Thermal Conductivity of ZrO₂, ZrSiO₄, (U,Zr)SiO₄ and UO₂: Numerical Approach

Abstract

The thermal conductivity of the products of the interaction of molten core with concrete was derived using number theory. A formula has been found that describes the thermal conductivity of ZrO2, ZrSiO4, (U,Zr)SiO4 and UO2 over a wide temperature range. Formula is expressed in terms of the atomic numbers of elements, their valencies, the crystal structure of substances, and the thermal conductivities of individual chemical elements of the corium.

Relationship Between the Mechanical Properties of an Irradiated Metal Alloy and the Mechanical Properties of the Irradiated Elements of the Alloy

“…This conclusion is also confirmed by the result on the superconductivity transition temperatures of high-temperature Y-and Hg-cuprates [4]. We have shown that in limited ranges of temperatures [1,2] or mole fractions of mixtures of actinide oxides [3], such weighted sums are multiplied by a constant. In other ranges of temperatures or mole fractions, we describe the physical properties of nuclear materials in terms of a weighted sum multiplied by a variable that changes according to the change in lattice parameters with mole fractions of the elements or temperature [3].…”

“…From our previous results regarding thermal conductivity [1,2] and melting/solidification temperature [3] of nuclear fuel fragments, oxide nuclear fuel and other nuclear ceramics, we concluded that for an arbitrary material, we can express its arbitrary physical property through atomic weighted or mass weighted sum of the corresponding physical properties of the elements of this material. This conclusion is also confirmed by the result on the superconductivity transition temperatures of high-temperature Y-and Hg-cuprates [4].…”

“…depending on the dependence of the lattice parameters of AnBmCk… on the elements  and h  Q (set of rational numbers) [1][2][3]. h() is associated in (1) with the most electronegative element, in our case it is the symbol C. Presence of the atomic numbers of all elements of the given complex compound is necessary because charges of nuclei define electronic structure of the solid body.…”

“…It turned out that for some    the structure parameter h is a constant: h()  h [1], [2], [3]. In this case the physical observable LAnBmCk…() can be represented in the next form:…”

“…Mechanical tests when measuring the yield strength 0.2 and ultimate tensile strength t of these samples were carried out at the same temperatures: Tirrad = Ttest. To apply formula (1), it is necessary to know the same mechanical values for all elements of the alloy (Ta, Hf and W) in the same radiation doses and temperature ranges as for the alloy. The authors of [5] found this out only for the Ta solvent.…”