D.K. Smith, S.Q. Hoyle & G.G. Iohnson,
`
`"Phase Identification Using Whole-Pattern
`
`Matching", Adv. X-Ray Analysis,
`
`V. 36 (1993) pp. 287-299
`
`RS 1029 - 000001
`
`

`
`PHASE IDENTIFICATION USING WHOLE-PATTERN MATCHING
`
`D. K. Smith, S. Q. Hoyle,
`and G. G. Johnson, Jr.
`
`Department of Geosciences and
`Materials Research Laboratory
`The Pennsylvania State University
`University Park, PA 16802, USA
`
`ABSTRACT
`
`The use of whole-pattern matching techniques for phase
`identification provides increased confidence in the phases
`determined compared with d—I matching and enhances the
`potential for determining the existence of phases present in
`low concentretions.- Reference patterns from a database of
`selected phases were compared with the experimental pattern
`obtained from an unknown, and the results were ranked using
`figures-of-merit designed to distinguish the best pattern
`matches. Several different figures-of-merit have been eval-
`uated, all of which proved successful in recognizing the
`strongest phase but varied with respect to the other phases.
`
`Low-concentration phases are revealed when the patterns
`of the more abundant phases are stripped from the experimen-
`tal trace using the best-fit scaled reference traces. Pat-
`tern stripping is improved by pattern shifting and profile
`shape matching which are provided for in the matching pro-
`gram.
`
`INTRODUCTION
`
`For over fifty years, X—ray powder diffraction has been
`used effectively for the identification of phases in mix-
`tures.
`The search method developed by Hanawalt and Rinn
`(1936) and Hanawalt, Rinn and Frevel
`(1933) has been the
`primary procedure for recognizing d-spacing-intensity
`matches when comparing the d-I data sets of reference com-
`pounds with derived values from an experimental sample.
`This method was developed for manual analysis. Other manual
`procedures have been proposed, but none have proved more
`efficient or effective than the Hanawalt method.
`
`Advances in X—Ray Amtysis. Vol. 36, Ediued by
`J.V. Giltrich at :11, Phnuln Press, New Yolk. 1993
`
`RS 1029 - 000002
`
`

`
`Vl. WHOLE PATFERN FITFING. PHASE ANALYSIS BY DIFFRACTION METHODS
`
`Since 1962, efforts have been directed toward employing
`the computer for the identification procedures by using com-
`plex algorithmic comparisons with a database of d—I data.
`These programs provide the user with a list of candidate
`phases ordered on a figure-of-merit, based on various crite-
`ria evaluating the d and I matches,
`from which the user must
`decide on the most correct phase (Frevel 1965, Nichols,
`1966; Johnson and Vand, 1967: Gcehner and Garbauskas, 1982).
`Although the mechanics of the search algorithms differ some-
`what,
`the principal goal is to recognize the pattern of d’s
`and I's of the reference phases in the pattern of d’s and
`I's obtained from the unknown. Computers are faster and
`more tireless compared with humans, and most identifications
`of unknowns made in the 1990's will be made with computer
`assistance. All the currently available programs employ d's
`and I's derived from the experimental diffraction pattern
`and most use the ICDD Powder Diffraction File, PDF, as the
`principal database.
`
`with the decreased cost and increased availability of
`storage on computer systems, it is now feasible and more
`effective to store and examine directly the full digitized
`diffraction pattern rather than reduce the pattern to d‘s
`and I's prior to the analysis.
`one of the analytical steps
`which can be applied to the full pattern is phase identifi~
`cation. This paper is a report on studies optimizing oom-
`puter—based procedures for phase identification using digit-
`ized diffraction-trace databases.
`
`GENERAL PRINCIPLES OF PATTERN IDENTIFICATION
`
`The problem of phase identification is truly a problem
`in one—dimensional pattern recognition.
`The diffraction
`pattern is a single-valued function of intensity and dif-
`fraction angle with a fixed angle scale. Because the pat—
`tern obtained from a mixture is a simple weighted sum of the
`patterns contributed by each phase in the mixture,
`the prob~
`lem is to recognize the existence of each "reference" pat-
`tern in the pattern of the "unknown".
`The weighting factor
`is related to the concentration of the phase in the mixture
`complicated by the relative absorption effects and the abso-
`lute scattering power of each phase.
`The problem of pattern
`recognition is analogous to overlaying a strip chart of a
`pure~phase pattern on the strip chart of the pattern of the
`unknown sample to confirm its presence in the pattern. The
`user must mentally scale the reference pattern to fit it to
`the unknown pattern to confirm the presence of the phase in
`the sample.
`one must effectively program this fitting
`procedure to develop an identification procedure based on
`the full diffraction trace.
`
`The algorithms for recognition must evaluate the proba-
`bility of the existence for each member of the database in
`an efficient manner and then prepare an output listing in
`the order of the abundance of the reference phases in the
`mixture.
`Ideally, each component pattern should be recog-
`nizable, but overlap of peaks and general masking of pet-
`
`RS 1029 - 000003
`
`

`
`D.K.HMflTlETAL
`
`terns of low-abundance phases complicates the recognition
`procedures.
`It is up to the user to confirm the choices.
`
`To be successful in any identification procedure invol-
`ving a database of source patterns, the phases to be identi-
`fied must exist in the database. Establishing useful data-
`bases is critical in fu11—pattern matching because the pat-
`tern-recognition procedures require considerable time even
`with today's supercomputers. Test databases on a DEC Micro-
`VAX are most conveniently limited to 500 entries. Higher
`speed computers might utilize databases containing up to
`5000 entries.
`The present PDF contains over 56000 active
`entries.
`
`Selection of patterns to be included in the working
`databases may not be as serious a problem as it appears at
`first analysis. Most laboratories rarely encounter more
`than a few hundred different phases in any given year. and
`in most cases, the diffractionist can assemble a database of
`the most likely phases based on the types of samples to be
`submitted. Selection criteria may be defined in many other
`ways. Examples are specific groups of minerals such as the
`rock-forming minerals, all the minerals of a certain ele-
`ment, all phases formed from a specific combination of ele-
`ments, all zeolites, all cement phases, or all superconduct-
`ing compounds. This approach is analogous to using subfiles
`or chemical pre-screening during d-I identification.
`
`Currently evaluated algorithms involve testing the pat-
`terns in the selected database against the experimental pat-
`tern of the mixture. Patterns are compared at each digital
`interval over a specified angular range, and a figure-of-
`merit, FOM, must be devised that will emphasize the refer-
`ences which have the highest probability of being a compo-
`nent of the unknown pattern.
`Ideally,
`the FOH should be
`insensitive to the abundance of the phase, but this crite-
`rion is difficult to implement in practice.
`
`The algorithms used for testing pattern fits must also
`be able to compensate for aberrations of the diffraction
`traces due to the instrument or the sample.
`Instrumental
`effects include slit aberrations and misalignment which
`affect the profile shapes and peak positions-
`Sample
`effects such as solid-solution, sample transparency,
`and sample displacement affect the profile position, whereas
`small crystallite sizes and strain affect the profile shape.
`Exact matching of all these effects is impossible._ Peak
`shifting and profile matching may be accommodated in the
`testing algorithm either automatically or with user inter-
`vention.
`In all cases the ultimate test is whether the FOM
`values discriminate the true answerts)
`in the list of evalu-
`ated phases.
`
`In§_QQEEg§§£_EzQgI§m The full-trace identification pro-
`gram, MATCHDB,
`(smith, Johnson and Hoyle, 1901) operates
`under VMS on a DEC MicroVAX II. Digitized dlffract1onOP5t'
`terns are collected over the experimental range 5 - 75
`29
`
`RS 1029 - 000004
`
`

`
`290
`
`VI. WHOLE PATTERN F|T|'|NG, PHASE ANALYSRS BY DIFFHACTION METHODS
`
`with a 0.02° 26 step size. Reference patterns are processed
`to remove the background and are stored in appropriate data-
`bases that can accommodate up to 500 data sets.
`In the most
`recent version of HATCHDB,
`the user can start the analysis
`with one database and then switch to another database to
`continue the analysis. Reference patterns may be experimen-
`tal, simulated from d-I sets, or calculated from crystal
`structure descriptions. All patterns are normalized to have
`the same maximum intensity.
`
`The basic search algorithm allows the examination of
`each pattern in the selected database. Each reference pat-
`tern is effectively superimposed on the pattern of the
`unknown and scaled and shifted +/- on the 26 scale up to 10
`step intervals to achieve the optimum fit.
`The optimum fit
`is indicated by maximizing the selected figure—of—merit.
`The scale, shift, and FOM values are retained until the
`search is complete when the list of reference patterns is
`ordered on the FOE,
`then printed out for the user.
`The pro-
`gram allows the user to compensate for variable and fixed“
`slit patterns to match the form used in the database.
`The
`user also defines the intensity minimum to be considered in
`the pattern comparison.
`The success of the search scheme
`depends on a good definition of a figure—o£-merit.
`
`In the current study, several figures-
`Eiggrgs of Merit
`of-merit have been employed. Three different philosophies
`have been used for constructing the FUN. First, a minimum
`acceptable intensity value is established as the pattern
`threshold, and it is usually a user-supplied value.
`It is
`defined as a fraction of the strongest intensity in the ref-
`erence pattern such as 0.1 or 0.01.
`The lower the value,
`the more of the profile tails that will be evaluated.
`If
`the threshold is set high, such as 0.5,
`then only the stron-
`gest peaks in the pattern will be considered. Once the
`threshold is established,
`the procedure is to compare only
`that part of the unknown pattern which corresponds to the
`accepted reference information. All the FOM’s are only
`evaluated within the pattern regions where there is some
`minimum intensity for the reference being tested.
`compari-
`sons in regions where there is no reference intensity would
`be meaningless in its evaluation.
`
`one of the philosophies used is to evaluate the perfec-
`tion of fit in the test region once the reference is scaled
`to the unknown.
`Ideally, if the reference matches the
`unknown perfectly,
`the traces should be exactly superim-
`posed.
`In practice, especially in mixtures,
`the fit will
`never be perfect, and the ease of recognizing a match will
`be degraded.
`one FOH is based on finding the pattern scale
`multiplier which provides the best fit possible for each of
`the reference patterns when superimposed on the unknown
`trace.
`A variant of this FOM retains the scale multiplier
`in the formulation to normalize weaker phases. These FOM's
`are expressed as follows, where i is the digital interval of
`the diffraction trace, and sums are only calculated for
`those i’s where Ifref} is greater than the threshold:
`
`RS 1029 - 000005
`
`

`
`D.K.SMHT1ETAL
`
`FOM(AV) and I-'OM(AVS}
`
`Ref. > Unk.
`
`Unk. > Rel’.
`
`ESE munumwr
`
`I§§Imtwmnr
`
`Figure 1. Graphical representation of the various figures
`of merit.
`The cross-hatched regions indicate the
`areas compared by the FDR's. The arrow indicates
`where the two traces are in contact.
`
`211
`FOM(AV} — ---------------------- --
`E1CI(r9f:i)/I(unk:i)}
`
`Z11
`roncavs) =- ---------------------- --
`Xi[aI(ref,i}/I(unk,i)]
`
`“ = XEI(r9f;i)l/X[I(Uflk.i)]
`
`(3)
`
`A perfect fit or the reference.and unknown patterns would
`yield a value of 1.0 for the FOH's. These FOM’s may depart
`either higher or lower than this value.
`The geometrical
`interpretation of these Fox's is illustrated in Figure 1A.
`
`RS 1029 - 000006
`
`

`
`292
`
`VI. WHOLE PATFEFIN F|T|'lNG. PHASE ANALYSIS BY DIFFRACTION METHODS
`
`The inclusion of the scale multiplier does not change the
`geometric picture. The effect of the Fonfhv} and FOM(AVS)
`relationships is to make the differential area, where the
`to
`reference trace is greater than the unknown trace, equal
`the area where the unknown trace is greater as illustrated
`in Figure 1A.
`The use of the scale factor, a, weights
`weaker reference patterns more like the stronger patterns.
`
`The second philosophy is to determine the maximum scale
`factor that does not create any overlap of the reference
`pattern on the unknown pattern at any point within the
`threshold acceptable range. This FOM is expressed as:
`
`FOH[PK) = HAXi[I(ref,i)/I(unk,i)]
`
`(4)
`
`Because all reference patterns and the unknown patterns are
`normalized to the same maximum intensity value for the com-
`parisons,
`the maximum possible value for FOM(PK)
`is 1.0.
`The effect of this FOM is illustrated in Figure 1B.
`
`The third philosophy is to use FUN values related to the
`traditional R—factors used in Rietveld analysis which rate
`the fit with respect to the reference pattern.
`The FOM's
`used in this test are expressed as:
`
`E1MIN[aI(ref,iJ,I(unk,)]
`FOM(RK) - -------—-—---- ————————— -—---
`Zi[cI(ref,i)]
`
`Ei[hBS{oI(ref,i)-I(unk,1)}]
`FOH(RD) = 1.0 — —————— --~-— ——————~ ————————— -— (5)
`E1[cI(ref,i)]
`
`Both of these FoH’s are designed to have the best value
`equal to 1.0 for comparisons with the other FOH's.
`The
`interpretations of these Fon's are illustrated in Figures 1C
`and 1D.
`
`Effe9tixe_satteru_suhrrastien A major advantage of
`full-trace identification is the successful subtraction of a
`selected reference pattern once the optimum fit has been
`determined.
`optimizing the fit involves profile matching as
`well as scaling and shifting the pattern.
`HATCHDB allows
`the user to convolute a crystallite size function with the
`reference pattern to approximate the broadening. When the
`broadening is satisfactory,
`the reference pattern is sub-
`tracted from the unknown pattern, and the residual pattern
`is then revsearched to locate the other phases present.
`Removing the pattern of the most abundant phase may reveal
`low-concentration phases not evident in the original pat-
`tern. Up to ten phases have been identified in samples of
`sedimentary rocks by sequential subtraction and re-
`searching.
`subtraction using the full-trace method is more
`effective than with d—I data sets because overlapped peaks
`are processed more correctly.
`
`RS 1029 - 000007
`
`

`
`D.K.SMHTlETAL.
`
`RESULES
`
`The results of two examples will illustrate the power of
`full-pattern identification procedures. The first example
`is a sample of bauxite which contains measurable quantities
`of 13 minerals, all of which exist in the sample as crystal-
`lites smaller than 1pm.
`For this study, a special database
`composed of bauxite minerals,
`including four different types
`of goethite pertinent to the primary study, was employed.
`Because of the difficulty of isolating pure-phase samples of
`the minerals involved, all the patterns were simulated from
`d-I data sets from the PDF or calculated from crystal struc-
`ture information. all the patterns were convoluted with a
`pre—determined, appropriate crystallite-size function for
`the bauxites under study. Bauxitee are difficult to study,
`and X-ray powder diffraction is the best technique for their
`characterization and quantification. This sample will be
`used to compare the results obtained from the different fig-
`ures-of-merit and choice of threshold.
`
`The second example is a mixture of zeolite minerals.
`Because the sample is known to contain only minerals, it is
`appropriate to select a mineral database or one that con-
`tains only zeolite phases and related compounds.
`The data-
`base used contains patterns that have been simulated from
`appropriate d-I patterns in the PDF and includes 475 pat—
`terns. This sample will be used to demonstrate the effec-
`tiveness of sequential search and subtraction.
`FOHIAV) was
`used throughout this experiment.
`
` mrmm Table 1 lists only the top
`seven candidates from the results of five searches on the
`same unknown bauxite pattern using a different FOH for each
`search.
`Independent quantification of this sample by
`GMQUANT (Smith at al., 1987)
`indicates the following propor-
`tions of the component minerals: gibbsite, 68.2%: goethite,
`3.0%: hematite, 4.9%: nordstrandite, 4.0%: bayerite, 3.7%:
`boehmite, 3.3%: quartz, 1.4%: anatase, 1.3%: hydroxyapatite,
`1.3%: rutile, 1.2%: kaolinite, 1.0%; calcite, 0.8%: and
`crandallite, 0.5%. Obviously, only the major phases are
`identified in this example using only one pass.
`
`the dominant mineral, gibbsite,
`For all searches,
`resides at the top of the list. However,
`the second most
`abundant mineral, goethite, is rarely the second choice.
`Instead, hematite is usually the second choice.
`The rest of
`the list varies considerably for each FOM. Except for sod-
`alite, which appears on the two R-factor lists, all the
`other phases are known to be present in the sample. Goeth-
`ite appears at different levels in each list.
`The differ-
`ences are even more distinct when examining more of the list
`than is presented in Table 1. Although all FOM’s effec-
`tively distinguish the phases in the sample in this example,
`no one FOM appears to be more effective than any other POM.
`This test suggests that the optimum figure-of-merit has yet
`to be defined.
`
`RS 1029 - 000008
`
`

`
`VI. WHOLE PATTERN FITTING, PHASE ANALYSIS BY DIFFHACTION METHODS
`
`Table 1.
`
`Tests of the figures-of-merit using the bauxite
`sample.
`The active POM is indicated in bold
`type.
`|:|=n £5
`
`=33-nu-—
`
`—_ =
`
`—B——'E==
`
`0
`1
`10
`5
`-2
`6
`-3
`23
`7 -10
`a
`2
`11
`10
`9
`-1
`
`1.202
`0.193
`0.180
`0.179
`0.176
`0.170
`0.147
`0.138
`
`0.383 Gibbsite A1{0H)3 7-324
`0.355
`0.704 Goethite FeO(0I-I) 29-?13
`0.035
`0.699Gceth1te—o(!'e.3,A1.2)
`0.053
`0.53a0oet1-.11-.e-d (re.75,n1.25)
`0.054.
`0.717 Goethite 3
`(3e,JL1)ooH
`0.031
`0.786 Hematite F0203
`0.067
`0.055 . 0.707 Quartz 5102 33-1161
`0.052
`0.568 Anatnse T102 21-1276
`
`POM Type lb (scaled), Threshold = 0.1
`BAUXITE
`-— fl—--Q —- - xzntnjnfi-$===|-ufi‘—-H-—='==
`
`1
`3
`23
`6
`5
`7
`11
`9
`
`1
`2
`1
`1
`6
`-6
`10
`1
`
`1080
`0008
`0005
`0593
`0578
`0576
`0A95
`0328
`
`0.717
`0.530
`0.395
`0.397
`0.336
`0.337
`0.334
`0.264
`
`0.907 Gibbsite n1(0H}3 7-324
`0.736 Hematite 30203
`0.713 Goethite-d (Fe.75,a1.25)
`0.707 Goethita-o (?e.3,n1.2)
`0.737 Goethite Fao[0H) 29-713
`0.714 coethite 3
`(Fe,A1)0oH
`0.707 Quartz S102 33-1161
`0.574 Anataaa T102 21-1276
`
`301-: Type 2 Peak, Threshold = 0.1
`BAUXITE
`$33 fl$—$Z F$H$$$§j—?—_
`Q3 $ =flZ3
`
`0
`1
`0
`3
`-6
`6
`23 -10
`11
`10
`9
`0
`4
`2
`7
`-1
`
`1.202
`0.163
`0.176
`0.174
`0.147
`0.137
`0.031
`0.152 -
`
`0355
`0.071
`0.068
`0.062
`0.055
`0.054
`0.015
`0.024
`
`0.333 Gibbsite A1(oH)3 7-324
`0.730 Hematite 1='e203
`0.691 Goethite-O {re.a,n1.2)
`0.577 aoathit-.n—0 (Pe.75,n1.25)
`0.707 Quartz 3102 33-1161
`0.531 Anatasa TiO2 21-1276
`0.512 Bayerite J\1(OH}3
`0.692 Goethite 3
`(Pe,A1}0OH
`
`POM Type 33 Hinimun R-FACTOR, Threshold I 0.1
`BAUXITE
`-33 =I==%‘= 35C
`
`0
`1
`0
`3
`10
`11
`-4
`5
`0
`1?
`-1
`7
`-6
`6
`23 -10
`
`1.202
`0.163
`0.147
`0.121
`0.009
`0.152
`0.176
`0.114
`
`0.855
`0.071
`0.055
`0.024
`0.000
`0.024
`.0.063
`0.062
`
`0.808 Gibbsite 31(03):: 7-324
`0.780 Hematite F0203
`0.707 quartz 3102 33-1161
`0.697 aoethite reo(0I-:1 29-713
`0.696 Sodalita-.-CO3 15-469
`0.693 Goethite 3 (Fo,1t1)0oH
`0.691 Goathita-O (Fe.3,n1.2}
`0.67? coathita-cl (I'e.75,A1.25}
`
`POM Type 313 Difference R—FAC'I‘OR, Threshold I 0.1
`1,: i_..__——=-aefiih-xwj——— &flfl2 ==E——jF0
`
`1.202
`0.163
`0.003
`0.147
`0.121
`0.176
`0.152
`0.174
`
`0.355
`0.071
`0.000
`0.055
`0.024
`0.063
`0.024
`0.062
`
`0.814 Gflabsite A1 (0333 7-324.
`0.564 Hematite 170203
`0.457 Sodalite-C03 15-469
`0.423 Quartz 3102 33-1151
`0.398 Goethita FeO(O!l) 29-713
`0.331 GO&‘I'.1'l1t3"‘O (I-‘a.8,J11.2)
`0.379 Goethite 3
`[Fe,A1)O-OH
`0.365 Goethite-d (l"e.?5,A.1.25)
`
`RS 1029 - 000009
`
`

`
`D.K.3hflT¥lET.AL
`
`Table 2. Tests of d1fferent threshold options. The active
`FOM is indxcated in bold type.
`
`50100 FHAV2 rHP(Hax} rMP(R}
`113% 2'$C.jZ—fi'§
`0
`1102
`0.055
`10
`0J9B
`0.035
`2
`0J70
`0.067
`10
`0J4?
`0.055
`-1
`0138
`0.052
`1.
`0.081
`0 . 023
`2
`0005
`0.002
`-10
`0001
`0.012
`0
`0058
`0.010
`
`0.000 Gibbsite PBF-7-324
`0.704 Goathite PhF*29-713
`0.706 Hematite calculated
`0.707 Quartz PDF-33-1161
`0.560
`lnatase P00-21-1276
`0. 509
`Bayerite calculated
`0.516 Nordstrandita C010.
`0.637 Rutile PD?—21—1272
`0.661
`Silicon PD?-
`
`MH9-‘uh-Okfiuhlfll-‘@U'|)-'
`
`
`
`
`
`
`
`FOH(AVS){_sca1od), Threshold - 0.1RUN 2_—————q.....................___.._.._._ —_.»-..___..————.......-...___
`
`PHASE
`SHIFT FHAV2 FHPQIAX) 1'IIP(R]
`:01:
`uzjfl w$a=:-:1
`1
`1.030
`0.71?
`0.90? Gibbsite PD?-‘J’--324!
`2
`0.688
`0.580
`0.786 Hematite Calculated
`1
`0505
`0.395
`0.713 Goethite-0 Gala.
`10
`009
`0.304
`0.707
`Quartz PD?-33-1161
`1
`0328
`0.264
`0.574
`Anntasn PD]?-31-12'J6
`-10
`0001
`0.116
`0.473
`Bayerite Calculated
`-10
`0.191
`0.061
`0.617 Nordltrandita Cale.
`0
`0JJO
`0.000
`0.609
`000110 PD?-21-1272
`
`RUN 3 FOH(AV](unsca1ed), Threshold - 0.01
`
`P0000
`00100 0002 ruptnnx) 000(0)
`===i —Z3—ZZ&'$=‘_'=$
`02 0026603
`
`1582
`0344
`0225
`0217
`0.186
`0J48
`0J38
`0132
`0.110
`
`0.514
`0.007
`0.012
`0.010
`0. 005
`0.002
`0.004
`0.014
`0 . 004
`
`01009100 PD?-?-324
`0.810
`0.493 Gocthito pnr—29—713
`0.676 Hanatite Calculated
`0.493 Anatase PDF-21-1276
`0 . 442
`Bayorite Calculated
`0.456 Nordstrandita C010.
`0.505 Rntile PDF-21-12?2
`0.512
`Silicon
`0 . 375
`cancrinita-C03
`
`.__._______..__—-__-.--.._.— --—
`——___-..—-.__.—-—_—.—.---—-..___—
`RUN 4 FOH(1VS}(sc-aled), Threshold - 0.01.
`
`PHASE
`SHIFT 00002 FflP(HAX} 000(0)
`bjfl U-jflHHI flQh —Z———8—fi$fl
`
`0369
`0322
`0.474‘.
`0353
`0338
`0360
`0.304
`0.275
`0261
`
`0.074
`0.250
`0.013
`0.047
`0.000
`0.058
`0.011
`0.011
`0.035
`
`0.011 Gibhsite por—7—324
`0.601 Hematite Calculated
`0.539
`G00t.hito—o Cale.
`0.492 Anataaa PDF-21-1276
`0.510
`silicon
`0.493
`Boebmite calculated
`0.447
`Bayerita Calculated
`0.505 Rutila 'PDI?—21—12'I2
`0.460
`calcite PD?-5-$86
`
`RS 1029 - 000010
`
`

`
`VI. WHOLE PATTERN FITTING. PHASE ANALYSIS BY DIFFRACTION METHODS
`
`Sequential match and subtraction results for a
`sample of mixed bauxites. At each stage, the
`top candidate was used for the next subtraction.
`The active F014 is indicated in bold type.
`_—_—_—————————_—n.—_..s..
`_____...¢n......a----..____.__._
`
`PHASE
`039 SHIFT PHJLV2 FHP(NJ\XJ 1049(3)
`flE- HIS-C nfi:=: j§ T .....___==u-EDD.
`1
`1.137
`0 . 862
`0 .305
`41-1473 nnalcilla
`375
`0336
`0.766
`0.365
`19-1173 Herschelite
`135
`0.031
`0.214
`0.301
`33-0319
`synthetic
`75
`0.679
`0.520
`0.797
`39-1375 Phillipsite
`374
`0.667
`0. 174
`0 . 770
`19-1130 nnalcime
`353
`0.600
`0. 459
`0 .731
`20-0759 Natrolite
`
`Search results after subtraction at analcine
` C
`It 012 &1&§j
`Zj
`3 7 5
`0.815
`0 . 102
`19- 1178 Herschel its
`75
`0.135
`0 . 534
`39-1375 Phillipsita
`3 53
`0.664
`0 . 473
`20-0759 Nan-.ro11te
`205
`0.630
`0.193
`34-0542
`synthetic
`132
`0.599
`0.153
`33-0322
`synthetic
`
`0 . 90 0
`0 . 316
`0 .790
`0.711
`0.769
`
`Search results after subtraction 01 harschelita
`=:- udmflfi
`-ms$ I "'
`
`1-28:38:
`
`75
`353
`205
`213
`371
`
`L02‘!
`0.940
`0.729
`0.683
`0.664
`
`0.451
`0. 753
`0 . 150
`0.331
`0.153
`
`0.912
`0. 901
`0. 743
`0.792
`0.533
`
`39-1375 Phinipsito
`20-0759 Hatrolite
`34-0542
`synthetic
`27-0505 Cristohnlite
`19—-1135 Natrolite
`
`Search results after subtraction of phillipsite
`0 H0
`flt$3
`=
`—
`
`=_?...—_..nfij
`
`0
`1
`
`353
`371
`333
`210
`291
`
`0868
`0.107
`0.069
`0.045
`0.020
`
`0. 046
`0. 001
`0.009
`0.001
`0.020
`
`0 . 934
`0 .32 1
`0.729
`0.573
`0.444
`
`Ilatrolite
`20-0759
`llatrolite
`19-1135
`24-0027 calcite
`33-1205
`'1'etranat.r.
`25-0395
`2-‘K-9.’ (dah
`
`Search raaults after subtraction of natrolita
`0 1:3 H=%——j-=: n—==
`333
`0.150
`0.005
`0.792
`24-0027 Calcite
`291
`0.113
`0.113
`0.401
`26-0095 0-K-I (dab
`353
`0.062
`0.002
`0.035
`20-0'15? Natrolite
`474
`0.045
`0.004
`0.943
`5-0586 Calcite
`279
`0.035
`0.031
`0. 364
`26-1885
`synthetic
`
`Search results after subtraction of calcite
`ZS: ==$=€ E—$“%==1Z%I=—T
`—$§jj0$Z=€=.==$2
`
`279
`231
`353
`371
`59
`
`0.031
`0.024
`0.020
`0.018
`0.017
`
`0.023
`0.020
`0.001
`0.001
`0.001
`
`0.413
`0.377
`0.335
`0.590
`0.304
`
`23-1335 Synthetic
`26-1803 Synthetic
`20-0759 Natrolite
`19-1185 Natrolite
`40-0101
`socialite typ
`
`RS 1029 - 000011
`
`

`
`D.K.SMHT{ETAL
`
`297
`
`Table 2 shows the results of lowering the threshold from
`0.1 to 9.01 times I{nax}. These data are to be compared
`with the first two entries in Table 1. Again the first few
`entries are not affected, but the lower entries are quite
`varied.
`The lower threshold usually eliminates the false
`inclusion of phases with unusually simple diffraction pat-
`terns.
`
`Table 3 shows the top
`actio
`ch
`ent'
`five candidates produced by the sequence of search and sub-
`traction of the top-rated phase on the zeolite mixture.
`In
`the first search, analcime is the first candidate, but her-
`schelite is also a strong second choice because its FOH(AVJ
`is closer to 1.0. Analcime was selected in this case, and
`the subtraction of its pattern yields a residual pattern
`which produces the second search with herschelite as the top
`candidate. Subtraction of herechelite brings phillipsite to
`the top, and subtraction of phillipsite brings natrolite to
`the top. All of these zeolites were in the top ten on the
`initial search list, and the user could have identified
`their presence by using the graphical options of HATCHDB.
`Subtraction of natrolite brings calcite to the top of the
`list, and graphical matching confirms its presence in the
`sample. Calcite was not in the fifteen top candidates in
`the first list which demonstrates the importance of subtrac-
`tion of the stronger patterns to reveal phases of low con-
`centration. Using the five identified phases for quantifiw
`cation, GHQUANT (Smith, at al., 1937) yields analcime,
`31.9%; herschelite, 29.0%; phillipsite, 18.9%: natrolite,
`11.4%: and calcite, 2.0%.
`It is not surprising that the
`small amount of calcite was masked by the other minerals in
`the initial search.
`
`DISCUSSION
`
`Pattern-matching techniques using reference patterns
`from a database containing up to 500 phases have proved to
`be successful. ‘Databases have been constructed to contain
`related phases for efficiency of phase identification. Top-
`ical datahases may include the common rock—forming minerals,
`all the phases of an element or combination of elements,
`superconductor related phases, common ceramic oxides, or
`similar criteria. Usually,
`the limit of 500 phases is not a
`hindrance to successful identification because most labora-
`tories can define easily the most likely phases to be
`expected in a list of around 200 candidates.
`
`In principle, identification of phases by whole-pattern
`matching is the ideal means for using powder diffraction
`data. when the diffraction patterns of the reference phases
`match the patterns that comprise the pattern of the unknown
`phase,
`their contribution may be effectively eliminated
`revealing phases in lower concentration. Effective subtrac-
`tion will also allow more phases to be identified compared
`with standard d-I matching. Effective subtraction of all
`known phases from the pattern of an unknown may also produce
`a residual pattern that can be analyzed in other ways.
`
`'1
`
`RS 1029 - 000012
`
`

`
`VL WHOLE PATTERN Fl"|TlNG, PHASE ANALYSIS BY DIFFFIACTION METHODS
`
`The main advantages other than effective pattern sub-
`traction include better interpretation of complex peak clus-
`ters, more information on the identified phases, and pat-
`terns of poorly crystalline phases may be employed.
`Peak
`clusters in the unknown pattern that contain contributions
`from several component phases, which are difficult to reduce
`to d-I values, are easily confirmed when the graphical
`traces are superimposed during the identification procedure.
`Information contained in the profile shapes, such as crys-
`tallite size,
`is not lost as is the case when the pattern is
`reduced to d-I values. Poorly crystalline phases, such as
`clay minerals, can be matched more meaningfully than through
`d—I matching because the trace contains so much information
`on the stacking characteristics. The extreme of the poorly
`crystalline state is the amorphous phase which may also have
`a characteristic pattern useful in matching and identifica-
`tion.
`
`The main disadvantages of the whole-pattern method are
`the same as for the d-I method. Preferred orientation in
`the sample may distort the intensities sufficiently so that
`the phases are unrecognizable by either method.
`The whole-
`pattern method probably compensates better for low levels of
`orientation, but the residual patterns will always be
`affected. Extreme cases of orientation are probably best
`approached by d—I methods where the role of intensity may be
`downweighted or ignored. Profile matching is more critical
`in whole—pattern methods where sequential subtraction/search
`is utilized.
`In d-I methods,
`the patterns are reduced to
`discrete numbers depending on the peak~analysis algorithm or
`the whims of the analyst.
`In both techniques, the reference
`pattern may not match the phase in the unknown because of
`physical or chemical differences. Additionally,
`in whole-
`pattern matching, the patterns may have been obtained on
`different diffraction systems. Convolution of appropriate
`functions with the reference patterns during the matching
`procedure can compensate for some of the misfit. Crystalli-
`te-size broadening, for example, has been successfully
`modeled.
`The main disadvantage unique to who1e—pattern
`matching is the time required to build the reference data-
`base (the PDF has already been assembled}.
`
`wide—spread use of whole-pattern identification will
`ultimately depend on the availability of databases and
`faster algorithms and/or laboratory computers.
`‘Although the
`50D—pattern limit has not proved to be a hindrance in iden-
`tifying phases in samples of known character, phases for
`which absolutely no information is available will require
`larger databases.
`Identifying rare minerals will require a
`database of around 4000 entries, and metals and alloys or
`general ceramic databases would have to be much larger.
`Regardless,
`the level of success with smaller databases for
`special studies justifies continued development in whole-
`pattern identification methods.
`
`RS 1029 - 000013
`
`

`
`D.K.SMHTlETAL
`
`REFERENCES
`
`Frevel, L. K.
`
`(1965) Anal. chem. 11, 471-432.
`
`Goehnar, R. P. and Garbafiskas, M. F.
`zg, 81-86
`
`(1992) Adv. x-ray Anal.
`
`Hanawalt, J. D. and Rinn, H. W.
`Eda
`gt
`
`(1936)
`
`Ind. Eng. Cham.,
`
`Hanawalt, J. D., Rinn, H. W. and Fraval, L. K.
`Eng.
`chem., Anal. Ed., 1g, 457-512.
`
`(1933) Ind.
`
`Johnson, G. 6., Jr..and Vand, V.
`19-31.
`
`(1967) Ind. Eng. Chem. fig,
`
`(1966) Twenty—fourth Pittsburgh Diffraction
`Nichols, M. C.
`Conference, Paper No. B-3.
`
`smith, D. K., Johnson, G. G., Jr., scheihle, 3., Wimms, A.
`W., Johnson, J. L. and Hilburn, H. L.
`(1987) Powd. Diff. 2,
`73-77.
`
`Smith, D. K., Johnson, G. G., Jr. and Hoyle, S. Q.
`Adv.
`X—ray Anal. 3;, 377-385.
`
`(1991)
`
`RS 1029 - 000014