EM

KS

a

ARRA

KMWVP

1

pMplcttooiwnaaraa[r

em

0d

Materials Chemistry and Physics 129 (2011) 990– 994

Contents lists available at ScienceDirect

Materials Chemistry and Physics

jo u rn al hom epage : www.elsev ier .com/ locate /matchemphys

ffect of the W addition content on valence electron structure and properties ofoSi2-based solid solution alloys

e Peng, Maozhong Yi ∗, Liping Ran, Yicheng Getate Key Laboratory for Powder Metallurgy, Central South University, Changsha 410083, China

r t i c l e i n f o

rticle history:eceived 29 October 2010eceived in revised form 15 April 2011ccepted 19 May 2011

a b s t r a c t

Based on the empirical electron theory (EET) of solids and molecules, the valence electron structures(VES) of MoSi2-based solid solution alloys have been analyzed using the average atom model. The resultsshowed that with the increase of the W addition content, the hybridization steps of Mo and Si atom of thealloys occurred in C3 and 1, respectively. The hybridization step of W was always C5. The bond energy

eywords:olybdenum disilicide

substitutionalence electron structureroperties

of the main bond branch, the covalence electron number on the strongest bond and the percentage ofthe total covalent electron numbers accounting for the total valence electron number of (Mo1−x, Wx)Si2solid solutions increased with the increase of W addition content. These suggested that the addition of Wwould increase the melting point, hardness and strength and decrease the fracture toughness of (Mo1−x,Wx)Si2 solid solutions. Based on those results, MoSi2-based solid solution alloys were manufactured, andthe results of the experiments were in accordance with those of the theory.

. Introduction

Transition-metal disilicides have received great attentions asotential high temperature structural materials. In particular,oSi2 with the C11b structure has been considered to be the most

romising material because of its high melting temperature, excel-ent oxidation resistance, relatively low density and high thermalonductivity [1,2]. However, poor fracture toughness at ambientemperature and low strength and creep resistance at elevatedemperature (>1200 ◦C) have seriously limited the developmentf MoSi2-matrix structural materials. Thus, many recent studiesn the development of MoSi2-based materials have focused onmproving such poor mechanical properties through forming alloys

ith other elements or composites with a second phase [3,4]. Sig-ificant property improvement has been readily gained throughlloying MoSi2 with WSi2, which also possesses the C11b structurend forms a complete solid solution with MoSi2. WSi2 has beeneported to be a suitable addition to MoSi2 because of the remark-ble increase of the elevated temperature strength [5], hardnessnd fracture toughness of MoSi2 with the addition of WSi2 [6]. Bose7] has demonstrated that high temperature (1200 ◦C) creep waseduced by a factor of 10 by alloying with WSi2.

In the theoretical aspects, many researchers have attempted tostablish a relationship between the basic crystal structure andacro-properties. For example, Alouani et al. [8] have studied

∗ Corresponding author. Tel.: +86 731 88830894; fax: +86 731 88836081.E-mail address: yimaozhong@126.com (M. Yi).

254-0584/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.matchemphys.2011.05.049

© 2011 Elsevier B.V. All rights reserved.

the elastic constants and structural properties of MoSi2 by full-potential linear muffin-tin-orbitals (FP-LMTO) method. Friak et al.[9] have simulated the tensile test in ideal crystals of MoSi2 andWSi2 loaded along the [0 0 1] axis by using first-principles fullpotential electronic structure calculations. They have found thatthese compounds have covalent and metallic bonds, and the cova-lent bond contributes to the macro-properties mostly. However,there is little quantitative analysis on the valence electron structurefor these systems that restricts the interpretation of their macro-properties in physical sense. Moreover, for the solid solution, thefirst principle is not commonly used since the structure type is verylimited [10]. On the other hand, the EET of solids and moleculesformulated by Yu [11,12] is much simpler and more observable. Inthis article, the VES of MoSi2-based solid solution alloys was cal-culated using the EET of solids and molecules, and the effect of Waddition on the VES and the properties of MoSi2-based alloys havebeen studied. To simplify the calculation, the average atom modelof the EET has been used and assumed that the added content of Wincreased progressively from 0 to 50 mol% by a step of 10%.

2. Crystalline structure

Both MoSi2 and WSi2 have a tetragonal C11b-type crystal struc-ture with the space group of I4/mmm. Refractory metal atomsoccupy the 2a site at the position, (0,0,0), and Si atoms occupy the 4e

site at the position, (0,0,u). The cell parameters of MoSi2 and WSi2are as a = 0.32056 nm, c = 0.78450 nm, u = 0.3353c; a = 0.32138 nm,c = 0.78299 nm, u = 0.3347c, respectively [13]. The unit cell of theC11b structure is shown in Fig. 1.

K. Peng et al. / Materials Chemistry an

oo[a

a

c

w

3

3

ll

3

att‘wat

e

lg rD = lgnD

nA= DMe−Si(nA) − DSi−Si(nD) + RSi(l) − RMo(l)

ˇ(8c)

lg rE = lgnE

n= DMe−Si(nA) − DSi−Si(nE) + RSi(l) − RMo(l)

ˇ(8d)

Fig. 1. Crystal structure of MeSi2 with the C11b structure.

A previous investigation has showed that the crystal structuref (Mo, W)Si2 is the same as that of MoSi2. The lattice parametersf (Mo1−x, Wx)Si2 solid solution can be calculated by Vegard’s law14]. The equations for calculating lattice parameters ax and cx ares follows:

x = (1 − x)3.2056 + x3.2138 (1)

x = (1 − x)7.8450 + x7.8299 (2)

here x is the mole fraction of W atoms.

. VES of MoSi2-based solid solution alloys

.1. VES results of MoSi2

The VES of MoSi2 has been analyzed in detail based on the bondength difference (BLD) method of EET. The calculated results areisted in Table 1 [15].

.2. Meaning of average atom model

For the binary alloy or solid solution, because of its disorderedtomic arrangement, we assume in the first order approximationhat all positions in the solid solution were the same atoms, andhe atoms were neither the matrix atom nor the solute atom, but avirtual’ atom. The characteristic parameter of this atom was the

eighted average of the characteristic parameter of the matrix

tom and that of the solute atom. This kind of atom with the charac-eristic parameter of weighted average was called ‘average atom’.

The (Mo, W)Si2 solid solution is formed by substituting Mo bylement W. Thus, it is reasonable to consider that Mo and W atoms

d Physics 129 (2011) 990– 994 991

have randomly occupied the stations of the Mo atoms. The distri-bution should be statistical. The single-bond semilengths, RMe (l),and the total covalence-electron pairs, nMe

c (l), of the solid solutionscan be calculated according to the average atom theory [12]. Theequations for calculating RMe (l), nMe

c (l) and nMel

(l) are as follows:

RMe(l) = (1 − x)RMo(l) + xRW(l) (3)

nMec = (1 − x)nMo

c + xnWc (4)

nMel = (1 − x)nMo

l + xnWl (5)

Here, RMe (l), RMo (l), and RW (l) represent the single-bondsemilengths of metallic atoms (or average atoms composed(1 − x)Mo and xW), Mo atom, and W atom, respectively; andnMe

c , nMoc , and nW

c denote the total number of covalent electronpairs of metallic atoms, Mo atom, and W atom, respectively; andnMe

l, nMo

l, and nW

ldenote the lattice electron number of metallic

atoms, Mo atom, and W atom, respectively.

3.3. Calculation of the VES

With the known crystal structure, experimental covalent bondlength, i.e., the distance between any two atoms in the unit cell,can be calculated by knowledge of solid geometry. Each kind ofcovalent bond has its own number of equivalent bond, I˛, whichis very important for the rest calculation. I˛ was calculated usingthe formula in Ref. [11]. The equivalent bond numbers of (Mo,W)Si2 solid solution are the same to those of MoSi2 as shown inTable 1.

Based on the EET of solids and molecules, the theoretical cova-lent bond length Duv(n˛) between atom u and atom v is as follows[11]:

Duv(n˛) = Ru(l) + Rv(l) − ̌ lg n˛ (6)

where Ru (l) and Rv (l) are the single bond radii of the atom u and v,respectively; n˛ is pair number of bond covalent electrons, ̨ = A, B,C,. . ., F, and ̌ = 0.060 nm is the empirical constant. The theoreticalbond lengths in C11b crystal are represented as:

DMe−Si(nA) = RMe(l) + RSi(l) − ̌ lg nA (7a)

DSi−Si(nB) = 2RSi(l) − ̌ lg nB (7b)

DMe−Si(nC ) = RMe(l) + RSi(l) − ̌ lg nC (7c)

DSi−Si(nD) = 2RSi(l) − ̌ lg nD (7d)

DSi−Si(nE) = 2RSi(l) − ̌ lg nE (7e)

DMe−Me(nF ) = 2RMe(l) − ̌ lg nF (7f)

Eq. (7a) subtracts Eqs. (7b)–(7f), respectively, and we can get:

lg rB = lgnB

nA= DMe−Si(nA) − DSi−Si(nB) + RSi(l) − RMo(l)

ˇ(8a)

lg rC = lgnC

nA= DMe−Si(nA) − DMe−Si(nC )

ˇ(8b)

A

lg rF = lgnF

nA= DMe−Si(nA) − DMe–Me(nF ) − RSi(l) + RMo(l)

ˇ(8e)

992 K. Peng et al. / Materials Chemistry and Physics 129 (2011) 990– 994

Table 1Valence electron structure and bond energies of MoSi2.

Bond Bonded atom I˛ n˛ D(n˛) (nm) D̄(n˛) (nm) �D (nm) E˛ (kJ mol−1)

A Mo–Si 32 0.25888 0.26092 0.26022 6.96 × 10−4 26.420B Si–Si 16 0.33465 0.26322 0.26252 6.96 × 10−4 21.487C Mo–Si 8 0.23874 0.26303 0.26233 6.96 × 10−4 24.169

0.2 −4

0.30.3

b(

ne

n

wr

(t

3

c

E

w

E

wsrb

f

w

3

ee

T

wat

f

D Si–Si 4 0.40203

E Si–Si 16 0.03706

F Mo–Mo 8 0.01859

In addition, the sum of the covalent electron pairs num-er derived from all the covalent bonds in the unit celldesignated as nA

∑˛

I˛r˛) is equal to the total covalent electron

umber of all atoms in the unit cell (designated as∑

nc), so anquation for nA can be established, which is expressed as:

A =∑

nc∑˛

I˛r˛

(9)

here the values of r˛ reflect the relative value of nB, nC,. . ., nF withespect to nA in each bond B, C,. . ., and F, respectively.

From these equations, different theoretical bond lengths D̄(n˛) ̨ = A, B,. . ., F) can be calculated through selecting hybrid states of

he various kinds of atoms.

.4. Calculation of the bonding energy

The covalent bond energy between two same atoms can be cal-ulated by [12]:

˛ = bfn˛

D̄(n˛)(10)

hile that between two different atoms can be calculated by

′˛ = B̄˛F̄˛n˛

D̄(n˛)(11)

here B̄˛ =√

bubv, F̄˛ = (fu + fv)/2; b is a factor related to thehield effect of the electron on the nucleon charge, and f is a factorelated to the bonding ability of the atoms, which can be calculatedy the following equation:

= √ ̨ +

√3 ̌ +

√5� (12)

here ˛, ̌ and � are constants of s, p and d electrons in the bonds.

.5. Calculation of the melting point

According to above achieved valence electron structural param-ters, the melting point can be calculated by use of the followingquation [12]:

m = b

3R

{nA

D(nA)f + nlf

′

I�D̄

}103 (13)

here R = 8.31 J mol−1 K, b, f, nA, D(nA) represent the same meaningss in the formula of the bonding energy, f′ is bonding capability of

he lattice electrons, and given by the following equation:

′ =√

2nl

nT(14)

5844 0.25774 6.96 × 10 26.2922056 0.31986 6.96 × 10−4 1.9532056 0.31986 6.96 × 10−4 2.278

where nT is the valence electron number. D̄ is an equivalent exper-imental bond length, which is expressed as follows:

D̄ =

∑˛

I˛D̄(n˛)

∑˛

I˛(15)

4. Experimental procedure

Elemental powders of Mo (2 �m, 99.9% purity), W (2 �m, 99.9% purity), andSi powder (5 �m, purity >99% purity) were used as starting materials. A homoge-neous powder blent with the composition according to a certain stoichiometric ratio(Mo:W:Si = (1 − x):x:2, x = 0, 0.1, 0.2, 0.3, 0.4, 0.5). Then, MoSi2 and (Mo1−x , Wx)Si2composites powders were synthesized by the thermal explosion mode of SHS [16].The as-combusted samples were easily ground into powder and were wet-milled inethanol in a planetary high-energy ball miller for 5 h. These powders were packedinto carbon dies, which were coated with BN and then hot pressed at 1650–1700 ◦Cfor 60–90 min in Ar atmosphere with 30 MPa applied uniaxial pressure.

Flexural strengths were determined by a three-point bending test on3 mm × 4 mm × 36 mm bars with a span of 30 mm, and the cross-head speed was0.5 mm min−1. The hardness was evaluated by Vickers indentation under a condi-tion of a 98 N load and a loading duration of 15 s, and the fracture toughness wasdetermined simultaneously by the indentation fracture method [17].

5. Results and discussion

5.1. Calculation results

While performing calculation for a known structure, the data inthe hybridization list of atoms can be scanned using a computerso as to find all solutions. When �D =

∣∣D̄(n˛) − D(n˛)∣∣ ≤ 0.005 nm,

it is thought that the theoretical bond length is consistent withthe experimental covalent bond length, and the resolution can beconsidered as the actual state of selected hybrid step coincidenceatoms in the cell.

After the comparison with the calculated results, the hybridsteps of all atoms of MoSi2-based solid solution alloys were deter-mined. Compared with the MoSi2 matrix, the hybridization stepsof Mo and Si atoms of solid solutions were always C3 and 1, respec-tively, without influencing the W substitution. The hybridizationstep of W was always C5. The covalent electron number, � (thepercentage of the total covalent electron numbers accounting forthe total valence electron numbers), the bonding energy and themelting point were shown in Table 2.

5.2. Experimental results

By adjusting the sintering process, the relative densities of the(Mo, W)Si2 solid solutions and monolithic MoSi2 were above 98%,and the and average grain sizes were 15–17 �m. The effects of thecontent of added W on the mechanical properties of the (Mo, W)Si2solid solutions were illustrated in Figs. 2 and 3.

5.3. Hardness and the strongest bonding energy

Hardness is the resistance of a material to localized defor-mation. When plastic deformation occurs, covalent bonds in the

K. Peng et al. / Materials Chemistry and Physics 129 (2011) 990– 994 993

Table 2The calculated results about the valence electron structure of the solid solutions and matrix.

x a (nm) c (nm) �D (nm) nA EA (kJ × mol−1) EB (kJ × mol−1) � (%) Tm (K)

0.0 0.32056 0.78450 6.96 × 10−4 0.25888 26.420 21.487 64.39 22300.1 0.32064 0.78435 5.90 × 10−4 0.26249 26.985 21.846 64.88 22680.2 0.32072 0.78420 4.80 × 10−4 0.26612 27.557 21.198 65.38 23050.3 0.32081 0.78405 3.67 × 10−4 0.26975

0.4 0.32089 0.78390 2.49 × 10−4 0.27339

0.5 0.32097 0.78374 1.28 × 10−4 0.27705

ctmelh

cntbtbtot21

FW

Fig. 2. Effect of content of W on hardness of (Mo1−x , Wx)Si2 solid solutions.

rystals will be broken. The more the covalent electron pairs are,he stronger the ability of the crystal to resist deformation. On the

acroscopic, the material hardness rises. So the product of thequivalent bond numbers of the strongest bonds and that of cova-ent electron pairs on this bond can be the criterion to compare theardness.

As presented in Tables 1 and 2, the strongest bonds in the unitell of MeSi2 are Me–Si bonds along 〈3 3 1〉 direction, of which theumber of equivalent bond is 32. It has an obvious regularity abouthe covalent electron numbers and bonding energy of the strongestond when W is added to the MoSi2 matrix. As shown in Table 2,he covalent electron numbers and bonding energy of the strongestond increased, when the W content increased. It suggested thathe addition of W would increase the hardness and bonding energyf solid solutions. When the additional content reached 50 mol%,

he electron numbers and bonding energy increased to 0.27705 and9.306 kJ mol−1, respectively. Namely, they increased by 7.01% and0.92%, respectively.

ig. 3. Effect of content of W on flexural strength and fracture toughness of (Mo1−x ,x)Si2 solid solutions.

28.134 22.543 65.87 234228.717 22.880 66.36 237929.306 23.211 66.86 2415

From Fig. 2, we can observe that when the additional content ofW increased, the hardness increased progressively. The hardnessof (Mo0.5, W0.5)Si2 nanocomposite was 9.28 GPa, which increased12.1% compared with that of the monolithic MoSi2.

5.4. Melting point

In the solid, the atoms with three-dimensional periodic arrange-ment are in their balancing position at absolute zero. The atomsvibrate around their balancing position with the temperatureincreasing. Atomic thermal vibration amplitude of the solid crys-tal increased with the temperature. Based on the EET of solids andmolecules, the only thing needs to do to melt the crystal is to destroythe bond network backbone which maintains the atoms to arrangein a three-dimensional period. When the temperature increases tothe melting temperature, the vibration energy of atom is strongenough to destroy the covalent bonds among adjacent atoms, thatis to say, the vibration energy of atom equals to bond energy of thebond network backbone, resulting in the destroyed bond networkbackbone and melted crystal [12].

For the crystal with C11b-type body-centered tetragonal struc-ture, the bond network backbones were A bond with the equivalentbond numbers of 32 and B bond with the equivalent bond numbersof 16. Therefore, only destroying both A bond and B bond could meltthe crystal. The melting point from our calculation of MoSi2, 2227 K,agrees well with the experimental value, 2303 K [1]. The small error(3.30%) showed that our calculation result was accurate. The effectof W addition content on the melting point of the solid solutionswas shown in Table 2. As presented in Table 2, when the added Wcontent increased, the melting point increased progressively. Whenthe concentration reached 50 mol%, the rise of the melting point ofMoSi2 solid was 183 K. Namely, it increased by 8.22%.

5.5. Strength and toughness

The strength and toughness of materials could be expressed as�, and the calculation formula is as follows:

� = nc

nT= nc

nc + nl

Previous study has found that with the increase of � resulting inthe increase of strength and decrease of toughness of materials [12].nc characterizes the atomic covalent binding strength. The more ofthe percentage of nc accounting for the total valence electron num-bers, the more firmly between the combination of atoms, and thehigher the strength of alloy phase. When the main bonds are bro-ken in the crystals, the lattice will take action. The lattice electronsin the crystal space keep the temporary bonds with atoms. Thus,the lattice electrons have relations with the toughness of crystals.The toughness of materials will increase with the percentage of thelattice electron numbers accounting for the total valence electronnumbers.

As shown in Table 2, � increased with the increase of W addedcontent, indicating that with the increase of W content, the strengthof (Mo1−x, Wx)Si2 solid solutions increased and the toughnessdecreased. As presented in Fig. 3, with the increase of W content, the

9 stry an

sn3ifTt

6

(

(

(

(

(

[[[

[[14] H. Inui, T. Nakamoto, K. Ishikawa, M. Yamaguchi, Mater. Sci. Eng. A 261 (1999)

94 K. Peng et al. / Materials Chemi

trength of (Mo1−x, Wx)Si2 solid solutions increased and the tough-ess decreased. Among which, the strength of (Mo0.5, W0.5)Si2 was63 MPa, and the fracture toughness was 2.94 MPa m1/2. The bend-

ng strength increased 40.7% compared with that of MoSi2, andacture toughness decreased 13.0% compared with that of MoSi2.herefore, the experimental results are in accordance with those ofheoretic calculation.

. Conclusion

1) Based on the EET of solids and molecules, the VES of MoSi2-based solid solution alloys have been analyzed. Compared withthe MoSi2 matrix, the hybridization steps of Mo and Si ofthe solid solutions were still C3 and 1, respectively, and thehybridization step of W was always C5.

2) As shown in Table 2, covalent electron numbers and bondingenergy of the strongest bond increased with the increase of theW content; it suggested that the addition of W would increasethe hardness and bonding energy of solid solutions.

3) The increase of W added content made the melting points of(Mo, W)Si2 solid solutions increase linearly.

4) With the increase of W added content, the percentage of thetotal covalent electron numbers accounting for the total valenceelectron numbers increased, resulting in the increase of the

strength and decrease of toughness of (Mo, W)Si2 solid solu-tions.

5) The experimental results showed that with the increase of Wcontent, the bending strength and hardness of (Mo1−x, Wx)Si2

[[[

d Physics 129 (2011) 990– 994

composites gradually increased, and the toughness decreased.The experimental results were in accordance with those of the-oretic calculation.

Acknowledgements

The research was financially supported by the National Nat-ural Science Foundation of China under project No. 51004117,and Hunan Provincial Natural Science Foundation of China underproject No. 10JJ4031.

References

[1] J.J. Petrovic, A.K. Vasudevan, Mater. Sci. Eng. A 261 (1999) 1.[2] R. Mitra, Int. Mater. Rev. 51 (2006) 13.[3] J.J. Petrovic, Intermetallics 8 (2000) 1175.[4] A.A. Sharif, A. Misra, J.J. Petrovic, Intermetallics 9 (2001) 869.[5] J.J. Petrovic, R.E. Honnell, Ceram. Eng. Sci. Proc. 11 (1990) 734.[6] H.A. Zhang, P. Chen, M.J. Wang, Rare Metals 21 (2001) 304.[7] S. Bose, Mater. Sci. Eng. A 155 (1992) 217.[8] M. Alouani, R.C. Albers, M. Methfessel, Phys. Rev. B 43 (1991) 6500.[9] M. Friak, M. Sob, V. Vitek, Phys. Rev. B 68 (2003) 184101.10] W.H. Li, F.Z. Ren, Z.H. Ma, Chin. J. Nonferrous Met. 18 (2008) 94.11] R.H. Yu, Chin. Sci. Bull. 23 (1978) 217.12] R.L. Zhang, Empirical Electron Theory of Solids and Molecules, Jilin Science and

Technology Publishing House, Changchun, 1993.13] K. Tanaka, K. Nawata, H. Inui, Mater. Res. Soc. 646 (2001) 4.

131.15] K. Peng, M.Z. Yi, H.J. Tao, L.P. Ran, Chin. J. Nonferrous Met. 17 (2007) 216.16] K. Peng, M.Z. Yi, L.P. Ran, Rare Metal Mater. Eng. 35 (2006) 554.17] G.R. Anstis, P. Chantikul, B.R. Lawn, J. Am. Cream. Soc. 64 (1981) 533.