Pecharsky V.K., Zavalij P.Y. Fundamentals of Powder Diffraction and Structural Characterization of Materials

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Preliminary data processing and phase analysis

371

Table

4.2.

Major differences in profile fitting algorithms realized in DMSNT and WinCSD.

Property DMSNT WinCSD

Peak shape function Pearson VII or split Pearson pseudo-Voigt

VII

Parameters per peak

(Pearson VII) or

(split

Pearson VII)

Common parameters

Background Must be subtracted Refined as a second order

polynomial

FWHM Individual Individual or

common for all peaks

Exponent

(P)

Individual N/A

Mixing parameter

(q)

N/A Common for all peaks

Asymmetry Individual using split Common for all peaks

Pearson VII

4.4

Phase identification and analysis

Each powder diffraction pattern is characterized by a unique distribution

of both positions and intensities of Bragg peaks, where peak positions are

defined by the unit cell dimensions and reflection intensities are established

by the distribution of atoms in the unit cell of every crystalline phase present

in the sample (see

Table

2.7

in Chapter

2).

Thus, every individual crystalline

compound has its own "fingerprint", which enables the utilization of powder

diffraction data in phase identification.]

digitized representation of powder data is quite compact and is

especially convenient for comparison with other patterns, provided a suitable

database is available.

addition to a digitized pattern, each entry in such a

database may (and usually does) contain symmetry, unit cell dimensions,

and other useful information: phase name, chemical composition, references,

basic physical and chemical properties, etc. Powder diffraction databases

find substantial use in both simple identification of compounds (qualitative

analysis) and in quantitative determination of the amounts of crystalline

phases present in a mixture (quantitative analysis).

The diffraction pattern from a single crystal is also unique but due to the complexity of a

three-dimensional distribution of intensities, phase recognition is difficult to formalize.

Powder data are one-dimensional, and they can be converted into digitized patterns, which

are in a way, unique barcodes enabling automated pattern recognition.

Chapter

4.4.1

Crystallographic databases

Phase identification using powder diffraction data requires a comparison

of several key features1 present in its digitized pattern with known

compounds/phases. This is usually achieved by searching powder diffraction

database(s) for records, which match experimentally measured and digitized

pattern. Thus, a powder diffraction database or at least its subset should be

available in addition to a suitable search-and-match algorithm.

The most complete and most often used powder diffraction database is

the Powder Diffraction FileTM (PDF), which is maintained and periodically

updated by the International Centre for Diffraction Data (ICDD'). PDF is a

commercial database, and complete information about both the ICDD and

Powder Diffraction File is available on the Web at http://www.icdd.com.

This database is quite unique: it contains either or both the experimentally

measured and calculated digitized powder patterns for hundreds of thousands

of compounds, including minerals, metals and alloys, inorganic materials,

organic compounds and pharmaceuticals. The PDF is available as a whole or

in subsets. Each record in the database is historically called the

card.2

example of a PDF record is shown in

Figure

4.18. There are eight

fields on the card; they contain the following information (the numbers listed

below are identical to the numbering of the fields in

Figure

4.18):

1. Card number (48-1

X13) on the left and data quality (Indexed) on the

right. Quality assignments are made by the ICDD editors using stringent

criteria.

It is unfeasible to include the entire digitized powder pattern in the search and comparison

because of inevitable random errors in both peak positions and intensities. Therefore, most

often search-and-match is accomplished by using positions of several of the strongest

Bragg reflections, which are least affected by variations in data collection and processing

parameters. A method in which the initial match is based on three strongest Bragg peaks

present in a powder diffraction pattern, known as the "Hanawalt search" [J.D. Hanawalt,

H.W. Rinn, and L.K. Frevel, Chemical analysis by x-ray diffraction, Ind. Eng. Chem.,

Anal.

Ed.

10,

457 (1938)], remains in use today. For more details see R. Jenkins and R.L.

Snyder, Introduction to x-ray powder diffractometry, John Wiley

Sons,

(1996).

Early versions of the Powder Diffraction File (also known as the JCPDS file) were

distributed on index cards. The first edition of the file dates back to the 1941 release

containing 4,000 cards describing powder diffraction patterns of -1,300 compounds. It

was compiled by the Joint Committee on Chemical Analysis by X-ray Powder Diffraction

Methods and published by the American Society for Testing and Materials (ASTM). In

1969, the Joint Committee on Powder Diffraction Standards (JCPDS) was registered as a

Pennsylvania nonprofit corporation and the current name (International Centre for

Diffraction Data) was adopted in 1978. See

Wong-Ng, H.F. McMurdie, C.R. Hubbard,

and A.D. Mighell, JCPDS-ICDD research associateship (cooperative program with

NBSINIST), J. Res. Natl. Inst. Stand. Technol.

106,

1013 (2001).

Card (record) number consists of two parts: set number (48 in this example) and sequential

number of the entry in the set (1 152 for this particular card).

Preliminary data processing and phase analysis

373

48-1152 Quality: Indexed

Li0.6 Vl.67 03.67

Lithium Vanadium Oxide Hydrate

Rad:CuKal Lambda:l.54056 Filter: d sp:Diffractometer

Cutoff: lnt:Diffractometer I/lcoc

RekWhittingham, M., SUNY at Binghamton. MaterialsResearch Center, NY. USAChyrayil,

T.,

Zavalij,

P.,

Whittingham. M., (1,

Sys:Tetragonal SG.:I4/1nmm

a:3.7047f0.0003

c:15.804+0.002

/;\

reflections in pattern.

Dx:2.53 Dm:2.541 WOM: F30=46.5(0.0161.40) Volume[CD]:216.91

€a:

nub:

sign:

ZV:

(6J

Int.

Color:

Prepared by hydrothermal treatment of tetramethylammonium hydroxide, vanadium pentoxide and

H\acidified to pH 2-5

for 3 days at 200 C. Pattern taken at 23(1) C.

hkl

0 11

0 3

Figure

4.18.

Example of a record extracted from the ICDD Powder Diffraction File.'

General information about the compound:

Chemical, moiety or structural formula;

Compound name and moiety, mineral or other names, if any.

Experimental conditions:

Radiation, wavelength and experimental details;

Reference for the source of diffraction data.

Crystallographic data:

Crystal system and space group;

Unit cell dimensions, number of formula units in the unit cell

(Z),

melting point, if known;

Reference

source of crystallographic data if different from the

source of diffraction data;

Calculated and measured gravimetric density,

30)

figure of

merit (see section

5.5.1

in Chapter

and unit cell volume in

A3.

Properties and corresponding reference, if any.

The output shown here was obtained using LookPDF routine, which is available with the

DMSNT software (Scintag Inc. and Radicon). Other programs may display PDF cards in

different format. This card and records shown in

Figure

4.21

and

Figure

4.22

are courtesy

the ICDD.

374 Chapter 4

6. Color.

7. Comments, which include:

- Source and preparation of the compound;

- Temperature, pressure and other preparation conditions.

8. Digitized pattern. Each observed Bragg reflection is listed with:

- ^/-spacing or 29 angle;

- Intensity normalized to 100;

- Miller indices hkl, if the pattern has been indexed.

The ICDD's PDF is well suited for identifying digitized powder patterns,

and many manufacturers of powder diffractometers offer optional software

for searching this database. Nonetheless, the PDF is not a complete database,

which is nearly impossible to achieve anyway. The information included in

the PDF is mostly collected from published powder data and from records

produced upon ICDD request.

At the time of writing this book, the ICDD

database exists in two formats: PDF-2 preserves a classic text-based format

that allows one to search-match using positions and intensities of several

strong Bragg peaks in addition to searching a limited number of other fields;

PDF-4 is build on relational database technology that provides searchable

access to all data fields.

In addition to a vast number of included entries and a comprehensive

quality control, the usefulness of the Powder Diffraction File is established

by the ability to perform searches based strictly on the digitized patterns, i.e.

without prior knowledge of the unit cell dimensions and/or other

crystallographic and chemical data. Similar searches may also be carried out

using several different existing databases: e.g. Pauling File and Mineralogy

Database and, perhaps, a few others (see Table 4.3), which are, however, not

as comprehensive as the PDF. For example, the Pauling File is currently

limited to binary compounds,

while the Mineralogy Database is dedicated to

naturally occurring and synthetic minerals. More detailed and recent (as of

2002) information about a variety of crystallographic databases can be found

in a special joint issue of Acta Crystallographica, Sections B and D (also see

references 6 through 13 in section 4.5).

ICDD makes limited funds available to researchers interested in processing and submitting

new experimental patterns for incorporation into the Powder Diffraction File. More

information about the ICCD's Grant-in-Aid program can be found at

http://www.icdd.com.

A multinary edition of the Pauling File is planned for the year 2005.

Acta Crystallographica is an international journal published by the International Union of

Crystallography in five sections: Section A (Foundations of Crystallography); Section B

(Structural Science); Section C (Crystal Structure Communications); Section D

(Biological Crystallography), and Section E (Structure Reports Online). Special joint

issue: Acta Cryst. B58, 317-422 (2002) and Acta Cryst. D58, 879-920 (2002). Table of

contents is available at http://journals.iucr.org/index.html.

Preliminary data processing and phase analysis

375

Table

4.3.

Common computer searchable crystallographic databases.

Database Content/Compounds No. of entries

ICDDa

Powder Diffraction

PDF-2 or PDF-4 Full File. Both

-1

49.000:

File

NIST~

Crystal Data

Pauling Filec

ICSD~

Inorganic Crystal

Structure Data

CSDe

Cambridge Structural

Database

CRYSMET~

Metals and

Alloys Database

PDB

Protein Data Bank;g

Nucleic Acids

at abase^

IZA'

Zeolite database

Mineralogy Database'

experimental and calculated from ICSD

data.

PDF-4 Organics: organic and metal

organic compounds. Both experimental

and calculated from CSD data.

Unit cell, symmetry and references.

All inorganic

(i.e. compounds without

C-H bonds) ordered solid materials.

Contains structural, diffraction,

constitutional (phase diagrams), and

physical property data.

Inorganic crystal structures, with

atomic coordinates,

to date.

Crystal structures of organic and metal

organic compounds (carbon containing

molecules with up to

1000 atoms)

Critically evaluated crystallographic

data for metals, including alloys,

intermetallics and minerals.

Structures of proteins.

Structures of oligonucleotides and

nucleic acids.

All zeolite structure types:

crystallographic data, drawings,

framework, and simulated patterns

Mineral species descriptions with links

to structure and properties. X-ray

diffraction list (3 strongest peaks).

>137,000:

-1 22,000CALC

-25,000EXPER

>200,000

28,300 structures,

30,000 patterns,

8,000 diagrams

17,300 property

data

64,734

136 types

Release 2002. The International Centre for Diffraction Data (http://www.icdd.com).

Release 1997. National Institute of Standards and Technology (http://www.nist.gov/

srdlnist3.htm). Distributed by ICDD.

Release 2002. The Binaries edition database developed in cooperation between JST

(Japan Science and Technology Corporation, Tokyo, Japan) and MPDS (Material Phases

Data System, Vitznau, Switzerland);

http://www.paulingfile.com/.

Release December 2002. The ICSD is produced by FIZ

(Fachsinformationzentrum)

Karlsruhe, Germany

(http://www.fiz-informationsdienste.de/en/DB/icsd/produkte.html),

in collaboration with NIST, U.S.A.

Release April 2002. Produced by Cambridge Crystallographic Data Centre (CCDC)

(http://www.ccdc,cam.ac.uk~prods/csd/csd.html).

CRYSTMETB is maintained by Toth Information Systems, 2045 Quincy Avenue,

Gloucester, Ontario

J 6B2, Canada.

(http://www.tothcanada.com/Crystmet.htm).

Release August 2002. PDB is maintained by the Research Collaboratory for Structural

Bioinformatics

(http://www.rcsb.org/pdb/holdings.html).

Release July 2002. Rutgers University, NJ, U.S.A.

(http://ndb-mirror-2.rutgers.edu/)

IZA (International Zeolite Association) zeolite database is maintained by IZA structure

commission. Available on-line at

http://www.iza-structure,org/databases/.

Update July 2002. Mineralogy Database is available on-line at http://webmineral.com/.

376

Chapter

When experimental data remain unidentified using a digitized pattern-

based search-match, different databases should be checked before drawing a

conclusion that a material is new. Continuing searches, however, usually

require unit cell dimensions and therefore, a powder pattern should be

indexed prior to the search. There are a variety of databases dedicated to

different classes of compounds and containing different information as

shown in

Table

4.3.'

For example, two comprehensive databases, ICSD and CSD, contain

crystallographic data and structural information about inorganic, and organic

and metal organic compounds, respectively, while NIST database

encompasses all types of compounds but provides only crystal data with

references. Other databases are dedicated to specific classes of materials,

such as metals and alloys, proteins and macromolecules, minerals or zeolites.

Search-match utilities are usually provided with databases or they may be

obtained separately.

Given a large variety and differences in the contents of existing

databases, a material can be identified from its powder diffraction pattern by

first, searching an appropriate powder diffraction

databaselfile using a

digitized powder diffraction pattern. If a search was successful, the

identification may be considered complete after matching the entire digitized

pattern, not just the few key features included in the search. If a search was

unsuccessful, the pattern should be indexed and unit cell dimensions should

be determined (see Chapter

5).

When both symmetry and unit cell are

known, all relevant databases should be ~earched.~

the case of a suspected

match, the powder diffraction pattern should be modeled from the known

crystal structure of a material found in a database. Both the observed and

computed patterns should be compared as a whole, in order to ensure proper

identification.

Recently the ICDD Powder Diffraction File underwent a substantial and

useful upgrade: calculated patterns based on single crystal data from the

ICSD file have been included into the

PDF-2lPDF-4 Full File; calculated

patterns of structures stored in the CSD file, have been included into the

PDF-4 Organics (see

Table

4.3).

These additions make it possible to conduct

searches and find matches with computed digitized powder patterns in

addition to experimentally measured powder

diffraction

data, thus improving

automation, simplifying phase identification process and considerably

expanding the applicability of the powder method for a qualitative phase

analysis.

Full list of databases related to crystallography can be found at

http://www.iucr.org/cww-

top/data.index.html.

It makes little sense to search organic and metal organic structures database if the material

from which powder diffraction data were collected is inorganic, and

vice versa.

Preliminary data processing and phase analysis

4.4.2

Phase identification and qualitative analysis

Qualitative and quantitative phase analyses are, basically, the two sides

of a coin because they answer two questions: "What?" and "How much?",

respectively, applicable to crystalline phases present in a powder. No matter

how straightforward phase identification,

i.e, qualitative analysis, may

appear (it simply implies comparison of positions and intensities of observed

Bragg reflections with those stored in a database), the problem is far from

trivial. The complexity in finding the right pattern arises from unavoidable

experimental errors that are present in all patterns, i.e. the analyzed and those

located in a database, and from ambiguities that are intrinsic to comparing

images. Thus, phase identification may be performed either or both visually

and/or using automatic searches.

reality, qualitative analysis is nearly

always a combination of both.

The manual approach is simple and doable when a small subset of

database entries is singled out as potential matches with the observed powder

pattern. Practically always, it is employed as a final step to finalize the

automatic search and to select the best among several feasible matching

patterns. A manual search may be done visually, by comparing a plot

representing raw or digitized experimental pattern with digitized patterns

found in a database, or it may be performed digitally, by comparing lists of a

few strong, usually low Bragg angle reflections. Strictly manual searches are

justified when there are a few unidentified reflections in a pattern, a case

when an automatic search is ineffective and usually fails.

Manual phase identification can be performed using searchable or

alphabetical

PDF

indexes, available from the

ICDD.

These indexes include

detailed instructions about what information is required and how to

accomplish the search. A searchable index is split into groups (classes)

according to the d-spacing of the second strongest line, and phases inside the

same group are sorted according to the d-spacing of the strongest line.

alphabetical index is usually employed when exact or at least approximate

elemental composition of the phase is known.

automatic search-and-match can be done much faster, and most

importantly, using multiple Bragg reflections by seeking through enormous

arrays of data, which a typical database contains. The algorithms employed

to conduct automatic searches vary extensively, however, parameters that are

critical in any search include the following:

The number of Bragg reflections that should match in their positions (d-

spacings, Q-values, or Bragg angles), and sometimes in their relative

intensities.

The number of strongest reflections from a database record included in

the comparison.

378

Chapter

Window (or tolerance)

a difference in positions between the observed

and database peaks: as long as the deviation remains below the tolerance

(i.e. within the window), peaks are considered matching. The window

may be specified as a range or

28, d-spacing, or other means commonly

used to express peak positions.

Automatic searches may generate, and often do, a massive number of

matches fi-om which the right solution, if any, should be selected manually

(more exactly

visually) by the user. To help in visual selection, matching

patterns are usually sorted in order of a certain numerical figure of merit that

includes an average difference in peak positions, number of matching

reflections and, optionally, matching relative intensities. For example, the

DMSNT search-match utility generates a list of up to

200

potentially similar

patterns and the user may easily display histograms extracted from the

Powder Diffraction File together with the observed powder pattern, as shown

Figure

4.19.

Depending on both the complexity and quality of the powder pattern, the

number of found "matches" may become overwhelming. For example, if

more than

200

similar patterns are found when using the DMSNT search

utility, they cannot be stored for visual analysis and search parameters

should be adjusted to narrow the range within which the patterns are

accepted as similar. The number of hits can be reduced by using a narrower

window, or by requesting more reflection positions to coincide, or use only

the strongest reflections.

adjustment of parameters, however, should not

be done from the very beginning because the correct solution may be easily

overlooked. A common practice is to start from default search-match

parameters and if the search was unsuccessful, increase the window or

decrease the request for the number of matching reflections.

A powerful way to narrow the searching field is to include restrictions on

the elemental composition. For example, the list of chemical elements can be

specified and used in combination with the following search options:

"Inclusive

limits the search to phases containing at least one of the

listed elements and any other elements, not included in the list;

2. "Inclusive AND" considers only phases containing all listed elements

plus any chemical element not included in the list;

"Exclusive

checks phases containing any combination of the listed

elements but no other chemical elements are allowed;

"Exclusive AND" seeks only patterns fi-om phases containing all listed

elements and nothing else.

Preliminav data processing and phase analysis

379

Bragg angle, 20 (deg.)

Figure

4.19.

Illustration of an incorrect match: Bragg peaks observed in the experimental

diffraction pattern of NiMn02(OH), shown on top and in the middle (solid lines), do not

match those present in the nickel manganese oxide,

ICDD

PDF

card No. 12-0269 shown at

the bottom and overlapped with the plot on top (dashed lines).

12-0269

NICKEL MANGANESE OXIDE

\,,I,

The last option is the most restrictive, while the first alternative is the

most relaxed. For example, when

and

are included in the list, then

"Exclusive

AND"

limits the search only to oxides of vanadium, while

compounds containing other elements (e.g. vanadium hydroxides, vanadates,

etc.) will not be considered and analyzed. On the other hand, "Inclusive

AND"

searches among all compounds containing both

and

combination with any other chemical elements. The latter option may be

useful, for example, when intercalates of vanadium oxides are suspected or

studied.

When visually comparing potentially identical patterns, the following

important issues should always be considered:

When there are a few strong reflections in the database record, all should

be present in the analyzed experimental pattern. When even one of the

strong peaks is missing in the analyzed pattern or it is present but has

very low intensity, this match is likely incorrect, unless an extremely

strong preferred orientation is possible in either pattern (but not in the

both) and there is a legitimate reason for the two to be different.

Relative intensities should be analyzed carefully because significant

discrepancies between experimental data and database entries may occur

380 Chapter 4

due to different wavelengths, diffractometer geometry, sample shape, or

the presence and extent of preferred orientation. Preferred orientation is

an important factor, and in many cases, it is unavoidable. Furthermore,

texture may be substantially different in different experiments,

e.g. yours

and that present in the database. Thus, the following rule should be

applied when comparing intensities: a strong reflection in the database

record should correspond to a strong peak in the analyzed pattern, and a

weak reflection in the database record should correspond to a less intense

peak in the analyzed pattern.

Even though all automatically found patterns are ranked according to

certain matching criteria, visual analysis of at least several solutions (better

yet, all that appear reasonable) is always recommended.

Once again, we will consider experimental data used as an example

throughout this chapter (Figure 4.3). They were converted into a digitized

pattern by background subtraction,

Ka2

stripping and smoothing, followed

by automatic peak detection. The PDF search-match was restricted to phases

containing Ni, Mn and

with the "Inclusive AND" option. Since relatively

rigid restrictions were imposed on the chemical composition, search

parameters were quite relaxed: the window was 0.06" of 20 and only

Bragg reflections were required to coincide within the tolerance established

by the window. About 20 matching patterns total were found. One of the

suspected matches [NiMn03, card No. 12-02691 is shown in Figure 4.19.

This record is far from the best match according to a calculated figure of

merit and we use it as an example to illustrate the difference between good

(Figure 4.20) and poor (Figure

4.19)

matches.

It is easy to see from Figure 4.19 that most Bragg reflections coincide

only approximately (within a few tenths of a degree). Several strong peaks

present in the database record have no match in the experimental pattern,

e.g.

the reflection at 20

55".

The strongest peak at -33.7O matches only

approximately, but its intensity is much greater than that observed

experimentally. Thus, this "match" may be easily dismissed, especially

taking into account that better matches with much higher figures of merit

were found.

Two PDF records coincide with the experimental pattern much better

among all others, including both peak positions and their intensities. They

are shown in Figure 4.20: NiMn02(OH) (card No. 43-0318, Figure 4.21)

and

NiMn03 (card No. 49-1 170, Figure 4.22). Actually, the latter two are

isostructural compounds and, therefore, their patterns should be practically

identical. The first record 43-03 18 is, however, unindexed and consequently,

the digitized pattern has doubtful quality (see the upper right corner in

Figure 4.21).