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Capture Radius DB (Analytical Form)@

  • This is a REQUIRED file.
  • This file inputs analytical expressions for capture radii or interaction radii of defects
  • If a defect has no analytical expression, then it is inputted via a different input file
  • Lines starting with # (hash symbols) are considered as comments.
    • Each line has to be commented individually with #.
    • There is NO option to comment multiple lines simultaneously.

Notation@

  • The notation of pvpid = value represents the parameter value (pv) of a parameter with ID = pid.
  • As noted in the section on defect file format
    • pv1 corresponds to the type of a defect and,
    • pv2 corresponds to the total size of a defect complex.
    • pv3 corresponds to the № of vacancies or № of SIAs in a defect complex

  • In the example below to describe the format of the capture radius database.
    • pv1 = 0 represents a vacancy cluster.
    • pv1 = 1 represents an SIA cluster.
    • pv1 = 2 represents a He or trap cluster.
    • pv1 = 3 represents a vacancy & He (trap) complex.
    • pv1 = 4 represents a SIA & He (trap) complex.

DB Format@

All comments should be above the hash symbol
#
5 5
0 1 1 0   1 2     2 pi 3.14159 sz 1    2 sqrt(3)/2.0+(((3/pi)^(1/3))*((x-sz)^(1/3))) x
1 1 1 1   1 2     2 pi 3.14159 sz 1    2 1.15*sqrt(3)/2.0+1.15*(((3/pi)^(1/3))*((x-sz)^(1/3))) x
2 1 1 2   1 4     2 pi 3.14159 sz 1    2 2+pow(0.6/pi,1.0/3.0)*((x^(1.0/3.0))-1) x
3 1 1 3   1 3     2 pi 3.14159 sz 1    2 (sqrt(3)/2.0)+((3/pi)^(1/3))*((x^(1/3))-1) x
4 1 1 4   1 2     2 pi 3.14159 sz 1    2 1.15*(sqrt(3)/2.0+(((3/pi)^(1/3))*((x-sz)^(1/3)))) x

Description@

line 2 : #  Marks the end of comment line
line 3 : 5 5 :  Ist Number (№ of Lines)     IInd Number (Maximum № of Parameters)0

Line 4

\(\underbrace{\text{0}}_{~~~~\text{Line}\\ \text{Number}}~~~\underbrace{\text{1}}_{~~~~\text{№ of}\\ \text{parameters}^{\color{blue}1}}~~~\underbrace{1\quad 0}_{~~~\text{pid}\quad\text{pv}}~~~\underbrace{1\quad\;\; 2}_{~~\text{npid}^{\color{blue}2}\quad\text{pid}^{\color{blue}3}}~~~\underbrace{2}_{~~\text{nc (№ of}\\ \text{Constants)}}~~~\underbrace{\text{pi}\;\;3.141592\quad sz\;\;1}_{~~\text{cid1}\;\;\text{cv1}\quad\text{cid2}\;\;\text{cv2}}~~~\underbrace{2}_{~~\text{№ of}\\ \text{terms}^{\color{blue}4}}~~~\underbrace{\text{sqrt(3)/2.0+(((3/pi)^(1/3))*((x-sz)^(1/3)))}}_{\text{Analytical Exp.}}~~~\underbrace{\text{x}}_{~~\text{Variable}}\)

pid =  parameter id
pv =  parameter id value
npid =  № of parameter variables2
cid =  ID of a constant
cv =  value of the constant

0 Maximum number of parameters in this file and in the input file for initial simulation state should be the same

1 It is the number of parameters that will used to match a defect to the capture radius expression.

2npid is the number of parameter values that will used as variables in the capture radius expressions
  (equal to the number of independent variables in the capture radius expression)

3 npid is followed by the pids of parameters whose values (pv) will be used as independent variables in the capture radius expression

4 № of terms = capture radius expression + number of independent variables

  • In this particular example, line 4 specifies the capture radius of a vacancy cluster since pv1 = 0
  • npid = 1 specifies the number of independent variables that will be used to calculate the capture radius, which in this case is one.
  • This is followed by pid = 2, specifies the IDs of the parameter whose value would be used as the independent variable. In this case, the value of pv2, which is the total size of the vacancy cluster, will be used as the independent variable.
  • The next number is nc = 2 is the number of constants that would be used in the analytical expression, which is followed by the pairs of constant ID and numerical value of the constants.
  • In this case pi and sz with numerical values equal to 3.141592 and 1, respectively.

Syntax ⇔ Analytical Form@

This table shows the conversion of an analytical expression and how it is denoted in the input file.

DB Syntax Analytical Form
sqrt(3)/2.0+(((3/pi)^(1/3))*((x-sz)^(1/3))) \(\frac{\sqrt{3}}{2}+\sqrt[3]{\frac{3}{\pi}(x-sz)}\)
1.15*sqrt(3)/2.0+1.15*(((3/pi)^(1/3))*((x-sz)^(1/3))) \(1.15\Big(\frac{\sqrt{3}}{2}\Big)+1.15\Big(\sqrt[3]{\frac{3}{\pi}(x-sz)}\Big)\)
2+pow(0.6/pi,1.0/3.0)*((x^(1.0/3.0))-1) \(2.0+ \sqrt[3]{\frac{0.6}{\pi}}(\sqrt[3]{x}-1)\)
(sqrt(3)/2.0)+((3/pi)^(1/3))*((x^(1/3))-1) \(\frac{\sqrt{3}}{2}+\sqrt[3]{\frac{3}{\pi}(x-sz)}\)
1.15*(sqrt(3)/2.0+(((3/pi)^(1/3))*((x-sz)^(1/3)))) \(1.15\Big(\frac{\sqrt{3}}{2}\Big)+1.15\Big(\sqrt[3]{\frac{3}{\pi}(x-sz)}\Big)\)

Function Parser Library

𝕂𝕊𝕆𝕄𝔼 uses Function Parser Library for C++ v4.5.3 developed by Juha Nieminen, Joel Yliluoma. For more details on the parser please visit their website.

For more details on the syntax used to input an analytical expression go to the help page on syntax

Additional Details@

In the example above, the capture radius of a defect is defined based only on its type and is always a function of the defect’s total size. However, the key idea behind the format of this database is to define the capture radius based on a combination of defect parameters. Therefore, it is possible to define more than one analytical expression for the capture radius for a given defect type based on its other parameters. For example, it is possible to define two different capture radii for a given defect type based on the total size or sizes of individual components of a defect complex, as shown below:

  • line 1: specifies the capture radius of a defect type 0 or a vacancy cluster when the vacancy cluster size (Svac) is 1 ≤ Svac ≤ 200
  • line 2: specifies the capture radius of a vacancy cluster for all cluster sizes
  • Note: The specification of capture radius for all sizes comes after the specification for sizes 1 - 200. Therefore, the cluster radius of a vacancy cluster for sizes ≥ 201 is calculated using the expression specified on line 2.
    • Otherwise, the capture radius is always calculated using the expression specified on line 2 because always the first match is selected.
1 3 1 0 2 1 2 200  1 2     2 pi 3.14159 sz 1    2 2+pow(0.6/pi,1.0/3.0)*((x^(1.0/3.0))-1) x
2 1 1 0            1 2     2 pi 3.14159 sz 1    2 (sqrt(3)/2.0)+((3/pi)^(1/3))*((x^(1/3))-1) x

It is also important to note that one can use more than one variable to calculate the capture radius. For example, if one would like to use two variables then npid = 2, which is followed by the *pid*s of the parameters which will be used as the independent variables












This page was last updated on Jan. 13, 2023, 8:50 PM (PST)
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