Post on 27-Dec-2015
. 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
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atom types& coordinates
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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
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)
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)
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)
?
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?
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 .
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.
(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.
(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 =