Genetic Algorithm based X-Ray Diffraction Analysis for Chemical
Control of Aluminium Smelters Baths
Shakhnaz Akhmedova
1
, Igor Yakimov
2
, Aleksandr Zaloga
2
, Sergey Burakov
1
, Eugene Semenkin
1
,
Petr Dubinin
2
, Oksana Piksina
2
and Eugene Andryushenko
2
1
Siberian State Aerospace University, Krasnoyarsk, Russia
2
Siberian Federal University, Krasnoyarsk, Russia
Keywords: Aluminium Industry, Aluminium Electrolyte, Cryolite Ratio, Bath Ratio, X-Ray Diffraction Analysis,
Rietveld Method, Genetic Algorithms, Chemical Control.
Abstract: Aluminium production is based on the high-temperature electrolysis of alumina in molten fluoride salts. Part
of the fluoride compounds continuously evaporates, which violates the optimal composition of the
electrolyte in the electrolytic baths. It causes a technological necessity for regular adjustment of the
electrolyte composition by the addition of fluorides according to results of automatic express analysis of the
electrolyte. Control of the main composition characteristics is performed automatically by XRD phase
analysis of crystallized electrolyte samples. The XRD method, usually used on aluminium smelters, requires
periodic calibration with reference samples, whose phase composition is exactly known. The preparation of
such samples is a rather complicated problem because samples include 5-6 different phases with variable
microcrystalline structure. An alternative diffraction method is the Rietveld method, which does not require
reference samples to be used. The method is based on the modelling of the experimental powder patterns of
electrolyte samples as the sum of the phase of component powder patterns, calculated from their atomic
crystal structure. The simulation includes a refinement of the profile parameters and crystal structure of
phases by the nonlinear least squares method (LSM). The problem with the automation of this approach is
the need to install a set of initial values of the parameters that can and should be automatically refined by
LSM to exact values. To solve this problem, the article proposed an optimization method based on an
evolutionary choice of initial values of profile and structural parameters using a genetic algorithm. The
criterion of the evolution is the minimization of the profile R-factor, which represents the weighted
discrepancy between the experimental and model powder patterns of the electrolyte sample. It is shown that
this approach provides the necessary accuracy and complete automation of the electrolyte composition
control.
1 INTRODUCTION
Aluminium production is based on the electrolysis of
alumina consisting of various forms of Al
2
O
3
.
Electrolytes of aluminium electrolysis baths in their
composition comprise melts of the senary system
Na-Al-Ca-Mg-F-O at a temperature of 930- 950
о
С.
Part of the components continuously evaporates
from the baths, which shifts the composition of the
electrolyte from the optimum point. It causes a
technological need for the regular adjustment of the
electrolyte composition by fluoride salts. The
amount of fluoride salt for addition into the
electrolysis bath is calculated from the results of
operational analysis of the chemical composition of
crystallized electrolyte samples.
The bath chemistry composition or more exactly
the bath ratio (BR is wt. NaF/AlF
3
) or cryolite ratio
(CR is mol. NaF/AlF
3
, CR=2BR) is a principal and
fundamental cell parameter to achieve the best
performance of electrolytic baths. The cryolite ratio
has a direct impact on the temperature control,
alumina solubility, ledge formation and current
efficiency of baths. The industrial characterization of
the bath electrolyte for process control is generally
carried out using two automatic calibrating methods:
a combined X-ray diffraction (XRD) analysis of CR
32
Akhmedova S., Yakimov I., Zaloga A., Burakov S., Semenkin E., Dubinin P., Piksina O. and Andryushenko E..
Genetic Algorithm based X-Ray Diffraction Analysis for Chemical Control of Aluminium Smelters Baths.
DOI: 10.5220/0005561900320039
In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2015), pages 32-39
ISBN: 978-989-758-122-9
Copyright
c
2015 SCITEPRESS (Science and Technology Publications, Lda.)
Figure 1: Scheme of the system of X-ray process control.
and X-ray fluorescence (XRF) analysis of CaF
2
and
MgF
2
. The technologically required accuracy of the
CR analysis is characterized by standard deviation in
0.02 CR units. The XRD method performs
quantitative phase analysis (QPA) of the mineral
composition of the electrolyte samples, and then the
CR is calculated from the found mineral phase
concentrations. Appropriate electrolyte reference
samples are required in the XRD and XRF
instrument calibration on crystalline phases and on
calcium and magnesium, respectively.
Figure 1 shows a scheme of the system of X-ray
process control and correction of electrolyte
composition, acting on the aluminium smelters.
Sampling from the cells is performed manually
by certain regulations. The preparation of samples
for analysis (grinding and fitting of powder in the
cell) is performed automatically, along the sample
preparation lines. Pressing quality control is carried
out visually, and X-ray phase analysis on an
automatic diffractometer. As a result of analysis the
mass of fluoride compounds to be added in the bath
to adjust the composition of the electrolyte to the
optimum is calculated. Reproducibility and accuracy
of analysis is periodically randomly checked on
routine and reference samples, respectively. In a
case of unsatisfactory results, the identification of
causes and, if necessary, re-calibration of the X-ray
equipment is carried out.
An alternative standardless XRD method is
quantitative phase full-profile analysis by the
Rietveld method (Young, 1993). The estimation of
the CR from XRD data by the Rietveld method is
possible with the technologically desired accuracy.
In addition, the Rietveld method universally applies
to baths from various plants that are sampled with
different methods and that are characterized by
different crystallinity and very diverse chemical
compositions. However, the Rietveld method is
interactive and time-consuming, and the industrial
electrolyte samples analysis from many hundreds of
baths should be fully automatic. Even the best
attempts to automate the full-profile CR analysis by
the Rietveld method has not yet provided
satisfactory accuracy (Feret, 2008). This is due to
the need for automatic refinement not only of the
profile parameters of X-ray diffraction patterns, but
also of the crystal structure parameters of some
fluoride electrolyte phases, which can vary in
different samples and critically affect the accuracy
of the CR determination.
An automatic method for XRD CR electrolyte
analysis is proposed in this article. The method is
based on an evolutionary hybrid genetic algorithm,
which controls the full-profile analysis by the
Rietveld method.
2 THE METHOD OF
EVOLUTIONARY
FULL-PROFILE
PHASE ANALYSIS
Evolutionary genetic algorithms simulate the
biological processes of natural selection in wildlife
and are successfully used in various fields of science
and technology (Paszkowicz, 2013). Genetic
algorithms are also used in diffraction structural
analysis (Feng, 2007; Kenneth, 2009) to determine
the approximate models of the atomic crystal
structure of materials by their X-ray powder
diffraction patterns. Crystal Structure includes the
coordinates of atoms in the symmetrically
independent part of the unit cell of crystal material
and some additional parameters. This information is
GeneticAlgorithmbasedX-RayDiffractionAnalysisforChemicalControlofAluminiumSmeltersBaths
33
accumulated in the Crystal Structure Databases
(ICSD, CSD).
The essence of the approach is to generate a
random set (population) of trial crystal structures
and evolve it using probabilistic formal genetic
operations: selection, crossover, mutation, etc.
Evolutionary selection is based on the offspring
structure evaluation by fitness function, which
represents here the weighted difference between the
model profile (calculated from the trial structure)
and the experimental diffraction pattern, i.e. one
must minimize the profile R
wp
-factor of the Rietveld
method. The crystal structure model found is refined
by the Rietveld method based on the nonlinear least
squares. The Rietveld method is also used for the
quantitative X-ray analysis of multiphase materials.
The possibility of refinement of the actual crystal
structure of multiphase material phases makes QPA
"structurally sensitive" and thereby greatly increases
its accuracy.
A two-level hybrid genetic algorithm (GA) of
structural analysis (Yakimov, 2009) is used mainly
to analyse the crystal structure of inorganic
substances. This GA performs the evolution of
profile and structural parameters of the Rietveld
method and controls its refinement by the derivative
difference minimizing method (DDM) (Solovyov,
2008) (an analogue of the Rietveld method).
The DDM method is based on the minimization
of difference curve derivatives:
()
()
min
2
2
2
2
2
1
+
=
YcYow
YcYowMF
θ
θ
,
(1)
where Y
o
and Y
c
are observed and calculated profile
intensities, correspondingly,
θ
is the diffraction
angle, w is the weight coefficient and the summation
is fulfilled over the entire XRD powder profile.
The calculated profile is
,),,()(),(

Ω=
ji
jhprofistrihij
PPISKPYc
θ
θ
θ
(2)
where К is constant; S
i
are scale factors of the
calculated diffraction profile for phase i; I
in
is the
integral intensity of diffraction reflexes h for phase i,
and I
ih
is a function of the crystal structure
parameters for the phase i;
i
is the profile function
of diffraction reflexes;
),(
strprof
PPP =
is the vector
of the profile and crystal structure parameters.
The DDM method includes a refinement of the
profile and crystal structure parameters
P
of phases
by the nonlinear least squares method (LSM). The
initial values of the parameters are determined by
the hybrid GA.
The GA fitness function is the R-factor of the
DDM, which represents a numerical derivative of
the relative difference between the calculated and
experimental powder pattern and is computed in a
similar way to the usual Rwp-factor of the Rietveld
method.
The authors of (Yakimov, 2012) have shown that
it is possible to perform the automated standardless
full-profile quantitative X-ray analysis on the basis
of a two-level hybrid GA with the DDM.
The concept of evolutionary XRD QPA is the
searching on the 1st level of the GA for the initial
approximation of a profile and refinable structural
parameters within given value ranges and then its
refinement by the DDM on the 2nd level of the GA.
The QPA feature is that the crude initial values of
the parameters can be determined in advance. For
example, the atomic coordinates of the crystal
structures are taken from the Crystal Structure
Databases. Therefore, the search for more accurate
initial values by the GA can be performed within
narrow ranges of parameter values. The flowchart of
the GA is shown in Figure 2.
The profile parameters include the width of the
diffraction reflexes, their shape, etc. Refinable
structural parameters include the coordinates of
atoms in the common positions of phase crystal
lattices. Together with them, the dimensions of
crystalline cell axes and texture parameters
(preferred orientation of particles) are refined, as
well as the scale factors S
j
of calculated diffraction
profiles of phases in the powder patterns of the
material. The listed parameters are binarized and
encapsulated in a string, the GA chromosome.
Objects of the evolution in GA2 are bit strings
B
.
Each bit set in ‘1’ specifies a corresponding
parameter of
P
to be refined by the DDM on the
current generation. The better the refining has been,
the higher B-type fitness is assigned. Thus genetic
operations over B-individuals generate strategies of
P-individuals refinement.
The evolution of the parameters in the iterative
execution process on both GA levels provides a
selection of good initial approximations for the
DDM. Periodic refinement of the best parametric
strings by DDM leads to a convergence of any of
them to low R
wp
-factor values (less than 10%).
Then, the optimized scaling factors S
j
of the
calculated diffraction profiles of phases are used to
calculate the phase concentrations С
j
in the material:
ICINCO2015-12thInternationalConferenceonInformaticsinControl,AutomationandRobotics
34
=
=
N
j
jjjjjjjjj
VMZSVMZSC
1
/
(3)
where V
j
, Z
j,
M
j
are, respectively, the cell volume,
the number of formula units per cell and the
molecular weight of phase j; N is the number of
crystalline phases in the samples.
Figure 2: The flowchart of the two-level hybrid GA.
The XRD QPA procedure by the GA can be
divided into three stages.
(a) Search and refinement of profile parameters,
optionally together with the parameters of the
anisotropic broadening of lines caused by
microblocks and microstresses; decomposition of the
diffraction pattern and an initial refinement of
profile parameters are performed by the Le Bail
algorithm built into DDM.
(b) Search and refinement of structural
parameters together with texture parameters. Search
intervals of refinable atomic coordinates are given in
the neighbourhood of their positions in the
structures, taken from the database.
(c) Joint refinement of all parameters by DDM
under the control of the 2nd level of the GA.
The precision of the method, estimated on high-
quality test data from the International Round Robin
on QPA CPD IUCr (Scarlett, 2002), was shown to
be 0.45 wt. % per phase.
3 ACCURACY EVALUATION
OF THE CR ANALYSIS AND
DISCUSSION
The method of the evolutionary full-profile QPA can
be configured for an automatic analysis of multiple
samples with the same type of phase composition as
a result of a selection of relevant search intervals and
settings of genetic operations. Industrial electrolytic
samples of aluminium production are suitable for
this purpose.
The phase composition of the electrolyte samples
is shown in Table 1, and the crystal structure of
these phases are taken from the database ICSD
(Inorganic Crystal Structure Database)
The high-quality industry reference samples
(IRS) of chemical and phase composition (Yakimov,
2008) prepared directly from the industrial
electrolyte samples of four large aluminium
smelters, containing calcium and magnesium, were
used for testing and accuracy evaluation of the
method.
The search intervals and settings of genetic
operations for the automatic analysis of the profile,
which were universal for this task, as well as the
structural parameters of fluoride phases have been
identified in special experiments of preliminary
studies.
Table 1: The phase composition of the electrolyte samples.
# Phases Chem. formula
Fraction
(% mass)
CR area
1. Cryolite Na
3
AlF
6
0~90 > 1.67
2. Chiolite Na
5
Al
3
F
14
0~85 < 3.0
3. Fluorite CaF
2
0~9 > 2.45
4. Ca-cryolite 1 NaCaAlF
6
0~15 < 3.0
5. Ca-cryolite 2 Na
2
Ca
3
Al
2
F
14
0~20 < 2.95
6. Weberite Na
2
MgAlF
7
0~15 < 2.85
7. Neiborite NaMgF
3
0~6 > 2.5
8.
Sodium
fluoride
NaF 0~5 > 3.0
9.
α-,
β
-,
γ
-
alumina
Al
2
O
3
2~5
GeneticAlgorithmbasedX-RayDiffractionAnalysisforChemicalControlofAluminiumSmeltersBaths
35
CR values calculation from the found phase
concentrations were fulfilled according to the
formula:
==
i
ii
i
ii
CR
C
C
2
mol,AlF total
molNaF, total
3
β
α
(4)
where С
i
is the concentration of the i-th phase (%
mass), calculated according to (1); α
i
, β
i
are the
mass fractions of NaF and AlF
3
, respectively.
An analysis of 26 IRS was conducted. Figure 3
shows an example of a plot of the convergence in
the evolutionary full-profile QPA for one of them.
On the 1st level of the GA, the profile and some
structural parameter values are searched for in the
specified search range including atomic coordinates,
allowing variation in a given neighbourhood of its
positions in the structures of fluoride phases taken
from the structural data base ICSD, as well as
texture parameters of the phases. Level 2 of the GA
controls the gradual full-profile DDM-based
refinement of the best current solutions found on the
1st level of the GA. The sizes of test solution
populations were: 30 for the 1st level of the GA and
10 for the 2nd level of the GA. The alternation of
GA levels brings the iterative search process to the
true solution with R
wp
= 5.6% after 37 generations of
evolution (in this example).
On the first three GA1 cycles, the best solution in
the population of the parametric strings gradually
improved and the R-factor decreased from 13.7% to
9.7%. However, a good approximation for the local
search has not yet been found and the refinement
with DDM cannot reduce the R
wp
value (even-
numbered bands in Figure 3). Finally, on the 4th
GA1 cycle, the R-factor dropped less (from 9.7% to
8.8% in generations 27-31) and the approximation
was found which could be refined with the local
search. This approximation was refined with DDM
through the choosing of various parameter
combinations by the GA2 within the last 4
generations. After refinement, the R-factor
decreased from 8.8% to 5.6% and then was
stabilized.
After the final refinement of all parameters by
DDM, the R
wp
was equal to 5.3% and the phase
concentrations calculated by (1) were used for the
CR calculation according to (2). The comparison of
the experimental and calculated final powder
patterns is shown in Figure 4.
Figure 3: The plot of convergence in the evolutionary XRD QPA from analysis of sample H803 from IRS; the x-axis
depicts the evolution generation number, the y-axis depicts the profile R
wp
-factor; dotted vertical lines show the time of the
shift from the level 1 GA to the level 2 GA and back; the red line is the current best fitness value, blue dots show the current
worst fitness value, green dots show an average fitness value for the current population.
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Figure 4: The experimental (red) and calculated (green) diffraction patterns for reference electrolyte sample Н803 and the
difference between them (blue, contains background from an amorphous phase of alumina); radiation with CuK
wavelength; R
wp
-factor = 5.3%.
A feature of the method is the refinement of the
crystal structure of the electrolyte main phase. The
crystal structure of cryolite, chiolite and calcium
cryolite may vary slightly from sample to sample.
This is caused by the nonequilibrium crystallization
of sample dew, its sampling from the bath and
variable sampling factors such as the electrolyte
composition and temperature, mold mass and
temperature, weight of the sample, time since
loading the bath with alumina, etc. Figure 5 shows
the atomic crystal structure of cryolite and identifies
its main differences in two reference samples (C363
and C460).
The main structural variations are in the change
of the inclination angle and the geometric
dimensions of [AlF6]
-3
octahedras, and in the
corresponding shifts of Na atoms, located in the
common position for (Na2). This is reflected in the
variation of the lattice parameters, in particular, with
the c-axis size and the value of monoclinic angle β,
same as its intensity value. The difference in lattice
parameters leads to a perceptible shift of the
analytical diffraction reflexes of cryolite to about
2Θ ~ 0,02
О
- 0,03
О
, and the difference in the
coordinates of the atoms leads to a relative change in
the integrated intensity of the reflexes of up to 4%.
Neglect of these distortions of the crystal structure
significantly affects the accuracy of the electrolyte
analysis and the corresponding errors of the CR
determination are about 0.01-0.02.
Figure 5: Structure of cryolite and the main differences in
the samples C363 and C460, respectively:
- inclination angle of octahedras axis relative to the с-axis:
18.69
о
and 19.51
о
;
- edges and the angle of parallelogram in the base of the
octahedras: 2.484 Å, 2.727 Å, 88.50
о
and 2.513 Å, 2.569
Å, 89.04
о
;
- Na2 - Na1 distance: 3.249 Å and 3.188 Å.
GeneticAlgorithmbasedX-RayDiffractionAnalysisforChemicalControlofAluminiumSmeltersBaths
37
a
b
Figure 6: Regression charts for the estimation of the full-profile analysis accuracy:
(a) – for CR values, calculated by the data of evolutionary XRD QPA, to the certified CR values for electrolyte IRS
(b) – for BR values (BR = CR / 2), calculated by the automatic Rietveld analysis, to the certified BR values for electrolyte
reference samples (Alcan International Ltd, 2005).
The left side of Figure 6 shows the regression
graph of the corresponding calculated and certified
CR values for a set with 26 IRS of industrial
electrolyte. The calculated CR values correspond to
the certified CR values with precision, characterized
by
a standard deviation (SD) in 0,019 CR units. The
achieved accuracy completely satisfies the
technological requirements of the production.
The advantages of determining the CR by the
evolutionary XRD QPA method of relatively
automatic full-profile CR analysis by the Rietveld
method can be estimated by comparing the results
with the data of (Karsten Knorr, 2012). It should be
remembered that many of the aluminium factories,
instead of the cryolite ratio, apply its counterpart –
the bath ratio (BR), which is related as BR = CR/2.
The right side of Figure 5 shows the regression
graph of the corresponding BR values, calculated
according to the automatic full-profile BR analysis
by the Rietveld method, to the certified values for
the standard electrolyte samples of the company
ALCAN International Ltd (Alcan International Ltd,
2005), taken from (Karsten Knorr, 2012).
Unfortunately, the standard deviation value for the
BR graph in Figure 6 in (Karsten Knorr, 2012) was
not provided. To compare the graphs for BR and CR
on the same scale, all values along each of the axes
on the right graph should be doubled. After
performing this procedure it becomes apparent that
the standard deviation of the evolutionary XRD
QPA is at least twice as good.
4 CONCLUSIONS
The increased accuracy of the analysis by the
evolutionary QPA method can be explained through
the fact that the genetic algorithm searches various
variants of the approximate values of profile and
structural parameters (i.e. adapts them to a particular
sample) as well as periodically refining the best ones
on the 2nd level of the GA by the DDM – full-
profile analysis method. However, a variant of full-
profile analysis by the Rietveld method
automatically specifies the pre-selected initial values
(i.e. does not adapt to a particular sample) of the
profile and structural parameters.
The disadvantage of the current version of the
evolutionary QPA method is that the amount of
computational time is significantly higher than for
the existing calibration XRD methods of CR process
control. However, the development and optimization
of the evolutionary method certainly will increase
the processing speed of CR full-profile analysis and
bring it to a comfortable level.
Thus, this approach opens up new prospects for
electrolyte CR automatic standardless determination
by XRD data for chemical control on aluminium
smelting baths.
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38
ACKNOWLEDGEMENTS
Research is fulfilled within state assignment of the
Ministry of Education and Science of the Russian
Federation for the Siberian Federal University
(project 3098)
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