Corresponding author: Izatullo N. Ganiev ( ganiev48@mail.ru ) © 2020 Izatullo N. Ganiev, Firdavs A. Aliev, Haydar O. Odinazoda, Ahror M. Safarov, Jamshed H. Jayloev.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Ganiev IN, Aliev FA, Odinazoda HO, Safarov AM, Jayloev JH (2020) Heat capacity and thermodynamic functions of EAlMgSi (Aldrey) aluminum conductor alloy doped with gallium. Modern Electronic Materials 6(1): 2530. https://doi.org/10.3897/j.moem.6.1.55277

Aluminum is a metal having permanently broadening applications. Currently aluminum and its alloys successfully replace conventional metals and alloys in a number of application fields. The wide use of aluminum and its alloys is primarily stipulated by its advantageous properties e.g. low density, high corrosion resistance and electrical conductivity as well as the possibility of applying protective and decorative coatings. In combination with great abundance and relatively low cost which has been almost constant in recent years, this permanently broadens the application range of aluminum. The electrochemical industry is one of the promising application fields of aluminum. The EAlMgSi type (Aldrey) conductor aluminum alloy has high strength and ductility. This alloy acquires high electrical conductivity upon appropriate heat treatment. Products made from it are used almost exclusively for overhead power lines. This work presents data on the temperature dependence of heat capacity, heat conductivity and thermodynamic functions of the EAlMgSi (Aldrey) aluminum alloy doped with gallium. The studies have been carried out in "cooling" mode.
It has been shown that with an increase in temperature the heat capacity and thermodynamic functions of EAlMgSi (Aldrey) alloy doped with gallium increase while the Gibbs energy decreases. Gallium doping to 1 wt.% reduces the heat capacity, enthalpy and entropy of the initial alloy and increases the Gibbs energy.
aluminum, EAlMgSi (Aldrey) alloy, gallium, heat capacity, heat conductivity, "cooling" mode, enthalpy, entropy, Gibbs energy
Aluminum and its alloys are widely used in electrical engineering as conductor and structural materials. As a conductive material, aluminum is characterized by high electrical and thermal conductivity (after copper, the maximum level among all technically used metals). Aluminum also has a low density, high atmospheric corrosion resistance and resistance to chemicals.
Another advantage of aluminum is its neutrality to insulators, e.g. oils, lacquers and thermoplastics, including at high temperatures. Aluminum differs from other metals by a low magnetic permeability and the formation of a nonconductive easily removable powdered product (Al_{2}O_{3}) in the electric arc [
The use of aluminum and its alloys for the manufacturing of switching devices, power transmission line poles, cases of electric motors and switches etc. is regulated by special guidelines or general design rules.
The economic feasibility of using aluminum as a conductive material is explained by the favorable ratio of its cost to the cost of copper. In addition, one should take into account that the cost of aluminum has remained virtually unchanged for many years [
When using conductive aluminum alloys for the manufacture of thin wire, winding wire, etc., certain difficulties may arise in connection with their insufficient strength and a small number of kinks before fracture.
One method to increase the strength of aluminum alloys is doping. Doping elements should be chosen so as to provide an increase in alloy strength while retaining sufficiently high electrical conductivity. Most of impurities increase the strength of aluminum but reduce its electrical conductivity. One can chose impurities which improve the mechanical properties of aluminum while reducing its electrical conductivity but slightly, and introduce them aiming to increase the strength of aluminum.
Aluminum alloys have been developed in recent years which even in a soft state have strength characteristics that allow them to be used as a conductive material [
Silicon doping gives the best results. However the strength of this alloy in a hardened state is insufficient. A successful combination of high mechanical strength and electrical conductivity can be achieved by producing ternary and more complex composition aluminum alloys with silicon, magnesium, iron and other elements. Special heat treatment of these alloys provides for the desired results. These alloys and collectively referred to as Aldrey [
One wellknown Aldrey alloy is aluminum with the following impurities: 0.3–0.5% Mg, 0.4–0.7% Si and 0.2–0.3% Fe. The compulsory impurities which determine the advantageous properties of Aldrey are magnesium and silicon whose concentration ratio should meet the formula of the Mg_{2}Si compound forming in the alloy and acting as a hardening agent that delivers the good mechanical properties. However practical applications should be designed taking into account that the alloy always contains iron which is a still unavoidable yet often detrimental impurity in any technical grade of aluminum that forms a silicon containing compound (Al_{6}Fe_{2}Si_{3}). Therefore in order to provide for the formation of the Mg_{2}Si compound one should dope the alloy with a certain excess of silicon (0.4–0.5%) compared with its theoretically required amount [
The hardening action of the Mg_{2}Si compound is accounted for by the fact that its solubility in solid aluminum declines with a decrease in temperature. For example the maximum Mg_{2}Si solubility in aluminum at 595 °C is 1.85% while at 200 °C this figure is only 0.2%. Therefore if an Aldrey type alloy is heated to above 500 °C (at this temperature all the Mg_{2}Si is in the solid solution) and rapidly cooled (quenched), a supersaturated Mg_{2}Si solution in aluminum is produced [
Longterm resting of the alloy leads to the precipitation of excess Mg_{2}Si from the solid solution in the form of a finegrained component which increases the mechanical strength of the alloy (precipitation hardening). This resting of alloy is referred to as natural aging. The effect delivered by aging can be accelerated and amplified by slightly heating the alloy (to 150–200 °C), i.e., applying artificial aging. During aging the Mg_{2}Si impurity precipitates from the solid solution and increases the electrical conductivity of the alloy [
The heat treatment process route of Aldrey type alloy wire includes water quenching of rolled or pressed wire at 510–550 °C followed by drawing and artificial aging at 140–180 °C [
The tensile strength of Aldrey is two times higher than that of aluminum. Given the same electrical conductivity this provides for a 1.5 times higher strength of Aldrey wire than that of copper wire, with a two times smaller specific weight. This advantage allows one to increase the pole spans of power transmission lines. The higher hardness of Aldrey reduces the risk of wire damage during installation in comparison with aluminum or steelaluminum.
The aim of this work is to study the effect of gallium doping on the thermophysical properties and thermodynamic functions of EAlMgSi (Aldrey) aluminum conductor alloy with the 0.5 wt.% Si and 0.5 wt.% Mg chemical composition.
The alloys were synthesized in a SShOL type resistance laboratory shaft furnace at 750–800 °C. A6 grade aluminum which was additionally doped with the calculated amount of silicon and magnesium was used as a charge in the preparation of the EAlMgSi alloy. When doping aluminum with silicon, the metallic (0.1 wt.%) silicon present in primary aluminum was taken into account. Magnesium wrapped in aluminum foil was introduced into the molten aluminum using a bell. The metallic gallium was introduced into the melt in a form wrapped in aluminum foil. The alloys were chemically analyzed for silicon and magnesium contents at the Central Industrial Laboratory of the State Unitary Enterprise Tajikistan Aluminum Company. The alloy compositions were controlled by weighing the charge and the alloys. Synthesis was repeated if the alloy weight deviated from the target one by more than 1–2% rel.u. Then the alloys were cleaned from slag and cast into graphite molds in order to obtain samples for thermophysical study. The cylindrical samples had a diameter of 16 mm and a length of 30 mm.
The cooling rate was determined by plotting cooling curves for the samples. The cooling curves were sample temperature dependences on time of cooling in air [
The process of heat transfer from a hotter body to a colder one tends to establish a thermodynamic equilibrium in a system consisting of an extremely large number of particles. Therefore this is a relaxation process which can be described by an exponential function of time. In the case in question the heated body transfers heat to the environment, i.e., a body having an infinitely large heat capacity. The ambient temperature can therefore be taken to be constant (T_{0}). Then the body temperature dependence on time τ can be written in the following form: ∆T = ∆T_{1}e^{τ/τ1} where ∆T is the difference between the temperatures of the heated body and the environment; ∆T_{1} is the difference between the temperatures of the heated body and the environment at τ = 0; τ_{1} is the cooling constant which is equal to the time during which the difference between the temperatures of the heated body and the environment decreases by e times.
Schematic of the heat capacity measurement unit used in our experiment is shown in Fig.
a, b, p, k, ab and pk coefficients in Eq. (2) for EAlMgSi (Aldrey) alloy with gallium.
Gallium content in EAlMgSi (Aldrey) alloy, wt.%  a, К  b · 10^{3}, s^{1}  p, K  k · 10^{5}, s^{1}  ab · 10^{1}, K/s  pk · 10^{3}, K/s 

0  165.61  4.46  314.72  2.27  7.38  7.14 
0.05  172.18  4.55  314.99  2.20  7.83  6.92 
0.1  159.14  4.71  314.85  2.02  7.49  6.35 
0.5  153.82  4.64  313.99  1.81  7.13  5.67 
1.0  159.234  4.73  315.17  2.10  7.54  6.62 
Standard (Al Grade A5N)  494.26  5.01  319.92  2.57  0.25  8.23 
Solid body "cooling" mode heat capacity measurement unit: 1 automatic transformer, 2 thermocontroller, 3 electric furnace, 4 sample, 5 standard, 6 electric furnace platform, 7 multichannel digital thermometer and 8 recording device (PC).
The multichannel digital thermometer used for temperature measurements allowed PC recording of measurement results in a tabular form. The temperature measurement accuracy was 0.1 °C, the temperature recording time interval being 1 sec. The relative temperature measurement error in the 40 to 400 °C was ±1%. The heat capacity measurement error for this method was within 4–6% depending on temperature.
The measurement results were processed with MS Excel and data charts were built with Sigma Plot. The correlation coefficient was R_{corr} > 0.999 confirming the correct choice of approximating function.
The experimental temperature vs time curves of the samples (Fig.
$T=a{e}^{b\tau}+p{e}^{k\tau}$, (1)
where a, b, p and k are constants and τ is the cooling time.
Differentiating Eq. (1) with respect to τ we obtained the following sample cooling rate equation:
$dT/d\tau =ab{e}^{b\tau}pk{e}^{k\tau}$. (2)
From Eq. (2) we calculated the cooling rates of the EAlMgSi (Aldrey) alloy samples doped with gallium (Fig.
Values of the a, b, c and d coefficients in Eq. (4) for samples of EAlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N).
Gallium content in EAlMgSi (Aldrey) alloy, wt.%  а ,  b ,  с ,  d ,  R , % 
J/(kg·K)  J/(kg·K ^{2})  J/(kg·K ^{3})  J/(kg·K ^{4})  
0  10394.96  84.30  0.21  1.71  0.9925 
0.05  10394.96  82.90  0.20  1.66  0.9899 
0.1  13788.22  106.85  0.26  2.11  0.9950 
0.5  19463.50  152.21  0.38  3.15  0.9980 
1.0  10147.32  78.49  0.19  1.51  0.9989 
Standard (Al Grade A5N)  645.88  0.36  0  0  1.0 
Temperature as a function of cooling time for (1) standard (aluminum Grade A5N) and (2–6) EAlMgSi (Aldrey) alloy samples with different gallium contents, wt.%: (2) 0, (3) 0.05, (4) 0.1, (5) 0.5 and (6) 1.0.
Temperature dependences of cooling rate for (1) standard (aluminum Grade A5N) and (2–6) EAlMgSi (Aldrey) alloy samples with different gallium contents, wt.%: (2) 0, (3) 0.05, (4) 0.1, (5) 0.5 and (6) 1.0.
Then, based on the calculated alloy cooling rates and using Eq. (3), we determined the specific heat capacity of the EAlMgSi (Aldrey) alloy doped with gallium and the standard (Al Grade A5N):
${C}_{{P}_{2}}^{0}={C}_{{P}_{1}}^{0}\frac{{m}_{1}}{{m}_{2}}\xb7\frac{{\left(\frac{dT}{d\tau}\right)}_{1}}{{\left(\frac{dT}{d\tau}\right)}_{2}}$, (3)
where m_{1} = ρ_{1}V_{1} is the standard weight; m_{2} = ρ_{2}V_{2} is the test sample weight; ${\left(\frac{dT}{d\tau}\right)}_{1},{\left(\frac{dT}{d\tau}\right)}_{2}$ are the cooling rates of the alloy and standard samples at the specific test temperature.
Applying a polynomial regression we obtained the temperature dependence equation of the specific heat capacity of the EAlMgSi (Aldrey) alloy doped with gallium:
${C}_{{P}_{0}}^{0}=a+bT+c{T}^{2}+dT{.}^{3}$ (4)
The values of the а, b, c and d coefficients in Eq. (4) are summarized in Table
Results of heat capacity calculations for the alloys using Eq. (3) for different temperatures are summarized in Table
$a=\frac{{C}_{p}^{0}m\frac{dT}{d\tau}}{\left(T{T}_{0}\right)\xb7S}$, (5)
where Т and Т_{0} are the sample and environment temperatures, respectively; and S and m are the surface area and weight of the sample. The temperature dependences of the heat conductivity coefficient for the EAlMgSi (Aldrey) alloy doped with gallium are shown in Fig.
Temperature dependences of heat conductivity coefficient for (1) standard (aluminum Grade A5N) and (2–6) EAlMgSi (Aldrey) alloy samples with different gallium contents, wt.%: (2) 0, (3) 0.05, (4) 0.1, (5) 0.5 and (6) 1.0.
Temperature dependence of specific heat capacity (kJ/(kg·K)) of EAlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N).
Gallium content in EAlMgSi (Aldrey) alloy, wt.%  ${C}_{{P}_{0}}^{0}$ , kJ/(kg · K)  
300 K  325 K  350 K  375 K  400 K  450 K  
0  751.00  855.36  907.62  923.83  920.00  916.37 
0.05  678.55  794.12  858.13  886.15  893.72  909.80 
0.1  574.54  731.23  820.21  861.25  874.13  894.55 
0.5  531.77  712.59  802.69  831.60  828.86  846.53 
1.0  531.62  658.39  733.81  772.05  787.26  805.20 
Standard (Al Grade A5N)  854.62  877.90  901.55  925.45  949.48  997.46 
To calculate the temperature dependence of the enthalpy H, entropy S and Gibbs energy G we used integral specific heat capacities (Eq. 4):
$\left[{H}^{0}\left(T\right){H}^{0}\left({T}_{0}\right)\right]=a\left(T{T}_{0}\right)+\frac{b}{2}\left({T}^{2}{T}_{0}^{2}\right)+\frac{c}{3}\left(T{T}_{0}^{3}\right)+\frac{d}{4}\left({T}^{4}{T}_{0}^{4}\right)$; (6)
$\left[{S}^{0}\left(T\right){S}^{0}\left({T}_{0}\right)\right]=a\mathrm{ln}\frac{T}{{T}_{0}}+b\left(T{T}_{0}\right)+\frac{c}{2}\left({T}^{2}{T}_{0}^{2}\right)+\frac{d}{3}\left({T}^{3}{T}_{0}^{3}\right)$; (7)
$\left[{G}^{0}\left(T\right){G}^{0}\left({T}_{0}\right)\right]=\left[{H}^{0}\left(T\right){H}^{0}\left({T}_{0}\right)\right]T\left[{S}^{0}\left(T\right){S}^{0}\left({T}_{0}\right)\right]$, (8)
where T_{0} = 298.15 K.
Results of enthalpy, entropy and Gibbs energy calculations using Eqs. (6)–(8) with a 25 K step are summarized in Table
Temperature dependences of thermodynamic functions of EAlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N).
Gallium content in EAlMgSi (Aldrey) alloy, wt.%  Thermodynamic Functions  

300 K  325 K  350 K  375 K  400 K  450 K  
[H^{0}(T) – H^{0} (T_{0}^{*})], kJ?kg for alloys  
0  1.3799  21.5847  43.7138  66.6654  89.7383  135.4471 
0.05  1.2451  19.7762  40.5196  62.3809  84.6546  129.5626 
0.1  1.1125  18.4786  38.9238  60.9993  83.7508  129.9372 
0.5  0.9674  16.7417  35.8409  56.3663  77.1572  118.5852 
1.0  0.9726  15.9695  33.4642  52.3503  71.8750  111.5986 
Standard (Al Grade A5N)  1.5795  23.2351  45.4777  68.3149  91.7514  140.4266 
[S^{0}(T) – S^{0} (T_{0}^{*})], kJ/(kg·K) for alloys  
0  0,0046  0,0692  0,1348  0,1982  0,2577  0,3654 
0.05  0.0042  0.0634  0.1248  0.1852  0.2427  0.3484 
0.1  0.0037  0.0592  0.1198  0.1807  0.2394  0.3482 
0.5  0.0033  0.0536  0.1102  0.1669  0.2205  0.3181 
1.0  0.0033  0.0512  0.1030  0.1551  0.2055  0.2991 
Standard (Al Grade A5N)  0.0053  0.0746  0.1405  0.2035  0.2640  0.3786 
[G^{0}(T) – G^{0} (T_{0}^{*})], kJ/kg for alloys  
0  0.0043  0.9209  3.4739  7.6429  13.3499  28.9837 
0.05  0.0038  0.8394  3.1931  7.0741  12.4299  27.2549 
0.1  0.0034  0.7732  3.0065  6.7655  12.0232  26.7576 
0.5  0.0031  0.6922  2.7354  6.2028  11.0526  24.5595 
1.0  0.0030  0.6705  2.5947  5.8237  10.3367  22.9901 
Standard (Al Grade A5N)  0.0049  1.0111  3.7068  8.0133  13.8629  29.9625 
*T_{0} = 298.15 K 
The increase in the enthalpy, entropy and Gibbs energy of the EAlMgSi (Aldrey) alloy upon gallium doping can be accounted for by an increase in the heterogeneity of the structure of the alloys [
The heat capacity of the AlMgSi (Aldrey) alloy doped with gallium was determined in "cooling" mode based on the known heat capacity of a A5N aluminum standard. Using the obtained polynomial dependences we showed that with an increase in temperature the heat capacity, enthalpy and entropy of the alloys increase and the Gibbs energy decreases. Gallium doping within the experimental concentration range (0.05–1.0 wt.%) reduce the heat capacity, enthalpy and entropy of the initial AlMgSi (Aldrey) alloy but increase the Gibbs energy. The increase in the heat capacity, heat conductivity, enthalpy and entropy of the alloys with gallium content is accounted for by the modifying action of gallium on the structure of the αAl solid solution and hence an increase in the heterogeneity of the structure of the multicomponent alloys.