Journal of Materials Science 【-逻*辑*与-】amp; Technology, 2020, 49(0): 7-14 doi: 10.1016/j.jmst.2020.02.023

Research Article

## Evaluation on the interface characteristics, thermal conductivity, and annealing effect of a hot-forged Cu-Ti/diamond composite

Lei Lei1, Yu Su1, Leandro Bolzoni, Fei Yang,*

Waikato Centre for Advanced Materials and Manufacturing, School of Engineering, University of Waikato, Hamilton, 3240, New Zealand

Corresponding authors: * E-mail address:fei. yang@waikato.ac.nz(F. Yang).

First author contact:

1 Equal contribution.

Received: 2019-11-12   Revised: 2020-01-10   Accepted: 2020-01-12   Online: 2020-07-15

Abstract

A Cu-1.5 wt.%Ti/Diamond (55 vol.%) composite was fabricated by hot forging from powder mixture of copper, titanium and diamond powders at 1050 °C. A nano-thick TiC interfacial layer was formed between the diamond particle and copper matrix during forging, and it has an orientation relationship of (111)TiC//(002)Cu&[1 $\ bar {1}$ 0]TiC//[1 $\bar{1}$ 0]Cu with the copper matrix. HRTEM analysis suggests that TiC is semi-coherently bond with copper matrix, which helps reduce phonon scattering at the TiC/Cu interface and facilitates the heat transfer, further leading to the hot-forged copper/diamond composite (referred as to Cu-Ti/Dia-0) has a thermal conductivity of 410 W/mK, and this is about 74 % of theoretical thermal conductivity of hot-forged copper/composite (552 W/mK). However, the formation of thin amorphous carbon layer in diamond particle (next to the interfacial TiC layer) and deformed structure in the copper matrix have adverse effect on the thermal conductivity of Cu-Ti/Dia-0 composite. 800 °C-annealing eliminates the discrepancy in TiC interface morphology between the diamond-{100} and -{111} facets of Cu-Ti/Dia-0 composite, but causes TiC particles coarsening and agglomerating for the Cu-Ti/Dia-2 composite and interfacial layer cracking and spallation for the Cu-Ti/Dia-1 composite. In addition, a large amount of graphite was formed by titanium-induced diamond graphitization in the Cu-Ti/Dia-2 composite. All these factors deteriorate the heat transfer behavior for the annealed Cu-Ti/Dia composites. Appropriate heat treatment needs to be continually investigated to improve the thermal conductivity of hot-forged Cu-Ti/Dia composite by eliminating deformed structure in the copper matrix with limit/without impacts on the formed TiC interfacial layer.

Keywords： Copper/diamond composite ; Hot forging ; Interface characteristics ; Thermal conductivity ; Heat treatment

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Lei Lei, Yu Su, Leandro Bolzoni, Fei Yang. Evaluation on the interface characteristics, thermal conductivity, and annealing effect of a hot-forged Cu-Ti/diamond composite. Journal of Materials Science & Technology[J], 2020, 49(0): 7-14 doi:10.1016/j.jmst.2020.02.023

## 1. Introduction

Heat dissipation is a crucial issue for high-power electronic devices due to the power output and circuit integrated level are continually increasing. Considerable efforts have been made to develop advanced heat-sink materials that are used as a chip substrate in the high integrated circuits of high-power electronic devices [[1], [2], [3], [4], [5]]. Copper/diamond composites are regarded as promising materials, which have a great potential to achieve high thermal conductivity and tailored coefficient of thermal expansion, since diamond has a high thermal conductivity (1500~2000 W/mK) [6,7] and a low coefficient of thermal expansion [8], and copper also has reasonable high thermal conductivity. However, the poor wettability of copper and diamond make it difficult to form an effective bond between the two materials, so that the synthesised diamond/copper composites usually have low thermal conductivity [9,10]. Furthermore, the acoustic impedance mismatch between the diamond and the copper causes low interfacial thermal conductance [11]. Two methods are usually used to help form an interfacial carbide layer between the diamond and the copper to improve the composites’ thermal conductivity: metal matrix alloying (CuX, X = Ti, B, Cr, Zr) [[12], [13], [14], [15], [16], [17], [18]] and diamond surface metallisation by carbide forming elements (W, Cr, B, Ti, Zr, Mo) [[19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29]]. The metal carbide interlayer with appropriate acoustic impedance (ZCu<Zcarbide<ZDiamond) acts as a bridge to reduce the acoustic mismatch and increase the interfacial bonding strength between the copper and the diamond [7,11], leading to improving interfacial thermal conductance.

Theoretically, the interlayer features such as crystallinity and thickness could affect heat transfer across the interlayer structure. It reported that a disordered interface layer disturbs the propagation of vibrational waves and increases phonon scattering, which in turn reduces thermal conductivity [30]. The interfacial thermal conductance also decreases with the increase of interlayer thickness due to its increased thermal resistance. Furthermore, the content of carbide elements added may affect thermal conductivity by changing the interfacial layer thickness and solubility in the copper matrix [12,13]. However, the effect of interfacial layer’s microstructure on thermal conductivity is rarely studied, which is crucial to provide guidance in designing the interface microstructure of copper/diamond composites to achieve required thermal conductivity.

Extensive research has been carried out to synthesise copper/diamond composite by infiltration [[31], [32], [33], [34]], spark plasma sintering (SPS) [[35], [36], [37]] and high pressure/high-temperature process [38]. As an alternative cost-effective method, hot-forging has been proved as a feasible approach to rapidly fabricate copper/diamond composites from powders [39,40]. In this work, we prepare a copper-titanium/diamond composite by hot forging of elemental powder mixture and investigate the detailed interface microstructure, effect of annealing heat treatments, and resultant thermal conductivity.

## 2. Experimental procedure

### 2.1. Materials preparation

The raw materials used were copper powder (99.7 % purity, <45 μm), MBD8 diamond (Octagonal shape, 70-80 μm, supplied by Henan Huanghe Whirlwind Co., China), and hydride-dehydride titanium powder (99.6 % purity, <75 μm). The copper/diamond composite with a nominal composition of Cu-1.5 wt.%Ti/55 vol.%Diamond (Cu-Ti/Dia) was fabricated by hot forging of cold-pressed powder preform at 1050 °C. The powder mixture was blended in a V-type blender at 60 rpm for 90 min. After that, the powder mixture was mechanically pressed into a compact of 40 mm diameter and 33 mm height. The compact was then loaded in a steel can, heated up to 1050 ℃ and forged into a pancake in an argon atmosphere, and the forged pancake was slowly cooled down to room temperature. The detailed processing procedures could be found in Refs. [39,40]. For comparison, the pure copper and Cu-1.5 wt.%Ti (referred to as Cu-Ti) alloy billets were prepared by hot-pressing of Cu or Cu and Ti powder mixture at 1050 °C for 1.5 min (similar to hot forging). The cylindrical specimens, with a diameter of 12.7 mm, were cut from the hot-forged Cu-Ti/Dia composite billet by electrical discharge machining, subsequently encapsulated in quartz tubes with a vacuum of 1 × 10-5 Pa, and then heat treated at 800 °C for desired time. The heat treatment parameters for the encapsulated specimens are listed in Table 1. We named the forged Cu-Ti/Dia composite sample as Cu-Ti/Dia-0, and the heat treated samples as Cu-Ti/Dia-1 and Cu-Ti/Dia-2, respectively.

Table 1   The heat treatment parameters for the encapsulated specimens.

SampleHeating rate (℃/min)Temperature (℃)Holding time (h)Cooling rate (℃/min)
Cu-Ti/Dia-13080015
Cu-Ti/Dia-2580025

### 2.2. Materials characterisation

The phase constitutions of the hot-forged and heat treated Cu-Ti/Dia composites were identified by X-ray diffraction (XRD, Cu Ka radiation). Field emission scanning electron microscope (SEM, HITACHI, S4700), equipped with EDS, was used to observe the composite matrix’s microstructure, diamond morphology and tensile fracture surface (tensile tests were conducted using an Instron (33R4204) machine at a strain rate of 10-3 s-1 at room temperature, and the tensile specimens have a dog-bone shape with gauge dimension of 2 mm × 2 mm × 20 mm). Two methods were used to prepare SEM samples for the observation of matrix microstructure and diamond morphology: (1) the bulk Cu-Ti/Dia composites were polished first and then etched with 30 % nitric acid for 4 min; and (2) the diamond particles were completely extracted from the composites using nitric acid. The detailed interface characteristics, including phase constitution, composition, and microstructures, were examined by TEM (FEI Tecnai G2 F20, USA) that equipped with a bruker detector for energy dispersive x-ray spectroscopy (EDX) analysis. A dual beam focused ion beam workstation system (FIB, FEI Helios NanoLabTM 600i, USA) was used to prepare TEM specimens from the hot-forged composite.

### 2.3. Thermal conductivity measurement

The thermal conductivity (λ) was calculated using the equation λ = α ρ cp, where α is the thermal diffusivity, ρ is sample density, and cp is specific heat capacity. The thermal diffusivity was measured by a laser flash technique using an LFA 467 instrument (Netzsch, Germany) at room temperature, the rule of mixture (ROM) was used to calculate the specimen’s specific heat capacity based on the mass fraction of each component, and ρ was measured by the Archimedes principle. For measuring thermal diffusivity, the cylindrical samples used were cut from the Cu-Ti/Dia-0, Cu-Ti/Dia-1 and Cu-Ti/Dia-2 composites and had a dimension of Φ12.7 mm × 3 mm. All samples were ground with abrasive papers coded as 320# and 1000# and then cleaned ultrasonically in ethanol for 1 min.

## 3. Results and discussion

### 3.1. Phase constitution

Fig. 1 shows the XRD patterns of Cu-Ti, Cu-Ti/Dia-0, Cu-Ti/Dia-1 and Cu-Ti/Dia-2 composites. Only the diffraction peak of copper appeared in the Cu-Ti sample, indicating that the titanium powders dissolved into the copper matrix to form Cu (Ti) solid solution. The peaks for diamond, TiC and Cu are detected in the other three composite samples, and the intensity of TiC peak is increased in the Cu-Ti/Dia-2 composite comparing to both Cu-Ti/Dia-0 and Cu-Ti/Dia-1 composites. This indicates that titanium is reacted with diamond to form TiC during hot forging, the phase constitution of titanium carbides in the composites keeps unchanged while annealing at 800 °C, but the amount of TiC is increased with prolonging annealing time. We can speculate that Ti is not completely reacted with diamond during hot forging at 1050 °C/1.5 min, and there is still a small amount of titanium to remain in the Cu-Ti/Dia-0 composite, which is not detectable by XRD due to its quantity is small or forming Cu (Ti) solid solution. The remained titanium or Cu(Ti) solid solution is further reacted with diamond under the annealing condition of 800 °C for 2 h to form more TiC, leading to that more TiC phase is detected in Cu-Ti/Dia-2 composite, showing higher intensity of TiC peak comparing to other two composites. The graphite peak is also identified in the Cu-Ti/Dia-2 composite but not in the other two composites, meaning that the diamond is transformed into graphite (the quantity is large enough to be detected by XRD) at 800 °C and holding the temperature for 2 h. It is reported that the transition elements could promote the transformation of sp3 bond to sp2 bond on the diamond surface and induce the graphitization of diamond [13]. This suggests that there is a high possibility for titanium remains in the Cu-Ti/Dia-0 composite, and the diamond particle is induced to be graphitized by the existence of titanium in the composite while annealing at 800 °C for 2 h.

### Fig. 1.

Fig. 1.   XRD patterns of (a) Cu-Ti, (b) Cu-Ti/Dia-0, (c) Cu-Ti/Dia-1, and (d) Cu-Ti/Dia-2 composites.

### 3.2. Microstructure

Fig. 2 shows the SEM microstructures of Cu-Ti/Dia-0, Cu-Ti/Dia-1 and Cu-Ti/Dia-2 composites. It is clear that the diamond particles are uniformly distributed in the copper matrix (Fig. 2a), and no visible gaps are observed between the diamond and the copper matrix, except that only several diamond particles are detached from the copper matrix to leave pits showing the original diamond shape (indicated by red arrow), and the detachment of diamond from copper is likely caused by mechanical polishing during preparing SEM specimens. This suggests that the interfacial bonding between the diamond and the copper matrix is strong for the hot-forged composite (Cu-Ti/Dia-0). After annealing at 800 °C, it can see more pits formed by the detachment of diamond from copper matrix, as shown in Fig. 2d and g, and large cracks are visible between the diamond and the copper in the Cu-Ti/Dia-1 composite (Fig. 2e and f), which are not observed in the Cu-Ti/Dia-0 composite (Fig. 2b and c). This implies that the interfacial bonding between the diamond and the copper for the Cu-Ti/Dia-1 and Cu-Ti/Dia-2 composites becomes weaker than that of the Cu-Ti/Dia-0 composite. High magnification SEM images suggest that the thickness of the formed interface is thicker in diamond-{100} facets than in diamond-{111} facets for all the copper/diamond composites, as shown in Fig. 2b, c, e, f, h and i.

### Fig. 2.

Fig. 2.   SEM microstructures of Cu-Ti/Dia-0 (a-c), Cu-Ti/Dia-1 (d-f) and Cu-Ti/Dia-2 (g-i) composites.

To further investigate the microstructure of interface formed between the diamond and the copper, the morphology of extracted diamond particles from the Cu-Ti/Diam-0, Cu-Ti/Dia-1 and Cu-Ti/Dia-2 composites are presented in Fig. 3, respectively. It can be seen that the interface is formed on both diamond-{100} and -{111} facets for those three composites (Fig. 3a, d and g), and the statistical analysis results suggest that the coverage of diamond particles by the interface is over 95 %. We have already reported that TiC interfacial layer is easy to form and grow on the diamond-{100} facets comparing to the diamond-{111} facets for the hot-forged copper-Ti/diamond composites [40], because the C atoms are bonded by two C—C bonds on diamond-{100} facets and three C—C bonds on diamond-{111} facets, resulting in the solubility of C atoms from the{100}facets being higher than that from the {111} facets [38]. This leads to a dense TiC layer form on the diamond-{100} facets (Fig. 3b) and a porous and network-like TiC layer structure form on the diamond-{111} facets (Fig. 3c). After annealing, the interface microstructures on both of diamond -{100} and -{111} facts of the 800 °C-heat treated composites are distinct with those of the as-hot-forged Cu-Ti/Dia-0 composite, as shown in Fig. 3e, f, h and i. Besides the TiC particles grow coarse, several cracks are visible on the diamond-{100} facets for Cu-Ti/Dia-1 composite (Fig. 3e), but no cracks are observed on the diamond-{100} facets for Cu-Ti/Dia-2 composite (Fig. 3h). Crack-free interface formed in the Cu-Ti/Dia-0 composite is mainly attributed to (1) constrained deformation during the process of steel-can forging and (2) controlled cooling afterward. However, since the coefficients of thermal expansion (CTE) of diamond, copper, and titanium carbides are distinct (2.3 × 10-6 /K for diamond [16], 16.5 × 10-6 /K for pure copper [16], and about 9.5 × 10-6 /K for titanium carbides [41]), the crack is easy to form in the composite during fast heating and cooling. Furthermore, TiC is formed by the reaction of the added titanium and diamond particle, indicating that the bond between the TiC and the diamond is relatively stronger than that between the TiC and the copper matrix. This leads to the cracks are visible between the TiC interface and the copper matrix in the Cu-Ti/Dia-1 composite. The formed cracks are easy to cause spallation of the interfacial layer on the diamond surface, and this may be the primary reason to result in the weak interfacial bonding between the diamond and the copper and formation of gaps in the Cu-Ti/Dia-1 composite. A dense TiC layer structure can be seen in both Cu-Ti/Dia-1 (Fig. 3f) and Cu-Ti/Dia-2 (Fig. 3i) composites, and TiC particle clusters (marked as yellow arrow) are visible in Fig. 3h and i, meaning that some TiC particles grow significantly and agglomerate during annealing, and the agglomeration of TiC particles become serious with increasing annealing time. This is evidenced by more TiC particle clusters are observed on the diamond-{111} facets in Cu-Ti/Dia-2 composite than in Cu-Ti/Dia-1 composite.

### Fig. 3.

Fig. 3.   Surface morphology of the extracted diamond particles from the copper/diamond composites: (a-c) Cu-Ti/Dia-0, (d-f) Cu-Ti/Dia-1, (g-i) Cu-Ti/Dia-2.

Fig. 4 shows the TEM microstructure and EDS analysis results of the interface structure between the diamond-{100} facet and the copper matrix in the Cu-Ti/Dia-0 composite. Three distinct regions are visible in Fig. 4a (as indicated by the red dash line), which are bright region (A), layered structure region (Bi and Bii), and dark region (C). To determine the phase constitutions, EDS point analysis was performed to identify the chemical composition at the related positions in Fig. 4a. Results (Fig. 4b) show that the chemical composition at points 1, 3 and 4 is composed of 100 wt. %C, 100 wt. %Cu and 100 wt.% Cu, respectively, and at point 2 contains 35.87 wt. %Cu, 60.85 wt. %Ti, and 3.28 wt. %Cu. The EDS line scanning analysis across the layered structure region (the line position is as indicated in Fig. 4a), as exhibited in Fig. 4c, clearly shows that a layer that has a thickness of 80 nm-100 nm in the layered structure region is rich in both of Ti and C. Combining the XRD analysis results, it suggests that the regions A and C primarily consist of diamond and copper, respectively, Bi layer (in the layered structure region) is the new formed TiC interfacial layer (about 80-100 nm) between the diamond and the copper, and Bii layer is part of copper matrix but have a distinct boundary with the copper matrix in region C, which may be caused by different deformation distribution between the Bii copper layer and the copper matrix in region C during hot forging (This will be discussed in the later section). The interface between the diamond and the TiC layer is continuous and straight, while the interface between the TiC layer and the Bii-copper layer has a serration shape. This indicates that the TiC nucleates on the diamond surface heterogeneously and then grows preferentially from the diamond surface into copper matrix along a certain crystal orientation. Furthermore, there are no voids and minor cracks visible between the interfacial TiC layer and the diamond/copper, suggesting that the diamond and copper matrix is well bridged by the new formed TiC layer in Cu-Ti/Dia-0 composite.

### Fig. 4.

Fig. 4.   TEM analysis of Cu-Ti/Dia-0 composite: (a) interface, (b) point EDS, and (c) line-scanning EDS.

More detailed interface characteristics analysis results by HRTEM are presented in Fig. 5. There are two interfaces between the TiC interfacial layer and its adjacent layers of diamond and Bii-copper (Fig. 5a), which are marked as interfaces 1 and 2 in Fig. 5a, respectively. The interface between Bii-copper and primary copper matrix (region C in Fig. 5a) is marked as interface 3. FFT and IFFT analysis, conducted at the square b area in Fig. 5a, shows that a thin layer of amorphous carbon is formed (Fig. 5b). This implies that the diamond is transformed to amorphous carbon, and this is likely induced by the existence of titanium since carbide forming elements can act as a catalyst for that transformation [13]. This further suggests that titanium remains in the hot-forged Cu-Ti/Dia-0 composite and it helps form a large amount of graphite in Cu-Ti/Dia-2 composite during long period of annealing. Next to the amorphous carbon, TiC layer is identified (Fig. 5b and d), attributed to the measured lattice interplanar spacing is 0.246 nm in Fig.5d, which matches the spacing of TiC-(111) plane. Therefore, it can speculate that the interfacial TiC layer, between the diamond and the copper, is formed by the reaction of diamond/amorphous carbon and Ti during hot forging. For the interface 2, high resolution TEM image, acquired at the square c in Fig. 5a, is shown in Fig. 5c and the related FFT and IFFT analysis results are presented in Fig. 5e and f. The Cu-(111), -($\bar{11}$ 1), and -(002), and TiC -(111) planes are indexed. The FFT diffraction spots clearly show that the planes of (111)TiC and (002)Cu approximately overlap with each other along the zone axis of [1 $\bar{1}$ 0]TiC or [1 $\bar{1}$ 0]Cu, having the orientation relationship: (111)TiC//(002)Cu&[1 $\bar{1}$ 0]TiC//[1 $\bar{1}$ 0]Cu. Based on the measurement of inter-planar spacing from the IFFT image (Fig. 5e), the lattice mismatch(ε) between Cu and TiC is determined to be 14.6 % by ε = 2(αTiC-αCu)/(αTiC+αCu) (where α refers to the respective lattice parameter of each phase) [42]. According to the Bramfitt lattice matching theory [43], a semi-coherent interface is formed, suggesting that the TiC/Cu interface is bonded semi-coherently in the Cu-Ti/Dia-0 composite. It is well accepted that the semi-coherent interface has lower interface energy than that of the incoherent interface and the diffusion/mechanical interface [44]. Thus, a strong interface bonding between the interfacial TiC layer and the copper matrix is formed in the Cu-Ti/Dia-0 composite. A certain amount of TiC-bonded Cu is defective, which results in periodic loss of the lattice and formation of a distortion region at the TiC/Cu interface, as shown in Fig. 5e. The interface distortion zone usually contains high density of dislocations to accommodate the internal stress caused by the hot forging and formation of TiC [45], which in turn helps to improve the adhesion of the interface. Therefore, the generated semi-coherent bonding and interface distortion area both contribute to the enhanced interfacial bonding of the TiC/Cu interface. The FFT/IFFT results obtained at the square g in Fig. 5a confirm the presence of (111), ($\bar{11}$ 1) and (002) planes of Cu (Fig. 5g), further suggesting that the formation of interface 3 is caused by copper texture not phase differences. This is because the strong semi-coherent copper-titanium carbide interface restrains the deformation of copper near titanium carbide during hot forging, however, the deformation of copper that is far away from the interface is relatively large, thus resulting in the formation of a deformation interface within the copper matrix.

### Fig. 5.

Fig. 5.   Interface characteristics of copper-Ti/diamond. (a) Representative TEM image; (b) and (c) HRTEM images recorded at the marked b and c regions in (a); (d), (e) and (f) HRTEM images recorded at the marked d, e, f regions in (b) and (c); and (g) HRTEM images recorded at the marked g region in (a).

### 3.3. Thermal conductivity

The thermal conductivity (k) and thermal diffusivity (α) of Cu-Ti/Dia-0, Cu-Ti/Dia-1, Cu-Ti/Dia-2 composites, hot-pressed pure Cu and Cu-Ti (Cu-1.5 wt.%Ti) alloy are presented in Fig. 6. The fabricated pure Cu billet (98 % of the theoretical density) has lower thermal conductivity (224 W/mK) than the pure copper (385-400 W/mK), and this is mainly caused by the deformed structure (such as high dislocation density and a large number of sub-grains) [40]. With adding 1.5 wt. % of titanium into the copper matrix, the thermal conductivity of Cu-Ti alloy is significantly decreased, having a value of 64 W/mK, attributed to the disturbing (scattering) of phonon movement by the dissolved Ti atoms besides the influence of deformed structure [13,46]. The measured thermal conductivity of Cu-Ti/Dia composite is 410 W/mK, which is almost 7 times higher than that of the Cu-Ti alloy, and twice that of the hot-pressed pure copper billet. 800 °C-annealing has an adverse effect on the thermal conductivity of the Cu-Ti/Dia-0 composite, leading to the thermal conductivity is reduced to 250 W/mK for the Cu-Ti/Dia-1 composite and 193 W/mK for the Cu-Ti/Dia-2 composite.

### Fig. 6.

Fig. 6.   (a) Thermal conductivity and thermal diffusivity of hot-pressed Cu and Cu-Ti alloy, and Cu-Ti/Dia-0, Cu-Ti/Dia-1, and Cu-Ti/Dia-2 composites, (b) thermal conductivity comparison between current research and published papers.

Differential effective medium (DEM) model has been widely used to predict the copper/diamond composite’s theoretical thermal conductivity, in which both interfacial thermal conductance and diamond particle size are taken into consideration [7]:

$\left( 1-{{\text{V}}_{\text{d}}} \right){{\left( {{\text{k}}_{\text{c}}}/{{\text{k}}_{\text{m}}} \right)}^{1/3}}=\left( \text{k}_{\text{d}}^{\text{eff}}-{{\text{k}}_{\text{c}}} \right)/\text{k}_{\text{d}}^{\text{eff}}-{{\text{k}}_{\text{m}}})\text{withk}_{\text{d}}^{\text{eff}}={{\text{k}}_{\text{d}}}/(1+{{\text{k}}_{\text{d}}}/\left( \text{R}{{\text{G}}_{\text{c}}} \right))$

where kc, kd and km are the thermal conductivity of composite, diamond reinforcement and matrix, respectively, kdeff is the effective thermal conductivity of diamond reinforcement, R is diamond radius, Vd is the volume fraction of diamond reinforcement, and Gc is the interfacial thermal conductance. To calculate the theoretical thermal conductivity of Cu-Ti/Dia-0 composite using the DEM model, the adopted thermal conductivity of diamond and Cu matrix are 1500 and 224 W/mK, respectively. The average diamond radius is taken as 38 μm and diamond volume fraction is 55 %.

For simplifying the calculation, the thinner amorphous carbon layer is neglected and we consider the interfacial layer between the diamond and the copper is TiC. Therefore, the interfacial thermal conductance (Gc) can be expressed as follows [7,11]:

$1/G_{c}=1/{{\text{G}}_{\text{Cu}/\text{TiC}}}+\text{d}/{{\text{k}}_{\text{TiC}}}+1/{{\text{G}}_{\text{TiC}/\text{diamond}}}$

Where kTiC thermal conductivity of TiC, d is the interface thickness, and GCu/TiC and GTiC/diamond are the thermal conductance of Cu/TiC and TiC/diamond, respectively, which can be determined by the acoustic mismatch model (AMM) [7]:

G = 0.25CAνAqABαAB

Where C is the heat capacity per unit volume, ν is the phonon velocity, q is the fraction of phonons incident within a critical angle (θc) at interface, and α is the transmission coefficient of phonons incident within the critical angle. The subscript “A” and “B” denote the incident and outgoing side of phonons, respectively. Thus, the calculated GCu/TiC and GTiC/diamond are 2.01 × 108 W/m2K and 5.8 × 108 W/m2K, following Eq(3).

Taking d = 80 nm (in current research) and kTiC = 21 W/mK [7], the calculated theoretical thermal conductivity of Cu-Ti/Dia-0 is 552 W/mK, suggesting that the thermal conductivity of the hot-forged Cu-Ti/Dia-0 composite is about 74 % of its theoretical value. The thermal conductivity of Cu-Ti/Dia-0 composite is comparable and even better than that of the reported copper/diamond composites with a diamond particle size of about 75 μm [37,[47], [48], [49], [50], [51], [52], [53]] (as shown in Fig. 6b). This illustrates that effective bonding is established between the diamond and the copper in the Cu-Ti/Dia-0 composite by adding 1.5 wt. % titanium, enabling the composite’s thermal conductivity significantly improved. The primary reasons include the following aspects: (1) A crack-free TiC interface layer, with a serrated shape and thickness of about 80 nm, is formed between the diamond and the copper, having a strong bonding strength and benefiting interfacial thermal conductance. It can also be proved by the composite’s tensile fracture surface (Fig. 7), where the copper matrix is attached to the diamond surface, the ductile dimples of the copper matrix are observed, and diamond particles’ transgranular fractures are visible; (2) semi-coherent interface can significantly reduce the interface strain energy comparing to the non-coherent interface, and ordered interface improve phonon transmission so that benefiting interfacial thermal conductance [54]; (3) TiC interlayer acts as a bridge and help reduce the acoustic mismatch between the diamond and the copper (ZCu<Zcarbide<ZDiamond) [7,11], decreasing phonon scattering between the diamond and the copper and thereby reducing interfacial thermal resistance; and (4) Pressure at the interface induced by hot forging can alter the vibrational properties and interactions between atoms, leading to decreasing atomic distance and increasing the frequency of atom’s vibration [30]. This helps obtain better interface contact, resulting in reducing phonon scattering to achieve higher thermal conduction. However, an amorphous carbon layer formed between TiC and diamond, the intrinsically disordered structure in the amorphous carbon layer leads to a tortuous path for the propagation of vibrational waves and thus increases the phonon scattering. Therefore, the formation of amorphous carbon layer in diamond particle near to the interface layer has an adverse effect on the thermal conductivity of Cu-Ti/Dia-0 composite.

### Fig. 7.

Fig. 7.   The tensile fracture surface of Cu-Ti/Dia-0 composite.

The formation of crack, interface spallation, agglomeration of TiC particles, etc., leading to weak interface bonding between the diamond and the copper matrix in the 800 °C-annealed copper/diamond composites (Cu-Ti/Dia-1 and Cu-Ti/Dia-2), this is the primary reason to cause significant decrease in the thermal conductivity (250 W/mK for Cu-Ti/Dia-1 and 193 W/mK for Cu-Ti/Dia-2, comparing to 410 W/mK for Cu-Ti/Dia-0). Furthermore, the serious graphitization of diamond is another reason to further reduce the thermal conductivity of Cu-Ti/Dia-2 composite due to the graphite’s thermal conductivity is relatively small comparing to the diamond. Thus, we may further improve the hot-forged Cu-Ti/Dia composite’s thermal conductivity by (1) eliminating the deformed structure through appropriate heat treatment without coarsening the interfacial TiC particles and causing interface spallation, (2) optimizing the thickness of formed TiC interfacial layer to reduce the interface thermal resistance and acoustic mismatch, and (3) increasing the diamond particle size to reduce the amount of interface. We will address these factors in our future publications.

## 4. Conclusions

(1) An effective TiC interfacial layer, with a thickness of about 80 nm, was formed between the diamond particle and the copper matrix in the hot-forged Cu-Ti/Dia-0 composite. TiC interfacial layer is continuous in the fabricated composite, and it has an orientation relationship of (111)TiC//(002)Cu&[1 $\bar{1}$ 0]TiC//[1 $\bar{1}$ 0]Cu with the copper matrix.

(2) Semi-coherent bond was formed between TiC and Cu matrix. This interface structure enables the Cu-Ti/Dia-0 to have higher thermal conductivity than the most of reported data, with a value of 410 W/mK (this is about 74 % of the theoretical value).

(3) Titanium may induce the diamond surface to graphitize and form graphite/amorphous carbon layer in diamond particles during forging and long-period annealing at 800 °C, and this has a detrimental effect on the hot-forged Cu-Ti/Dia composite together with formation of deformation structure in the copper matrix.

(4) The TiC morphology difference between diamond-{100} and-{111} facets is eliminated after 800 °C-annealing, but the annealing causes TiC particles to grow coarse and become agglomeration, and TiC interfacial layer cracking and spallation, which has an adverse effect on the composite’s thermal conductivity.

(5) Appropriate heat treatments need to be optimised to improve the thermal conductivity of hot-forged Cu-Ti/Dia composite by eliminating deformed structure in the copper matrix with limit/without impacts on the formed TiC interfacial layer.

## Acknowledgments

This material is based upon work supported by the Air Force Office of Scientific Research under awasrd number FA2386-17-1-4025.

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Next-generation high-performance structural materials are required for lightweight design strategies and advanced energy applications. Maraging steels, combining a martensite matrix with nanoprecipitates, are a class of high-strength materials with the potential for matching these demands. Their outstanding strength originates from semi-coherent precipitates, which unavoidably exhibit a heterogeneous distribution that creates large coherency strains, which in turn may promote crack initiation under load. Here we report a counterintuitive strategy for the design of ultrastrong steel alloys by high-density nanoprecipitation with minimal lattice misfit. We found that these highly dispersed, fully coherent precipitates (that is, the crystal lattice of the precipitates is almost the same as that of the surrounding matrix), showing very low lattice misfit with the matrix and high anti-phase boundary energy, strengthen alloys without sacrificing ductility. Such low lattice misfit (0.03 +/- 0.04 per cent) decreases the nucleation barrier for precipitation, thus enabling and stabilizing nanoprecipitates with an extremely high number density (more than 10(24) per cubic metre) and small size (about 2.7 +/- 0.2 nanometres). The minimized elastic misfit strain around the particles does not contribute much to the dislocation interaction, which is typically needed for strength increase. Instead, our strengthening mechanism exploits the chemical ordering effect that creates backstresses (the forces opposing deformation) when precipitates are cut by dislocations. We create a class of steels, strengthened by Ni(Al,Fe) precipitates, with a strength of up to 2.2 gigapascals and good ductility (about 8.2 per cent). The chemical composition of the precipitates enables a substantial reduction in cost compared to conventional maraging steels owing to the replacement of the essential but high-cost alloying elements cobalt and titanium with inexpensive and lightweight aluminium. Strengthening of this class of steel alloy is based on minimal lattice misfit to achieve maximal precipitate dispersion and high cutting stress (the stress required for dislocations to cut through coherent precipitates and thus produce plastic deformation), and we envisage that this lattice misfit design concept may be applied to many other metallic alloys.

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