A method for determining the thermal conductivity of granulated silicon in which alkali metal atoms are included

УДК 621.315:629.7
A METHOD FOR DETERMINING THE THERMAL CONDUCTIVITY OF GRANULATED SILICON IN WHICH ALKALI METAL ATOMS ARE INCLUDED.
S.Zaynabidinov¹, Z.M.Soxibova², M.Nosirov^1
1Andijan State University, Uzbekistan, city of Andijan
²Andijan Machine-Building Institute.


Annotation: This paper describes a comparative method for determining the thermal conductivity χ of granulated silicon. According to him, the thermal conductivity of granulated silicon which alkali metal atoms are included was studied in the process of temperature increase. The essence of the method of comparison is that first a sample is prepared from the material whose thermal conductivity is being studied. It is then placed between two standart samples (E1 and E2) for which the thermal conductivity value in a similar shape and size is known. As a standard, a sample made of a special mark of brass (L63) was used.
Keywords: granulated silicon, thermal conductivity, standard, comparative method, alkali metal atoms.

Thermal conductivity is one of the main parameters of thermoelectric materials. One of the directions of increasing the figure of merit of a thermoelectric material is precisely what implies a decrease in its thermal conductivity, for example, by creating a material of the "phonon glass - electronic crystal" type [2, p.14–18]. Monocrystalline silicon is not considered a thermoelectric material, including because of its high thermal conductivity, which is ~ 150 W/м*К. [5, p.1–3]. In recent years, many scientific studies have been conducted to reduce and determine the thermal conductivity of silicon samples. For example, the manufacture of plates from pressed and then sintered at 1400 K in a vacuum of silicon powders. As reported in [1, c.2–3], this made it possible to reduce the thermal conductivity to ~ 79 W/м*К, that is, almost 2 times in comparison with monocrystalline silicon.

There are currently many ways to determine the thermal conductivity. For example, the Egor and Disselhorst method is one of the most widely used methods for determining the thermal conductivity of rod-shaped metals and other conductive materials.[3, 192 б]. Also, one of the most common and effective methods for determining the thermal conductivity of granulated silicon powder is the comparative method. Accordingly, a model in the form of a simplified multilayer system of the sample is selected to determine the thermal conductivity of the powder [4, p.209 - 212]. The temperature between each heat-conducting layer is measured separately.
Thus, in this case, the passage of heat flux through a three-layer disc, the thickness of which is small relative to the diameter, is considered, which makes it possible to ignore the heat loss through the side surfaces. The thermal conductivity equation for each layer of the disk can be written as follows:
_{ } (1)
where Q is the amount of heat transferred from a layer with temperature _{ } to a layer with temperature _{ } per unit time, D is the thickness of the layer, and S is the surface. Assuming that the same amount of heat Q - enters from the side of the disk surface (B), then passes through all its layers and leaves the surface into the environment, for each disk layer with area S we can write:
_{ } (2)
_{ } (3)
_{ } (4)
where χ₁, χ₂, χ₃, respectively, are the thermal conductivity coefficients for each layer. Dividing (2) and (4) by (3), we obtain

; _{ } (5)

As can be seen from the above expression, knowing the thermal conductivity of the first (χ₁) and third (χ₃) layers, we are able to determine the thermal conductivity of the middle (χ₂) layer.
We used the comparison method described in Figure 1 to determine the thermal conductivity of granulated silicon.
The essence of the method of comparison is that first a sample is prepared from the material whose thermal conductivity is being studied. It is then placed between two standart samples (E₁ and E₂) for which the thermal conductivity value in a similar shape and size is known. In our case, a special mark of brass (L63) was used as reference samples. At room temperature, the thermal conductivity of this material is 110 W/m*K. The geometric dimensions of each of the sample and standard under study are 5 mm in length and 13 mm in diameter. Between the samples, four meteorologically certified thermocouples were placed as shown in Figure 1. Thermostats placed on both ends of the system using a heater (H) and a cooler (C) generate the temperature gradient.