KALMATRON® KF-αβγ RADIATION SHIELDING MATERIAL
■ DESCRIPTION of KF-αβγ
KF-αβγ is a radioactive shielding material for attenuation of radiation and liquid permeability.
This is non-organic cementitious gray powder without odor, dry bulk density of 2,200 Kg/m3. After mixing with water it becomes like plastic dough with wet density of 3,500 Kg/m3. The density after drying is about 2,450 Kg/m2.
- After 4 to 6 hours it works also as a waterproofer. Works as a radioactive protection immediately after
application even in a powder form.
- Any paint is applicable on the surface of a KF-αβγ layer.
- The durability of KF-αβγ layer depends on the thickness of layer and outside conditions.
- The best conditions for KF-αβγ are wet surface and humid air. By cementitious nature, the durability of KF-αβγ in dry and normal conditions is equal to durability of high dense concrete.
- Shielding layer is easy reparable and replaceable in a case of casual damages.
- We are able to produce various compositions of KF-αβγ and technologies of applications for the different
levels of radioactive protection.
■ USES of KF-αβγ:
KF-αβγ is applicable as a coating on any structure by plaster technology or admixture into concrete mix or strewing directly on a source of radiation. Application is also recommended by injections into concrete, soil, masonry and reinforced concrete structures. The fields of application are nuclear plants, storage of nuclear wastes, isolation of civil buildings, roads, tunnels, bridges and injections into mines, sinkholes, tunnels, pipes, tubes, deactivation of dusts, fly ash, etc.
■ RECOGNITION of KALMATRON®KF- αβγ
Before any operations, it is a necessity to determine the consumption of KF-αβγ per square unit in accordance with the source of radiation and required level of protection. Determination of the effective thickness of layer on a job site is available by application of a few spots with size 30cm x 30 cm and minimum thickness at 5 mm. If attenuation is not sufficient, apply another 5 mm layer and farther until the radiation is stopped.
■ PREPARATION OF KF-αβγ
- Use the chosen consumption of KF-αβγ per square unit of concrete surface.
- Add 1 part of water into 4 parts of KF-αβγ by volume and mix it for 1 minute.
■ PREPARATION OF SURFACE and CURING
Wet surfaces with water till soaked condition. For wooden, plastic or metal structures use the flat wire net before application of KF-αβγ. After 6 hours spray water on applied surface.
■ QUALITY CONTROL
- Use the standard methods and equipment for evaluation of leak or remainder of radiation.
- Repeat the Quality Control in accordance with local requirements.
■ BENEFITS
- KF-αβγ has the most workable and inexpensive technology for new structures and also for restoration of resistance of building structures against radiation.
- Deactivation of civil infrastructures by plaster technology without training of staff.
- Protective layer of KF-αβγ is applicable on wet, contaminated and deteriorated surfaces.
- Highest variability of the methods of application and variable improvement of durability.
- Applicable in solid and powder conditions.
■ THEORETICAL BASE OF KALMATRON® KF-αβγ
The theory of protection from radiation based on enhancing of Material Radioactive Resistance (MRR) by increasing of density with heavy fillers. Actually the Compton effect is used for description of adsorption of radioactive particles. Most of these materials are poisons and have special limits for application on civil and industrial structures.
The invention of KALMATRON® KF-αβγ is based on dissipation of g-energy flux by the oscillator phenomenon and the effect of threshold density. Specially formulated chemical compound KF-αβγ hardens after mixing with water. After application by metal trowel or shotcrete technology on a concrete or masonry surface, it becomes a solid and smooth top layer. This product has safety requirements as for any cementitious products. KF-αβγ has four functional ingredients as follows below.
1. ACTIVE FILLER
Active Filler are artificially produced crystals. These crystals are singular singonies with weakened gratings, which are very similar to ice crystals. We call them Active Filler. Randomly distributed in the protective layer, particles of Active Filler act as a series of structural gratings. After collisions with heavy particles these gratings get free fluctuations or might be partly deformed, or displaced which causes crumbling of shielding structure with degradation of thickness. From equation of Mass Attenuation Coefficient we can get logarithmic distribution of radioactive particles in SM [1]:
Ni+1 ρi+1 Li+1 2 2
∫dN/N = μm ∫rdr ∫dL = 0.5 μm (ρi+1 -ρi)( Li+1 – Li) = Ln |Ni+1/Ni|, [1]
Ni ρi Li
wherein: N is a number of radioactive particles incident normally upon a layer of SM;
μm – Mass Attenuation Coefficient of given SM;
ρ - density of SM;
dL – thickness of SM
Obviously, the limits between Ni+1 and Ni are the range of N-distribution where statistical fluctuations of absorbed particles are important. The less number of Ni+1 is the better protective feature of SM as follows from following equation:
2 2
0.5 μm (ρi+1 - ρi) (ΔL) →0
Ni+1 = Ni e ; [2]
herein the thickness of defected shielding layer after interaction with particles is:
2 2
ΔL = (Li+1 - Li ) = 2 Ln |Ni+1/Ni|/ μm (ρi+1 -ρi); [3]
2 2
Therefore, this is the necessity to provide structural threshold of density “(ρ i+1 - ρi)” to get a minimum thickness of defected layer, which is a main function of Active Filler.
2. PASSIVE FILLER
This is another type of crystals with strongly related gratings, but they have low density because of long distance between ties of grating. Actually, most of mineral salts have such type of grating under the particular temperature of evaporation, when the growing mass of the crystal body delays the growing volume, i.e. some sort of crystallized bubbles. Randomly integrated in the protective layer, particles of passive filler provide the effect of threshold density on a boundary contact between themselves and material of layer, which also reduces the transferring energy of gamma-particles.
This is a known example. The radioactive resistance of a 100mm concrete slab is weaker than two jointed concrete slabs of 50mm each and weaker than a 70mm concrete slab coated by a 30mm stucco layer. Therefore, combination of layers with variable densities is more effective than one layer, because every boundary layer works like a diffractor for γ- particles.
Flux of energy on both surfaces of the boundary layer reduces its initial level by fringe dissipation and deceleration on a threshold of density between jointed layers. We will described it by the known equation [4] about mass stopping power, integrated for the medium with variable density:
-1
for one layer: S/ρ = ρ ·dES / dL; [4]
wherein:
S/ρ - mass stopping power;
ρ - density of given media;
dL - distance of traversing energy, or L-1 =μ - coefficient of the linear suppression;
dES - average of energy lost by a charged particle of specific energy;
The integral, taken twice by two variables dr and dL from they initial parameter “i” till parameter “i+1”, gives the next equitation [5]:
ρi+1 Li+1 -1 -1
for two layers: S/ρ = ES∫ ∫ dρ/ρ · dL = ES(Li+1 - Li ) ln |ρi+1 / ρi |; [5]
ρi Li
wherein:
-1
Li = thickness of the first layer or initial distance of transferring energy;
-1
Li+1 - thickness of consequent layer or final distance of transferring energy;
ln |ρi+1 /ρi | - logarithmic decrement of threshold density;
Obviously, the most practically operable parameter of influence is logarithmic decrement of threshold density:
ln |ρi+1 /ρi| - logarithmic decrement of threshold density, [6]
wherein: ρi - density of Passive Filler;
ρi+1 - density of protective layer, where Passive Filler has been distributed.
According to logarithmically nature of equation [6], existence of threshold effectiveness is real in a limited mathematical space and need to be found out by experimental patches before industrial application. Combination both of Active and Passive fillers distributed into protective layer provide highest MRR, which is more advanced by effectiveness of protection, safety and workability than any known material and technologies. For instance, for one protective layer by [4], we can operate with thickness and density only, but for multiple layer by [5], we can get effective attenuation of radiation by simple and practical technologies.
3. BINDER
Another part of KF-abg is Portland Cement Type I;II, mixed with sand, powdered gravel or another chemically neutral heavy powder and plastisizers like lime and graphite. It provides strength and low shrinkage, which are important features for durability of shielding coatings.
4. CHEMICAL ACTIVE PART
For early strengthening and acceleration of density we use chemical compound (USA patent # 5,728,428). After mixing with BINDER, ACTIVE and PASSIVE FILLERS and water, this compound provides complete hydration activity of cement with the highest content of the gel of cement rock. It provides liquid impermeability for layers and high resistance to chemical corrosion and freeze-thaw.
■ TECHNOLOGY OF APPLICATION
We have practical experience about the most effective protection from radiation by technological methods of KALMATRON® KF-αβγ application. These methods are:
- application layer on layer with different densities instead of one layer;
- application with diffractor between layers.
During of KF-abg testing we’d comprised different layers in collimator camera (Fig.1) with Co 60. Measurements were provided by dosimeter model #3100 Survey Meter, serial # 9511-014. The averages of the test results are shown in table 1.
The results of experiments shown in table 1 are illustration of equations [4] and [5]. Obviously for massive structures the effectiveness of applications with diffractor and multiple layers is more effective than for specimens that used in our testimony.
The traditional way of increasing of shielding resistance by m (i.e. just the thickness of shielding material) or density ρi+1 by heavy fillers or other compaction technology is very expensive and causes thick and heavy shielding. This is not suitable for most known practical applications, where overweight of structure requires special retrofitting of whole project and additional protective technologies for waterproofing, chemical resistance, etc.
■DURABILITY of KALMATRON® KF-αβγ
The durability of SM is a period of time when material keep stable ability to resist to radiation. The main damage of SM from radiation is crumbling of microstructure that cause the of defect mass. The principle of durability is that the required durability “Ө” multiplied by an initial mass “m” should be equal to observing durability Өo multiplied by defect of mass “Δm” :
Өm = Өo · Δm; wherein m = ρi Vi = ρi a Li = ρi Li dN/E ; [7]
As it follows from [7], observing durability is calculable by [8]:
Ө·m
Өo = ------------ ; [8]
Δm
Therefore, stability of shielding material (thereafter SM) to resist to radiation penetration might be described by equitation of defect mass:
Δm = A· L/Sm · dEs / dL ; [9]
wherein:- A is a square of contact of SM with flux of radioactive particles with dA= dN/E = ρi Li ;
Sm – is a Mass Stopping Power;
-1
Li – is an observed thickness of SM with dL= dN· (ρN μm ) ;
Es - is the average energy lost by a charged particles;
The Mass Stopping Power is never been in practice of shielding operation by [9]. Research shows that that parameter is the most powerful for improving and control of SM. Obviously it has positive influence on evaluation of durability [8], where defect of mass is only operable figure in that equation. Below is the calculations of Mass Stopping Power [4] with different shapes of fillers. The sizes of sides, diameters, widths and heights are 5 mm for every shape of filler.
3 3
Sphere: V= 3.14d/6 =1/6 x 3.14 x 0.5 =0.065 [cm3];
m = ρm xV = 2.50 x 0.065 =0.163 [gr];
2 2
A = 3.14d = 3.14 x 0.5 = 0.785 [cm2];
ρA=m/A =0.163 : 0.785 = 0.167 [gr/cm2];
Sm=Ey/ρA=1.25 : 0.167 = 7.485[MeV cm2/ gr].
3 3
Cube: V = a = 0.5 = 0.125 [cm3 ];
m = ρm x V = 2.50 x 0.125 = 0.313 [gr];
2 2
A = 6xa = 6 x 0.5 = 1.5 [cm2];
ρA = m/A = 0.313 : 1.5 = 0.209 [gr/cm2];
Sm = Ey/ρA = 1.25 : 0.209= 5.98[MeVcm2/gr].
2 2
Cone: V = 1/3x3.14xr xh=1/3x 3.14x 0.25 x 0.5=0.033[cm3];
m = ρm x V = 2.50 x 0.033= 0.083 [gr];
2 2
A=1/2x3.14xdxl+3.14r =1/2x3.14x1.0x0.56+3.14x0.25 = 0.636 [cm2];
ρA = m/A = 0.083 : 0.636= 0.131 [gr/cm2];
Sm=Ey/ρA=1.25:0.131= 9.54 [MeV cm2/gr].
2 2
Cylinder: V= 3.14xr xh = 3.14x0.25x0.5 = 0.098[cm3];
m=ρm x V = 2.5 x 0.098 = 0.245[gr];
2
A= 2x3.14xrxh + 2x3.14xr = 1.178[cm2];
ρA = 0.245 :1.178 = 0.206[gr/cm2];
Sm= 1.25 : 0.206 = 6.1[MeV cm2/gr].
Wherein: ρm = 2,500 Kg/m3 is a Mass density offiller; Sm - is a Mass Stopping Power;
ρA - is an Arial density ; A - is a square of surface;
Ey = 1.25[MeV/ hr] is an energy of radiation.
Therefore, the most effective shape of filler is a cone with biggest Mass Stopping Power up to 27% with average of others. The best source for creating of fillers is artificial crystals with size at 0.001 mm to 0.015 mm. Bulk density of these crystals is about 2,000 Kg/m3, but every crystal has density at 3,500 Kg/m3 to 5,000 Kg/m3. Combination of crystals with different densities provides highest stopping energy in accordance with equation [5]. As it shown on Fig.1 and modeled calculations of Sm, the density of SM is not only leading parameter, but one of them which is proved by KALMATRON® KF-αβγ. Final equation of SM durability might be described as follows:
mxSmxdL
Өo= Өi ------------------ ; [10]
AxLxdEs
that gives the field of mathematical operations like modeling of Ferme’ surfaces or multifunctional rows. Result is always approximate because of climate conditions, landfill’ dynamic, required mass of structure, etc. are different. But grateful to these calculations we have ability to comprise shielding solutions with each other and evaluate feasibility of desirable durability.
As it shown in [10] the mass “m” of SM, thickness “L” and square “a” are dominating parameters of durability. Below are
some test results of KALMATRON® KF-αβγ applied by layers on the concrete slabs comprised with concrete and lead. Applicable as a coating, admixture and strewing, KALMATRON® KF-αβγ provides reliable protection from radiation penetration.
