1. 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 +

2. 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.

3. R0 of some selected atoms
Metal
Ligand R0
Metal
Ligand R0
V O
V O
V O
Cr O
Cr O
Co O
Co O
Cu O
Cu O
Cu O
Na O
Rb O
Cs O
Ag O
Be O
Ca O
Ba O
Al O
As O
As O

4. The relationship between coordination and valence of vanadium
International Journal of Inorganic Materials 2 (2000)

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

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

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

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

9. What will be the coordination number for Ag?si
BVS = 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.

10. The coordination number and BVS for Rb atom

11. The coordination number and BVS for Rb atom
bond length gap

12. Atom x y z Ueq
Na(1) (1) (1) (2) (5)
Na(2) 1/ (2) -1/ (8)
Na(3) (5) (5) (1) (3)

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

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

15. P21/c

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

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

21. 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

22. Atomic coordinates and thermal parameters

23. 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 .

25. Least-square planes
# MPLN: molecular plane

26. 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.

27. (3) The CIF files

30. Structure factor table

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

32. (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.

33. (4) Respresentation of molecular and 3D structures

34. 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?

35. (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 Å?
• Are bond lengths and angles reasonable?
• Do metal atoms possess proper coordinaton geometry?
• Has the charge been balenced in the chemical formula?
• ……...

36. 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

37. 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.

38. 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

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