What Are Effective Neutron Moderators in Nuclear Reactors?

[parazit]

Hello everyone...
I've been trying to make a list about moderator materials used in nuclear reactors. So far I've found some but still wondering if there exists more than I learned and also wondering if they are correct.

Please see the list below and feel free to correct my mistakes or to add new materials.

- Deuterium
- Oxygen
- Hydrogen
- Carbon (Graphite)
- Beryllium
- Lithium
- Boron-10
- Boron-11
- Vanadium
- H₂0 (Water)
- D₂0 (Heavy Water)
- BeO (Beryllium Oxide)
- ZrH_0.9, ZrH_1.5, ZrH_1.6, ZrH_1.65, ZrH_1.7, ZrH_1.85
- ZrH₂ (Zirconium Hydride)
- YH₂ (Yttrium (II) Hydride)
- YH₃ (Yttrium (III) Hydride)
- LiH (Lithium Hydride)
- ZrD₂ (Zirconium Deuteride)
- UZrH (Uranium Zirconium Hydride)
- UH₃ (Uranium Hydride)
- TiH₂ (Titanium Hydride)
- C19H16 (Triphenylmethane)
- FLiBe (Mixture of LiF-Lithium Floride- and BeF2-Beryllium Floride)

And please do not hesitate to share your knowledge about the materials.

Best regards...

 

[Evanish]

Maybe Helium but it has issues.
https://www.physicsforums.com/threads/helium-as-moderator.637730/

 

[parazit]

Maybe Helium but it has issues.
https://www.physicsforums.com/threads/helium-as-moderator.637730/

I saw Helium in the forum and than learned that its moderation ratio is so small. For that and due to the other issues mentioned in the page, I can not decide about it.

 

[QuantumPion]

I think you will have trouble trying to use boron as a moderator.

 

[parazit]

I think you will have trouble trying to use boron as a moderator.

Honestly, I do not know. If you say such thing, you probably know something. The reason of adding Boron to the list was due to the Wikipedia page.
You said that since boron is a highly effective neutron absorber, right?

 

[mathman]

http://en.wikipedia.org/wiki/Sodium-cooled_fast_reactor

sodium

 

[Astronuc]

Honestly, I do not know. If you say such thing, you probably know something. The reason of adding Boron to the list was due to the Wikipedia page.
You said that since boron is a highly effective neutron absorber, right?

¹⁰B is a highly effective neutron absorber (σ_α ~ 5000b), which is why it is used as a soluble neutron absorber (buffered with LiOH or KOH) in PWRs, as an absorber on the surface of fuel pellets (ZrB2), as a solid absorber in wet-annular burnable absorbers (WABAs) or as pyrex in burnable absorber assemblies (BPAs), and in PWR and BWR control elements. Boron is often enriched above 50% ¹⁰B.

⁶Li has a strong σ_α as well, so it and B would be consumed rather quickly and compete for neutrons, so they are used in low concentrations in PWRs. ⁷Li would be better.

Vanadium (A=51) is not much of a moderator, but perhaps like Fe, has a good fast removal cross-section.

He is a gas, so in a high temperature, graphite moderated reactor, it is as a coolant.

Be is best used with a stabilizing element like Y.

 

[parazit]

http://en.wikipedia.org/wiki/Sodium-cooled_fast_reactor

sodium

In here, sodium indicated as coolant I think, not as moderator. But the there also exists a sentence "In contrast, sodium atoms are much heavier than both the oxygen and hydrogen atoms found in water, and therefore the neutrons lose less energy in collisions with sodium atoms." Is this the reason that you add the sodium to the list as moderator ?

 

[parazit]

¹⁰B is a highly effective neutron absorber (σ_α ~ 5000b), which is why it is used as a soluble neutron absorber (buffered with LiOH or KOH) in PWRs, as an absorber on the surface of fuel pellets (ZrB2), as a solid absorber in wet-annular burnable absorbers (WABAs) or as pyrex in burnable absorber assemblies (BPAs), and in PWR and BWR control elements. Boron is often enriched above 50% ¹⁰B.

⁶Li has a strong σ_α as well, so it and B would be consumed rather quickly and compete for neutrons, so they are used in low concentrations in PWRs. ⁷Li would be better.

Vanadium (A=51) is not much of a moderator, but perhaps like Fe, has a good fast removal cross-section.

He is a gas, so in a high temperature, graphite moderated reactor, it is as a coolant.

Be is best used with a stabilizing element like Y.

Thanks for your explanations. So removing Vanadium, Boron and He will give me a more accurate list I assume.

 

[QuantumPion]

A more accurate list would simply be: hydrogen, deuterium, beryllium and carbon; and any low-absorption compounds containing those elements.

I've never heard of lithium being used as a moderator but I guess depleted Li7 would work, although I don't know much about it.

 

[parazit]

A more accurate list would simply be: hydrogen, deuterium, beryllium and carbon; and any low-absorption compounds containing those elements.

I've never heard of lithium being used as a moderator but I guess depleted Li7 would work, although I don't know much about it.

Thanks a lot QuantumPion. I also would like to know your opinions about ZrH₂ ,YH₂, YH₃, UH₃, TiH₂ basically metal hydrides.

 

[mathman]

In here, sodium indicated as coolant I think, not as moderator. But the there also exists a sentence "In contrast, sodium atoms are much heavier than both the oxygen and hydrogen atoms found in water, and therefore the neutrons lose less energy in collisions with sodium atoms." Is this the reason that you add the sodium to the list as moderator ?

The reactor described in the article uses sodium as the moderator.

 

[Astronuc]

The reactor described in the article uses sodium as the moderator.

I'm not so sure. The reference to moderator in the article on the sodium-cooled fast reactor is "An advantage of liquid metal coolants is high heat capacity which provides thermal inertia against overheating. Water is difficult to use as a coolant for a fast reactor because water acts as a neutron moderator that slows the fast neutrons into thermal neutrons." [my bold]

Fast reactors do not employ moderators, otherwise, they would not be fast reactors. Lithium, particularly ⁷Li, would a better moderator. It's all about the atomic mass and atomic density, and how many collisions it takes to slow fast neutrons to epithermal or thermal range.

 

[Astronuc]

Thanks a lot QuantumPion. I also would like to know your opinions about ZrH₂ ,YH₂, YH₃, UH₃, TiH₂ basically metal hydrides.

I've seen some fuel designs that incorporate metal hydrides, e.g., the TRIGA reactor at the university where I studied nuclear engineering use U-Zr hydride fuel.

http://www.ga.com/triga-fuels

Thermal stability of metal hydrides is important. The hydrogen needs to stay put.

The form of the moderator is important. Water is circulated, while Be/BeO and C are solid. In the case of FLiBe, the salt is liquid at operating temperature, but moderation is facilitated by graphite (C). Changes in moderator density are important to consider since this affects the neutron energy spectrum.

Voids due to boiling of water hardens the spectrum. In the case of Na, voiding adds positive reactivity since the voids remove Na that otherwise 'absorbs' neutrons.

 

[mheslep]

ZrH1.6 is the moderator chosen for the Transatomic molten salt reactor proposal, enabling 86 MWth/m³, a very high power density.

 

[snorkack]

Listing the minimum cross-sections of elements:
H 0,519 mb D; 332,6 mb
He 0 4; 7,47 mb
Li 45,4 mb 7; 70,5 b
Be 7,6 mb 9; M
B 5,5 mb 11; 768 b
C 1,37 mb 13; 3,5 mb
N 0,024 mb 15; 1,9 b
O 0,1 mb 16; 0,19 mb
F 9,6 mb 19; M
Ne 36 mb 20; 39 mb
Na 530 mb 23; M
Mg 38,2 mb 26; 63 mb
Al 231 mb 27; M
Si 101 mb 29; 171 mb
P 172 mb 31; M
S 150 mb 36; 530 mb
Cl 433 mb 37; 33,5 b
Ar 660 mb 40; 675 mb
K 1,46 b 41; 2,1 b
Ca 410 mb 40; 430 mb
Sc 27,5 b 45; M
Ti 179 mb 50; 6,09 b
V 4,9 b 51; 5,08 b
Cr 360 mb 54; 3,05 b
Mn 13,3 b 53; M
Fe 1,28 b 58; 2,56 b
Co 37,18 b 59; M
Ni 1,52 b 64; 4,49 b
Cu 2,17 b 65; 3,78 b
Zn 92 mb 70; 1,11 b
Ga 2,18 b 69; 2,75 b
Ge 160 mb 76; 2,2 b
As 4,5 b 75; M
Se 44 mb 82; 11,7 b
Br 2,7 b 81; 6,9 b
Kr 3 mb 86; 25 b
Rb 120 mb 87; 380 mb
Sr 58 mb 88; 1,28 b
Y 1,28 b 89; M
Zr 11 mb 90; 185 mb
Nb 1,15 b 93; M
Mo 15 mb 94; 2,48 b
Ru 280 mb 96; 2,56 b
Rh 144,8 b 103; M
Pd 226 mb 110; 6,9 b
Ag 37,6 b 107; 63,3 b
Cd 75 mb 116; 2520 b
In 12 b 113; 194 b
Sn 114 mb 114; 626 mb
Sb 3,8 b 123; 4,91 b
Te 215 mb 128; 4,7 b
I 6,15 b 127; M
Xe 260 mb 136; 24 b
Cs 29 b 133; M
Ba 270 mb 138; 1,1 b

 

[Astronuc]

Listing the minimum cross-sections of elements:
H 0,519 mb D; 332,6 mb
He 0 4; 7,47 mb

Minimum with respect to what?

What is one attempting to indicate with these data?

 

[snorkack]

Minimum absorption of all stable isotopes, and which isotope it is. If an element has a single isotope, it is marked with M; otherwise the absorption of natural composition is given for comparison.

Note that boron is actually a pretty good moderator - better than beryllium!

Another relevant feature, though, would be scattering cross-section.
D has scattering cross-section 7,64 barns. Which means the number of scatterings per capture is 7,64 b/0,519mb=14 700
Whereas H has extremely high cross-section for scattering: 82,03 b (probably thanks to virtual deuterons). So the number of scatterings per capture is 82,03/0,3326=246,6. Still fairly good despite high capture cross-section. And H is a very good neutron reflector even at low densities, which D is not.

He-4 scattering cross-section is 1,34 b. So even though absorption is zero and He-4 is a perfect mirror, it has to be pretty thick and dense to prevent transmission - much thicker than H and even thicker than D.
Natural He has absorption 7,47 mb (all due to He-3), scattering 1,34 b - thus 179 scatterings per capture. Worse than H.

Furthermore, another relevant quality factor is energy loss per scattering.
It depends on the nuclear mass, but how to quantify it?

 

[snorkack]

Li-7: scattering 1,4 b, absorption 45,4 mb, so 31 scatterings per absorption - not a good moderator. Not to mention natural Li has scattering 1,37 b, absorption 70,5 b, so 0,02 scatterings per absorption.
Be-9: scattering 7,63 b, absorption 7,6 mb, so 1004 scatterings per absorption
B-11: scattering 5,77 b, absorption 5,5 mb, so 1050 scatterings per absorption. Only slightly better than Be, and considering the lower mass of Be, Be is probably the better moderator after all. Of course, natural B has scattering 5,24 b, absorption 768 b, thus 0,007 scatterings per absorption!
C-13: scattering 4,84 b, absorption 1,37 mb, so 3530 scatterings per absorption. For natural C, scattering 5,55 b, absorption 3,5 mb, so 1600 scatterings per absorption.
N-15: scattering 5,21 b, absorption 0,024 mb, so 220 000 scatterings per absorption. For natural N, scattering 11,51 b, absorption 1,9 b, so 6 scatterings per absorption.
O-16: scattering 4,232 b, absorption 0,1 mb, so 40 000 scatterings per absorption. For natural O, scattering 4,232 b, absorption 0,19 mb, so 22 000 scatterings per absorption.
F-19: scattering 4,018 b, absorption 9,6 mb, so 420 scatterings per absorption.
Ne-20: scattering 2,965 b, absorption 36 mb, so 75 scatterings per absorption. For natural Ne, scattering 2,628 b, absorption 39 mb, so 57 scatterings per absorption.
Na-23: scattering 3,28 b, absorption 530 mb, so 6,2 scatterings per absorption.
Mg-26: scattering 3 b, absorption 38,2 mb, so 80 scatterings per absorption. For natural Mg, scattering 3,71 b, absorption 63 mb, so 59 scatterings per absorption.
Al-27: scattering 1,503 b, absorption 231 mb, so 6,5 scatterings per absorption.
Si-29: scattering 2,78 b, absorption 101 mb, so 27,5 scatterings per absorption. For natural Si (popular construction material component, O in silicates is much less absorbing!), scattering 2,167 b, absorption 171 mb, so just 12,7 scatterings per absorption.
...
K-41: scattering 1,2 b, absorption 1,46 b, so 0,8 scatterings per absorption. For natural K, scattering 1,96 b, absorption 2,1 b, so 0,93 scatterings per absorption.
...
Ti-50: scattering 4,8 b, absorption 179 mb, so 27 scatterings per absorption. For natural Ti, scattering 4,35 b, absorption 6,09 b, so 0,7 scatterings per absorption.
V-51: scattering 5,09 b, absorption 4,9 b, so 1,04 scatterings per absorption. For natural V, scattering 5,1 b, absorption 5,08 b, so 1,00 scatterings per absorption.
Cr-54: scattering 2,6 b, absorption 360 mb, so 7,2 scatterings per absorption. For natural Cr, scattering 3,49 b, absorption 3,05 b, so 1,14 scatterings per absorption.
...
Fe-58: scattering 28 b, absorption 1,28 b, so 22 scatterings per absorption. For natural Fe, scattering 11,62 b, absorption 2,56 b, so 4,54 scatterings per absorption. Note how good reflector even natural Fe is compared to the other common construction elements like Mg, Al or Si - but still, Fe-58 (0,3% in natural Fe) is much more useful!
...
Zn-70: scattering 4,5 b, absorption 92 mb, so 50 scatterings per absorption. For natural Zn, scattering 4,131 b, absorption 1,11 b, so 3,7 scatterings per absorption.
Ga-69: scattering 7,89 b, absorption 2,18 b, so 3,62 scatterings per absorption. For natural Ga, scattering 6,83 b, absorption 2,75 b, so 2,48 scatterings per absorption.
...
Kr-86: scattering 8,2 b, absorption 3 mb, so 2700 scatterings per absorption. For natural Kr, scattering 7,68 b, absorption 25 b, so 0,3 scatterings per absorption.
Rb-87: scattering 7,1 b, absorption 120 mb, so 59 scatterings per absorption. For natural Rb, scattering 6,8 b, absorption 380 mb, so still 18 scatterings per absorption. Compare K above. Na and Rb do form an eutectic, with -5 Celsius melting at 82 atom % Rb, so even natural NaRb should be much more useful than NaK!
...
Y-89: scattering 7,7 b, absorption 1,28 b, so 6 scatterings per absorption.
Zr-90: scattering 5,1 b, absorption 11 mb, so 460 scatterings per absorption. For natural Zr, scattering 6,46 b, absorption 185 mb, so 35 scatterings per absorption.
...
Mo-94: scattering 5,81 b, absorption 15 mb, so 390 scatterings per absorption. For natural Mo, scattering 5,71 b, absorption 2,48 b, so 2,3 scatterings per absorption.
...
Cd-116: scattering 5 b, absorption 75 mb, so 67 scatterings per absorption. For natural Cd, scattering 6,5 b, absorption 2520 b, so 0,0025 scatterings per absorption.
...
Sn-114: scattering 4,8 b, absorption 114 mb, so 42 scatterings per absorption. For natural Sn, scattering 4,892 b, absorption 626 mb, so 7,81 scatterings per absorption. Note that Sn-114 (0,7 % natural) is a middle isotope.
...
Hg-204: scattering unknown (as of 1999), absorption 430 mb. For natural Hg, scattering 26,8 b, absorption 372 b, so 0,07 scatterings per absorption, yet was successfully used as coolant of a reactor (Clementine).
Tl-205: scattering 11,4 b, absorption 104 mb, so 110 scatterings per absorption. For natural Tl, scattering 9,89 b, absorption 3,43 b, so 2,88 scatterings per absorption.

 

[snorkack]

Pb-208: scattering 11,34 b, absorption 0,48 mb, so 24 000 scatterings per absorption. For "natural" Pb, scattering 11,1 b, absorption 171 mb, so 65 scatterings per absorption.
Note that Pb-208 is natural and does not need isotope separation - just choose ore which on formation included Th-232 to the exclusion of any preexisting Pb and U.
Bi-209: scattering 9,156 b, absorption 33,8 mb, so 271 scatterings per absorption.

 

[snorkack]

Now, simply dividing the scattering/absorption ratio with isotope mass, for isotopes of interest:
H: 246,6
D: 14 700/2=7 350
He-4: infinity
Natural He: 179/4=45
Be: 1004/9=111,5
B-11: 1050/11=95,5
C-13: 3530/13=271,5
Natural C: 1600/12=133
N-15: 220 000/15=14 700
O-16: 40 000/16=2500
Natural O: 22 000/16=1400
F: 420/19=22
Kr-86: 2700/86=31,5
Zr-90: 460:90=5,1
Mo-94: 390/94=4,15
Tl-205: 110/205=0,54
Pb-208: 24 000/208=115
Bi: 271/209=1,3

 

[Astronuc]

There is a lot more to moderation than microscopic cross-sections.

For one, it is the macroscopic cross section, Σ, which is the product of the atomic density, N, and microscopic cross section, σ, which is important. A nuclide with a high scattering cross section, low absorption cross section, is not very effective if the atomic density is low, as in the case of He (gas). He is a good coolant, but a poor moderator because of its low density. Hence, most He gas-cooled cores require graphite moderation, and the power conversion system is either Brayton (direct) and/or Rankine (indirect) with heat passed through a heat exchanger. Hydrogen moderation can work in the form of water, either pressurized (PWR) or saturated and boiling (BWR), or it could be in the form of solid metal hydrides.

However, power systems require high temperatures, and that means liquids have reduced density, or could involve a phase change (liquid to vapor), or it could mean a gas. Power systems require cooling, which means heat transfer, which is manifest in thermal to mechanical conversion. Not all the thermal energy is however converted to mechanical energy (think Carnot efficiency), but some has to be rejected to environment. Higher efficiency can be achieved through higher temperatures, but that then introduces matters of materials compatibility and matters of degradation (corrosion and dimensional stability, e.g., creep).

Materials degradation is a critical factor in all power systems. Components have to be periodically be replaced.

Materials at high temperature (e.g., in the core of a reactor, or in the combustor and turbine of a jet engine) experience stresses, which at high temperature, drives creep, which results in dimensional changes. Engineers must develop 'creep resistant' materials to serve at time temperature.

In addition to high temperature, the neutron irradiation environment causes both radiation damage, in which atoms are knock out of their positions in the crystal lattices, i.e., displacements, and transmutation, in which nuclei absorb neutrons and decay/transform (usually by beta emission) to a different element, of increased atomic mass. So the material and system design must address the various consequential physical and chemical phenomena.

Then one must address the consequences of the fission (or fusion) process. In fission, a nucleus fissions/splits into two atoms, and they occupy roughly twice the volume as the original atom, so swelling (volumetric change/increase) of the fuel materials must be accommodated. In addition, for U and Pu fission, a substantial fraction of the fission products are isotopes of Xe and Kr, which are noble gases, so they add to the pressure within the fuel system (for a conventional system in which the fuel is materially and mechanically confined and separate from the coolant). The innovation in liquid fuel concepts, e.g., MSR, is the ability to chemically remove the fission products from the fuel system.

Fuel and core (reactor) design is an iterative and evolutionary process.

 

[snorkack]

There is a lot more to moderation than microscopic cross-sections.

For one, it is the macroscopic cross section, Σ, which is the product of the atomic density, N, and microscopic cross section, σ, which is important. A nuclide with a high scattering cross section, low absorption cross section, is not very effective if the atomic density is low, as in the case of He (gas). He is a good coolant, but a poor moderator because of its low density.

And relatively low cross-section, too. 1 molecule of He-4 has 1 atom with 1,34 bar scattering cross-section, let´s then call it 335 mb moderation cross-section - I´m sure I´m missing some logarithmic factor here.
1 molecule of natural O2 has 2 atoms with 8,46 bar scattering, so 530 mbar moderation cross-section - better than He! And a better coolant, too, because 5 degrees of freedom not 3.
1 molecule of CO2 has 3 atoms - the said 530 mbar moderation cross-section from two oxygens, plus the say natural C having 5,55 b/12=460 mb moderation cross-section total 990 mbar. But because the molecule is linear, still just 5 degrees of freedom, not 6.

Hence, most He gas-cooled cores require graphite moderation,

Why graphite, not say BeO? BeO also is a solid.

and the power conversion system is either Brayton (direct) and/or Rankine (indirect) with heat passed through a heat exchanger. Hydrogen moderation can work in the form of water, either pressurized (PWR) or saturated and boiling (BWR), or it could be in the form of solid metal hydrides.

Are solid, liquid and gaseous hydrocarbons useful hydrogen moderators?