Atomic Laboratory for Interactive Numerical Experiments
Contents
1. Ay p 6 In particular the Sutton Chen potential used here was originally introduced for a general description of various fcc metals 19 20 and the parameters set in the program are suitable for describing a Cu overlayer on a Ni substrate 6 3 Programming potential parameters It is possible to program a variation of the potential parameters of type 2 atoms in the same window appearing when the Interatomic Potential is selected in the Environment menu This option has been introduced and used to reliably determine the critical misfit at thermal equilibrium of a mismatched hetero structure as described in detail in Ref 6 Currently only the length scale of the second potential can be varied The variation is stopped either when a lower limit to L2 is reached or when temperature overcomes a given threshold This last possibility represents the system becoming irreversibly unsta ble which is monitored effectively through a temperature increase and in greater detail works in the following way When the temperature increase is produced only as a consequence of the variation of L2 then the thermo stat is applied for a certain number of steps in order to bring the system to the new state of thermal equilibrium For instance if the equilibrium dis tance of the potential is varied a little it is possible that nothing particular happens apart from a temperature variation and the corresponding expan sion contraction of the specimen If t2. callback c for buttons bars etc of graphical windows calc c which prepares the initial configuration simu c for MD cycles 26 The computation of the equilibrium bulk lattice constant is now is made in calc c from the potential felt by a bulk atom Notice that this is a good equilibrium distance only at T 0 and for a bulk atom that is for an atom which is not near the surface C 1 Times Finally something can be said about the velocity of the code in order to compare it with boundary2D or to check the changes in the program speed produced by some change To this aim it is useful to introduce the time tau required by the code to make 1 MD cycle for 1 particle defined as T ta N I where ttot is the total CPU time used J the total number of time steps done and N the total number of particles The quantity can be checked by selecting Times in the Information menu For the sake of simplicity the quantity 7 is computed from the total time ttot in seconds since the code started after a sufficient number of MD cycles a value of I 200 is enough to make small the overestimate due to the time needed to set the initial conditions The following table is not updated but can provide some information about the relative speed of boundary2D and ALINE For short range LJ potentials ris approximately constant as expected that is it does not depend on N or J Noise and dissipation are switched off during the estimate of
3. 1993 251 310 M W Finnis J E Sinclair A simple empirical n body potential for transition metals Phil Mag A 50 1984 45 A P Sutton J Chen Long range finnis sinclair potentials Phil Mag Lett 61 3 1990 139 146 H Rafii Tabar A P Sutton Long range finnis sinclair potentials for fcc metallic alloys Phil Mag Lett 63 4 1991 217 224 Rasmol Home Page URL www rasmol org M P Allen T J Tildesley Computer Simulation of Liquids Clarendon Press NY 1989 29
4. also allows the user to decide whether and how the potential parameters vary in time This possibility may look odd at first sight since potential parameters are by definition fixed properties of the material but actually it represents an interesting property which can be exploited in some numerical gedanken experiment as shown below The LJ potential energy at time t between two generic particles 7 and j at r t and r t respectively is given by Wo ri t 1 t where Wo r is defined in its basic form as 00 12 00 6 Wat e 28 2 alr 4 2 2 1 In numerical simulations it is useful to introduce a finite cut off re such that Wo r gt re 0 In order to ensure continuity of Wo r and of its first derivative the cut off corrected potential W r is actually used W r Wo r r re Wo re Wore 2 where Wi rc represents the dWo r dr computed at r re However as discussed in Section C one has to be aware of the changes introduced by the cut off correction First of all Eq 2 does not represent the LJ potential anymore since a linear term in r is present Correspondingly it is to be expected that all its features are different in particular the position and the value of its minimum In order to avoid that the introduction of a finite cut off deeply changes the nature of the potential use on can correct the parameters of the potential in order to preserve some of its properties For th
5. be related to the general environment in which atoms are 6 1 Noise and dissipation By selecting Noise and dissipation a window is open in which one can set the main features of the thermal environment that is temperature T and friction coefficient gamma One can also choose if only one type or both types of atoms are to be thermalized and if the thrmostatting is needed to keep the system hot or cold enough or within a given temperature window Currently only the Langevin thermostat and a velocity scaling thermostat for testing purposes is available Also it is possible to program a smooth change in temperature by spec ifying the final temperature and the temperature increment done at every time step The thermostat is also used by another option of the program see section 6 2 for details 6 2 Interaction Potential Selecting Interatomic Potential in the menu Environment opens the win dow of the potential parameters by call of the program InterProgram in the source file graphics c Potential parameters are available currently for two different types of atoms Furthermore two types of potentials can be used i e Lennard Jones LJ and the Sutton Chen SC EAM potential 14 6 2 1 The LJ potential For the LJ potential the parameters are the well depth the length pa rameter g and the cut off re If only one type of atom is present in the system the values of the parameters of the second material are ignored The window
6. box in the interface window see Sec 5 1 The crack option is not active until the ON button is pushed If the crack obtained is satisfactory by pressing the button CONFIRM in the crack window one makes that crack permanent On the other hand by pressing the button CANCEL one goes back to the previous configuration before the crack was made Once a crack is confirmed the configuration is permanently stored and one can click the Crack button again to make another crack The procedure can be reiterated to make many cracks and shape a sample in a certain way e g to make a dot on a substrate The crack parameters can also be suitably set to remove a plane or a half plane of atoms from the sample to create a vacancy in the bulk or on the surface or to make a tip by rotating the box and moving it near the sample surface 13 5 3 Displacements Through the selection of Displacements in the Specimen menu a window opens in which one can displace atoms in order to create a linear dislocation This is achieved by displaying atom according to classical elasticity theory 10 and the type of dislocation is either of edge or screw type as selected through the variable DISLTYPE in initial h The geometry of the disloca tion id specified through the Cartesian coordinates of a point lying on its core and the angles of its direction 6 Environment In the menu Environment some features of the models system have been conventionally grouped which can
7. criteria used for selecting and visual izing atoms in crystal defects can be used for reducing the total number of atoms and the corresponding data to be stored to the same fraction boundary Program Info Environment Specimen Qutput Visualize Help kt 23 t 0 230000 mee N 33600 atons Nx 50 Ny 21 Nz 16 Crystal Type 1 1 Materials_Types ESS sy E N 6 736716 U N 6 738143 K N 0 001427 T1 0 000951 T 0 000951 min Max 7 170 1 807 a paT Update steps mirs UsPotential Energy e i ri A o Ld 3 FILTER ON OFF Min 13 5 f Jal Mm 1 COLOR ON OFF 10000 Min 13 5 yal 1000 Width 3 a a es SCAN 1 Figure 1 Main GUI of ALINE in color visualization mode according to single particle potential energy The system is a cubic sample of size equal to 16 lattice constants The upper window shows the system in physical space the lower window the corresponding histogram in potential energy In the example of Fig 1 a fcc cube of linear size equal to 16 lattice constants and 33600 atoms is represented with atom color according to po tential energy Colors of atoms in the upper window are in correspondence with those of the histogram peaks visible in the lower graphical window Blue color of atoms in the upper window or peaks in the lower window corresponds to the bulk of the sample with lower potential ener
8. detected by selecting a suitable window of values of potential energy Once satisfactory criteria for selecting atoms within or around crystal defects have been found it is possible to use them in the automatic tracking procedure and therefore to follow the time evolution of the shape and position of the crystal defect At any time through the GUI the user can switch between atom visualization modes which use different color mappings and selection criteria It should be noticed that in order to achieve the same flexibility of graph ical representation by using a standard MD code the quantities needed for all the various types of visualization formats should be computed at any time steps The main advantage of the GUI is however that the search for the optimal quantity and corresponding limits to track dislocations is carried out much more easily in interactive mode rather than by repeated storage and analysis of data Another advantage is the possibility to greatly reduce the amount of data to be stored in those case in which information at various times is needed e g in the preparation of a video about the the time evolution of a crystal defect since extended crystal defects usually influence only a small fraction of the total number of atoms If for simplicity the sample is assumed to be of cubic shape the percentage of atoms close or within a crystal defect ranges from about N 3 for 1D dislocations to N 3 for 2D grain boundaries The
9. different values of the cut off In order to solve this problem we did not change the form of the potential or the correction terms leaving furthermore the cut off ra dius as a free parameter Instead after the cut off correction we have replaced the parameters epsilon and sigma with new rescaled pa rameters epsilon and sigma such that the equilibrium distance and the corresponding equilibrium energy of the corrected potential assume the same values of the original unperturbed potential Actu ally a scaling of the energy parameter epsilon only was sufficient to achieve this aim with a relative precision of a few part over 1000 This can be justified by inspection of the table above where differences be tween equilibrium distances are smaller than those between potential minimum values In other words we have assumed that the position of the minimum does not change and limited ourselves to rescale the well depth It is to be noted that in principle the choice of the parameters which have to be changed and of those which remain unchanged is ar bitrary In other problems it could been convenient e g to fix the core radius sigma and the frequency of oscillation around the equilibrium position w d U dr Structure As a byproduct of the previous changes the file with the procedure fitsgma has been eliminated and there are again only the four basic c files in the ALINE package graphics c which menages graphical windows
10. produce if requested some out put files containing information about snapshots of the system The various types of snapshots can be done at any time through the menu Output A first type of information that can be stored are atom co ordinates in xyz format by selecting XYZ in the menu Output The corresponding name of the file is runname nnnn xyz where runname is the name of the run as specified in the file initial h and nnnn is a progressive integer of the form 0000 0001 0002 etc it is as sumed that no more than 9999 coordinate files are needed for making a video If only a subset of atoms was selected to be represented in the graphical window only the coordinates of the atoms in that sub set will be stored This can save much space on disk especially in the preparations of videos If one wants information about all atoms to be stored one just has to switch selection criteria off in the main graphical window We recall that xyz format files contain the number of atoms N in the first line then a second line reserved for comments used by the program to store time step number k and time k x dt where dt is the time step and finally N lines with information on single atoms These lines have five fields each one namely atom name two characters x y and z coordinates the so called temperature field The temperature field contains the value of the same quantity selected for the visualization mode in the main window n
11. specific problem For completeness it should be added that C compilers e g cc or gcc are usually C compilers which can compile also C programs so that as it often happens by using even a few apparently innocuous commands of C one is actually programming in C even if one thinks one is programming in C As a consequence a pure standard ANSI C compiler could not compile many programs considered to be C programs such as also ALINE probably However this should have no importance on the practical side 2 3 Modifying the graphics part Also the graphical part of the program can be changed by the user The graphical functions of OpenMotif are C functions and are called from inside C code lines as normal functions so that no other language besides C is required in principle However a knowledge not only of the OpenMotif library functions which define e g windows widgets etc but also of how it works in general is needed to implement new graphics in the program To this aim there are various free manuals available on line 7 8 9 In general it is much easier to begin by making small changes on templates and programs already tested To have the feeling of how it works to modify the graphical part of an existing code and to check that it is not so difficult there is a short paragraph in Ref 1 for the case of the program boundary2D 2 2 4 Downloading the program The program can be downloaded at the URI in Ref 3 as a gzi
12. tau It is noteworthy that the value of 7 does not depend appreciably on the number of cycles between 2 consecutive updates of the graphical window The quantity 7 does not give an absolute estimate of the run speed which can been obtained through a profiler since it will depend on the CPU load and the current computer status but it can be used to compare how the code works just before and after a change has been made 27 Table 5 Normalized execution times in seconds for a single cycle per particle program time boundary2D 0 000005 ALINE version 01 01 2002 0 000016 ALINE version 20 02 2002 0 000019 ALINE version 23 02 2002 0 000017 References 1 J Merimaa L F Perondi K Kaski Comp Phys Comm 124 1999 60 2 boundary2d s Home Page URL www hel fi kuronen boundary2D 3 ALINE s Home Page URL www lce hut fi marco aline 4 Laboratory of Computational Engineering Helsinki University of Tech nology URL www 1lce hut fi 5 M Patriarca M Robles K Kaski Microscopic method for dislocation tracking arXiv cond mat 0212318 6 M Patriarca A Kuronen M Robles K Kaski Three dimensional in teractive Molecular Dynamics program for the study of defect dynamics in crystals Comp Phys Comm in press 7 The Open Group Open Motif Documentation Supplement Vol M213 214a 214b 214c 216 2001 URL http www opengroup org openmotif docs 8 A Fountain J Huxtable P Ferguson D Heller
13. to 20 that of a canonical ensemble where the average temperature remains under user s control All the parameters of the thermostat can be varied through graphical interfaces which are described in next section All energies as well as temperature are measured in the energy scale e of the first mate rials in case there are two types of materials and analogously for lengths which are measured in units of The time unit is chosen in such a way to make the rescaled mass in Eq 7 equal to one 9 Source files The basic structure of ALINE is basically unchanged respect to the 2D version 1 and is represented in Fig 3 Also the names of the files and procedures are either the same ones or similar ones The program is written in C and developed for an X11 Window System platform The program windows and all graphics are based on the MOTIF library 9 The program source files are four C files and the corresponding interfaces together with the additional interface file initial h for some initial settings The source files are listed in Table 1 e The main file is graphics c This file also manages all the graphical windows that is the main graphical window Fig 1 and all the other windows than can be open by the user from the main window All the graphical windows represent communication channels from program to user passing information both in graphical and text format e On the other hand the actual communication channel
14. ALINE Atomic Laboratory for Interactive Numerical Experiments www lce hut fi marco aline Foreword This is the user manual for the interactive Molecular Dynamics program ALINE How to download and compile the program the program structure how to use it and some applications are described here as well as the latest features added and changes in course ALINE was born as a 3D extension of fracture 1 so it has initially received a direct contribution from all the coauthors of fracture Later also from the authors of contributors to its renewed and extended version boundary2D 2 from which some features are from time to time exported to ALINE In addition the other direct contributors are Kimmo Kaski Antti Kuronen Marco Patriarca Miguel Robles and Peter Szelestey Contents Q WU gt Introduction General features of the program 2 1 Motivation 00 2 2 Modifying the molecular dynamics part 2 3 Modifying the graphics part 2 4 Downloading the program 2 5 Expanding the program package 2 6 Compiling the program Visualization modes Initial Configuration 4 1 Initial Configuration from File 4 2 New Configuration from scracth Specimen 5 1 Interface naon nee ly BA ee ee 5 2 Cracks and indentations 5 3 Displacements Environment 6 1 Noise and dissipation 6 2 Interaction Potential 6 2 1 The LJ po
15. Motif Programming Manual for Motif 2 1 Open Source Edition Vol 6A and 6B Imperial Software Technology Limited Reading UK 2001 URL http www opencontent org openpub 9 A D Marshall The X Motif Library http www cs cf ac uk dave x_lecture 28 10 11 17 18 19 20 21 22 J P Hirth J Lothe Theory of Dislocations Wiley New York 1982 A E Carlsson Beyond Pair Potentials in Elemental Transition Met als and Semiconductors Vol 43 of Solid State Physics Advances in Research and Applications Academic New York 1990 p 1 N W Ashcroft N D Mermin Solid State Physics Saunders College Philadelphia 1976 M S Daw M I Baskes Semiempirical quantum mechanical calcu lation of hydrogen embrittlement in metals Phys Rev Lett 50 17 1983 1285 1288 M S Daw M I Baskes Embedded atom method Derivation and application to impurities surfaces and other defects in metals Phys Rev B 29 12 1984 6443 6453 S M Foiles Application of the embedded atom method to liquid tran sition metals Phys Rev B 32 6 1985 3409 3415 S M Foiles M I Baskes M S Daw Embedded atom method func tions for the fcc metals Cu Ag Au Ni Pd Pt and their alloys Phys Rev B 33 12 1986 7983 7991 erratum Phys Rev B 37 10378 1988 M S Daw S M Foiles M I Baskes The embedded atom method a review of theory and applications Mater Sci Rep 9 7 8
16. Potential parameters Parameters of interaction potential can be changed in real time or programmed e Initial conditions The initial condition are chosen according to the optimal lattice length which minimizes the bulk energy As a re sult there are now almost no initial elastic waves propagating in the sample giving rise to oscillation of the crystal structure due to the relaxation process toward the equilibrium configuration To quan tify the distance of the initial configuration from equilibrium one can mention the residual kinetic energy of the system which initially is at zero temperature all particle velocities equal to zero and after re laxation is at T 1 K of residual kinetic relaxation energy if the Lennard Jones parameter epsilon is assumed to be epsilon 1 eV The optimal lattice parameter is evaluated by direct minimization of a sample atom interacting with all atoms within one cut off radius The procedure is independent on the cut off and also on the particular type of basic cell that is of the offset vectors e Unit of length The 2D code had its own special way to define the unit of length The user cannot change the absolute value of the LJ length parameters sigma or re cutoff radius The LJ parame ter sigma is instead changed by the program so that the minimum equilibrium distance between 2 atoms in the bulk is equal to a given reference value This is useful in that one can always take the lattice consta
17. ages the new configuration window called NEW RUN the name appears at the top of the window This procedure in turns can call other procedures all in the source file calc c devoted to the creation of the initial configuration Currently only a crystal with fcc structure can be built Notice however that one can e g melt the system by increasing the temperature or set an arbitrary lattice constant in order to distribute the atoms on a larger volume by selecting set a0 The NEW RUN window allows one to set various parameters e Sizes The sample created has the shape of a box and z y and z are the linear sizes of the specimen measured in units of the corresponding lattice constants 11 e Boundary conditions BC It is possible to select between different types of BC independently for the x y and z directions Possible BC are Periodic boundary conditions are implemented on the basic cell with the sizes specified above assuming as lattice constant the equilibrium lattice constant of the ideal lattice at T 0 Cur rently there is no algorithm e g constant pressure MD which can find the optimal lattice constant automatically at arbitrary temperatures Therefore if T gt 0 the value of the lattice con stant along a given axis is to be supplied by the user This can be done by selecting set a0 Fixed boundary conditions in a certain direction means that the atoms cannot move along that direction but only in the plane pe
18. amely for building 18 the color map and eventually setting the selection criteria It repre sents the actual temperature only in the case in which such quantity is the single particle kinetic energy but it can be any other quantities such as e g mean potential energy In this way the file can be used by image visualizers such as Rasmol 21 for setting atom colors and reproducing the same picture in the main window in a high quality for mat suitable for publication For numerical simulations of theoretical models in which particle do not correspond to real atoms atom types can be set arbitrarily However they are set differently for different types of atoms in order to distinguish e g the two materials at an interface The xyz files need to be processed by a molecular visual izer such as Rasmol in order to produce pictures See 3 for some examples of videos realized by the animation option use of Rasmol to convert the xyz file into PPM figures and finally the linux utility ppmtompeg to convert the PPM figures into a mpeg video We mention also the possibility to store files containing atom velocities or force components see Table 3 xwd figures The program can also save a snapshot directly into graphical xwd format by dumping the drawing window to a file called draw nnnn xwd In this case one obtains exactly the same picture appearing in the graphical window A warning should be given for this type of output If some atoms
19. an dard MD code is that the amount of data to be stored can be drastically reduced Inspection of the system in real time in one of the various visual ization modes available can provide a large amount of information about its geometrical structure and internal properties In this way the user can both effectively select the configurations to be stored and reduce if not eliminate the subsequent data analysis Secondly many system parameters related e g to the interatomic in teraction or to the external environment such as temperature and applied fields can be varied continuously during the numerical simulation The be havior of the system can then be tested under several conditions similarly to what is done in a real experiment without restarting the simulation from the very beginning with the additional advantage of being able to vary even parameters which are usually fixed e g of the interatomic potential The information thus obtained can be used as a feedback for tuning the sys tem parameters in order to reproduce find a certain state of or a certain phenomenon taking place in the system 2 2 Modifying the molecular dynamics part The program is written in C and no commands related to the graphics part based on the OpenMotif library appear in the files containing the MD routines Thus the user only needs some knowledge of basic C in order to modify the physical features of the system simulated and can adapt the code to a
20. are outside the visible field for any reasons they will not appear in the xwd picture as well since the pictures is a perfect copy of the part of the screen corresponding to the drawing window Furthermore if the main graphical window is covered by another window a part of the other window will appear in the picture in place of the image of the system under study Also it can happen that if the main window is minimized or the computer is locked or in screen saver mode the xwd picture will be empty Animations It is also possible to make snapshots at regular intervals of time by selecting Animation in the same menu This can be useful in order to produce coordinate files to be used for preparing a video Atom distributions For every snapshot taken the program can also store the corresponding histogram of the atom distribution at the same time and according to the same microscopic quantity written in the temperature field of the coordinate files The distribution is normalized to the total number of atoms just as in the histogram in the plotting window The format is dat and the file is basically a 19 Table 3 Output files file name description of the file runname nnnn xyz coordinates runname nnnn vel velocity components runname nnnn frc force components runname nnnn his atom distribution top nnnn xwd main window draw nnnn xwd drawing window plot nnnn xwd histogram window two column file microscopic quantity value and
21. ations of the system which are provided by the program at any instants of time in the drawing and in the plotting windows of the main graphical window e In the upper drawing window of the GUI atoms are represented in physical space The image in the drawing window can be magnified translated and rotated through various buttons in the right column Atoms can be colored according to one of the properties listed in table 2 selectable through a widget in the left column of the GUI It is also possible to select and visualize only atoms within a slice of the system cut perpendicularly to the observation direction If two types of atoms are present one can chose to draw only one of them Important ad ditional information can be displayed through atom colors The color mapping is defined according to the value of a given atomic property e g kinetic or mean potential energy or simply atom type which can be selected by the user In the left column it is possible to set selective windows for the same quantity chosen for the visualization mode or for adjusting the color scale It is also possible to select and visualize atoms within a slice of the system cut perpendicularly to the obser vation direction by selecting the visualization mode corresponding to depth e The same quantity which defines the color mapping in the drawing window is used in the lower plotting window for the system distribution in the corresponding space In the example shown i
22. constructed by combining theoretical considerations with the fitting of free parameters to reproduce certain material properties obtained either from experiments or ab initio calculations The EAM potential energy of a metal system is modeled by the sum of a pair wise core core repulsion between atoms and an additional contribution depending on the embedding function F describing the interaction between an atom and the electrons of the material Ey gt Rila 5 built 3 i tA Here py is the host electron density at atom 7 due to the rest of the system and F p is the energy to embed the atom i to electron density p The elec tron density at the site of atom 7 is usually approximated by a superposition of individual atomic densities Phi So pF rig 4 j i where pi r is the electron density of atom j at a distance r The repulsive potential is assumed to take the form g r 050 5 where Z r is the effective charge of atom i at distance r In order to de scribe the potential one has to determine the embedding function F p the atomic electron density p r and the effective charge Z r The nonlinear character of the embedding function is the relevant physical ingredient of the EAM model a linear embedding function F p x p makes the EAM model 16 reduce to a pair potential In the following we use a Finnis Sinclair FS potential for details see Ref 18 which assumes an embedding function F o
23. corresponding number of atoms The file is named spectrum nnnn dat where nnnn is the usual progressive integer 8 Time evolution Using the potentials illustrated above the system is evolved in time by a standard MD Verlet algorithm 22 which conserves energy and simulates a system in a microcanonical ensemble In addition some controls on the thermal properties of the environment were added For instance a Langevin Thermostat can be activated which adds a viscous force and a thermal white noise to the MD algorithm so that the equation of motion for the i th particle becomes iZi Here fj is the deterministic force due to the interaction with j th particle through the potentials described above y is the inverse relaxation time and R Rj R2 R3 is the thermal noise force which is a Gaussian ran dom process properly rescaled in order that in the continuous time limit Ra t 0 and Ra t Rg s 2mykgT ag t s with a 8 1 2 3 From the numerical point of view at any time step tg k x At where k 1 2 and At is the integration time step three Gaussian random numbers Ra t are independently extracted for each particle such that Raltk 0 and Ro tp Re th Qn ykpT At dagdx n Also a velocity rescaling thermostat is included in the program for testing purposes which simply rescales all velocities at every time step according to a given tem perature The thermostat switches the Newton microcanonical dynamics
24. e present program the choice was made to keep the potential well depth fixed when the cut off re is varied other choices are possible and convenient for other types of problems The parameter appearing in the potential energy window represents the actual potential well depth of the rescaled potential 2 This is to be distinguished from the parameter 9 which is the well depth of the unperturbed potential Wo r in Eq 1 Every time re is changed the parameter o of the unperturbed potential Wo r is suitably rescaled in order that assumes the required constant value On the other hand the parameter sigmag is not rescaled so that the actual sigma is that of the unperturbed potential i e sigma equivsigmag because the corresponding percentage variation of the position of the potential minimum 15 is much smaller This scaling procedure is explained in greater detail in the Appendix C 6 2 2 EAM potential Pair potentials cannot describe well some real materials properties as for instance vacancy formation energies 11 Also they imply the validity of the Cauchy relation C12 C44 for the elastic constant tensor which is in general not obeyed 12 From the point of view of MD simulations semi empirical potentials such as those based on the Embedded Atom Method EAM 13 14 15 16 17 represent a good compromise between the require ments for a high computational speed and accuracy Such model potentials are
25. gy green to its surfaces yellow to its edges and red to its vertices Compare also the relative populations of the peaks in the lower graphical window 4 Initial Configuration When the program is started a default configuration is built and the main graphical window of ALINE is open to visualize it 10 CRYSTAL TYPE BOUNDARY CONDITIONS Tit 0 0 001 v Al fee 110 110 001 n z 2 v per v per EEE w Fcc 100 010 001 MAREE vfix yv fix Y v fix z CONFIRM SIZE s fix h Pix Y v fix Z CANCEL ooo l Aset a0 1 5579 F al Nx 50 T A he a Border Width Lattice Constant Ratio Nz 16 v al m x al w Fix K w fix Y v fix Z free A free free Figure 2 Initial condition builder window appearing at the starting of the program To simulate a different system the new configuration window can be open at any moment by selecting New Configuration in the menu Program The initial configuration builder is shown in Fig 2 4 1 Initial Configuration from File The option to build a new configuration from a previously written config uration file or an equivalent restart option is not implemented yet Notice however that the user can set some default values such as the size of the sample in the library file initial h 4 2 New Configuration from scracth The procedure NewSimDialog in the source file graphics c man
26. hermal equilibrium is reached then the variation of the interatomic potential parameter is reiterated If on the other hand this is not possible this is interpreted as the system undergoing an irreversible transition e g a dislocation is nucleated and the variation program stops For an example of application of this option to dislocation nucleation see Ref 6 7 Output Besides information given to the user through the graphical windows the program can also produce information in other formats as listed below It also write messages and warnings and it can print snapshots of the system to 17 data or graphical files as well as the corresponding distributions according to a given quantity in similar file formats The output files are listed in Table 3 e Messages The program writes all its information and warning mes sages on the standard output that is on the monitor if not set oth erwise This can be used to check what the program is doing and for debugging the program Messages are usually of the form Pname where Pname indicates the name of the local procedure where the message is printed from Messages can be written to file by simply redirecting the output with the unix gt operator Fur thermore many more commented message commands can be found in the codes in the most of the procedures which can eventually be uncommented temporarily for debugging reasons e xyz format files The program can
27. lattice mismatched hetero structures To this aim the program has been given some particular visualization and in teractive features described below in detail The program is intended to be user friendly so that it is not necessary to read the manual before trying the first simulation runs However for editing the code for the study of specific problems or a more detailed overview of its functioning and possibilities the present notes may be useful The content of this manual partially overlaps with that of Refs 5 6 Latest changes and added features of ALINE can be found here as well in the program web page 3 2 General features of the program 2 1 Motivation In the first place ALINE is born as a MD code and as such can be used for standard simulations of 3D many particle systems whose particles interact either via a pair wise or a many body potential However the program is also provided with some special numerical tools which enable the user to study and visualize easily a wide range of phenomena in condensed matter systems This is possible thanks to the coupling between the MD code and a Graphical User Interface GUI based on the Motif Library While the MD code performs the standard computations for evolving the system in time the GUI allows the user to change the system parameters in real time and chose a suitable visualization mode of the particles A first advantage of a program with such a structure respect to a st
28. n Fig 1 mean potential energy is used to color atoms in the drawing window and at the same time is the independent variable for the atom distribution plotted in the mean potential energy space represented in the plotting window In this way one can analyze the atom distribution in a given property mean potential energy in this example and at the same time check how such a property is distributed in physical space This can be very useful for instance when looking for a crystal defect hidden inside the bulk of the crystal Instead of inspecting physical space e g by slicing the system where the crystal defect could be difficult to observe directly one can study the distribution of atoms according to their values of their mean potential energy In fact it turns out that often crystal defects occupy characteristic Table 2 Single particle quantities corresponding to the available color visu alization modes variable for the i th atom description of the variable atom type type i 1 2 kinetic energy K v 2 potential energy Ui 1 2 jz Vay total energy Ei Ki Ui depth along view line A time averaged potential energy U t 1 K BET U i tk total displacement or ri t r 0 time dependent diffusivity D t A KAt ee Ar tr centrosymmetry parameter CG DE r eee 2r number of neighbors ni number of atoms j with r r lt Re regions of the potential energy space and can be easily
29. nt as a reference unit length but on the other hand has some 24 drawbacks because there is no specific length unit For instance in this situation it is difficult to carry out any simulations involving com parative studies of lengths since the length unit is always rescaled in a way difficult to predict So this has been changed in this way All the LJ parameters epsilon sigma and r are now the basic input parameters which can be fixed by the user and are by default assigned the rescaled values epsilon 1 sigma 1 and r sigma 2 5 while the equilibrium lattice constant a is computed by minimizing the interaction energy with the neighbors This does not create big problems because it is expected that if sigma is of the order of unity also the lattice constant a will be of the same order of magnitude Energy unit Also the energy units has been changed respect the 2D version code but for a different reason Notice that the same problem illustrated here below which led to this change of unit could appear in principle in any codes using cut off corrected potentials The energy unit if there is only the short range LJ potential is usually taken as the potential depth epsilon and this apart from a fixed scaling factor is true also for the 2D code However when the cutoff correction is made in the usual way see section in order to have continuity of potential and force at the cutoff radius re the additional poten
30. on callback c program which manages buttons arrows bars etc simu c program with the Molecular Dynamics algorithm graphics h library file calc h library file callback h library file simu h library file xmkmf make Makefiles make On many systems these commands can be replaced by xmkmf a make but this does not work e g on some mac computers while the previous command sequence has been found to work well anyway By compilation the executable file aline is produced If the compilation is repeated because for any reasons it may be necessary to first give the command make clean One can then execute the program by simply giving the command aline When this command is given the first dialog window of ALINE is open The use of this and the other windows to create the initial configuration of the system and simulate its time evolution by MD are described in the next sections 3 Visualization modes The main GUI consists of two main graphical windows in the center two lateral columns and a menu list as shown in Fig 1 The text windows on the left hand side provides basic information about the system such as current time step number of atoms system size energy conservation temperature and boundary conditions and can be suitably selected from the menu Information A series of menu lists on the top of the window allow the user to modify the system in other respects There are basically two different graphical represent
31. pped tar archive aline tar gz suitable for unix environments In particular the program has been tested so far on True64 UNIX Linux i386 Mac OS X 10 3 and 10 4 2 5 Expanding the program package After downloading the package can be expanded by the commands gunzip aline tar gz tar xvf aline tar One will find a folder alinefiles containing three subfolders src exe and data The folder exe is empty and can be possibly used as a working area after compilation to save various versions of the executable files The folder data initially empty is needed by the program for some output files and should not be deleted The folder src contains e An Imakefile to be used to create the corresponding executable file as explained below e The C source files see table 1 e The library h files see table 1 2 6 Compiling the program The Imakefile creates a suitable Makefile according to the environment of the machine used This is a very simple noteworthy method to compile and we quote directly the OpenMotif manual The easiest way to compile note added is to use imake a pro gram supplied with the X11 distribution that generates proper Makefiles on a wide variety of systems type Table 1 Source files of the program ALINE file description initial h library file with some initial settings and default values graphics c main file which also manages graphical windows calc c program which prepares the initial configurati
32. ram A Main Variables It can be useful to know the names of some main variables Atoms are characterized by the following coordinates n 1 nAtom rin x r n y r n z current coordinates r0 n x rO n y rO m z initial coordinates vr n x vr n y vr n z velocity ar n x ar n y ar n z acceleration atype n type of atom atypeO n initial type of atom 1 or 2 Notice however that the values of atype n and atypeO n are 1 atom of type 1 1 fixed atom of type 1 2 atom of type 2 2 fixed atom of type 2 btype n position of the atom in the sample values of btype n 0 bulk atom not on surface edge corner 1 X border on the border parallel to yz plane at x 0 1 X border 2 Y border 2 Y border 3 2 border 3 Z border 23 B Further details e Allocation and re allocation depending on the current number of atoms nAtom are now in the separate subroutines AllocateN nAtom and ReAllocateN nAtom so they can be called from any function without repeating the corresponding commands e The procedures SaveO and Restore0 are used to save the current co ordinates in temporary vectors and to resume them respectively while making changes to the current configuration C Differences with previous 2D versions This section is particularly intended for users of the 2D version boundary2D in order to check some differences with ALINE e
33. rpendicular to it The fixed boundary conditions can be chosen independently on the surfaces at positive or negative coordinates For example choosing the option X causes atoms on the surface perpendicular to the z axis and at x gt 0 to have their x degrees of freedom frozen while moving freely in the y z plane The option X produces the same effect on the surface at x lt 0 while the option X applies the same constraint at both surfaces By surface it is meant the set of atoms made up by the layers within a certain thickness from the sample surface as defined by the parameter Border Width in units of lattice constant which can be set in the same window Free boundary conditions are actually no conditions at all i e atoms are free to move wherever e Initial temperature The initial temperature To defines the modulus of the initial velocities of atoms which are assigned with random direc tions according to the Maxwell Boltzmann distribution with the initial temperature To Pressing the button OK produces the selected initial configuration which can now be further modified with some options described below 5 Specimen From the Specimen menu one can manipulate the model specimen in order e g to produce cracks and indentations make an interface introducing a 12 second type of atoms or introduce some defects such as a screw or an edge dislocation 5 1 Interface Selecting Interface in the menu Specimen calls
34. s from user to program are represented by the various buttons and similar widgets in the windows and are managed by the file callback c They allow the user e g to select a particular initial configuration and modify the visualization mode and the system parameters e The preparation of the initial configuration together with all its pos sible variants is carried out by the procedures in the file calc c e Finally time evolution during a single generic time step is carried out in the file simu c whose procedures are called by the main program every time step 21 callback c N file xyz fig xwd P Figure 3 Scheme of the program ALINE The main program graphics c represented by the GUI in the center manages the graphical windows and produces the output In the upper part the library file initial h is shown where some default values can be set by the user and the program calc c used for constructing the initial configuration The right side represents the programs simu c for the molecular dynamics algorithm and callback c for undertaking the actions set by the GUI buttons Below the GUI the main outputs are symbolically represented namely the atomic configuration files in xyz format the upper and lower graphical window of the GUI in xwd format and various information about the program status on the standard output 22 Appendices Inside the prog
35. tential 6 2 2 EAM potential 6 3 Programming potential parameters Output Time evolution Source files Main Variables Further details Differences with previous 2D versions Gale TimeSs 2 iedala Bate Ray aba ie A 10 Ea Mets fe ahah a toy 11 So AN goat iS Be bits 11 12 Bh i ARG dee of 13 Se Mes aie E titan Cae 13 Se Maat he aM salt a 14 14 ped Ro DEAT dee a 14 east ESEE 14 Seth Tepes too oe Ae ah ate 15 AE E Sais ae tt Ee 16 Se Rott ats Me raat de 17 17 20 21 23 24 24 1 Introduction Here the program ALINE 3 for interactive Molecular Dynamics MD sim ulations is illustrated in various respects The program was originally con ceived as an extension of fracture 1 a program for the study of frac ture phenomena in two dimensional 2D crystals and hetero structures also developed as ALINE at the Laboratory of Computational Engineering Helsinki University of Technology 4 The program ALINE extends fracture in some directions e g the possibility of studying three dimensional 3D systems and of varying some interatomic potential parameters At the same time some features such as the automatic counting of crystal de fects have not been implemented in ALINE yet due to the difficulties of a three dimensional generalization One of the goals of the program was a satisfactory understanding at atomic level of complex phenomena in solids such as dislocation nucleation in
36. the procedure Interface in the source file graphics c which opens the interface window The inter face window allows the user to change the types of atoms in a box centered at XO YO and ZO with its x y plane oriented along the direction defined by the angles theta and phi and of linear sizes SIZE 1 SIZE 2 and SIZE 3 The interface is not really created in the sample until the CONFIRM button is pushed In case the system can also be reset to a single type of atoms It is to be noticed that in order to visualize the two different materials the view mode Atom Type must be selected It can be useful to recall that it is possible to visualize one of the two types of atoms a time Furthermore one should be aware that the actual differences between the two materials ynamely their potential parameters cannot be set in this window The distinction between type 1 and type 2 atoms is so far only formal if it is not set by the user in the interaction potential window to be open through the menu button see Sec 6 2 5 2 Cracks and indentations Selecting Crack button in the menu calls the procedure Crack in the source file graphics c which opens the crack window The various pa rameters specify position orientation and sizes of the box in which the crack indentation is done that defines which atoms are to be eliminated in the current configuration The crack has the shape of a box with center orientation and sizes defined similarly to the
37. tial term which is linear in r changes the whole shape of the potential As a result both the depth and the position of the minimum of the potential vary From a rigorous point of view the new potential cannot be called a LJ potential it is in fact called cut off corrected LJ potential just to avoid confusion because it is different from the original LJ potential In particular it has lost the main characteristic of the LJ potential namely its long range tail rl 6 and it contains aterm xr Thus if one uses a cut off corrected potential one is actually simu lating a system different from that selected originally Of course one would like to know exactly the parameters of the new corrected poten tial The change in the parameters may be not so small The default value of the 2D code for the cutoff ratio is re sigma 2 which lead to a difference larger than 10 for the potential depth epsilon and consequently for all the other relative energies such as temperature which are measured in units of epsilon between the unperturbed and the corrected potentials Here are some values of the relative variations 25 Table 4 Relative changes in the potential well depth Ue U re min U r and in the equilibrium distance re as a function of the cutoff Te re sigma AU A re sigma 1 5 2 3 gt 5 50 1 10 0 1 1 0 05 lt 0 1 lt 0 05 of epsilon respect to the unperturbed LJ potential for some
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