Cleaving hcp in materials studio full#

Range (1.6, 2.8) is chosen for bisection method. part of Fig3 in order to show details of convergence Range (1.6, 2.8) The local minimum is 2.356194.ДЇig 3 and 4 show the convergence properties of the two methods.ДЇig 3.В difference of each stepВ Оµ vs iteration steps at range (1.4, 2.6)ДЇig 4. The local minimum is 2.356194.ДЇor NewtonвЂ™s method, the initial estimate is 1.4. Range (1.4, 2.6) is chosen for bisection method. The same pattern could be found for following ranges. But the NewtonвЂ™s method converges needing less steps. part of Fig1 in order to show details of convergenceД«oth of the methods converge to the same local minimum under the convergence criterion of 1E-06. difference of each stepВ Оµ vs iteration steps at range (1.2, 2.4)ДЇig2. Fig 2 shows a part of Fig1 in order to show the convergence detail.ДЇig1. The local minimum is 2.356194.ДЇig 1 shows the convergence properties of bisection method and NewtonвЂ™s method. Range (1.2, 2.4) is chosen for bisection method, the local minimum is 2.356194.ДЇor NewвЂ™s method, 1.2 is the initial estimate. Comparison for convergence property between bisection and newtonвЂ™s method Range (1.2, 2.4)

Cleaving hcp in materials studio full#

Full data could be got through the link attach at the end of this post. The difference of each step Оµ is defined as x value is this iteration minus x value in last iteration.ДЇollowing figures show the calculation results.

Since NewtonвЂ™s method converges to different local minimums with bisection method at 3.0, 3.2, 3.4, smaller boundary values of each range(1.2, 1.4, 1.6, 1.8, 2.0, 2.2) are adopted for NewtonвЂ™s method when we comparing these two methods at each range. So, when we doing comparison, choosing which value for NewtonвЂ™s method should be paid attention. The range selection for bisection is stopped at (2.2, 3.4) (the change step is 0.2 between each range) otherwise the reference value will fall outside the range.ДЄnother tricky thing is that bisection method has two initial estimates, which form a range for later iteration, while NewtonвЂ™s method only needs one. The convergence criterion used here is 0.000001(1E-06). How many decimal places is determined by the precision we set. The initial estimates of NewtonвЂ™s method are consistent with that of bisection method, which is designed for comparison between these two methods.ДЄ reference local minimum for the studied function is x=2.356194490вЂ¦. Initial estimates are boundary values of each range for bisection method. The function used here is f(x)=exp(-x)cos(x). So the following content will study how the initial guess changes convergence properties of these two methods. An initial estimate is needed to use these two methods and no guidance is provided by the methods themselves. These two methods are iterative and can only provide approximations, which is controlled by the convergence criterion. Here, only optimization in one dimension is studied and methods adopted are bisection method and NewtonвЂ™s method. Normally, the later one is more difficult. This locally lowest value search could be called numerical optimization, which could happen in one dimension or more than one dimension. There are various methods that could search local minimums for a function. How initial estimates change convergence properties of bisection method and NewtonвЂ™s method This entry was posted in 2018, 2nd Post 2018, Hafnium, Student Post on Apby Jonathan Schirmer. et al.В First principles methods using CASTEP. In this work, the packing ratio was found to be 1.574, approximately a 4% difference. Furthermore, it is known that the ideal packing ratio for spheres arranged in an hcp lattice is c/aв‰€1.633. This is found to be well in agreement with a result obtained in a previous post. The unit cell volume was found to beВ 45.163544В Г…^3. The minimized energy was found to beВ -15.73336 keV and the corresponding lattice constants were found to be a=b=3.2117В Г… and c=5.0557В Г…. The values above gave a well-converged energy with a reasonable runtime. K-points: 9x9ењ† (36 points in the irreducible part of the Brillouin zone (IBZ))Д«oth the number of k-points and the energy cutoff were varied to ensure reasonable convergence. The following settings were used for Geometry Optimization in CASTEP:ДЎs2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 4f14 5s2 5p6 5d2 6s2 We maintain Throughout the calculation, symmetry demands that a=b, but a and c are allowed to vary. These values are provided by examples within Materials Studio and are accepted experimental values. The initial values of the lattice parameters are a=b=3.1956В Г… and c=5.0511В Г…. Initial cell provided for CASTEP calculation.