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**Contents:**

A related objective was to compare the results with those for natural uranium NU fuel. The lattice is comprised of the outer heavy-water moderator region, a Zircaloy-2 calandria tube CT , a CO 2 gas gap, a Zr F igure 2. F igure 3. Lattice concept LC is a blanket-type fuel bundle made of pure ThO 2.

This bundle is similar to those described in previous studies [ 5 ]. Zirconia is a candidate material for use in the central displacer rod because it is a stable, inert matrix ceramic material that can operate at high temperatures, it is chemically compatible with zirconium-alloy clad, and it is a relatively low neutron absorber. Although there would be a reduction in lattice reactivity and exit burnup, the option exists to add dopants or burnable neutron absorbers such as dysprosia Dy 2 O 3 to the ZrO 2 to reduce the CVR even further, if desired [ 4 ].

Of course, it is potentially feasible to use other materials, such as MgO, or perhaps nuclear-grade graphite for the central displacer rod. The U used for LC could be obtained from an external source, such as recycled ThO 2 blanket fuel such as LC from either a fast or thermal-spectrum breeder reactor.

The impact is that the U content in the end pellets would be reduced from 1. This down-blending in the end region fuel pellets is expected to help reduce axial power peaking. Other lattice concepts are under investigation, but are not discussed or described here. Based on the experience gained from the light-water breeder reactor research program in the s [ 13 ], it is known that undermoderating a pure ThO 2 blanket fuel will harden the neutron energy spectrum, help promote direct fast-fission of Th, and suppress the thermal fission of U This condition will allow the U content to build up to higher levels before removal of the blanket fuel for subsequent reprocessing and recycling.

Within a PT-HWR, a simple way to harden the spectrum in the blanket fuel channels is to displace the heavy-water moderator by using an enlarged calandria tube. The calandria tube CT radius was varied from the nominal value 6. In addition, a hypothetical case with no moderator was also set up for comparison. The key parameters evaluated were the k inf and the fissile uranium Pa, U, and U content. The isotope Pa is treated as a fissile isotope because it will decay to U after the blanket fuel is removed from the reactor.

F igure 4. Selected examples of expanded calandria tube radii. Key performance parameters evaluated were the lattice infinite multiplication factor k inf , the CVR at different values of burnup, and the exit burnup. The CVR was obtained by reducing the coolant density to 0. The CVR is an important safety parameter because it contributes to the power coefficient of reactivity PCR for a reactor. The exit burnup was determined to be the burnup at which the integrated k inf , or burnup-averaged k inf was equal to 1. The effective multiplication factor of the reactor core is related to the burnup-averaged k inf through: 3 where L is the reactivity loss due to neutron leakage from the finite-sized reactor core and A is the reactivity loss due to neutron absorption in reactor core components not associated with the fuel bundle lattice, such as various reactivity devices adjusters, guide tubes, liquid zone controllers, and others that would be inserted into the PT-HWR core during normal operations [ 4 , 8 ].

The burnup-averaged k inf value of 1. Lattice physics calculations were also performed to evaluate the impact of zirconium enrichment in the various zirconium alloys used in the structural components Zircaloy-4 for clad, Zr The LC bundle has a higher mass of zirconium due to the central ZrO 2 displacer rod. Instead of using natural zirconium All cases were run to exit burnup and beyond, and comparisons were made for k inf , CVR, and exit burnup. It is known that the reactivity and burnup of thorium-based fuels in a PT-HWR or any reactor can be increased by operating at a lower neutron flux and a lower specific power [ 9 , 14 ].

One way to reduce the specific power is simply to reduce the reactor power, although such an approach may not always be desirable if the cumulative savings in fuel costs through increased burnup are less than the increase in the capital costs per kW e -h generated. An alternative approach [ 9 ], is to reduce the time-average specific power in the fuel by burning it partially, then removing it completely from the core, and storing it for some time before re-inserting it.

The strategy of partially burning, removing, and storing at zero power and then re-inserting the fuel in the core could be carried out a number of times as a fuel bundle moves through the reactor core, although it would increase the number and complexity of refueling operations. An additional irradiated fuel storage facility would also be required. However, it could still be advantageous to carry out at least 1 out-of-core storage period for a group of fuel bundles 2 or more per fuel channel in a PT-HWR [ 4 , 8 , 9 ].

For a base comparison, a lattice calculation was performed with a constant power history with no zero-power period. Then, 3 other lattice calculations were performed where the fuel was burned at full power for 1, 2, or 3 dwell-time periods, and then set to zero power which approximates what would happen if the fuel was removed from the reactor for 1 dwell period before being run at full power to exit burnup and beyond. Two different specific power settings were used for the power history calculations: high power, F igure 5. Power histories for temporary out-of-core storage of fuel.

It is seen that the increase of the CT radius from 6. Even with a substantial reduction in the moderator volume, there is still a significant thermal neutron population with a Maxwellian distribution. It is only when the moderator is completely removed that there is a drastic shift to a predominantly fast spectrum. The peak thermal flux per unit lethargy at In comparison, the peak fast flux per unit lethargy at the 6. F igure 6. Growth in fissile content and the lattice k inf is rapid for the first 2. With the harder neutron energy spectrum in the unmoderated lattice, fission is suppressed due to the lower fission cross-section of U and also U in the fast spectrum.

In addition, neutron capture in Pa, U, and U are also reduced. While the lattice multiplication factor is reduced, the fissile uranium content is allowed to build up to higher values at the same value of burnup. F igure 7. F igure 8. Fissile content vs. If it was desired to reach a fissile content in the blanket fuel that was comparable to that of LC 1. However, further design changes to a PT-HWR core would be required to completely exclude the moderator in blanket-type lattices.

Simply increasing the calandria radius would appear to be insufficient. It would also be necessary exclude the heavy-water moderator from the blanket channels by using a suitably designed baffle wall between the moderated seed channels and the unmoderated blanket channels. Results for k inf and CVR at different values of burnup zero, close-to-mid, close-to-exit , burnup-averaged CVR, and exit burnups for the base case, and with the moderator purity or coolant purity increased to With increased moderator purity, the reactivity of the lattices increased by approximately 3—5 mk, while the CVR dropped by 0.

With increased coolant purity, the reactivity of the lattices increases only very slightly, by 0. Impact of higher coolant purity on the exit burnup is only a slight increase, ranging from 0. F igure 9. F igure CVR vs. The increase in the Zr content and the associated decrease in the content of the heavier zirconium isotopes results in a significant increase in the lattice reactivity and exit burnup for both the LC and LC lattices.

The increase in the fuel exit burnup was quite significant. There is also a noticeable impact on the CVR. The first noticeable difference is that the low-power case has a significantly higher exit burnup The net economic impact of a power reduction has not been assessed in this study. As mentioned earlier, in addition to the base case, the LC was burned for 1, 2, and 3 dwell-time periods before implementing a zero-power period for 1 dwell-time period, followed by operating at full power until reaching the exit burnup. Schopper, H. Atomic Data and Nuclear Data Tables 44, Neutron News 3, No.

Prince ed. This does not include the absorption cross section. Scale to your beam by dividing by periodictable. This is tabulated but not used. Instead, the incoherent cross section is computed from the total cross section minus the coherent cross section even for single atoms so that results from compounds are consistent with results from single atoms. For elements, the scattering cross-sections are based on the natural abundance of the individual isotopes. For scattering calculations, the scattering length density is the value of interest. This serves to set the element info for elements with only one isotope.

If energy is specified then wavelength is ignored. The actual cross sections depend on the incoming neutron energy and sample temperature, especially for light elements. For low energy neutrons cold neutrons , the tabulated cross sections are generally a lower limit. For example, the incoherent scattering cross section of H2O is 5. The scattering potential is often expressed as a scattering length density SLD. This is just the number density of the scatterers times their scattering lengths, with a correction for units. For example, it can be treated as an absorption in specular reflectivity calculations since the incoherently scattered neutrons are removed from the multilayer recurrence calculation.

Similarly, scattering cross section includes number density If you instead want to calculate the effective shielding of the sample, you should recalculate penetration depth without the coherent scattering. This might be because the material has no atoms or it might be because the density is zero. Returns the scattering length density of the compound. This is useful for operations on large molecules, such as calculating a set of contrasts or fitting a material composition. Table lookups and partial sums and constants are precomputed so that the calculation consists of a few simple array operations regardless of the size of the material fragments.

Z-Symbol-A This is the atomic number, the symbol and the isotope.

If Z-Symbol only, the line represents an element with scattering determined by the natural abundance of the isotopes in laboratory samples. If there is only one isotope, then there is no corresponding element definition. Numbers in parenthesis represents uncertainty.

Numbers may be given as limit, e. Also accepts a limited range, e. Missing values are set to 0. This is used to checking the integrity of the data and formula.

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This is useful for checking the integrity of the data and formula. Usage:: python -m periodictable. You signed in with another tab or window. Reload to refresh your session. You signed out in another tab or window. This program is public domain.

Author: Paul Kienzle. Neutron scattering factors for the elements and isotopes. Individual isotopes may have their own scattering.

Print a table of coherent scattering length densities for isotopes. There are a number of functions available in periodictable. Return neutron energy given wavelength. Return wavelength given neutron energy. Return wavelength given neutron velocity. Computes scattering length density, cross sections and. Computes scattering length density for a compound.

Returns a scattering length density for a compound whose composition. Lists isotopes with energy dependence.

Lists scattering length densitys for all elements in natural abundance. Compares the imaginary bound coherent scattering length to the. Compares the bound coherent scattering length to the. Compares the total scattering cross section to the sum of the. The neutron scattering information table is reproduced from the Atomic.

The above site has references to the published values for every entry in. We have included these in the documentation directory.

Enteries in the table have been measured independently, so the values. Neutron Data Booklet second edition , A. Neutron scattering lengths. Atomic Data Nuclear Data Tables 49, Resonance effects in neutron scattering lengths of rare-earth nuclides. Tables for Crystallography C. Kluwer Academic Publishers. Neutron scattering lengths and cross sections. The forward scattering of cold neutrons by mixtures of light and heavy water. Wiley InterScience.

In some implementations, it is desirable to surround the moderating material with a material that is more resistant to chemical corrosion than the moderating material is, e. An isotope or nuclide can be classified according to its neutron cross section and how it reacts to an incident neutron. Mathieu, X. For example, in some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results. The combination of these three factors primarily determines the distribution of neutrons in space and energy throughout the reactor core and, thereby, the rate of the reactions occurring in the reactor core Atomic Data and Nuclear Data Tables 44, Return wavelength given neutron energy.

Incoherent Neutron Scattering from Multi-element Materials. Since plancks constant is in eV. Convert neutron energy to wavelength.

Energy is converted to wavelength using. Convert neutron velocity to wavelength. Velocity is converted to wavelength using. Convert neutron wavelength to energy. Wavelength is converted to energy using. Convert neutron scattering length density to energy potential. Scattering length density. Scattering potential. Neutron scattering factors are attached to each element in the periodic.

If no information is available,. Even when neutron. The following fields are defined:. Bounds coherent scattering length. This does not include the. To compute the total collision cross. Scale to your beam. Additional fields not used for calculation include:. Imaginary bound coherent scattering length. This is.

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Imaginary portion of bp and bm. Do not use this data if scattering is energy dependent. Coherent scattering cross section. In theory coherent scattering is related to bound coherent scattering. In practice, these values are. This is tabulated but. Instead, the incoherent cross section is computed from the.

For elements, the scattering cross-sections are based on the natural. Individual isotopes may have. Isotope abundance used to compute the properties of the element in. For scattering calculations, the scattering. This is computed from the. Returns scattering length density for the element at natural.

Values may not be correct when the element or isotope has. Compute number and absorption density assuming isotope has. PAK compute incoherent cross section from total cross section. Compute SLD. Returns neutron scattering information for the element at natural.