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Atomic and Nanometer-Scale Modification of Materials: Fundamentals And Applications (Nato Science Series E: (Closed)) Softcover reprint of the original 1st ed.
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دریافت Atomic and Nanometer-Scale Modification of Materials: Fundamentals and Applications |سی بی

Ordered intermetallics constitute a unique class of metallic materials which may be developed as new-generation materials for structural use at high temperatures in hostile environments. The system that we have developed addresses this problem. We have added a 3D motion control system to our STM that helps in making any required tip trajectory and combined it with a molecular dynamics MD simulator that simulates in real-time the manipulation process going on in the STM.

The MD simulation not only provides information about the atomic scale structure of the junction, but also serves as a visual feedback to the operator in real-time who can then choose to make a desired trajectory for better control of the manipulation process. This is especially important in the case of 3D manipulation of single molecules and atomic chains, as there are no predefined accurate trajectories [5,6] that one can set to do those manipulations.

Therefore an adaptable trajectory is the only solution where the operator can continuously communicate with the experiment through the real-time MD simulation and define the trajectory at will using the motion control system. This human—machine augmented system thus provides a far better control of the manipulation process and can moreover be used for 3D manipulation.

Previously, for better control of atomic manipulations, an audible feedback has been used [7]. This is certainly helpful, but it does not reveal where it has hopped, only that it hops. In this article first we will start with describing the experimental setup and sample preparation technique. After that we report on using this system for a new lateral manipulation methodology that we refer to as point contact pushing PCP technique, followed by a 3D trajectory that enabled us to lift in a controlled way a chain of gold atoms above a metal surface. These atomic chains are known to show parity oscillations in conductance [8] while going from even to odd number of atoms in the chain.

We detect this phenomenon while controllably lifting the chain of atoms and putting it back on the surface. The 3D motion control system is an LED tracker made with two cameras tracking the x — y -motion and y — z -motion of the LED respectively. A mono-crystalline gold sample cut along the surface is prepared by repeated argon sputtering and annealing cycles to obtain an atomically flat Au facet showing herringbone surface reconstruction.

We further prepare the surface at low temperature by creating a localized stress pattern [] on the surface using gentle indentation of the STM tip at a spot on the surface remote from the area of investigation. This creates new crystalline facets and provides straight step edges in the three crystallographic directions of Au i.

The STM tips used in the experiments are hand-cut PtIr tips that get covered by Au atoms on indentation of the surface. Figure 1: Schematic of the experimental setup.

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Figure 2: a Atomically flat Au surface with herringbone reconstruction and straight step edges in crystallographic directions i. Images obtained at about 3 K after the temperature was stabilized within a few millikelvins. Figure 2: a Atomically flat Au surface with herringbone reconstruction and straight step edges in crys A conventional atomic manipulation operation using STM involves a pre-defined trajectory controlled by the operator or by an automated procedure of the STM tip. An example is reducing the tip—sample distance and moving the tip in a desired direction assuming an isotropic nature of adsorption bonds [19] in metallic systems.

In contrast, in our setup the operator receives a continuous visual feedback from the real-time MD simulation. The operator can then respond to the predicted structural evolution of the junction during the manipulation operation and alter the trajectory at will. The 3D motion tracking sensor sends the same x , y , z - signals to both the STM and the simulator simultaneously and therefore the MD simulation is required to have a minimal time delay in its response for smooth real-time operation. The probe speed is determined by the operator, and depends on the speed with which the 3D motion control sensor is moved.

We perform a classical MD simulation here in which we ignore the electronic effects which in fact give rise to interatomic forces and take the forces as coming from parameterised equations that only depend on the interatomic distances.

Definition

This is typically called a force-field simulation. A more accurate method would be obtained by using ab initio calculations that take into account both the nuclear and the electronic degrees of freedom. But these ab initio calculations are computationally very expensive and thus are not suitable for our purpose.


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The simulation we discuss in this article is only made for metallic systems, so in this case all the atoms involved are Au atoms. This allows for fast computation of a large number of atoms involved because of its simple analytical potential functions. The potential energy is given by. The increase in kinetic energy for the conduction electrons confined between two approaching atoms gives rise to the repulsive term [22] , while the attractive interaction originates from the band structure and is found by a second-moment approximation to the tight-binding Hamiltonian [20].

From this potential energy, forces can be calculated using. Since providing visual feedback is one of the main objectives of the simulation, a graphics library is necessary to show visual output on the screen.

We choose an object-oriented approach to keep the code well structured. One separate class is used to keep track of the individual atoms i. We differentiate between three types of gold atoms, corresponding to the role they play in the simulation.

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These are gold atoms that are not entirely frozen [24] but feel an additional force to confine their positions. A 3D parabolic potential well for each boundary atom, centered at positions resembling a bulk lattice layer, keeps the metal slab and the tip in shape by fixing the boundaries. The potential wells mimic the presence of atoms beyond the boundaries. This approach allows for dynamics even for the boundary atoms, making it possible to apply a thermostat and have realistic interaction with the other normal gold atoms.

There are two types of such boundary atoms: tip boundary atoms and surface boundary atoms. For surface boundary atoms, the position of the potential wells stays the same throughout the simulation. For tip boundary atoms, the position of the potential wells can be changed to simulate tip motion [24].

As there is a huge discrepancy in timescales between experiment and simulation, a tip motion of some angstroms in several seconds in experiments happens within picoseconds in the simulation, yielding a much higher tip velocity and acceleration in the simulation. This large amount of kinetic energy pumped into the system has to be drained out using a suitable thermostat. A Berendsen thermostat [25] is implemented into the simulation that provides a gradual temperature decay instead of sudden rescaling. Here the instantaneous temperature changes proportional to the temperature difference with the reference temperature T 0 with an adjustable coupling to a heat bath:.

In our case only the boundary atoms are subject to temperature control by a thermostat. This way kinetic energy is transferred through the normal atoms to the boundary atoms, where temperature is controlled, as is also done by Henriksson and co-workers [27]. In order to prevent strongly disturbing the system a special procedure is used to displace the tip boundary atoms. By simply moving the potential wells, the tip boundary atoms would feel strong forces and acquire high velocities. As described above, this amount of kinetic energy would be problematic for the thermostat to dissipate.

Instead, we change the position of the tip boundary atoms and their potential wells simultaneously by directly adding smooth displacements. This way, they change position without additional energy transferred to the system and therefore they will not acquire high temperatures.


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  6. The thermostat then only has to take care of the velocities induced by interactions with the normal atoms in the tip. Figure 3: Snapshot of the molecular dynamics simulation showing the different atom types. Several optimizations and approximations are implemented to speed up the computation so that the simulation can run in real time. If r ij , the distance between two evaluated atoms, is larger than the cutoff radius, the respective pair of atoms will not be taken into account in the energy and force calculations.

    Because of the exponential decay with distance in the potential, their contribution is very small.

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    Moreover, as described in the book by Andrew Leach [28] , just using a force cutoff would not give a decent speed-up as to use a force cutoff radius one has to compute first all the atomic distances involving evaluating a square root, which is also computationally expensive and then calculate the forces only within the cutoff radius. Since, in the system we study through molecular dynamics, most of the atoms do not change their nearest neighbours very often, we can avoid calculations of all distances at each time step.

    Instead, we introduce another cutoff radius, now for the calculation of the distances between atoms. Moreover, we do not need to know the distance between atoms that are far apart, since their contributions will not be taken into account because of the cutoff radius for forces and energy. The larger distances are updated less frequently, only once every 50 simulation steps.

    Secondly, we implement a lookup table to increase the calculation speed of the exponential functions that still need to be found. This means that the exponential function is evaluated for a long list of relevant interatomic distances at the initialization of the simulation.

    Every time it needs to be calculated during runtime, a linear interpolation of the precalculated values around the given distance is used instead of calculating the exponential itself. Looking up the value from the lookup table is faster than calculating it, resulting in better performance. We have compared this speed up in simulation due to the aforementioned approximations with a standard implementation of the MD simulations without any approximations. Using these optimization methods, a speed-up of almost fold in energy and force calculation is recorded by a standard profiling tool.