Research Progress on Thermal Conductivity of High-Pressure Die-Cast Aluminum Alloys

Abstract

High-pressure die casting (HPDC) has been extensively used to manufacture aluminum alloy heat dissipation components in the fields of vehicles, electronics, and communication. With the increasing demand for HPDC heat dissipation components, the thermal conductivity of die-cast aluminum alloys is paid more attention. In this paper, a comprehensive review of the research progress on the thermal conductivity of HPDC aluminum alloys is provided. First of all, we introduce the general heat transport mechanism in aluminum alloys, including electrical transport and phonon transport. Secondly, we summarize several common die-cast aluminum alloy systems utilized for heat dissipation components, such as an Al–Si alloy system and silicon-free aluminum alloy systems, along with the corresponding composition optimizations for these alloy systems. Thirdly, the effect of processing parameters, which are significant for the HPDC process, on the thermal conductivity of HPDC aluminum alloys is discussed. Moreover, some heat treatment strategies for enhancing the thermal conductivity of die-cast aluminum alloys are briefly discussed. Apart from experimental findings, a range of theoretical models used to calculate the thermal conductivity of die-cast aluminum alloys are also summarized. This review aims to guide the development of new high-thermal-conductivity die-cast aluminum alloys.

1. Introduction

Presently, aluminum and aluminum alloys are significant metallic materials because of their outstanding advantages such as high specific strength, great corrosion resistance, low density, exceptional thermal conductivity, ease of processing, and abundant resources in the Earth’s crust [1,2,3,4,5,6]. Recently, to address the increasingly severe environmental and energy challenges, the lightweight concept was proposed and applied rapidly in the automobile industry. The density of the aluminum is only ~2.7 g cm⁻³ [3], which causes aluminum alloys to gradually replace steel on the structural parts of automobiles to reduce CO₂ emissions and energy consumption [7]. Moreover, aluminum is also known as a green metal because it is recyclable to cyclic utilization all the time [8]. The trend of the lightweight and environmentally friendly requirement further broadens the manufacture and applications of aluminum alloys in modern industries. Particularly, compared with other metals [9,10,11], as shown in Figure 1, aluminum has an excellent thermal conductivity of 237 W m⁻¹ K⁻¹ with a low density. Aluminum alloys are extensively used in the thermal management field to produce heat dissipation components. Correspondingly, thermal conductivity of aluminum alloys is an important consideration to meet different heat conduction requirements. Therefore, thermal conductivity of aluminum alloys has become a research frontier and a focused area in the structural aluminum alloy field.

Among all casting techniques for aluminum alloys, high-pressure die casting stands out as a near-net-shape forming technology extensively used for light metals such as Al, Mg, and Zn alloys [12]. It is one of the most common and efficient methods for mass-produced aluminum products. HPDC is capable of producing aluminum castings with complex and thin-wall structures, high dimensional accuracy, and low surface roughness [13,14,15]. The whole process of HPDC is shown in Figure 2 [16]. The melt during HPDC process mainly undergoes three periods: slow-shot filling in the shot sleeve, fast-shot filling in the die cavity, and a pressure intensification period in the die cavity. Initially, the mold is closed and the aluminum melt is poured into the shot sleeve (see Figure 2a). Then, the melt in the injection chamber is pushed by a piston gradually at a slow speed until the front melt reaches the gate position of the mold (see Figure 2b,c). During this slow-shot filling period, the temperature of the melt in contact with the shot sleeve decreases below the liquidus temperature, and some of the liquid solidifies, forming primary phases, namely externally solidified crystals (ESCs). Depending on different alloy compositions, the categories of ESCs are different such as the primary α-Al phase, the primary silicon phase, and the primary iron-rich phase [17,18,19]. Since ESCs nucleate in the shot sleeve, they commonly exhibit large sizes in castings [20]. In the fast-shot period, the piston speed increases significantly and the liquid mixture is rapidly filled into the die cavity (see Figure 2d). Because of the high interfacial heat transfer coefficient between the die and the melt [21], the liquid mixture solidifies under a very high cooling rate [22]. At the same time, the piston transports the pressure to the solidifying casting to ensure the integrity of the castings (see Figure 2e). Hence, die castings usually have great mechanical properties. Recently, vacuum-assisted high-pressure die casting has been developed and enhances the properties of aluminum alloys further [23]. Owing to these benefits, HPDC technology has been used for industrial aluminum structural parts including heat dissipation components in automobile, communication, and consumer electronics fields (see Figure 3) such as battery pack housing in automobiles, particularly new-energy vehicles, fifth-generation (5G) base station housing in communications, and mobile phone heat exchanger components in consumer electronics products [24,25,26].

In recent years, with the help of Giga Press equipment, Tesla Inc. started to implement Giga-Casting technology for the single super-sized rear floor of electric vehicles. Compared to the traditional procedure, the advanced technique can reduce costs by ~40% and weight by ~30% via producing only a single casting to replace several steel parts for a complete aluminum rear floor [27,28,29]. The revolutionary technology has guided many factories all over the world in the development of new electric vehicles [30,31,32], which brings a new development of HPDC. However, such a super-sized vehicle component does not suit the heat treatment process used traditionally. Hence, in the HPDC field, a new frontier is the development of non-heat-treatable HPDC alloy materials, which means that alloys should have excellent properties in the as-cast state to meet the usage requirement. Worth mentioning is that non-heat-treatable HPDC alloys are proposed firstly for the Giga-Casting of electric vehicles. However, because of their advantages in cost and property, this kind of material is also imperatively needed in other structural parts like heat dissipation components.

Thermal conductivity is the most important property of a HPDC alloy in the heat dissipation component field.

Table 1. Thermal conductivity and yield strength of commercial die-cast aluminum alloys.

Alloy Designation	Temper	Thermal Conductivity (W m−1 K−1)	Yield Strength (MPa)	Refs.
A390	F	97	240	[35,36]
ADC12	F	92	165	[37]
A380	F	96	160	[38]
A360	F	113	170	[39]
384	F	96	170	[40]
413	F	113	145	[41]
Castasil®-37	F	130	135	[25]

shows the thermal conductivity and mechanical properties of some commercial die-cast aluminum alloys. We can see that thermal conductivity of die-cast aluminum alloys is quite low. This is because of the rapid cooling rate and the unique solidification microstructure of HPDC. The cooling rate of the HPDC process particularly in the die cavity, as shown in Figure 4, can reach up to ~100 K s⁻¹ [22]. Hence, the solute concentrations of elements in α-Al solid solutions of die castings are usually higher than those of gravity castings [33]. Additionally, die castings have smaller grain sizes because of rapid solidification and more porosity because of melt turbulence and solidification order. Moreover, Table 1 also shows that the alloys with high thermal conductivity have low yield strength. This indicates that two crucial properties are contradictory in die-cast alloys because the requirement of precipitates and micro-defects in the alloys are truly different in thermal conductivity and strength [34].

More significantly, with the development of electronics, the power density of devices has increased, which brings about an increase in heat flow density. For electric vehicles, battery capacity increases with the emergence of plug-in hybrid electric vehicles and larger electric cars [42]. The maximum charging current and power also increase. However, the optimal temperature range of Li-ion batteries in electric vehicles is only 15 °C~35 °C [43]. For 5G communication, the typical 5G base station will consume ~11.5 kW, which is ~70% higher than the typical 4G base station because of the extensive utilization of the Active Antenna Unit (AAU) [44]. Correspondingly, the operation frequency of 5G mobile phones is 28 or 39 GHz, which is higher than the operation frequency of ~2000 MHz for 4G phones [45], bringing more heat to be dissipated. However, the work temperature of the chips should be below 85 °C to avoid a decrease in chip performance [46]. From the facts above, there is a huge contradiction between the rapid increase in heat generation of components and the operating temperature. Therefore, the development of non-heat-treatable HPDC aluminum alloys with high thermal conductivity for heat dissipation components is truly imminent. Moreover, when improving the thermal conductivity of HPDC aluminum alloys, it is also necessary to ensure adequate mechanical properties to obtain high-performance die-cast aluminum components.

Factors affecting the thermal conductivity of HPDC aluminum alloys are numerous. The first factor is alloy composition. Generally, alloying elements in the HPDC aluminum alloy can form solid solutions via solute atoms and form precipitates via compounds. Thermal conductivity is affected by the content of these two existing states. In the die-cast industry, many studies focused on composition optimization to develop new die-cast aluminum alloys with high thermal conductivity. In addition, the properties of die-cast alloys are also influenced by die-casting process parameters. Recently, some efforts have been made to investigate the relationship between processing parameters and thermal conductivity of die-cast aluminum alloys. Furthermore, although non-heat-treatable die-cast alloys have been a trend in the HPDC industry, there is no denying that heat treatment is an effective way to improve the thermal conductivity of aluminum alloys by optimizing the microstructure [47,48]. Therefore, research on the effect of heat treatment on the thermal conductivity of die-cast aluminum alloys still holds significant value in guiding the design of new alloys. At last, as a helpful tool, theoretical models of thermal conductivity for aluminum alloys have also been employed to explain some experimental results about the relationship between the microstructure and thermal conductivity of die castings and even predict the property. Although many valuable works concerning the aspects discussed above are carried out, a systematic review about these studies on thermal conductivity of HPDC aluminum alloys is absent.

This review offers a comprehensive review of the research progress on the thermal conductivity of high-pressure die-cast aluminum alloys. Our review begins with a brief introduction of heat transport in aluminum alloys. Secondly, several common die-cast aluminum alloy systems applied for heat dissipation components are discussed. Regarding the manufacturing process, the effects of the die-casting process and heat treatment process on the thermal conductivity of HPDC aluminum alloys are summarized. Finally, the progress in theoretical models of thermal conductivity for die-cast aluminum alloys is discussed. This review provides an overview of the current research status in the field of thermal conductivity of die-cast aluminum alloys and guides the development of new high-thermal-conductivity die-cast aluminum alloys.

2. Heat Transport in Aluminum Alloys

In nature, heat transfer includes heat conduction, heat convection, and heat radiation [49]. In solids like metals, the dominant way for heat transfer is usually heat conduction. Thermal conductivity is a crucial parameter for describing and quantifying heat conduction in materials and is defined as the following equation [50]:

$$\lambda =-\frac{\overrightarrow{Q}}{\overrightarrow{\nabla }T}$$

(1)

where $\overrightarrow{Q}$ is the heat flux across a unit cross section perpendicular to $\overrightarrow{Q}$, $\overrightarrow{\nabla }T$ is the temperature gradient, and $\lambda$ is the thermal conductivity.

However, in actual heat conduction situations, it is difficult to measure the heat flux and the temperature gradient directly to obtain the thermal conductivity. Subsequently, the thermal conductivity can be written as the following equation [49]:

$$\lambda =\alpha C_p\rho$$

(2)

where $\alpha$ is the thermal diffusivity of the material, $C_p$ is the specific heat capacity of the material, and $\rho$ is the density of the material.

The formula can also be used to measure the thermal conductivity of metals in experiments [51]. If we consider the particles in a solid as a gas, then, according to the kinetic formula of the gas, thermal conductivity from each kind of particle can be given by the following [52]:

$$\lambda =\frac{1}{3}Cvl$$

(3)

where $C$ is the total heat capacity of the particles, $v$ is the velocity of the particles, and $l$ is the mean free distance of particles. Thermal conductivity has a positive correlation with the heat capacity, velocity, and mean free distance of particles.

For metals, the chemical bond is the metallic bond, which comprises the electrostatic attraction between free electrons and metal ions in lattice sites. Hence, heat conduction in aluminum alloys is mainly divided into two types, electron transport (the movement of free electrons) and phonon transport (the vibration of the metallic ions). Then, thermal conductivity is divided into electrical thermal conductivity and phonon thermal conductivity. A formula can express the relationship as follows [50]:

$$\lambda ={\lambda }_e+{\lambda }_p$$

(4)

where ${\lambda }_e$ is the electrical thermal conductivity, and ${\lambda }_p$ is the phonon thermal conductivity.

For the electrical thermal conductivity, a classical theory, namely the Wiedemann–Franz law, considers that the electrical thermal conductivity of aluminum alloys is linear with the electrical conductivity $\sigma$, which is easier to measure in experiments. The relationship is given by the following:

$${\lambda }_e=L_{0}T\sigma$$

(5)

where $T$ is the absolute temperature mentioned in the Formula (1) above, and $L_0$ is the Lorentz constant.

The theoretical Lorentz constant is calculated by the following [53]:

$$L_0=\frac{{\pi }^2}{3}\frac{{k_B}^2}{e^2}$$

(6)

where $e$ is the charge of the element and $k_B$ is Boltzmann’s constant. However, the value of the Lorentz constant depends on the material and temperature in actual experiments. The value of the Lorentz constant for aluminum alloy is ~2.1 × 10⁻⁸ V² K² [53].

For the phonon thermal conductivity, it is more difficult to measure directly. Some studies use the simulation method to calculate the phonon thermal conductivity in non-metallic materials [54,55]. In general, the phonon thermal conductivity is a function of the temperature. In pure aluminum, the phonon thermal conductivity is shown as follows [56]:

$${\lambda }_p={(\frac{T}{1700}+\frac{50}{T^2})}^{-1}$$

(7)

In aluminum alloys, the phonon thermal conductivity is expressed via the Wiedemann–Franz law [57]:

$$\lambda =\frac{L_{0}T}{\rho }+{BT}^n$$

(8)

$$\rho =\frac{1}{\sigma }$$

(9)

where $\rho$ is the electrical resistivity of aluminum alloys, $B$ is a constant, and the range of the parameter $n$ is from −1~0.

It occupies only a small ratio of ~2.4% in the total thermal conductivity of aluminum [58]. In aluminum alloys, the temperature slightly affects the phonon thermal conductivity according to a previous study [57]. Accordingly, the phonon thermal conductivity is often seen as a constant by fitting the linear Wiedemann–Franz law in aluminum alloys.

$$\lambda =L_{0}T\sigma +C$$

(10)

In the literature, $C$ values are given from 10.5~12.6 W m⁻¹ K⁻¹ [53]. However, in metals, although the ratio of the phonon thermal conductivity is quite small, it is a part of the thermal conductivity of aluminum alloys. Moreover, the phonon thermal conductivity in pure aluminum is ~6 W m⁻¹ K⁻¹ as calculated by Formula (7) at 298 K. However, the fitting phonon thermal conductivity of aluminum alloys is much higher than this value, and different references about different alloys have different values of the phonon thermal conductivity. This shows that the phonon thermal conductivity also varies with alloy compositions. Thus, more in-depth studies about the relationship between the phonon thermal conductivity and alloy compositions in aluminum alloys are still needed.

Actual aluminum alloys often consist of an Al lattice with impurities of different states introduced by alloying elements. Therefore, the real heat transfer of aluminum alloys is often affected by them. Then, the scattering process emerges to hinder the heat transfer. electrons cause electron–electron scattering, electron–phonon scattering, and electron–impurity scattering. Phonons cause phonon–phonon scattering (U-process) and phonon–impurity scattering [58,59]. Because of the dominant heat transfer role of free electrons, the previous three scattering processes involving electrons are often considered in aluminum alloys. A schematic of the main scattering patterns is shown in Figure 5. Compared to the two other intrinsic scattering mechanisms, electron–impurity scattering is of greater importance and concern in alloys. Regarding reducing the electron–impurity scattering, many investigators tried to control the impurity in die-cast aluminum alloys to improve their thermal conductivity. Experiments and theoretical results are discussed in detail in following sections.

3. Die-Cast Aluminum Alloys for Thermal Conductivity

In die-cast aluminum alloys, there are many species with different major alloying elements like Si, Mg, Cu, etc. Affected by alloying elements, different kinds of aluminum alloys have distinct thermal conductivities. According to Matthiessen’s rule [60], the electrical resistivity (thermal conductivity) is affected by the lattice, solid solution, precipitate, grain boundaries, dislocations, vacancies, etc., which is written as follows:

$$\rho ={\rho }_p\left(T\right)+\sum _i{\rho }_s^i{c}_s^i+\sum _i{\rho }_p^i{c}_p^i+{\rho }_g+{\rho }_d+{\rho }_v$$

(11)

where the ${\rho }_p\left(T\right)$ is the basic electrical resistivity of the pure Al matrix which is a function of temperature $T$, ${\rho }_s^i$ is the resultant electrical resistivity increase when the element i increases by 1 wt.% in the Al solid solution, ${\rho }_p^i$ is the resultant electrical resistivity increase when the element i increases by 1 wt.% as the precipitate, $c_s^i$ is the content of the element i in the Al solid solution, $c_p^i$ is the content of the element i as the precipitate. ${\rho }_g$ is the electrical resistivity due to grain boundaries, ${\rho }_d$ is the electrical resistivity due to dislocations, and ${\rho }_v$ is the electrical resistivity due to vacancies. For alloying elements, the content of the element in the Al solid solution and the secondary phase, and the electrical resistivity increase caused by the increase of per wt.% of the element in the Al solid solution and the secondary phase determine the electrical resistivity.

Therefore, ${\sum }_i{\rho }_s^i{c}_s^i$ and ${\sum }_i{\rho }_p^i{c}_p^i$ are the main factors. In a previous study [59], the quantitative values of the effect extents of different additions of elements on electrical resistivity in aluminum (${\rho }_s^i$, ${\rho }_p^i$) are summarized in

Table 2. Effect of alloying elements in solid solutions and precipitates on electrical resistivity of aluminum (ordered by the maximum solubility of elements in α-Al) [61].

Alloying Element	Maximum Solubility in α-Al (wt.%)	$\mathbf{Increase} \mathbf{in} \mathbf{Electrical} \mathbf{Resistivity} \mathbf{in} \mathbf{Solid} \mathbf{Solutions} {\mathit{\rho }}_{\mathit{s}}^{\mathit{i}}$ (μΩ cm wt.%−1)	$\mathbf{Increase} \mathbf{in} \mathbf{Electrical} \mathbf{Resistivity} \mathbf{in} \mathbf{Precipitates} {\mathit{\rho }}_{\mathit{p}}^{\mathit{i}}$ (μΩ cm wt.%−1)	${\mathit{\rho }}_{\mathit{s}}^{\mathit{i}}/{\mathit{\rho }}_{\mathit{p}}^{\mathit{i}}$
Zn	82.8	0.094	0.023	4.09
Mg	14.9	0.54	0.22	2.45
Cu	5.65	0.344	0.03	11.47
Li	4	3.31	0.68	4.87
Mn	1.82	2.94	0.34	8.65
Si	1.65	1.02	0.088	11.59
Ti	1	2.88	0.12	24
Cr	0.77	4.00	0.18	22.22
V	0.6	3.58	0.28	12.79
Zr	0.28	1.74	0.044	39.55
Fe	0.05	2.56	0.058	44.14
Ni	0.05	0.81	0.061	13.28

Note: The values of ${\rho }_p^i$ are limited to twice the maximum solubility of elements in α-Al except Mg (limited to ~10 wt.%) and Zn (limited to ~20 wt.%).

. From Table 2, the harmful effect of a solid solution containing alloying elements on electrical resistivity (thermal conductivity) is much higher (mostly over 10 times) than that of the precipitate state according to the value of ${\rho }_s^i/{\rho }_p^i$.

Furthermore, the basic regularity of the influence trend of alloying elements on the thermal conductivity and electrical conductivity of aluminum has been also investigated using theoretical and experimental methods [58,62,63,64], shown in Figure 6. Among several common elements, the orders of the detrimental effect on electrical conductivity and thermal conductivity in Figure 6a,b are Zn < Cu < Si < Mg < Zr < Ti < V < Mn < Cr and Zn < Cu < Mg < Si (Si < Mg in Figure 6c) < Zr < Ti < Mn < V < Cr, respectively. Reference [63] also revealed that rare elements had a small effect on the electrical conductivity of aluminum. Obviously, the element Si influences the thermal conductivity to a reduced extent compared with Zr, Ti, V, Mn, and Cr and also has excellent castability and acceptable strength for die-cast aluminum alloys compared to elements before Si [65]. Thus, Al–Si alloys are the most common system for die-cast heat dissipation components. In addition, in order to avoid the primary phase of the secondary element reducing thermal conductivity severely, the general composition of die-cast Al alloys with high thermal conductivity should be on the hypoeutectic side.

3.1. Al–Si Alloys

Generally, the Si content is often near-hypoeutectic in high-strength and high-ductility die-cast Al-Si alloys, ranging from 9 wt.% to 12 wt.%, such as Silafont^®-36 (AlSi10MnMg), Silafont^®-38 (AlSi9MnMgZn), Castasil^®-37 (AlSi9MnMoZr), ADC12 (AlSi11Cu3), and A380 (AlSi9Cu3) [66,67]. However, the thermal conductivity of these alloys only ranges from 90 to 130 W m⁻¹ K⁻¹ in Table 1. For example, Celal Cingi et al. [68] found that the A380 die-cast alloy exhibited a thermal conductivity of ~115 W m⁻¹ K⁻¹ and a hardness of ~83 HV. The microstructure consisted of primary α-Al grains with ~10 μm and a large area fraction of eutectics enriching Si and Cu. These eutectics played an important role in improving the hardness and reducing the thermal conductivity. Furthermore, die-cast alloys developed by Rheinfelden [25], Silafont^®-36, Silafont^®-38, and Castasil^®-37, contain a large area fraction of eutectic silicon in their microstructures. Additionally, Jiao et al. [69] investigated the Silafont^®-36 die-cast alloy and tested concentrations of elements in primary α-Al. The maximum Si, Mg, and Mn contents were 4.26 wt.%, 0.39 wt.%, and 0.20 wt.%, respectively, higher than the solubility at room temperature. This means that in die-casting processes with a high solidification rate, the α-Al grains are supersaturated. Therefore, the main reasons for the low thermal conductivity of these alloys are as follows, as shown in Figure 7. On the one hand, to ensure high strength, these alloys often contain high contents of Si, Mg, Cu, Mn, etc. [70]. The maximum solubility values of Si, Mg, Cu, and Mn in aluminum are 1.65 wt.%, 14.9 wt.%, 5.67 wt.%, and 1.82 wt.%, which are not very low. However, the detrimental effect of transition metals like Mn is quite serious as shown in Figure 6 and Table 2. Therefore, there are plenty of solid solutions containing alloying elements (Si, Mg, Cu, Mn, etc.) in the alloy and the solubility in the substrate of die casting is higher than that of the equilibrium state. These solid solutions increase the scattering of electrons [71]. On the other hand, high contents of elements such as Si and Cu result in a large volume fraction of eutectic particles in the die-cast alloy, which causes impurity scattering from precipitates [72,73]. Therefore, to address these problems, some methods are employed to obtain die-cast Al–Si alloys with higher thermal conductivity. Firstly, one method is to reduce Si and other elements’ contents to mitigate the detrimental effect of the major elements. Then, adding minor elements into Al–Si alloys to optimize the microstructure to improve the thermal conductivity is also a key method. The method can be divided into two parts, including reducing the solute concentration of trace elements in the solid solution and modifying the eutectic particles.

3.1.1. Reducing the Content of Major Elements

For the first method, many studies firstly concentrate on reducing Si and other elements’ contents. Rheinfelden company [25] developed Castasil^®-21 alloy (AlSi9Sr) by removing other alloying elements like Cu, Mg, and Mn as well as maintaining a Si content of 9% and a Fe content within 0.5~0.7%. In the as-cast state, the die-cast alloy obtains a yield strength, ultimate tensile strength, and elongation of 90~100 MPa, 200~230 MPa, and 6~9%, respectively, which are lower than those of other high-strength die-cast Al–Si alloys. However, the thermal conductivity of the die-cast alloy is over 160 W m⁻¹ K⁻¹. To increase thermal conductivity, the alloy should be annealed at 250 °C~350 °C. Considering the high Si content, some studies aimed to reduce the Si content to enhance thermal conductivity. Qi et al. [74] studied Al–8Si heat dissipation die casting containing Fe without involvement of other elements and there were plenty of eutectic Si phases and needle-like β-Al₅FeSi eutectic phases in the microstructure as shown in Figure 8a. Thermal conductivity of the casting reached 156 W m⁻¹ K⁻¹ and the tensile strength was 211 MPa. To obtain higher strength, researchers added some other elements based on Al–(6~8)Si alloys. M. Payandeh et al. [75] considered using ~2 wt.% Cu and below 1 wt.% Zn in Al–6Si die-cast alloys. In Figure 8b, Al₂Cu particles in the alloy improved the hardness to 75 HV and maintained thermal conductivity within 140~150 W m⁻¹ K⁻¹ for the die-cast alloy. Furthermore, except Zn, Jae-Cheol Jang et al. [76] added elements Ni and Cu with different contents into Al–6Si die-cast alloys. The strength increased by over 300 MPa mainly due to the solid solution strengthening from element Cu. However, the thermal conductivity decreased to 120~130 W m⁻¹ K⁻¹, caused by high Cu content in the substrate [77,78,79]. In addition, L. Kumar et al. [80] designed three die-cast alloys with Si contents from 6~8 wt.% and Mg or Cu with contents over 1 wt.% to strengthen the alloy. The thermal conductivity and tensile strength values of three alloys were 160.3 W m⁻¹ K⁻¹, 153.0 W m⁻¹ K⁻¹, and 146.0 W m⁻¹ K⁻¹ and 307 MPa, 331 MPa, and 350 MPa as shown in Figure 8c. The study also confirmed that secondary phases (Al₅Cu₂Mg₈Si₆, Al₇Cu₂M, and β-AlFeSi phases) strongly increased the mechanical properties and the thermal conductivities of the three samples were negatively correlated with the fraction of these secondary phases. Cr and Ti were also added into the Al–7Si–3Mg die-cast alloy [81]. The tensile strength improved to over 340 MPa, but thermal conductivity decreased below 140 W m⁻¹ K⁻¹ because of the strongly detrimental effect of Cr and Ti (Table 2). These studies successfully provide a strategy that, if the contents of strengthening elements are suitable, using a low-Si die-cast alloy with these strengthening alloying elements can achieve a similar strength to that of high-strength alloys and a higher thermal conductivity. According to the above results, low Si (around 6 wt.%) and suitable Cu contents for strengthening are preferred to synergistically improve comprehensive properties compared to traditional die-cast Al–Si alloys because the low ${\rho }_s^i$ value (0.344 μΩ cm wt.%⁻¹) (Table 2) reduces the electron scattering in the solid solutions.

Meanwhile, some studies [82,83] focus on Al–Si die-cast alloys with ultra-low Si content within 1~2 wt.%. Although these alloys can achieve a high thermal conductivity of over 180 W m⁻¹ K⁻¹, the low elemental contents make the ultimate tensile strength below 150 MPa and significantly reduce the fluidity compared to ADC12. Y. H. Cho et al. [84] studied the effect of Ni on Al–2Si alloy and increased the cooling rate to approximate the real die-casting process. At the high cooling rate, the thermal conductivity of Al–2Si–xNi could be within 170~190 W m⁻¹ K⁻¹. With the increase in Ni contents, the Al₃Ni phase was formed to decrease thermal conductivity. Notably, the increase in Ni content could decrease the Si solutes in the matrix, thereby mitigating the decrease in thermal conductivity. Regarding the fluidity, because of the (α-Al + Al₃Ni + Si) ternary eutectic point (Ni content is ~0.47 wt.%) with a low solidification range as shown in Figure 9, the fluidity length of Al–2Si–0.5Ni increased at the top. However, it still only achieved 80% of the fluidity of ADC12 alloy. These three studies discussed above uncover a big problem of ultra-low Si alloys in that they cannot obtain enough castability and strength like commercial Al alloys and pose a challenge for real die-cast production, although having great thermal conductivity.

3.1.2. Reducing the Solute Concentration of Trace Elements in Solid Solutions

Regarding reducing the solute concentrations of trace elements in the solid solution, trace solutes in the solid solution include alloying elements and impurity elements. Lumley et al. [61] found that sometimes an increase in Mn content could increase the thermal conductivity by ~10 W m⁻¹ K⁻¹ of Al–Si die-cast alloys containing Fe and Mn as shown in Figure 10a, which was contrary to the common sense related to the high ${\rho }_s^i$ of Mn. This was because the primary phase Al₁₅(Mn, Fe)₃Si₂ in the alloy, which was one of the iron-rich phases in the Al–Si alloys [85,86,87], would precipitate from the liquid before primary α-Al in the as-cast alloy. It nearly consumed most Mn to form block-like compounds combined with Fe and only a very small number of solutes were in the matrix. Moreover, for reducing impurity elements, boron treatment is one of the common methods to improve the thermal conductivity and electrical conductivity of aluminum alloys [88,89,90]. In aluminum alloys, there are plenty of transition metals like Ti, Zr, Cr, V, etc. Although their contents are quite small, they can cause large lattice distortion in Al substrates [88]. This can lead to the high ${\rho }_s^i$ value shown in Table 2 and can be severely harmful to electrical and thermal conductivity. In general, boron forms AlB₂ with Al. However, considering elements Ti, Zr, Cr, and V, because the Gibbs free energy of these borides is lower than that of AlB₂ (TiB₂, ZrB₂, VB₂, CrB₂) [91], these atoms react with the borides to replace Al atoms through diffusion [71,92,93,94]. Accordingly, various kinds of precipitate-state borides with transition metals are formed. Due to the high atomic order of transition metals, borides containing these metals have a higher density than aluminum. As a result, they tend to settle at the bottom of the furnace, carrying solutes with them, as depicted in Figure 10b. Thus, the solutes in the solid solution decrease, which increases the average path of electrons, and the electrical and thermal conductivity are improved. Yang et al. [95] added a trace amount of B (<0.05 wt.%) to ADC12 alloy. Electrical conductivity increased from 18.48 MS m⁻¹ to 19.22 MS m⁻¹ after adding 0.02 wt.% B, as shown in Figure 10c. Moreover, the decrease in solutes was confirmed by the variation in the lattice constant determined from XRD peaks in Figure 10c. Veijo Rauta et al. [96] also investigated the effect of B on Anticorodal^®-04 alloy (AlSi0.5Mg) for HPDC. Similar results showed that the thermal conductivity of Anticorodal^®-04 alloy after boron treatment improved by about 3.8–4.4% with a decrease in transition metal elements. Unfortunately, the results above are both alloys for die casting but used the gravity-casting process. However, there is still limited research on the thermal conductivity variation of die-cast samples after boron treatment.

3.1.3. Modification of Eutectic Particles

For the modification of the eutectic particles (i.e., eutectic silicon particles in Al–Si alloys), the particle morphology is changed from a plate shape to a fibrous shape [97]. The most commonly used element for modifying Si is Sr. Other elements like Ca, Sb, Na, and rare earth (RE) elements were also reported [98]. The modification mechanisms of eutectic silicon mainly include the impurity-induced twinning growth mechanism [99] and the twinning plane re-entrant edge mechanism [100]. The evolution of eutectic silicon morphology increases the free path of electrons by reducing the barriers imposed by secondary phases with low thermal conductivity and by mitigating lattice distortions in α-Al grains as shown in Figure 11a,b [24,51]. Wen et al. [51] compared the thermal conductivities of gravity-cast Al–7Si alloys modified with various trace elements (Sr, RE, Sb). The alloy treated with strontium exhibited fully modified eutectic silicon, obtaining the greatest improvement in thermal conductivity compared to other elements. Based on the excellent modification of Sr, in die-cast Al–Si alloys, various composite modifications of eutectic silicon that include strontium have been developed. Hiromi Nagaumi et al. [101] investigated the effect of Sr and Ca on the thermal conductivity of a eutectic Al–Si alloy. The thermal conductivity was the highest with absolute modification when the addition of Ca and Sr were both 0.05 wt.%. Then, they developed a fully modified Al12Si–HTC alloy using both Sr and Ca to produce a die-cast communication enclosure with a thermal conductivity of up to 160 W m⁻¹ K⁻¹. The simulation results indicated that the optimized alloy had an improvement of 41.6% in thermal conductivity compared to Al12Si. Additionally, Liu et al. [102,103] incorporated Sr and Ce, Sr, and Er into AlSi10MnMg alloy to improve thermal conductivity and mechanical properties simultaneously. The addition of Ce to achieve the best comprehensive properties was significantly smaller than that of Er. A study [104] demonstrated that rare earth elements could also react with Si to decrease the solubility of Si in the solid solution. However, its effect was smaller than that of the modification and has not been given much attention. Moreover, a study [105] reported that with the increase in cooling rate, the eutectic silicon was also modified without other elements, which indicated direct modification from the die-casting process with a high solidification rate.

However, the strategies mentioned above have their disadvantages. The first strategy requires decreasing the Si content, which compromises the casting ability of Al–Si alloys at the same time [106]. Moreover, the improvement in thermal conductivity achieved by adding trace elements is also limited. Neither of these methods can meet the higher requirements for thermal conductivity due to the major element Si having a high eutectic point. Accordingly, many researchers have begun to focus on other aluminum alloys that do not contain Si to develop new die-cast alloys with high thermal conductivity.

3.2. Silicon-Free Aluminum Alloys

3.2.1. Al–Ni Alloys

In Table 2, we can see that Ni has low solubility in Al (~0.05 wt.%) and that the value of ${\rho }_s^i$ (0.81 μΩ cm wt.%⁻¹) is quite small. The element mainly exists as the secondary phase in the alloy. This indicates that Ni has a minimal detrimental effect on thermal conductivity. Moreover, the eutectic point is ~5.7 wt.% [107], which is much lower than that of Al–Si alloys. This means that the Ni content is much lower than Si in the near-eutectic-composition alloys. Furthermore, the morphology of the eutectic Al₃Ni in the Al–Ni alloys is fibrous [108], which allows for easy electron transport. Therefore, Ni becomes a potential element for developing high-thermal-conductivity die-cast alloys. Tesla Inc. [109] developed a near-hypoeutectic die-cast Al–5.3Ni–0.35Fe–0.03Ti alloy with an electrical conductivity of 50% IACS and a yield strength of 90 MPa for automobile parts in 2018. In addition, for microstructure optimization, Yb [110] was also employed to modify eutectic Al₃Ni phases and improve the thermal conductivity and mechanical properties of an Al–5Ni gravity-cast alloy. However, the high cost of Ni also restricted the application of Al–Ni alloys. Nikkei MC Aluminum Co. [111] developed the DX26 die-cast alloy (Al–2Ni–Fe) with a thermal conductivity of 190 W m⁻¹ K⁻¹ by reducing Ni content. However, the concentration is so far away from the eutectic point that the castability becomes a possible issue for applications. In conclusion, because of the trade-off between cost and castability, implementing this system for high-thermal-conductivity applications is still challenging.

3.2.2. Al–Fe(–Ni) Alloys

To solve the problem regarding Al–Ni alloys and search for an element with a lower eutectic point to ensure castability and cost, Fe draws attention to developers because of the similar low solubility (~0.05 wt.%) in the Al matrix. Most Fe combines with Al to form a plate-like Al₁₃Fe₄ phase [112]. The eutectic point of Fe is ~1.75 wt.%, which is much lower than that in Al–Ni and Al–Si binary systems [113]. This indicates that an Al–Fe system can be used to obtain ultra-high thermal conductivity because of the low elemental contents. Meanwhile, Fe is crucial for the die-casting process due to its soldering resistance characteristic [59]. Nikkei MC Aluminum Co. [111] also developed the DX01 die-cast alloy (Al–Fe) with a thermal conductivity of over 200 W m⁻¹ K⁻¹. However, the yield strength is only 57 MPa, which is similar to that of pure Al. Ki-Tae Kim et al. [114] added Zn, which has a low ${\rho }_s^i$ value (0.094 μΩ cm wt.%⁻¹), with Fe into a die-cast Al alloy. When the Zn (1.91 wt.%) and Mg (0.17 wt.%) contents were low, thermal conductivity was over 190 W m⁻¹ K⁻¹ and tensile strength was slightly above 100 MPa. Some studies under the gravity-cast state also discussed ways toward microstructure optimization of Al–Fe alloys. La [115], Ce [116], and Co [117] were used to modify the eutectic Al₁₃Fe₄ phase from a plate-like shape to a spotted shape and improved the mechanical properties and thermal conductivity. However, there is no similar study about die-cast Al–Fe alloys and the positive modification effects on the microstructure and thermal conductivity of die-cast Al–Fe alloys cannot be verified. Considering the strengthening effect and minimal adverse impact on the thermal conductivity of Ni, a new ternary Al–Fe–Ni alloy was designed. The eutectic composition Al–1.75Fe–1.25Ni was used to maintain a low solidification range [118]. In the Al–Fe–Ni ternary alloy, a new fibrous eutectic Al₉NiFe phase, which was similar to Al₃Ni, was formed [119,120]. The thermal conductivity of the gravity-cast Al–1.75Fe–1.25Ni alloy could be over 200 W m⁻¹ K⁻¹ [121]. Luo et al. [122] studied the effects of several elements including Co, Ce, and Yb on the thermal conductivity of the eutectic Al–1.75Fe–1.25Ni gravity-cast alloy. Only Yb could refine the (α-Al + Al₉NiFe) eutectic cell and improve the strength and thermal conductivity simultaneously.

In summary, many silicon-free HPDC aluminum alloys have been developed for new-generation heat dissipation applications with high thermal conductivity as shown in

Table 3. Physical properties and yield strength of silicon-free (Al–Ni, Al–Fe, Al–Fe–Ni) die-cast (DC)/gravity-cast (GC) aluminum alloys.

Alloy	Process	Temper	Electrical Conductivity (% IACS)	Thermal Conductivity (W m−1 K−1)	Yield Strength (MPa)	Ref.
Al–5.3Ni–0.35Fe–0.03Ti	DC	F	50	-	90	[109]
DX01	DC	F	51	205	57	[111]
DX02	DC	F	51	200	64	[111]
DX26	DC	F	48	190	68	[111]
Al–1.75Fe–1.25Ni	GC	F	52	207	-	[121]

. However, although some studies were carried out on gravity-cast aluminum alloys, there are few systematical and deep studies about the microstructure and thermal conductivity of die-cast Al–Ni/Al–Fe(–Ni) aluminum alloys like the Al–Si series. Moreover, the low alloy compositions allow these alloys to improve mechanical properties while maintaining high thermal conductivity and castability to break the trade-off between strength, castability, and thermal conductivity by microstructure optimization. Furthermore, for the practical application of large-size products, die castings produced by these alloys should be optimized and adjusted combined with several processing parameters.

4. Effect of Die-Cast Processing on Thermal Conductivity in Die-Cast Aluminum Alloys

4.1. Processing Parameters of High-Pressure Die Casting

The HPDC process affects the microstructure including primary α-Al, eutectics, and porosity in die-cast aluminum alloys, which also significantly determines the thermal conductivity of die-cast aluminum alloys. The main processing parameters include slow-shot speed, fast-shot speed, intensification pressure, and vacuum [17,23,67,69]. J.K. Chen et al. [123] studied different shot speeds and intensification pressures and their effects on the porosity and thermal conductivity of die-cast Al–10Si alloy. With an increase in die-cast speeds and a decrease in pressure, the volume fraction of porosity increased. Because of the low thermal conductivity of the air, more porosities caused lower thermal conductivity of die-cast Al–10Si alloys as shown in Figure 12a. From the calculation, per percentage of porosity brought a ~4.7 W m⁻¹ K⁻¹ decrease in thermal conductivity. Hu et al. [124] compared the thermal conductivity of a die-cast Al–12Si alloy with different vacuum levels. When the vacuum level increased from 275 mbar to 72 mbar, the volume fraction of pores decreased from 0.152% to 0.046%, and thermal conductivity increased 3.84% as shown in Figure 12b,c. However, these studies only considered the effect of porosity variation on the thermal conductivity of die-cast aluminum alloys. Different processing parameters also influence other parts of microstructure and these effects have not been considered yet. Liu et al. [125] tried to control the fraction of ESCs in a die-cast Al–Mg–Si alloy using a new shot sleeve with a ceramic layer, thus changing the solute concentrations in the Al matrix and improving the thermal conductivity as shown in Figure 12d,e.

4.2. Rheological High-Pressure Die Casting

Apart from the traditional HPDC technique, the rheological die-casting process is also used in fabricating aluminum die castings. This technique includes the use of a slurry maker in conjunction with a traditional die-cast machine [126]. In the slurry maker, under the stirring of a screw, the melt has a high shearing rate and strong turbulence, and then the melt becomes a high-viscosity semisolid slurry with spherical particles under heat transfer. Then, the slurry is poured into the shot sleeve and the general die-casting process is performed. By incorporating the slurry maker process, die castings with lower porosity fractions and better mechanical properties can be obtained [127,128]. These advantages have led to increased interest in the rheological die-casting process for manufacturing high-quality die castings. Through the rheological die-casting process, Al–Si die casting with a higher thermal conductivity than traditional die casting was prepared because of the lower Si concentration in the Al matrix [75]. Qi et al. [36,129] employed an air compressor in the rheological die-casting process (ACSR Rheo-HPDC process) to help lower the temperature of the melt and produced the semisolid slurry shown in Figure 13. By adjusting the proper airflow, the Al–Si die-cast alloy could achieve an improvement in thermal conductivity from 167 W m⁻¹ K⁻¹ to 184 W m⁻¹ K⁻¹ and a higher elongation of over 10%. The improvement of thermal conductivity was attributed to an increase in the nucleation rate due to the air cooling the melt, which refined the secondary phases in the alloy and increased the free path of electrons for the heat transfer.

Recently, some commercial software in the market was used to simulate the heat conduction of filling and solidification during the die-casting process successfully [130]. Assisted by MAGMASOFT^® and ANSYS Fluent^®, K. Arunkumar et al. [131] developed a coupled simulation strategy to determine accurate heat transfer coefficients of the die-cooling channel and optimized the key parameters in the solidification of the die casting. Furthermore, ANSYS Fluent^® was also used to obtain the interface heat transfer coefficients during the die-casting process and clarified the influence factors (injection pressure, injection second phase velocity, casting temperature, vacuum, etc.) had on the interface heat transfer coefficients combined with experimental and numerical results [132]. Furthermore, simulations of the temperature field distribution in the mold during the melt filling process have also been studied by software like FLOW-3D CAST^TM, ProCAST, and MAGMASOFT^® [133,134,135,136]. These excellent works have guided optimization of the parameters of the HPDC process in industry.

From the results above, processing parameters of HPDC significantly influence the thermal conductivity of Al alloys. Vacuum-assisted HPDC has been the main application direction. However, the effect of parameters on microstructure and thermal conductivity is complex, and research on fully elucidating the effect mechanism of processing on solute contents, eutectics, and porosity is still inadequate. Therefore, aiming at different die-cast alloys, how to adjust and optimize the processing parameters reasonably remains a critical factor and challenge to obtain die castings with excellent properties. With the development of commercial software, the optimization of the processing parameters of die-cast aluminum alloys with high thermal conductivity with the help of advanced software is a feasible method.

5. Heat Treatment for Die-Cast Aluminum Alloys

In die-cast aluminum alloys, the common heat treatment methods consist of solution treatment and aging treatment [137,138,139]. The solution treatment involves the transfer of atoms in precipitates into solid solutions as solutes with variations in solubility at different temperatures. Then, the alloy is quenched to maintain the supersaturated solid solutions at room temperature. Next, aging treatment should be carried out to precipitate these solutes at a lower temperature compared to the solution treatment. In general, equipped with different aging treatments, there are four heat treatment methods [140]: solution treatment and natural aging (T4), solution treatment and artificial under-aging (T5), solution treatment and artificial peak aging (T6), and solution treatment and artificial over-aging (T7). Although heat treatment is not expected to be widely used in large-size thin-wall die castings because of the danger of bending and surface blistering [141], we also give a brief review on the effect of heat treatment on the thermal conductivity of die-cast aluminum alloys. The beneficial effects of heat treatment on the thermal conductivity of die-cast Al alloys can be mainly divided into the following four parts from several gravity-cast alloys:

(1)

Decreasing the number of defects like dislocations and point defects at elevated temperatures [142];

(2)

Promoting the spheroidization of eutectic Si at elevated temperatures [143];

(3)

Promoting precipitations like Mg₂Si from the solid solutions during the aging process [144];

(4)

Controlling the interfacial structure to be semi-coherent or incoherent during the aging process [145].

In die-cast Al alloys, Lumley et al. [61,146] conducted excellent work on the heat treatment of Al–Si die castings. After T4, T6, and T7 processes, the thermal conductivity of the A380 die casting increased from ~110 W m⁻¹ K⁻¹ (as-cast state) to ~120 W m⁻¹ K⁻¹ (T4), ~129 W m⁻¹ K⁻¹ (T6), and ~135 W m⁻¹ K⁻¹ (T7) because of the spheroidization of eutectic Si and a large number of fine dispersions of precipitate Al₂Cu phases. In addition, more Al–Si die castings were treated under the T7 process for one hour and showed improvements in both thermal conductivity and mechanical properties. Alloy 5 (Al–7.2Si–1.8Cu–0.24Fe–0.46Mn–0.22Mg–0.43Zn–0.1Ti) with lower contents of alloying elements, especially Si, had a lower increase in thermal conductivity. J.K. Chen et al. [123] also confirmed the spheroidization behavior of eutectic Si in the Al–Si die casting and with an increase in the time of T6 heat treatment, thermal conductivity increased. In rheological Al–Si die castings, a T6 peak aging heat treatment could also increase the thermal conductivity from 153 W m⁻¹ K⁻¹ to 182 W m⁻¹ K⁻¹ [75]. The increases in thermal conductivity by solution and aging heat treatment have been listed in

Table 4. Thermal conductivity of die-cast aluminum alloys after heat treatment.

Alloy	Heat Treatment	Thermal Conductivity (W m−1 K−1)	Improvement Ratio (%)	Ref.
A380	T4	120	9.1	[146]
A380	T6	129	17.3	[146]
A380	T7	135	22.7	[146]
Al–10.5Si–1.75Cu–0.71Fe–0.16Mn–0.23Mg–0.76Zn	T7	155	61.6	[61]
Al–10.6Si–2.41Cu–0.85Fe–0.2Mn–0.22Mg–0.75Zn	T7	150	59.8	[61]
Al–10.07Si–2.16Cu–0.25Fe–0.49Mn–0.1Mg	T7	125	16.2	[61]
Al–10.4Si–2.25Cu–0.25Fe–0.47Mn–0.22Mg	T7	117	16.9	[61]
Al–7.2Si–1.8Cu–0.24Fe–0.46Mn–0.22Mg–0.43Zn–0.1Ti	T7	121	12.6	[61]
Al–10Si–0.6Cu–0.9Fe–0.7Zn	T4	147	16.2	[123]
Al–10Si–0.6Cu–0.9Fe–0.7Zn	T6 (1 h)	149	17.1	[123]
Al–10Si–0.6Cu–0.9Fe–0.7Zn	T6 (4 h)	152	19.6	[123]

. It is shown that the T4 process with natural aging results in a low improvement in thermal conductivity and the T7 process has a higher increase. If the alloy contains more alloying elements, especially Cu, Mg, and Zn, which have a large variation in solubility under different temperatures, the enhancement of thermal conductivity can be more obvious.

Recently, direct aging treatment without solution treatment was also used to increase the thermal conductivity and mechanical properties of Al alloys. Camille et al. [147] tried to use direct aging to optimize the electrical conductivity (17 MS m⁻¹ → 26.5 MS m⁻¹) and yield strength (134~137 MPa → 334~337 MPa) successfully by mainly precipitating Al₃Zr fine precipitates in Al–Fe–Zr alloy. Another work also used the direct aging process at 180 °C in Al–Ni–Mg–Si conductor cast alloys. After the aging treatment, the microhardness and electrical conductivity both increased mainly because β′ and β″ nanoparticles precipitated from the substrate [148]. This kind of method is suitable for aluminum die castings because of the supersaturated solid solutions. Additionally, the aging treatment can also omit the solution treatment with a very high temperature to avoid the die castings being discarded. However, studies regarding this method in die casting to optimize thermal conductivity are still limited and worth deeply investigating.

6. Models of Thermal Conductivity for Die-Cast Aluminum Alloys

To date, plenty of theoretical models have been applied to aluminum alloys. Matthiessen’s rule mentioned in Section 3 was widely used in predicting the thermal conductivity of aluminum alloys and studying the effect of alloying elements on electrical conductivity and thermal conductivity in combination with the Wiedemann–Franz law [58,60]. However, this model only considers the effect of alloying element contents on thermal conductivity. Further, the calculation of Matthiessen’s rule depends on ${\rho }_s^i$ and ${\rho }_p^i$. The reported values of these two parameters do not cover all elements such as rare elements. Thus, it is important to expand the database of ${\rho }_s^i$ and ${\rho }_p^i$ to apply this model further. In addition, in real alloys, the distribution of different components and their shape also affect thermal conductivity and should be considered. Therefore, considering aluminum alloys as composites, many models on the effective thermal conductivity of two-component composites are proposed. The formulas are listed in

Table 5. Thermal conductivity models of two-component composites for aluminum alloys.

Model	Phase Arrangement	Formula	Refs.
Series model		${\lambda }_s{=(\frac{V_1}{{\lambda }_1}+\frac{V_2}{{\lambda }_2})}^{-1}$	[149]
Parallel model		${\lambda }_p=V_1{\lambda }_1+V_2{\lambda }_2$	[149]
Eutectic model (lamellae)		$\lambda =\frac{1}{4}[{\lambda }_p+\sqrt{{{\lambda }_p}^2+8{\lambda }_p{\lambda }_s}]$	[150]
$\mathrm{Maxwell}–\mathrm{Eucken} \mathrm{model} 1 ({\lambda }_1$$: \mathrm{continuous} \mathrm{phase}, {\lambda }_2$$: \mathrm{dispersive} \mathrm{phase}, {\lambda }_1$$> {\lambda }_2$)		$\lambda ={\lambda }_1\left[\frac{{\lambda }_2+2{\lambda }_1-2V_2\left({\lambda }_1-{\lambda }_2\right)}{{\lambda }_2+2{\lambda }_1+V_2\left({\lambda }_1-{\lambda }_2\right)}\right]$	[149,151]
$\mathrm{Maxwell}–\mathrm{Eucken} \mathrm{model} 2 ({\lambda }_1$$: \mathrm{dispersive} \mathrm{phase}, {\lambda }_2$$: \mathrm{continuous} \mathrm{phase}, {\lambda }_1$$> {\lambda }_2$)		$\lambda ={\lambda }_2\left[\frac{{\lambda }_1+2{\lambda }_2-2V_1\left({\lambda }_2-{\lambda }_1\right)}{{\lambda }_1+2{\lambda }_2+V_1\left({\lambda }_2-{\lambda }_1\right)}\right]$	[149,151]
Modified Maxwell–Eucken model		$\lambda ={\lambda }_1\left[\frac{{\lambda }_2+(n-1){\lambda }_1-(n-1)V_2\left({\lambda }_1-{\lambda }_2\right)}{{\lambda }_2+(n-1){\lambda }_1+V_2\left({\lambda }_1-{\lambda }_2\right)}\right]$	[151,152]
Effective medium model		$V_1\frac{{\lambda }_1-\lambda }{{\lambda }_1+2\lambda }+V_2\frac{{\lambda }_2-\lambda }{{\lambda }_2+2\lambda }=0$	[149]
General effective medium model		$V_1\frac{{{\lambda }_1}^{1/t}-{\lambda }^{1/t}}{{{\lambda }_1}^{1/t}+A{\lambda }^{1/t}}+V_2\frac{{{\lambda }_2}^{1/t}-{\lambda }^{1/t}}{{{\lambda }_2}^{1/t}+A{\lambda }^{1/t}}=0$	[151,153]

. The series model and parallel model were built to address the situation where phases are perpendicular and parallel to the heat dissipation direction [149]. In general, the distribution of phases in alloys is not parallel or perpendicular; the series model and parallel model are the lower and upper boundaries of the real thermal conductivity. Furthermore, combining series and parallel models, a model suitable for lamellar eutectics was calculated [150]. For more situations, aimed at dispersive phases, a Maxwell–Eucken model was proposed [149,151]. The model supposes that the dispersive phase is distributed in the continuous phase and the distance of the dispersive phase should be long enough that they cannot interact with each other. Two-form equations are listed in Table 5 according to relative values of the thermal conductivity of dispersive and continuous phases. Furthermore, considering the effect of morphology of dispersive phases, a modified Maxwell–Eucken model is established in Table 5 [151,152]. For cases involving interactions between different dispersive phases, an effective medium model was deduced [149]. Like the modified Maxwell–Eucken model, a general effective medium model was further obtained considering geometry and distribution parameters [151,153] and is listed in Table 5.

In die-cast Al alloys, there are few related studies on the theoretical calculation of thermal conductivity. Thermal conductivity considering porosity was calculated by the Maxwell–Eucken model [123]. They set the thermal conductivity of pores to zero and successfully calculated the total thermal conductivity of die casting. Lumley et al. [61] used Matthiessen’s rule and the Wiedemann–Franz law to calculate the as-cast and heat-treated Al–Si high-pressure die castings. In the work, the calculation was similar to experiment results. However, the solute concentrations of alloying elements were supposed and estimated in all Al grains, and the values were assumed to be the same for each element. For die-cast alloys, the microstructure is complex, including ESCs and α-Al in the die cavity for primary phases, and the Al solid solutions are supersaturated [154]. This indicates that the solute concentration is difficult to directly estimate from the phase diagram. Therefore, using Matthiessen’s rule to calculate the thermal conductivity of die castings is simplistic and cannot fully reflect the relationship between different parts of the microstructure. Accordingly, in order to understand the relationship between microstructure and thermal conductivity accurately, a new model applied for die-cast alloys should be proposed in the future.

7. Conclusions and Perspectives

This review summarized the thermal conductivity of high-pressure die-cast aluminum alloys from fundamental theory, alloy development, casting processing parameters, heat treatment strategies, and numerical models. Several conclusions and perspectives are written as follows:

(1)

In aluminum alloys, the thermal conductivity can be divided into electrical thermal conductivity and phonon thermal conductivity. The former is dominant in aluminum alloys. As a whole, the fundamental theory of the electrical heat conduction in aluminum alloys is abundant. For the phonon thermal conductivity, the relationship between the phonon thermal conductivity and temperature is clear. However, deep studies about the relationship between the phonon thermal conductivity and alloy compositions in aluminum alloys are lacking and can be performed further.

(2)

For alloy development, the Al–Si system is still the main system of die-cast alloys used for heat dissipation components. Reducing the major elements and adding trace elements to optimize the microstructure through decreasing solute concentrations in the substrate and modifying eutectic particles are the main methods used to improve thermal conductivity of alloys. In order to obtain higher thermal conductivity, a series of die-cast Al alloys only containing Fe or Ni are developed. However, more studies on the relationship between thermal conductivity and microstructure under the die-cast condition are needed. In addition, the mechanical properties of the alloys need to be improved for applications while ensuring high thermal conductivity and castability.

(3)

The thermal conductivity of die-cast aluminum alloys is affected by microstructure and porosity under different processing parameters. Moreover, the rheological die-casting process can improve the thermal conductivity and mechanical properties synergistically. However, the definite influence relationships between processing and thermal conductivity are still insufficient and needed. Strategies to optimize the die-casting processing parameters for die-cast alloys with highly comprehensive properties are also of great interest for future studies. The optimization of processing parameters of die-cast aluminum alloys with high thermal conductivity with the help of advanced software is a feasible method.

(4)

Solution and aging heat treatment processes can improve the thermal conductivity of die-cast aluminum alloys mainly through the precipitation from solid solutions and the spheroidization of eutectics. The T7 process has a significant increase in thermal conductivity of die-cast alloys. To adjust the requirement of the trend of large-size die castings, the direct aging process after casting, which can be applied to improve the comprehensive properties of die-cast alloys, is worthy of further studies.

(5)

Many theoretical models of composites have been proposed to calculate the thermal conductivity of aluminum alloys, and some of them have been used in die-cast alloys. However, a single model cannot describe the complex microstructure formed in multiple steps during the die-casting process. Therefore, to comprehensively understand the relationship between the microstructure and thermal conductivity in die-cast alloys, a new thermal conductivity calculation model for die-cast alloys needs to be built.

In summary, numerous excellent works have been performed to develop high-thermal-conductivity die-cast aluminum alloys, and many of them have been used successfully in industry. However, in each part of this review, the number of studies on the thermal conductivity of gravity-cast alloys is larger than that of die-cast alloys. Therefore, scientific studies on die-cast aluminum alloys with high thermal conductivity should be enhanced in the future and are expected to guide the development of new aluminum alloys for industrial applications.