# XSProc Standard Composition Examples¶

## Infinite homogeneous medium unit cell data¶

EXAMPLE 1. A single mixture 1.

Consider a single cylindrical configuration of mixture 1, composed of 10% enriched UO

_{2}having a radius of 35 cm and a height of 20 cm. This fuel region is sufficient large to model as an infinite medium. Mixture 100 may be used in subsequent multigroup neutron transport calculations.

```
INFHOMMEDIUM 1 CELLMIX=10 END
```

XSDRNPM will calculate the eigenvalue of an infinite mass of 10%
enriched UO_{2}.

## LATTICECELL unit cell data¶

Examples of “regular” **LATTICECELL** unit cells are given in
Examples 1–5, and examples of “annular” **LATTICECELL** unit cells are
given in Examples 6–10 below.

EXAMPLE 1. SQUAREPITCH (infinitely long cylindrical pins in a square-pitched array).

Consider a large array of UO

_{2}fuel pins having a fuel O.D. of 0.79 cm, a 0.015-cm gap, and a 0.06-cm-thick aluminum clad. The array is a square-pitched array with a center-to-center spacing of 1.60 cm and is completely flooded with water. In the standard composition data, UO_{2}is defined to be mixture 1, the aluminum clad is defined to be mixture 2, and the water moderator is defined to be mixture 3.

```
LATTICECELL SQUAREPITCH PITCH=1.60 3 FUELD=0.79 1 CLADD=0.94 2 GAPD=0.82 0 END
```

EXAMPLE 2. TRIANGPITCH (infinitely long cylinders in a triangular-pitched array).

Consider an array of UO

_{2}pins with a diameter of 0.635 m. The outside diameter of the clad is 0.78 cm. There is no gap between the fuel and clad. The array is a triangular-pitched array with a center-to-center spacing of 5.0 cm and is flooded with water. In the standard composition data, the UO_{2}is defined to be mixture 1, the aluminum is defined to be mixture 2, and the water moderator is defined to be mixture 3.

```
LATTICECELL TRIANGPITCH PITCH=5.0 3 FUELD=.635 1 CLAD=.78 2 END
```

EXAMPLE 3. SPHSQUAREP (spheres in a square-pitched array).

Consider a large array of U

_{3}O_{8}spheres having a fuel O.D. of 18.6 cm, with an aluminum clad that is 0.18 cm thick. The array is a triangular-pitched array with a center-to-center spacing of 19.0 cm and is unmoderated. In the standard composition data, the aluminum is defined to be mixture 1 and the U_{3}O_{8}is defined to be mixture 2. There is no moderator material, so 0 will be used to represent a void. Also, have XSDRNPM make a cell weighted material 20 from this unit cell.

```
LATTICECELL SPHSQUAREP PITCH=19.0 0 FUELD=18.6 2 CLADD=18.96 1 CELLMIX=20 END
```

EXAMPLE 4. SPHTRIANGP (spheres in a triangular-pitched array).

Consider a large array of U

_{3}O_{8}spheres having a fuel O.D. of 18.6 cm, with an aluminum clad that is 0.18 cm thick. The array is a triangular-pitched array with a center-to-center spacing of 19.0 cm and is flooded with water. In the standard composition data, the aluminum is defined to be mixture 1, the U_{3}O_{8}is defined to be mixture 2, and the water moderator is defined to be mixture 3.

```
LATTICECELL SPHTRIANGP PITCH=19.0 3 FUELD=18.6 2 CLADD=18.96 1 END
```

EXAMPLE 5. SYMMSLABCELL (slabs repeated in a symmetric fashion).

Consider a system of alternating slabs of U

_{3}O_{8}and low-density water. Each U_{3}O_{8}region is 1.27 cm thick, and each water region is 15.0 cm thick. In the standard composition data, the U_{3}O_{8}is defined to be mixture 1, and the low-density water is defined to be mixture 2.

```
LATTICECELL SYMMSLABCELL PITCH=16.27 2 FUELD=1.27 1 END
```

EXAMPLE 5a. SYMMSLABCELL (slabs repeated in a symmetric fashion).

Consider a system of alternating slabs of U

_{3}O_{8}and low-density water. Each U_{3}O_{8}region is 1.27 cm thick, and each water region is 15.0 cm thick. The U_{3}O_{8}regions have a 0.01-cm gap and 0.24-cm-thick aluminum clad on each face. In the standard composition data, the U_{3}O_{8}is defined to be mixture 1, the aluminum is defined to be mixture 2, and the low-density water is defined to be mixture 3. Also, have XSDRNPM make a cell-weighted material 100 from this unit cell.

```
LATTICECELL SYMMSLABCELL PITCH=16.77 3 FUELD=1.27 1
CLADD=1.77 2 GAPD=1.29 0 CELLMIX=100 END
```

EXAMPLE 6. ASQUAREPITCH (infinitely long annular cylindrical rods in a square-pitched array).

Consider an array of uranium metal pipes having an inside diameter of 5.0 cm and an outer diameter of 6.75 cm. A gap of 0.025 cm and a clad of 0.25 cm exist on both the inner and outer surfaces of the fuel. The fuel rods are arranged in a square-pitched array. The center-to-center spacing is 8.0 cm. The array is completely flooded with water. In the standard composition data, the uranium metal is defined to be mixture 1, the outer clad is mixture 2, the inner clad is mixture 7, the inner moderator is Plexiglas and is mixture 3, the gap is a void, and the external moderator is water, defined to be mixture 4.

```
LATTICECELL ASQUAREPITCH PITCH=8.0 4 FUELD=6.75 1 GAPD=6.8 0
CLADD=7.3 2 IMODD=4.45 3 ICLADD=4.95 7 IGAPD=5.0 0 END
```

EXAMPLE 6a. ASQUAREPITCH (infinitely long annular cylindrical rods in a square-pitched array).

Consider an array of uranium metal pipes having an inside diameter of 5.0 cm and an outer diameter of 6.75 cm arranged in a square-pitched array. The center-to-center spacing is 8.0 cm. The array is completely flooded with water. In the standard composition data, the uranium metal is defined to be mixture 1, the water moderator is defined to be mixture 2, and the inside water moderator is defined as mixture 3.

```
LATTICECELL ASQUAREPITCH PITCH=8.0 2 FUELD=6.75 1 IMODD=5.0 3 END
```

Note

This problem defines two water mixtures. If mixture 2 were entered twice, i.e., for both the inner and outer moderator, an error message would be printed and the calculation terminated.

EXAMPLE 7. ATRIANGPITCH (infinitely long annular cylindrical rods in a triangular-pitched array).

Consider an array of uranium metal pipes having an inside diameter of 8.0 cm and a wall thickness of 0.75 cm arranged in a square-pitched array. The center-to-center spacing is 9.75 cm. The array is completely flooded with water. A Plexiglas rod fills the center of the uranium pipe. In the standard compositions data, the uranium metal is defined to be mixture 1, the Plexiglas is defined to be mixture 2, and the external water moderator is mixture 3.

```
LATTICECELL ATRIANGPITCH PITCH=9.75 3 FUELD=9.5 1 IMODD=8.0 2 END
```

EXAMPLE 8. ASPHSQUAREP (spherical annuli in a square-pitched array).

Consider a large array of hollow U

_{3}O_{8}spheres having a fuel I.D. of 8.0 cm and O.D. of 18.6 cm. The centers of the spheres are empty. The external moderator is water. The spheres are stacked in a square-pitched array with a center-to-center spacing of 19.0 cm. In the standard composition data, the U_{3}O_{8}is defined to be mixture 1, and the water is defined to be mixture 2. The centers of the spheres are defined to be void, mixture 0.

```
LATTICECELL ASPHSQUAREP HPITCH=9.5 2 FUELR=9.3 1 IMODR=4.0 0 END
```

EXAMPLE 9. ASPHTRIANGP (spheres in a triangular-pitched array).

Consider a large array of hollow U

_{3}O_{8}spheres having a fuel I.D. of 8.0 cm and a fuel O.D. of 18.6 cm. A 0.18-cm-thick aluminum clad exists outside the fuel. The interior of each sphere is void. The array is a triangular-pitched array with a center-to-center spacing of 19.0 cm and is flooded with water. In the standard composition data, the aluminum is defined to be mixture 1, the U_{3}O_{8}is defined to be mixture 2, and the water moderator is defined to be mixture 3. The void in the center of each sphere is entered as mixture 0.

```
LATTICECELL ASPHTRIANGP HPITCH=9.5 3 FUELR=9.3 2 IMODR=4.0 0 CLADR=9.48 1 END
```

EXAMPLE 10. ASYMSLABCELL (repeated slabs having different moderator conditions on the left and right boundaries).

Consider an array of U

_{3}O_{8}slabs with an inner moderator region composed of full-density water with a half thickness of 8.0 cm, and a low-density water outer moderator with a 16 cm half thickness of 16 cm half thickness. Each U_{3}O_{8}slab is 10.54 cm thick. In the standard composition data, the U_{3}O_{8}is defined to be mixture 1, the full density water is defined to be mixture 2, and the low-density water is mixture 3. Also, have XSDRNPM create a cell weighted mixture 100 from this unit cell.

```
LATTICECELL ASYMSLABCELL CELLMIX=100 IMODR=8.0 2 FUELR=18.54 1 HPITCH=34.54 3 END
```

EXAMPLE 10a. ASYMSLABCELL (repeated slabs having different moderator conditions on the left and right boundaries).

Consider an array of U

_{3}O_{8}fuel plates with an inner moderator region of full-density water with a half-thickness of 8.0 cm, and with a 16 cm thick low-density outer moderator. Each fuel plate includes a 10.54 cm thick U_{3}O_{8}slab with a 0.01 cm gap and 0.24-cm-thick aluminum clad on each face. In the standard composition data, the U_{3}O_{8}is defined to be mixture 1, the full density water is defined to be mixture 2, and the low-density water is mixture 3, the inner aluminum is mixture 4, the outer aluminum clad is mixture 5, and both gaps are voids.

```
LATTICECELL ASYMSLABCELL IMODR=8.0 2 ICLADR=8.24 5 IGAPR=8.25 0 FUELR=18.79 1
GAPR 18.80 0 CLADR 19.04 4 HPITCH=27.04 3 END
```

## MULTIREGION unit cell data¶

Examples of **MULTIREGION** unit cells follow:

EXAMPLE 1. SLAB.

Consider a 5-cm-thick slab of fuel (mixture 1) with 0.5 cm of aluminum (mixture 3) and 15 cm of water (mixture 2) on each face. The unit cell data for this problem could be entered as follows:

```
MULTIREGION SLAB LEFT_BDY=REFLECTED RIGHT_BDY=VACUUM ORIGIN=0 END
1 2.5 3 3.0 2 18.0 END ZONE
```

EXAMPLE 2. CYLINDRICAL.

Consider a large array of fuel pins. Each pin is UO

_{2}(mixture 1) with a radius of 0.465 cm, a 0.009-cm gap (mixture 0), and a Zircaloy clad (mixture 9) 0.062 cm thick, centered in a water (mixture 8) region surrounded by a flooded support structure represented by homogenized water and Zircaloy (mixture 10). The outer radius of the water-Zircaloy region is 0.844 cm and it is 0.037 cm thick. This problem cannot be described as aLATTICECELLproblem because theLATTICECELLconfiguration is limited to fuel-gap-clad-cell boundary and this problem is fuel-gap-clad-moderator-outer region. WhenMULTIREGIONis used, lattice effects are accounted for by specifying aWHITE,PERIODIC, orREFLECTEDright boundary condition, as long as the CENTRM/PMC self-shielding method is used.MULTIREGIONcells should not be used for arrays if BONAMI-only method is specified

```
MULTIREGION CYLINDRICAL RIGHT_BDY=WHITE END
1 0.465 0 0.474 9 0.536 8 0.807 10 0.844 END ZONE
```

EXAMPLE 3. SPHERICAL.

Describe a bare sphere of uranium metal 8.72 cm in radius. The uranium metal is defined to be mixture 1. Also, have XSDRNPM create a cell weighted mixture 100 and calculate and eigenvalue. The unit cell data for this problem could be entered as follows:

```
MULTIREGION SPHERICAL CELLMIX=100 END 1 8.72 END ZONE
```

EXAMPLE 4. BUCKLEDSLAB.

Consider a plate of fuel 4 cm thick, reflected by 3 cm of water on both faces. The plate is 32 cm tall and 16 cm deep. The fuel is mixture 1 and the water is mixture 2. Also, have XSDRNPM create a cell weighted mixture 100 and calculate and eigenvalue.

```
MULTIREGION BUCKLEDSLAB CELLMIX=100 LEFT_BDY=REFLECTED RIGHT_BDY=VACUUM
DY=32 DZ=16.0 END 1 2.0 2 5.0 END ZONE
```

EXAMPLE 5. BUCKLEDCYL.

Consider a solution of uranyl nitrate contained in a cylindrical stainless-steel container reflected by 33 cm of water. The inside dimensions of the steel container are 7.62 cm in radius and 130.0 cm tall. The steel is 0.15 cm thick. The uranyl nitrate is defined to be mixture 1, the steel is defined to be mixture 2, and the water is defined to be mixture 3.

```
MULTIREGION BUCKLEDCYL DY=130 END
1 7.62 2 7.77 3 40.77 END ZONE
```

## DOUBLEHET unit cell data¶

Unit cell data are always required for **DOUBLEHET** calculations. As
many unit cells as needed may be defined in the problem. If
**CELLMIX**=*mx* is entered after the fuel element (macro cell)
description, XSProc calls XSDRNPM to calculate the eigenvalue of the
cell and to create a homogenized cell-weighted cross section having the
characteristics of the doubly-heterogeneous cell configuration.

EXAMPLE 1: A doubly-heterogeneous spherical fuel element with 15,000 UO_{2} particles in a graphite matrix.

Grain fuel radius is 0.025 cm. Grain contains one coating layer that is 0.009-cm-thick. Pebbles are in a triangular pitch on a 6.4-cm-pitch. Fuel pebble fuel zone is 2.5‑cm in radius and contains a 0.5-cm-thick graphite clad that contains small amounts of

^{10}B. Pebbles are surrounded by^{4}He. Assume the composition block is below:

```
' UO2 FUEL KERNEL
U-235 1 0 1.92585E-3 293.6 END
O 1 0 4.64272E-2 293.6 END
' FIRST COATING
C 2 0 5.26449E-2 293.6 END
' GRAPHITE MATRIX
C 6 0 8.77414E-2 293.6 END
' CARBON PEBBLE OUTER COATING
C 7 0 8.77414E-2 293.6 END
B-10 7 0 9.64977E-9 293.6 END
HE-4 8 0 2.65156E-5 293.6 END
```

The cell data for the **DOUBLEHET** cell follows:

```
DOUBLEHET FUELMIX=10 END
GFR=0.025 1 COATT=0.009 2 MATRIX=6 NUMPAR=15000 END GRAIN
PEBBLE SPHTRIANGP RIGHT_BDY=WHITE HPITCH=3.2 8 FUELR=2.5 CLADR=3.0 7 END
```

In this case we designated the homogenized mixture as mixture 10. If we
have a KENO V.a or KENO-VI input section, we would use mixture 10 in
that section. Note that the keyword “**FUELR**=” is followed by the
fuel dimension only, i.e., no mixture number. That is because the fuel
mixture number is specified with “**FUELMIX**=” and therefore need
not be repeated.

EXAMPLE 2: Same as Example 1, except volume fraction of the grain type is known and is 0.037732.

```
DOUBLEHET RIGHT_BDY=WHITE FUELMIX=10 END
GFR=0.025 1 COATT=0.009 2 MATRIX=6 VF=0.037732 END GRAIN
PEBBLE SPHTRIANGP RIGHT_BDY=WHITE HPITCH=3.2 8 FUELR=2.5 CLADR=3.0 7 END
```

EXAMPLE 3: Same as Example 1, except halfpitch of the grain type is known and is 0.10137 cm.

```
DOUBLEHET FUELMIX=10 END
GFR=0.025 1 COATT=0.009 2 HPITCH=0.10137 MATRIX=6 END GRAIN
PEBBLE SPHTRIANGP RIGHT_BDY=WHITE HPITCH=3.2 8 FUELR=2.5 CLADR=3.0 7 END
```

EXAMPLE 4: A doubly-heterogeneous spherical fuel element with 10,000 UO2 particles and 5,000 PuO2 particles in a graphite matrix.

Grain fuel radii for UO

_{2}and PuO_{2}particles are 0.025 cm and 0.012 cm, respectively. UO_{2}grains contain one coating layer that is 0.009‑cm-thick. PuO_{2}grains contain one coating layer that is 0.0095-cm-thick. Pebbles are in a triangular pitch on a 6.4-cm-pitch. Fuel pebble fuel zone is 2.5-cm in radius and contains a 0.5-cm-thick graphite clad that contains small amounts of^{10}B. Pebbles are surrounded by^{4}He. Assume the composition block is given below:

```
' UO2 FUEL KERNEL
U-235 1 0 1.92585E-3 293.6 END
O 1 0 4.64272E-2 293.6 END
' FIRST COATING
C 2 0 5.26449E-2 293.6 END
' GRAPHITE MATRIX
C 6 0 8.77414E-2 293.6 END
' CARBON PEBBLE OUTER COATING
C 7 0 8.77414E-2 293.6 END
B-10 7 0 9.64977E-9 293.6 END
HE-4 8 0 2.65156E-5 293.6 END
' PUO2 FUEL KERNEL
PU-239 11 0 1.24470E-02 293.6 END
O 11 0 4.60983E-02 293.6 END
' FIRST COATING
C 12 0 5.26449E-2 293.6 END
' GRAPHITE MATRIX
C 16 0 8.77414E-2 293.6 END
```

The cell data for the **DOUBLEHET** cell follows:

```
DOUBLEHET FUELMIX=10 END
GFR=0.025 1 COATT=0.009 2 MATRIX=6 NUMPAR=10000 END GRAIN
GFR=0.012 11 COATT=0.0095 12 MATRIX=16 NUMPAR=5000 END GRAIN
PEBBLE SPHTRIANGP RIGHT_BDY=WHITE HPITCH=3.2 8 FUELR=2.5 CLADR=3.0 7 END
```

Since number of particles is entered, the total volume fraction and the pitch can be calculated by the code.

EXAMPLE 5: Same as Example 4 above except the volume fractions of UO_{2}
and PuO_{2} grains are 0.02511 and 0.00318, respectively.

```
DOUBLEHET RIGHT_BDY=WHITE FUELMIX=10 END
GFR=0.025 1 COATT=0.009 2 MATRIX=6 VF=0.02511 END GRAIN
GFR=0.012 11 COATT=0.0095 12 MATRIX=16 VF=0.00318 END GRAIN
PEBBLE SPHTRIANGP RIGHT_BDY=WHITE HPITCH=3.2 8 FUELR=2.5 CLADR=3.0 7 END
```

EXAMPLE 6: Same as Example 4 above except pitch is also known.

UO

_{2}grains have a pitch of 0.25 cm. PuO_{2}grains have a pitch of 0.20 cm.

```
DOUBLEHET FUELMIX=10 END
GFR=0.025 1 COATT=0.009 2
MATRIX=6 NUMPAR=10000 PITCH=0.25 END GRAIN
GFR=0.012 11 COATT=0.0095 12
MATRIX=16 NUMPAR=5000 PITCH=0.20 END GRAIN
PEBBLE SPHTRIANGP RIGHT_BDY=WHITE HPITCH=3.2 8 FUELR=2.5 CLADR=3.0 7 END
```

Since number of particles is sufficient to perform the homogenization,
it is used. However, instead of calculating the pitch for the 1-D cell
calculation for each grain type, the user input pitch is used. Hence,
the calculated *k*_{eff} of Example 6 will be different from those of
Examples 4 and 5.

**EXAMPLE 7: Same as Example 6 except the doubly-heterogeneous cell will
be cell-weighted.**

The final cell-weighted mixture number is 17.

```
DOUBLEHET FUELMIX=10 END
GFR=0.025 1 COATT=0.009 2
NUMPAR=10000 PITCH=0.25 MATRIX=6 END GRAIN
GFR=0.012 11 COATT=0.0095 12
NUMPAR=5000 PITCH=0.20 MATRIX=16 END GRAIN
PEBBLE SPHTRIANGP RIGHT_BDY=WHITE HPITCH=3.2 8 FUELR=2.5 CLADR=3.0 7 CELLMIX=17 END
```

EXAMPLE 8: A doubly-heterogeneous spherical fuel element with 15,000 UO_{2} particles in a graphite matrix.

Grain fuel radius is 0.012 cm. Grain contains four coating layers that are 0.0095, 0.004, 0.0035, and 0.004-cm-thick. Pebbles are in a square pitch on a 6.0‑cm-pitch. Fuel pebble fuel zone is 2.5-cm in radius and contains a 0.5-cm-thick graphite clad that contains small amounts of

^{10}B. Pebbles are surrounded by^{4}He. Assume the composition block is given below:

```
' UO2 FUEL KERNEL
U-235 1 0 1.92585E-3 293.6 END
O 1 0 4.64272E-2 293.6 END
' FIRST COATING
C 2 0 5.26449E-2 293.6 END
' INNER PYRO CARBON
C 3 0 9.52621E-2 293.6 END
' SILICON CARBIDE
C 4 0 4.77240E-2 293.6 END
SI 4 0 4.77240E-2 293.6 END
' OUTER PYRO CARBON
C 5 0 9.52621E-2 293.6 END
' GRAPHITE MATRIX
GRAPHITE 6 0 8.77414E-2 293.6 END
' CARBON PEBBLE OUTER COATING
C 7 0 8.77414E-2 293.6 END
B-10 7 0 9.64977E-9 293.6 END
HE-4 8 0 2.65156E-5 293.6 END
```

The cell data for the **DOUBLEHET** cell follows:

```
DOUBLEHET FUELMIX=10 END
GFR=0.012 1 COATT=0.0095 2 COATT=0.004 3 COATT=0.0035 4 COATT=0.004 5 MATRIX=6 NUMPAR=15000 VF=0.0245 END GRAIN
PEBBLE SPHSQUAREP RIGHT_BDY=WHITE HPITCH=3.0 8 FUELR=2.5 CLADR=3.0 7 END
```

Note that the grains are overspecified and the numbers are inconsistent.
A **VF** value of 0.0245 results in a total number of particles of
10652.32 which is considerably less than 15,000. In this case, the code
will issue a warning to this effect and will use **VF** value in the
calculations (i.e., ignore **NUMPAR**=15000 entry).

EXAMPLE 9: Similar to Example 8 except radii for grain regions are entered.

```
DOUBLEHET FUELMIX=10 END
GFR=0.012 1 COATR=0.0215 2 COATR=0.0255 3 COATR=0.029 4 COATR=0.033 5 MATRIX=6 NUMPAR=15000 VF=0.0245 END GRAIN
PEBBLE SPHSQUAREP RIGHT_BDY=WHITE HPITCH=3.0 8 FUELR=2.5 CLADR=3.0 7 END
```

EXAMPLE 10: A doubly-heterogeneous spherical fuel element with two UO_{2} grain types.

First grain type has a fuel radius of 0.025 cm. Second grain type fuel radius is 0.004 cm. First grain type has one coating that is 0.009-cm-thick. Second grain type has two coatings each 0.004-cm-thick. Each grain type has a volume fraction of 0.45. Pebbles are in a triangular pitch on a 7.0-cm-pitch. Fuel pebble fuel zone is 2.5-cm in radius and contains a 0.5-cm-thick graphite clad that contains small amounts of

^{10}B and^{11}B. Pebbles are surrounded by^{4}He. Assume the composition block is given below:

```
' FUEL KERNEL
U-238 1 0 2.12877E-2 END
U-235 1 0 1.92585E-3 END
O 1 0 4.64272E-2 END
B-10 1 0 1.14694E-7 END
B-11 1 0 4.64570E-7 END
' FIRST COATING
C 2 0 5.26449E-2 END
' INNER PYRO CARBON
C 3 0 9.52621E-2 END
' SILICON CARBIDE
C 4 0 4.77240E-2 END
SI 4 0 4.77240E-2 END
' FUEL KERNEL
U-238 5 0 2.12877E-2 END
U-235 5 0 1.92585E-3 END
O 5 0 4.64272E-2 END
B-10 5 0 1.14694E-7 END
B-11 5 0 4.64570E-7 END
' GRAPHITE MATRIX
C 6 0 8.77414E-2 END
B-10 6 0 9.64977E-9 END
B-11 6 0 3.90864E-8 END
' CARBON PEBBLE OUTER COATING
C 7 0 8.77414E-2 END
B-10 7 0 9.64977E-9 END
B-11 7 0 3.90864E-8 END
' HELIUM
HE 8 0.000164 END
' GRAPHITE MATRIX
C 9 0 8.77414E-2 END
B-10 9 0 9.64977E-9 END
B-11 9 0 3.90864E-8 END
```

The cell data for the **DOUBLEHET** cell follows:

```
DOUBLEHET FUELMIX=10 END
GFR=0.025 1 COATR=0.034 2 MATRIX=6 VF=0.45 END GRAIN
COATT=0.004 3 GFR=0.4 5 COATT=0.004 4 MATRIX=9 VF=0.45 END GRAIN
PEBBLE SPHTRIANGP RIGHT_BDY=WHITE HPITCH=3.5 8 FUELD=5.0
CLADD=6.0 7 END
```

EXAMPLE 11: A doubly-heterogeneous hexagonal block type fuel element
with UO_{2} grains in a cylindrical fuel region.

Grain fuel radius is 0.025 cm. Grain coating is 0.009-cm-thick. Grains have a volume fraction of 0.45. Hexagonal rods are in a 7-cm triangular pitch. Fuel rod fuel zone is 2.5-cm in radius, 10-cm-high and contains a 0.5-cm-thick graphite clad that contains small amounts of

^{10}B. Assume the composition block is below:

```
' FUEL KERNEL
U-238 1 0 2.12877E-2 END
U-235 1 0 1.92585E-3 END
O 1 0 4.64272E-2 END
B-10 1 0 1.14694E-7 END
' FIRST COATING
C 2 0 5.26449E-2 END
' GRAPHITE MATRIX
C 6 0 8.77414E-2 END
B-10 6 0 9.64977E-9 END
' CARBON PEBBLE OUTER COATING
C 7 0 8.77414E-2 END
B-10 7 0 9.64977E-9 END
' IRON CLADDING
FE 8 END
```

The cell data for the **DOUBLEHET** cell follows:

```
DOUBLEHET FUELMIX=10 END
GFR=0.025 1 COATR=0.034 2 MATRIX=6 VF=0.45 END GRAIN
ROD TRIANGP RIGHT_BDY=WHITE HPITCH=3.5 7 FUELD=5.0
FUELH=10 END
```

EXAMPLE 12: This is the same as Example 11 except the fuel elements (cylindrical rods) have 0.05‑cm-thick iron cladding.

The cell data for the **DOUBLEHET** cell follows:

```
DOUBLEHET FUELMIX=10 END
GFR=0.025 1 COATR=0.034 2 MATRIX=6 VF=0.45 END GRAIN
ROD TRIANGP RIGHT_BDY=WHITE HPITCH=3.5 7 FUELR=2.5
CLADD=5.1 8 FUELH=10 END
```

## Optional parameter data¶

The optional parameter data provide a means of providing additional
information or alternative data to the cross-section processing codes.
There are two types of optional parameter data. The first type of data
is used by XSDRNPM and BONAMI for cross-section processing and
cell-weighting cross sections. This type of data is initiated using the
keywords **MORE DATA** and ends with the keywords **END MORE**. This
input is described in Optional MORE DATA parameter data. The second type of optional
parameter data is used by CENTRM and PMC for cross-section processing.
This type of data is initiated using the keywords **CENTRM DATA** and
ends with the keywords **END CENTRM**. This input is described in
Optional CENTRM DATA parameter data. It is possible to input both types of data for a unit
cell. The optional parameter data specified apply only to the unit cell
that immediately precedes it.

MORE DATA examples

Consider a problem in which it is desirable to increase the number of inner iterations in XSDRNPM to 30 and to tighten the overall convergence criteria to a value of 0.000075. This could be accomplished by entering the data as follows:

```
MORE DATA IIM=30 EPS=0.000075 END
```

The order of the data entry is not important, and it can be continued across several lines. However, a keyword and its value cannot be separated across lines. The terminator for the optional parameter data, END, must not begin in column 1 unless you assign a name to it. An alternative method of entering the above data is given below.

```
MORE DATA
IIM=30 EPS=0.000075
END MORE
```

or,

```
MORE DATA IIM=30 EPS=0.000075 END MORE DATA
```

## CENTRM DATA examples¶

Consider a problem in which it is desirable to increase the upper energy of the CENTRM CE transport calculation from the default of 20000 eV to a value 50000 eV, and to extend the default lower energy from 0.001 eV to 0.0001. This is accomplished by entering the data as follows:

```
CENTRM DATA DEMAX=50000 DEMIN=0.0001 END CENTRM
```

As with the **MORE DATA** block, an alternative method of entering the
above data is given below.

```
CENTRMDATA
DEMAX=50000 DEMIN=0.0001
END CENTRMDATA
```

**CENTRM and PMC** computation options can also be controlled with
**CENTRM DATA.** A complete description of the CENTRM/PMC computational
methods and options can be found the corresponding sections of the SCALE
manual. The following example specifies that:

(a) discrete-level inelastic scattering will be used in CENTRM and processed in PMC [nmf6];

(b) the CENTRM 1D discrete S_{N} transport solver will be used in
the upper MG energy range [nfst] and the CE energy range [npxs], while
the infinitie medium model will be used for the thermal energy range
[nthr];

(c) a P3 scattering order [isct] will be used in the transport calculations;

(d) PMC will perform “consistent PN” corrections on Legendre moments of the 2D elastic matrices [n2d]; (e) additional output information will be provided by CENTRM [ixprt] and by PMC [nprt].

```
CENTRM DATA NMF6=0 NFST=0 NTHR=2 ISCT=3
N2D=-2 IXPRT=1 NPRT=1 END CENTRM DATA
```