Bal ) (I) (I) (I) (I) 9

43 Q theta ( ) (Q.P.A.) Q.P.A.: a-s 3 N 4 b-s 3 N 4 Q.P.A.: a-s 3 N 4 b-s 3 N 4 (FullProf) FullProf () ( ) {F hkl} : S 3N 4: 93% S 3N 4: 7% : S 3N 4: 91.6% bs 3N 4: 8.4% (I) (I) (I) (I) 13 Q.P.A. R.J. Hll & C.J. J. Appl. Cryst (1987) Quanttatve phase analyss from neutron powder dffracton data usng the Retveld method stran sze G.W. Brndley Phl. Mag (1945) The effect of gran or partcle sze on X-ray reflectons from mxed powders and alloys consdered n relaton to the quanttatve determnaton of crystallne substances by X-ray methods D.L. Bsh & S.A. J. Appl. Cryst (1988) Quanttatve phase analyss usng the Retveld method J.C. Powder Dffracton 6-9 (1991) Computer programs for standardless quanttatve analyss of mnerals usng the full powder dffracton profle R.J. Powder Dffracton (1991) Expanded use of Retveld method n studes of phase abundance n multphase mxtures FullProf (I) (II) (II) (II) 3 dsn d d0 d d 0 d hkl 0 hkl d 1 cot 0 ( ) d0,,.., const Ko Intensty (a.u) Q 0 K (II) (II) (II) (II) 7 Neutron beam from source Monochromator Beam defnng optcs for the ncdent beam Specmen and sheldng. Gauge Q volume Beam defnng optcs for the PSD dffracted beam and - sheldng Beam stop FullProf WnPLOTR IRF (Instrumental Resoluton Fle) FullProf IRF ZERO FWHM. (IRF) IRF (keywords) -. =7. keywords: ( ) ( ):. Instrumental Resoluton Functon 1: JOBT ob (character varable) wth ob = 'neuc' or 'NEUC' for obtyp = 3 ob = 'neut' or 'NEUT' for obtyp = 1 ob = 'tof or 'TOF' for obtyp = -1 ob = 'tofc' or 'TOFC' for obtyp = -3 ob = 'xr' or 'XR' for obtyp = 0 ob = 'xrc or 'XRC' for obtyp = : WAVE lambda1, lambda, rato (3 ) 3: PROF nprofle, shape1, shape, shape3 ) 4: ASYM S_L, S_D () (II) (II) (II) (II) 11

44 : CeO CeO PCR: CeO (FWHM): U, V, W, I G, X, Y IG HG U tan V tan W cos Y HL X tan cos (II) (II) (II) (II) 15 CeO : 0.9 D Bcos Intensty (a.u.) B Intensty (a.u.) B area = 5 a.u. ( 0 ) ( 0 ) (II) (II) (II) (II) (II) 19