- Email: [email protected]
Abrasive wear and electronic properties of materials
Wear, 126 (1988)
219 - 222
219
Research Report
Abrasive wear and electronic properties of materials E. V. SUBRAMANIAN Department Engineering, (Received
and Z. ELIEZER
of Mechanical Engineering and the Center for Materials Science The University of Texas at Austin, Austin, TX 78712 (U.S.A.)
March 21,1988;
accepted
and
April 11,1988)
An important electronic property, namely the electron density at the Wigner-Seitz atomic cell boundary, has been related to the abrasive wear resistance data in the case of pure metals. This property works as well as an indicator of wear as other solid state electronic properties such as bonding energy and cohesive strength that have hitherto been correlated with abrasive wear resistance of pure metals.
1. Introduction Abrasive wear resistance has been commonly related to bulk or surface hardness for a wide spectrum of metals. This criterion for wear applies well to metals in their pure or annealed state, particularly when they are classified according to the crystal structure, b.c.c., f.c.c. or h.c.p. However, numerous difficulties are encountered in attempting to find a similar relation between abrasive wear and this mechanical property while considering the effects of alloying and cold work; it has been found that conventional strengthening mechanisms, such as solid solution strengthening, cold work or precipitation hardening, fail to enhance wear resistance to a degree proportional to the increase in hardness-strength associated with these processes. Microscopically, the process of wear involves continuous creation and modification of new surfaces by breaking metallic or atomic bonds. The delamination theory for wear [l] relates wear to fracture mechanics and deals with wear as a crack propagation process. An attempt has been made in this study to examine wear in the light of fundamental electronic properties in the case of pure metals. 2. An electronic abrasive wear index There have been but a few studies on abrasive wear of metals and alloys, and their link to solid state electronic properties such as bonding 0043-1646/86/$3.60
@ Elsevier Sequoia/Printed
in The Netherlands
220
energy or cohesive strength. In one attempt [2], metal-to-metal bonding energy and melting point have been suggested as fundamental quantities correlating abrasive wear. In another study, cohesive energy [3] has been related to wear though large deviations exist for some metals. One of the parameters of fundamental interest is the electron density distribution which plays a vital role in influencing the bulk and surface properties of metals and alloys. Specifically, the electron density distribution at the Wigner-Seitz atomic cells has been correlated with compressibility [ 41, surface tension and heat of vaporization [5] in pure metals. This seems to suggest that electron density may be related to other physical and mechanical properties as well. With this as the background, the electron density data will be examined for transition and non-transition metals. Table 1 shows the values of relative abrasive wear resistance of several metals and the magnitudes of their electron density at the atomic cell boundary. The table also displays the values of metal-to-metal bond energy and the melting points of these metals. The electron density values were taken from ref. 5, and other data from ref. 2. Abrasive wear has been plotted against the listed properties in Figs. 1 - 3, and the coefficients of correlation have been determined for each linear plot. The factors of correlation with respect to relative abrasive wear resistance of bond energy and melting point TABLE 1 Abrasive wear and other properties of metals Metal
Pb Mg Sn Cd Al Zn Au CU Ag Pd Zr Pt Ni co Fe Mn Cr Rh MO Be W
Relative wear resistance
0.9
2.7 2.8 3.0 4.0 6.3 7.0 9.3 7.5 10.6 12.0 12.5 18.0 20.0 20.5 27.0 30.0 35.0 39.0 45.0 60.0
Electron density (density unit)a
Bond energy (kcal)
Melting point (“C)
1.52 1.60 1.91 1.91 2.69 2.30 3.87 3.18 2.69 4.66 2.69 5.64 5.36 5.36 5.55 4.17 5.18 5.45 5.55 4.10 5.93
7.8 6.0 12.1 8.9 12.5 10.4 14.6 13.5 11.4 15.0 24.4 22.7 16.9 16.9 16.6 11.7 23.6 22.1 39.6 13.0 50.5
327 650 232 321 660 420 1063 1084 960 1550 1852 1769 1452 1490 1535 1244 1875 2250 2610 1283 3410
*Note: 1 density unit = 6 X 10z2 electrons crne3.
221
880 70
f
I
60
!z 2
30
-
20 10 0
1000
0
3000
2000 metting point, C
Fig. 1. Melting point us. relative wear resistance.
.__ 90 8 5
*O 70
160 f
50
i
40
p
30
p
20 10 0
0
20 bondenergy, kul
Fig. 2. Bond energy VS.relative wear resistance.
90
10 0
1
2
3
olactrondkty,d.u.
5
6
Fig. 3. Electron density us. relative wear resistance.
are about 0.8. The correlation factor of electron density is about 0.7. From the data, it was found that there are deviations in the case of the two metals, Beryllium and Tungsten. The correlation improves by a significant amount if these metals are excluded; the correlation coefficient of the electron density
222
parameter then becomes 0.8. This has already been incorporated in the figures shown. From these, it can be concluded that the electron density parameter is certainly a good indicator for abrasive wear similar to other electronic properties such as bond energy. Moreover, this correlation applies well to a whole range of metals regardless of the crystal structure. This implies that electron density is more fundamental than hardness in terms of wear. 3. Discussion The abrasive wear-electron density correlation, though it appears unlikely at first, is found to be logical as the following argument points out. The electron density values used were calculated as the ratio of bulk modulus and atomic volume, This calculation is justified by the assumption that the electron density throughout the Wigner-Seitz atomic cell is constant. Clearly, electron density is related to bulk modulus; this together with the fact that bulk modulus or Young’s modulus is related to hardness which, in turn, is related to abrasive wear resistance in pure metals [6] shows that it is reasonable to expect a relation between these two parameters of central interest. This has indeed been found to be true in this study by direct verification. 4. Conclusion Electron density at the Wigner-Seitz atomic cell boundary has been found to be proportional to the relative abrasive wear resistance of pure metals. This parameter thus occupies a place along with other solid state properties like bond energy as a predictor of abrasive wear of metals. Further work may be directed towards including alloying and deformation effects to this unique electronic wear index.
1 2 3 4 5 6
N. P. Suh, Wear, 25 (1973) 111 - 124. A. K. Vijh, Wear, 35 (1975) 205 - 209. J. P. Giltrow, Wear, 15 (1970) 71 - 78. A. R. Miedema, F. R. De Boer and P. F. De Chatel, J. Phys. F, 3 (1973) A. R. Miedema and R. Boom, 2. Metallkd., 69 (1974) 183 - 190. M. M. Khruschov, Weor, 28 (1974) 69 - 88.
1558 - 1576.
219 - 222
219
Research Report
Abrasive wear and electronic properties of materials E. V. SUBRAMANIAN Department Engineering, (Received
and Z. ELIEZER
of Mechanical Engineering and the Center for Materials Science The University of Texas at Austin, Austin, TX 78712 (U.S.A.)
March 21,1988;
accepted
and
April 11,1988)
An important electronic property, namely the electron density at the Wigner-Seitz atomic cell boundary, has been related to the abrasive wear resistance data in the case of pure metals. This property works as well as an indicator of wear as other solid state electronic properties such as bonding energy and cohesive strength that have hitherto been correlated with abrasive wear resistance of pure metals.
1. Introduction Abrasive wear resistance has been commonly related to bulk or surface hardness for a wide spectrum of metals. This criterion for wear applies well to metals in their pure or annealed state, particularly when they are classified according to the crystal structure, b.c.c., f.c.c. or h.c.p. However, numerous difficulties are encountered in attempting to find a similar relation between abrasive wear and this mechanical property while considering the effects of alloying and cold work; it has been found that conventional strengthening mechanisms, such as solid solution strengthening, cold work or precipitation hardening, fail to enhance wear resistance to a degree proportional to the increase in hardness-strength associated with these processes. Microscopically, the process of wear involves continuous creation and modification of new surfaces by breaking metallic or atomic bonds. The delamination theory for wear [l] relates wear to fracture mechanics and deals with wear as a crack propagation process. An attempt has been made in this study to examine wear in the light of fundamental electronic properties in the case of pure metals. 2. An electronic abrasive wear index There have been but a few studies on abrasive wear of metals and alloys, and their link to solid state electronic properties such as bonding 0043-1646/86/$3.60
@ Elsevier Sequoia/Printed
in The Netherlands
220
energy or cohesive strength. In one attempt [2], metal-to-metal bonding energy and melting point have been suggested as fundamental quantities correlating abrasive wear. In another study, cohesive energy [3] has been related to wear though large deviations exist for some metals. One of the parameters of fundamental interest is the electron density distribution which plays a vital role in influencing the bulk and surface properties of metals and alloys. Specifically, the electron density distribution at the Wigner-Seitz atomic cells has been correlated with compressibility [ 41, surface tension and heat of vaporization [5] in pure metals. This seems to suggest that electron density may be related to other physical and mechanical properties as well. With this as the background, the electron density data will be examined for transition and non-transition metals. Table 1 shows the values of relative abrasive wear resistance of several metals and the magnitudes of their electron density at the atomic cell boundary. The table also displays the values of metal-to-metal bond energy and the melting points of these metals. The electron density values were taken from ref. 5, and other data from ref. 2. Abrasive wear has been plotted against the listed properties in Figs. 1 - 3, and the coefficients of correlation have been determined for each linear plot. The factors of correlation with respect to relative abrasive wear resistance of bond energy and melting point TABLE 1 Abrasive wear and other properties of metals Metal
Pb Mg Sn Cd Al Zn Au CU Ag Pd Zr Pt Ni co Fe Mn Cr Rh MO Be W
Relative wear resistance
0.9
2.7 2.8 3.0 4.0 6.3 7.0 9.3 7.5 10.6 12.0 12.5 18.0 20.0 20.5 27.0 30.0 35.0 39.0 45.0 60.0
Electron density (density unit)a
Bond energy (kcal)
Melting point (“C)
1.52 1.60 1.91 1.91 2.69 2.30 3.87 3.18 2.69 4.66 2.69 5.64 5.36 5.36 5.55 4.17 5.18 5.45 5.55 4.10 5.93
7.8 6.0 12.1 8.9 12.5 10.4 14.6 13.5 11.4 15.0 24.4 22.7 16.9 16.9 16.6 11.7 23.6 22.1 39.6 13.0 50.5
327 650 232 321 660 420 1063 1084 960 1550 1852 1769 1452 1490 1535 1244 1875 2250 2610 1283 3410
*Note: 1 density unit = 6 X 10z2 electrons crne3.
221
880 70
f
I
60
!z 2
30
-
20 10 0
1000
0
3000
2000 metting point, C
Fig. 1. Melting point us. relative wear resistance.
.__ 90 8 5
*O 70
160 f
50
i
40
p
30
p
20 10 0
0
20 bondenergy, kul
Fig. 2. Bond energy VS.relative wear resistance.
90
10 0
1
2
3
olactrondkty,d.u.
5
6
Fig. 3. Electron density us. relative wear resistance.
are about 0.8. The correlation factor of electron density is about 0.7. From the data, it was found that there are deviations in the case of the two metals, Beryllium and Tungsten. The correlation improves by a significant amount if these metals are excluded; the correlation coefficient of the electron density
222
parameter then becomes 0.8. This has already been incorporated in the figures shown. From these, it can be concluded that the electron density parameter is certainly a good indicator for abrasive wear similar to other electronic properties such as bond energy. Moreover, this correlation applies well to a whole range of metals regardless of the crystal structure. This implies that electron density is more fundamental than hardness in terms of wear. 3. Discussion The abrasive wear-electron density correlation, though it appears unlikely at first, is found to be logical as the following argument points out. The electron density values used were calculated as the ratio of bulk modulus and atomic volume, This calculation is justified by the assumption that the electron density throughout the Wigner-Seitz atomic cell is constant. Clearly, electron density is related to bulk modulus; this together with the fact that bulk modulus or Young’s modulus is related to hardness which, in turn, is related to abrasive wear resistance in pure metals [6] shows that it is reasonable to expect a relation between these two parameters of central interest. This has indeed been found to be true in this study by direct verification. 4. Conclusion Electron density at the Wigner-Seitz atomic cell boundary has been found to be proportional to the relative abrasive wear resistance of pure metals. This parameter thus occupies a place along with other solid state properties like bond energy as a predictor of abrasive wear of metals. Further work may be directed towards including alloying and deformation effects to this unique electronic wear index.
1 2 3 4 5 6
N. P. Suh, Wear, 25 (1973) 111 - 124. A. K. Vijh, Wear, 35 (1975) 205 - 209. J. P. Giltrow, Wear, 15 (1970) 71 - 78. A. R. Miedema, F. R. De Boer and P. F. De Chatel, J. Phys. F, 3 (1973) A. R. Miedema and R. Boom, 2. Metallkd., 69 (1974) 183 - 190. M. M. Khruschov, Weor, 28 (1974) 69 - 88.
1558 - 1576.