Results obtained from Crystal Structure Analysis . phase identification (PXRD) . optical property . pizeo/pyro-electricity cell constants & symmetry atom types& coordinates + . chemical bonds . coordination number . polyhedral distortion . L. S. molecular planes . & torsional angles . 3-D structure plots . chemical formula . density . bond-valence sums occupancy + temperature factors . superlattice . disordered problem . transport property +

BVS = i si Bond Valence Sum calculations si = exp [(r0 - ri )/B] Bond strength si = exp [(r0 - ri )/B] ri is an observed value; r0 empirical value with B = 0.37 • A bond-valence can be assigned to each bond If the interatomic distances are known, the bond-valences can be calculated. BVS = i si • The sum of the bond-valences at each atom is equal to the magnitude of the atomic valence Examples: Determine the BVS for V, Ag and Na atoms.

R0 of some selected atoms Metal Ligand R0 Metal Ligand R0 V +3 O -2 1.743 V +4 O -2 1.784 V +5 O -2 1.803 Cr +2 O -2 1.73 Cr +3 O -2 1.724 Co +2 O -2 1.692 Co +3 O -2 1.70 Cu +1 O -2 1.610 Cu +2 O -2 1.679 Cu +3 O -2 1.739 Na +1 O -2 1.803 Rb +1 O -2 2.263 Cs +1 O -2 2.417 Ag +1 O -2 1.842 Be +2 O -2 1.381 Ca +2 O -2 1.967 Ba +2 O -2 2.285 Al +3 O -2 1.620 As +3 O -2 1.789 As +5 O -2 1.767

The relationship between coordination and valence of vanadium International Journal of Inorganic Materials 2 (2000) 561-579

International Journal of Inorganic Materials 2 (2000) 561-579

[V3O4(OH)(PO4)2]2- nce V4+ ? V5+ ?

[(VVO2)(VIVO)2(OH)(PO4)2]2- BVS for V atoms [V3O4(OH)(PO4)2]2- (BVS) [(VVO2)(VIVO)2(OH)(PO4)2]2-

The coordination number and BVS for Ag atom Ag-O: 2.394 ~ 4.015 Å 2.394 (2x) 2.611 (2x) 2.659 (2x) 3.025 (2x) 3.382 (2x) 4.015 (2x)

What will be the coordination number for Ag? si BVS = 1.002 for C.N. = 8 2.394 (2x) 2.611 (2x) 2.659 (2x) 3.025 (2x) 3.382 (2x) 4.015 (2x) BVS = for C.N. = 10 What will be the coordination number for Ag? Both BVS and the gap between bond lengths should be considered.

The coordination number and BVS for Rb atom

The coordination number and BVS for Rb atom bond length gap

Atom x y z Ueq Na(1) 0.5932(1) 0.1926(1) -0.0298(2) 0.0191(5) Na(2) 1/3 -0.0528(2) -1/12 0.0251(8) Na(3) 0.3287(5) 0.1810(5) 0.044(1) 0.057(3)

The coordination number and BVS for Na atom C.N. = 6 C.N. = 5

Determination of chemical formula: What is the molecular formula of the organic component? (see ORTEP)

P21/c

Determination of chemical formula and coordination number for K atoms: ?

Crystallographic Data (1) Tables of crystal data, atomic coordinates, thermal parameters Crystallographic Data Journal: Inorg. Chemistry

wrong if the atom is non-positive definite Atomic coordinates and thermal parameters what’s the chemical formula? wrong if the atom is non-positive definite

Atomic coordinates and thermal parameters

A “bond” exists between two atoms A and B when DAB  RA + RB +  inter-atomic distance ionic radii tolerance  = 0.5Å (default value) To look for H-bonds or other interatomic interactions beyond regular covalent or ionic bonds,  can be set to larger values, say, 1 ~ 2 Å .

Least-square planes # MPLN: molecular plane

Torsional (or dihedral) angles The torsional (or dihedral) angle  of four atoms A, B, C, D with a chemical bond between AB, BC and CD, is defined as the angle between the two planes through A, B, C, and B, C, D. The torsional angle is considered positive when it is measured clockwise from the front substituent A to the rear substituent D and negative when it is measured anti-clockwise.

(3) The CIF files

Structure factor table

ORTEP diagram (4) Respresentation of molecular and 3D structures Oak Ridge Thermal Ellipsoid Plot

(4) Respresentation of molecular and 3D structures Table S2. Atomic coordinates (x 104) and equivalent isotropic displacement parameters (Å2x 103) for NTHU-2. ___________________________________________________________ x y z U(eq)a Zn(1) -495(1) 11778(1) -5962(1) 18(1) Zn(2) -4516(1) 11782(1) -5881(1) 24(1) P(1) -266(1) 10803(1) -3046(1) 18(1) P(2) -4766(1) 10775(1) -3011(1) 24(1) O(1) -326(1) 12031(3) -4062(3) 26(1) O(2) -217(1) 11431(3) -1613(3) 24(1) O(3) 163(1) 9848(4) -3285(4) 36(1) O(4) -737(1) 9809(4) -3126(4) 40(1) O(5) -4672(1) 11974(3) -4024(3) 28(1) O(6) -5242(1) 9981(4) -3266(4) 36(1) O(7) -4768(1) 11379(4) -1591(3) 33(1) O(8) -4352(1) 9596(4) -3111(4) 42(1) O(9) -1183(1) 11325(4) -6196(4) 37(1) O(10) -3819(1) 11657(4) -6160(4) 39(1) O(11) -1431(1) 13054(5) -7639(5) 51(1) O(12) -3565(1) 10408(5) -4341(5) 57(1) N(1) 4283(2) 14100(8) -5628(6) 60(2) N(2) 676(1) 13818(5) -5432(5) 37(1) C(1) -1503(2) 12044(6) -6842(5) 33(1) C(2) -2019(2) 11645(5) -6534(5) 28(1) C(3) -2400(2) 12320(7) -7279(6) 42(1) C(4) -2876(2) 12088(6) -6947(6) 40(1) C(5) -2980(2) 11191(6) -5859(5) 32(1) C(6) -2604(2) 10456(6) -5178(6) 35(1) C(7) -2126(2) 10700(6) -5502(5) 35(1) C(8) -3496(2) 11056(6) -5402(6) 34(1) C(9) 4230(2) 12996(10) -4822(9) 73(3) C(10) 3804(2) 12823(8) -4172(6) 50(2) C(11) 3434(2) 13815(6) -4348(6) 36(1) C(12) 3507(2) 14971(7) -5210(7) 50(2) C(13) 3936(3) 15094(9) -5851(8) 67(2) C(14) 2977(2) 13663(8) -3567(7) 51(2) C(15) 2509(2) 13809(7) -4395(7) 45(2) C(16) 2073(2) 13599(8) -3503(7) 50(2) C(17) 801(2) 12646(6) -4689(6) 42(1) C(18) 1254(2) 12562(6) -4101(7) 42(1) C(19) 1583(2) 13668(6) -4238(5) 31(1) C(20) 1450(2) 14882(6) -5039(6) 39(1) C(21) 984(2) 14938(6) -5622(6) 38(1) ________________________________________________________________________________ aU(eq) is defined as one third of the trace of the orthogonalized Uij tensor.

(4) Respresentation of molecular and 3D structures

About the agreement factors About the intensity data (5) Justification of the crystal structure results About the agreement factors • Is R1 (or RF) below 5%? If not, any rational explanation? • Is R1 close to Rint? • Is GOF (goodness-of-fit, or S) close to 1? About the intensity data • Is the resolution of the data collected below 0.9 Å? • Has absorption correcton been applied? • Are the criteria for “observed” data set properly?

(5) Justification of the crystal structure results About the refinement • Has a proper weighting scheme been chosen? • Is the data-to-parameter ratio larger than 8? • Does the refinement converge without significant correlation? • Are thermal eliposids normal? • Has the absolute configuration been considered if acentric? • Can all H atoms be located on Fourier difference map? About the results • Are the esds’in bond lengths smaller than 0.005 Å? • Are bond lengths and angles reasonable? • Do metal atoms possess proper coordinaton geometry? • Has the charge been balenced in the chemical formula? • ……...

Point-group symmetry and physical properties of crystals The point group of a crystal is a subgroup of the symmetry group of any of its physical properties. We can derive information about the symmetry of a crystal from its physical properties (Neumann’s principle) Certain interesting physical properties occur only in non-centrosymmetric crystals. Enantiomorphism Enantiomerism Chirality Dissymmetry These terms refer to the same symmetry restriction, the absence of improper rotations in a crystal or molecule

In particular, the absence of a center of symmetry, 1-bar, and of a mirror plane, m, but also of a 4-bar axis. As a consequence, such chiral crystals or molecules can occur in two different forms, which are related as a right and a left hand; hence they are called right-handed and left-handed forms. These two forms of a molecule or a crystal are mirror-related and not superimposable (not congruent). Thus the only symmetry operations which are allowed for chiral objects are proper rotations. Such objects are also called dissymmetric, in contrast to asymmetric objects which have no symmetry. The terms enantiomerism and chirality are mainly used in chemistry and applied to molecules, whereas the term enantiomorphism is preferred in crystallography if reference is made to crystals.

About Oral presentation 1. Background of your crystalline sample species, color, size, stability, growth, …etc. 2. Justification of your intensity data 3. Justification of the assigned space group 4. How well is the first structure model? 5. The progression of your structure refinements 6. List a complete table of Crystal Data 7. List a complete table of atomic coordinates 8. List selected bond distances and angles 9. Prepare a CIF for your structure 10. Description of your structure ORTEP and 3D plots, geometric calculations, and structure features

Table A-1a. Crystal data and structure refinement for Na5InSi4O12. --------------------------------------------------------------------------------------------------------------------- Empirical formula InNa5O12Si4 Formula weight 534.13 Color; Habit colorless; rod Crystal size 0.05 x 0.05 x 0.15 mm3 Crystal system; space group Rhombohedral; R-3c Unit cell dime nsions a = 21.7158(9) Å c = 12.4479(7) Å Volume 5083.7(4) Å3 Z 18 Reflection for cell 4715 Density (calculated) 3.140 Mg/m3 Absorption coefficient 2.776 mm-1 F(000) 4608 Temperature 295 K Wavelength 0.71073 Å Theta range for data collection 1.88 to 28.29° Index ranges -28 ≤ h ≤ 28, -28 ≤ k ≤ 28, -16 ≤ l ≤ 7 Reflections collected 11968 Independent reflections 1415 (1363  2 (I)) [R(int) = 0.0755] Completeness to theta = 28.29° 100.0 % Absorption correction semiempirical (based on 1815 reflections) Max. and min. transmission 0.968 and 0.860 Refinement method Full-matrix least-squares on F2 Data / restraints / parameters 1415 / 0 / 111 Goodness-of-fit on F2 1.574 Final R indices [I>2sigma(I)] R1a = 0.0452, wR2b = 0.0947 R indices (all data) R1 = 0.0468, wR2 = 0.0951 Largest diff. peak and hole 0.621 and -1.072 e∙Å-3 aR1 = Σ||FO|-|FC|| / Σ| FO | bwR2 = [Σ w(FO 2－FC 2)2 / Σ w(FO 2)2]1/2, w = 1 / [2(FO2) + ( 0.0147P )2 + 82.37P] where P =