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2 RIETAN-FP [1] VESTA [2] { } { Y,Y,!,Y 1 2 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
3 L2 L2 L2 { Y j } y j p normal ( Y j ) = Y 1, Y 2,!, Y N Y 1,Y 2,!,Y N L2 { } { σ j } ( ) 2 1 exp Y y j j 2 2πσ j 2σ j { } P( Y 1,Y 2,!,Y N ) = p normal ( Y 1 ) p normal ( Y 2 )! p normal ( Y N ) = = ( ) 2 1 exp Y y πσ 1 2σ 1 ( ) 2 1 exp Y y πσ 2 2σ 2 ( ) 2 1 N exp Y y j j ( 2π ) N 2 σ 1 σ 2!σ j=1 2σ j N { σ j } ( ) 2! 1 exp Y y N N 2 2πσ N 2σ N L 2 = j=1 N 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 σ = σ =! = σ N 1 2 N
4 0, 1, 2,... p Poisson ( Y j ) = 1 Y j { Y j } y j ( ) Y j ( )! y j σ j = y j exp( 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
5 L = lim ν N j=1 Y j y j σ j ν L L ν 1/ν = max Y y j j σ j { } 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)
6 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 bond valence parameter [3] b BVS AtomWork AtomWork AtomWork (MatNavi) AtomWork
7 (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
8 (1) Shift Shift Shift Shift (2) CtrlC (3) CtrlV (4) CtrlF (5) CtrlS (6) CtrlZ 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: (4) Web RIETAN-FP VENUS Windows_versions.zip (A)
9 Z: D: (5) Windows_versions_ zip (T) Z: Windows_versions_ Z: (6) Windows_versions_ Windows_versions RIETAN_VENUS RIETAN_VENUS_examples (7) RIETAN_VENUS Z: Program Files (8) RIETAN_VENUS_exapmles Z: RIETAN-FP RIETAN-FP (1) RIETAN_VENUS_examples FapatiteJ (2) FapatiteJ *.ins, *.int Ctrl (3) Web FapatiteJ.bat.txt FapatiteJ FapatiteJ.bat (4) FapatiteJ.bat (5) *.lst
10 VESTA VESTA VESTA edsys VESTA (1) Web Web VESTA (2) Web VESTA
11 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
12 (3) AtomWork (MatNavi) (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, (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 = nm, b = nm, c = nm, α = 90º, β = 90º, γ = 90º (9) Crystal Structure (Standardized) Atom coordinates Ba, S, O1, O2, O3 RIETAN-FP *.bat RIETAN-FP *.ins
13 (1) FapatiteJ FapatiteJ.ins BaSO4 BaSO4.ins Web BaSO4.bat (2) BaSO4.ins RIETAN-FP BaSO4.ins (*.ins) *.ins (1) 33 Fluorapatite, Ca5F(PO4)3 Barite, BaSO4 (2) NBEAM = 1: 38 BaSO4 (3) NMODE = 0: 43 (4) NPRINT = 051 (5) NTARG = 4: 72 CuKα (6) R12: Kα2/Kα1 77 BaSO4 BaSO4.int Kα2 R12 = 0.5:... R12 = 0.0:... (7) CTHM1 = : 78
14 (8) NSURFR = 0: 80 (9) NTRAN = 0: 87 - (10) 134 O- P Ca2+ F- / Ba S O / (11) PHNAME1: 170 PHNAME1 = 'Fluorapatite': ( 25 ). PHNAME1 = 'Barite': ( 25 ). (12) VNS1: 172 VNS1 = 'A-176': (Vol.No. of Int.Tables: A or I)-... VNS1 = 'A-62': (Vol.No. of Int.Tables: A or I)-... (13) HKLM1: 175 HKLM1 = 'P 63/m ': hkl m Hermann-Mauguin... HKLM1 = 'P n m a ': hkl m Hermann-Mauguin... (14) LPAIR1: Bijvoet 182 Barite hkl h k l (15) INDIV1: 191 (16) IHA1, IKA1, ILA1: (17) IHP1, IKP1, ILP1:
15 IHP1 = 1 IKP1 = 0 ILP1 = 0 (18) IHP2, IKP2, ILP2, IHP3, IKP3, ILP3: (19) NPRFN: 234 NPRFN = 1 (20) NSHIFT: 249 NSHIFT = 4 (1) SHIFTN: 289 SHIFTN E E E SHIFTN (2) ROUGH: 293 (3) BKGD: #, bj (j = 0 11). BKGD E E E (1) SCALE: 315 (2)
16 # : pseudo-voigt, :... #, U, V, W, a dummy. FWHM E E E #, a0, a1, a2, a dummy. ASYM E #, eta_l0, eta_l1, eta_h0, and eta_h1. ETA #, Ue and Pe. ANISOBR # 16. DUMMY # : pseudo-voigt, :... #, U, V, W, a dummy. FWHM E E E #, a0, a1, a2, a dummy. ASYM E #, eta_l0, eta_l1, eta_h0, and eta_h1. ETA #, Ue and Pe. ANISOBR # 16. DUMMY (3) PREF: 394 PREF PREF
17 (4) CELLQ: 399 BaSO4 AtomWork CELLQ CELLQ (5) 409 BaSO4 AtomWork O1/O O2/O O3/O E P/P Ca1/Ca E Ca2/Ca E F/F Ba/Ba S/S O1/O O2/O O3/O (1) NCUT: (2) NEXC: (3) NINT: 1 (4) NRANGE:
18 (5) PC: 7.00 (6) NLESQ: (NLESQ = 0) (7) NESU: (8) NAUTO: (9) NCYCL: 100 (10) CONV: (1) (11) NCONV: (2) 6 (12) NC: 0 (13) TK, FINC: (14) NUPDT: NUPDT = 0:... NUPDT = 1!... NUPDT = 0!... NUPDT = 1:... (15) NPAT: Igor Pro *.itx RIETVIEW.EXE NPAT = 1:... *.plt *.gpd NPAT = 2!... Igor*.itx NPAT = 3!... RietPlot *.itx NPAT = 1!... *.plt *.gpd NPAT = 2:... Igor*.itx NPAT = 3!... RietPlot *.itx
19 (16) IWIDTH, IHEIGHT, IYMIN, IYMAX, LBG, LDEL, IOFFSETD, IPSIZE, IFSIZE, ILSIZE: (17) INDREF: (18) IOFFSET1: (19) NDA: NDA = 1 (20) NFR: (21) NMEM: NPRINT = 0 *.lst NMEM = 1 (22) LANOM, LGR, LFOFC, EPSD, TSCAT1, TSCAT2: *.ins *.ins *.ins VESTA (1) VESTA (2) File Open... BaSO4.ins (3) [Edit] [Bonds...] Bonds - BaSO4.ins (4) [New] Search 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
20 (6) [Apply] S O (7) [Ok] Bonds - BaSO4.ins (8) [Style] Style Polyhedral (9) (10) *.ins VNS1 CELLQ VESTA *.ins
21 *.ins (1) BaSO4.bat (2) RIETVIEW (3) 6,000 (4) RIETVIEW (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 S 4c x 1/4 z O1 4c x 1/4 z O2 4c x 1/4 z O3 8d x y z
22 O3 8d 4c x, 1/4, z Ba, S, O1, O2 y 0.25 (i) (ii) (iii) (iv) (v) Ba O B (1) BaSO4.ins SHIFTN SHIFTN (2)
23 IYMAX = 20000: y ( ). IYMAX = 7000: y ( ). (3) BaSO.ins (4) BaSO4.bat (5) PDF Viewer (1) BaSO4.ins (2) (U, V, W) # : pseudo-voigt,... #, U, V, W, a dummy. FWHM E E E FWHM E E E BaSO4.ins U W V (3) BaSO4.bat (4) PDF Viewer (1) BaSO4.ins (2) (a0, a1, a2) # : pseudo-voigt,... #, U, V, W, a dummy. FWHM E E E #, a0, a1, a2, a dummy.
24 ASYM E FWHM12 ASYM E (3) BaSO4.bat (4) PDF Viewer (1) BaSO4.ins (2) (eta_l0, eta_l1, eta_h0, eta_h1) # : pseudo-voigt,... #, U, V, W, a dummy. FWHM E E E #, a0, a1, a2, a dummy. ASYM E #, eta_l0, eta_l1, eta_h0, and eta_h1. ETA FWHM12 ASYM12 ETA (3) BaSO4.bat (4) PDF Viewer
25 (1) BaSO4.ins (2) Ba x z Ba y 0.25 Ba/Ba Ba/Ba Ba y (3) BaSO4.bat (4) PDF Viewer (1) BaSO4.ins (2) Ba BS, O1, O2, O3 x, y, z Ba, S, O1, O2 y 0.25 Ba/Ba S/S O1/O O2/O O3/O Ba x, z Ba/Ba S/S O1/O O2/O O3/O (3) BaSO4.bat (4) PDF Viewer
26 (1) BaSO4.ins (2) S, O1, O2, O3 B Ba/Ba S/S O1/O O2/O O3/O Ba B S, O1, O2, O3 x, y, z Ba/Ba S/S O1/O O2/O O3/O (3) BaSO4.bat (4) PDF Viewer PDF Viewer
27 R (1) PDF Viewer 20º 50º (2) RIETAN BaSO4.lst (3) Reliability factors,... R- reliability factor residual factor RwP RP Rwp 12 % % Re 10 % Re Rwp Re Re RIETAN-FP RwP Re S S 1.3 (4) BaSO4.lst *** Summary of possible reflections (based on the refined... (5) PDF Viewer BaSO4.lst hkl 2-theta Iobs Ical (Iobs < Ical)
28 (Iobs < Ical) (Iobs > Ical) (Iobs < Ical) (Iobs > Ical) (Iobs < Ical) hkl2-theta Iobs 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 PREF
29 (4) BaSO4.bat (5) PDF Viewer (6) BaSO4.lst (7) *** R factors, final parameters, and... Preferred-orientation parameter, r (14) March-Dollase [4] (0 1 0) BaSO4 b b (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
30
31 (1) Cu Kα1 (2) (3) (4) (5) (6) (7) (8) Rwp (9) (10) (11) (1) (2) (3) (4) (5)
32 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 (9) 1/ (9) 0.739(18) S... O1... O2... O3... [1] F. Izumi and K. Momma, Solid State Phenom., 130, (2007). [2] M. Miyake, I. Minato, H. Morikawa and S. Iwai, Am. Mineral., 63, (1978).
33 BVS; Bond Valence Sum SO4 2 (1) VESTA [File] [Open...] BaSO4.ins (2) [Edit] [Bonds...] Bonds - BaSO4.ins (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.ins (7) [Style] Style Polyhedral (8) Select Select (9) SO4 (10) bond angle bond angle (11) O1 S O2 O1 S O2
34 SO4 Bond type length (A ) S O (8) S O (8) S O3, S-O (4) Bond type angle (º) O1-S-O (3) O2-S-O3, O2-S-O (3) O1-S-O3, O1-S-O (3) O3-S-O (3) BVS Ba BVS Bond Valence Sum (1) Web documents VESTA bvparm2013.cif (2) bvparm2013.cif Ba 2 O Ba +2 O 2 bond valence parameter r 0 b 0.37 VESTA BVS b 0.37 (3) VESTA [Edit] [Bonds...] Bonds - BaSO4.ins (4) S O Ba O (5) [Ctrl] [Shift] Ba Mac [Shift]+[Command]+
35 (6) Bond valence parameter bvparm2013.cif (7) VESTA bond valence sum BVS 0.2 r 0 [5] M. Miyake, I. Minato, H. Morikawa and S. Iwai, Am. Mineral., 63, (1978). URL: (1) [5] BaSO4 EPMA (2) [5] 0.15 mm
36 (3) [5] (4) (5) [5] VESTA
37 A PDF (Portable Document Format) Microsoft Word
38 (1) xx (2) (3) (4) Introduction
39 results discussion results and discussion x discussion Acta Crystallographica discussion discussion
40 conclusion [1] F. Izumi and K. Momma, Solid State Phenom., 130, (2007). [2] K. Momma and F. Izumi, J. Appl. Crystallogr., 44, (2011). [3] I. D. Brown and D. Altermatt, Acta Cryst. B 41, (1985). [4] W. A. Dollase, J. Appl. Crystallogr., 19, (1986). [5] M. Miyake, I. Minato, H. Morikawa and S. Iwai, Am. Mineral., 63, (1978).
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