第三组元掺杂下Ti_5Si_3弹性性质和电子结构的第一原理计算
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摘要
本文选取置换金属原子Zr、V、Nb、Cr,及间隙原子B、C、N和O作为第三组元添加入Ti5Si3中,利用基于密度泛函的第一原理超软赝势平面波法对合金化元素在Ti5Si3的占位及合金元素对其电子结构、弹性性质的影响做了分析。
置换金属元素在Ti5Si3的占位是由元素半径决定的。半径大于Ti原子的元素Zr倾向于占据非链上空间较大的Ti6g位置,半径小于Ti原子的V和Cr倾向于占据链上的Ti4d位置,Nb具有与Ti原子相当的半径,可以同时占据Ti4d位和Ti6g位。Zr元素对Ti5Si3的韧性没有影响,而V、Nb和Cr可以有效提高Ti5Si3的韧性,但是各自的机制不同。置换元素对Ti5Si3的韧性改善与其半径无关,而是由电子在靠近费米能附近的d(Me4d)–d(Me4d)成键态、反键态和d(Me6g)非键态的占据决定。成键同时有利于体模量B和剪切模量G;非键的增加则会增加体模量B,降低剪切模量G;反键会同时降低体模量B和剪切模量G。
间隙原子的添加会降低Ti5Si3的韧性。这是由于间隙原子p层电子与d(Ti6g)电子成键态加强,体模量和剪切模量同时增加。另一方面,Ti6g非键态在减少,降低了材料的体模量,提高了剪切模量。综合结果导致体模量和剪切模量都在增加,只不过体模量增加的程度没有剪切模量的大。这就导致间隙原子添加后,Ti5Si3的韧性反而在降低。
Titanium silicide, Ti5Si3 has been extensively investigated over the past few decades as a candidate material suitable for high temperature applications, due to its high melting point, low density, relatively high hardness, capacity to retain high strength up to 1200 oC, as well as good oxidation and creep resistance at and below 850 oC. However, the development and applications of Ti5Si3 are still severely restricted in recent years due to its low fracture toughness (~2.5 MPam1/2) below the ductile–brittle transition temperature. To overcome this deficiency, several toughening methodologies have been developed, including refining grains, incorporation of a second reinforcing phase to form composites, and solid solution alloying, etc. Among these approaches, element alloying is considered as a comparative way to improve the comprehensive properties of intermetallics to meet the application demands. Alloysing which can be achieved by doping with interstitial atoms, or by incorporation of substitutional atoms into Ti5Si3, has received considerable attention in recent years, can change the electronic structure, the bonding characteristics and the degree of long-rate order to enhance the ductility of crystals. Fracture studies have shown that brittleness at room temperature is not only decided by the grain boundary but also may be influenced by the chemical bonding. Therefore, it is necessary to investigate the crystal structure and chemical bonding of Ti5Si3 theoretically and systematically.
As the first principles density functional theory method develops, this approach has been widely used to investigate many intermetallic alloys. Site occupancy of alloying elements in intermetallics, the electronic structure, and the mechanical properties improvement mechanism of alloying elements using first principle calculations are the hotspot. Recently, Ti-Al, Ni-Al, Fe-Al system intermetallics have been widely investigated. However, transition-metal silicon compounds are rarely researched.
The present article has selected several alloying elements which had been investigated experimentally to be added into Ti5Si3. Substitional elements are as following: Zr, V, Nb and Cr. Interstitial elements are B, C, N and O. Site occupancy and the influence of alloying elements on the electronic structures and elastic properties have been studied through first–principles plane–wave pseudopotential total energy calculation.
The results are mainly concluded as below:
(1) The site occupancy behaviors of subtitutional elements in Ti5Si3, determined by their atom radius, are consistent with the available experimental observations: alloying elements with atomic size larger than Ti prefer to substitute the Ti in more closed space and the atoms with atomic size smaller than Ti prefer to occupy the Ti in less closed space in Ti5Si3. Among these four substitutions, only V, Nb and Cr can improve the ductility of Ti5Si3 more effectively. However, the mechanism of ductility improvement varies from each other. Both the increase of bulk modulus B and the decrease of shear modulus G are responsible for the ductility improvement in Ti5Si3 with V substitution, while Cr substitution enhances the ratio of B/G predominately through increasing the bulk modulus B, and Nb by decreasing the shear modulus G. It is shown that the ductility enhancement effect of substitutions in Ti5Si3 almost has nothing to do with the atomic size of substitutions, but can only be understood in terms of the states near EF dominated by d(Me4d)–d(Me4d) bonding, anti–bonding and d(Me6g) non–bonding states. The strengthening of d(Me4d)–d(Me4d) bonding is beneficial to increase the bulk and shear moduli. The anti–bonding of d(Me4d)–d(Me4d) can result in decrease in both the bulk and shear moduli, while the enhancement of d(Me6g) non–bonding states is beneficial to increase the bulk modulus, but adverse to the shear modulus.
(2) Investigation shows that the lattice parameter variation trend of Ti5Si3 due to interstitial additions calculated by us is consistent with references. Interstitial atom B can increase both the a and c value, C increase c value but decrease c value, and N, O derease both a and c. It is found that interstitial atoms have negative effects on the ductility of Ti5Si3. The result is found to be correlated with the bonding between Ti6g and interstitial atoms, and the decrease of Ti6g non-bonding. The Ti6g-Z bonding lead to both the increase of bulk modulus and shear modulus, but the decrease of Ti6g non-bonding reduce the bulk modulus and increase the shear modulus. The overall result increase both the bulk modulus and shear modulus, but the extent of increase in bulk modulus is not as large as that of shear modulus. Therefore, interstitial atom addtitons lower the ductility of Ti5Si3.
置换金属元素在Ti5Si3的占位是由元素半径决定的。半径大于Ti原子的元素Zr倾向于占据非链上空间较大的Ti6g位置,半径小于Ti原子的V和Cr倾向于占据链上的Ti4d位置,Nb具有与Ti原子相当的半径,可以同时占据Ti4d位和Ti6g位。Zr元素对Ti5Si3的韧性没有影响,而V、Nb和Cr可以有效提高Ti5Si3的韧性,但是各自的机制不同。置换元素对Ti5Si3的韧性改善与其半径无关,而是由电子在靠近费米能附近的d(Me4d)–d(Me4d)成键态、反键态和d(Me6g)非键态的占据决定。成键同时有利于体模量B和剪切模量G;非键的增加则会增加体模量B,降低剪切模量G;反键会同时降低体模量B和剪切模量G。
间隙原子的添加会降低Ti5Si3的韧性。这是由于间隙原子p层电子与d(Ti6g)电子成键态加强,体模量和剪切模量同时增加。另一方面,Ti6g非键态在减少,降低了材料的体模量,提高了剪切模量。综合结果导致体模量和剪切模量都在增加,只不过体模量增加的程度没有剪切模量的大。这就导致间隙原子添加后,Ti5Si3的韧性反而在降低。
Titanium silicide, Ti5Si3 has been extensively investigated over the past few decades as a candidate material suitable for high temperature applications, due to its high melting point, low density, relatively high hardness, capacity to retain high strength up to 1200 oC, as well as good oxidation and creep resistance at and below 850 oC. However, the development and applications of Ti5Si3 are still severely restricted in recent years due to its low fracture toughness (~2.5 MPam1/2) below the ductile–brittle transition temperature. To overcome this deficiency, several toughening methodologies have been developed, including refining grains, incorporation of a second reinforcing phase to form composites, and solid solution alloying, etc. Among these approaches, element alloying is considered as a comparative way to improve the comprehensive properties of intermetallics to meet the application demands. Alloysing which can be achieved by doping with interstitial atoms, or by incorporation of substitutional atoms into Ti5Si3, has received considerable attention in recent years, can change the electronic structure, the bonding characteristics and the degree of long-rate order to enhance the ductility of crystals. Fracture studies have shown that brittleness at room temperature is not only decided by the grain boundary but also may be influenced by the chemical bonding. Therefore, it is necessary to investigate the crystal structure and chemical bonding of Ti5Si3 theoretically and systematically.
As the first principles density functional theory method develops, this approach has been widely used to investigate many intermetallic alloys. Site occupancy of alloying elements in intermetallics, the electronic structure, and the mechanical properties improvement mechanism of alloying elements using first principle calculations are the hotspot. Recently, Ti-Al, Ni-Al, Fe-Al system intermetallics have been widely investigated. However, transition-metal silicon compounds are rarely researched.
The present article has selected several alloying elements which had been investigated experimentally to be added into Ti5Si3. Substitional elements are as following: Zr, V, Nb and Cr. Interstitial elements are B, C, N and O. Site occupancy and the influence of alloying elements on the electronic structures and elastic properties have been studied through first–principles plane–wave pseudopotential total energy calculation.
The results are mainly concluded as below:
(1) The site occupancy behaviors of subtitutional elements in Ti5Si3, determined by their atom radius, are consistent with the available experimental observations: alloying elements with atomic size larger than Ti prefer to substitute the Ti in more closed space and the atoms with atomic size smaller than Ti prefer to occupy the Ti in less closed space in Ti5Si3. Among these four substitutions, only V, Nb and Cr can improve the ductility of Ti5Si3 more effectively. However, the mechanism of ductility improvement varies from each other. Both the increase of bulk modulus B and the decrease of shear modulus G are responsible for the ductility improvement in Ti5Si3 with V substitution, while Cr substitution enhances the ratio of B/G predominately through increasing the bulk modulus B, and Nb by decreasing the shear modulus G. It is shown that the ductility enhancement effect of substitutions in Ti5Si3 almost has nothing to do with the atomic size of substitutions, but can only be understood in terms of the states near EF dominated by d(Me4d)–d(Me4d) bonding, anti–bonding and d(Me6g) non–bonding states. The strengthening of d(Me4d)–d(Me4d) bonding is beneficial to increase the bulk and shear moduli. The anti–bonding of d(Me4d)–d(Me4d) can result in decrease in both the bulk and shear moduli, while the enhancement of d(Me6g) non–bonding states is beneficial to increase the bulk modulus, but adverse to the shear modulus.
(2) Investigation shows that the lattice parameter variation trend of Ti5Si3 due to interstitial additions calculated by us is consistent with references. Interstitial atom B can increase both the a and c value, C increase c value but decrease c value, and N, O derease both a and c. It is found that interstitial atoms have negative effects on the ductility of Ti5Si3. The result is found to be correlated with the bonding between Ti6g and interstitial atoms, and the decrease of Ti6g non-bonding. The Ti6g-Z bonding lead to both the increase of bulk modulus and shear modulus, but the decrease of Ti6g non-bonding reduce the bulk modulus and increase the shear modulus. The overall result increase both the bulk modulus and shear modulus, but the extent of increase in bulk modulus is not as large as that of shear modulus. Therefore, interstitial atom addtitons lower the ductility of Ti5Si3.
引文
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