One of the crystalline materials structures is cubic. An

experimental study has been done about developing a scheme to identify the cubic structure types in single or multi component materials. This scheme is using fingerprints created from the calculation of quadratic Miller indices ratios and matches it with the ratio of the sin20 values from the diffracted data of material obtained by X-Ray Diffraction (XRD) method. These manual matching processes are complicated and sometimes are tedious because the diffracted data are complex and may have more than

one fingerprint inside. This paper proposes an application of multi-layered back-propagation neural network in matching the fingerprints with the diffracted data of crystalline material to quickly and correctly identify  its cubic structure component types

Budiarto, Rahmat

Pasha, Muhammad Fermi

Syukur, Mohammad

English

Repository@USM

IJCSNS lntemational Joumal of computer Science and Network security, VoL.7 No.2, February 2007A Neural Nehnrork-Based Application to Identifr CubicSbructurcs in Multi Component Crystalline Materials using X-Ray Diftaction DataMohammad Syukurr, Muhammad Fermi Pashatt, and Rahmat Budiartottttu..,ltrt of Mathematics and Natural Sciences, University of Sumatera lJtara,20155 Medan, Sumut, Indonesia"School of Computer Sciences, Universif of Sains Malaysi4 1 1800 Minden, Pulau Pinang, Malaysia49SummaryOne of the crystalline materials structures is cubic. Anexperimental study has been done about developing a scheme toidentify the cubic structure types in single or multi componentmaterials. This scheme is using fingerprints created from thecalculation of quadratic Miller indices ratios and matches it withthe ratio of the sin20 values from the diftacted data of materialobtained by X-Ray Diftaction (XRD) method. These manualmatching processes are complicated and sometimes are tediousbecause the diffracted data are complex and may have more thanone fingerprint inside. This paper proposes an application ofmulti-layered back-propagation neural network in matching thefingerprints with the difhacted data of crystaltine material toquickly and correctly identiS its cubic structure componenttypes.Key words:Artificial Neural Network, XRD Methads, pattern Matching,Cubic Snucnre Fingerprints, Material Science.IntroductionCrystallography has always been one of the mostchallenging research fields since eighteenth century.Following the discovery of X-ray for diffraction byRdntgen in 1895 [], X-ray diftaction method has beenapplied to many different sub-area of crystallography suchas identification of crystalline phases, qualitative andquantitative analysis of mixtures and minor constituents,distinction between crystalline and amorphous states, side-chain packing of protein structures, identification ofcrystalline material, etc. The evolution of crystallographyresearch usrng X-ray diffraction method has always beenkemendous and eventually touches the use of artificialintelligence techniques to fasten the process and increasethe accuracy ofthe results.This paper proposes an application of neural network intoone of crystallography research area of identification ofcrystalline material. X-ray diftaction data interpretationfor most crystalline materials is a very complex andManuscript received February 5, 2007,Manuscript rcvised February 25, 2007.difficult task. This is due to the condition that differentcrystalline material may contain more than one cubicstructures component type and after being diffracted usingX-ray di{fraction method, the diffracted data are complex.Hence, the data can be so ambiguous and not easy to trackand understand. Neural networksfundamentally different approach toprovide acrystallinematerial identification problem.The ability of neural network to perform pattemrecognition task has been proven to be good and useful inmany physics and engineering applications. Attempts toapply neural network on crystallography researchproblems has been a great success so far. To name a few,Milik et al. [3] used it to evaluate the side-chain packingof protein structures, Berntson et al. [7) developed anapplication of a neural network to produce a high-throughput protein crystallography, Gallagher and Deacon[5] proposed an application ofneural networks to classifymineralogical samples using X-ray spectra, Baker et al. [6]used it to recognize patterns in craniofacial X-ray imageanalysis and Su et al. [4] applied it to X-ray imageSegmentation. The main intent of this paper is to examinefurther the ability of neural network to identiff the cubicstructures on multi component crystalline materials byperforming fingerprints matching.2. Cubic Structure Fingerprint CalculationThere are four cubic structures for crystalline material, theSimple Cubic (SC), Body Centered Cubic (BCC), FaceCentered Cubic (FCC) and Diamond. [n our previouswork [2], a formula has been proposed to calculate thefingerprints for tlese four cubic structures. The formulautilizes the Miller index (h,lql) [8]. The proposed formulacan be written as follows:canthissinz o=*(h2 +k-2 +t2)4a' (l)50(2)wherc 0^ and 0, are the diffracting angles for two peakassociated with the diffracting planes {h*k*l-) and{h,,k*l,\ respectively for ratio R',,.The fingerprint for each crystalline material's cubicstructure is calculated by taking 10 peaks from the X-raydifhaction data and calculates the two peaks combinationsfrom that l0 peaks. That is, each fingerprint is actuallycontains 45 values of the quadratic sinus ratio from Eq. 2since Cjo equal to 45. Table I and Table 2 show thefingerprint for Face Centered Cubic (FCC) and Diamondrespectively.IJCSNS Intemational Joumal of Computer Science and Network Security, VOL.7 No.2, February 2007 IIn this paper we only use these two fingerprints on ourexperiments due to limited availability of the crystallinematerials of other cubic structure component types. Therest ofthe fingerprint details are described at [2].3. Back-Propagation Neural NetworksFig. I depicts the architecture ofthe proposed application.The main module is parted into two parts. The first part isthe preprocessing and training part. This part will train theneural network for each fingerprint and save the resultednetwork preference.Since the wavelength of the incoming X-ray (),) and latticeconstant (a) are both constants, we can eliminate thesequantities from Eq. I and derive the ratio of two sin20 asfollows:^ sin' 0. h'^ + k; +l'.n'.'= ,in, e,= hrJkrtThe second part isapplication we useneural network itself. In thismulti-layered back-propagationneural network. It is a central and the most commonlyused tool on modeling and classification problems. Input-output pairs are presented to the network, and weights areadjusted to minimize the error between the network outputand the actual value. Our neural network consists of threelayers ofneurons, an input layer, two hidden layers and anoutput layer.The standard iterative gradient algorithm for back-propagation training is used by the proposed application. Itis desigrred to minimize the Mean Square Enor (MSE)between the predicted output and the desired output. Thetraining algorithm used is summarized as follows:l. lnitialize weighs and threshold values: set all weightsand threshold to small random values.2. Present input and desired output: present a continuousvalued input vector Xr, X2,.... )L, and speciff thedesired outputs Or, Oz, ... On.3. Compute the output of each node in both hiddenlaver:(3)4. Compute the output of each node in the output layer:- o.l/ (4',)and1f(x) = l+e-*and6r =Ot(l-OkXY-Ok)Compute both hidden layer error:6, =h,(r-n,Ia*w*,thether, = {tw'x, -oj)o* = f[i w*ix j(s)(6)5.ITable 1: Face Cubicl(rr=0.750RzJ =0.500l(3F -o.666R{,s =0.550l(cs =0.800Rr,r =4375l(z,l *0.3uRl,o =0.500ltlp -0.458lk.c =0.666Kt,l =0.273Kr< =n {rr Ktt =0.421 Kuo=o.407 K6,lo=0.593Kr,s -0.250&,0 =0.2s0Rr,s =0.400r'<s,o =0.750Rz,t -0.950&,c =0.187KzJ =0.210Rrp =0.333l(s.z =0.632Rzp =0.792RtJ =0.158R2$ *0.200Rlro=o.296&,s =0.600l(z,to =0.704Klt =0.150Rr,q =0.125Rzg =0.166Rz,to=0.148&s=0.916&.0 =n 6R7llcp =0.500&,ro=o.M4L&c =0.833&Jo=o.741Kr,lo=0.lllR3,l =0.727tQt =0.579Rc,z =0,842Kc,to =0.888Table Diamondl(r,z =0.375Rl3 =0.327Krs =0.579K s =0.500R6't =0.750RrJ *0.273Rzr =0.500R3,6 =o 45RRr,s =0.457&.c =0.686Rrr =0.187RrF =0.158Itrr =6.lqzr&,0 =0 3330.407Rr$ =n?/,/Rl.to =0.400Rs,o =0.792Ko,ro =0.600Rz.g =N 9.AAItr,o =0.125RrJ =0.296Rrg =0.314Rs;r =0.704*rp =0.771l(lt =0.111Rz,s =0.250R:,ro =0.275xc,s =0_594l(t,to =0.675t(lt0-094Rz,q =0.228R.ls =0.842l(sp =0.543Ksp g0.914KtJ =0.086Rz,to =0.200Rl,o =o 666l(clo =0.457R&ro =o Roo&,ro=0.075K:,4 =0.587&,2 =0.593Ret =o.889&,lo =n R7{(7)IJCSNS Intemational Joumal of computer Science and Network Security, voL.7 No.2, February 20076. Compute the output layer error between the target andthe observed output using Eq. 6.7. Re-compute both hidden layer error using Eq. 7.8. Adjust the weights and thresholds in the output layer:Wu,(t + 1) = W*,(t) + cr6*h, + t1(W*,1ty - Wkj(t - l)) (g)and4. Experiments and ResultsThe experiments are carried out using Philips' X-Raydevice diffractometer control PW17l0. The device wasusing PWl729 series of X-Ray generator, anode Cu tube,and PCAPD (PWl877) software version 3 integrated withour proposed application installed. In the overallexperiments, we use the same tube voltage and also thesame fube cutrent, i.e. 30kV and 20mA respectively.Three samples of crystalline material are used in theexperiment. The samples are Aluminium (Al) and Silicon(Si) materials. For the purpose to have a multi componentcrystalline material, we mix Al sample and Si sample andcreate the third sample which is a mixture of Al and Si.The neural network stucture presented on Fig. I waschosen after we train several neural network structuresusing the fingerprints on Table I and Table 2. The resultofthe training process is presented on Table 3.TableThe Silicon (Si) training results show that the lowest MeanSquare Enor (MSE) is 4.44 with 8 nodes in hidden layerwhile Aluminium (Al) training results show that thelowest MSE is 4.30 with 9 nodes in the hidden layer.Hence we construct our neural network with 8 nodes inthe hidden layer, 5 in the frst hidden layer and 3 in thesecond hidden laver.5lek(t+l)=0*(t)+cr6*9. Adjust the weights and thresholds in bothlayer:\,(t+l)= wr(t)+cr6,h, +n(wj,(t)-w!(r-l)) (10)and0,(t+l)=ej(t)+a6j (l l)10. Repeat steps 2 to 9 on the all pattem pairs until theoutput layer enor is within the specified tolerance foreach pattem and for each neuron.A[Ufrrdsnab l--rd \.Jrfit4e tuttHe0elr{r*uCiltufiddgFig. I The Proposed Application Architecture with Back-propagationNeural NetworkThe proposed application will behave as an integratedapplication with the XRD Diffractometer software toreceive the diffracted data directly for faster and reliableprocessing. At the end, a report will be generated whichcontains the cubic structure component type detected onthat particular crystalline material.(e)hiddenJ: Network ResultsFingerprint MSE # of Nodes on Hidden LayerAluminium (Al)4.80 )4.34 64.35 74.54 84.30 94.32 l04.59 lt4.36 t2Silicon (Si)4.86 54.59 64.614.44 I4.67 94,71 l04.60 ll4.66 t252 IJCSNS lntemational Joumal of Computer Science and Network Security, VOL.7 No.2, February 2007Fig.2 X-Ray Diffraction Pattem foi|!:,I"**. Sample ofAluminiu:nFig 2 visualizes the results obtained from X-ray diffractionmethod after we load the samples of the crystallinematerial into the X-ray diffractometer. The front pattern isthe diffraction data result for the mixture sample ofAluminium and Silicon, the middle pattern is thediffraction data result for Aluminium sample material, andthe last one on the back is the diffraction data result forSilicon sample material.From the resulted diffiaction data for the mixture sample,we can see that it has 17 peaks and therefore we appliedthe combination of two peaks from that 17 peaks (Cj')and we have the ratio R..n values shown on Table 5. Thesame calculation was performed on the resulted diffractiondata for the original Aluminium and Silicon samples andtheir ratio R,.n Ne shown at Table 4 and Table 6respectively. Next is our proposed application will pick upthese results and feed il into the previously trained neuralnetwork.Table 5: Diffracted Data for the Mixture Sample of Aluminium andRl,z =0.558l(zr+=0.168K4,tl =0_250t(?,S =0.842Rro,n =0.898Ktp *0.419Rz,rg *0.157Rl.rs -0.233t<zp =0.808&o,rz =o.799l(uo.375&,ro =0.t54R.r,rr =0.228ll?,ro =0.741l(to.t3 =o.149l{rs =0.273l:(z,rz =0.150rQ,rz =0.222Rlrr =o 666Kro,r4 =0.673Kl,6 =0.209Rll =0.897&,0 =0.764R?,r2 =0.593l(to,ts =0.631Rr.z =0.188Itr,s =0.652xr,z =0.687Rz,r :0.554Rro,ro =0 615xr,r =0.1 58R3,6 *0.500&,0 *0.s79Rr,l4 =0.500Rro.lz =o 6nnKt,r --0.1 52x.lJ *0-448x5,l =0.555Kr,rs =0.467K1r,r2 *0.889Rr,ro =0.139Rr,s =0.317l$,ro =0.509l(zlo =o-Aq6&t.rr =o t??l(r,tt =o t2sRr.r =n ?6?Ks,rr =o 4{Rl(z,rz =4.444l(rr,rl =0.750&,lz -0.11IRr.rc =0.r04K3,ro =0.333Rs.rr =0.299l$,lr =0.407R;t --0.381Rr,r =0.960Rs,ro =0.880lSrr,rs =0.701Rrr,ro =o 6R6l(rJl =0.093R3,:z =0.265l(s,tl =o 14iKg,u =0.792Ktr,17 =O.66(lRr,rs=0.087l(l,ll =0.250l$,rs =0.321lft.rz =0.7MRrz,r =o s?6Kl,t6 *o oRsRr,rl *a)t4 l{s,ro =0.313 l(8Jl =0_659 Ru.s =o *.AAl(l,tt =0.083Rg,rs =o.2ro&,rz =0.305Rs.u *0.593l(l2,rs =0 788-l(r r =0-750l(l,ro =o ).fi4rao.z =o Rsg&,rs =0.555K12,16 *0.770l(z,l =o.673l(r.tz =o )no r*,r =4.757Rs,ro =0.542Kr2,1? -0.749K2,5 *0.490x*,s =0.727Rep =0.727R&rz =0.527Rrc.l =0.899|{2,6 =0,375Kl,o =0.556l(o,to *0.666r(o.to =0-916Kn,rs =0.842K2t =o 1?6RlJ=0.500lktr =0.599l(l,lr =0.824l(t3,16 *o.822KzJ =o.281K.r,l =o 4)1R6,rz =o s??l9Jz =0.732Kr3,u =0.800Kz,g =0.272&p=0.404xqt3 -o 500Rq,n -0 6R6Rt+rz =0.936l(z.ro =o ).\o Kl,ro =0.370Kcu =0.448Ks,u =n 617Rrs,to =0.914Rz,tl ={t,224 &,rr =0.333Ko,rs =0.421l(1.t5 =o {7Rr(15,r? *O Rfl9|lr,rz =0.199R.a,lz =o,q6 Kc.rc =0,410l9,ro =o s64l(rc.rz =0.976l(2J3 =0.187Kl,r =o.277l(6,rr =0.400Rc,rz =0.550&,ro =0.950l(sJo =o q7?4: Diftacted Data for thet(r, *0.750RzJ =0.499RrJ =0.666&,s =0.550IQJ *o-666Rr,r =0.374K2,4 =0.363Rc,6 =0.501KlJ =0.458Rr,s =0.950Rrl =o.212ll.r < =0.5::xr, =0.421&,r =0.751Kzp =0.791ltrj :0.249Rr,c =n 250l(l,t =0.400Rs,; '0.632 o Rjj|(r,o =0.1 87xrJ =0.210RrJ =0.333Kg,* =0.600Rrt =0.158l(2i *n 200Kl,5 =0.916Rs,9 =0.500|(r,E =0.1 s0Rup =n 166l(lt =0.688Ikz =0.842RrB =0.125Rr,l =n 7)1 Rl,z =o {7s K5,s =0.79910Data for the Sample of SiliconKr,z =0.374t(z": :0.727RrF =0.579Kl,a =0.500lft,a =0.751xrJ =0.272Kz,l =0.500l(l,c =0.458Rr,q =0.458rq,c :0.687Rr,l =0.1 87Rz,s =0.421l(r,z =0.407Rr,lo=0.400Koro =0.600Rr,s =0.157l(z,e =0.333Rr,r =0.344l9,c =0.792Ru.s =0.845Rr,o =0.t25Rr;r =0.lllxzt =0.296Rz,a =0.250R:,s =0.3 l5Rr,ro =0.275l$,2 =0.704&,e =0.595Rrp =0.772Rz,lo =0.675Rr,a =0-094lsz,c =0.225&,s =0.842Ks,q =0.544l(tp0.9t4Kl,g *0.085l(2.t0 =o,?oo&,r =0.666rtro=o 475Its,ro =0.79Sl(t,ro =0.075&r=0.687tQ,r =0-593I(oz =O RRSl9,ro =0.875IJCSNS International Joumal of computer science and Network Security, vol.7 No.2, February 2007 53Table 6: DiflactedTable 7 depicts the results of the proposed neural network-based application. It is clear that the neural networksuccessfully recognizes the fingerprint inside thediftaction data of each sample. For the mixture sample,the results show that it has two cubic structure types, FaceCentered Cubic (FCC) and Diamond. The detectionaccuracy was 86% for FCC and 84Yo for Diamond. Thisresult is supported by the results of the originalAluminium and Silicon samples. The Aluminium samplewas detected to have a FCC type with detection accuracyof 92o/o while the Silicon sample was detected to have aDiamond type with detection accuracy of 9lyo.Lastly, the following was the report generated by theproposed application for experiment with the mixturesample. The reports for the other two samples are basicallythe same.SampleName: AI&SiDif fractionDataFile : File- 5- 0565DetectedTlpe: FCC, DiamondAccuracy: FCC(86t), Diamond (B4t)GeneratedOn : l-5 z L7 : 42-L4Feb200Z5. ConclusionIn this paper we propose an application that uses multilayer back-propagation neural network to identify cubicstructures on multi-component crystalline material. Theuse of neural network proves effrcient and faster inrecognizing the fingerprints inside the diffractedcrystalline material data.This work is a good start towards the use of neuralnetwork on crystalline material identification research.While this paper is being written, we axe in the process ofextending our experiments to include more crystallinematerials and extending the time duration in performingthe X-ray diffraction process in order to have moreconvincing outputs. Our future direction includesenhancing the neural network structure and applying rule-based fu2ry neural network to increase the accuracy.AcknowledgmentsAuthors would like to acknowledge the researchcollaboration between University of Sumatera Utara andUniversity of Sains Malaysia, Faculty of Mathematics andNatural Sciences and School of Computer Sciences inparticular, that have resulted in this paper.References[] Ewald, P.P. Fifty Years of X-Ray Diffiaction. IntemationalUnion of Crystallography, 1999.[2] Syukur, M. and Zarlis, M. A Standaxd Calculation forLattice Analysis on Cubic Structures' Solid Materials usingX-Ray Diffraction Method and its Experimental Study.Joumal of Solid State Science and Technology Letter, Vol.6, No.2, 1999.[3] Mililq M., Kolinski, A., and Skolnick, J. Neural NetworkSystem for the Evaluation ofSide-Chain Packing in ProteinStructures. Protein Engineering Vol. 8 No. 3, pp.225-236,l 995.Su, L., Sharp, B., and Davis, D. Neural Networks X-RayImage Segmentation. Proceedings of First IntemationalConference on Enterprise Information System, pp. 264-27 l,1999.Gallagher, M. and Deacon, P. Neural Networks and theClassification of Mineralogical Samples using X-RaySpectra. Proceedings of 9m Intemational Conference onNeuraf Information Processin g, pp . 2683-2687 , 2002 .Baker, B., Curry, S., and Baumrind, S. A Neural NetworkMethod for Solving Pattern Recognition problems incraniofacial X-Ray Image Analysis. Proceedings of theAnnual Intemational Conference of the IEEE Engineeringin Medicine and Biologr Society, pp. 1646 vol. 5, 1989.Bemtsorl A., Stojanoff, V., and Takai, H. Application of aNeural Network in High-throughput ProteinCrystallography. Joumal of Synchrotron RadiatiorU vol. 10,pp.445-449,2003.l4Jt5It6lable ResultsSamples Detected Type Detection AccuraqtAluminium (Al) FCC 920Silicon (Si) Diamond 9lo/oMixture of Al and SiFCC 86%Diamond 84%1117l54t8l Cullity, B.D. Elements of X-ray Diffraction' Addison-Wesley - London, 1978.[9] Suryanarayana, C. and Norton, M.G. X-Ray Diffraction - APractical Approach. Plenum Press - NewYork' 1998.[0] The Intemational Center for Difhaction Data,http://www.icdd.com.Mohammad Syukur received theB.Sc. degree in Physics fromUnivenity of Sumatera Utar4Indonesia and M.Sc. degrees inMaterials Physics from BandungInstitute of Technology, lndonesiait 1974 and 1982, respectively' Heis currently a senior lecturer and thehead of CrystallograPhy &Radiation Physics ResearchLaboratory at FacultY ofMathematics and Natural Sciences, University of Sumatera Utara'Indonesia. His research interests include Material Physics' X-Ray Diftaction methods, Artificial Intelligence Application andCrystallography. He has written two book chapters andnumerous refereed research papers.Muhammad Fermi Pasha receivedthe B.Comp.Sc. (Hons) and M.Sc.degrees both in ComPuter Sciencesfrom University of Sains MalaYsi4Penang in 2003 and 2005,respectively. He is cunentlypursuing his PhD in the field ofBrain Modeling at School ofComputer Sciences, UniversitY ofSains Malaysia. His other researchinterests include EvolutionaryAlgorithm, Intelligent Network Monitoring Fuzzy Systems'Neural Network Application and Computer Network Security.He is also working at iNetmon Sdn Bhd, a Malaysian softwarecompany providing network security solutions, as seniorsoftware architect.Rahmrt Budiarto received theB.Sc, degree in Mathematics fromBandung Institute of TechnologY,Indonesia in 1986. M.Eng. andDr.Eng. degrees both in ComPuterScience from Nagoya Institute ofTechnolory, Japan in 1995 and1998, respectively. He is currentlythe deputy director of MalaYsianNational Advanced IPv6 (NAv6)IJCSNS International Joumal of Computer Science and Network Security, VOL.7 No.2, February 2007IPv6, Computer Graphics, Network Monitoring and NetworkSecurity. He is also with the School of Computer Sciences,University of Sains Malaysia and has been a:r associate professorsince 2004. He has published over 70 refereed research papersand chaired 3 conferences/workshops.Center of Excellence. His main research interests are AI Systems,12

A Neural Network Method for Solving Pattern Recognition problems in craniofacial X-Ray Image Analysis.

Application of a Neural Network in High-throughput Protein Crystallography.

Fifty Years of X-Ray Diffiaction. Intemational Union of Crystallography,

Neural Network System for the Evaluation ofSide-Chain Packing in Protein Structures.

Neural Networks and the Classification of Mineralogical Samples using X-Ray Spectra.

Neural Networks X-Ray Image Segmentation.

X-Ray Diffraction - A Practical Approach.

A Neural Network-Based Application to Identify Cubic Structures in Multi Component Crystalline Materials Using X-Ray Diffraction Data.

http://eprints.usm.my/9385/1/A_Neural_Network-Based_Application_to_Indentify_Cubic_Structures_in_Multi_Component_Crystalline_Materials_Using_X-Ray_Diffraction_Data.pdf

A Neural Network-Based Application to Identify Cubic Structures in Multi Component Crystalline Materials Using X-Ray Diffraction Data.

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