4. Material

The material input module describes the composition of materials, including material density, the corresponding database of nuclides, nuclide fractions, and options for defining parameters related to continuous energy cross-sections or multi-group cross-section databases.

4.1. Material Input Options under the ACE Format Database

Ordinary Material Input Options can be defined as:

Mat <mat_id> <density>
    <zaid.xxx> <fraction>
    <zaid.xxx> <fraction>
    ……

where，

• Mat is the keyword for the Material input option;
• mat_id refers to the material ID，which corresponds to the filling material in the Cell input option;
• density refers to the overall material density. density > 0 indicates atomic density, where the units are 10²⁴atoms/cm³; density < 0 refers to mass density, where the units are g/cm³; density = 0RMC will automatically calculate the material density.
• zaid.xxx specifies the ACE database identifier cross-section database corresponding to the nuclide, where zaid is the nuclide ID and the suffix .xxx specifies the type of database. For ease of distinction, it is recommended that users use the suffix .xxc for continuous energy ACE databases and the suffix .xxm for multi-group databases when generating the database. For the specific nuclides and types corresponding to the cross-section database, please refer to the database index file xsdir;
• fraction refers to the fraction of the nuclide within the material. If fraction > 0 , the value represents the fraction of atomic density (relative value), while if fraction < 0 , the value represents the fraction of mass density (relative value). For a single material, all values of fraction must have the same plus/minus signs;

In addition to Ordinary Material Input Options, RMC also provides Thermal Material Input Options to specify the corresponding thermalization database for the continuous energy ACE cross-section.

Sab <mat_id> <zaid.xxx>
             <zaid.xxt>
             ……

where,

• Sab is the keyword for the Thermal Material Input Options;
• mat_id is the material ID, which is identical to the material ID defined in Mat ;
• zaid.xxx specifies the thermalization cross-section database identifier used by the nuclide. Please refer to the database index file xsdir for further details;

4.2. Material Input Card Based on HDF5 Format AIS Database

Currently, the HDF5 format AIS database supports neutron transport calculations for critical sources and fixed sources. The supported features include: all cross-section online processing functions, mesh, surface, and grid counters (type 1-8), cross-section counters, point counters, material perturbation, UFS method, source convergence diagnostics, and acceleration.

The input card for ordinary materials is:

Mat <mat_id> <density>
    <IsoSym> <FRACTION=...> <ENDFVERSION=...> <TMP=...>
    <IsoSym> <FRACTION=...> <ENDFVERSION=...> <TMP=...>
    ……

Where:

• Mat is the keyword for the material input card.
• mat_id is the material identifier, corresponding to the filling material in the Cell input card.
• density refers to the overall material density. density > 0 indicates atomic density, where the units are 10²⁴atoms/cm³; density < 0 refers to mass density, where the units are g/cm³; density = 0RMC will automatically calculate the material density.
• IsoSym specifies the isotope identifier; the HDF5 format AIS nuclear database is named based on isotope identifiers.
• FRACTIONrefers to the fraction of the nuclide within the material. If fraction > 0 , the value represents the fraction of atomic density (relative value), while if fraction < 0 , the value represents the fraction of mass density (relative value). For a single material, all values of fraction must have the same plus/minus signs;
• ENDFVERSIONspecifies the version of the data evaluation nuclear database upon which the HDF5 format AIS nuclear database is based. The program will index nuclear data files named with IsoSymunder the directory corresponding to that version.
• TMP specifies the Kelvin temperature of the nuclear database used for a certain isotope. When reading nuclear data, the program will read data files corresponding to temperature deviations of less than or equal to 0.1 K based on the user-input temperature value.

In addition to ordinary material input cards, RMC also provides a thermalized material input card to specify the corresponding thermalization database for continuous energy ACE cross-sections.

Sab <mat_id>
      <IsoSym> <ENDFVERSION=...> <TMP=...>
      <IsoSym> <ENDFVERSION=...> <TMP=...>
      ……

Where:

• Sabis the keyword for the thermalized material input card.
• mat_idis the material identifier that matches that in the Matcard and must be followed by a newline before entering the IsoSymparameter.
• IsoSymspecifies the identifier for the thermalization database used for nuclides.
• ENDFVERSION specifies the version of the data evaluation nuclear database upon which the HDF5 format AIS nuclear database is based. The program will index nuclear data files named with IsoSymunder that version’s directory.
• TMP specifies the Kelvin temperature of the nuclear database used for a certain isotope. When reading nuclear data, the program will read data files corresponding to temperature deviations of less than or equal to 0.1 K based on user-input temperature values.

4.3. Continuous energy ACE cross-section related Input Options

If the nuclide in the material input option uses a continuous energy ACE cross-section, you can set the relevant parameter options for it through the following input option.

CeAce [ErgBinHash = <flag>] [pTable = <flag>] [OTFPTB = <flag>] [OTFSAB=<flag>]
      [DBRC = <flag>] [TMS = <flag>] [TMSTally = <flag>] [OTFDB = <flag>]

where，

• CeAce is the keyword for the continuous energy ACE cross section related input option.

• ErgBinHash The tab specifies whether to use the program’s built-in hash table method to accelerate search speed of the energy mesh. When there are many nuclides, using the acceleration method can achieve higher computational efficiency, but it will also consume a small amount of additional memory. If the value of ErgBinHash = 1 (default value), hash table acceleration is used; if the value of ErgBinHash = 0 , hash table acceleration is not used.

• pTable specifies whether to use a probability table for unresolved resonances. This option is only available if the ACE cross section database used by the nuclide contains the UNR module. If the value of pTable = 1 (default), it indicates that the probability table is used, and pTable = 0 means the probability table is not used.

• OTFPTB specifies whether to use on-the-fly probability table interpolation for unresolvable resonance regions. This tab is used in conjunction with pTable , and on-the-fly probability table interpolation is used only when pTable = 1 . OTFPTB = 1 indicates that on-the-fly probability table interpolation is being used, and if OTFPTB = 0 (default value), on-the-fly probability table interpolation is not used.

• OTFSab specifies whether to use on-the-fly interpolation of thermal scattering data for the thermal energy zone (currently only on-the-fly interpolation of hydrogen in light water is supported). If OTFSab = 0 (default value), this indicates that on-the-fly thermal interpolation is not used, and if OTFSab = 1 , this means that on-the-fly thermal interpolation is used. Note: When using on-the-fly thermal interpolation, the cross-section library must be equipped with thermal cross-section libraries at several reference temperature points. At the same time, the corresponding thermal material “lwtr. ” in the material card can use a thermal library of any temperature in the cross-section library (only one thermal library needs to be filled in). “xsdir_sab ” is the index file of the thermal library during thermal interpolation. The file is placed in the same folder as the execution program. The internal structure of “xsdir_sab” is as follows:

  Datapath = // This is the folder where the thermal library for interpolation is located

  lwtr 293.6K lwtr01 // lwtr is the name of the thermalized material, here it is hydrogen in water; “293.6K “is the temperature of the thermalized nuclide, in K (Kelvins); lwtr01 is the name of the thermalization library used for interpolation.

• DBRC specifies whether to use the Doppler Broadening Rejection Correction (DBRC) algorithm. If the value of DBRC = 1, this means DBRC is being used, and if the value of DBRC = 0 (default), this means that DBRC is not used. Not using the DBRC algorithm will ignore the resonant elastic scattering of heavy nuclei in the epithermal region, and using the DBRC algorithm will increase the calculation time. The DBRC algorithm requires the use of the 0K database, and the nuclides in the 0K database must be named zaid.00c in the xsdir file. For example, if the user uses 1001.71c 8016.71c 92235.71c, then the xsdir file must contain the cross-section data of 1001.00c 8016.00c 92235.00c, and the cross-sections of these nuclides are all at 0K. Note that the user does not need to specify zaid.00c in the input card, but only has to add the relevant nuclides to the index file xsdir.

• TMS specifies whether to use the TMS (Target Motion Sampling) algorithm. The TMS algorithm can introduce the feedback effect of temperature changes on the cross section. The TMS algorithm requires the use of a nuclear database at 0K and the temperature of the nuclide cell. Using the TMS algorithm will increase the calculation time. If the value of TMS = 1 , this means that TMS is used, and TMS = 0 (default value) means that TMS is not used.

• TMSTally specifies whether TMS is used to calculate cross sections in Tally. When cross section information is used in Tally, TMSTally needs to be turned on, otherwise the Tally result will be inaccurate. When cross sections are not needed in Tally, turning off TMSTally does not affect the accuracy of the result. When TMS = 1 , TMSTally is turned on by default, but the user can specify TMSTally = 0 in the input card to reduce calculation time. When TMS is not used, TMSTally is turned off and cannot be turned on manually.

• OTFDB specifies whether to use the Gauss-Hermitian integration method for on-the-fly Doppler broadening. This method can be used when the temperature of the material filled in the cell does not match the cell temperature. When using this method, it is recommended to select a cross-section database around 300K. Using this method will increase the calculation time. If the value of OTFDB = 1 , this means that the Gauss-Hermitian integration method is used for on-the-fly Doppler broadening, and a value of OTFDB = 0 (default value) means that the Gauss-Hermitian integration method is not used for on-the-fly Doppler broadening.

• EDUEG specifies whether to interpolate the heat number data in the RMC_DATA/neutron_hdf5 database to obtain the heat number cross-section data corresponding to the energy mesh in the ACE file. This option is turned on by default, that is, EDUEG = 1 (default value).

  重要

  In general, the energy mesh of the thermal data does not match the energy mesh in the ACE file. This is caused by the difference in the NJOY program version and the basic evaluation library used when the two databases were created. In order to avoid cross-section calculation errors (usually manifested as infinite cross sections or NAN) due to energy mesh mismatch during cross-section interpolation, it is recommended that users do not turn off this option unless necessary. If the user has ascertained that the energy mesh in their ACE file matches the energy mesh in the thermal database, then the user can begin to consider turning off this option to reduce the calculation time of cross-section interpolation during initialization.

4.4. OTFDB Nuclide Input Card

If the OTFDB option is turned on in the CeAce input card, the Gauss-Hermitian integration method is used for on-the-fly Doppler broadening for all nuclides by default. At this time, the user can use this input option to specify which nuclides should use the Gauss-Hermitian integration method for on-the-fly Doppler broadening.

OTFDBNUC <zaid>
         <zaid>
         ……

where,

• OTFDBNUC is a nuclide input option for on-the-fly Doppler broadening using the Gauss-Hermitian integration method;
• zaid is the nuclide ID.

4.5. Material HDF5 File Input

In addition to reading material information and CEACE data from text files, the RMC program also supports reading material parameters from HDF5 files. Users can set the HDF5 file path as follows:

HDF5 <path_to_hdf5>

The program will read the material and CEACE information from the specified file.

注解

Due to the poor readability of HDF5 files for users, reading material information from HDF5 files typically occurs in large-scale nuclear thermal coupling calculations. This involves reading the material HDF5 file automatically generated by the RMC program from the previous burnup step to accelerate computation.

An HDF5 format material file contains the following sub-data blocks:

material_density:  Density of all user-defined materials. material_id:Identifiers for all user-defined materials. material_nuclide_number:  Number of nuclides in each user-defined material. material_sabnuclide_number:  Number of thermalized nuclides in each user-defined material. material_nuclides_id:  Identifiers for all nuclides in each user-defined material, such as 92235.30c, 54135.30c, etc. material_nuclides_density:  Density of all nuclides in each user-defined material. material_sabnuclides_id:  Identifiers for thermalized nuclides in each user-defined thermalized material, such as HinH2O.92t, etc.

注解

To speed up the program’s reading of material information, all data is stored in a one-dimensional array.

In addition to the basic data information mentioned above, the HDF5 file also includes two positional index variables for convenience:

material_nuclide_position:  Position of constituent nuclides of each material in the material_nuclides_id array. material_sabnuclide_position:  Position of constituent thermalized nuclides of each thermalized material in the material_sabnuclides_id array.

4.6. Multi-group ACE Cross-Section Related Input Card

If the nuclides in the material input option use multi-group ACE cross sections, *the user must use the following input card to specify the relevant parameter options for the multi-group cross sections.*

MgAce [ErgGrp = <grp_neu> <grp_pho>] [DelayNeuFamily = <grp>]
      [Beta = <fismat1> <grp1 value> <grp2 value> ... <grpn value>
              <fismat2> <grp1 value> <grp2 value> ... <grpn value>
              ...
              <fismatm> <grp1 value> <grp2 value> ... <grpn value>]
      [Lambda = <grp1 value> <grp2 value> ... <grpn value>]

where,

• MgAce is the keyword for the multi-group ACE cross-section related input option;
• ErgGrp specifies the group number of multi-group neutron and multi-group photon ACE cross sections. When in pure neutron transport mode, the photon group number behind can be written as 0 or omitted; when in pure photon transport mode, the neutron group number in front needs to be written as 0 and cannot be omitted.

The following options are commonly used for space-time dynamics calculations:

• DelayNeuFamily specifies the number of delayed neutron groups;
• Beta specifies the delayed neutron fraction of each group of each fission material, <fismatm> specifies the material number of the m-th fission material, <grpn value> specifies the delayed neutron fraction of the nth group of the corresponding fission material, and the number of <grpi value> should be consistent with the value of DelayNeuFamily.
• Lambda specifies the neutron generation time for each group of neutrons, and <grpn value> specifies the neutron generation time for the nth group of neutrons.

It should be pointed out that the multi-group cross-section database is closely dependent on the actual physical problem. Therefore, the publicly released RMC package does not provide a multi-group ACE database. Users can use other database processing software to generate a multi-group ACE cross-section database related to the actual problem.

4.7. Photonuclear reaction and photogenic reaction database selection input option

If you need to select a database of photonuclear reaction and photogenic reaction cross sections, you can set the relevant parameters for it through this input option. The format of the input option is:

MTlib
[Plib=<flag>]
[PNlib=<flag>]

where,

• MTlib is the keyword for selecting the input option of the photonuclear reaction and photogenic reaction cross section database.
• Plib specifies the photogenic reaction cross section database type. Plib = 04P (default value) specifies the mcplib04p photogenic reaction cross section database.
• PNlib specifies the photonuclear reaction cross section database type. PNlib = 24u (default value) specifies the endf24u photonuclear reaction cross section database.

4.8. Input Option for Adjusting the Average Fission Neutron Number

In some cases, the average number of fission neutrons needs to be adjusted proportionally to change the proliferation capacity of the system. For example, in quasi-static dynamics calculations, the initial state needs to be critical. If the model itself is not critical, this input option can be used to adjust it to be critical (input the effective multiplication factor keff).

The format of the input option is:

nubar [factor = <factor>]

where,

• nubar is the keyword for the Adjust Average Fission Neutron Number input option.
• factor is the factor for adjusting the average number of fission neutrons. Note that this factor is a divisor and the default value is 1 (indicating no adjustment). For example, if factor = 2 , the average number of fission neutrons used in the transport calculation will become 1/2 of the average number of fission neutrons in the database.

4.9. Dynamic material related input options

If the nuclides in the material input card use dynamic parameters that change over time, you can set the relevant parameter options for them through the following input options.

DynamicMat <mat_id> [time =<t1 t2 ... tn>] [Matdenvalue = <v1 v2 ... vn>] [Nucdenvalue = <a1 a2 ... axn>]

where,

• DynamicMat is the keyword for dynamic material related input cards;
• mat_id is the material serial number, which matches the material number in the Mat input option;
• time input option is used in combination with the Matdenvalue and Nucdenvalue input options, to describe the change rules of time, material density, and the relative proportion of each nuclide in the material. The number of values inputted into the time input option and Matdenvalue input option are equal, indicating that when the time exceeds \(t_{i}\), the corresponding parameter is taken as \(v_{i}\). The number of values entered in the Nucdenvalue input option is x times the number of values in the time input option, and x is the number of nuclides in the material.

4.10. Input Card for Continuously Varying Material

When a material in the input card is defined as a continuously varying material, you can use the following input card to set the relevant parameters and options:

cvmt <mat_id> [polytype = <polytype>] [dimension = <dimension>] [contitype = <contitype>]
              [order = <a1 a2 a3 a4>] [coeffs = <a1 a2 ... axn>] [bound = <a1 a2 a3 a4 a5 a6 a7>]

Where:

• cvmt keyword specifies the input card for defining continuously varying materials.
• mat_id is used to identify the material and must match the material ID defined in the Mat card.
• polytype parameter defines the type of function used for the continuous variation. Options include: Legendre polynomial (0), Zernike polynomial (1), 2D Legendre polynomial (2), 3D Legendre polynomial (3), Combined Legendre-Zernike polynomial (4), Power function (5), currently limited to 1D.
• dimension parameter determines the spatial dimension of the function. It supports 1D variations in the X, Y, or Z directions (values 0, 1, and 2, respectively), 2D variations on a circular disc (3), 3D variations in cylindrical (7) or Cartesian spaces (8), and variations using a power function (9).
• contitype parameter specifies the property that varies continuously. It can represent density variation (0) or temperature variation (1).
• order parameter defines the order of the variation function. For Legendre polynomials, the first three numbers specify the orders for each spatial dimension. For Zernike polynomials, the fourth number specifies the polynomial order. If a particular order is not used, the value -1 should be provided as a placeholder.
• coeffs parameter lists the coefficients for the terms in the variation function. For Legendre and Zernike polynomials, these coefficients must include normalization factors. The values should be provided as an*Pn, where an includes the normalization constant.
• bound parameter specifies the spatial boundaries for the continuously varying material. For Legendre and Zernike polynomials, the particle positions are normalized, so the input must reflect the true physical dimensions of the material region. In Cartesian coordinates, the boundaries should be specified as x_min x_max y_min y_max z_min z_max. For cylindrical geometry, the boundaries should be defined as x_point y_point z_min z_max r_max, where x_point and y_point represent the coordinates of the cylinder’s center.

4.11. Material module input example

4.11.1. Materials Module Using the Continuous Energy ACE Database

In the material module below, two materials UO₂and H₂O are first defined using the Mat input option. The mass density of UO₂is -10.196 g/cm³, and the atomic ratio of U235、U238 and O16 is 0.03 : 0.97 : 2.0 respectively. The atomic density of H₂O is 0.9997 bar^-1cm^-1, and the atomic ratio of H1 and O16 is 2 : 1 respectively. A thermalization database (lwtr.60t) is specified for H1 (1001.30c) in H₂O using the Sab input option. In the CeAce input option, pTable = 0 indicates that a probability table is not used, ErgBinHash = 1 means that a hash table to accelerate energy lookup is used, DBRC = 0 means the DBRC algorithm is not used, TMS = 0 means the TMS algorithm is not used, and OTFDB = 1 indicates that the Gauss-Hermitian integral method for on-the-fly Doppler broadening is used.

MATERIAL
mat 1 -10.196
    92235.30c 0.03
    92238.30c 0.97
    8016.30c 2.0
mat 2 0.9997
    1001.30c 2.0
    8016.30c 1.0
Sab 2 lwtr.60t
CEACE pTable = 0 ErgBinHash = 1 DBRC = 0 TMS = 0 OTFDB = 1

4.11.2. Material Module Using Continuous Energy HDF5 Format AIS Database

In the following material module,

In the following material module, UO₂and H₂O are defined separately using the Matinput card. The mass density of UO₂is -10.196 g/cm³, with atomic ratios of U-235, U-238, and O-16 being 0.03 : 0.97 : 2.0. The atomic density of H₂O is 0.9997 bar^-1cm^-1, with atomic ratios of H-1 and O-16 being 2 : 1.

Through the Sab input card, a thermalization database (h-h2o) is specified for H₂O containing H-1 (1001.30c). All databases use the HDF5 format AIS nuclear database from ENDF-B8.0 (the program will automatically look for corresponding nuclear data files under the AISNucDatabase/ENDFB8.0 directory), and this example uses nuclear data at a temperature of 293.6 K.

In the CeAce input card, pTable = 1 indicates the use of a probability table, ErgBinHash = 1 indicates the use of a hash table to accelerate energy lookup, DBRC = 1 indicates the use of the DBRC algorithm, TMS = 0 indicates that the TMS algorithm is not used, and OTFDB = 1 indicates that the Gaussian-Hermite integration method is used for on-the-fly Doppler broadening.

MATERIAL
mat 1 -10.196
    U235 fraction = 0.03 endfversion = 8.0 tmp = 293.6
    U238 fraction = 0.97 endfversion = 8.0 tmp = 293.6
    O16  fraction = 2.0  endfversion = 8.0 tmp = 293.6
mat 2 0.9997
    H1  fraction = 2.0   endfversion = 8.0 tmp = 293.6
    O16 fraction = 1.0   endfversion = 8.0 tmp = 293.6
Sab 2
    h-h2o endfversion = 8.0 tmp = 293.6
CEACE pTable = 1 ErgBinHash = 1 DBRC = 1 TMS = 0 OTFDB = 1

4.11.3. Material Module Using Multi-Group ACE Database

MATERIAL
mat 1 -10.198
    92235.50m 6.9100E-03
    92238.50m 2.2062E-01
    8016.50m 4.5510E-01
mat 2 -0.001
    8016.50m 3.76622E-5
mat 3 -6.550
    40000.50m -98.2
mat 4 -0.997
    1001.50m 6.6643E-02
    8016.50m 3.3334E-02
MgAce ErgGrp = 30

In the material module above, .50m is a multigroup ACE cross section library with 30 groups. The number of energy groups for the multigroup cross section is specified via the ErgGrp input option.

4.11.4. Material module using dynamic material changes

Material
mat 1   -15.0
        92235.71c  -5
        92238.71c  -10
DynamicMat  1     time=  0 200e-8 400e-8 500e-8 700e-8 900e-8 1000e-8
           Matdenvalue=-15 -15    -15    -15    -15    -15    -15
           Nucdenvalue=-5  -6.5   -14    -14    -6.5   -5     -5
                       -10 -8.5   -1     -1     -8.5   -10    -10

In the material module above, the parameters of the dynamic material that change with time are specified through the DynamicMat input option. The time input option specifies the time point, Matdenvalue specifies the material density corresponding to the time, the first row of the Nucdenvalue input option corresponds to the relative fraction of nuclide 92235 over time, and the second row corresponds to the relative fraction of nuclide 92238 over time. The program will determine the values between time points by interpolation. For example, when the fraction of nuclide 92235 at the time point 100e-8 is required, the program will first determine the interpolation position through time, and then interpolate the corresponding time parameter [-5,-6.5] of the nuclide.

4.11.5. Using the Continuously Varying Material Module

Material
mat 1   -15.0
        92235.71c  -5
        92238.71c  -10
cvmt 1 polytype = 4 dimension = 7 contitype = 0 order = -1 -1 1 2 coeffs = 0.0 1.0 2.0 3.0 4.0 5.0 7.0 6.0 8.0 9.0 10.0 11.0

In the material module above, the cvmt card is used to define parameters for a continuously varying material. The polytype card specifies that the variation function is a combination of Legendre and Zernike polynomials. The dimension card indicates that the geometry is a 3D cylindrical space. The contitype card sets the material to have a continuous density variation. The order card specifies the polynomial orders: no Legendre polynomial is defined in the x and y directions (-1 placeholders), while a first-order Legendre polynomial is applied in the z direction, and the Zernike polynomial is of the second order. The coeffs card provides the coefficients for the polynomial terms. In this case, there are (1+1)*(1+2+3)=12(1+1)*(1+2+3)=12 coefficients, which are explicitly defined.