In class we showed that for a Lennard-Jones 6/12 interatomic potential one would predict theideal strength of a material to be −2.69U 0 a03 , where U 0 is the bond energy and a0 is theequilibrium bond spacing. Based on the same assumptions, show that Young’s Modulus, E, isgiven by −72U 0 a03 . Assuming U 0 = −1 eV and a0 = 2 Å , provide an order of magnitudeestimate of E in GPa. (While both the predicted ideal strength and value of Young’s modulus area bit on the high side when using the Lennard-Jones 6/12 potential, their ratio (72/2.69 ≈ 27), isrepresentative of that for many materials. In other words, Young’s modulus can be expected tobe ~30 times the value of a material’s ideal strength, which is typically 10-100 times its actualyield strength, making values of Young’s modulus typically ~1,000 times the yield strength.
In class we showed that for a Lennard-Jones 6/12 interatomic potential one would predict the
ideal strength of a material to be −2.69U 0 a0
3 , where U 0 is the bond energy and a0 is the
equilibrium bond spacing. Based on the same assumptions, show that Young’s Modulus, E, is
given by −72U 0 a0
3 . Assuming U 0 = −1 eV and a0 = 2 Å , provide an order of magnitude
estimate of E in GPa. (While both the predicted ideal strength and value of Young’s modulus are
a bit on the high side when using the Lennard-Jones 6/12 potential, their ratio (72/2.69 ≈ 27), is
representative of that for many materials. In other words, Young’s modulus can be expected to
be ~30 times the value of a material’s ideal strength, which is typically 10-100 times its actual
yield strength, making values of Young’s modulus typically ~1,000 times the yield strength.
Step by step
Solved in 2 steps
