Data Validation and Quality Marks Suri Kabekkodu ICDD

Background Powder Diffraction File population (Inorganic+Organic) is more than half a million now !! Quality marks are essential while working with larger database with similar diffraction patterns Data validation and the quality mark assignments is the most important step in the editorial process

Quality Mark (QM) Types Experimental patterns Calculated Patterns (based on experimentally determined crystal structures)

QM for Experimental Patterns Star (Well characterized chemically and crystallographyically, No unindexed lines,∆2ө≤0.03º) I (Well characterized chemically No unindexed strong lines,∆2ө≤0.06º) O (Poorly characterized, with editorial comment explaining the reason) B (Do not meet the criteria for *, I, O) R (d values from Rietveld refinement) C (author calculated d values) H (Hypothetical)

What are calculated patterns? If we know the crystal structure, we can calculate the diffraction pattern using the equation LP factor Cell Volume Multiplicity Structure factor Crystal structure Displacement parameters (temp. factors)

It is extremely important to make sure that the crystal structure used for the calculation is correct. In fact it is the rate determining step in the editorial process

Reference Intensity Ratio All the calculated patterns have I/Ic I/Ic =   c /c c   (2)  = Linear attenuation coefficient  = Absolute scale factor  = Density (“c “ corresponds to corundum) Scale factor depends on the structural parameters used. Incomplete or incorrect structure will result in wrong RIR and will lead to misleading results in quantative phase analysis

We need to have a reliability index Which is the Quality Mark in Powder Diffraction File Powder Diffraction File is the only crystallographic database that categorizes data on its quality

QM for Calculated Patterns A calculated patterns quality mark task group was formed during the ICDD spring meeting 2003 in order to develop a method to assign quality marks to calculated patterns. S. Kabekkodu (Chair), C. Hubbard, J. Kaduk, E. Antipov, M. Bennett, P. Wallace, F. Rotella

Calculated Patterns Quality Mark The major step in this method involves several crystallographic and editorial checks by the ICDD, followed by the extraction and flagging of the structural database warnings/comments. Resulting calculated patterns will be classified into various categories based on the significance and nature of the warnings/comments. In the final step, a quality mark (QM) will be assigned to a calculated pattern based on its category.

The Method ICDD editorial checks (mainly crystallographic, chemistry) Identification and extraction of external database comments

The Method Editor classifies and flags warnings Minor warning (W1) Significant warning (W2) Major warning (W3) QM will be assigned SQL query based on warning code.

Calc. QM Notations Category QM No Warning * Minor Warning I Significant warning B Assigned structure (Prototype) P Hypothetical H Major warning O

ICDD Editorial Checks In this step, crystal structure from structural databases (ICSD, CSD, LPF, NIST) will be tested for completeness and various possible errors. Based on the test result, the database will be updated with appropriate warnings.

ICDD Editorial Checks Atomic coordinates Vs Space group description That is ~21 million coordinates are verified with their symmetry operator Transformation of non-standard space groups, author’s choice of origin Reported site multiplicity from the source database should match one generated by symmetry operators Typographic error in space group symbol etc. Consistency between reported Z and the sum of site multiplicity

Example Mg2 (SiO4), Fd-3m, a=8.12, Z=8 Space group origin at 4-3m So if we operate all the 192 symmetry operators of Fd-3m (Int. Tbl for Crystallography Volume A), by the lattice description we should get 16 Mg, 8 Si and 32 O atoms We get 8 Mg, 16 Si and 32 O atoms! What could be wrong?

Answer Lets change the origin to -3m Now we get 16 Mg, 8 Si and 32 O atoms Using incorrect origin will result in wrong diffraction patterns and RIR

Wrong Significantly different diffraction patterns

Does the space group represent true symmetry? Several crystal structures get published (in non-crystallographic journals) without checking for possible higher symmetry When looked carefully some structures are reported in sub group They may have reasonable bond lengths and angles but does not represent the true symmetry (important from the physical property point of view)

Example LiRhO2 in F4132 Rh 16c 1/8,1/8,1/8 Li 16d 5/8,5/8,5/8 O 32e x,x,x LiRhO2 in Fd-3m Rh 16c 1/8,1/8,1/8 Li 16d 5/8,5/8,5/8 O 32e x,x,x F4132 is a subgroup of Fd-3m

Application of reduced cell to identify incorrect space groups a=6.609 b=7.318 c=7.485 Å, α=69.08 β=62.24 γ=64.72° in P-1 with Z=1 Reduced cell a=6.609 b=7.318 c=7.323 Å, α=88.83 β=64.76 γ=64.72° Vectors 011, 0-11,100 defines a C-centered lattice a=10.458 b=10.246 c=6.609 Å, α=89.99 β=126.69 γ=89.96° The correct space group is C2/m

ICDD Editorial Checks on Temperature factors (Displacement Parameters) Temperature factors are good indicator of quality refinement. Usually Editor’s favorite one when we look beyond popular statistical parameters like R-factors There are good number of published structures (more than 8,000 found) with attractive R-factors but meaningless temperature factors ICDD’s editorial system checks all the anisotropic tensor coefficients for the positive definite matrix (i.e all the eigenvalues must be positive) Non positive definite temperature factors are physically meaningless

ICDD Editorial Checks on Temperature factors (Displacement Parameters) Anisotropic tensor coefficient is not permitted by the site symmetry Magnitude of temperature factor is outside the range (0.001<U<0.1) Isotropic temperature factor is negative Identify and convert mixed type of temperature factors (U+B, Beta+U, etc) to a standard type.

ICDD Editorial Checks Check the cell dimensions for missing decimal point, e.s.d and magnitude of the e.s.d etc. Check the R factors close to the theoretical limit (0.83 for centrosymmetric and 0.59 for noncentrosymmetric structure) (useful check for % to value conversion) Check for site occupation factor >1.0

ICDD Editorial Checks Part of the structure was refined as a group without locating positions of the constituent atoms (e.g. C60 compounds) Means approximation of scattering factors Check for possible typographic errors in the element symbol by comparing chemical formula, atomic coordinate list and chemical name (e.g., frequently observed misprints in case of: Mn,Mg; Ti,Tl etc.) Trivial fix once found. Can result in major error in the calculated intensities When measured density is available, check the percentage of difference in measured and calculated density (check cell dimension, Z and related parameters when the difference is significant)

Structure Vs Lattice comparison For a completely solved crystal structure Z*FW / N*V = ( M*SOF*AW )/N*V Z=Total number of molecules per unit cell FW= Formula weight calculated based on reported composition M= Site multiplicity factor SOF= Site occupation factor AW= Atomic weight of the occupying atom N= Avogadro’s number V= Unit cell volume Summation is over number of occupied sites in the structure On simplification, Z*FW =  M*SOF*AW

Structure Vs Lattice comparison Inequality in equation (2) arise when Missing atoms in the refined structure Incorrect/poor refinement of occupation factor Z is inconsistent with the refined structure Misspelled atom symbol in coordinate list or formula Improper choice of space group origin In the case of incomplete structures the value [Z*FW - M*SOF*AW / Z*FW]*100 is proportional to the percentage of missing electron density.

External Database Warnings/Comments Editorial comments on unusually short or long bond lengths or questionable bond angles (comment needs to be very specific for structures showing disorder or partial/mixed occupancy) Comment on questionnable space groups, cell dimensions etc. Published coordinates are wrong Type of experiment (single crystal/powder)

External Database Warnings/Comments Radiation used (X-ray, Neutron, Synchrotron, Electron) Temperature/Pressure of data collection Comments on method of structure solution/refinement (Rietveld, ab-initio calculation etc) Editorial comment on the structure Reference to a contradicting structure

External Database Warnings/Comments Description of type of disorder Comments on modulated structure Atomic coordinates are assigned based on structure prototype (LPF entries) R factor not reported Any correction to the published coordinates

Warning Classification Minor Warning Significant Warning Major Warning Density calculated from reported and calculated compositions differ (1%< x 3%) Density calculated from reported and calculated compositions differ (3%<x15%) Density calculated from reported and calculated compositions differ (15%<x) No e.s.d. Reported/abstracted on the cell dimension Unit cell dimensions taken from figure (approximated) Incorrect cell dimension Magnitude of e.s.d. on cell dimension is >1000 ppm Missing decimal point in the cell dimension Incorrect space group

Warning Classification (Contd-) Minor Warning Significant Warning Major Warning 7%<R factor <12% (for single crystal), 10%<Rfactor>15% (powder) 12%<R factor (for single crystal), 15%<R factor (powder) Incommensurate modulated structure. Only average structure of the sub cell is given No R factor Reported/abstracted Anisotropic temperature factor is non positive definite Published atomic coordinates are wrong Reported Z is inconsistent with the sum of site multiplicity Anisotropic tensor coefficient is not permitted by the site symmetry Structural database removed the entry corresponding to a published calculated pattern

Warning Classification (Contd-) Minor Warning Significant Warning Major Warning Type of experiment (single crystal/powder) not mentioned. (When unspecified, powder is assumed for ICSD, NIST,LPF entries) Magnitude of temperature factor is outside the range (0.001<U<0.1) Structure corrected by the editor (usually for cases with obvious abstraction/possible typographical error) Negative isotropic temperature factor Metric symmetry exceeds crystal symmetry Source database (LPF/ICSD/NIST/CSD) warning on bond length/angle

Warning Classification (Contd-) Minor Warning Significant Warning Major Warning Misprint in the original paper was corrected in the database Average structure of the modulated structure. Site occupation factor>1.0 Probable site occupation factor is deduced from the nominal composition Percentage of difference in measured and calculated density differ>2% (for non-porous materials) >5% Part of the structure was refined as a group without locating position of the constituent atoms

Warning Classification (Contd-) Minor Warning Significant Warning Major Warning Comments containing reference to a contradicting crystal structure exist Structure determined from projections Structure determined using electron diffraction

Population of star patterns in the experimental set

R-factor trend by year

Quality Mark Population

Incomplete Structures

Example PDF Card

Structure Type Assignments and Classifications

Structure Type Notation Popular structure type descriptions are Traditional Notation Based on unit cell, Pearson Symbol and chemistry (usually assigned manually by comparing the diffraction patterns) ANX Formula Based on type of ion and their site occupation Example Ca Ti O3 is of ABX3 type Fe3O4 is of AB2X4 type Long descriptive Notation following Parthe’s method Based on detailed crystallographic analysis Example Cu3 As,cI64,220 (Structure Type Formula, Pearson Symbol, Space group number) Sensitive to prototype branching based on atomic environment

Structure Type requirements Must crystallize in the same space group Similar cell parameter ratio Same Wyckoff positions (Wyckoff sequence) When all the above 3 conditions satisfy, we have similar atomic environments

Possible structural representations Lets take diamond structure as an example. This structure belongs to Fd-3m. Atomic coordinates can be expressed as Origin choice 1, C at 8a site (0,0,0) Origin choice 1, C at 8b site (1/2,1/2,1/2) Origin choice 2, C at 8a site (1/8,1/8,1/8) Origin choice 2, C at 8a site (3/8,3/8,3/8)

Standardization of Crystal Structure First proposed by Parthe and Gelato (Acta Cryst. (1984), A40, 169-183) The method uses standardization parameter N is number of atom sites, x,y,z are fractional coordinates

Standardization Procedure Represent the structure in standard space group (i.e. Int. Tbl. Crystallography) Derive Niggli reduced cell or cell with a<b<c Choice of representative coordinate triple considering permitted origins, rotation of coordinate system and eantiomorphic structure representation Ordering and renumbering atoms in the final list

Standardization Criteria (-Contd) Additional constraints Triclinic space groups: Niggli reduced cell Monoclinic with b-axis unique Orthorhombic a b  c (when not fixed by the space group) Trigonal space group with R lattice (triple hexagonal cell) Choice of origin: at the inversion center Enantiomorphic space groups: smallest index on the relevant screw axis

How to account for shape of the unit cell? Γ is based exclusively on fractional coordinates. Centre of Gravity (CG) parameter is useful to identify unit cell shape difference when we encounter same space group and wyckoff sequence N=Number of atom sites, V=cell volume, a,b,c,α,β,γ Unit cell dimensions, x,y,z are atomic coordinates

Special Cases In general standardization procedure can directly compare candidates for isotypic compounds. However there are some special cases: Refinable coordinate very close to zero

Lets standardize diamond structure Possible structure reprenation in Fd-3m are Origin choice 1, C at 8a site (0,0,0) Origin choice 1, C at 8b site (1/2,1/2,1/2) Origin choice 2, C at 8a site (1/8,1/8,1/8) Origin choice 2, C at 8a site (3/8,3/8,3/8) After applying the condition that inversion center as the standard choice of origin we have excluded representation 1 and 2 Γ values for 3 and 4 are 0.22 and 0.65 Standard representation is #3

Why standardized data for comparison? CeCu2, Imma, a=4.425,b=7.057, c=7.475 Cu (8h) 0 0.051 0.1648 Ce (4e) 0 0.25 0.5377 KHg2, Imma, a=8.10,b=5.16, c=8.77 Hg (8i) 0.190 0.25 0.087 K (4e) 0 0.25 0.703 Standardization Standardization CeCu2, Imma, a=4.425,b=7.057, c=7.475 Cu (8h) 0 0.051 0.1648 Ce (4e) 0 0.25 0.5377 KHg2, Imma, a=5.16,b=8.10, c=8.77 Hg (8i) 0 0.06 0.163 K (4e) 0 0.25 0.547

Stored procedure seeking for Ca Ti O3 like structure (1% Tolerance)

The result set of 165 patterns were imported into HighScorePlus and the comparison of their diffraction patterns corroborates the method.

Structure Type Applications Deriving Starting Model for Rietveld Refinements Traditionally starting model for Rietveld refinements was developed based on chemical/crystallographic intuition. In other words it is individual’s knowledge of structure types Databases with Structure Type information can make seminal contributions to this effort. Powder Diffraction File in particular is advantageous as one can perform search match based on their diffraction pattern to explore the possible models.

Structure Type Applications Structural chemistry information Database search results can also be sorted based on their structural chemistry Can be used to explore the database from the materials design point of view 3D crystalline structure related properties Ferrolectric, Piezoelectric, Non Linear Optics,Transport

Database Classifications Primary Patterns When multiple entries are available, primary pattern is chosen by the editor based on QM and experimental conditions Alternate Patterns Closely related to primary pattern. Deleted Patterns Low precision pattern (and better pattern is in the database) Major error identified by the editor that can not be fixed (or to be fixed (rare))

Subfiles Classified into various categories based on chemistry, properties and application Each subfile is defined by set of rules approved by the concerned subcommittee Subcommittee members review the file and continuously improvise it

Classification Overview

Mineral Classification Family-Related by partial structural similarities such as framework, chain etc Subfamily-Collection within the family based on specific similarities Homologous- Composed of two structural units interlayered in differenet proportions (e.g. Humite, Mg2SiO4•xMg(OH)2 Homotypes- Derivative structures based on a master structure (e.g.Perovskite)

Mineral Classification Supergroup- Highest symmetry phases where the structure arrangement remains unchanged. Group- Composed of Isostructural phases Subgroup- Groups further classified based on chemistry (oxides, sulfides) Related Structures- Based on structural distortions from the group structure (e.g. Bunsenite (NiO) is distortion of NaCl structure)

Example: Mineral and Zeolite Classification

Example: Sphalerite

Crystallographic basis of Symmetry Relationship

Zeolite Classification Zeolite Name Framework Code

Example Zeolite Names

Example- Zeolite Classification Aluminum Silicate, Mutinaite