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Elastic Moduli and Elastic Constants of Alloy AuCuSi With FCC Structure Under Pressure

  • Nguyen Quang Hoc , Bui Duc Tinh ORCID logo EMAIL logo and Nguyen Duc Hien
Published/Copyright: September 26, 2018
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High Temperature Materials and Processes
From the journal High Temperature Materials and Processes Volume 38 Issue 2019

Abstract

This paper studies on the dependence of the mean nearest neighbor distance, the Young modulus E, the bulk modulus K, the rigidity modulus G and the elastic constants C11, C12, C44 on temperature, pressure, the concentration of substitution atoms and the concentration of interstitial atoms for alloy AuCuSi (substitution alloy AuCu with interstitial atom Si) with FCC structure by the way of the statistical moment method (SMM). The numerical results for alloy AuCuSi are compared with the numerical results for main metal Au, substitution alloy AuCu, interstitial alloy AuSi, other calculated results and experiments.

Keywords: substitution and interstitial alloy; Young modulus; bulk modulus; rigidity modulus; elastic constant; Poisson ratio

Introduction

There are many theoretical and experimental works on thermodynamic and elastic properties of metals and alloys [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26].

The main metal in alloy AuCuSi is Au. At 0.1 MPa, Au has a FCC structure with a=0.40785 nm at 25 °C and melting point at 1064  C. The melting curve of Au was studied by the Hugoniot calculation and by the statistical moment method (SMM) [8, 9, 10].

Thermodynamic and elastic properties of metals, substitution alloy and interstitial alloy are studied by the SMM [11, 12, 13]

This paper derives the theory of elastic deformation for substitution alloy AB with interstitial atom C and face-centered cubic (FCC) structure under pressure by the SMM and the obtained theory is applied to alloy AuCuSi.

Content of research

Analytic results

In interstitial alloy AC with FCC structure, the cohesive energy of the atom C (in body center of cubic unit cell) with the atoms A (in face centers and peaks of cubic unit cell) in the approximation of three coordination spheres with the center C and the radii r1,r13,r15 is determined by [11, 12, 13]

(1)u0C=12∑i=1niφAC(ri)=12[6φAC(r1)+8φAC(r13)+24φAC(r15)]=           =3φAC(r1)+4φAC(r13)+12φAC(r15),

where φAC is the interaction potential between the atom A and the atom C, ni is the number of atoms on the ith coordination sphere with the radius ri(i=1,2,3),r1≡r1C=r01C+y0A1(T) is the nearest neighbor distance between the interstitial atom C and the metallic atom A at temperature T, r01C is the nearest neighbor distance between the interstitial atom C and the metallic atom A at 0 K and is determined from the minimum condition of the cohesive energy u0C, y0A1(T) is the displacement of the atom A1 (the atom A stays in the face centers of cubic unit cell) from equilibrium position at temperature T. The alloy’s parameters for the atom C in the approximation of three coordination spheres have the form [11, 12, 13].

(2)kC=12∑i∂2φAC∂uiβ2eq=φAC(2)r1+2r1φAC(1)r1+43φAC(2)r13++839r1φAC(1)r13+4φAC(2)r15+855r1φAC(1)r15,γ1C=148∑i∂4φAC∂uiβ4eq=124φAC(4)(r1)+14r12φAC(2)(r1)−−14r13φAC(1)(r1)+154φAC(4)(r13)+2327r1φAC(3)(r13)−−227r12φAC(2)(r13)+2381r13φAC(1)(r13)+17150φAC(4)(r15)++85125r1φAC(3)(r15)+125r12φAC(2)(r15)−5125r13φAC(1)(r15),γ2C=648∑i∂4φAC∂uiα2∂uiβ2eq=12r1φAC(3)(r1)−34r12φAC(2)(r1)++34r13φAC(1)(r1)+14φAC(4)(r12)+28r1φAC(3)(r12)++78r12φAC(2)(r1C2)−7216r13φAC(1)(r1C2)+425φAC(4)(r15)++265125r1φAC(3)(r15)−325r12φAC(2)(r15)+35125r13φAC(1)(r15),γC=4γ1C+γ2C,

where φAC(m)(ri)=∂mφAC(ri)/∂rim(m=1,2,3,4),α,β=x,y,z,α≠β and uiβ is the displacement of the ith atom in the direction β.

The cohesive energy of the atom A1 with the atoms in crystalline lattice and the corresponding alloy’s parameters in the approximation of three coordination spheres with the center A1 is determined by [11, 12, 13].

(3)u0A1=u0A+φAC(r1A1),kA1=kA+12∑i[(∂2φAC∂uiβ2)eq]r=r1A1=kA+φAC(2)(r1A1),γA1=4(γ1A1+γ2A1),γ1A1=γ1A+148∑i[(∂4φAC∂uiβ4)eq]r=r1A1=γ1A+124φAC(4)(r1A1),γ2A1=γ2A+648∑i[(∂4φAC∂uiα2∂uiβ2)eq]r=r1A1=γ2A+14r1A1φAC(3)(r1A1)−12r1A12φAC(2)(r1A1)+12r1A13φAC(1)(r1A1)

where r1A1=r01A1+y0C(T) is the nearest neighbor distance between the atom A1 and atoms in crystalline lattice at temperature T, r01A1 is the nearest neighbor distance between the atom A1 and atoms in crystalline lattice at 0 K and is determined from the minimum conditioning of the cohesive energy u0A1, y0C(T) is the displacement of the atom C from equilibrium position at temperature T and u0A is the cohesive energy between atoms in clean metal A.

The cohesive energy of the atom A2 with the atoms in crystalline lattice and the corresponding alloy’s parameters in the approximation of three coordination spheres with the center A2 is determined by [11, 12, 13].

(4)u0A2==u0A+φACr1A2,kA2=kA+12∑i∂2φAC∂uiβ2eqr=r1A2=kA+2φAC(2)r1A2+4r1A2φAC(1)r1A2,γ1A2=γ1A+148∑i∂4φAC∂uiβ4eqr=r1A2=γ1A+124φAC(4)(r1A2)+14r1A2φAC(3)(r1A2)−18r1A22φAC(2)(r1A2)++18r1A23φAC(1)(r1A2),γ2A2=γ2A+648∑i∂4φAC∂uiα2∂uiβ2eqr=r1A2=γ2A+18φAC(4)(r1A2)++14r1A2φAC(3)(r1A2)+38r1A22φAC(2)(r1A2)−−38r1A23φAC(1)(r1A2),γA2=4γ1A2+γ2A2,

where r1A2=r01A2+y0A2(T),r01A2 is the nearest neighbor distance between the atom A2 and atoms in crystalline lattice at 0K and is determined from the minimum condition of the cohesive energy u0A2,y0A2(T) is the displacement of the atom A2 at temperature T.

In eqs. (3) and (4), u0A,kA,γ1A,γ2A are the corresponding quantities in clean metal A in the approximation of two coordination sphere [11, 12, 13].

The equation of state for interstitial alloy AC with FCC structure at temperature T and pressure P is written in the form

(5)PvX=−r1X16(∂u0X∂r1X+θxXcthxX12kX∂kX∂r1X),vX=4r1X333.

At 0 K and pressure P, this equation has the form

(6)PvX=−r1X(16∂u0X∂r1X+ℏωX4kX∂kX∂r1X) .

If knowing the form of interaction potential φi0,eq. (6) permits us to determine the nearest neighbor distance r1XP,0X=C,A,A1,A2 at 0 K and pressure P. After knowing r1XP,0, we can determine alloy parameters kX(P,0),γ1X(P,0),γ2X(P,0),γX(P,0) at 0 K and pressure P. After that, we can calculate the displacements [11, 12, 13]

(7)y0X(P,T)=2γX(P,0)θ23kX3(P,0)AX(P,T),       AX=a1X+∑i=25(γXθkX2)iaiX,kX=mωX2,xX=ℏωX2θ,a1X=1+YX2,a2X=133+476YX+236YX2+12YX3,a3X=−(253+1216YX+503YX2+163YX3+12YX4),                 a4X=433+932YX+1693YX2+833YX3+224YX4+12YX5,      a5X=−(1033+7496YX+3633YX2+7333YX3+1483YX4+536YX5+12YX6),a6X=65+5612YX+14893YX2+9272YX3+7333YX4+1452YX5+313YX6+12YX7,YX≡xXcothxX.

From that, we derive the nearest neighbor distance r1XP,T at temperature T and pressure P

(8)r1C(P,T)=r1C(P,0)+yA1(P,T),r1A(P,T)=r1A(P,0)+yA(P,T),r1A1(P,T)≈r1C(P,T),r1A2(P,T)=r1A2(P,0)+yC(P,T). 

Then, we calculate the mean nearest neighbor distance in interstitial alloy AC by the expressions as follows [11, 12, 13]

(9)r1A(P,T)‾=r1A(P,0)‾+y(P,T)‾,r1A(P,0)‾=1−cCr1A(P,0)+cCr′1A(P,0),r′1A(P,0)≈2r1C(P,0),y(P,T)‾=1−15cCyA(P,T)+cCyC(P,T)+6cCyA1(P,T)+8cCyA2(P,T),

where r1A(P,T)‾ is the mean nearest neighbor distance between atoms A in interstitial alloy AC at pressure P and temperature T, r1A(P,0)‾ is the mean nearest neighbor distance between atoms A in interstitial alloy AC at pressure P and 0 K, r1A(P,0) is the nearest neighbor distance between atoms A in clean metal A at pressure P and 0K, r1A′(P,0)is the nearest neighbor distance between atoms A in the zone containing the interstitial atom C at pressure P and 0K and cC is the concentration of interstitial atoms C.

In alloy ABC with FCC structure (interstitial alloy AC with atoms A in peaks and face centers, interstitial atom C in body centers and then, atom B substitutes atom A in face centers), the mean nearest neighbor distance between atoms A at pressure P and temperature T is determined by

(10)aABC(P,T,cB,cC)=cACaACBTACBT‾+cBaBBTBBT‾,BT‾=cACBTAC+cBBTB,cAC=cA+cC,aAC=r1A‾(P,T),BTAC=1χTAC,BTB=1χTB,χTAC(P, T,cC)=aAC(P, T,cC)a0AC(P,0,cC)32P+23aAC(P, T,cC)13N∂2ψAC∂aAC2T,∂2ψAC∂aAC2T=∂2ψAC∂r1A‾2(P,T)T≈1−15cC∂2ψA∂aA2T+cC∂2ψC∂aC2T+6cC∂2ψA1∂aA12T+8cC∂2ψA2∂aA22T,13N∂2ΨX∂aX2T=16∂2u0X∂aX2+ℏωX4kX∂2kX∂aX2−12kX∂kX∂aX2,aX≡r1X(P,T).

The mean nearest neighbor distance between atoms A in alloy ABC at pressure P and temperature T is determined by

(11)a0ABC(P, T,cB,cC)=cACa0ACB0TACB0T‾+cBa0BB0TBB0T‾.

The free energy of alloy ABC with FCC structure and the condition cC<<cB<<cA has the form

(12)ψABC=ψAC+cB(ψB−ψA)+TScAC−TScABC,ψAC=(1−15cC)ψA+cCψC+6cCψA1+8cCψA2−TScAC,ψX≈U0X+ψ0X+3N{θ2kX2[γ2XXX2−2γ1X3(1+XX2)]++2θ3kX4[43γ2X2XX(1+XX2)−2(γ1X2+2γ1Xγ2X)(1+XX2)(1+XX)]},ψ0X=3Nθ[xX+ln(1−e−2xX)],XX≡xXcothxX.

where ψX is the free energy of atom X, ψAC is the free energy of interstitial alloy AC, ScAC is the configuration entropy of interstitial alloy AC and ScABC is the configuration entropy of alloy ABC.

The Young modulus of alloy ABC with BCC structure at temperature T and pressure P is determined by

(13)EABC=cBEB−EA+EAC=cBEB+cAEA−cA+cBEA+EAC=EAB−cA+cBEA+EAC,EAB=cAEA+cBEB,EAC=EA1−15cC+cC∂2ψC∂ε2+6∂2ψA1∂ε2+8∂2ψA2∂ε2∂2ψA∂ε2,EA=1π.r1AA1A,A1A=1kA1+2γA2θ2kA41+12xActhxA1+xActhxA,xA=ℏωA2θ,∂2ψX∂ε2=12∂2U0X∂r1X2+34ℏωXkX∂2kX∂r1X2−12kX∂kX∂r1X24r01X2++12∂U0X∂r1X+32ℏωXcthxX12kX∂kX∂r1X2r01X,xX=ℏωX2θ,ωX=kXm,

where ε is the relative deformation, EABC=EABC(cB,cC,P,T),EAB=EABcB,P,T is the Young modulus of substitution alloy AB and EAC=EACcC,P,T is the Young modulus of interstitial alloy AC.

The bulk modulus of alloy ABC with FCC structure at temperature T and pressure P has the form

(14)KABCcB,cC,P,T=EABcB,cC,P,T3(1−2νA).

The rigidity modulus of alloy ABC with FCC structure at temperature T and pressure P has the form

(15)GABCcB,cC,P,T=EABCcB,cC,P,T21+νA.

The elastic constants of alloy ABC with FCC structure at temperature T and pressure P has the form

(16)C11ABCcB,cC,P,T=EABCcB,cCP,T1−νA1+νA1−2νA,
(17)C12ABCcB,cC,P,T=EABCcB,cC,P,TνA1+νA1−2νA,
(18)C44ABCcB,cC,P,T=EABCcB,cC,P,T21+νA.

The Poisson ratio of alloy ABC with FCC structure has the form

(19)νABC=cAνA+cBνB+cCνC≈cAνA+cBνB=νAB.

where νA,νB and νC respectively are the Poisson ratios of materials A, B and C and are determined from the experimental data.

When the concentration of interstitial atom C is equal to zero, the obtained results for alloy ABC become the corresponding results for substitution alloy AB. When the concentration of substitution atom B is equal to zero, the obtained results for alloy ABC become the corresponding results for interstitial alloy AC. When the concentrations of substitution atoms B and interstitial atoms C are equal to zero, the obtained results for alloy ABC become the corresponding results for main metal A.

Numerical results for alloy AuCuSi

For alloy AuCuSi, we use the n-m pair potential

(20)φ(r)=Dn−mmr0rn−nr0rm,

where the potential parameters are given in Table 1 [14]

Table 1:

Potential parameters m,n,D,r0 of materials.

MaterialmnD10−16ergr010−10m
Au5.510.56462.5402.8751
Cu5.511.04693.5182.5487
Si6.012.045128.242.2950

Considering the interaction between Au and Si and between Au and Cu, we use the following approximation

(21)φAu−Cu≈12φAu−Au+φCu−Cu,φAu−Si≈12φAu−Au+φSi−Si

and ignore the interaction between Cu and Si.

The calculated results are summarized in tables from Table 2 to Table 8 and illustrated in figures from Figure 1 to Figure 8.

Figure 1: Dependence of elastic moduli E, G, K (1010Pa) on pressure for alloyAu-10%Cu-5%Si at T=300 K.
Figure 1:

Dependence of elastic moduli E, G, K (1010Pa) on pressure for alloyAu-10%Cu-5%Si at T=300 K.

Figure 2: Dependence of elastic constants C11, C12, C44 (1010Pa) on pressure for alloyAu-10%Cu-5%Si at T=300 K.
Figure 2:

Dependence of elastic constants C11, C12, C44 (1010Pa) on pressure for alloyAu-10%Cu-5%Si at T=300 K.

Figure 3: Dependence of elastic moduli E, G, K (1010Pa) on concentration of Si for alloy Au-10%Cu-xSi at P=30GPa and T=300 K.
Figure 3:

Dependence of elastic moduli E, G, K (1010Pa) on concentration of Si for alloy Au-10%Cu-xSi at P=30GPa and T=300 K.

Figure 4: Dependence of elastic constants C11, C12, C44 (1010Pa) on concentration of Si for alloy Au-10%Cu-xSi at P=30GPa and T=300 K.
Figure 4:

Dependence of elastic constants C11, C12, C44 (1010Pa) on concentration of Si for alloy Au-10%Cu-xSi at P=30GPa and T=300 K.

Figure 5: Dependence of elastic moduli E, G, K (1010Pa) on concentration of Cu for alloy Au-xCu-5%Si at P=30 GPa and T=300 K.
Figure 5:

Dependence of elastic moduli E, G, K (1010Pa) on concentration of Cu for alloy Au-xCu-5%Si at P=30 GPa and T=300 K.

Figure 6: Dependence of elastic constants C11, C12, C44 (1010Pa) on concentration of Cu for alloy Au-xCu-5%Si at P=30GPa and T=300 K.
Figure 6:

Dependence of elastic constants C11, C12, C44 (1010Pa) on concentration of Cu for alloy Au-xCu-5%Si at P=30GPa and T=300 K.

Figure 7: Dependence of elastic moduli E, G, K (1010Pa) on temperature for alloy Au-15% Cu-5%Si at P=70 GPa.
Figure 7:

Dependence of elastic moduli E, G, K (1010Pa) on temperature for alloy Au-15% Cu-5%Si at P=70 GPa.

Figure 8: Dependence of elastic constants C11, C12, C44 (1010Pa) on temperature for alloy Au-15%xCu-5%Si at P=70 GPa.
Figure 8:

Dependence of elastic constants C11, C12, C44 (1010Pa) on temperature for alloy Au-15%xCu-5%Si at P=70 GPa.

Table 2:

Nearest neighbor distance and elastic moduli E, K, G of Au at P=0, T=300 K calculated by the SMM and from EXPT [15, 16].

Methoda(Ao)E1010PaK1010PaG1010Pa
SMM2.84548.9614.943.20
EXPT2.88388.91 [15]16.70 [16]3.10 [16]

According to our numerical results, for alloy AuCuSi at the same pressure, temperature and concentration of substitution atoms when the concentration of interstitial atoms increases, the mean nearest neighbor distance also increases. For example for alloy AuCuSi at T=300 K, P=70 GPa and cCu=10% when cSi increases from 0% to 5%, r1 increases from 2.3228Aoto2.7086Ao.

For alloy AuCuSi at the same temperature, concentration of substitution atoms and concentration of interstitial atoms when pressure increases, the mean nearest neighbor distance decreases. For example for alloy AuCuSi at T=300K, cCu=10%, cSi=5% when P increases from 0 to 70 GPa, r1 decreases from 2.8740Ao to 2.7086Ao.

For alloy AuCuSi at the same pressure, temperature and concentration of interstitial atoms when the concentration of substitution atoms increases, the mean nearest neighbor distance decreases. For example for alloy AuCuSi at T=300 K, P=30 GPa, cSi=5% when cCu increases from 0% to 15% r1 decreases from 2.8630Ao to 2.1550Ao.

For alloy AuCuSi at the same pressure, concentration of substitution atoms and concentration of interstitial atoms when temperature increases, the mean nearest neighbor distance increases. For example for alloy AuCuSi at P=0, cCu=10 % và cSi=3 % when T increases from 50 K to 1000 K, r1 increases from 2.8447Ao to 3.2793Ao.

For alloy AuCuSi at the same pressure, temperature and concentration of substitution atoms when the concentration of interstitial atoms increases, the elastic moduli E, G, K decreases. For example for alloy AuCuSi at T=300K, P=70GPa and cCu=10% when cSi increases from 0% to 5%, E decreases from 3.5604.1011 Pa to 1.2905.1011Pa.

For alloy AuCuSi at the same temperature, concentration of substitution atoms and concentration of interstitial atoms when pressure increases, the elastic moduli E, G, K increases. For example for alloy AuCuSi at T=300K, cCu=10%, cSi=5% when P increases from 0 to 70 GPa, E increases from 0.6966.1011Pa to 1.2950.1011Pa.

For alloy AuCuSi at the same pressure, temperature and concentration of interstitial atoms when the concentration of substitution atoms increases, the elastic moduli E, G, K increases. For example for alloy AuCuSi at T=300K, P=30GPa, cSi=5% when cCu increases from 0% to 15%, E increases from 0.9558.1011 Pa to 0.9697.1011Pa.

For alloy AuCuSi at the same pressure, concentration of substitution atoms and concentration of interstitial atoms when temperature increases, the elastic moduli E, G, K decreases. For example for alloy AuCuSi at P=0, cCr=10%, cSi=3% when T increases from 50 K to 1000 K E decreases from 0.9991.1011 Pa to 0.7959.1011Pa.

For alloy AuCuSi at the same pressure, temperature and concentration of substitution atoms when the concentration of interstitial atoms increases, the elastic constants C11,C12, C44 decreases. For example for alloy AuCuSi at T=300K, P=10GPa, cCu=10% when cSi increases from 0% to 5%, C11 decreases from 4.4653.1011 Pa to 2.2478.1011Pa.

For alloy AuCuSi at the same temperature, concentration of substitution atoms and concentration of interstitial atoms when pressure increases, the elastic constants C11,C12, C44 increases. For example for alloy AuCuSi at T=300K, cCu=10%, cSi=1% when P increases from 0 to 70GPa, C11increases from 3.0798.1011 Pa to 3.8446.1011Pa.

For alloy AuCuSi at the same pressure, temperature and concentration of interstitial atoms when the concentration of substitution atoms increases, the elastic constants C11,C12, C44 decreases. For example for alloy AuCuSi at T=300K, P=30GPa, cSi=5% when cCu increases from 0% to 15% C11 decreases from 3.0977.1011 Pa to 2.6097.1011Pa.

For alloy AuCuSi at the same pressure, concentration of substitution atoms and concentration of interstitial atoms when temperature increases, the elastic constants C11,C12, C44 decreases. For example for alloy AuCuSi at P=70GPa, cCu=10%, cSi=5% when T increases from 50 K to 1000 K, C11 decreases from 4.1345.1011 Pa to 3.6188.1011Pa.

When the concentration of substitution atoms and the concentration of interstitial atoms are equal to zero, the mean nearest neighbor distance, the elastic moduli and the elastic constants of alloy AuCuSi respectively becomes the mean nearest neighbor distance, the elastic moduli and the elastic constants of metal Au. The dependence of mean nearest neighbor distance, the elastic moduli and the elastic constants on pressure and concentration of interstitial atoms for alloy AuCuSi is the same as the dependence of mean nearest neighbor distance, the elastic moduli and the elastic constants on pressure and concentration of interstitial atoms for interstitial alloy AuSi, respectively. The dependence of mean nearest neighbor distance, the elastic moduli and the elastic constants on pressure and concentration of substitution atoms for alloy AuCuSi is the same as the dependence of mean nearest neighbor distance, the elastic moduli and the elastic constants on pressure and concentration of substitution atoms for substitution alloy AuCu, respectively.

Table 2 gives the nearest neighbor distance and the elastic moduli of Au at T=300K, P=0 according to the SMM and the experimental data [15, 16]. Table 3 gives the atomic volume and the rigidity modulus of Au near the melting temperature calculated by the SMM and other calculation [17]. Table 4 gives the elastic moduli E, K, G of Au at P=0 and in different temperatures calculated by the SMM. Table 5 gives the elastic constants C11, C12, C44 of Au at P=0 and T=300K calculated by the SMM and from EXPT [15]. Table 6 gives the elastic constants C11, C12, C44 of Au at T=300K and P=0 calculated by the SMM, other calculations [18, 19, 26] and from EXPT [16]. Table 7 and Table 8 give the dependences of elastic moduli E, K, G and elastic constants C11, C12, C44 on temperature and concentration of substitution atoms Cu for substitution alloy AuCu at P=0.

Table 3:

Atomic volume and rigidity modulus of Au near melting temperature calculated by the SMM and other calculation [17].

V[10–30 m3]SMM17.29
CAL [17]17.88
G1010PaSMM15.88
CAL [17]15.20
Table 4:

Elastic moduli E, K, G of Au at P=0 and in different temperatures calculated by the SMM.

T(K)1002003005007001000
E1010Pa9.569.278.968.277.496.15
K1010Pa15.9315.4514.9413.7912.4810.24
G1010Pa3.413.313.202.952.672.19
Table 5:

Elastic constants C11, C12, C44 of Au at T=300 K and P=0 calculated by the SMM and from EXPT [15].

C11[1011Pa]SMM1.92
EXPT [15]1.92
C12[1011Pa]SMM1.28
EXPT [15]1.63
C44[1011Pa]SMM0.32
EXPT [15]0.42
Table 6:

Elastic constants C11, C12, C44 of Au at T=300 K and P=0 calculated by the SMM, other calculations [18, 19, 20, 21, 22, 23, 24, 25, 26] and from EXPT [16].

SMMEXPTOther calculations
[16][18][19][20][21][22][23][24][25][26]
C11[1011Pa]1.921.921.921.831.792.091.361.501.971.842.00
C12[1011Pa]1.281.651.661.541.471.750.911.291.841.541.73
C44[1011Pa]0.320.420.390.450.420.310.490.700.520.430.33
Table 7:

Dependence of elastic moduli E, G, K (1010Pa) on temperature and concentration of substitution atoms Cu for substitution alloy AuCu at P=0.

AlloyT(K)200300400500600700800
Au-1%CuE13.4413.1412.8112.4712.1111.7311.34
K20.3219.8619.3718.8618.3217.7517.15
G4.844.734.614.494.364.224.08
Au-3%CuE13.4813,1712.8412.4912.1211.7411.33
K20.3019.8319.3318.8118.2617.6817,07
G4.854.744.624.494.364.224.08
Au-5%CuE13.5113.2012,8612.5112.1311.7411.32
K20.2719.7919.2918.7618.2117.6217.00
G4.874.754.634.504.384.234.08
Au-7%CuE13.5513.2312.8812.5212.1411.7411.31
K20.2419.7619.2518.7218.1517.5516.93
G4.884.764.644.514.374.234.07
Au-10%CuE13.6013.2712.9212.5512.1611.7411.30
K20.2019.7119.2018.6518.0717.4616.82
G4.904.784.664.524.384.234.07
Table 8:

Dependence of elastic constants C11, C12, C44 (1011Pa) on temperature and concentration of substitution atoms Cu for substitution alloy AuCu at P=0.

AlloyT(K)200300400500600700800
Au-1%CuC112.682.622.552.482.412.342.26
C121.711.671.631.591.541.491.44
C440.480.470.460.450.440.420.41
Au-3%CuC112/682.612.552.482.412.222.25
C121.711.671.621.581.531.491.46
C440.490.470.460.450.440.420.41
Au-5%CuC112.672.612.552.482.402.332.24
C121.701.661.621.581.531.481.43
C440.490.480.460.450.440.420.41
Au-7%CuC112.672.612.542.472.402.322.23
C121.701.661.621.571.521.471.42
C440.490.480.460.450.440.420.41
Au-10%CuC112.672.612.542.472.392.312.22
C121.691.651.611.561.511.461.41
C440.490.480.470.450.440.420.41

Conclusion

The analytic expressions of the free energy, the mean nearest neighbor distance between two atoms, the elastic moduli such as the Young modulus, the bulk modulus, the rigidity modulus and the elastic constants depending on temperature, concentration of substitution atoms and concentration of interstitial atoms for substitution alloy AB with interstitial atom C and BCC structure under pressure are derived by the SMM. The numerical results for alloy AuCuSi are in good agreement with the numerical results for substitution alloy AuCu, interstitial alloy AuSi and main metal Au. Temperature changes from 5 to 1000 K, pressure changes from 0 to 70 GPa, the concentration of substitution atoms changes from 0% to 10% and the concentration of interstitial atoms changes from 0% to 5%.

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Received: 2018-02-16
Accepted: 2018-07-21
Published Online: 2018-09-26
Published in Print: 2019-02-25

© 2019 Walter de Gruyter GmbH, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Articles in the same Issue

  1. Frontmatter
  2. Review Article
  3. Research on the Influence of Furnace Structure on Copper Cooling Stave Life
  4. Influence of High Temperature Oxidation on Hydrogen Absorption and Degradation of Zircaloy-2 and Zr 700 Alloys
  5. Correlation between Travel Speed, Microstructure, Mechanical Properties and Wear Characteristics of Ni-Based Hardfaced Deposits over 316LN Austenitic Stainless Steel
  6. Factors Influencing Gas Generation Behaviours of Lump Coal Used in COREX Gasifier
  7. Experiment Research on Pulverized Coal Combustion in the Tuyere of Oxygen Blast Furnace
  8. Phosphate Capacities of CaO–FeO–SiO2–Al2O3/Na2O/TiO2 Slags
  9. Microstructure and Interface Bonding Strength of WC-10Ni/NiCrBSi Composite Coating by Vacuum Brazing
  10. Refill Friction Stir Spot Welding of Dissimilar 6061/7075 Aluminum Alloy
  11. Solvothermal Synthesis and Magnetic Properties of Monodisperse Ni0.5Zn0.5Fe2O4 Hollow Nanospheres
  12. On the Capability of Logarithmic-Power Model for Prediction of Hot Deformation Behavior of Alloy 800H at High Strain Rates
  13. 3D Heat Conductivity Model of Mold Based on Node Temperature Inheritance
  14. 3D Microstructure and Micromechanical Properties of Minerals in Vanadium-Titanium Sinter
  15. Effect of Martensite Structure and Carbide Precipitates on Mechanical Properties of Cr-Mo Alloy Steel with Different Cooling Rate
  16. The Interaction between Erosion Particle and Gas Stream in High Temperature Gas Burner Rig for Thermal Barrier Coatings
  17. Permittivity Study of a CuCl Residue at 13–450 °C and Elucidation of the Microwave Intensification Mechanism for Its Dechlorination
  18. Study on Carbothermal Reduction of Titania in Molten Iron
  19. The Sequence of the Phase Growth during Diffusion in Ti-Based Systems
  20. Growth Kinetics of CoB–Co2B Layers Using the Powder-Pack Boriding Process Assisted by a Direct Current Field
  21. High-Temperature Flow Behaviour and Constitutive Equations for a TC17 Titanium Alloy
  22. Research on Three-Roll Screw Rolling Process for Ti6Al4V Titanium Alloy Bar
  23. Continuous Cooling Transformation of Undeformed and Deformed High Strength Crack-Arrest Steel Plates for Large Container Ships
  24. Formation Mechanism and Influence Factors of the Sticker between Solidified Shell and Mold in Continuous Casting of Steel
  25. Casting Defects in Transition Layer of Cu/Al Composite Castings Prepared Using Pouring Aluminum Method and Their Formation Mechanism
  26. Effect of Current on Segregation and Inclusions Characteristics of Dual Alloy Ingot Processed by Electroslag Remelting
  27. Investigation of Growth Kinetics of Fe2B Layers on AISI 1518 Steel by the Integral Method
  28. Microstructural Evolution and Phase Transformation on the X-Y Surface of Inconel 718 Ni-Based Alloys Fabricated by Selective Laser Melting under Different Heat Treatment
  29. Characterization of Mn-Doped Co3O4 Thin Films Prepared by Sol Gel-Based Dip-Coating Process
  30. Deposition Characteristics of Multitrack Overlayby Plasma Transferred Arc Welding on SS316Lwith Co-Cr Based Alloy – Influence ofProcess Parameters
  31. Elastic Moduli and Elastic Constants of Alloy AuCuSi With FCC Structure Under Pressure
  32. Effect of Cl on Softening and Melting Behaviors of BF Burden
  33. Effect of MgO Injection on Smelting in a Blast Furnace
  34. Structural Characteristics and Hydration Kinetics of Oxidized Steel Slag in a CaO-FeO-SiO2-MgO System
  35. Optimization of Microwave-Assisted Oxidation Roasting of Oxide–Sulphide Zinc Ore with Addition of Manganese Dioxide Using Response Surface Methodology
  36. Hydraulic Study of Bubble Migration in Liquid Titanium Alloy Melt during Vertical Centrifugal Casting Process
  37. Investigation on Double Wire Metal Inert Gas Welding of A7N01-T4 Aluminum Alloy in High-Speed Welding
  38. Oxidation Behaviour of Welded ASTM-SA210 GrA1 Boiler Tube Steels under Cyclic Conditions at 900°C in Air
  39. Study on the Evolution of Damage Degradation at Different Temperatures and Strain Rates for Ti-6Al-4V Alloy
  40. Pack-Boriding of Pure Iron with Powder Mixtures Containing ZrB2
  41. Evolution of Interfacial Features of MnO-SiO2 Type Inclusions/Steel Matrix during Isothermal Heating at Low Temperatures
  42. Effect of MgO/Al2O3 Ratio on Viscosity of Blast Furnace Primary Slag
  43. The Microstructure and Property of the Heat Affected zone in C-Mn Steel Treated by Rare Earth
  44. Microwave-Assisted Molten-Salt Facile Synthesis of Chromium Carbide (Cr3C2) Coatings on the Diamond Particles
  45. Effects of B on the Hot Ductility of Fe-36Ni Invar Alloy
  46. Impurity Distribution after Solidification of Hypereutectic Al-Si Melts and Eutectic Al-Si Melt
  47. Induced Electro-Deposition of High Melting-Point Phases on MgO–C Refractory in CaO–Al2O3–SiO2 – (MgO) Slag at 1773 K
  48. Microstructure and Mechanical Properties of 14Cr-ODS Steels with Zr Addition
  49. A Review of Boron-Rich Silicon Borides Basedon Thermodynamic Stability and Transport Properties of High-Temperature Thermoelectric Materials
  50. Siliceous Manganese Ore from Eastern India:A Potential Resource for Ferrosilicon-Manganese Production
  51. A Strain-Compensated Constitutive Model for Describing the Hot Compressive Deformation Behaviors of an Aged Inconel 718 Superalloy
  52. Surface Alloys of 0.45 C Carbon Steel Produced by High Current Pulsed Electron Beam
  53. Deformation Behavior and Processing Map during Isothermal Hot Compression of 49MnVS3 Non-Quenched and Tempered Steel
  54. A Constitutive Equation for Predicting Elevated Temperature Flow Behavior of BFe10-1-2 Cupronickel Alloy through Double Multiple Nonlinear Regression
  55. Oxidation Behavior of Ferritic Steel T22 Exposed to Supercritical Water
  56. A Multi Scale Strategy for Simulation of Microstructural Evolutions in Friction Stir Welding of Duplex Titanium Alloy
  57. Partition Behavior of Alloying Elements in Nickel-Based Alloys and Their Activity Interaction Parameters and Infinite Dilution Activity Coefficients
  58. Influence of Heating on Tensile Physical-Mechanical Properties of Granite
  59. Comparison of Al-Zn-Mg Alloy P-MIG Welded Joints Filled with Different Wires
  60. Microstructure and Mechanical Properties of Thick Plate Friction Stir Welds for 6082-T6 Aluminum Alloy
  61. Research Article
  62. Kinetics of oxide scale growth on a (Ti, Mo)5Si3 based oxidation resistant Mo-Ti-Si alloy at 900-1300∘C
  63. Calorimetric study on Bi-Cu-Sn alloys
  64. Mineralogical Phase of Slag and Its Effect on Dephosphorization during Converter Steelmaking Using Slag-Remaining Technology
  65. Controllability of joint integrity and mechanical properties of friction stir welded 6061-T6 aluminum and AZ31B magnesium alloys based on stationary shoulder
  66. Cellular Automaton Modeling of Phase Transformation of U-Nb Alloys during Solidification and Consequent Cooling Process
  67. The effect of MgTiO3Adding on Inclusion Characteristics
  68. Cutting performance of a functionally graded cemented carbide tool prepared by microwave heating and nitriding sintering
  69. Creep behaviour and life assessment of a cast nickel – base superalloy MAR – M247
  70. Failure mechanism and acoustic emission signal characteristics of coatings under the condition of impact indentation
  71. Reducing Surface Cracks and Improving Cleanliness of H-Beam Blanks in Continuous Casting — Improving continuous casting of H-beam blanks
  72. Rhodium influence on the microstructure and oxidation behaviour of aluminide coatings deposited on pure nickel and nickel based superalloy
  73. The effect of Nb content on precipitates, microstructure and texture of grain oriented silicon steel
  74. Effect of Arc Power on the Wear and High-temperature Oxidation Resistances of Plasma-Sprayed Fe-based Amorphous Coatings
  75. Short Communication
  76. Novel Combined Feeding Approach to Produce Quality Al6061 Composites for Heat Sinks
  77. Research Article
  78. Micromorphology change and microstructure of Cu-P based amorphous filler during heating process
  79. Controlling residual stress and distortion of friction stir welding joint by external stationary shoulder
  80. Research on the ingot shrinkage in the electroslag remelting withdrawal process for 9Cr3Mo roller
  81. Production of Mo2NiB2 Based Hard Alloys by Self-Propagating High-Temperature Synthesis
  82. The Morphology Analysis of Plasma-Sprayed Cast Iron Splats at Different Substrate Temperatures via Fractal Dimension and Circularity Methods
  83. A Comparative Study on Johnson–Cook, Modified Johnson–Cook, Modified Zerilli–Armstrong and Arrhenius-Type Constitutive Models to Predict Hot Deformation Behavior of TA2
  84. Dynamic absorption efficiency of paracetamol powder in microwave drying
  85. Preparation and Properties of Blast Furnace Slag Glass Ceramics Containing Cr2O3
  86. Influence of unburned pulverized coal on gasification reaction of coke in blast furnace
  87. Effect of PWHT Conditions on Toughness and Creep Rupture Strength in Modified 9Cr-1Mo Steel Welds
  88. Role of B2O3 on structure and shear-thinning property in CaO–SiO2–Na2O-based mold fluxes
  89. Effect of Acid Slag Treatment on the Inclusions in GCr15 Bearing Steel
  90. Recovery of Iron and Zinc from Blast Furnace Dust Using Iron-Bath Reduction
  91. Phase Analysis and Microstructural Investigations of Ce2Zr2O7 for High-Temperature Coatings on Ni-Base Superalloy Substrates
  92. Combustion Characteristics and Kinetics Study of Pulverized Coal and Semi-Coke
  93. Mechanical and Electrochemical Characterization of Supersolidus Sintered Austenitic Stainless Steel (316 L)
  94. Synthesis and characterization of Cu doped chromium oxide (Cr2O3) thin films
  95. Ladle Nozzle Clogging during casting of Silicon-Steel
  96. Thermodynamics and Industrial Trial on Increasing the Carbon Content at the BOF Endpoint to Produce Ultra-Low Carbon IF Steel by BOF-RH-CSP Process
  97. Research Article
  98. Effect of Boundary Conditions on Residual Stresses and Distortion in 316 Stainless Steel Butt Welded Plate
  99. Numerical Analysis on Effect of Additional Gas Injection on Characteristics around Raceway in Melter Gasifier
  100. Variation on thermal damage rate of granite specimen with thermal cycle treatment
  101. Effects of Fluoride and Sulphate Mineralizers on the Properties of Reconstructed Steel Slag
  102. Effect of Basicity on Precipitation of Spinel Crystals in a CaO-SiO2-MgO-Cr2O3-FeO System
  103. Review Article
  104. Exploitation of Mold Flux for the Ti-bearing Welding Wire Steel ER80-G
  105. Research Article
  106. Furnace heat prediction and control model and its application to large blast furnace
  107. Effects of Different Solid Solution Temperatures on Microstructure and Mechanical Properties of the AA7075 Alloy After T6 Heat Treatment
  108. Study of the Viscosity of a La2O3-SiO2-FeO Slag System
  109. Tensile Deformation and Work Hardening Behaviour of AISI 431 Martensitic Stainless Steel at Elevated Temperatures
  110. The Effectiveness of Reinforcement and Processing on Mechanical Properties, Wear Behavior and Damping Response of Aluminum Matrix Composites
https://doi.org/10.1515/htmp-2018-0027
Keywords for this article
substitution and interstitial alloy; Young modulus; bulk modulus; rigidity modulus; elastic constant; Poisson ratio
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Articles in the same Issue

  1. Frontmatter
  2. Review Article
  3. Research on the Influence of Furnace Structure on Copper Cooling Stave Life
  4. Influence of High Temperature Oxidation on Hydrogen Absorption and Degradation of Zircaloy-2 and Zr 700 Alloys
  5. Correlation between Travel Speed, Microstructure, Mechanical Properties and Wear Characteristics of Ni-Based Hardfaced Deposits over 316LN Austenitic Stainless Steel
  6. Factors Influencing Gas Generation Behaviours of Lump Coal Used in COREX Gasifier
  7. Experiment Research on Pulverized Coal Combustion in the Tuyere of Oxygen Blast Furnace
  8. Phosphate Capacities of CaO–FeO–SiO2–Al2O3/Na2O/TiO2 Slags
  9. Microstructure and Interface Bonding Strength of WC-10Ni/NiCrBSi Composite Coating by Vacuum Brazing
  10. Refill Friction Stir Spot Welding of Dissimilar 6061/7075 Aluminum Alloy
  11. Solvothermal Synthesis and Magnetic Properties of Monodisperse Ni0.5Zn0.5Fe2O4 Hollow Nanospheres
  12. On the Capability of Logarithmic-Power Model for Prediction of Hot Deformation Behavior of Alloy 800H at High Strain Rates
  13. 3D Heat Conductivity Model of Mold Based on Node Temperature Inheritance
  14. 3D Microstructure and Micromechanical Properties of Minerals in Vanadium-Titanium Sinter
  15. Effect of Martensite Structure and Carbide Precipitates on Mechanical Properties of Cr-Mo Alloy Steel with Different Cooling Rate
  16. The Interaction between Erosion Particle and Gas Stream in High Temperature Gas Burner Rig for Thermal Barrier Coatings
  17. Permittivity Study of a CuCl Residue at 13–450 °C and Elucidation of the Microwave Intensification Mechanism for Its Dechlorination
  18. Study on Carbothermal Reduction of Titania in Molten Iron
  19. The Sequence of the Phase Growth during Diffusion in Ti-Based Systems
  20. Growth Kinetics of CoB–Co2B Layers Using the Powder-Pack Boriding Process Assisted by a Direct Current Field
  21. High-Temperature Flow Behaviour and Constitutive Equations for a TC17 Titanium Alloy
  22. Research on Three-Roll Screw Rolling Process for Ti6Al4V Titanium Alloy Bar
  23. Continuous Cooling Transformation of Undeformed and Deformed High Strength Crack-Arrest Steel Plates for Large Container Ships
  24. Formation Mechanism and Influence Factors of the Sticker between Solidified Shell and Mold in Continuous Casting of Steel
  25. Casting Defects in Transition Layer of Cu/Al Composite Castings Prepared Using Pouring Aluminum Method and Their Formation Mechanism
  26. Effect of Current on Segregation and Inclusions Characteristics of Dual Alloy Ingot Processed by Electroslag Remelting
  27. Investigation of Growth Kinetics of Fe2B Layers on AISI 1518 Steel by the Integral Method
  28. Microstructural Evolution and Phase Transformation on the X-Y Surface of Inconel 718 Ni-Based Alloys Fabricated by Selective Laser Melting under Different Heat Treatment
  29. Characterization of Mn-Doped Co3O4 Thin Films Prepared by Sol Gel-Based Dip-Coating Process
  30. Deposition Characteristics of Multitrack Overlayby Plasma Transferred Arc Welding on SS316Lwith Co-Cr Based Alloy – Influence ofProcess Parameters
  31. Elastic Moduli and Elastic Constants of Alloy AuCuSi With FCC Structure Under Pressure
  32. Effect of Cl on Softening and Melting Behaviors of BF Burden
  33. Effect of MgO Injection on Smelting in a Blast Furnace
  34. Structural Characteristics and Hydration Kinetics of Oxidized Steel Slag in a CaO-FeO-SiO2-MgO System
  35. Optimization of Microwave-Assisted Oxidation Roasting of Oxide–Sulphide Zinc Ore with Addition of Manganese Dioxide Using Response Surface Methodology
  36. Hydraulic Study of Bubble Migration in Liquid Titanium Alloy Melt during Vertical Centrifugal Casting Process
  37. Investigation on Double Wire Metal Inert Gas Welding of A7N01-T4 Aluminum Alloy in High-Speed Welding
  38. Oxidation Behaviour of Welded ASTM-SA210 GrA1 Boiler Tube Steels under Cyclic Conditions at 900°C in Air
  39. Study on the Evolution of Damage Degradation at Different Temperatures and Strain Rates for Ti-6Al-4V Alloy
  40. Pack-Boriding of Pure Iron with Powder Mixtures Containing ZrB2
  41. Evolution of Interfacial Features of MnO-SiO2 Type Inclusions/Steel Matrix during Isothermal Heating at Low Temperatures
  42. Effect of MgO/Al2O3 Ratio on Viscosity of Blast Furnace Primary Slag
  43. The Microstructure and Property of the Heat Affected zone in C-Mn Steel Treated by Rare Earth
  44. Microwave-Assisted Molten-Salt Facile Synthesis of Chromium Carbide (Cr3C2) Coatings on the Diamond Particles
  45. Effects of B on the Hot Ductility of Fe-36Ni Invar Alloy
  46. Impurity Distribution after Solidification of Hypereutectic Al-Si Melts and Eutectic Al-Si Melt
  47. Induced Electro-Deposition of High Melting-Point Phases on MgO–C Refractory in CaO–Al2O3–SiO2 – (MgO) Slag at 1773 K
  48. Microstructure and Mechanical Properties of 14Cr-ODS Steels with Zr Addition
  49. A Review of Boron-Rich Silicon Borides Basedon Thermodynamic Stability and Transport Properties of High-Temperature Thermoelectric Materials
  50. Siliceous Manganese Ore from Eastern India:A Potential Resource for Ferrosilicon-Manganese Production
  51. A Strain-Compensated Constitutive Model for Describing the Hot Compressive Deformation Behaviors of an Aged Inconel 718 Superalloy
  52. Surface Alloys of 0.45 C Carbon Steel Produced by High Current Pulsed Electron Beam
  53. Deformation Behavior and Processing Map during Isothermal Hot Compression of 49MnVS3 Non-Quenched and Tempered Steel
  54. A Constitutive Equation for Predicting Elevated Temperature Flow Behavior of BFe10-1-2 Cupronickel Alloy through Double Multiple Nonlinear Regression
  55. Oxidation Behavior of Ferritic Steel T22 Exposed to Supercritical Water
  56. A Multi Scale Strategy for Simulation of Microstructural Evolutions in Friction Stir Welding of Duplex Titanium Alloy
  57. Partition Behavior of Alloying Elements in Nickel-Based Alloys and Their Activity Interaction Parameters and Infinite Dilution Activity Coefficients
  58. Influence of Heating on Tensile Physical-Mechanical Properties of Granite
  59. Comparison of Al-Zn-Mg Alloy P-MIG Welded Joints Filled with Different Wires
  60. Microstructure and Mechanical Properties of Thick Plate Friction Stir Welds for 6082-T6 Aluminum Alloy
  61. Research Article
  62. Kinetics of oxide scale growth on a (Ti, Mo)5Si3 based oxidation resistant Mo-Ti-Si alloy at 900-1300∘C
  63. Calorimetric study on Bi-Cu-Sn alloys
  64. Mineralogical Phase of Slag and Its Effect on Dephosphorization during Converter Steelmaking Using Slag-Remaining Technology
  65. Controllability of joint integrity and mechanical properties of friction stir welded 6061-T6 aluminum and AZ31B magnesium alloys based on stationary shoulder
  66. Cellular Automaton Modeling of Phase Transformation of U-Nb Alloys during Solidification and Consequent Cooling Process
  67. The effect of MgTiO3Adding on Inclusion Characteristics
  68. Cutting performance of a functionally graded cemented carbide tool prepared by microwave heating and nitriding sintering
  69. Creep behaviour and life assessment of a cast nickel – base superalloy MAR – M247
  70. Failure mechanism and acoustic emission signal characteristics of coatings under the condition of impact indentation
  71. Reducing Surface Cracks and Improving Cleanliness of H-Beam Blanks in Continuous Casting — Improving continuous casting of H-beam blanks
  72. Rhodium influence on the microstructure and oxidation behaviour of aluminide coatings deposited on pure nickel and nickel based superalloy
  73. The effect of Nb content on precipitates, microstructure and texture of grain oriented silicon steel
  74. Effect of Arc Power on the Wear and High-temperature Oxidation Resistances of Plasma-Sprayed Fe-based Amorphous Coatings
  75. Short Communication
  76. Novel Combined Feeding Approach to Produce Quality Al6061 Composites for Heat Sinks
  77. Research Article
  78. Micromorphology change and microstructure of Cu-P based amorphous filler during heating process
  79. Controlling residual stress and distortion of friction stir welding joint by external stationary shoulder
  80. Research on the ingot shrinkage in the electroslag remelting withdrawal process for 9Cr3Mo roller
  81. Production of Mo2NiB2 Based Hard Alloys by Self-Propagating High-Temperature Synthesis
  82. The Morphology Analysis of Plasma-Sprayed Cast Iron Splats at Different Substrate Temperatures via Fractal Dimension and Circularity Methods
  83. A Comparative Study on Johnson–Cook, Modified Johnson–Cook, Modified Zerilli–Armstrong and Arrhenius-Type Constitutive Models to Predict Hot Deformation Behavior of TA2
  84. Dynamic absorption efficiency of paracetamol powder in microwave drying
  85. Preparation and Properties of Blast Furnace Slag Glass Ceramics Containing Cr2O3
  86. Influence of unburned pulverized coal on gasification reaction of coke in blast furnace
  87. Effect of PWHT Conditions on Toughness and Creep Rupture Strength in Modified 9Cr-1Mo Steel Welds
  88. Role of B2O3 on structure and shear-thinning property in CaO–SiO2–Na2O-based mold fluxes
  89. Effect of Acid Slag Treatment on the Inclusions in GCr15 Bearing Steel
  90. Recovery of Iron and Zinc from Blast Furnace Dust Using Iron-Bath Reduction
  91. Phase Analysis and Microstructural Investigations of Ce2Zr2O7 for High-Temperature Coatings on Ni-Base Superalloy Substrates
  92. Combustion Characteristics and Kinetics Study of Pulverized Coal and Semi-Coke
  93. Mechanical and Electrochemical Characterization of Supersolidus Sintered Austenitic Stainless Steel (316 L)
  94. Synthesis and characterization of Cu doped chromium oxide (Cr2O3) thin films
  95. Ladle Nozzle Clogging during casting of Silicon-Steel
  96. Thermodynamics and Industrial Trial on Increasing the Carbon Content at the BOF Endpoint to Produce Ultra-Low Carbon IF Steel by BOF-RH-CSP Process
  97. Research Article
  98. Effect of Boundary Conditions on Residual Stresses and Distortion in 316 Stainless Steel Butt Welded Plate
  99. Numerical Analysis on Effect of Additional Gas Injection on Characteristics around Raceway in Melter Gasifier
  100. Variation on thermal damage rate of granite specimen with thermal cycle treatment
  101. Effects of Fluoride and Sulphate Mineralizers on the Properties of Reconstructed Steel Slag
  102. Effect of Basicity on Precipitation of Spinel Crystals in a CaO-SiO2-MgO-Cr2O3-FeO System
  103. Review Article
  104. Exploitation of Mold Flux for the Ti-bearing Welding Wire Steel ER80-G
  105. Research Article
  106. Furnace heat prediction and control model and its application to large blast furnace
  107. Effects of Different Solid Solution Temperatures on Microstructure and Mechanical Properties of the AA7075 Alloy After T6 Heat Treatment
  108. Study of the Viscosity of a La2O3-SiO2-FeO Slag System
  109. Tensile Deformation and Work Hardening Behaviour of AISI 431 Martensitic Stainless Steel at Elevated Temperatures
  110. The Effectiveness of Reinforcement and Processing on Mechanical Properties, Wear Behavior and Damping Response of Aluminum Matrix Composites
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