. chemical bonds

. coordination number

. polyhedral distortion

. L. S. molecular planes

. & torsional angles

. 3-D structure plots

temperaturefactors

. superlattice

. disordered problem

. transport property

++

. phase identification (PXRD)

. optical property

. pizeo/pyro-electricity

cell constants & symmetry

. chemical formula

. density

. bond-valence sums

Results obtained from Crystal Structure AnalysisResults obtained from Crystal Structure Analysis

occupancy

++

atom types& coordinates

++

Bond Valence Sum calculations

Bond strength

si = exp [(r0 - ri )/B]

BVS = i si

ri is an observed value; r0 empirical value with B = 0.37

Examples:

Determine the BVS for V, Ag and Na atoms.

• A bond-valence can be assigned to each bond

• The sum of the bond-valences at each atom is equal to the magnitude of the atomic valence

If the interatomic distances are known, the bond-valences can be calculated.

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 1.803Rb +1 O -2 2.263Cs +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

R0 of some selected atoms

Metal Ligand R0 Metal Ligand R0

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-

V4+ ?

V5+ ?nce

nce

[(VVO2)(VIVO)2(OH)(PO4)2]2-

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

(BVS)

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)

si

BVS = 1.002 for C.N. = 8

What will be the coordination number for Ag?

BVS = for C.N. = 10

Both BVS and the gap between bond lengths should be considered.

2.394 (2x)

2.611 (2x)2.659 (2x)

3.025 (2x)

3.382 (2x)

4.015 (2x)

The coordination number and BVS for Rb atom

BVS = 1.02

bond length gap

The coordination number and BVS for Rb atom

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)

C.N. = 6

C.N. = 5

The coordination number and BVS for Na atom

Determination of chemical formula:Determination of chemical formula:

What is the molecular formula of theWhat is the molecular formula of theorganic component? (see ORTEP)organic component? (see ORTEP)

P21/c

?

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

(1) Tables of crystal data, atomic coordinates, thermal parameters

Crystallographic Data

Journal: Inorg. Chemistry

Atomic coordinates and thermal parameters

wrong if the atom is non-positive definitewhat’s the chemical formula?

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 betweenthe 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 tablel

(4) Respresentation of molecular and 3D structures

ORTEP diagram

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)aZn(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

a

bc

(5) Justification of the crystal structure results

• 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 agreement factors

• Is the resolution of the data collected below 0.9 Å?

• Has absorption correcton been applied?

• Are the criteria for “observed” data set properly?

About the intensity data

(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?

• 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?

• ……...

About the results

Point-group symmetry and physical properties of crystalsThe 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 innon-centrosymmetric crystals.

EnantiomorphismEnantiomorphism Enantiomerism Enantiomerism Chirality Chirality DissymmetryDissymmetry

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 chiralchiral 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 right-handed and left-handed formsforms. These two forms of a molecule or a crystal are mirror- mirror-relatedrelated and not superimposable (not congruent). Thus the only symmetry operations which are allowed for chiral objects are proper rotations. Such objects are also called dissymmetricdissymmetric, in contrast to asymmetricasymmetric objects which have no symmetry.

The terms enantiomerismenantiomerism and chiralitychirality are mainly used in chemistry and applied to molecules, whereas the term enantiomorphismenantiomorphism is preferred in crystallography if reference is made to crystals crystals.

About Oral presentation About Oral presentation

1. Background of your crystalline sample1. Background of your crystalline sample

2. Justification of your intensity data2. Justification of your intensity data

species, color, size, stability, growth, …etc.

3. Justification of the assigned space group 3. Justification of the assigned space group

4. How well is the first structure model? 4. How well is the first structure model?

5. The progression of your structure refinements 5. The progression of your structure refinements

6. List a complete table of Crystal Data 6. List a complete table of Crystal Data

7. List a complete table of atomic coordinates 7. List a complete table of atomic coordinates

8. List selected bond distances and angles 8. List selected bond distances and angles

10. Description of your structure 10. Description of your structure

ORTEP and 3D plots, geometric calculations, and structure features

9. Prepare a CIF for your structure 9. Prepare a CIF for your structure

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) ÅVolume 5083.7(4) Å3Z 18Reflection for cell 4715Density (calculated) 3.140 Mg/m3Absorption coefficient 2.776 mm-1F(000) 4608Temperature 295 KWavelength 0.71073 ÅTheta range for data collection1.88 to 28.29°Index ranges -28 ≤ h ≤ 28, -28 ≤ k ≤ 28, -16 ≤ l ≤ 7Reflections collected 11968Independent reflections1415 (1363 2 (I)) [R(int) = 0.0755]Completeness to theta = 28.29° 100.0 % Absorption correction semiempirical (based on 1815 reflections)Max. and min. transmission0.968 and 0.860Refinement method Full-matrix least-squares on F2Data / restraints / parameters1415 / 0 / 111Goodness-of-fit on F2 1.574Final R indices [I>2sigma(I)]R1a = 0.0452, wR2b = 0.0947R indices (all data) R1 = 0.0468, wR2 = 0.0951Largest diff. peak and hole0.621 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 =