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2013 6 6!! 25!!

RIETAN-FP [1] VESTA [2]

{ y 1, y 2,, y N } { Y 1,Y 2,,Y N } { σ 1,σ 2,,σ N }! L ν = N j=1 ν Y j y j ν σ j 1/ν ν L2 L2 L2 { Y j } { y j } { σ j }! p normal ( Y j ) = ( ) 2 1 exp Y y j j 2 2πσ j 2σ j Y 1, Y 2,, Y N { Y 1,Y 2,,Y N }! P( Y 1,Y 2,,Y N ) = p normal ( Y 1 ) p normal ( Y 2 ) p normal ( Y N )!! = ( ) 2 1 exp Y y 1 1 2 2πσ 1 2σ 1 ( ) 2 1 exp Y y 2 2 2 2πσ 2 2σ 2 ( ) 2 1 exp Y y N N 2 2πσ N 2σ N

( ) 2 1 N!! = exp Y y j j ( 2π ) N 2 σ 1 σ 2 σ j=1 2σ j N { σ j } L2! L 2 = N j=1 2 Y j y j 2 σ j 1/2 P( Y 1,Y 2,,Y N ) { Y 1,Y 2,,Y N }! = Y 1 + Y 2 + + Y N N L2 y 1 = y 2 = = y N σ 1 = σ 2 = = σ N { Y j } 0, 1, 2,... { y j }! p Poisson Y j ( ) = 1 ( ) Y j ( Y j )! y j exp( y j ) σ j = y j ν < 2 ν < 2 L1! L 1 = N j=1 Y j y j σ j L1

{ Y 1,Y 2,,Y N } L1 L1 L1 ν > 2 ν ν! L = lim ν N j=1 Y j y j σ j ν ν 1/ν = max Y y j j σ j L L { Y 1,Y 2,,Y N } L

L2 (1) (2) (3) (4) (5) (1) g x, y, z B (2) a, b, c, α, β, γ(3), (4), (5) Pauling Bond valence Brown Altermatt Bond valence sum n! BVS = exp r r 0 j b j=1 n r j r 0 bond valence parameter b 0.37 A Brown Altermatt 1985 141 bond valence parameter [3] b BVS

AtomWork AtomWork AtomWork (MatNavi) AtomWork (1) AtomWork Web AtomWork NIMS (2) AtomWork AtomWork TeraPad Windows 7 TeraPad

(1) Z: Program Files Program Files (2) TeraPad (3) TeraPad (4) TeraPad Program Files (x86) (5) TeraPad Program Files Program Files TeraPad TeraPad Crrl (1) Shift Shift Shift Shift (2) Ctrl C (3) Ctrl V (4) Ctrl F (5) Ctrl S (6) Ctrl Z RIETAN-FP RIETAN-FP

RIETAN-FP (1) Web Web RIETAN-FP VENUS RIETAN-FP VENUS (2) RIETAN-FP VENUS documentation.zip (3) documents Readme_Win.pdf C: Z: Windows_versions RIETAN-FP Install_RIETAN_VENUS.bat (4) Install_RIETAN_VENUS.bat (5) C: Z: (6) (7) RIETAN-FP Install_RIETAN_VENUS.bat (8) RIETAN_VENUS_examples Program Files RIETAN_VENUS RIETAN-FP RIETAN-FP (1) RIETAN_VENUS_examples FapatiteJ

(2) FapatiteJ *.bat, *.ins, *.int Ctrl (3) FapatiteJ.bat... C: Z: (4) FapatiteJ.bat (5) *.lst RIETVIEW (6) Windows_versions VESTA VESTA VESTA edsys VESTA (1) Web Web VESTA (2) Web VESTA

BaSO4 (1) BaSO4 (2) RIETAN_VENUS RIETAN_VENUS_examples BaSO4_LB BaSO4 BaSO4.int BaSO4 (3) BaSO4.int BaSO4.int...... TeraPad.exe OK TeraPad (4) GENERAL 2Θ Y (5) BaSO4.int BaSO4 (1) Web AtomWork Web

(2) AtomWork AtomWork (3) AtomWork (MatNavi) e-mail (4) Search materials Inorganic Material Database Find materials that have... Chemical system - e.g. Mg Al Ba S O Search materials Ba S O (5) Ba[SO4] (6) BaSO4 Miyake 1978 American Mineralogist Am. Mineral. [M. Miyake, I. Minato, H. Morikawa and S. Iwai, Am. Mineral. 63, 506 510 (1978)] Web Data type Structure (7) Space group Space group: Pnma, No. 62 (8) Crystal Structure (Standardized) cell parameters Crystal structure (Published)... (Standardized) Cell parameters: a = 0.8884 nm, b = 0.5457 nm, c = 0.7157 nm, α = 90º, β = 90º, γ = 90º (9) Crystal Structure (Standardized) Atom coordinates Ba, S, O1, O2, O3

RIETAN-FP *.bat RIETAN-FP *.ins (1) RIETAN_VENUS_examples FapatiteJ Fapatite Fapatite_LB FapatiteJ.bat FapatiteJ.ins BaSO4 (2) FapatiteJ.bat C: Z: SET SAMPLE=FapatiteJ SET SAMPLE=BaSO4 (3) FapatiteJ.bat FapatiteJ.ins BaSO4.bat, BaSO4.ins (4) BaSO4.ins RIETAN-FP BaSO4.ins (*.ins) *.ins (1) 45 Fluorapatite, Ca5F(PO4)3

Barite, BaSO4 (2) NBEAM = 1: 48 BaSO4 (3) NMODE = 0: 51 (4) NPRINT = 062 (5) NTARG = 4: 76 CuKα (6) R12: Kα2/Kα1 81 BaSO4 BaSO4.int Kα2 R12 = 0.5:... R12 = 0.0:... (7) CTHM1 = 0.7998: 82 (8) NSURFR = 0: 84 (9) NTRAN = 0: 91 - (10)135 O- P Ca2+ F- / Ba S O / (11) PHNAME1: 168 PHNAME1 = 'Fluorapatite': (25). PHNAME1 = 'Barite': (25). (12) VNS1: 170 VNS1 = 'A-176': (Vol.No. of Int.Tables: A or I)-...

VNS1 = 'A-62': (Vol.No. of Int.Tables: A or I)-... (13) HKLM1: 173 HKLM1 = 'P 63/m ': hklm Hermann-Mauguin... HKLM1 = 'P n m a ': hklm Hermann-Mauguin... (14) LPAIR1: Bijvoet 180 Barite (15) INDIV1: 189 (16) IHA1, IKA1, ILA1: 192 194 (17) IHP1, IKP1, ILP1: 204 206 IHP1 = 1 IKP1 = 0 ILP1 = 0 (18) IHP2, IKP2, ILP2, IHP3, IKP3, ILP3: 208 214 (19) NPRFN: 231 NPRFN = 1 (20) NSHIFT: 246 NSHIFT = 4 (1) SHIFTN: 285 SHIFTN 7.11466E-2 2.42176E-2 3.77026E-3 0.0 1000

SHIFTN 0.0 0.0 0.0 0.0 0000 (2) ROUGH: 289 (3) BKGD: 292 293 #, bj (j = 0 11). BKGD 114.731-1.26701E2 139.203-1.01934E2 68.1125-3.94252E123.2694-7.40064-2.04399 3.59303 0.0 0.0 111111111100 10 9 (1) SCALE: 309 (2) 347 362 # : pseudo-voigt, :... #, U, V, W, a dummy. FWHM12 5.77812E-3-1.63943E-3 5.65595E-3 0.0 1110 #, a0, a1, a2, a dummy. ASYM12 1.04564 0.14424-4.14686E-2 0.0 1110 #, eta_l0, eta_l1, eta_h0, and eta_h1. ETA12 0.6106 0.13955 0.502513 0.177147 1111 #, Ue and Pe. ANISOBR12 0.0 0.0 00 # 16. DUMMY12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0000000000000000 # : pseudo-voigt, :... #, U, V, W, a dummy.

FWHM12 5.77812E-3-1.63943E-3 5.65595E-3 0.0 0000 #, a0, a1, a2, a dummy. ASYM12 1.04564 0.14424-4.14686E-2 0.0 0000 #, eta_l0, eta_l1, eta_h0, and eta_h1. ETA12 0.6106 0.13955 0.502513 0.177147 0000 #, Ue and Pe. ANISOBR12 0.0 0.0 00 # 16. DUMMY12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0000000000000000 (3) PREF: 386 PREF 1.0 0.998462 0.0 0.0 0.0 0.0 010000 PREF 1.0 1.0 0.0 0.0 0.0 0.0 000000 (4) CELLQ: 389 BaSO4 AtomWork CELLQ 9.36903 9.36903 6.88384 90.0 90.0 120.0 0.0 1010000 CELLQ 8.884 5.457 7.157 90.0 90.0 90.0 0.0 1110000 (5) 397 BaSO4 AtomWork O1/O- 1.0 0.324174 0.485349 0.25 0.744733 01101 O2/O- 1.0 0.591772 0.469808 0.25 0.743478 01101 O3/O- 1.0 0.339147 0.257266 6.98124E-2 0.835736 01111 P/P 1.0 0.397305 0.367871 0.25 0.552323 01101 Ca1/Ca2+ 1.0 0.333333 0.666667 1.33243E-3 0.648404 00011 Ca2/Ca2+ 1.0 0.241797-7.95224E-3 0.25 0.531459 01101

F/F- 1.0 0.0 0.0 0.25 1.42612 00001 Ba/Ba 1.0 0.1845 0.25 0.6585 0.5 00000 S/S 1.0 0.0625 0.25 0.1911 1.0 00000 O1/O 1.0 0.4122 0.25 0.394 1.0 00000 O2/O 1.0 0.1823 0.25 0.0494 1.0 00000 O3/O 1.0 0.0801 0.0298 0.3114 1.0 00000 (1) NCUT: (2) NEXC: (3) NINNT: 1 (4) NRANGE: (5) NPAT: (6) IWIDTH, IHEIGHT, IYMIN, IYMAX, LBG, LDEL, IOFFSETD, IPSIZE, IFSIZE, ILSIZE: (7) INDREF: (8) IOFFSET1: (6) PC: 7.00 (7) NLESQ: (8) NESD: (9) NAUTO: (10)NCYCL: 100 (11)CONV: (1) 0.0001 (12)NCONV: (2) 6

(13)NC: 0 (14)NUPDT: NUPDT = 0:... NUPDT = 1!... NUPDT = 0!... NUPDT = 1:... (15) NFR: (16) NMEM: NPRINT = 0 *.lst NMEM = 1 (17) NDA: NDA = 1 (18) TITLE: *.fos TITLE = 'Fluorapatite' TITLE = 'Barite' (19) LANOM, NPIXA, NPIXB, NPIXC, LGR, LFOFC, EPSD, TSCAT1, TSCAT2: *.ins *.ins

*.ins VESTA (1) VESTA (2) File Open... BaSO4.ins (3) [Edit] [Bonds...] Bonds - BaSO4.ins (4) [New] Seach mode Search A2 bonded to A1 Boundary mode Search additional atoms if A1 is included in the boundary (5) A1: S A2 O Max. length: 3 S 3 A O (6) [Apply] S O (7) [Ok] Bonds - BaSO4.lst (8) [Style] Style Polyhedral (9)

(10) *.ins VNS1 CELLQ VESTA *.ins *.ins (1) BaSO4.bat (2) RIETVIEW (3) RIETVIEW EditUndo Axis 6,000 (4) RIETVIEW Click OK to quit the output window OK (5) RIETAN-FP BaSO4.lst

(6) *.lst R (7) R Rwp Rwp 20 % Structure parameters Atom Site neq * g =... Ba 4c x 1/4 z 4 1.0000... - -... S 4c x 1/4 z 4 1.0000... - -... O1 4c x 1/4 z 4 1.0000... - -... O2 4c x 1/4 z 4 1.0000... - -... O3 8d x y z 8 1.0000... - -... O3 8d 4c x, 1/4, z Ba, S, O1, O2 y 0.25 (i) (ii) (iii) (iv) (v)

Ba O B 0.5 1.0 (1) BaSO4.ins SHIFTN 0.0 0.0 0.0 0.0 0000 SHIFTN 0.0 0.0 0.0 0.0 1110 (2) IYMAX = 20000: y ( ). IYMAX = 7000: y ( ). (3) BaSO.ins (4) BaSO4.bat (5) RIETVIEW (1) BaSO4.ins (2) (U, V, W) # : pseudo-voigt,...

#, U, V, W, a dummy. FWHM12 5.77812E-3-1.63943E-3 5.65595E-3 0.0 0000 FWHM12 5.77812E-3-1.63943E-3 5.65595E-3 0.0 1110 BaSO4.ins U W V (3) BaSO4.bat (4) RIETVIEW (1) BaSO4.ins (2) (a0, a1, a2) # : pseudo-voigt,... #, U, V, W, a dummy. FWHM12 5.77812E-3-1.63943E-3 5.65595E-3 0.0 1110 #, a0, a1, a2, a dummy. ASYM12 1.04564 0.14424-4.14686E-2 0.0 0000 FWHM12 ASYM12 1.04564 0.14424-4.14686E-2 0.0 1110 (3) BaSO4.bat (4) RIETVIEW (1) BaSO4.ins (2) (eta_l0, eta_l1, eta_h0, eta_h1) # : pseudo-voigt,...

#, U, V, W, a dummy. FWHM12 5.77812E-3-1.63943E-3 5.65595E-3 0.0 1110 #, a0, a1, a2, a dummy. ASYM12 1.04564 0.14424-4.14686E-2 0.0 1110 #, eta_l0, eta_l1, eta_h0, and eta_h1. ETA12 0.6106 0.13955 0.502513 0.177147 0000 FWHM12 ASYM12 ETA12 0.6106 0.13955 0.502513 0.177147 1111 (3) BaSO4.bat (4) RIETVIEW (1) BaSO4.ins (2) Ba x z Ba y 0.25 Ba/Ba 1.0 0.1845 0.25 0.6585 0.5 00000 Ba/Ba 1.0 0.1845 0.25 0.6585 0.5 01010 Ba y (3) BaSO4.bat (4) RIETVIEW (1) BaSO4.ins

(2) Ba B S, O1, O2, O3 x, y, z Ba, S, O1, O2 y 0.25 Ba/Ba 1.0 0.1845 0.25 0.6585 0.5 01010 S/S 1.0 0.0625 0.25 0.1911 1.0 00000 O1/O 1.0 0.4122 0.25 0.394 1.0 00000 O2/O 1.0 0.1823 0.25 0.0494 1.0 00000 O3/O 1.0 0.0801 0.0298 0.3114 1.0 00000 Ba x, z Ba/Ba 1.0 0.1845 0.25 0.6585 0.5 01011 S/S 1.0 0.0625 0.25 0.1911 1.0 01010 O1/O 1.0 0.4122 0.25 0.394 1.0 01010 O2/O 1.0 0.1823 0.25 0.0494 1.0 01010 O3/O 1.0 0.0801 0.0298 0.3114 1.0 01110 (3) BaSO4.bat (4) RIETVIEW (1) BaSO4.ins (2) S, O1, O2, O3 B Ba/Ba 1.0 0.1845 0.25 0.6585 0.5 01011 S/S 1.0 0.0625 0.25 0.1911 1.0 01010 O1/O 1.0 0.4122 0.25 0.394 1.0 01010 O2/O 1.0 0.1823 0.25 0.0494 1.0 01010 O3/O 1.0 0.0801 0.0298 0.3114 1.0 01110 Ba B S, O1, O2, O3 x, y, z Ba/Ba 1.0 0.1845 0.25 0.6585 0.5 01011

S/S 1.0 0.0625 0.25 0.1911 1.0 01011 O1/O 1.0 0.4122 0.25 0.394 1.0 01011 O2/O 1.0 0.1823 0.25 0.0494 1.0 01011 O3/O 1.0 0.0801 0.0298 0.3114 1.0 01111 (3) BaSO4.bat (4) RIETVIEW RIETVIEW

R (1) RIETVIEW 20º 50º (2) BaSO4.lst (3) Reliability factors,... Rwp 12 % % Re 10 % Re Rwp Re Re (4) BaSO4.lst *** Summary of possible reflections (based on the refined... (5) RIETVIEW BaSO4.lst RIETVIEW hkl! 2-theta! Iobs!! Ical 011! 20.472! 12447! 13676! (Iobs < Ical) 111! 22.814! 41762! 46866! (Iobs < Ical) 002! 24.884! 31995! 29778! (Iobs > Ical) 210! 25.874! 92965! 97218! (Iobs < Ical) 102! 26.863! 76833! 68112! (Iobs > Ical) 020! 32.837! 39397! 46934! (Iobs < Ical)

hkl2-thetaiobs 100000 Ical (6) h0l Iobs > Ical0k0 Iobs < Ical b b (1) BaSO4.ins (2) IHP1, IKP1, ILP1: IHP1 = 1 IKP1 = 0 ILP1 = 0 IHP1 = 0 IKP1 = 1 ILP1 = 0 (3) PREF 1.0 1.0 0.0 0.0 0.0 0.0 000000 PREF 1.0 1.0 0.0 0.0 0.0 0.0 010000 (4) BaSO4.bat (5) RIETVIEW

(6) BaSO4.lst (7) *** R factors, final parameters, and... Preferred-orientation parameter, r1 1.1016(14) (8) Reliability factors,... Rwp 9 % Re 10 % Rwp Re (9) *** Summary of possible reflections (based on the refined... POF (preferred orientation correction) hkl! 2-theta! Iobs!! Ical!! POF 011! 20.468! 25230! 27636! 0.865 111! 22.810! 41763! 44912! 0.911 002! 24.879! 32048! 32047! 1.156 210! 25.869! 92955! 95074! 0.957 102! 26.858! 76871! 77113! 1.156 020! 32.831! 36265! 35715! 0.748

(1) Cu Kα1 (2) (3) (4) (5) (6) (7) (8) Rwp (9) (10) (11) (12) (1) (2) 1 2 1 2 (3) (4) (5)

CuKα1 X 2Θ: 20º 130º 0.02º BaSO4 RIETAN-FP [1] 10 Miyake [2] Pnma (#62) Rwp =?.?? %... Site g a =?.????(?) A b =?.????(?) A c =?.????(?) A Vcell =???.???(?) A 3 Z =? dcalc =?.?? Mg/m 3 Atom site g x y z B (A 2 ) Ba 4c 1 0.18443(9) 1/4 0.65894(9) 0.739(18) S... O1... O2... O3... [1] F. Izumi and K. Momma, Solid State Phenom., 130, 15 20 (2007). [2] M. Miyake, I. Minato, H. Morikawa and S. Iwai, Am. Mineral., 63, 506 510 (1978).

BVS; Bond Valence Sum SO4 2 (1) VESTA [File] [Open...] BaSO4.lst (2) [Edit] [Bonds...] Bonds - BaSO4.lst (3) [New] Search mode Search A2 bonded to A1 Boundary mode Search additional atoms if A1 is included in the boundary (4) A1: S A2 O Max. length: 3 (5) [Apply] S O (6) [Ok] Bonds - BaSO4.lst (7) [Style] Style Polyhedral (8) Select Select (9) SO4 (10) bond angle bond angle (11) O1 S O2 O1 S O2

SO4 Bond type length (A ) S O1 1.418(8) S O2 1.508(8) S O3, S-O3 1.476(4) Bond type angle (º) O1-S-O2 117.5(3) O2-S-O3, O2-S-O3 107.0(3) O1-S-O3, O1-S-O3 107.9(3) O3-S-O3 109.3(3) BVS Ba BVS Bond Valence Sum (1) Web documents VESTA bvparm2011.cif (2) bvparm2011.cif Ba 2 O -2... Ba +2 O 2 bond valence parameter r 0 b 0.37 VESTA b 0.37 (3) VESTA [Edit] [Bonds...] Bonds - BaSO4.lst (4) S O B O (5) [Ctrl] [Shift] Ba Mac [Shift]+[Command]+

(6) Bond valence parameter bvparm2011.cif r 0 (7) VESTA bond valence sum BVS 0.2 [4] M. Miyake, I. Minato, H. Morikawa and S. Iwai, Am. Mineral., 63, 506 510 (1978).

ishizawa.nobuo@nitech.ac.jp ida.takashi@nitech.ac.jp 2013 A4 507 0071 10 6 29 PDF (Portable Document Format) Microsoft Word

(1) xx (2) (3) (4) Introduction

results discussion results and discussion x discussion Acta Crystallographica discussion discussion

conclusion [1] F. Izumi and K. Momma, Solid State Phenom., 130, 15 20 (2007). [2] K. Momma and F. Izumi, J. Appl. Crystallogr., 44, 1272-1276 (2011). [3] I. D. Brown and D. Altermatt, Acta Cryst. B 41, 244 247 (1985). [4] M. Miyake, I. Minato, H. Morikawa and S. Iwai, Am. Mineral., 63, 506 510 (1978).