New Insight into the Effect of Alloying Elements on Elastic Behavior

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New Insight into the Effect of Alloying Elements on Elastic Behavior, Hardness and Thermodynamic Properties of Ru2B3 Yong Pan, Yuanhua Lin, and Chuangchuang Tong J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b06668 • Publication Date (Web): 06 Sep 2016 Downloaded from http://pubs.acs.org on September 10, 2016

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The Journal of Physical Chemistry

New Insight into the Effect of Alloying Elements on Elastic Behavior, Hardness and Thermodynamic Properties of Ru2B3 Yong Pan*, Yuanhua Lin*, and Chuangchuang Tong School of Materials Science and Engineering, Southwest Petroleum University, Chengdu, Sichuan 610500, China ABSTRACT: How to improve the mechanical

and

thermodynamic

Replaced site

properties is still a big challenge for TMBs. Alloying method is a good route based

on

the

valence

electronic

discrepancy. However, the mechanism of alloying addition is unknown. In this paper, the influence of alloying elements (TM=Mo, W, Os and Re) on the structural stability, elastic properties, hardness and thermodynamic properties of Ru2B3 is studied by first-principles approach. Phonon dispersion, elastic properties, hardness, electronic structure, Debye temperature and heat capacity of Ru2B3 with alloying elements are calculated. It is found that Ru2B3 with alloying elements are thermodynamic stability and dynamic stability at the ground state. We predicted that the alloying elements can improve the elastic properties and hardness for Ru2B3. Owing to the high valence electronic density, the shear deformation resistance of Ru2B3 with alloying elements of Re and W is up to 12.7 % and 11.1 % in comparison with the perfect Ru2B3. We suggested that heavy alloying elements can result in charge transfer from TM atom to B atom, and forms the strong B-B covalent bond. Finally, we concluded that alloying can improve the Debye temperature for Ru2B3.

result, alloying element alters the chemical

■ INTRODUCTION Although the mechanical properties of

bonding

and

overall

such

hardness

as

transition metal borides (TMBs) are widely

mechanical

investigated1-9, how to improve the intrinsic

thermodynamic properties etc. For example,

hardness is a big challenge. According to design

earlier works have shown that the measured

principle, the mechanical properties of TMBs are

Vickers hardness of OsB2 is 34.8 GPa11, but the

derived from the valence electronic density and

Vickers hardness of Os0.5W0.5B2 is about of 40.4

10

properties,

properties

and

covalent bonding . Therefore, alloying method

GPa12. Wang et al have found that the calculated

can effectively improve the properties (such as

hardness of Os-based ternary borides is larger

elastic properties, hardness and thermodynamic

than that of OsB213-16. Recently, Mohammadi

properties etc) for TMBs because alloying

and Kaner17 have demonstrated that the Vickers

addition changes the charge interaction. As a

hardness of WB4 increases from 43.3 GPa to

1

ACS Paragon Plus Environment


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49.8 GPa when the introduction of Re (1at %)

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phase. In particular, the Vickers hardness of

into the WB4. However, the mechanism of

Ru2B3-type structure is related to the chemical

alloying addition is unknown.

bonding at the layered-by-layered structure26.

On the other hand, thermal stability should

Therefore, Ru2B3-type structure is of great

be considered under high temperature condition.

interest in TMBs superhard materials. To explore

As we known, diamond cannot be used to cut

the effect of alloying addition on the structure

Fe-based alloys when temperature is bigger than

and properties for TMBs, we consider the Ru2B3

600 °C

18,19

. Therefore, it is necessary to find

phase in this paper. The purpose of alloying is to

other ways to improve the thermodynamic

change the localized hybridization and chemical

properties for TMBs. However, thermodynamic

bonding at layered-by-layered structure in order

properties of TMBs are still lacking. The

to improve the properties.

influence

of

alloying

element

on

the

It is well known that Ru2B3 in the

thermodynamic properties for TMBs is scarce.

Os2B3-type structure with the space group of

In particular, keeping the balance of high

P63/mmc (No.194). The lattice parameters of

hardness and excellent thermal stability is still a

this structure are a=b=2.905 Å and c=12.816 Å27.

big conundrum. That is to say, it is necessary to

To examine the correlation between the alloying elements and properties for Ru2B3, the 2×2×1

study the overall performance for TMBs. By means of ab-initio calculation, in this paper,

we

systematically

investigated

supercell Ru2B3 is built. The structural model is

the

shown in Figure 1. It can be seen that the force

relationship between the alloying element and

between layer and the layer is mainly determined

overall properties for Ru2B3. Considering the

by the bond strength of Ru-B bond. The

valence electronic discrepancy, we select the

calculated bond length of Ru-B bond at

alloying elements including 4d- Mo, 5d- W, 5d-

layered-by-layered is 2.163 Å after structural

Os and 5d- Re. To examine the alloyed effect,

optimization, According to the design principle,

the impurity formation energy and phonon

one Ru atom in Ru2B3 supercell is replaced by

dispersion are calculated. Additionally, the finite

TM (TM=Mo, W, Os and Re) atom.

temperature thermodynamic properties of Ru2B3 with

alloying

elements,

such

as

Debye

temperature and heat capacity are predicted. The calculated results show that alloying elements of Re and W not only improve the elastic properties and hardness, but also improve the Debye temperature for Ru2B3.

B

■ THEORETICAL METHODS

Replaced site

Among these TMBs, ReB220, OsB221, WB412 and CrB422 are considered to be potential

Ru

superhard materials. However, the Vickers hardness

of

Ru-based

borides

retains

controversy23. It is found that although the measured Vickers hardness of RuB2 is 24.4 GPa24, the Vickers hardness of Ru-based borides film (Ru2B3+RuB2) is bigger than 40 GPa25.

Figure 1. Drawing schemes of Ru2B3 structure

According to Rau′s viewpoint, the nature of

(space group: P63/mmc, No. 194).

superhard of the film is derived from the Ru2B3

2


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In this paper, all calculation of Ru2B3 with

formation enthalpy (∆H) of Ru2B3 with alloying

alloying elements at the ground state were

elements of Mo, W, Os and Re, together with the

carried out by using the CASTEP code28. The

perfect Ru2B3. It is concluded that Ru2B3 with

exchange-correlation energy was treated by

alloying elements are thermodynamic stability

using the local density approximation (LDA)

because the calculated values of ∆H of Ru2B3

functional29. The k-point grid of 19×19×10 was

with alloying elements are negative. We note

used for Ru2B3 with alloying elements, together

that the value of Ef for alloyed Re is lower than

with the perfect Ru2B3. The cutoff energy of a

that of other alloying elements, and the ∆H of

plane-wave basis was 400 eV. The total energy

alloying element Re is also smaller than that of

of alloyed system was calculated by using the

Ru2B3 at the ground state. On the contrary, the

density-mixing scheme. The SCF tolerance was

∆H of alloying element of Mo, W and Os are

smaller than 1.0×10-6 eV/atom and the maximal

larger than that of Ru2B3. Therefore, we can

displacement

Å.

conclude that alloying element of Re is more

Additionally, the alloyed system was fully

thermodynamic stability than that of other

relaxed during the structural optimization.

alloying elements.

was

lower

than

0.001

The elastic modulus of Ru2B3 and Ru2B3

To further examine the structural stability,

with alloying elements is estimated by the

Figure 2 displays the calculated ∆H of Ru2B3

correlation between the strain and stress30. The

and Ru2B3 with alloying elements under pressure

elastic properties of a solid include volume

(0~100 GPa). It is observed that the value of ∆H

deformation resistance (bulk modulus: B), shear

of Ru2B3 and Ru2B3 with alloying elements

deformation resistance (shear modulus: G) and

increases

elastic stiffness (Young′s modulus: E), which are

pressure, the repulsive force in small region

with

increasing

pressure.

Under

obtained by the elastic constants (Cij). To

becomes strong, in contrast to the attraction

examine the dynamic stability for Ru2B3 with

becomes weak. As a result, pressure leads to

alloying elements, the phonon dispersion is

electronic compression and collapse among

31

calculated by using the PHONOPY code . The

atoms. It is worth noticing that the value of ∆H

finite temperature thermodynamic properties are

in whole pressure range is consistent with the

used by the quasi-harmonic Debye model, as

zero pressure, confirming that alloying element

32

implemented in the Gibbs code .

of Re is more thermodynamic stability than that

■ RESULTS AND DISCUSSION

of Ru2B3.

To explore the influence of alloying elements on the elastic properties, hardness and thermodynamic

properties

for

Ru2B3,

the

stability of alloying addition should be checked first. To the best of our knowledge, the structural stability of a solid depends not only on the thermodynamic stability but also on the dynamic stability.

The

thermodynamic

stability

is

estimated by the impurity formation energy (Ef). However, the dynamic stability is originated from the vibrational frequency of a material, which is examined by the phonon frequency. Table

1 lists

the

equilibrium

lattice

Figure 2. Calculated formation enthalpy of Ru2B3 with alloying elements as a function of pressure.

parameters, density (ρ), volume (V), Ef and

3



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Table 1. Lattice parameters (Å), density, ρ (g/cm-3), volume, V (Å3), impurity formation energy, Ef (eV/atom) and formation enthalpy, ∆H (eV/atom) of Ru2B3 with alloying elements, together with the perfect Ru2B3. Element

Method

a

c

ρ

V

Ru2B3

Cal

2.870

12.652

8.631

90.3

8.357

92.2

27

Mo

Exp

2.905

12.816

Theo33

2.864

12.813

Cal

2.630

12.995

Ef

∆H -0.347

-1.063

-0.321

W

Cal

2.864

13.001

9.926

92.3

-1.484

-0.318

Os

Cal

2.876

12.684

10.204

90.8

-1.519

-0.326

Re

Cal

2.865

12.813

10.110

91.0

-2.514

-0.366

Figure 3. Phonon dispersion curves for (a) Ru2B3, (b) Alloying element of 4d-Mo, (c) Alloying element of 5d-W, (d) Alloying element of 5d-Os and (e) Alloying element of 5d-Re, respectively. In order to estimate the dynamic stability

the future experiment.

for alloying addition, Figure 3 shows the

It should be mentioned that the phonon

calculated phonon dispersion of Ru2B3 with

spectrum of Ru2B3 (see Figure 3(a)) can be

alloying elements, together with the perfect

divided into three parts: (1) the low frequency

Ru2B3. It is clear that no any imaginary phonon

mode (0 - 9.19 THz-1), (2) medium frequency

frequency

Ru2B3,

range (12.92 THz-1 - 16.91 THz-1) and (3) the

demonstrating that Ru2B3 is a stable structure. In

high frequency mode (20.24 THz-1 - 21.65

particular, no any imaginary phonon frequency

THz-1). However, the medium frequency region

is observed in Ru2B3 with alloying elements of

of Ru2B3 with alloying elements increases in

Mo, W, Os and Re, indicating that Ru2B3 with

comparison with Ru2B3. This result indicates

alloying

is

found

elements

are

in

perfect

stability.

that alloying elements can improve thermal

Although there is no experimental data for

dynamic

activation for Ru2B3. It is demonstrated by the

comparison, our work can be provided helpful to

phonon density of state (Phonon DOS).

4


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Figure 4. Calculated phonon DOS of Ru2B3 with alloying elements, (a) Ru2B3, (b) Alloying element of 4d-Mo, (c) Alloying element of 5d-W, (d) Alloying element of 5d-Os and (e) Alloying element of 5d-Re, respectively. To reveal the nature of dynamic stability,

above, we suggested that the low-temperature

Figure 4 shows the total and partial phonon DOS

thermodynamic

properties

of

Ru2B3

are

of Ru2B3 with alloying elements, together with

dominated by Ru atom and alloying elements.

the perfect Ru2B3. It is found that these borides

This discrepancy is derived from the valence

are mechanical stability because no negative

electronic density. Moreover, the vibration

frequency could be observed for Ru2B3 and

frequency of alloying element of Re at low

Ru2B3 with alloying elements. For Ru2B3 (see

frequency range is stronger than that of other

Figure 4(a)), the phonon DOS below 9.19 THz-1

alloying elements. The electronic contribution

mainly originates from the vibration of the Ru

for alloyed Re is stronger than that of other

atom,

alloying elements. It is well explained why the

meaning

thermodynamic

that

the

properties

low-temperature of

Ru2B3

are

dominated by Ru atom. However, the phonon -1

thermodynamic stability for alloying element of Re is better than that of other alloying elements.

DOS above 9.19 THz is almost entirely from

To reveal the stability for alloying addition,

vibration of the B atom. That is to say, the

the structural information is discussed follow.

thermodynamic

high

From Table 1, we first observed that the

temperature are determined by the Ru-B and

equilibrium lattice parameters of perfect Ru2B3

B-B covalent bond.

are in good agreement with the experimental

properties

under

Comparing Figure 4(a) and Figure 4(b)-(e),

data and theoretical results27,33. According to the

the phonon DOS of Ru2B3 with alloying

bonding feature, the bond covalency in TMBs

elements is different from the Ru2B3. Alloying

exhibits strong bond strength in comparison with

elements participate in the low frequency range.

metallic or ionic bond34,35. Therefore, the

Thus, the vibration of alloying element at low

mechanical properties of TMBs may be related

temperature changes the localized hybridization

to other factors. From Figure 1, we suggested

between Ru atom and the B atom, and then leads

that the elastic properties and hardness of Ru2B3

to the variation of properties. As mentioned

are mainly determined by the cohesive force

5



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between Ru layer and the B layer. When Ru

resistance for Ru2B3 because the C44 of Ru2B3

atom is replaced by the alloying elements, the

with alloying elements is also larger than the

strong interaction between B atom and 4d- and

corresponding C44 for Ru2B3. In particular, we

5d- TM atom forms the strong TM-B bond in

can predict that 5d- Re can obviously improve

comparison with Ru-B bond, resulting in lattice

the elastic properties in comparison with other

shrinkage in a-b plane. The lattice parameters of

alloying elements because the C11, C33 and C44 of

alloyed system verify the results. From Table 1,

alloyed Re are bigger than that of other alloying

the lattice parameter of Ru2B3 with alloying

elements and Ru2B3. Moreover, the C12 and C13

elements along the a-axis is lower than the

indicate the degree of Poisson effect in a

a-axis for perfect Ru2B3. On the contrary, the

hexagonal system14. From Table 2, the calculated

lattice parameter

C12 and C13 for Ru2B3 with alloying elements of

of Ru2B3

with alloying

elements along the c-axis is bigger than the

Mo,

W

and

Re

are

smaller

than

the

c-axis for perfect Ru2B3. Thus, we can conclude

corresponding C12 and C13 for perfect Ru2B3.

that alloying elements change the charge

However, the calculated value of C13 for alloyed

interaction between the TM and B atoms.

Os is smaller than the corresponding C13 for

Owing to the strengthening mechanism, alloying method is best way to enhance the

perfect Ru2B3, in contrast to the C12 of alloyed Os is larger than that of Ru2B3.

elastic properties and hardness for TMBs. Table

Following, we further found that the

2 lists the Cij, B, G, E, B/G ratio and Vickers

calculated B and G of Ru2B3 are 339 GPa and

hardness of Ru2B3 with alloying elements,

197 GPa, respectively, which are very similar to

together

Before

other theoretical results. The calculated B of

examining the elastic properties of Ru2B3 with

Ru2B3 with alloying elements of Mo and W is

with

the

perfect

Ru2B3.

alloying elements, the mechanical stability of

smaller than that of Ru2B3, in contrast to the B of

Ru2B3

be

Ru2B3 with alloying elements of Os and Re is

considered first. As listed in Table 2, we found

slightly larger than that of Ru2B3. Obviously,

that Ru2B3 and Ru2B3 with alloying elements are

alloying elements does not obviously improve

mechanical stability because obtained elastic

the volume deformation resistance for Ru2B3.

with

alloying elements

should

constants satisfy the Born stability criteria.

For a solid, the measure of shear strength is

For Ru2B3, the deformation resistance

the G, which estimates the applied shear stress

along the c-axis is stronger than that of a-axis

under the shearing of a bond. Namely, the

because the calculated C33 (887 GPa) is larger

Vickers hardness of TMBs is reflected by the

than C11 (514 GPa). In addition, the calculated

value of G. From Table 2, the G of Ru2B3 with

C33 of Ru2B3 is larger than the corresponding C33

alloying elements of Mo and Os is slightly larger

for MoB24 and OsB236. Therefore, we suggested

than that of Ru2B3. However, the calculated G of

that Ru2B3 is expected to have the strong

Ru2B3 with alloying elements of W and Re are

deformation resistance compared with other

219 GPa, and 222 GPa, respectively, which are

TMB2.

11.1 % and 12.7 % larger than that of perfect

When Ru atom is substituted by the TM

Ru2B3. On the other hand, we found that

atom, the calculated C11 and C33 for Ru2B3 with

alloying elements can improve the elastic

alloying elements are larger than that of Ru2B3,

stiffness because the variation of E for alloying

implying that alloying elements can improve the

elements is similar to the G. Thus, we concluded

deformation resistance of Ru2B3 along the a-axis

that the heavy alloying element improve the

and c-axis, respectively. In addition, these heavy

hardness of Ru2B3. The reason is that the G and

alloying elements improve the shear deformation

E are determined not only by the valence

6


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Table 2. Calculated elastic constants, Cij (in GPa), bulk modulus, B (in GPa), shear modulus, G (in GPa), Young′s modulus, E (in GPa), B/G ratio and Vickers hardness, Hv (in GPa) of Ru2B3 with alloying elements, together with the perfect Ru2B3. Elements

Method

C11

C12

C13

C33

C44

C66

B

G

E

B/G

Hv

Ru2B3

Cal

514

216

194

887

217

149

339

197

495

1.72

20.3

33

Theo

515

218

211

793

255

339

203

508

Mo

Cal

535

198

168

811

219

169

324

207

512

1.57

23.8

W

Cal

565

191

173

834

224

187

334

219

539

1.53

25.6

Os

Cal

530

226

186

898

221

152

344

202

507

1.70

20.9

Re

Cal

571

206

178

897

230

183

346

222

548

1.56

25.1

Table 3. Calculated shear anisotropic factors (A1, A2 and A3) and percentage anisotropy AB and AG of Ru2B3 with alloying elements, together with the perfect Ru2B3. Elements

A1

A2

A3

AB

AG

Ru2B3

0.857

0.857

1

0.024

0.036

Mo

0.867

0.867

1.003

0.012

0.019

W

0.851

0.851

1

0.012

0.016

Os

0.837

0.837

1

0.019

0.037

Re

0.827

0.827

1.003

0.014

0.023

electronic density but also by the chemical

The Vickers hardness of Ru2B3 in this paper

bonding. We suggested that the heavy 5d-TM

is examined by Chen et al model39. The

atom can improve the charge interaction between

calculated theoretical Vickers hardness of Ru2B3

the TM and B atoms, and then forms the strong

is 20.3 GPa. However, we found that the

TM-B bond. In particular, TM-B bond just

calculated Vickers hardness of alloyed W and Re

locates at the shear deformation direction. Thus,

is 25.6 GPa and 25.1 GPa, respectively, which

it seems that the TM-B bond is dominant in

are bigger than that of Ru2B3. Therefore, this

elastic properties and hardness.

result demonstrates that alloying elements

Although the brittle behavior is a negative factor for TMBs, it indirectly reflects the trend

improve the intrinsic hardness for Ru2B3. Furthermore,

elastically

anisotropic

of

of hardness. Following, the brittle behavior of

TMBs provides key information for their

Ru2B3 with alloying elements is studied. Based

practical

on the Pugh criterion, the brittle or ductile of a

anisotropic factors (A1, A2 and A3) imply the

37

application.

Generally,

the

shear

solid is estimated by the B/G ratio (B/G=1.75) .

anisotropic degree of bond along the different

It is clear that the value of B/G ratio for Ru2B3 is

planes40. A1, A2 and A3 indicate the (100) shear

about of 1.72. However, the value of B/G ratio

plane between [011] and [010] direction, (010)

of Ru2B3 with alloying elements is smaller than

shear plane between [101] and [001] direction,

that of Ru2B3, indirectly demonstrating that these

and (001) shear plane between [110] and [010]

alloying elements can improve the hardness for

direction, respectively. If A1=A2=A3, the solid

Ru2B3. In particular, the value of B/G ratio of

shows the isotropic, and vice versa, a material

alloying elements of W (1.57) and Re (1.56) is

exhibits anisotropic when A1=A2=A3≠1. In

smaller than that of other alloying elements. This

addition, AB and AG represent the percentage

38

trend is similar to the G and E .

anisotropy of a solid. If AB=AG=0, the solid 7



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demonstrates the elastic isotropy, and AB=AG=1,

element

the

mechanical properties for Ru2B3.

material

shows

the

largest

possible

anisotropy41,42.

is

Page 8 of 14

beneficial

for

improving

the

To reveal the bonding characteristic of

Table 3 lists the calculated shear anisotropic

Ru2B3 with alloying elements, Figure 6 shows

factors and percentage anisotropy of Ru2B3 with

the density of states (DOS) of Ru2B3 with

alloying elements and the perfect Ru2B3. It can

alloying elements, together with the perfect

be seen that Ru2B3 with alloying elements of W

Ru2B3. It is observed that the DOS profile of

and Os show elastically isotropic for (001) shear

Ru2B3 (see Figure 6(a)) separates three parts.

plane and anisotropic for (100) and (010) shear

The first part between -13.82 eV and -8.38 eV,

planes. However, the alloyed Mo and Re exhibit

consists of B-2s state and Ru-4d state. The

anisotropic for (100), (010) and (001) shear

charge interaction between the Ru and B atoms

planes.

forms the Ru-B bond. In this region, we found

In order to further reveal the nature of

that B-2p state stretches into the B-2s state,

elastic properties and Vickers hardness, Figure 5

demonstrating the existence of B-B covalent

displays the charge density distribution in (100)

bond in Ru2B3. The second part from -8.38 eV to

plane for Ru2B3 with alloying elements, together

Fermi level, is contributed by the B-2p state and

with the perfect Ru2B3. We observe the

Ru-4d state. It should be mentioned that the

directional B-B and Ru-B bond in perfect Ru2B3

charge transfer from B-2s state to B-2p state

(see Figure 5(a)), and the bond lengths of Ru-B

would form different Ru-B bonds. Considering

and B-B bonds are 2.161 Å and 1.830 Å,

the bond orientation for Ru2B3, therefore, we

respectively. In this structure, Ru-B and B-B

concluded that the structural stability and

covalent bonds are parallel to the b-axis, which

mechanical properties of Ru2B3 are determined

can improve the elastic stiffness and shear

by the Ru-B bond. The last part between Fermi

deformation. Importantly, the cohesive force of

level and 7.56 eV, consists of Ru-4d state and

layered-by-layered is linked by the Ru-B bond.

B-2p state, forming Ru-B antiboding state.

Thus,

the

bond

strength

of

Ru-B

bond

determines the volume deformation resistance.

Comparing

with

the

Ru2B3,

alloying

addition would change the charge interaction

When Ru atom in Ru2B3 is substituted by

between the TM and B atoms. For B atom, the

TM atom, alloying elements result in charge

PDOS profiles have shown that alloying addition

transfer from TM-B atoms to B-B atoms. It is

results in charge transfer from low energy region

demonstrated by the variation of bond length.

to Fermi level, which enhances the charge

From Figure 5, the calculated bond length of

interaction between the B and B atoms. On the

TM-B bond is shorter than the corresponding

other hand, the d-state of 4d- and 5d- alloying

site for Ru-B bond, meaning that alloying

elements

elements improve the charge interaction between

contribution, which forms the TM-B bond.

would

take

part

in

electronic

the B and B atoms for Ru2B3. Furthermore, we

For TMBs, thermodynamic properties are

observed that the charge interaction between the

of great important in industrial application.

TM and B atoms for Ru2B3 with alloying

However, earlier works have focused on the

elements is also stronger than that of Ru2B3

structure and hardness for TMBs43-45. To explore

because the valence electronic density of

the thermodynamic behavior for TMBs, in this

alloying elements is bigger than Ru atom. It

section, the thermodynamic properties including

explains the reason why heavy alloying elements

Debye temperature and heat capacity are

improve the elastic properties of Ru2B3. As

predicted

mentioned above, we suggested that alloying

approximation. Figure 7 shows the Debye

by

using

the

quasiharmonic

8


Page 9 of 14

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(a)

(b)

Ru 1.830Å

2.161Å

B

B

Ru

2.222Å

B

1.791Å

Ru 2.231Å

2.160Å

1.832Å B

B

B

2.193Å

Mo

(e)

Ru

1.789Å B

B

2.161Å

Ru

(d)

(c)

2.189Å

W

2.184Å

Os

Ru

2.191Å

1.810Å

B

B

2.174Å

Re

Figure 5. Calculated charge density distribution of Ru2B3 with alloying elements along the (100) plane, (a) Ru2B3, (b) Alloying element of 4d-Mo, (c) Alloying element of 5d-W, (d) Alloying element of 5d-Os and (e) Alloying element of 5d-Re, respectively.

Figure 6. Density of states (DOS), (a) Ru2B3, (b) Alloying element of 4d-Mo, (c) Alloying element of 5d-W, (d) Alloying element of 5d-Os and (e) Alloying element of 5d-Re, respectively. temperature (θD)

with alloying

approaches to a constant (900 K). When alloying

elements at the temperature from 0 to 3000 K.

of Ru2B3

addition into the Ru2B3, the trend of Ru2B3 with

We observed that the Debye temperature of

alloying elements is similar to the Ru2B3.

Ru2B3 and Ru2B3 with alloying elements

However, the calculated Debye temperature of

increases rapidly under low temperature. The

Ru2B3 with alloying elements follows the order

calculated Debye temperature of Ru2B3 at 50 K

of Ru2B3< alloyed Mo < alloyed Os < alloyed W

is about of 612 K. With increasing temperature,

< alloyed Re. This result confirms that alloying

the Debye temperature of Ru2B3 is almost

elements improve the charge interaction between 9



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Page 10 of 14

the TM and B atoms, and indirectly enhance the

properties, hardness, electronic structure, Debye

mechanical properties for Ru2B3. Importantly,

temperature and heat capacity of Ru2B3 with

the Debye temperature of Ru2B3 with alloying

alloying elements are calculated by using the

element of Re is 929 K under high temperature.

first-principles approach. It is concluded that Ru2B3

with

alloying

elements

are

thermodynamic stability and dynamic stability. 5d-TM is more thermodynamic stability than that of 4d- TM. The calculated phonon DOS shows that the vibrational frequency of alloying element shifts towards the low frequency region in comparison with Ru2B3. Therefore, alloying elements can improve the thermal activation for Ru2B3. Alloying elements can strengthen the shear Figure 7. Calculated Debye temperature (θD) of Ru2B3 with alloying elements as a function of temperature.

deformation resistance and Vickers hardness for Ru2B3. The calculated elastic modulus of Ru2B3 with alloying elements of 5d-TMs is larger than that of alloying element of 4d-TM due to the

However, the alloying element does not markedly change the heat capacity (Cv) for Ru2B3. Figure 8 represents the isochoric heat capacity (Cv) of Ru2B3 with alloying elements, together with the perfect Ru2B3. It is clear that Cv of Ru2B3, and Ru2B3 with alloying elements increases rapidly when the temperature increases from 0 to 460 K. When T>660 K, Cv increases slowly under high temperature, and Cv almost approaches to a constant. The calculated constant of Cv of Ru2B3 is 59.3 J·mol-1·K-1.

valence

electronic

discrepancy.

The

shear

deformation resistance of alloying elements of Re and W are 12.7 % and 11.1 % larger than that of Ru2B3. The increasing of elastic modulus is due to the fact that alloying addition leads to charge transfer from TM-B to B-B. According the bonding arrangement, the shear deformation resistance and Vickers hardness mainly depend on the bond strength of B-B covalent bond. The volume deformation resistance of Ru2B3 is determined by the TM-B bond. In addition, alloyed Mo and Re shows anisotropic for (100), (010) and (001) shear planes. Although alloying element does not influence the heat capacity for Ru2B3, it improves the Debye temperature for Ru2B3. As mentioned above, we suggested that alloying method is useful for providing a significance guideline to improve the overall properties of TMBs. ■ AUTHOR INFORMATION Corresponding Author: [email protected].

Figure 8. Calculated heat capacity (CV) at

*E-mail:

constant pressure as a function of temperature.

+86-028-83037401. *E-mail:

■ CONCLUSION In summary, the structural stability, elastic

[email protected].

Tel: Tel:

+86-028-83037401. Notes

10


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The authors declare no competing financial interest.

Liu, H.; Wang, Y.; Zhang, J.; Gou, H. Unraveling

■ ACKNOWLEDGMENTS

First-Principles Computations. J. Phys. Chem. C

This work is supported by grants from the

2015, 119, 21649-21657.

Stable Vanadium Tetraboride and Triboride by

National Natural Science Foundation of China

(10) Kaner, R. B.; Gilman, J. J.; Tolbert, S.

(No. 51274170 and 51262015). We acknowledge

H. Designing Superhard Materials. Science 2005,

the discussion from Lady Yun Zheng.

308, 1268-1269. (11) Weinberger, M. B.; Levine, J. B.;

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Page 14 of 14

TOC

Replaced site

TOC Synopsis: Alloying elements are thermodynamic and dynamical stability in Ru2B3. We found that alloying elements can not only improve the shear deformation resistance and elastic stiffness, but also enhance the Debye temperature for Ru2B3. Therefore, we concluded that 5d- alloying elements can improve the overall properties of Ru2B3. Our work would be significant for further designing and improving the overall performances of TMBs materials.

14


New Insight into the Effect of Alloying Elements on Elastic Behavior

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