Diffraction, Non-Crystallinity, and the PDF Database pdf

The Integral Index• The Integral Index is a numerical value based on a point comparison of two digitized X-ray diffraction pattern This numerical value ranges from 0-100 and is based on

Diffraction, Non-Crystallinity , and

the PDF Database

Cyrus E Crowder, ICDD

Tim Fawcett, ICDD

Classical Diffraction

• Classic ‘Bragg’ scattering is characterized by discrete

peaks arising from long-range crystallographically

ordered planes:

λ = 2d hkl sinθ hkl

• The 2009 PDF databases have > 660,000 entries based

on the concept of discrete Bragg peaks arising from

Classical XRPD NaCl – An Example

1 1 1 2 0 0 2 2 0

2 2 2

3 1 1

The XRPD Pattern of a Common

Pharmaceutical Excipient

The process of identifying this material by conventional XRPD search/match

techniques is compromised by the small number of clearly defined diffraction

maxima and the difficulty in specifying the precise positions of these maxima Further, these ‘maxima’ are likely shifted from the true underlying positions of the major Bragg peaks due to the significant overlap

Use of full pattern matching for phase

• An automated full-pattern comparison would be

desirable to screen the database for most-likely

matches.

The Integral Index

• The Integral Index is a numerical value based on a point comparison of two digitized X-ray diffraction pattern This numerical value ranges from 0-100 and is based on the

point-by-Hofmann and Kuleshova similarity index [1]:

• The lower the index value, the better the match, giving 0 a perfect match and 100 a complete non-match

• We can use this relationship to rank the match between full patterns from a given database set with the pattern from the unknown material

i

i

calc

j I

i I

j I

i I

0

0 0

1

Example Using Integral Index to Identify Nanocrystalline Material

• To facilitate comparison, the

background is removed before

computing the integral indices

• To facilitate speed, the

database is limited to a likely

subset of entries, in this case

anything with cellulose in the

name

• If unsuccessful, other subfiles,

i.e., polymers, fillers, or

forensics, could be specified

Perform Integral Index Calculations

• An estimated crystallite size parameter

is used to compute comparible FWHMs

for peaks, in this case, 3.5 nm.

• The software simulates a pattern for

each database entry, using the d-space

and intensity values.

• Each simulated database pattern is

compared with the unknown pattern to

generate integral index values

Patterns Generated from Crystal Structure

Where Available

References for Form I alpha,

Form I beta and Form II

Simulation of microcrystallinestates of cellulose

Via PDF-4+

Scardi, Leoni Faber

PDF 00-056-1717 Cell II PDF 00-056-1718 Cell I beta PDF 00-056-1719 Cell I alpha

Patterns Generated from Experimental d-I list if

Crystal Structure is Not Available

Use of Integral Index

Integral Index = 2.26Cellulose 1β

Comparing with all 16 PDF

experimental entries that

contain ‘cellulose’ in the name,

the integral index values vary

from 2.26 up to 19.28 for these

entries

The best integral index fit is

with 50-2241 – cellulose Iβ

Comparison of Simulated Cellulose Patterns to Experimental Pattern

Cellulose IβIntegral Index = 2.26

Cellulose IIIntegral Index = 5.93

Red – experimental pattern

Blue – ‘Standard’ database pattern

Clearly, the cellulose 1β polymorph

is a better match than the cellulose II

polymorph

Non-crystalline Material

This is an X-ray ‘diffraction’ pattern for amorphous cellulose (Sigma Cellulose ground 13 hours) The same pattern is obtained after long periods of grinding, regardless of whether the starting cellulose was form Iα, Iβ, or II (Courtesy Ewa Bucher, International Paper)

The lack of long range order means we have no conventional “Bragg” diffraction, but instead, rather broad features based on the distribution of interatomic distances within the disordered structure

Nanocrystalline Cellulose Iα?

Comparison of X-ray diffraction patterns for amorphous cellulose and that for the cellulose Iα crystalline form with a simulated crystallite size of 1.5 nm

Nanocrystalline Cellulose Iβ?

Comparison of X-ray diffraction patterns for amorphous cellulose and that for the cellulose Iβ crystalline form with a simulated crystallite size of 1.5 nm

Nanocrystalline Cellulose II?

Comparison of X-ray diffraction patterns for amorphous cellulose and that for the cellulose II crystalline form with a simulated crystallite size of 1.5 nm

Amorphous Standards

• Clearly the database should be expanded to include full  patterns for standard amorphous materials since these  cannot be generated from Bragg peak positions or 

crystallographic information. 

• This would allow integral index comparisons to be 

performed for both amorphous standards as well as  nanocrystalline variations of crystalline materials 

already in the database.

Raw Polymer Pattern for Identification

using Integral Index

Background Removal

Integral Index Calculations for

Polymer Pattern

PDF-4+ 2009 database searched for entries containing ‘poly’ in the name and having elements only within the set of C, H, N, O, F, and

Cl Found: 651

Using a crystallite size of ~15 nm, Integral Index values were

computed for this experimental pattern that ranged from ~2.5 to 45 (Roughly 20 seconds to compute on a 2-year-old Dell Inspiron.)

The top three are examined closer on the next slide.

Integral Index Results for Polymer

2-Unlike polypropylene, many have only one or two significant Bragg peaks making conventional search/match identification difficult

Automated full pattern comparisons have the potential to be a better identification tool for XRPD patterns of many polymers

Disordered Structures

Faulted clay materials

The Editorial Challenge of a “Full

Pattern” Database

• How many ‘different’ entries are needed for

a given material (i.e chain branching,

molecular weight, melting point, degree of crystallinity, etc)?

Cough DropSaw Palmetto

3 SourcesCellulose*

*Courtesy of Ewa Bucher

International Paper

SunTheanine

Amorphous Materials and Blends

Tools that assist in identifying materials with poor crystallinity

• Data and databases

• Simulations – crystallite size , pair distribution functions, cluster analyses, total pattern fitting,

“random-walk”models, Rietveld refinement,

integral index

• Any knowledge of specimen chemistry,

processing and composition

• Complimentary data – melting point,

infrared,nmr, functional groups