As the preceding section on fission emphasized, each fission reaction of an U235 atom leads to the release of an average of 2.5 neutrons. Hence, to sustain a continu­ous fission reaction (i. e., a chain reaction), these neutrons should be able to initiate the fission of at least another fissile atom. Note the schematic of a chain reaction involving U235 atoms in Figure 1.1. A majority of the neutrons (~99.25%) produced due to the fission reaction of U235, known as prompt neutrons, are released instanta­neously (within 10-14 s). But there are about 0.75% neutrons that are released over

Figure 1.1 A schematic chain reaction of U235 fissile atoms in progress (for the sake of simplicity, it is assumed that two neutrons are released due to the fission of one U235 atom and fission fragments created in each fission are also not shown).

a longer period (over ~20 s) and these neutrons are called delayed neutrons. These delayed neutrons play a very important role in controlling the fission chain reaction.

There is always a competition for neutrons between various processes, namely, (i) fission reaction of fissile atom nuclei, (ii) nonfission capture of neutrons by uranium and other reactions, (iii) nonfission capture of neutrons by other components in the reactor core, and (iv) leakage of neutrons from the core. The reaction can be termed as a chain reaction when the number of neu­trons consumed in the processes (ii)-(iv) is at least equal to or less than that consumed in the process (i). Thus, neutron economy plays a very important role in the design of a nuclear reactor. The need for a favorable neutron economy necessitates certain conditions to be met by a chain reacting system. For a given geometry, there is a certain minimum size of a chain reacting system, called the critical size (in terms of volume), for which the production of neu­trons by fission just balances the loss of neutrons by leakage and so on, and the chain reaction can be sustained independently. The mass corresponding to the critical size is called critical mass. Dependent on the relative generation of fission neutrons and their loss, the reactor is said to be in different stages: subcritical (neutron loss more than the production), critical (balance between the neutron production and loss, к = 1), or supercritical (the neutron produc­tion is more than the loss, к > 1). The multiplication factor к is often used to express the criticality condition of a reactor. This factor is basically the net number of neutrons per initial neutron.

1.6

A lot of space in crystals is empty and not occupied by lattice atoms(recall the definition of atomic packing factor). However, understanding interstitial sites in all the common lattice structures is an important step to understanding more complex crystal structures. Furthermore, interstitial impurity/alloying elements and self-interstitial atoms generally locate themselves in such sites. Figure 2.15a illustrates the octahedral position at the center of an FCC unit cell. Similar octahedral locations can be imagined at the center of each cube edge indicated by an “open” circle. However, to depict fully these octahedral positions just as shown in the center of the cube, one needs to construct addi­tional neighboring unit cells. Tetrahedral interstitial positions (indicated by the “open” circles) of the FCC unit cell are shown in Figure 2.15b. Note that all the tetrahedral positions are entirely within the unit cell unlike the octahedral positions. Figures 2.16 and 2.17 show similar octahedral and tetrahedral sites in both BCC and HCP unit cells.

Figure 2.16 BCC unit cell. (a) Octahedral positions. (b) Tetrahedral positions (the “filled” circles represent the lattice atoms and the “open” circles interstitial positions).

2.1.7

A simple model for calculating the atomic displacements is due to Kinchin and Pease [3], known as the Kinchin-Pease model. Before discussing this model, let us consider a case of collision between a high-energy neutron of mass M1 and a lattice atom of mass M2 (Figure 3.5). At certain energy ranges, neutron-nucleus interac­tion can be described by an elastic scattering process, where both kinetic energy and momentum of the particles are conserved before and after the collision. In the majority of the events like this, binary (two-body) collision is an appropriate approx­imation. A neutron has no electrical charge (i. e., neutral particle), and hence does not get perturbed by electrical fields exerted by the nucleus or electrons.

Let E1 be the energy of the neutron and due to the collision, the atom is scattered with energy T transferred from the neutron. There exists a threshold energy Ed for the atom to be displaced that is related to the binding energy of the atom. Thus, the struck atom will be displaced only if the transferred energy T is at least equal to or greater than this threshold value. As we have noted before, the displacement threshold energy is very small on the order of ~25 eV, while the transferred energy might be in keV or MeV range. Thus, there is a very high probability that the struck atom will get displaced and become a PKA. This PKA with reasonably high energy will thus interact with other atoms and displace them from their positions leading to secondary, tertiary, and other higher order knock-on atoms.

In the collision process between the incoming high-energy particle and the atom being displaced, if the knocked-on atom flies away with energy, T the incoming neutron will have energy E1 — T — Ed, at a scattering angle of в. In general, how­ever, the energy consumed in the scattering process is assumed negligible and thus the scattered neutron will have energy equal to E1 — T. Of course, the neutron

Figure 3.5 Various characteristics of an elastic collision event are shown in (a) the laboratory coordinates and (b) in the center-of-mass coordinates.

with energy [E1 — T] and the PKA with energy Tproduce other knock-on atoms. A simple calculation can show the likelihood of neutron-nucleus interaction. If we consider a neutron scattering cross section (a) as 1 b (i. e., 10—24 cm) and the num­ber density of atoms (N) in a material as 0.85 x 1023 cm—3 (typical of alpha-Fe), the distance between collisions, that is, the mean free path of the neutron (calculated by 1/Na) will be several centimeters (in this case, ~11.8 cm).

Analytical derivation based on the assumption of the kinetic energy and momen­tum conservation for an isotropic elastic scattering event between a neutron and an atom nucleus gives the following relations:

where Л — (4M1M2 )/(M1 + M2)2 and En is a generalized form of average incident neutron energy and is essentially equal to E10.

From Eq. (3.8), it is clear that the value of Tdepends on the scattering angle, the energy of the incident particle and the masses of the collided particles.

We can see that the maximum energy that can be transferred is given for the angle of scattering of 180°. In other words, the minimum possible value of cos(e), that is, —1, gives the transferred energy the highest value (Tmax), which is then given by the following relation:

T LE

max — L n

Of course, the minimum energy (Tmin) that can be transferred would be zero given a в value of0°.

Table 3.2 A summary of maximum percentage energy transfer that takes place from a 2 MeV neutron to different nuclides in the event of an isotropic elastic scattering (mass of neutron = 1.008665 amu). Nuclides Nuclide mass M2 (amu) , 4MnM2 L =——————— 2 (Mn + M2 )2 Tmax — AEn (MeV) %Energy approximately transferred H1 1.007825 1.0000 2.0000 100 H2 2.014102 0.8894 1.7787 89 C12 12.000000 0.2861 0.5722 28.6 Si12 27.976927 0.1344 0.2687 13.4 Au197 196.96654 0.0203 0.0406 2.0

However, the neutron-nucleus elastic scattering event could lead to glancing col­lisions. In that case, the use of average recoil energy (Tavg) is more appropriate:

Tavg = AEn • (3.10)

Table 3.2 lists the maximum percentage energy that can be transferred to differ­ent nuclides in the event of an elastic collision between a fast neutron (kinetic energy of 2 MeV) and the nuclides. One important observation from this table could be that the neutron transfers more energy to lighter nuclei. Thus, nuclides with low mass numbers generally act as good moderators. As we have discussed in brief, the materials often used are light water (H2O), heavy water (D2O), and graphite (C).

Even though earlier in the chapter we assumed that neutrons are scattered through every possible direction (Isotropic Scattering), in reality they tend to scatter preferentially in the forward directions, and hence the scattering behavior is aniso­tropic. That is why Eqs (3.9) and (3.10) may need to be corrected using a correction factor (f). The value off varies with the nuclide type; for example, for Be it is 0.56, whereas for C and Cu they are 0.84 and 0.6, respectively.

■ Example 3.2

A beryllium (Be) reflector is exposed to a neutron of 1 MeV energy. Let us assume the masses of the neutron and the Be atom are 1 and 9.01 amu, respectively. (a) Calculate the maximum and average energies transferred from the neutron to the beryllium atom based on isotropic elastic scattering event. (b) Determine the average energy transferred if the anisotropic scat­tering occurs (f— 0.56).

Solution

From Eq. (3.8), we know that Tmax = AEn, where Л = (4M1M2)/ (M1 + M2 )2.

a) In order to find out Tmax, we need to first calculate Л. Given M1 = 1 amu and M2 = 9.01 amu,

(4)(1)(9.01) (1 + 9.01)2

Hence, Tmax = (0.36) x (1 MeV) = 0.36 MeV.

Tavg = -^ = 0.18 MeV.

b) For anisotropic elastic scattering event, Taniso(avg) = f (LEn/2) = (0.56 x 0.18 MeV) = ~0.1 MeV.

Now, let us try to get an expression of the displacement damage rate (Rd) defined as the number of displacements per unit volume (cm3) per second. Rd is basically proportional to the number of target atoms per cm3, N (i. e., number density of atoms), and the displacement cross section od(En) for neutrons with energy En, and the neutron flux W(En), and can generally be written as

Rd = N ■ Od(En)- W(En). (3.11)

The important unit of radiation damage, displacements per atom (or dpa), can now be defined as

for neutrons with energies varying from 0 to 1.

Note that the neutrons with En < Ed/L do not generate any displaced atoms since Tshould be >Ed (i. e., the maximum transferable energy given by LEn > Ed to pro­duce a knock-on atom).

The displacement cross section is a function of the sum of the number of atomic displacements, n(T), produced by PKAs with energies T from Ed (the minimum needed) to Tmax(= LEn). The interaction probability is given by the differential energy transfer cross section, od(En, T)dE, for producing a PKA with energy (T, dT) due to the interaction with a neutron of energy En.

Therefore, we can write

Г LEn

Od(En)= On(En, T)■ n(T)dT. (3.13)

Ed

Note that the minimum energy of the PKA to produce displacements is Ed (Л = 1) since scattering between like atoms and the maximum energy of PKA is Tmax = LEn.

The Kinchin-Pease model is the simplest of all radiation damage models. It gives an estimate of the number of displacements produced by a PKA. The model is based on certain assumptions:

1) The cascade is created due to a sequence of binary (two-body) elastic collisions and the potential is based on the hard sphere model approximation.

2) Atomic displacements occur only when T> Ed (i. e., no quantum effects).

3) No energy is passed to the lattice during the collision phase.

4) Energy loss by electronic stopping is given by a cutoff energy known as elec­tronic cutoff energy (Ec). If the PKA energy is more than Ec, no additional displacements occur until electron energy losses reduce the PKA energy to Ec. For all energies less than Ec, electronic stopping is ignored and only atomic collisions take place.

5) Atomic arrangement is random (i. e., the effect of crystal structure is neglected).

6)

No annihilation of defects is assumed.

For the derivation of the K-P model, readers are referred to Refs [4, 5]. Here, we present the end result of the K-P model derivation:

According to Eq. (3.14), the number of displaced atoms can be plotted as a func­tion of PKA energy, as shown in Figure 3.6. The relation (3.14a) is self-explanatory from the very definition of Ed. That is, if T is less than Ed, we expect no atom dis­placement (i. e., n(T) = 0). However, for the relation (3.14b), when Tis greater than Ed but less than 2Ed, there could be two possibilities. One scenario could be that the struck atom does not get energy Ed from the PKA and stays in the same place. Second scenario could be that the struck atom gets more than Ed energy to be dis­lodged from the lattice site. But the PKA now with less than Ed energy falls back to

the original site of the lattice atom. So, in either case, only one displacement takes place. When the PKA energy is greater than 2Ed but less than Ec, the number of displacements increases monotonically with PKA energy until it reaches the elec­tronic cutoff energy (Ec). Beyond that, the number of displacements does not change. Even though in the simple K-P model it was assumed that all energy losses of the PKA go toward elastic collisions, with the increasing PKA energy, a greater fraction of energy will be lost into electronic excitation and ionization. In this case, we need to recognize that PKAs are basically fast ions. So, the number of displace­ments calculated at higher PKA energy would not be all consumed in creating the displacement damage. There are several modifications to the simple K-P model depending on the relaxation of the various assumptions.

Now getting back to the expression of Rd developed in Eq. (3.11) and combining with Eq. (3.13), we get the following expression:

From the theory of isotropic elastic scattering and hard sphere approximation, we can get a relation between double differential energy transfer cross section and scattering cross section:

where elastic collision cross section weakly depends on the neutron energy (En). Thus, it can be shown that

and

where Ф is the total integrated neutron flux given by

Ф = / W(En)dEn.

J0

(3.20)

■ Example 3.3

Consider 0.5 MeV neutrons (ael = 3 b) with a flux of 5 x 1015ncm-2s-1 interacting with alpha-iron (atomic mass number 56, lattice constant 0.287 nm) target. Find Rd.

Solution

Given are En = 0.5 MeV, ael = 3 b, Ed = 24 eV, Ф = 5 x 1015 n cm-2 s-1, and a0 = 0.287 nm.

From Eq. (3.17), we have

We have values of all the terms in the above equation except N and Л.

For Fe, we can calculate the number density of atoms (N) in the target material. There are two ways to do it.

1) If the material is a crystalline solid and we know its crystal structure (here, alpha-Fe that is BCC), we first find out the volume (Vcell) of the unit cell of alpha-iron from its lattice parameter (a0 = 0.287 nm). We know that the effective number of atoms (q) in a BCC unit cell is 2. So, N = q/Vcell = 2/a03 = 2/(0.287 nm)3 = 0.85 x 1023 atoms per cm3.

2) Another way to calculate N can be applied to all state of matter. This has been explained in Chapter 1. This needs knowledge of density and atomic mass of the material.

For Л, we use

Hence,

(0.85 x 1023 cm-3)(0.069)(3 x 10-24 cm2) , , w 2

Rd =±—————— 4(24 eV) —————- “ ^0’5 x 106 eV (5 x 1015 n cm-2 s^1)

=~ 4.5 x 1017 displacements cm-3 s_1.

Now if we divide Rd just by N, we obtain ~5 x 10 6dpas x.

We can also find the dpa value by multiplying the above number by the days of neutron exposure (say, 30 days), we get a dpa of (~5 x 10-6 dpa s-1). (30 x 24 x 3600s) = ~13.0.

Furthermore, if we wish to calculate the number of displaced atoms per neutron, we can use the following expression:

ЛЕn (0.069)(0.5 x 106eV)

4Ed = 4(24 eV)

3.3

Summary

In this chapter, we focused our attention on understanding the concepts of primary radiation damage involving neutron-nucleus collision and subsequent PKA and lattice atoms interaction leading to the formation of displacement cascades. The displacement threshold concept is elucidated with a simple example. The value of displacement energy is generally about 25 eV. Then, the K-P model is introduced. This gives the number of atomic displacements produced by a PKA. Finally, the methods of calculating the damage displace­ment rate and dpa are described. The field of radiation damage is vast, but discussion on all these aspects is out of the scope of this chapter. Interested readers may refer to texts listed in Bibliography.

Problems

1.1 a) If a copper target (mass number 64) is exposed to monoenergetic neutrons

of flux 2 x 1015 n cm-2 s-1 for 6 days continuously, show that the number of atomic displacements per atom (dpa) is 2.856 (Ed = 22 eV, ael = 2 b).

b) What will be the enhancement in self-diffusion in copper at 600 °C if only vacancy survived for million displacements (due to in situ annealing)? Given: Coordination number of copper = 12, lattice constant = ~0.22 nm, vacancy formation energy = 20kcalmol-1, and vacancy migration energy = 18 kcal mol-1.

1.2 a) Using the simple Kinchin-Pease model, evaluate the number of atomic

displacements per atom (dpa) of iron due to a monoenergetic neutron (2MeV) flux of 3 x 1015ncm-2s-1 for 1 year (assume isotropic elastic scattering ael = 3 b and Ed = 40 eV. Iron is BCC with A = 56 and q = 7.9 g cm-3).

b) Calculate the dpa for neutrons of energy 0.25 MeV and compare with the above.

1.3 a) Calculate the average energy of primary knock-ons for Zr when struck with 2MeV neutrons (Zr: (HCP) A — 91, a — 3.23A, c — 5.147A, Ev — 30kcal mol_1, Ed — 59kcalmol_1, sel — 2 b, Ed — 25eV).

b) If in a zirconium target exposed to high-energy neutrons, PKAs were pro­duced with 240 keV, calculate the number ofatoms displaced due to a PKA (assume Kinchin-Pease model).

c) Where do the displaced atoms go to and what is the primary defect created by these atomic displacements?

d) Some of these zirconium specimens were exposed to high-energy neutrons and dpa was calculated tobe2.5, while only one vacancy survived for billion displacements. Calculate the vacancy concentration in the irradiated sample at 500 °C.

e) Evaluate the %increase in lattice diffusivity ofthe irradiated material.

There are two basic mechanisms of precipitation strengthening: (a) particle shear­ing (particle cutting mechanism), and (b) dislocation bowing or bypassing mecha­nism (Orowan’s theory).

Corrosion couples can be categorized into three broad categories: (i) composition cells, (ii) concentration cells, and (iii) stress cells.

5.3.2.1 Composition Cells

A composition cell can be established between two dissimilar metals. One example of it is the galvanized steel in which zinc coating is applied to carbon steel to protect it from rust and other environmental attacks. Here, zinc coating acts as a sacrificial anode, which means that the steel underneath is protected while zinc coating gets corroded. Thus, a metal higher on the electrochemical series can be used to reduce corrosion to a less active one. Note that from the relative positions of iron and zinc on the electrochemical series in Table 5.4, zinc is more anodic than iron. The unique aspect of sacrificial anode is that even if there is an accidental scratching on the zinc coating exposing the steel surface, the steel will still be protected until all zinc coating gets corroded. However, tin coating on iron or steel sheets is also used for protection in which case protection remains only up to the point when the tin coating acts as a barrier and is not compromised. However, if tin coating gets scratched or punctured, the corrosion effect will be concentrated in that punctured region (anode) with respect to remaining tin coating (cathode).

In the galvanized steel example, we found out benefits of the composition cell in corrosion protection. However, there are many other engineering examples of com­position cells wherever dissimilar metals/alloys are made to work in contact and that situation is not desirable at all from an engineering point of view. A couple of examples include steel bolts in brass naval components and steel piping connected to a copper valve. Whenever a materials selection decision is made to use dissimilar metals/alloys in engineering applications, due care must be exercised. If not, com­position cells will be set up and would cause undue galvanic corrosion problems. Galvanic cells can also be created at microlevel. Usually the single-phase metallic alloys are more corrosion resistant. As more second-phase particles are formed through precipitation, galvanic microcorrosion cells are set up between the particle and the matrix metal and lead to a poor corrosion resistance.

Gen-IV reactors are the futuristic reactors for which research and development efforts are currently in progress. These reactors will be more efficient, safer, longer lasting (60 years and beyond), proliferation-resistant, and economically viable com­pared to the present nuclear reactors. Six reactor designs were selected at the out­set. They are summarized in Table 1.4 including information on the type (fast or thermal spectrum) of the reactor, coolants, and approximate core outlet tempera­tures. Two reactor concepts, sodium fast reactor (SFR) — along with the advanced burner reactor (ABR) concept under the erstwhile Advanced Fuel Cycle Initiative Program) — and very high-temperature reactor (VHTR) under the Next Generation Nuclear Plant (NGNP) are of the highest priority in the United States (Figure 1.15a and b, respectively). VHTR is the reactor concept employed for the Next Generation Nuclear Plant program where the heat generated will cogenerate electricity and hydrogen.

The demanding service conditions (higher neutron doses, exposure to higher temperatures, and corrosive environments) that the structural components will experience in these reactors would pose a significant challenge for the structural materials selection and qualification efforts. Because of the stringent requirements noted above, the materials employed in today’s commercial reactors are not suitable for use in Gen-IV reactors. For example, zirconium alloys (Zircaloy-2, Zircaloy-4, Zr-2.5Nb, M5) have been used routinely as fuel cladding and other reactor internals in both light and heavy water reactors because of their low neutron capture cross section and acceptable mechanical and corrosion resistance in high temperature

Table 1.4 A summary of Gen-IV reactor system designs. Reactor system Priority/timeline Coolant Neutron Core outlet spectrum temperature TO Gas-cooled fast Medium/long term Gas (e. g., He) Fast ~850 reactor (GFR) Lead-cooled Medium/long term Liquid metal Fast 550-800 reactor (LFR) (e. g., Pb, Pb-Bi) Molten salt Low/long term Molten salt Thermal 700-800 reactor (MSR) (e. g., fluoride salts) Sodium-cooled High/mid term Liquid metal (Na) Fast ~550 fast reactor (SFR) Very high- High/mid term Gas (e. g., He), Thermal > 900 temperature reactor (VHTR) CO2 Supercritical Medium/long term Water Thermal/fast 280-620 water-cooled reactor (SCWR)

Figure 1.15 Schematics of (a) a sodium fast reactor and (b) a very high-temperature reactor. (Courtesy: US Department of Energy Gen-IV Initiative)

(probably never exceeding 350-380 °C under normal service conditions) aqueous environment. However, higher temperatures envisioned in Gen-IV reactors would limit the use of zirconium alloys because of increased susceptibility to hydrogen embrittlement due to severe hydride formation, allotropic phase changes at higher temperatures (a-fi phase), poor creep properties, and oxidation. It is instructive to note that some high-performance zirconium alloys may be of possible use in rela­tively low-temperature Gen-IV reactor design (such as SCWR). Furthermore, the out-of-core components (pressure vessel, piping, etc.) may need to be made from materials other than the low-alloy ferritic steels (e. g., A533B) currently employed primarily because similar components in Gen-IV reactors are expected to withstand much higher temperatures and neutron doses. Some of the fabrication difficulty involved in the VHTR construction demands mention here. For example, the pres­sure vessel for VHTR reactor as shown in Figure 1.16 is about double the size of the currently operating PWRs. Heavy component forgings will be needed in the construction of these huge pressure vessels.

Figure 1.16 A schematic size comparison between the reactor pressure vessels in a typical PWR and a conceptual VHTR. Courtesy: Nuclear News.

Test Reactors So far we have discussed the past, current, and future nuclear reactors in detail. Now let us discuss about a test reactor. One of the well-known test reactors in the United States is the Advanced Test Reactor located at the Idaho National Laboratory near Idaho Falls, ID. ATR is a flagship reactor that serves the US Department of Energy, Naval Nuclear Propulsion Program, and different other governmental and commercial entities. It also acts as a user facility that the university-led teams can use to irradiate materials and perform postirradiation examination (PIE) upon going through a competitive proposal process. ATR started its operation in 1967 and is being operated continuously since then with 250+ days of operation in an average year. A view section of the ATR is shown in Figure 1.17. ATR is a pressurized, light water cooled and moderated, 250 MWth reactor with beryllium reflectors and hafnium control drums. The metallic fuel (U or U — Mo) is in the plate morphology clad in an aluminum alloy. There are 40 fuel assemblies in the reactor core; each core contains 19 fuel plates. At 250 MW, maximum thermal neutron flux is ~1015 n cm-2 s-1, and the maximum fast neu­tron flux could reach 5 x 1014 ncm~2s~ Thus, ATR can be used to study the radiation damage under the fast neutron spectrum. The ATR has 77 irradiation positions (4 flux traps, 5 in-pile tubes, and 68 in-reflector) (for details, see Figure 1.18). The reactor pressure vessel is made of stainless steel, and is 3.65 m in diameter and ~10.67 m in height. Table 1.5 lists some of the differ­ences between ATR and a typical PWR. ATR even though used for neutron irradiation experiments is not a fast reactor facility. Note that at present the United States does not have any operating/underconstruction fast reactor test facility (EBR-II and FFTF facili­ties were shut down during 1990s) as opposed to countries like France (Phe — nix), India (prototype fast breeder reactor (PFBR)), Japan (Joyo and Monju), Russia (BOR-60), and China (China experimental fast reactor (CEFR). The lack of a fast reactor facility is a challenge for the US nuclear R&D commu­nity. The proposed Advanced Burner Test Reactor (ABTR), a sodium-cooled fast reactor, is still under the planning stage, and there is no further confir­mation of its installation yet.

1.9 Read More 26.08.2015   An Introduction to Nuclear Materials Substitutional Atoms When solute atoms substitute the parent lattice atoms from their original sites, the solid solution is called a substitutional solid solution. There could be two possibilit­ies: First, solute atoms can substitute the host lattice atoms randomly, forming a random (or disordered) substitutional solid solution. An overwhelming majority of substitutional alloys are of this type. Second, an ordered (substitutional) solid solu­tion results when the solute and solvent atoms are arranged in a regular fashion on the lattice sites (Figure 2.27). Perfect order becomes possible when the two metals are mixed in some fixed proportions such as 3 : 1, 1: 1, and so on and at under certain temperature. For example, Cu3Au (75 at% of Cu and 25 at% of Au) alloy can exhibit an ordered structure at lower temperature range, but above a certain tem­perature range the ordered alloy loses perfect order, thus becoming disordered. However, the Cu-Ni alloy system at all compositions and in all conditions are dis­ordered, which is the norm most times. Figure2.27 Schematic structures of the (a) ordered and (b) disordered alloys. Hume-Rothery studied a number of substitutional alloys and developed a set of basic rules for substitutional solid solubility. The principles derived from his study are known as the Hume-Rothery’s rules: 1) “The atom size difference between the host atom and the solute atom should be less than 15%.” If the size difference becomes higher, more intense stress fields are created. This observation is true for both large and small solute atoms. Generally, a large atom induces a compressive stress field around itself, while a small atom tends to introduce a tensile stress field. These stress fields can increase the potential energy of the crystal. Therefore, the solid solubility becomes more limited as the size difference increases. This is known as the size factor effect. For example, the atomic radii of copper and nickel are 145 and 149 pm., respectively. The percentage size difference is only about 2.8%. They have wide solid solubility in each other. 2) “The electronegativity difference between the solvent and the solute should be small.” Electronegativity is defined as the ability of an atom to attract electrons to itself. The electronegativity difference between two elements can be calcu­lated from Pauling’s electronegativity scale. The difference is generally quite small between typical metallic elements. If the electronegativity difference is more, the tendency would be to create compounds rather than alloys. This is called chemical affinity effect. For example, the Pauling electronegativity values of copper and nickel are 1.9 and 1.91, respectively, thus giving the difference of only 0.01. 3) “The valency of the atoms constituting the alloy must be the same for extensive solid solubility.” However, when the valencies are different, a metal with lower valency tends to dissolve in a metal of higher valency more readily than vice versa. It is found that an excess of electrons is more readily tolerated rather than a deficiency of bonding electrons. This is known as relative valency effect. For instance, zinc (two valence electrons) dissolves appreciable amount of copper (up to 38%), whereas copper (one valence electron) dissolves only about 3% in zinc. 4) “The crystal structures of the solvent and solute should be the same for achiev­ing extensive solid solubility, known as crystal structure effect.” This implies that solute atoms can substitute the host lattice atoms continuously, forming a series of solid solutions. A nice example of this is the isomorphous system of copper and nickel (both have FCC crystal structure). Read More 26.08.2015   An Introduction to Nuclear Materials Stress Field of Dislocations The dislocations are associated with elastic stress fields around them. This stress field is crucial for the dislocation to interact with other dislocations and crystal defects. For a straight edge and screw dislocation in an isotropic medium, the stress/strain field analysis is quite straightforward. However, it becomes compli­cated with the elastic anisotropy of the crystal and other variations in dislocation characteristics. Read More 26.08.2015   An Introduction to Nuclear Materials Macrohardness Testing Brinell Hardness Test In 1900, J. A. Brinell of Sweden invented ways to determine hardness by measuring the impression (or indentation) made by a steel ball forced into the metal under static loads. The definite advantage of this technique is that a single linear scale can be used to determine hardness. The standard Brinell test requires a 3000 kg load applied through a 10 mm diameter hardened steel or tungsten carbide ball. Brinell Hardness Number (BHN) is given by 2P BHN = =-, (5.25) pD(D — D2 — d2) where P is the applied load in kgf and D and d are the diameters of the ball and the impression, respectively, in mm. Read More 26.08.2015   An Introduction to Nuclear Materials Is Void Swelling Observed Only in Stainless Steels? Void formation is not unique to stainless steels only; as a matter of fact, all metals and alloys swell through void formation in the homologous temperature range of 0.3-0.55Tm (where Tm is the melting point of the material in Kelvin). There may well be a variation in void swelling behavior depending on the material composi­tion, He content, grain size, temperature, and cold working. (Void formation is also a problem in the fusion technology. Fast neutrons produced from the plasma can cause void formation in the first wall blanket material with (n, a) reactions for neutron energy increasing above 5 MeV. Increase in helium content generally increases the propensity for void swelling. The problem of void swelling may be expected to be more severe in fusion reactors than in LMFBRs due to the relatively higher neutron energies.) Read More Календарь Май 2024 Пн Вт Ср Чт Пт Сб Вс   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31   Рубрики 1 BIOFUELS A Look Back at the U. S. Department of Energy’s Aquatic Species Program: Biodiesel from Algae A. Worrall ABOUT THE AUTHOR ACCELERATOR DRIVEN SUBCRITICAL REACTORS ADVANCED BIOFUELS Advanced Biofuels and Bioproducts Advanced separation techniques for nuclear fuel reprocessing and radioactive waste treatment ADVANCES IN Advances in Biochemical Engineering/Biotechnology Advances in Biofuels Advances in Biorefineries Alcoholic Fuels Algae Energy All alternative energy Alternative transportation An Indispensable Truth An Introduction to Nuclear Materials AN INTRODUCTION. TO THE ENGINEERING. OF FAST NUCLEAR REACTORS ANNEX III. AHWR. Bhabha Atomic Research Centre, India ATOMIC ACCIDENTS BACKGROUND Bioenergy Bioenergy — Realizing the Potential Bioenergy from Wood BIOENERGY. RESEARCH:. ADVANCES AND. APPLICATIONS BIOETHANOL BIOFUEL'S ENGINEERING PROCESS TECHNOLOGY BIOFUELS BIOFUELS 1 Biofuels and Bioenergy Biofuels for Road Transport Biofuels from Agricultural Wastes and Byproducts BIOFUELS FROM ALGAE Biofuels Refining and Performance BIOGAS BIOGAS 1 BIOMASS — DETECTION, PRODUCTION AND USAGE Biomass and Biofuels from Microalgae Biomass Conversion Biomass Gasification and Pyrolysis BIOMASS NOW — CULTIVATION AND UTILIZATION BIOMASS NOW — SUSTAINABLE GROWTH AND USE Biomass Recalcitrance Biomasses identities Biotechnological Applications of Hemicellulosic Derived Sugars: State-of-the-Art Biotechnological Applications of Microalgae Biotechnology. for Fuels and Chemicals Cellulosic Energy Cropping Systems Comprehensive nuclear materials DESIGN FEATURES TO ACHIEVE. DEFENCE IN DEPTH IN SMALL AND. MEDIUM SIZED REACTORS Design of Reactor Containment Systems for Nuclear Power Plants ENERGY Energy Efficiency ENERGY SERVICES IN THE HINDU KUSH HIMALAYAN REGION Energy Storage Estimating Loss-of-Coolant Accident (LOCA) Frequencies Through the Elicitation Process EUROSUN 2008 EuroSun2004 EuroSun2008-10 EuroSun2008-11 EuroSun2008-13 EuroSun2008-2 EuroSun2008-3 EuroSun2008-4 EuroSun2008-5 EuroSun2008-7 EuroSun2008-9 EXAMPLES OF REACTIVITY-CONTROL SYSTEMS Exploitation des creurs REP Fast Breeder Reactor Programs: History and Status Fast Reactor Safety. (Nuclear science. and technology) Fertilization Frequency Response Testing. in Nuclear Reactors Fuels and Chemicals. from Biomass Gebaudetypologie Bayern Geothermal Energy GREEN BIORENEWABLE. BIOCOMPOSITES Handbook Nuclear Terms Handbook of biofuels production Handbook of Small Modular Nuclear Reactors Hydrogen — Fuel Cells Hydropower IAEA RADIATION TECHNOLOGY SERIES No Infrastructure and methodologies for the. justification of nuclear power programmes Innovative Biofibers from Renewable Resources Integral design concepts of advanced water cooled reactors Introduction to Nuclear Power Liquid Biofuels: Emergence, Development and LIQUID, GASEOUS AND SOLID BIOFUELS — CONVERSION TECHNIQUES Management von Biogas-Projekten Materials' ageing and degradation in. light water reactors Microbes and biochemistry of gas fermentation Modern Power Station Practice Natural circulation data and methods for advanced water cooled nuclear power plant designs Natural gas Neutron Scattering Applications and Techniques Nuclear and Radiochemistry Nuclear Back-end and Transmutation Technology for Waste Disposal NUCLEAR CHEMICAL ENGINEERING NUCLEAR ELECTRIC POWER Nuclear energy Nuclear Power and the Environment Nuclear power plant life management processes: Guidelines and practices for heavy water reactors NUCLEAR POWER PLANTS NUCLEAR POWER the PUBLIC Nuclear Reactor Design NUCLEAR REACTOR ENGINEERING Nuclear Reactors 1 NUCLEAR REACTORS 2 Others Particle Image Velocimetry (PIV) Passive Safety Systems and Natural Circulation in Water Cooled Nuclear Power Plants PHYSICS OF. HIGH-TEMPERATURE. REACTORS POWER Pretreatment Techniques for Biofuels and Biorefineries Principles of Fusion Energy PROCESS SYNTHESIS. FOR FUEL ETHANOL. PRODUCTION Production of Biofuels and Chemicals with Ionic Liquids Progress, Challenges, and Opportunities for. Converting U. S. and Russian Research Reactors Pumping Pyrolysis Radioactive waste management and contaminated site clean-up Recycling of Biomass Ashes Renewable Energy Products Rudiger Meiswinkel, Julian Meyer, Jurgen Schnell Second Generation Biofuels and Biomass Small modular reactors (SMRs) the case of Russia solar energy Solar Thermal and. Biomass Energy Sonar-Collecttors SonSolar Springer Series in Materials Science Study on Neutron Spectrum of Pulsed Neutron Reactor Sustainable Biotechnology Switchgrass Technologies for Converting Biomass to Useful Energy The Asian Biomass Handbook The Experimental Analyze Of The Solar Energy Collector The Future of Nuclear Power Thermal biomass. conversion and utilization —. Biomass information. system Thoria-based Nuclear Fuels Type of Membrane Contactor Suitable for CO2-O2 Exchanges in Culture Broth Vereinfachtes Verfahren WAS INTENTIONALLY LEFT BLANK Why We Need Nuclear Power wind power WORKSHOP ON NUCLEAR REACTION DATA AND. NUCLEAR REACTORS:. PHYSICS, DESIGN AND SAFETY Автономное энергообеспечение Альтерантивная энергия Альтернативные источники энергии и энергосбережение Без рубрики Биотопливо Ветровая энергия Ветрогенераторы, солнечные батареи и другие полезные конструк­ции Возобновляемые источники энергии ВОПРОСЫ ТЕОРИИ. И ИННОВАЦИОННЫХ РЕШЕНИЙ. ПРИ ИСПОЛЬЗОВАНИИ. ГЕЛИОЭНЕРГЕТИЧЕСКИХ СИСТЕМ ГЕЛИОЭНЕРГЕТИКА Другая энергия Зарядные станции Источники питания Источники энергии ИСУ Концентраторы солнечного излучения КРЕМНИЕВЫЕ СОЛНЕЧНЫЕ БАТАРЕИ Получение кремниевых пластин для солнечной энергетики Применение солнечной энергии Разное Солнечная электроэнергия Солнечная энергия Солнечная энергия — использование Солнечные батареи Солнечные коллекторы Солнечный ДОМ ТОНКОПЛЕНОЧНЫЕ. СОЛНЕЧНЫЕ ЭЛЕМЕНТЫ. НА ОСНОВЕ КРЕМНИЯ ФОТОЭЛЕКТРИЧЕСКОЕ. ПРЕОБРАЗОВАНИЕ. 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