Chem a Eur J ATW Full Paper

8/14/2019 Chem a Eur J ATW Full Paper

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FULL PAPER

DOI: 10.1002/chem.2008())

Design of a Full-Profile Matching Solution for High-Throughput Analysis of Multi-Phases Samples Through Powder X-Ray Diffraction

Laurent A. Baumes*, Manuel Moliner and Avelino Corma

*[a]

Abstract: Few solutions that aim atidentifying crystalline materials fromthe analysis of powder X-ray

diffraction (XRD) data have beenreported so far. A careful inspection ofthe latter and the correspondinghighlight of specific failures when usedfor the discrimination ofcrystallographic phases of zeolitesamong mixtures, has allowed thecreation of the recently proposedstrategy called Adaptable TimeWarping (ATW). Here, the designprocess is thoroughly detailed in a step by step manner allowing a deepunderstanding of the motivations,

improvements, and the resultingremarkable properties of ourmethodology. As the use of high-

throughput techniques for the discoveryor the synthesis space enlargement ofnew microporous crystalline structuresmakes the trustworthiness of search-match methods a critical point to beassessed, a meticulous evaluation of thereliability and the robustness is provided and supported by bothempirical comparisons andmathematical proofs. The resultsoffered by our methodology, as itclearly outperforms the well-established solutions, open the way

toward a total automation of such aroutine procedure, eliminatinglaborious and time-consuming controls,

preliminary treatments and settings.Consequently, the proposed solution isof great interest and appears to be very promising considering the numerous potential applications of X-raydiffraction in material science, but alsothe possible extent to several othercharacterization techniques.

Keywords: x-ray diffraction fullprofile warping distance mixture high-throughput

Introduction

The knowledge of the structure at atomistic/molecular level of a

material is required for any advanced understanding of its

performance. In order to have access to the material micro-structure,

numerous generic characterization tools exist, each of them

providing very specific information either on the structure or the

chemical properties, but they are time-consuming. While most of the

methods are performed ex-situ, in-situ characterization techniques

are developing rapidly, with a major effort for parallelization and

high-throughput[1] (HT). Nevertheless HT characterization allows

saving machine time, the corresponding high volume of data

generated requires an automatic data analysis system to avoid

slowing down the whole process. With respect to the targeted

information, most of the responses take the form of series where the

measurements follow an ordered variable; for example, temperature

(thermogravimetry analysis e.g. TGA, temperature programmed

desorption-reduction-oxidation, e.g. TPD, TPR, TPO), the time (gas

chromatography, e.g. GC), the wave length (photoluminescence,

infra-red, e.g. IR, ultraviolet-visible adsorption, e.g. UV-vis), the

voltage (voltammetry), or the angles (x-ray diffraction, e.g. XRD),

etc. Here, we focus on powder diffraction data to be automatically

labeled by their corresponding phases (single or mixture). Moreover,

such analysis is intended not only to identify crystalline materials by

comparing diffraction data against a database, but also to detect the

formation of an unknown phase. Few solutions[2,3,4] that aim at

extracting phases ID directly from powder X-ray diffraction data

have been reported so far. Despite the excellent results[5,6] reported

for these techniques, their application on mixtures of zeolite

crystallographic phases gave us motivations to further investigatetheir reliability and robustness. A careful inspection of the latter and

the corresponding highlight of specific/representative failures

brought us to create a new technique called Adaptable Time

Warping (ATW).[7] Here, the design process of the recently

proposed ATW strategy is thoroughly detailed in a step by step

manner. This allows a deep understanding of the motivations,

improvements, and the resulting remarkable properties of the

methodology.

Three different studies and the corresponding results using the

commercial software PolySnap2[3,4] from Bruker-AXS are

presented in the first part of thus report. Then, a close examination

of the responses will allow to point and understand the weaknessesof such an approach for the type of problems under study. This will

be illustrated by the selection of few representative mistakes for

[a] Dr. L. A. Baumes, Dr. M. Moliner, Dr. Prof. A. Corma

Instituto de Tecnologia Quimica

CSIC-Universidad Politecnica de Valencia

UPV, Av. de los Naranjos, s/n E-46022 Spain

Fax: (+34) 963879444

E-mail: {baumesl; mmoliner; acorma}@itq.upv.es

Supporting information for this article is available on the WWW under

http://www.chemeurj.org/


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which some corrective adaptations of the methodology are described

in the third section. It is shown how such modifications can be

merged together making the so-called Adaptable Time Warping a

fundamentally different, powerful and innovative approach. Its

evaluation on numerous benchmarks allows supporting empirically

the mathematical proofs of ATW robustness and reliability property.

Finally, results using ATW for the same cases will show the clear

superiority of this methodology with respect to those previously

reported.

Figure 1. The automatic analysis of the 192 X-Ray diffraction data of the discovery

program of the zeolite ITQ-33 is expected to identify the different crystallographic

phases present in each sample, allowing the creation of the corresponding phase

diagram (8 different phases, numerous mixtures, and among them the presence of a new

material has to be established).

Identification of Zeolite Crystallographic Phases

Zeolites are crystalline alumino-silicates, whose structures are

3D networks composed of channels and cavities of molecular

dimensions. Their microporous framework structures, the wide

range of chemical composition and surface acidity, and the

possibility of tuning their electric fields are key factors that render

zeolites versatile materials for an increasing number of

applications.[8]

Among them, is the use of zeolites as catalysts (for the

petrochemical industry, for pollution control and for the synthesis of

special chemicals), for gas adsorption and separation, electronics

and medical uses.[9] The discovery of new structures or enlarging the

synthesis space, and optimization of existing ones require a

considerable experimental effort. This can be diminished by using

high throughput (HT) technology (usually parallelization and

miniaturization)[10]

as also done for heterogeneous catalysts.[11]

As arecent example, this technique has allowed the synthesis of a very

unique zeolite structure that includes extra-large 18MR connected

with medium 10MR pores (ITQ-33).[12] The unusual conditions


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needed to synthesize this new material were found by using HT

techniques to cover a wide range of possible synthesis conditions.

That study required the generation of 192 diffractograms to follow

the formation of the different crystallographic phases and mixtures

of phases depending on the synthesis conditions, and from those

mixtures of phases the presence of a new zeolite structure had to be

established, see Figure 1. To achieve this is not obvious when

complex mixtures of several crystalline phases exist in the same

samples and consequently, the identification of the phases is time

consuming. At the same time when increasing the amount of

experiments to cover a broader synthesis range, it becomes

mandatory to develop an automatic data treatment not to slow down

the whole process.[13] Therefore an important step in this direction is

the automatic classification of crystalline structures through XRD

data, as it has been previously pointed by Takeushi et al.[6] For doing

this PolySnap2[3] has been selected as a reference because the

software is representative and highly relevant considering the

current state of the art in HT identification of phases through full

profile examination. Detailed explanations are available, while

merging various techniques: principle component analysis (PCA),

multi-dimensional scaling (MDS), cluster analysis,

[14]

and statisticaltests. As PolySnap2 offers an automatic analysis where user

interface is minimized to few options (allows x-shift and check

for amorphous have been selected), this mode is chosen for

comparison. Three datasets of experiments have been selected:

Zeolite ,[10b] ITQ-21/30,[10a,10d] and ITQ-33[12].

Zeolite - In order to optimise the preparation conditions for

the synthesis of beta zeolite, a factorial design (3242) is employed

for exploring different molar gel composition. The molar gel

composition is explored by varying the following molar ratios:

Na/(Si+Al), TEA/(Si+Al), OH/(Si+Al) and H2O/(Si+Al), while

Si/Al ratio is fixed. The experimental design considers the following

four molar ratios (level): Na/(Si+Al) (3) ranging from 0 to 0.5;TEA/(Si+Al) (4) from 0.1 to 0.6; OH-/(Si+Al) (4) from 0.15 to 0.52;

and H2O/(Si+Al) (3) from 5 to 15. The total number of samples

synthesised considering this factorial design is 144. The materials

obtained in the studied area are amorphous materials, zeolite beta,

and another dense material (named as UDM).

ITQ-21/30 - The gel composition is explored by varying the

following molar ratios: Al/(Si+Ge), MSPT/(Si+Ge), F-/(Si+Ge) and

Si/Ge. A factorial experimental design (4 x 32 x 22 =144) is selected

for studying simultaneously the crystallization time and the

composition of the gel varying the molar ratios of the components.

Two zeolites are found in the area of the phase diagram studied:

ITQ-21 and ITQ-30.

ITQ-33 - Hexamethonium is used as structure directing agent

(SDA). An initial experimental factorial design (343) is selected.

Si/Ge, TIII/(Si+Ge), OH-/(Si+Ge), and H2O/(Si+Ge) are the

synthesis variables. This experimental design considers the

following four molar ratios (level): Si/Ge (4) ranging from 2 to 30;

B/(Si+Ge) (4) from 0 to 0.05; OH-/(Si+Ge) (3) from 0.1 to 0.5; and

H2O/(Si+Ge) (4) from 5 to 30. The number of synthesized samples

is 192. Hexamethonium is a promising structure directing agent

(SDA), since this molecule has a high number of degrees of freedom.

Such flexibility allows different conformations that stabilize several

competing structures, such as EU-1, ITQ-17, ITQ-22, ITQ-24, SSZ-

31, a lamellar phase, and the new structure, ITQ-33.

When PolySnap2 is employed for the studies ITQ-33,

Zeolite , and ITQ-21/30 the overall recognition rates are

68.2%, 84.3%, 86.11% and respectively. Despite the relative

easiness of study and ITQ-21/30, i.e. only three different phases

(including amorphous) are present with their corresponding

mixtures, 15.7% and 13.89% of errors are respectively obtained.

Among them, the majority corresponds to the fact that partially

crystalline materials are not correctly identified. The same

observation can be done for ITQ-33 study. This makes the number

of false negative, i.e. the presence of a given crystallographic phase

which is not detected, relatively high, see the first line of the Tables

1 and 2. Confusion matrix for ITQ-21/30 study is given in

Supplementary information as Table S2. Among them, growing

phases represent the principal source of misidentifications, and it

can be observed that mixtures of pure phases (without the presence

of amorphous) are also poorly recognized.

Table 1. Confusion matrix with the real phases in the experimental design Beta study

versus predicted classes obtained with PolySnap2 indicated at the top of the cell, and

versus ATW indicated at the bottom of the cell (in italic and between brackets).

Considering the selected applications, an adapted methodology

is still lacking taking into account that one specific structure can

present large differences in peak intensity and diffraction angle

within the XRD diffractogram, depending on the level of

crystallinity, crystallite size, and chemical composition.

Subsequently, the synthesized powder which presents a mixture of

phases and impurities makes the automatic determination of

crystalline phases through X-ray diffraction data a real challenge. A

closer look on mistakes should allow understanding why the

methodology is failing. Therefore, some representative failures are

extracted from the above treatments, see Figures 1 to 3.

PolySnap2 operations[4] can be summarized as follows:

i) each input sample is checked against a database of known phases,

ii) the criterion based on the Pearson and Spearman correlation

Real phases

Amorphous

UDM

GrowingUDM

Beta

GrowingBeta

Mixture

GrowingMixture

Am.75

(76)

1 9

(1)

2 2 89

(77)

UDM11

(12)

2

(1)

13

(13)

Grow

UDM

0

(9)

0

(9)

Beta27

(28)

2 29

(28)

Growing

Beta

0

(1)

0

(2)

0

(3)

Mixture1 2 0

(1)

3

(1)

Growing

Mixture

0

(1)

0

(2)

0

(3)

Predictedphases

76 12 11 29 2 2 2 84.3%

(97%)


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coefficients is calculated taking into account all measured data

points (full profile), iii) if the pattern correlations do not indicate a

good match, then the percentage composition of the sample is

determined, i.e. quantitative analysis, using the singular value

decomposition (SVD) for matrix inversion, and all the known

phases as potential elements of the composition.

Table 2. Confusion matrix with the real phases in the experimental design ITQ-33

versus predicted classes obtained with PolySnap2 indicated on the left hand-side of

the cell, and versus ATW indicated on the right hand-side of the cell (in italic andbetween brackets).

[a] ITQ-24 + amorphous. [b] SSZ-31 + amorphous.

Figures 2-a ,3-b, and 2-c highlight a first problem inherent to

methodologies for which a statistical criterion based on a correlation

coefficient is employed to measure the strength (and direction) of

the relationship between diffractograms. As highest peaks get the

greatest influence on the variation of the criteria, the local

overlapping of diffractograms considering the reflections with high

intensities, such as for ITQ-22 and ITQ-24 at 11 and between 20

and 23, see Figure 2-a, can mislead the methodology when used in

the case of ITQ-33. The same confusion appears for the sample

containing both zeolite Beta and UDM in Figure 3-b. In this case,

smaller peaks belonging to UDM are clearly visible, but their

influence remains relatively too low compared to the main phase.

This problem is tackled in PolySnap2 as it integrates various

techniques and criteria in order to better handle such kind of

complications. Gilmore et al. define a general criterion as the linear

combination (half-half for the automatic mode) of Pearson and

Spearman coefficients.[3] Spearmans coefficient is a non-parametric

measure of correlation and a special case of Pearson product-

moment as the data is first converted to ranking before calculating

the coefficient. This has the advantage to decrease the influence of

the nominal peaks height. However, the criterion is not strongenough by itself. When combined with Pearson coefficient, it simply

behaves as an indicator for further user attention.

Figure 2. Predicted errors by using PolySnap2. a) The real phase is ITQ-22 (#19),

being the software prediction mixture ITQ-22 with ITQ-24, b) it is growing the

Lamellar phase, being the software prediction amorphous, and c) it predicts pure ITQ-

17 (#217), being a mixture between ITQ-17 and ITQ-24.

Predicted phases

Othermixtures

22+24+33

22+24

17+24

24+33

Lamellar+24

ITQ-17

Lamellar

SSZ-31

EU-1

ITQ-24

ITQ-22

Amorphous

55

55(55)

Am.

38

(2)

36(36)

2

ITQ-22

19

6(2)[a]

8(17)

2 3ITQ-24

3 1(3)

2EU-1

16

(1)[b]

13(15)

3

SSZ-31

46

18(46)

28

Lam.

0 0(0

)

ITQ-17

8 3 0(8)

1 2 2

Lam.+24

2 2 0(2)

24+33

2 1 0(2)

1

17+24

2 1 0(2)

1

22+24

1 0(1)

1

22+24+33

131/192=68.2%

(187/192=97.4%)

13(3)

0(1)

0(4)

0(2)

0(2)

0(8)

1(0)

19(46)

13(14)

1(2)

10(17)

40(36)

95(54)

Realphases


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Similarly, Figures 2-b and 3-a point the problem of detecting a

growing phase in presence of amorphous. As explained in Ref[3], if

the ratio of non-background to background intensity falls below a

default limit of 3% and if, additionally, there are less than a default

value of 3 peaks, the sample is flagged as non-crystalline. Here, the

conception of the methodology consisting in an a priori separation

of the different situations, i.e. one pure phase-mixture of phases-

amorphous sample, through thresholds explains such errors.

Another intricacy encountered during the analysis of ITQ-33

data is represented in Figure 4. It can be observed how the

increasing integration of Germanium modifies the dimension of the

unit cell due to [Ge-O] longer bond length than [Si-O], and

consequently shifts the diffractograms along x-axis. The difficulty

of such situation arises from the fact that the shifting is not constant

along the entire angle range as emphasized in Figure 4-b. This has a

direct influence on the criteria and thus on the identification as most

techniques use the Euclidian distance at the basis of their calculation,

i.e. the differences of intensity are calculated at the same angle

positions. The resulting is that most of these diffractograms are

interpreted as mixtures of ITQ-24 and another phase, i.e. falsepositive.

Figure 3. Predicted errors by using PolySnap2. a) Growing phases, UDM (#21) and

Beta (#45), being the software prediction amorphous. b) Mixtures between Beta and

UDM, being the software prediction Beta phase.

Figure 4. XRD patterns for ITQ-24 zeolites obtained in the ITQ-33 study with

different Si/Ge ratio a) full pattern, and b) small angle range (19-24).

To summarize, when facing difficult problems where samples

present large differences in the intensity of peaks and diffraction

angles, the traditional methodologies obviously fail. As basic

statistical correlation coefficients allow the identification of pure

phases in most of the cases, except for the latter, the real strength

and need of new strategies is expected where the current

methodologies does not succeed or simply warns for further user

attention. Such tricky situations can be divided into 5 groups: i) the

treatment of the highest peaks which either mislead the

crystallographic phase assignment due to local overlapping, Figure

2-a, or hide the formation of competitive phases due to their

relatively big weight into the criterion, Figure 2-c; ii) the

simultaneous occurrence of small peaks representative of a given

growing phase does not take enough importance among the evident

presence of another phase, Figure 3-b; iii) the treatment of partially

but predominantly amorphous samples, Figures 2-b and 3-a, is not

accurate enough leading to numerous false negatives; iv) similarly,

the shifting of diffractograms along angle axis, Figure 4,

undoubtedly appears as one of the limitation of Euclidian-based

criteria leading to uncertainty; iv) finally the effective detection of

the presence of a new phase, or zeolite structure, which remains oneof the most required feature of the strategy still needs improvements.

The three samples containing the growing ITQ-33 zeolite have been

classified as mixtures of other pure phases, Table 2.

Despite the fact that other full-profile techniques are available

either in PolySnap2 or from other sources, their overall conception

remains very similar and always refers to statistical criteria which

determine the similarity between the diffractograms. Such similarity

is used either for a direct labelling of the samples as shown before,

or for the visual representation of numerous XRD in a way to

provide a quick idea of how diffractograms may be grouped,[2,14]

such as principle component analysis (PCA), multi-dimensional

scaling (MDS), cluster analysis. However, these traditionalalgorithms initially created for multi-dimensional data are not

adequate when series are considered. The reason for this is mainly

due to the lack of knowledge on the intrinsic ordering data

particularity. Most of them are similarity/dissimilarity-based

approaches, where the similarity between instances is usually

explicitly expressed by the classical p-norm distance, e.g. Euclidian.

Numerous algorithms are available, but only few distances have

been proposed for the special treatment of series and, among them,

the Dynamic Time Warping[15] (DTW) appears as the most famous

one. As warping distances have never been integrated into search-

match approaches, we propose this first modification to tackle the

problem related to shifting. On the other hand, even though all

points are considered in full-profile search-match methodologies,the whole available information is not fully used. Before analyzing

unknown samples, the selection of potential pure phases can be a

priori analyzed, the information being contained in these patterns

should give precious indications on how the different phases can be

identified taking into account the presence of other ones. Such kind

of analysis can be handled by machine learning (ML) techniques.

The aim is to localize strategic traits/features of each individual

phase which makes them unique taking into account the competitive

phases. Moreover, additional information can be inserted before

launching the automatic phase recognition, such as previous

experiments, i.e. the use of internal databases, o theoretical

diffraction data simulating the formation of unsynthesized mixtures

or the integration of new elements into the crystal network, such asGermanium considering ITQ-33 dataset.


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crystallographic phases, previous experiments, and theoretical

calculations. The aim of analyzing additional data is to modify the

similarity between diffractograms in order to improve recognition of

mixtures, with or without the presence of amorphous. A way to

achieve this is to modify the influence of the intensities for each

angle position. Since the matrix which is employed for DTW

calculation is a squared matrix of dimension t, i.e. the total number

of angles steps, it can be used to integrate weights. A possible way

to correctly assign the values of each weight is to learn how

intensities must be interpreted or modified in order to get a correct

answer from the labelling procedure. Due to the large number of

angle positions, a machine learning (ML) approach must be

employed. By presenting various cases (better if complicated) either

from past experiments or theoretical calculations, we expect the

setting of weights to improve the classification results.

Our methodology Adaptable Time Warping (ATW) is designed,

as all warping (including the famous DTW), and p-norm distances

are particular cases of ATW. Let a tt matrix, be the set of

parameters required to compute ATW,+ = i j

[ ], 1, i j t . If ij=, ai is not allowed to be matched with bj.A(Ai, Bj, ij) is the recursive function that computes the distancebetweenAi andBj. ATW is defined by Equation 2.

Considering a set of n time series and a given classification

algorithm, we expect optimal settings for ATW distance consideringthe given problem and related data. Two different algorithms are

required: a classification technique, and another one for the

automatic weight setting. As an example and in order not to make

the methodology too complex, the instance-based learning (IBL)

method called k-nearest-neighbors (k-nn) is chosen as classification

strategy. An IBL approach also called memory-based or case-based

learning is defined as the generalizing of a new instance to be

classified from the stored training examples. Training examples are

processed when a new instance arrives. Each time a new query

instance is encountered, its relationship to the previously stored

examples is examined to assign a target function value for the new

instance. Three characteristics may define IBL algorithms: i) A

similarity function which tells the algorithm how close together two

instances are. ii) A typical instance selection function: this tells

the algorithm which of the instances to keep as examples. iii) A

classification function which relates a new case to the learned cases.

IBL approaches are chosen since the similarity function that is

employed plays a central role as stressed by the definition given

earlier. The following are the most common IBL methods: k-nearest

neighbors (k-nn), locally weighted regression, and radial basis

function (RBF). k-nn algorithm is selected for simplicity since it is

the most basic of all IBL methods, but also because the aim is to

stress on the proposed similarity measure and not on the algorithm

which uses it. Moreover, superior performances may be easily

obtained as k-nn algorithm can be refined by weighting the

contribution of each of the kneighbors according to their distance to

the query point giving greater weight to closer neighbors such as for

RBF. One very important trait of the methodology is its

independence from the classification algorithm, i.e. others could be

employed as well.

At this level of the design, it remains defining the procedure for

weight assignment. Since the aim is to improve labelling results, the

best matrix is defined as the matrix that minimizes the

classification error rate with ATW and the chosen learning strategy,

see Figure 7. The brute force solution would perform theclassification with all the possible values of , and finally keeps the

one that corresponds to the best error rate. Each possible matrix

must be tested for obtaining the error rate. However, the resulting

complexity in time of the exhaustive search is intractable. This

implies the use of a heuristic which aims at quickly finding a

solution, i.e. obtaining a locally optimal matrix . Genetic

algorithms (GAs) are selected because there is a body of theory

providing theoretical evidence to complement the empirical proof of

their robustness. Such techniques are now consistently used. The

reader is referred to Ref[26] for an introduction and advanced

discussions.

Figure 7. ATW conception. Based on classification errors of training samples, the

matrix is modified until reaching a given termination criterion, i.e. the convergence to a

minimum. Finally the best matrix is used for unseen test samples.

Let X be a set of n time series, X = {x1,,xn), and a

population ofp individuals {1,, p). Each individual is a

candidate matrixi that owns t variables. The terms individuals,

population, etc are used following the GA terminology. Each

cell of the matrix is a variable that the GA optimizes. The GA (i.e.

all individualsi) is initialized by assigning random values to every

cell ij. The evaluation, then the selection, and finally the

mutation/recombination are applied to each generation. The details

about the use of genetic algorithm as optimization tool are explained

in supplementary information. Our approach is a learning process

which uses a heuristic, and allows reaching near-optimal solutions.

According to a given classification problem, ATW approach adapts

itself for better capturing data specificity. ATW can be associated to both warping and non-warping distances as demonstrated by the

proof given in supplementary material. Therefore, whatever the

temporal classification problem, optimal parameters imply ATW

( ) ( )

( )

( )

( )( )

' '

' '

' '

1 ( 1)

' '

1 ( 1)

' '

1 ( 1)

' '

1

, , , , (Equation 2)

, ,

0, 1

, , , 1 1

, , , 1 1

, ,

min , ,

=

=

= =

= >

> == +

A t t t t

A i j i j

i j

A i j i j

A i j i j

i j i j

A i j i j

A i j i

ATW A B A B

with A B

if

if i j

A B if i and j

A B if i and j

a bA B

A B

( )

( )

[ ]

( 1)

' '

1 1 ( 1) ( 1)

11 1

1

,

, ,

, , 1,

+

=

j

A i j i j

t

i j

t t t

else

A B

with i j t


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8

to give results at least equal or superior to other distances, and

consequently ATW is always at least equivalent or superior to all

other distance use. In the following section, results for 20

benchmarks[27] and the three real datasets of zeolite investigations

are given, confirming empirically the mathematical proof.

Results and Discussion

The k-nn algorithm is employed with k=3. The calculation of the

error rate on the learning dataset is done using k-CV with k=5.

The lowest error rate on the validation set ( i.e. the winner matrix) is

kept for comparison with other techniques which have been

evaluated with the same validation set. The number of iteration (r)

for ATW matrices optimization is set to 50, and the population size

(p) is set to 4.pmutand q are respectively set to {0.1; 5}.

Figure 8 and Table S1 in supplementary material shows that

ATW always constitutes the lower bound of error rates when is

compared to both DTW and Euclidian distance use on the 20

different benchmarks.[27] ATW is superior to DTW (either with the

best delta value or without warping window) and the Euclidiandistance for 7 benchmarks (see bold values).

Figure 8. Evaluation of ATW of 20 different benchmarks. [27] For all the cases, ATW

reaches the lowest classification error indicated on the y-axis.

Considering zeolite dataset, DTW performs nearly two

times better than the Euclidian distance but here again ATW allows

to reach a better performance. For ITQ-21/30, DTW and

Euclidian distances perform equally while ATW decreases the error

rate by half. In those datasets there are only few different classes

with low number of mixtures between them. However, in the zeolite

synthesis, it is normal to crystallise a high quantity of different

materials, with mixtures of two or more different zeolites. The ATW

methodology can not only predict the pure phase but also the

mixture ordered by decreasing degree of crystallization of each one.

For doing that, the algorithm compares to next neighbours getting

the distance to them, and the output phase is ordered depending on

that distance. Moreover, depending on the crystal composition, it is

possible to obtain some shifts in the peak positions, although it is the

same phase. Therefore, one advantage of ATW is to consider peak

position shifts, which are common for zeolites with different Si/Ge

ratio. For this reason, the dataset ITQ-33 is an excellent proof to

check the ability of the ATW to classify such materials. There are

eight different materials (amorphous, ITQ-17, ITQ-22, ITQ-24, EU-

1, Lamellar phase, SSZ-31, and ITQ-33) with numerous mixtures

between them. The ratio Si/Ge is also varied in the study getting

variations in the peaks positions. The last challenge that shows the

experimental design is the discovering of a new crystalline phase,

ITQ-33, in a very narrow condition range. In Figure 1 it can be

observed the occurrence of each competing phase as a function of

the composition of the starting gel. Despite of the non-linearity of

the system, it is clearly defined the range of composition in which a

specific phase is formed. However, there are some narrow ranges of

composition in which two or more phases are competing. Zeolite

ITQ-33 was growing with ITQ-24 in an specific area of the phase

diagram. The conditions for ITQ-33 synthesis are extremely unusual,

due to the low OH-/(Si+Ge) ratio in a concentrated gel H2O/(Si+Ge)

= 5, in the presence of a trivalent element ((Si+Ge)/B = 20 or 50)

and germanium (Si/Ge = 2). When some variable was changed, the

ITQ-33 phase disappears and ITQ-22 or ITQ-24 are formed. WhenATW is applied, the classification error is below 4% (see Table 2),

considering all the mixtures obtained in the experimental design.

Moreover, if the confusion matrix is studied in detail, one can see

that 2 of the 5 errors are due to the fact that the algorithm predictsalso the amorphous materials that are contained in these samples,

being more accurate than our manual classification. Amorphous

material is considered as a regular phase, even when the amorphous

content is impurity. Two other errors come from two predicted

mixtures ITQ-22/ITQ-24 while the real phases are pure ITQ-22. In

fact, ITQ-24 was in the limit of significance, being a most minority

phase, and the SVD procedure assigns less than 3%.

Conclusion

ATW is a new time series distance that can be adapted

according to the classification issue, using a genetic algorithm. GA

components (chromosomes and operators) have been adapted for the

task in-hand. Such hybridization is shown of great interest for the

classification goal while the adaptation of the GA to the problem

0

0.1

0.2

0.3

0.4

0.5

0.6

SyntheticControl

Gun-Point

CBF

Face(all)

OSULeaf

SwedishLeaf

50Words

Trace

TwoPatterns

Wafer

Face(four)

Lightning-2

Lightning-7

ECG

Adiac

Yoga

Fish

Beef

Coffee

OliveOil

Euclide DTW(best d value)

DTW (no warping window) ATW


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form allows applying successfully the new strategy to complex

datasets. Besides its obvious identification superiority, a large

number of advantages are inherent to ATW such as the following:

there is no background removal, no peak extraction, no smoothing,

no interpolation, no region exclusion from the user, no pre-defined

shifts, no false negative, the best is automatically found, it handles

properly amorphous samples, captures phases characteristics while

reducing the user interaction to the minimum, and finally encounters

new crystallographic phases.

Figure 9. Coupling of ATW inside our platform hITeQ with ITQ existing HT tools

ATW clearly appears as a new method for automatically

deciphering X-ray diffraction patterns, allowing crystallographic

phases to be identified quickly and reliably. As XRD is used for a

wide range of purposes, from routine characterization in industrial

procedure control through in depth research investigations of the

most complex high technology materials, such kind of methodology

which can be easily coupled with existing high-throughput synthesis

apparatus, see Figure 9, is a real breakthrough. It has been shown

how the phase diagram corresponding to a broad research space can

be quickly revealed making clearer the way towards new structures.

Acknowledgements

EU Commission FP6 (TOPCOMBI Project) is gratefully acknowledged. We also thank

Santiago Jimenez for his important collaboration to set the hITeQ platform which

integrates all programming codes of the presented methodology. Laurent A. Baumes

thanks Stephan Schunk from hte Company for his comments on the technique.

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Received: ((will be filled in by the editorial staff))Revised: ((will be filled in by the editorial staff))

Published online: ((will be filled in by the editorial staff))


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Making clearer the way towards

new structuresLaurent A. Baumes

*, Manuel

Moliner and Avelino Corma*

Design of a Full-Profile

Matching Solution for High-Throughput Analysis of Multi-

Phases Samples Through

Powder X-Ray Diffraction

Design of ATW

methodology for

automatically, quickly and

reliably deciphering X-raydiffraction patterns

Chem a Eur J ATW Full Paper

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