IOTA - a Code to Study Ion Transport and Radiation Damage in Composite Materials

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1 Forshungszentrum Karlsruhe in der Helmholtz-Gemeinshaft Wissenshaftlihe Berihte FZKA 6984 IOTA - a Code to Study Ion Transport and Radiation Damage in Composite Materials C. H. M. Broeders, A. Yu. Konobeyev, K. Voukelatou Institut für Reaktorsiherheit August 2004

2 Forshungszentrum Karlsruhe in der Helmholtz-Gemeinshaft Wissenshaftlihe Berihte FZKA 6984 IOTA - a ode to study ion transport and radiation damage in omposite materials C.H.M. Broeders, A. Yu. Konobeyev, K. Voukelatou Institut für Reaktorsiherheit Forshungszentrum Karlsruhe GmbH, Karlsruhe 2004

3 Als Manuskript gedrukt Für diesen Beriht behalten wir uns alle Rehte vor Forshungszentrum Karlsruhe GmbH Postfah 3640, Karlsruhe Mitglied der Hermann von Helmholtz-Gemeinshaft Deutsher Forshungszentren (HGF) ISSN urn:nbn:de:

4 IOTA - ein Programm für Untersuhungen von Ionentransport und Strahlenshäden in Verbundwerkstoffen Zusammenfassung Der Code IOTA wurde mit dem Ziel entwikelt, primäre Shäden durh Bestrahlung mit Ionen in Verbundwerkstoffen untersuhen zu können. Der Code kann für die Berehnung der Gesamtzahl der primären Shäden in den Materialien, für Displaement-Wirkungsquershnitte und für die räumlihen Verteilungen der Strahlenshäden benützt werden. Die Berehnungen für den Transfer der kinetishen Energie des bewegenden Teilhens zum Atom im Gitter, basieren auf der Anwendung von tabellierten Daten oder auf analytishen Formeln für die differentiellen Wirkungsquershnitte. Die Simulation wurde mit der binary ollision approximation (BCA) und mit dem Monte Carlo Verfahren realisiert. Unter Verwendung von Rehnungsergebnissen nah der Methode der Molekular Dynamik (MD) kann der IOTA Code auh für hohenergetishe Rehnungen in gekoppelten BCA-MD Rehnungen angewandt werden. i

5 Abstrat The ode IOTA has been elaborated to study primary radiation defets in omposite materials irradiated by ions. The ode may be used for the alulation of the total number of primary defets reated in materials, for the displaement ross-setion and for the spatial defet distribution. The alulations are based on the use of tabulated data or of analytial expressions for the differential ross-setion for the transfer of the kineti energy from the moving ion to a lattie atom. The simulation is based on the binary ollision approximation and the Monte Carlo method. Using the results obtained with the help of the method of moleular dynamis (MD), the IOTA ode may also be applied for high energy alulations in joint BCA-MD alulations. ii

6 Content 1. Speifi features of the ode Brief desription of the method of alulations Monte Carlo simulation Integration Simple evaluation Combined BCA-MD alulation Flowhart of the ode Computer ompatibility Exeution of the IOTA ode Preparation of the main input file for the IOTA ode Examples of the INPUT file Preparation of the data for the stopping power Desription of the output file of the IOTA ode Example of the alulation Referenes Desription of the diskette with the IOTA ode distributed with this report. Windows version using GNU FORTRAN Compiler The text of the IOTA ode iii

7 Speifi features of the ode The ode IOTA (IOn TrAnsport) has been reated for the investigation of the primary radiation defets in omposite materials irradiated by ions. The ode alulates the total number of primary defets reated in materials, the displaement ross-setion and the spatial defet distribution. The alulations are performed with the help of the different approahes desribed below. The simulation of the ion movement in the media is based on the binary ollision approximation (BCA) and the Monte Carlo method. The IOTA ode an be applied for high energy alulations using the results obtained with the help of the method of moleular dynamis (joint BCA-MD alulations). History. The reation of the IOTA ode was initiated in January, 2003 and the first version of the ode was approved in April, The urrent version is realized in Deember, The servie ode SL_LNS4A used for the input data preparation was written in Now it was heked and rewritten. 1. Speifi features of the ode The IOTA ode an be applied for omposite materials having up to 21 different omponents. The ode is based on the use of any justified and approved differential ross-setion dσ(e,t)/dt [1-3] for the transfer of the kineti energy T from the moving ion to the lattie atom. The IOTA ode does not repeat any parts and algorithms of the popular odes based on the BCA approah [4-7]. The advantages of the IOTA ode are i) the possibility to simulate the damage proess based on the different ap proahes with the help of the Monte Carlo method, and by the numerial inte gration of the orresponding distributions in a single omputer run; ii) the algorithm allows easily inorporation of the results obtained by the MD method and to perform ombined BCA-MD alulations; iii) the faster running time omparing with the other BCA odes. 1

8 Brief desription of the method of alulations 2. Brief desription of the method of alulations For the inident ion with kineti energy E the radiation damage dose rate is defined by the partile flux and the atomi displaement ross-setion σ d (E). This rosssetion is alulated as follows dσ(e,t) σd (E) = ν(t) dt, (1) dt where dσ(e,t)/dt is the differential ross-setions for the transfer of a kineti energy T from the inident ion to a primary knoked-on atom (PKA), ν(t) is the asade funtion equal to the total number of displaed atoms produed by the PKA of kineti energy T. The IOTA ode alulates the value of the asade funtion ν(t), the spae distribution of the defets reated and the displaement ross-setion σ d (E). A single omputer run for the inident energy E gives the ν(t) values for the whole energy range below this energy Monte Carlo simulation The simulation of the ion transport an be desribed by the following sheme. 1. Firstly the mean free path L of the primary ion is alulated with the help of the expression 1 L =, (2) σ (E) int N 0 where E is the kineti energy of the projetile, N 0 is the number density of atoms in a material. The ross-setion σ int (E) in Eq.(2) orresponds to the interation of the primary ion with the lattie atom and the transfer to it of the portion of the kineti energy exeeding the threshold displaement energy E d. It is alulated as follows σ int (E) = N i= 1 w i σ (i) int (E) = N i= 1 w i T (i ) max E (i) d dσ (E,T), (3) i where w i is the atomi fration of the i-th omponent of the target material, E d (i) is the effetive threshold displaement energy for i-th omponent, T max (i) is the maximal energy transferred from the ion to the PKA defined by the kinematis. 2

9 Brief desription of the method of alulations In the present version of the IOTA ode the differential ross-setion for the transfer of the kineti energy T from the primary ion to the lattie atom dσ(e,t) is alulated as follows d dt 2t 2 1/ 2 σ i (E,T) = πa f (t ) 3/ 2, (4) where the funtion f(t 1/2 ) and the sreening length a are alulated based on the different approahes depending on the user hoie by input. i) The f(t 1/2 ) funtion and sreening length are defined aording to Ref.[2] (the IOTA ode parameter IDSDT on Card 2 with valid values 0, from Table 1) f (t 1/ 2 a = a ) = λt 1/ 2 m 1 m q 1/ q [ 1+ (2λ t ) ] 1/ 3 3 1/ ( 2 / 3 2 / Z + ) 2 0(9π /128) 1 Z2 2,, where the orresponding available sets of the λ, m and q parameters are listed in Table 1. Table 1 Sets of the λ, m and q parameters for the f(t 1/2 ) funtion alulation and the IOTA ode parameter IDSDT from Ref.[2] λ M q Referene IDSDT /3 2/3 [2] 0 or [13] [13] [13] [13] [14] 15 ii) The f(t 1/2 ) funtion and a are alulated aording to Ref.[3] (IDSDT =1 on Card 2) 3

10 Brief desription of the method of alulations f (t 1/ 2 ) = a t j/ 4 1 x + a (x + a 2 2 3) j=1, a 1 =0.088, a 2 =1, a 3 =0.2 for t 1/ j=1, a 1 =0.23, a 2 =1.3, a 3 =0.4 for 0.04 < t 1/2 1 j=0, a 1 =0.4563, a 2 =0, a 3 =0.3 for 1 < t 1/2 40 j=0, a 1 =0.5, a 2 =0, a 3 =0 for t 1/2 > 40 a = a 3 ( ) 1/ 2 1/ 2 2 / Z +, 2 1/ 3 0(9π /128) 1 Z2 For both ases i) and ii) 2 t = εt / α ε 0, a A 2 E ε = E / ε0 = 2, Z Z e (A + A ) α 2 4A1A = (A + A ) 2 where Z 1, A 1 and Z 2, A 2 are the atomi number and mass number of the projetile and the target material, respetively, a 0 is the Bohr radius. The values of the σ int (E) ross-setion are alulated by the SL_LNS4A ode before the IOTA ode run and stored on speial files. 2. The trajetory of the ion is divided in small steps. The step l is defined as a minimal value from the part of the mean free path L/n and the distane δx, where the ion energy loss is less than the part of the ion kineti energy γe. The values of parameters n and γ adopted in the urrent version of the ode are equal to 10 and 0.02 orrespondingly. The value of δx is obtained from the total stopping power. 3. For the defined l value the elasti interation of primary ion with a lattie atom is simulated by Monte Carlo. The elasti interation orresponds to the transfer of the energy to PKA more than the threshold displaement energy E d. 4. If the elasti event ours, the type of the PKA from the omposite material is defined by the stohasti method based on w i σ (i) int values (Eq.(3)). Than the kineti energy T of the PKA is obtained with the help of the dσ(e,t) distribution (Eq.(4) by the Monte Carlo rejetion method. 4

11 Brief desription of the method of alulations 5. The primary ion passes the distane l and losses the energy transferred to the PKA and for the eletroni exitation. The last energy is defined from the eletroni stopping power (de/dx) el. The PKA harateristis are stored for the further treatment. The new mean free path is defined for the primary ion and the proedure desribed above is repeated. 6. If the elasti ollision with the energy transfer exeeding E d does not our, the primary ion moves on the distane l. Its energy is dereased orresponding to the experimental eletroni stopping power (de/dx) el and the part of the nulear stopping 0 Ed power ( de / dx) n, whih orresponds to the energy transfer from the ion to the lattie atom from 0 to Ed value. The data ( de / dx) n are prepared by the SL_LNS4A 0 Ed ode before the IOTA ode run. 7. The primary ion is traing while its kineti energy is less than the minimal effetive threshold displaement energy E d (i) from all N-omponents of the omposite material. 8. The stored PKA s are treated as primary ions produing new knok-on atoms and proedure desribed above repeats. 9. The proess desribed above is repeated until the energy of all PKA s reated is less than the minimal E d energy and the omputer bank of PKA s is empty Integration Along with the Monte Carlo simulation the IOTA ode alulates the number of the primary defets ν(e) by the numerial integration of the ratio of the losses for damage prodution to the total stopping power. The total number of Frenkel pairs produed by the ion with the energy E 0 in the material is alulated using the following expression [1] (de / dx) dam ν(e ) = T ~ (E0 ) = 0 2E 2E (de / dx) + (de / dx) de d d E 0 0 el n, (5) where E 0 is the primary ion energy, T ~ is the energy going to the prodution of displaed atoms. The value (de/dx) dam in Eq.(5) is the speifi energy loss for the damage prodution, (de/dx) el is the eletroni stopping power and (de/dx) n is the speifi energy loss for the elasti sattering (nulear loss). The speifi energy loss for the damage prodution is alulated as follows 5

12 Brief desription of the method of alulations de dx dam = N 0 T max E d dσ(e,t) T ~ (T)dT, (6) dt where N 0 is the number density of atoms in a material, T ~ (T) is the energy for defets prodution, dσ(e,t) is alulated by Eq.(4). The energy for the damage prodution T ~ (T) is alulated aording to the NRT-approah [4,8] T T ~ NRT (T) = 1+ k g( ε) (kev), (7) g(ε)= ε 1/ ε 3/4 + ε, 32 m k = 3 π M e 2 1/ 2 (A A 1 3/ A (Z ) 3/ / Z Z 2 / / 3 2 Z ) 1/ 2 2 3/ 4, 2 [ A T /(A A )][ a /(Z Z e )] ε =, where m e is the mass of an eletron, M 2 is the mass of the atom of target material and the other values are defined above, e is the eletron harge. Note, that the value of k in Eq.(7) is defined aording to Robinson [4] and for the ase of Z 1 =Z 2, A 1 =A 2 it oinides with the NRT-value [8] equal to 1/6 1/ 2 k = Z ( Z / A ) Simple evaluation For the omparison with other alulations, the value of the asade funtion ν(e) is evaluated with the help of the NRT-formula [8] 0.8 ν ( E) T ~ NRT = NRT (E), (8) 2E d where T ~ NRT (E) is alulated by Eq.(7) Combined BCA-MD alulation The simulation desribed in Set.2.1 is performed up to a ritial ion energy T rit, below this energy the results of MD alulations are used to obtain the total number 6

13 Brief desription of the method of alulations of defets. This energy is applied as for the primary ion, as for PKA s produed in the ollision asade with the energy above T rit. The typial value of T rit is between 5 kev and 100 kev depending on the MD simulation. The results of the MD alulations are introdued in the ode in the form of the defet prodution effiieny. The effiieny is equal to the ratio of the total number of survived point defets (Frenkel pairs) to the number of defets alulated by the NRT model (Eq.(8)). The general expression for the defet prodution effiieny is as follows α2 η( E MD ) = α1 E MD + α3 E MD, (9) where the energy E MD is supposed equal to the T ~ NRT energy in Eq.(7), α i are fitting oeffiients. To perform the alulation the user should supply the values of the α i parameters in Eq.(9) or use the default values whih are available in the ode for a limited number of elements (Fe, Cu, W). 7

14 Brief desription of the method of alulations 2.5. Flowhart of the ode The flowhart of the ode is shown in Fig.1 Interation rosssetions prepared by SL_LNS4A ode User input data Stopping power data (Chapter 7) Preparation data for alulations Basi Monte Carlo alulations (Chapter 2.1) Integration (Chapter 2.2) Evaluation and printing results Fig.1 8

15 Computer ompatibility 3. Computer ompatibility The IOTA ode and the servie ode SL_LNS4A are written in FORTRAN. The IOTA ode uses a random number generator, whih an be different for different FORTRAN ompilers. The urrent version of the IOTA ode uses the GNU FORTRAN [9] built-in random number generator RAND. To substitute it by the other one it is neessary to hek the FUNCTION RANDOM in the IOTA ode. 4. Exeution of the IOTA ode The exeution of the IOTA ode inludes several steps. 1. The preparation of the main input file. The name is INPUT. The proedure is desribed below in Set The stopping power alulation by the SRIM ode [7] if the option SRIM is hosen in the input file (Set.5). The details are disussed in Set.7. If the SPAR option is seleted in INPUT, the stopping power is alulated by the IOTA ode and point 2. is omitted. 3. Run SL_LNS4A ode. The input file is the same as for the IOTA ode (the file INPUT). After the SL_LNS4A ode exeution the files with the information needed for the IOTA ode run are reated. After the file reation it is not neessary to exeute this ode again for the other IOTA ode runs with the same INPUT and other set of the primary ion energies, whih do not exeed the TLIM value (Set.5). 4. Run the IOTA ode. Analysis of the results. 5. Preparation of the main input file for the IOTA ode The main input file is alled INPUT. It is loated in the same diretory with the exeutable modules of the IOTA ode and the SL_LNS4A ode. The file INPUT 9

16 Preparation of the main input file for the IOTA ode All data are introdued in the file in the free format form inluding the names of the external files. Eah line beginning from the symbol, or! defines the omment ard. The length of the external file names should not exeed 12 haraters. The struture of the INPUT file is desribed below. (Card 1) The title of the task desribed in 80 haraters inluding blank spaes. (Card 2) Parameters IGRAPH, MAXPLAY, TLIM, IDSDT. Parameter IGRAPH is the damage profile printing option. The value IGRAPH = 0 suppresses the printing of the damage profiles (spae damage distribution). IGRAPH = 1 means the printing. The parameter MAXPLAY defines the maximal number of attempts to get the kineti energy T of PKA from the dσ(e,t)/dt distribution in the FUNCTION TPKA. The play of T value is performing by the Monte Carlo rejetion method. If after MAXPLAY attempts the definition of T failed, the kineti energy of PKA is taken aording to the ratio T max T max dσ(e,t') Tmean = T'dT' dσ(e,t' ) dt' E d E d, (10) the T mean values are alulated by the SL_LNS4A ode before the IOTA ode run. The possible values of MAXPLAY are i) atual number of attempts ii) MAXPLAY=1. In this ase the kineti energy T of PKA is substituted by T mean from Eq.(10). It greatly redues the time of the alulation at the high ion energies, but should be referred to a approximate alulations iii) MAXPLAY=0. It means the use of the default value of MAXPLAY equal to 250,000 iv) MAXPLAY < 0 means the unlimited number of attempts. It inredibly inreases the running time of the ode at the high energies of the primary ions. The value of TLIM defines the maximal energy (MeV) to be treated by the SL_LNS4A ode. It should exeed the maximal energy of the primary ion introdued in the IOTA ode input file (see below). The default value (TLIM=0) is equal to 5 GeV. 10

17 Preparation of the main input file for the IOTA ode Parameter IDSDT defines the method of the f(t 1/2 ) funtion alulation (Eq.(4)). The values IDSDT=0, orrespond to the f(t 1/2 ) funtion from Ref.[2] (see Table 1 for IDSDT definition). The value IDSDT=1 means the alulation of f(t 1/2 ) with the help of the approah from Ref.[3]. (Speial ards 1 and 2 ) These ards are used only for the ombined BCA-MD alulations. [Card 1 ] To initiate the alulations the ard should ontain the words BCA and MD in any ombination printed in the same line (See Example 3) [Card 2 ] CMD(1), CMD(2), CMD(3), ELOW, EHIGH, ECRIT The CMD(i) values orrespond to the oeffiients α i in Eq.(9) for the effiieny of the defet prodution obtained from the MD alulations. ELOW and EHIGH are the lowest and the highest E MD (or T ~ NRT ) energy in kev, where the effiieny supposed to be a onstant, η(emd < ELOW) = η(elow), η(e MD > EHIGH) = η(ehigh). The energy ECRIT (kev) is equal to the value of the E MD energy in Eq.(9) where the MD results for the defet prodution are used instead of the BCA alulations (Set.2.4). Usually, ECRIT is equal to EHIGH. The ritial energy T rit mentioned in Set.2.4 is alulated by the ode basing on the ECRIT value for the inident ion and the ions of the target material. The default values are taken if CMD(i),i=1,3; ELOW; EHIGH and ECRIT are set to zero. They are available for Fe, Cu and W in the urrent ode version (Card 3) The atomi number (Z) and the atomi weight (A) (amu) of the projetile. If A=0 the atomi weight is taken for the natural mixture of isotopes for this element (Z) from internal ode tables. (Card 4) The density of the target omposite material (RO), the number of the omponents of the ompound (NK) and the stopping power option (SO). The RO value is introdued in g/m 3. If RO=0, the density is taken from the internal ode table for this material. The NK value is equal to the number of unique atoms of the target. For example, the NK value is equal to 2 for Li 2 O, and equal to 3 for Al 2 (SO 4 ) 3. It is for the ase if only the single isotope of eah element is onsidered in the alulation. For the mixture of the isotopes the NK value should inlude their amount. If the lithium from the Li 2 O ompound is onsidered as a mixture of 6 Li and 7 Li isotopes, the NK value is equal to 3. The stopping power option (SO) is a harater variable desribing the method of the stopping power alulation. It an be equal as follows 11

18 Preparation of the main input file for the IOTA ode i) SRIM (or Ziegler ). The data for the stopping power are taken from the speial files prepared by the SRIM ode [7]. (See Card 6,9 and Set.7). This option is reommended. ii) SPAR (or Armstrong ). The stopping power is alulated in the IOTA ode by the SPAR routine [15,16]. It should be noted that for the heavy ions and high energies the auray of this method is less than of the SRIM ode. (Card 5, 6 or more if neessary) Names of files with the ross-setions and other information to be prepared by the SL_LNS4A ode. Eah name orresponds to the interation of the primary ion with the ertain material omponent. For example, for an α-partile projetile and Li 2 O target the names are introdued for α+o and α+li interations 1. The sequene of the file names should be the same as for the desription of the omponents of the omposite material (Card 7 and others). The names are separated by at least one blank spae. Any number of ards an be used for the total list of the file names. (Card 6 2 ) Name of file with stopping power data orresponding to the primary ion interation with the ompound (e.g. with Li 2 O). The format of the file orresponds to the SRIM ode output [7] (see Set. 7). If the SPAR option is seleted for the stopping power alulation (Card 4) the Card 6 should be omitted. (Card 7) The atomi number (Z), the atomi weight (A) (amu), the atomi onentration (W) and the effetive threshold displaement energy (ED) for the first omponent of the omposite material (target). If the zero value is introdued instead of A value (A=0), the atomi weight is taken for the natural mixture of isotopes with the atomi number Z from the internal ode table. The atomi onentration (W) is introdued in the normalized or the unnormalized form. For example, in the desription of the oxygen from Li 2 O ompound both values or 1 are orret. The displaement energy (ED) is introdued in ev. The default value (ED=0) is equal to 40 ev. (Card 8, 9 or more if neessary) Names of files with the data to be prepared by the SL_LNS4A ode for the interation of the ion desribed in Card 7 with eah omponent of the omposite material. For example, if the Card 7 desribes the oxygen from 1 it is supposed that Li 2 O onsists of single Li and single O isotope. 2 the number depends on the amount of ards used to desribe the names of files prepared by the SL_LNS4A ode (see Card number 5,6 or more) 12

19 Examples of the INPUT file Li 2 O, the urrent ard should inlude the file names for the O+O and O+Li interations. Note, the sequene of suh file names should oinide with the sequene of the different material omponents desription (given in the ards similar to the Card 7). (Card 9) Name of file with the stopping power data from the SRIM ode orresponding to the interation of the ion desribing in the Card 7 with the ompound. For example, if the Card 7 desribes the oxygen from Li 2 O ompound, the name of file given here is for the stopping power data for the O+Li 2 O interation. This ard is omitted for the SPAR option hosen for the stopping power alulation in Card 4. (Next ards similar to Cards 7-9). The same for other omponents of the ompound. For example, if the oxygen from Li 2 O is desribed in Cards 7-9 these ards are used for the lithium desription. (Card after the material desription). Names of the output files. Two file names are introdued for the usual alulations and three file names for the joint BCA-MD alulations. The first output file ontains the detail information about the alulation performed. The seond file repeats partly the data from the main output for the speial use, e.g. for the graphis representation. The third file ontains the results of the ombined BCA-MD simulation. (Next ards). The energy of primary ion (E) and the number of Monte Carlo events to perform the alulation at this energy (NHIST). The energy is introdued on the separate ards following one after another in MeV along with the unique NHIST number. The negative value shown in the list is onsidered as the last energy in the simulation. For example, to perform the alulation for inident energy equal to 10 kev with 999 Monte Carlo events and the primary energy equal to 1 GeV with 100 Monte Carlo events, one should introdue two suessive ards and Examples of the INPUT file A) Use the SRIM option for the stopping power alulation 13

20 Examples of the INPUT file The example of the INPUT file for the interation of 28 Si with the silion arbide is given below (Example 1) Example 1 The INPUT file for Si+SiC interations with the stopping power from SRIM ode IOTA ode input name of the task Test alulations Si+Silion Carbide Z, A of the projetile ion density (g/m3), number of omponents and stopping option SRIM name of files with the ross-setions from SL_LNS4A ode Si_Si.dat Si_C.dat de/dx for projetile + omposite media Si_SiC.Zie desription of the omponents for ompound Z, A, atomi fration, Ed (ev) ross-setions Si_Si.dat Si_C.dat de/dx Si_SiC.Zie C_Si.dat C_C.dat C_SiC.Zie names of output files messages mess2.dat energy of projetile and number of Monte Carlo events

21 Examples of the INPUT file B) Use the SPAR option for the stopping power alulation The example of the INPUT file is given here (Example 2). Example 2 The INPUT file for Si+SiC with the stopping power from the SPAR alulations IOTA ode input name of the task Test alulations Si+Silion Carbide Z, A of the projetile ion density (g/m3), number of omponents and stopping option SPAR name of files with the ross-setions from SL_LNS4A ode Si_Si.dat Si_C.dat desription of the omponents for ompound Z, A, atomi fration, Ed (ev) ross-setions Si_Si.dat Si_C.dat C_Si.dat C_C.dat names of output files messages mess2.dat energy of projetile and number of Monte Carlo events

22 Examples of the INPUT file C) Combined BCA-MD alulations The example of the INPUT file for the irradiation of natural tungsten by 167 Tm ions is given below (Example 3). The stopping power is obtained by the SRIM ode. The default parameters are used for the effiieny alulations at low energies. Example 3 The INPUT file for joint BCA-MD alulation for Tm+W interation IOTA ode input name of the task Test alulations Tm+W BCA + MD Z, A of the projetile ion density (g/m3), number of omponents and stopping option 0 1 Ziegler name of files with the ross-setions from SL_LNS4A ode tm_w.dat de/dx for projetile + media tm_w.zie Z, A, atomi fration, Ed (ev) ross-setions w_w.dat < de/dx > w_w.zie names of output files messages mess2.dat bamd.out energy of projetile and number of Monte Carlo events End 16

23 Preparation of the data for the stopping power 7. Preparation of the data for the stopping power This setion disusses the preparation of the stopping power data with the help of the SRIM ode. It orresponds to the reommended input option SRIM or Ziegler (see Set.5, Card 4) for the stopping power alulation. If the SPAR option is hosen in Card 4 of the INPUT file this setion should be omitted. The urrent version of the IOTA ode works with the output format of the SRIM ode [7]. The ode is distributed by the author [7] freely. To use the SRIM ode one should download it from Ref.[7] and install it on PC. If the SRIM ode is installed, the instrution to prepare the data for the stopping power suitable for the IOTA ode alulation is the following. 1. Selet Stopping/Range Tables in the main SRIM menu (general panel). 2. Selet the appropriate projetile and the target material. In the ase of the ompound one should introdue the orret density of the ompound. It is the same as in the Card 4 of the INPUT file of the IOTA ode (see Set.5). 3. Set the energy range of the projetile from 1 ev to 5.2 GeV (the maximal energy allowable in the IOTA ode). 4. Selet the units for the stopping power equal to MeV/(mg/m 2 )) (default in the main SRIM menu). 5. Perform the operation Calulate table and give the same name for the output file as shown in the file INPUT for the IOTA ode (Set.5). Store the output file in the same diretory where there are the exeutable modules of the SL_LNS4A ode and the IOTA ode. 6. Repeat this proedure for all atoms of the ompound, onsidered as a projetile. The example of the output of the SRIM ode for the ase of Si+SiC interation is given below (Example 4). Note. If the alulations are performed for the same material and the various projetiles with the equal atomi number and the different atomi weights it is not neessary to prepare the SRIM stopping power data for eah isotope. 17

24 Preparation of the data for the stopping power If the data are prepared for the ion with Z and A and the atual projetile in the task is Z and A, the eletroni stopping power is orretly realulated for a new energy grid (A /A)E. The nulear stopping power is renormalized aording to the following formula (de / dx) (de / dx) Z,A' n Z,A n A' = A t' / t / 1+ t' + ln( 1+ t + ln( t' + t + 1+ t') 1+ t ), t' 8 / 9 4 E A T = / 3 2 / 3 1/ 2 ZZT (A' A T )(Z ZT ), / 9 4 E A T t = / 3 2 / 3 1/ 2 ZZT (A A T )(Z ZT ), + + where E is the energy of projetile (MeV), Z T and A T are the atomi number and the atomi weight of the target material. The formula shown above is obtained from the analytial integration of T dσ(e,t)/dt, where dσ(e,t) is alulated by Eq.(4) and the f(t 1/2 ) funtion is defined by the λ, m and q parameters from the first line of Table 1. New data for the stopping power are written in the output file RENORM.STO. 18

25 Preparation of the data for the stopping power Example 4 The SRIM ode output for the S+SiC interation ================================================================== Calulation using SRIM-2003 SRIM version ---> SRIM Cal. date ---> Marh 24, 2003 ================================================================== Disk File Name = SRIM Outputs\Si_SiC.Zie Ion = Silion [14], Mass = amu Target Density = E+00 g/m3 = E+22 atoms/m3 ======= Target Composition ======== Atom Atom Atomi Mass Name Numb Perent Perent Si C ==================================== Bragg Corretion = 0.00% Stopping Units = MeV / (mg/m2) See bottom of Table for other Stopping units Ion de/dx de/dx Projeted Longitudinal Lateral Energy Ele. Nulear Range Straggling Straggling ev 6.406E E-02 1 A 1 A A 1.2 ev 6.406E E-02 1 A 1 A A 1.3 ev 6.667E E-02 1 A 1 A A 1.4 ev 6.919E E-02 1 A 1 A A 1.5 ev 7.162E E-02 1 A 1 A A 1.6 ev 7.397E E-02 1 A 1 A A 1.7 ev 7.624E E-02 1 A 1 A A 1.8 ev 7.845E E-02 1 A 1 A A 2 ev 8.270E E-02 1 A 1 A 1 A 2.25 ev 8.771E E-02 1 A 1 A 1 A ev 9.246E E-02 1 A 1 A 1 A ev 9.697E E-02 1 A 1 A 1 A ev 1.013E E-02 2 A 1 A 1 A ev 1.054E E-02 2 A 1 A 1 A ev 1.094E E-02 2 A 1 A 1 A LINES SKIPPED 1.80 GeV 1.658E E mm um um 2.00 GeV 1.529E E mm um um 2.25 GeV 1.398E E mm um um 2.50 GeV 1.291E E mm um um 2.75 GeV 1.203E E mm um um 3.00 GeV 1.128E E mm um um 3.25 GeV 1.065E E mm um um 3.50 GeV 1.009E E mm um um 3.75 GeV 9.611E E mm um um 4.00 GeV 9.186E E mm um um 4.50 GeV 8.471E E mm um um 5.00 GeV 7.893E E mm um um 5.20 GeV 7.702E E mm um um 4.50 GeV 8.471E F mm um um 5.00 GeV 7.893F E mm um um 5.20 GeV 7.702E E mm um um Multiply Stopping by for Stopping Units E+01 ev / Angstrom 19

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