Magnetic material selection using multiple attribute decision making approach

Materials and Design 36 (2012) 1–5

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Magnetic material selection using multiple attribute decision making approach Aditya Chauhan b, Rahul Vaish a,⇑ a b

School of Engineering, Indian Institute of Technology Mandi, Himachal Pradesh 175 001, India Galgotias College of Engineering and Technology, Greater Noida 201 306, India

a r t i c l e

i n f o

Article history: Received 29 August 2011 Accepted 10 November 2011 Available online 18 November 2011 Keywords: E. Magnetic H. Material property databases H. Weighting and ranking factors

a b s t r a c t A large number of magnetic materials have been fabricated and found to be promising for their technological applications. However, it is difficult to select an optimal material (for technological application) because of the conflicting tradeoffs between their properties. In this context, the screening of magnetic materials is an important task. In this article, an attempt has been made to select the soft and hard magnetic materials using Multiple Attribute Decision Making (MADM) approach. VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) and Technique for order preference by similarity to ideal solution (TOPSIS) methods (MADM techniques) are employed to evaluate the relative ranking of these materials understudy. The relative weights for the different attributes (properties) are calculated using Shannon’s entropy method. It is found that (Supermalloy, Magnifer 7904) (79Ni–15Fe–5Mo–0.5Mn) and Ferrite 4 (sintered) (SrO–6Fe2O3) are the optimal materials among studied soft and hard magnetic materials, respectively. Hierarchical clustering is used to classify magnetic materials under study. Pearson correlation coefficients are calculated between the attributes under study. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Magnetic materials have been exploited in enormous scientific and technological applications including signal transfer, data storage, permanent magnets, magnetic field screening, magnetron, frictionless bearings and quantum devices [1–5]. However, discovery of new magnetic materials has been imposed by the scientific/ technological demands [4,5]. The future applications of magnetic materials are dependent upon the improvement of their magnetic, mechanical, electrical and thermal properties [5]. Therefore there has been tremendous amount of renewed interest that is centered around the development of new magnetic materials. In the recent past, abundance of magnetic materials are fabricated and reported for their promising physical properties. These materials are usually classified in soft and hard magnetic materials based on values of remanence (Br) and coercive field (Hc) [1]. For soft magnetic materials the value of coercive field is very low [1,3]. While in case of hard magnetic materials, the values for coercive field and remanence magnetization are large. Hard magnetic materials are used in permanent magnets and have a high resistance to demagnetization [1,2]. The selection of magnetic materials of desired properties for technological applications from the large number of materials pool available in the literature is a difficult task. Materials selection for real engineering processes is based on several requirements which

⇑ Corresponding author. Tel.: +91 1905 237907; fax: +91 1905 237945. E-mail address: [email protected] (R. Vaish). 0261-3069/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2011.11.021

include functional requirements, processability requirements, cost and reliability requirements. In this context, materials attributes that need to be considered for final materials selection are thermal properties, electrical properties, mechanical properties, availability, materials impact on environment, etc. However, simultaneous consideration of all these attributes in materials selection is tedious task. Hence it is recommended to screen the materials based on properties of attributes. A systematic approach to material selection process is necessary in order to select the optimum material for device application. Initial screening of materials can be possible by first rigid (go-no-go) requirements. Various approaches have been proposed for selection of materials. Ashby [6] has discussed method for materials design and selection. He suggested the performance parameter of device which is a function of functional, geometric and materials parameters. In Ashby approach data is presented in chart format which is useful in initial screening of materials. Initial screening can be possible using Pareto-optimal solution [7]. Other methods (which are common in materials selection) are questionnaire method, artificial neural network and Multiple Attributes Decision Making Approaches (AHP, SAW, TOPSIS, VIKOR, Gray relational analysis, ELECTRE, etc.). These methods are explained in detail for materials selection viewpoint [8]. It is observed that all these methods give almost the same rankings of the objects while minor discrepancy between the rankings obtained by MADM methods is due to their mathematical modeling [9]. It would be interesting to make quantitative comparison of magnetic materials for their technological applications viewpoint. Through this paper, an attempt has been made for initial screening

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A. Chauhan, R. Vaish / Materials and Design 36 (2012) 1–5

and ranking vital magnetic materials using Multiple Attribute Decision Making (MADM) approach [10]. The MADM models are capable of sorting out materials on the basis of their multiple properties (attributes) [10,11]. In the present study, TOPSIS [10–15] and VIKOR [16–19] methods are used to rank the competing materials for their applications. Relative importance (weights) of the material properties (attributes) is estimated using Shannon’s entropy method [20–22]. In order to arrive at more concrete conclusions, these materials are also classified using hierarchical clustering technique [23,24].

2. Materials and methods A relatively large number of magnetic materials are available for a given application and only few of them are of commercial use owing to the difficulty in manufacturing process or fabrication limitations. Hard magnetic materials based on Alnico alloys are of great importance because of low cost and high Curie temperature (850 °C). However, ferrites are also viable materials due to low cost, wide availability and high electrical resistivity. The drawback associated with ferrites is their low maximum energy product. The inter-metallic phases of the rare earth and transition metals have received more attention owing to their higher magnetic anisotropy, Curie temperature, coercive field. These materials include samarium and cobalt-based inter-metallic phases. Whereas soft magnetic materials including Si-steels, permalloys, supermendur, rhometal and Mu-metals are widely used in modern technological applications. Tables 1 and 2 [1] list vital soft and hard magnetic materials, respectively along with their physical properties. The properties that have been selected for soft magnetic materials are: Curie temperature (Tc, °C), maximum relative magnetic permeability (lmax/l0), remanence magnetic induction (Br, T), coercive magnetic field (Hc, A m 1), saturation magnetic induction (Bs, T), electrical resistivity (q, lO cm). These properties have been selected based upon the relevance in field of application of soft magnetic materials [1,3]. Similarly the properties that are considered for hard magnetic materials are: maximum operating temperature (Tmax, °C), remanence magnetic induction (Br, T), coercive magnetic field (Hc, kA m 1), intrinsic coercive field (Hic, kA m 1) and maximum magnetic energy (BH)max, kJ m 3 (Table 2). Multiple Criteria Decision Making (MCDM) methods have been widely used to solve uncertainty problems. These methods can be categorized into Multi-Objective Decision Making (MODM) and MADM techniques. MODM includes optimization of an alternative on the bases of prioritized objectives whereas MADM models are

capable of selecting the best alternative out of a given list of alternatives based on their prioritized attributes. MADM models are used to calculate the relative ranks of the selected magnetic materials. Namely two methods (a) Technique for order preference by similarity to ideal solution (TOPSIS) [10,11,13] and (b) VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) [16–19] are employed to calculate and compare the relative rankings of the selected materials. Shannon’s entropy method has been used to calculate the relative weights of the attributes that are to be used in the decision making models [11,13]. It is based on the idea that the attribute having relatively more dispersion is assigned a greater weight. These weights decide the relative importance of a given attribute in materials selection. 2.1. TOPSIS approach TOPSIS model was first suggested by Hwang and Yoon in 1981 [10]. TOPSIS implies that a decision matrix having ‘m’ alternatives and ‘n’ attributes can be assumed to be problem of ‘n’ dimensional hyperplane having ‘m’ points whose location is given by the value of their attributes. The methodology consists of evaluating the Euclidean distance between given alternative and the positive ideal solution (best possible case) and the negative ideal solution (worst possible case) respectively. The ideology is that the best possible alternative will be the one having the least distance from the positive ideal solution and the most distance from the negative ideal solution. 2.2. VIKOR approach The VIKOR method is a compromise approach MADM model [17]. Even though the analysis of both the MADM models of TOPSIS and VIKOR are highly accurate and provide close to real solution, the difference in them lies in the fact that VIKOR method makes the use of utility weight, thus enabling the different users to apply expert opinion. The normalization norms used in VIKOR (linear) are different from that are used in TOPSIS (vector) approach. In VIKOR, the highest ranked material is the nearest to the ideal solution whereas it is not necessarily in case of highest ranked materials based on TOPSIS approach. 2.3. Pearson correlation coefficient In order to throw some light on statistical relation between the physical properties under study, Pearson correlation coefficient is

Table 1 Soft magnetic materials and their physical properties. TOPSIS ranks 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Materials

Composition (w/wt.%)

Tc

lmax/l0

Br

Hc

Bs

q

Supermalloy, Magnifer7904 MuMetal Permalloy 78 Hypernik V Sendust Alfenol 16 Iron (H2 reduced) Supermendur Iron (electrolytic) Iron (carbonyl) Permalloy 45 Ferrosilicon Rhometal Ferrosilicon Iron (Armco) Permendur 2V

79Ni–15Fe–5Mo– 0.5Mn 77Ni–16Fe–5Cu–2Cr 78.5Ni–21.5Fe 51Fe–49Ni 85Fe–10Si–5Al 84Fe–16Al 99.9Fe 49Fe–49Co–2V 99.9Fe 99.9Fe 55Fe–45Ni 96Fe–4Si 64Fe–36Ni 99Fe–1Si 99.99Fe 49Fe–49Co–2V

449

700,000

0.525

0.35

0.79

59

405 378 480 480 450 770 980 770 770 480 735 275 740 770 980

237,500 200,000 180,000 120,000 85,500.00 100,000 70,000 51,250 35,000 57,500 18,500 5000 7700.00 7000 4500

0.32 0.5 0.9 0.5 0.38 0.8 2.14 0.9 0.8 0.775 1.08 0.36 0.95 0.345 1.4

0.5 4 4.8 3.98 2.59 4 16 18.4 16 24 24 39.79 44.00 56 159

0.77 1.07 1.55 1 0.79 2.158 2.4 2.158 2.158 1.58 1.970 1 2.10 2.158 2.4

56 16 47 70 150.00 9.71 27 9.71 9.71 50 58 90 25.00 9.71 43

VIKOR ranks

TOPSIS index

VIKOR index

1

0.88355

0

2 3 4 6 5 7 8 10 11 9 12 13 14 15 16

0.61898 0.58422 0.57915 0.55669 0.55526 0.53649 0.50317 0.49121 0.49021 0.48893 0.47519 0.44274 0.42108 0.38935 0.06014

0.412027 0.49517 0.499844 0.555054 0.53922 0.605054 0.678238 0.693056 0.706765 0.679683 0.717848 0.746541 0.78218 0.794618 1

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A. Chauhan, R. Vaish / Materials and Design 36 (2012) 1–5 Table 2 Hard magnetic materials and their physical properties. TOPSIS ranks

Materials

Composition (wt.%)

Tmax

Br

Hc

Hic

(BH)max

0.40 1.13 0.92 0.86 0.80 1.06 1.34

175,000 640 720 640 535 115 58

185,000 640 1600 2000 1200 145 59

30 240 170 145 120 71.6 59.7

500

1.33

53

53

525

1.27

51

10

Alnico 8 (anisotropic, cast)

550

0.83

11

Alnico 8HC (anisotropic, cast) Alnico 8 (anisotropic, sintered) Alnico 6 (anisotropic, cast)

Sr0–6Fe2O3 Sm2Co17 SmCo5 SmCo5 SmCo5 34Fe–7Al–15Ni–35Co–8Ti 51Fe–8.5Al–14.5Ni–24Co– 3Cu 51Fe–8.5Al–14.5Ni–24Co– 3Cu 51Fe–8.5Al–14.5Ni–24Co– 3Cu 34Fe–7Al–15Ni–35Co– 4Cu–5Ti 29Fe–8Al–14Ni–38Co– 3Cu–8Ti 34Fe–7Al–15Ni–35Co– 4Cu–5Ti 48Fe–8Al–16Ni–24Co– 3Cu–1Ti 48Fe–8.5Al–14.5Ni–24Co– 3Cu–3Ti 47Fe–8Al–15Ni–24Co– 3Cu–3Ti 33Fe–6Al–18Ni–35Co–8Ti 55Fe–10Al–1913Co–3Cu 52Fe–10Al–19Ni–13Co– 3Cu–3Ti 20Fe–20Ni–60Cu 59Fe–12Al–21Ni–5Co–3Cu 60Fe–12Al–25Ni–3Cu 56Fe–12Al–27Ni–5Co 55Fe–12Al–28Ni–5Co 35Fe–7Al–14Ni–38Co– 3Cu–3Ti

460 500 250 500 500 520 500

9

Ferrite 4 Cobalt samarium 4 Cobalt samarium 1 Cobalt samarium 2 Cobalt samarium 3 Alnico 9 Alnico 5-7 (anisotropic, cast) Alnico 5DG (anisotropic, cast) Alnico 5 (anisotropic cast)

550

1 2 3 4 5 6 7 8

12 13 14 15 16 17 18 19 20 21 22 23 24

Alnico 5 (anisotropic sintered) Alnico 6 (anisotropic, sintered) Alnico 12 Alnico 2 (isotropic, cast) Alnico 2 (isotropic, sintered) Cunife Alnico 1 Alnico 3 Alnico 4 (isotropic, cast) Alnico 4 (sintered) Alnico 8HC (anisotropic, sintered)

TOPSIS rank index

VIKOR rank index

1 2 3 4 5 6 7

0.939247 0.067891 0.049141 0.042376 0.034780 0.020292 0.016845

0 0.95368321 0.96580880 0.96957258 0.97574836 0.98650162 0.98788585

57.7

8

0.016252

0.98830779

51

43.8

9

0.012128

0.99092233

131

148

42.2

10

0.011524

0.99240817

0.72

151

173

39.6

11

0.010732

0.99318049

540

0.74

119

134

31.8

14

0.008383

0.99469481

525

1.05

62

64

31

12

0.008242

0.99398262

540

1.07

49

50

30

13

0.007956

0.99411487

540

0.94

63

65

23.1

15

0.005849

0.99576169

480 540 480

0.60 0.75 0.71

64 45 44

76 46 45

14 13.5 11.9

18 16 17

0.002968 0.002910 0.002410

0.99888147 0.99832221 0.99893827

350 450 480 590 590 540

0.54 0.72 0.700 0.535 0.520 0.670

44 37 38 58 56 143

44 38 39 62 61 161

12 11.1 11 10 10 4.5

24 19 20 21 22 23

0.002327 0.002187 0.002144 0.001764 0.001756 0.000981

0.99997658 0.99916413 0.99917280 0.99958391 0.99965575 1

calculated. It is the degree of dependence between two variables [25]. Positive correlation indicates simultaneous increase and decrease in variable values. However, negative correlation indicates opposite behavior among the variables. Increase in one variable indicates decrease in other variable. The value of correlation coefficient can range from 1 to 1. It is to be noted that correlation does not equal causation. Correlated variables indicate that if one variable changes, the other correlated variable changes in a predictable way.

2.4. Hierarchical clustering technique In order to have further insight into the materials comparisons, these materials are classified using clustering technique. Clustering is grouping of objects based on their degree of similarities. A variety of methods has been proposed for data clustering [23,24]. Mainly, it can be classified into hierarchical and non-hierarchical methods. The present study is based on hierarchical clustering which represents materials in hierarchical structure (dendrogram). These clusters physically represent groups of data that are similar to each other. The two alternatives which are closest to each other are grouped together and are treated as a single entity or cluster. This primary cluster is now grouped with the alternative having the least distance from it, now these three elements have been grouped together as a secondary cluster. The dendrograms can be formed by using various linkage methods which are used to determine the distance between clusters [24]. The effectiveness of a dendrogram can be determined by the evaluation of cophenetic correlation coefficient. A higher value of this coefficient, closer to one, indicates the accuracy of physical

VIKOR ranks

clustering with respect to actual similarities between the selected alternatives.

3. Results and discussion The weighted coefficients (using the Shannon’s entropy method) for all the attributes understudy are tabulated in Table 3. According to the entropy method the properties of the soft magnetic materials in the decreasing order of priority are Hc > lmax/ l0 > q > Br > Bs > Tc. While for the hard magnetic materials, priorities for the properties are Hc > Hic > (BH)max > Br > Tmax. It is clear that coercive magnetic field is important property which substantially affects the ranking of soft and hard magnetic materials for technological applications. It is to be noted that coercive magnetic field is an important parameter which decided hysteresis losses in the magnetic materials and hence it distinguishes hard and soft magnetic materials. Traditionally the value of coercive magnetic field for the transition from soft magnetic materials to hard magnetic materials is 1000 A m 1 [26]. Permeability is the second important parameter for the performance of soft magnetic materials [26]. It correlates magnetic induction and magnetic field strength. However, permeability and coercive magnetic field have inverse relationship. While Curie temperature/maximum operating temperature is the least important property under study for both type (hard and soft) of magnetic materials. Hierarchy of priority for the properties understudy (using entropy approach) are in good agreement with that of observed based on physical approaches. Pearson correlation coefficients are calculated among the physical properties of soft and hard magnetic materials understudy (Ta-

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Table 3 Weights for various attributes of soft and hard magnetic materials. Properties

Tc

lmax/ l0

Br

Hc

Bs

q

Weights (soft magnetic materials)

0.0299

0.347

0.0738

0.3677

0.0376

0.144

Tmax

Br

Hc

Hic

(BH)max

0.00175

0.007033

0.4633

0.4521

0.07576

Weights (hard magnetic materials)

Table 4 Pearson correlation coefficient between the physical properties for soft magnetic materials. Soft magnetic materials

Tc

lmax/l0

Tc

1

0.4

lmax/l0

1

Br Hc Bs

Br

Hc

Bs

q

0.75 0.25 1

0.51 0.39 0.32 1

0.92 0.55 0.69 0.49 1

0.53 0.11 0.32 0.11 0.66 1

q

Table 5 Pearson correlation coefficient between the physical properties for hard magnetic materials. Hard magnetic materials

Tmax

Br

Tmax Br Hc Hic (BH)max

1

0.03 1

Hc

Hic

0.12 0.35 1

0.12 0.36 1 1

(BH)max 0.34 0.41 0.07 0.07 1

bles 4 and 5). It helps to understand the complex relationship between physical properties. Significantly high correlation are observed between Br–Tc, Bs–Tc, Bs–Br and Bs–q for soft magnetic materials understudy (depicted in bold in Table 4). It is also to be noted that q is negatively correlated with all other properties understudy except lmax/l0. Interestingly permeability and coercive magnetic field are negatively correlated ( 0.39) which is true in physical sense also. However, significant correlations are not observed between physical properties of hard magnetic materials understudy. In the recent study [27], correlation studies are used

to reduce attributes in MADM study. It is reported that correlation have no significant effect on final ranking using MADM approach. In order to rank of the soft and hard magnetic materials by TOPSIS model, weighted normalized matrix is determined. The desirable properties for electromagnetic application (for soft magnetic materials) are high Curie temperature, high maximum relative magnetic permeability, low remanence magnetic induction, low coercive field, high saturation magnetic induction and high electrical resistivity. However, the desirable properties are for hard magnetic materials are high operating temperature, high remanence magnetic induction, high coercive field, high intrinsic coercive field, and high magnetic energy density. Thus, Positive ideal solution and negative ideal solution are determined using the above criteria. The TOPSIS rank indices of the materials are estimated and are depicted in Table 1 (for soft magnetic materials) and Table 2 for hard magnetic materials. It can be seen that Supermalloy, Magnifer7904 is the best material (for the electromagnet applications) among the soft magnetic materials under study. While Permendur 2V stands on last rank. It is to be noted that most of the ferro-nickle alloys are ranked higher than the rest of the materials under study. Ferrite 4 is the optimal material among the hard magnetic materials while Alnico 8HC stands on last rank in this analysis. It is also noticed that all the alloys of the cobalt–samarium family are on higher rank than that of Alnico family materials under study. In order to further analyzed, these materials are shorted out using VIKOR approach. The VIKOR ranks of the soft and hard magnetic materials are given in Tables 1 and 2, respectively. It is found that the conditions for acceptable advantage and acceptable stability are satisfied by VIKOR ranking of soft and hard magnetic materials. Hence, first ranked material (in soft and hard magnetic materials) is the best choice among the materials understudy. These results are in good agreement with that of TOPSIS approach. In order to further visualize the relative distances of materials understudy, the MATLAB software is used to plot dendrograms for the soft and hard magnetic materials (Figs. 1 and 2) respectively. Euclidean distances are calculated using for the weighted normalized matrix. It is observed that the highest value of cophenetic correlation coefficient is obtained by average linkage method, hence, is has been used to plot the dendrograms. Figs. 1 and 2 depict the dendrograms for soft and hard magnetic materials, respectively. The materials are placed on the x-axis and are represented using their TOPSIS ranks (Tables 1 and 2 (column 1)). At macrolevel, soft magnetic materials are classified into the four clusters where Supermalloy, Magnifer 7904 (rank:1) and Permendur 2V (rank: 16) stand alone in clusters. Whereas hard magnetic materials are classified into the four distinct clusters and their patterns show good agreement with the outcome of TOPSIS analyses. These dendrograms can be used to judge the actual physical

Fig. 1. Dendrogram for soft magnetic materials.

A. Chauhan, R. Vaish / Materials and Design 36 (2012) 1–5

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Fig. 2. Dendrogram for hard magnetic materials.

relationship between materials regardless of their ranks. That is even though the materials may differ by several ranks, if they behave similarly they are grouped together. These dendrograms can be directly used for a close substitute of the given material under consideration and not for ultimate optimum. Present study is primary screening of vital magnetic materials based on magnetic properties. However, it can be extended by including other advanced materials including nanocrystalline, thin films, amorphous and composites. Fuzzy based approach can improve the analysis using subjective attributes. One cannot completely rely on these methods and hence physical approaches are required to improve the results. 4. Conclusions TOPSIS and VIKOR methods are employed for screening soft and hard magnetic materials. Physical properties for soft magnetic material selection are weighted in the order of Hc > lmax/l0 > q > Br > Bs > Tc. Whereas, for the hard magnetic materials, priorities for the properties are Hc > Hic > (BH)max > Br > Tmax. It is clear that coercive magnetic field is important property which substantially affects the ranking of soft and hard magnetic materials in technological applications. Supermalloy and Ferrite 4 are the optimal soft and hard magnetic materials understudy, respectively. These materials are classified using hierarchical clustering which groups the materials based on Euclidean distance between the attributes. These dendrograms show physical relationship between materials regardless of their ranks. These findings can be integrated with high-throughput experimentation for rapidly screening and designing materials. References [1] Cardarelli F. Materials handbook. New York: Springer; 2000. p. 487–516. [2] Krichmayr MR. Permanent magnets and hard magnetic materials. J Phys D: Appl Phys 1996;29:2763–78. [3] Gavrila H, Ionita VC. Crystalline and amorphous soft magnetic materials and their applications – status of art and challenges. J Optoelectron Adv Mater 2002;4:173–92. [4] Park JY, Allen MG. Development of magnetic materials and processing techniques applicable to integrated micromagnetic devices. J Micromech Microeng 1998;8:307–16.

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