Synthesis, characterisation and thermal behaviour of Cu-based nano-multilayer

Cu/AlN–Al₂O₃ nano-multilayer was deposited on top of 42CrMo4 (1.7225) steel plates (dimension of 10×7×4 mm, see chemical composition in Table 1) and α-Al₂O₃ wafers. Prior to deposition, the surface of the substrates was prepared by the following methods: mechanical grinding (grade of 500 and 800), polishing (down to 1 µm) followed by ultrasonic cleaning in acetone (5 min). The Cu/AlN–Al₂O₃ NML was produced in a high-vacuum chamber (initial pressure <5×10⁻⁶ mbar) by magnetron sputtering method, using two confocally arranged unbalanced magnetrons, equipped with Cu (purity: 99.999%) and Al (purity: 99.999%) targets. First, a 15 nm thick AlN–Al₂O₃ sublayer was deposited on top of the subtstrates followed by 200 repetitions of periodically alternating Cu (5 nm) and AlN–Al₂O₃ (5 nm) nanolayers, reaching a total thickness of 2000 nm. Consequently, the upmost layer was a 5 nm thick AlN–Al₂O₃ layer. The Cu layers served as metallic fillers, while the AlN–Al₂O₃ layers provided diffusion barriers for Cu. The related process parameters are listed in Table 2.

The surface morphology and cross-section of the multilayer was analyzed by Hitachi S4800 field emission scanning electron microscope (Japan) equipped with a Bruker AXS energy-dispersive X-ray spectrometer (EDS) system, and Helios G4 PFIB CXe plasma focused ion beam scanning electron microscope (Czech Republic) equipped with EDAX Octane Elect EDS System with APEX™ Analysis Software. Higher-magnification cross-sectional investigation was also carried out by FEI Tecnai G2 20 X-TWIN transmission electron microscope (TEM). Cross-sections for the measurement were prepared by mechanical method or with the use of Xe ion-beam milling and polishing function of the PFIB-SEM instrument, in order to obtain higher resolution.

XRD analysis of the as-deposited NML, and in-situ high-temperature X-ray diffraction (HT-XRD) measurements were performed using a Bruker D8 Discover X-ray diffractometer (Germany) with Cu K-alpha radiation, 40 kV and 40 mA generator settings. Measurements were recorded with 0.007°(2Th)/24 s speed. In situ high-temperature experiments were carried out in Anton Paar HTK 1200N chamber attached to the XRD, in flowing Ar atmosphere. The chamber was automatically heated with a heating rate of 60 °C/min and the spectra were recorded at every 100 °C between 25 and 600 °C, then at every 50 °C between 600 and 1000 °C. The total time required to record one spectrum was 16.5 min, during which the sample was kept at a constant temperature. Crystalline phases were identified by Search/Match algorithm of the Bruker DiffracPlus EVA, using ICDD PDF2 database. The PFIB-SEM and XRD measurements were performed in the 3DLab Fine Structure Analysis Laboratory of the University of Miskolc.

The thermal behaviour was further investigated by performing heat-treatments of the Cu/AlN-Al₂O₃ NML coated 42CrMo4 steel samples in the range of 200–950 °C. For this purpose, a horizontal vacuum tube furnace (Sunplant Ltd., Hungary) equipped with CCD camera was used. After the insertion of the samples, the furnace was heated up to the desired temperature, and the samples were isothermally annealed in a range of ± 10 °C for 10 minutes with a working pressure of 7±2×10⁻⁵ mbar. The samples were then cooled down to room temperature spontaneously inside the furnace. Wetting tests of Cu on the surface of AlN–Al₂O₃ ceramic layer were also preformed in the horizontal vacuum tube furnace, at a temperature of 1095 ± 5 °C for 2 minutes, at a pressure of 2.5×10^-4 mbar. The contact angle of the Cu droplet was measured with the use of the KSV software.

The thermal behaviour of the multilayer was investigated by means of differential scanning calorimetry (DSC). In order to minimise any interfering sign of the substrate, α-Al₂O₃ substrates were used. Accordingly, smaller samples (appr. 3×4 mm) were cut out of the previously coated Al₂O₃ plate to fit in the crucible of the instrument. The measurement was performed in vacuum atmosphere of about 10^-4 mbar with a heating rate of 10 °C/min. Before pumping, the instrument was filled with 99.999 % Ar several times to purge the system.

Microstructural images of the as-deposited Cu/AlN–Al₂O₃ NML are shown in Figure 1. The surface is relatively uniform without cavities. However, the traces of the polishing process preceding the NML deposition are slightly tracked by the multilayer (Fig. 1a). The grain-like morphology of the surface is characteristic of PVD coatings, but does not indicate a real grain/crystallite structure, rather it is a consequence of the increasing waviness of each deposited layer, observed similarly in the case of metal-based [32] and ceramic-based nano-multilayers [33, 34]. High-resolution cross-sectional PFIB-SEM image of the individual layers is shown in Figure 1b. The lighter layers indicate Cu while the darker layers indicate AlN–Al₂O₃. Fig. 1c shows a higher magnification TEM image of the cross-section of the multilayer. In this image, the darker layers show Cu and the lighter ones show the ceramics. The laterally continuous structure of the individual layers is well resolved. The actual thickness of the Cu layers is measured about 6.4 nm, the same for the AlN–Al₂O₃ barrier layers is found about 4.2 nm, while that for the first AlN–Al₂O₃ layer is found about 15.5 nm. The measured total thickness of the multilayer is 2250 nm. Some waviness of the layers is observed, which might be attributed to the combined effect of the unevenness of the substrate surface as seen in Fig. 1b, and to the 3D growth mode of the layer during the PVD process [29, 35]. The waviness of the layers can be characterised by the vertical peak-to-valley distance, which is found in the interval of 6.8–12.3 nm for Cu and 4.9–10.6 nm for the AlN–Al₂O₃ layers. The elemental composition of the multilayer, obtained on the surface of the multilayer is listed in Table 3. The presence of Fe originates from the steel substrate, suggesting that the interaction depth of the electron beam is somewhat larger than 2250 nm, being the full thickness of the NML (see above). It is worth noting that EDS is not sufficiently accurate to measure the O and N contents, thus no further conclusions can be drawn from Table 3.

The XRD diffractogram of the as-deposited Cu/AlN–Al₂O₃ NML is shown in Figure 2. The reflections of α-Fe (ferrite) originate from the 42CrMo4 steel substrate. In the range of 2Θ = 41°–44.5° superimposed reflections are identified, originated from the multilayer: Cu (111), AlN (200) and from the surface of the steel: FeO (200) and Fe₃N (\(\overline{1}\ \overline{1}\) 1). In addition to superimposition, the presence of Cu is indicated by a broader peak at 2Θ = 43.2°, which is attributed to its nanocrystalline structure and may also reflect to residual stresses developed during the deposition process [36]. Lower intensity peaks of AlN (111) and (200), as well as α-Al₂O₃ (104) and (024) are indicative of the complex phase-structure of the barrier layers. The presence of Fe₃N and FeO are the reaction products between the Fe surface atoms of the steel substrate and the plasma-activated N and O, during the deposition of the first AlN–Al₂O₃ sublayer. However, it is worth noting that superlattice reflections, originated from the periodic layered structure might also contribute in the ranges between 2Θ = 33°–38° and 2Θ = 41°–45° as observed for other nano-layered systems [29, 37, 38].

The evolution of the phase structure was monitored and investigated by high-temperature X-ray diffraction (HT-XRD) measurement. Changes of the superimposed reflections in the range of 41°–44.5° can be seen even at lower temperatures (200–300 °C), reflecting some structural transformation within the multilayer (Fig. 3). The Cu (111) reflection became more pronounced at and above the temperature of 400 °C, which is characteristic of microscale grain structure, indicating coarsening of Cu nanocrystallites. However, the broadened character of the curve in the vicinity of the evolving Cu reflection is still observed, indicating that some part of Cu remains in nano-confinements.

The evolution of α-Al₂O₃ (104) reflection into a more characteristic one with increasing temperature is another process being detected. At the same time, the peak of AlN (200) declines with temperature, indicating that AlN is continuously converted into Al₂O₃ with increasing temperature, which is a thermodynamically favoured process in the presence of excess oxygen/nitrogen (see Fig. 4). The AlN→Al₂O₃ conversion leads to the release of nitrogen and to the additional formation of the Fe-nitride phase, confirmed by the intensity growth of the Fe₃N (110) peak in Fig. 3 (see also Fig. 4). Heating from 600 to 1000 °C results in further decrease in the amout of AlN, which eventually disappears at about 800 °C. The appearence of austenite reflections at about 800 °C indicates the allotropic transformation of the steel substrate. The broad peak in the vicinity of the Cu reflection (2Θ = 43.2°) is continuously suppressed, suggesting a decrease in the proportion of nano-thin Cu layers, that remained within the NML structure.

The wetting properties of Cu/AlN–Al₂O₃ system was also investigated, as an important feature to understand the behaviour of the nano-multilayered system. For this purpose, a 340 nm thick AlN–Al₂O₃ ceramic monolayer was deposited on C45 (1.0503) steel plate by magnetron sputtering method. Then, a small piece of Cu (purity of 99.76%) was placed on top of the ceramic layer, and the assembly was inserted in the vacuum tube furnace. Images of the Cu can be seen in Fig. 5 before (Fig. 5a) and rigth after (Fig. 5b) melting. The obtained contact angle of Cu is θ=123 ± 5°, refering to poor wetting (see Fig. 5b). This result is in close agreement with the literature data [41, 42]. Poor wetting in the Cu/AlN–Al₂O₃ system ensures that melting point depression takes place [16] and the melted Cu would escape the NML instead of remaining there, both being prerequisites of successful joining.

In order to get a deeper understanding of the thermal behaviour of the multilayer, heat-treatment experiments were performed at temperatures of 200, 250, 350, 450, 550, 650, 750, 850 and 950 °C. SEM images of the surface of the multilayer, isothermally kept at 450 °C are shown in Fig. 6. Different line-shaped structures as well as separate protrusions can be observed on the surface. The linearly arranged formations are identified as Cu crystals (Fig. 7). These Cu crystals were found to appear on the top surface on the multilayer from the temperature of 250 °C. Although a similar phenomenon was previously reported by Lehmert et al. [27] at 750 °C, let us mention that in our case the same is observed at much lower temperatures. It is worth noting, that the appearance of Cu on the top surface of the multilayer is a criterion considering joining applications. Higher magnification (see Fig. 6b) reveals that these linear structures are made up of irregularly shaped, but faceted Cu crystals with their sizes above a micrometer. Thus, the original Cu nano-layers appeared at least partly on the top surface of the NML and are transformed into micron-sized crystals. The linear arrangement of the Cu crystals is remarkable, and can be explained by a surface crack of the top AlN-Al₂O₃ layer(s) (see Fig. 6b), which is partially filled by the Cu crystals. In other words, the Cu micro-crystals appeared on the top surface through the cracks in the ceramic layers.

These observations are explained here by the large difference between the linear expansion coefficient of Cu (α_Cu=16.5×10^-6 1/K) [43] and that of the ceramic barrier layers (α_Al2O3=8.1×10^-6 1/K [44] and α_AlN=4.8×10^-6 1/K [45]). During heating, this heat expansion mismatch lead to a continuosly increasing inner pressure within the NML, which eventually resulted in the cracking of the ceramic barrier layers, which allowed the outflow of copper to the surface. Moreover, as these cracks represent a lower energy state, Cu is preferentially located along them on the top of the NML. This phenomenon is similar to the hypothesis made in connection with the thermally annealed Cu/W nano-multilayers [29], although contrary to our present paper no visible cracks were detected in that paper (see also [46]).

The elemental map (Fig. 7) and the line-scan across the crystals (Fig. 8) confirm that the crystals observed at the top surface of NML are indeed pure Cu crystals and are only slightly oxidised on their surface. This confirms that while Cu is within the NML in the form of 6.4 nm thin nano-layers, it is safe from oxidation. However, when it is flown out to the top of the NML through the cracks, its surface is oxidised below 900 °C, in accordance with the phase diagram of Fig. 9 (see the cross section of the „Cu₂O/Cu(s)” line with the „p2” line). Similarly, Cu(O) was observed on the surface of Ag₆₀–Cu₄₀/AlN nano-multilayer, heat-treated in air atmosphere [26]. As follows from Fig. 9, the vacuum with residual pressure of 7 ± 2 × 10⁻⁵ mbar used in our experiments is sufficient to ensure oxide-free Cu only above 900 °C. On the other hand, after the Cu-oxide layer with thickness of about 10 nm is formed on the top of micron-sized Cu crystals, further oxidation is slowed down as it is limited by solid-state diffusion.

It is worth to mention that the Cu crystals on top of the NML seem natural metallic in light microscope, confirming the oxide layer is not too thick on them. Although oxide films might change the visible color of metals [47], but only above a critical thickness [48]. Using Eq.(10a) of [48] the smallest thickness of the copper oxide layer of 37 nm is found that ensures the minimum of 400 nm wavelength of destructive interference if the refractive index of the CuO/Cu₂O taken as 2.7 ± 0.1 (see p. 236 of [44]), where 400 nm is the lowest wavelength of light visible by humans. This means the thickness of the oxide layer on the micron-sized Cu-crystals is surely below 37 nm, which is less than 2 % of the total size of the Cu-crystals, explaining why the presence of oxygen on Cu crystals seems negligible in Figs 7, 8. From this maximum oxide thickness of 37 nm and from the molar volumes of Cu (7.09 cm³/mol [43]), CuO (12.4 cm³/mol [44]) and Cu₂O (23.9 cm³/mol [44]) one can estimate the initial thickness of the Cu layer that is oxidised being below 11 nm. As for joining application metallic Cu is required, these findings suggest that the degree of Cu oxidation can be considered negligible in the used vacuum environment.

In addition to Cu-crystals aligned along a line due to the long crack below them, there are also separate surface protrusions visible in Fig. 10a, where a locally protruded part of the nano-multilayer can be seen surrounded by Cu. For further investigation, a slope cut was applied to obtain the cross-section of the multilayer (see Fig. 10b). Cu enrichment accumulated within the multilayer was found in a micron-sized reservoir with about 1.0 µm height and about 6.5 µm length. As the Cu reservoir is formed, the multilayer above it is locally protruded from its initial surface (Fig. 10a). The driving force for this process is surface energy reduction due to coarsening of initially nano-thin Cu layers [18] and the non-wetting property of Cu on the surface of AlN–Al₂O₃ [49], as our contact angle measurement confirmed it further (see Fig. 5b). As follows from Fig. 10b, a moment was captured by cooling the sample when the accumulated Cu in the reservoir only partly flew out to the top surface of the multilayer, via a channel formed within the Cu-depleted ceramic layers, leaving a void behind. Let us mention that to form a micron-sized Cu-reservoir in addition to the in-plane diffusion of Cu within one nano-layer also copper diffusion from a number of Cu-layers through the defects in the ceramic layers should have been taking place.

SEM images of the top surface of Cu/AlN–Al₂O₃ NML heat-treated at 550 °C, 650 °C, 750 °C, 850 °C and 950 °C are shown in Fig. 11. At 550 °C and 650 °C, typically faceted Cu crystal shapes were observed, with an increased size of above 1 µm (Fig. 11a and b). In addition, a very interesting process is shown in Fig. 11b, the formation of Cu whiskers from the faceted Cu crystals. The diameter of these whiskers is between 115 and 600 nm, while their length was found between a few hundred nm to 45–50 µm. These whiskers were observed on the top surface of the NML from the temperature of 350 °C. The largest amount of these whiskers were found at 650 °C, while with increasing temperature, the number of these whiskers decreased. The formation of whiskers is commonly observed in the case of tin (Sn), usually in contact with Cu [50]. The main driving force behind them is the generated mechanical stress as a result of intermetallic layer formation [51] or outer mechanical pressure [52]. The formation of the whiskers results in the relaxation of the accumulated stresses. Beside Sn, other metallic whiskers were observed in the case of Al [53] or Ag [54]. In the case of Cu, Cu₂O whisker formation was reported by Horváth et al. [55]. In their case, Sn–Cu alloy-coated Cu substrates were subjected to corrosive high-temperature and humidity (105 °C, 100% RH) which caused the formation and growth of Cu₂O whiskers from the Sn-Cu coating.

With increasing temperature the amount of the Cu crystals on the top of NML increased. Moreover, the faceted crystals found between 250–750 °C starts to turn into rounded (droplet shaped) when temperature becomes as high as 850 °C (Fig. 11d). Thus, it would follow that Cu was probably melted in the T-interval between 750 and 850 °C. However, Cu micro-crystals can not melt at this low temperature, as pre-melting could take place only within the NML structure. Let us mention that the faceted—rounded “transformation” can also take place via solid-state diffusion with its driving force being the reduction of the specific surface area of the crystal [18].

Cross-section of a Cu reservoir situated within the nano-multilayer, previously heat-treated at 650 °C is shown in Fig. 12a. A crack of the Cu-depleted AlN–Al₂O₃ layers is also observed below a surface Cu crystal (Fig. 12b), allowing Cu to get to the top surface. The width of one of these cracks is 24.6 nm. Let us note that not all copper appears on the top surface of the multilayer. As it follows from Fig. 12c, d, some copper remains within the NML in the form of accumulations even after it was heat-treated at 950 °C. The size of these accumulations are considerably larger than that of the reservoir sizes observed at lower temperatures. It is reasonably considered, that with increasing temperature the size of the Cu reservoirs grew steadily. Moreover, the separate small reservoirs that came into contact eventually merged, decreasing further their specific surface area. The previously observed voids (at 450 °C), that remained after the Cu outflow, are no longer visible at higher temperatures, referring to the restoration of the original positions of the nano-multilayer.

Furthermore, some part of Cu remained in nano-confinement as follows from Fig. 13, showing the remaining part of copper in between the ceramic layers as function of temperature. During the measurement, the diameter of the electron beam was approx. 1 µm, and the concentration of Cu was measured at a reasonable distance from the Cu reservoirs. It is shown that about 25% of Cu remained within the NML even after it was heat-treated at 950 °C. However, reaching the temperature of 1100 °C (above the bulk melting point of Cu) it was found that no Cu remained in between the ceramic layers of the NML.

Figure 14 shows the DSC graph obtained from the original Cu/AlN–Al₂O₃ NML deposited on alumina substrate. In Fig. 14 first a rather broad, low-intensity exothermic peak appears in the temperature range of 400–800 °C, followed by a second, also broad, but high-intensity endothermic peak in the temperature range of 954–1250 °C. Fig. 14 will be used to summarise (and confirm additionally) the processes discussed above.

The onset temperature of the exothermic process (around 400 °C, see Fig. 14) coincides with the beginning of the extensive grain coarsening of Cu nanocrystallites, observed during the XRD measurement (see Fig. 3). Let us mention that a similar exothermic peak was explained by Ohnuma et al. [56] by the „clustering” of Cu in their FINEMET type amorphous alloy. Let us check if clustering—coarsening of Cu nano-layers can indeed explain the exothermic process accompanied by −5.6 J/g heat relase, as follows from Fig. 14. As the total mass of the measured sample (together with alumina substrate) was 0.153 g, the total measured exothermic heat effect in Fig. 14 was re-calculated to −0.857 J. Now let us estimate how much heat can be released if all Cu in the NML is coarsened more than by 2 orders in magnitude, when its final specific surface area becomes negligible compared to its original specific surface area [18]. For that, first let us evaluate the initial surface area of Cu. The total surface area of one side of the small samples used for the measurement was around 132 mm². Multiplying this value by the number of Cu nanolayers (200), by 2 (for the two sides of each Cu nano-layer), by 2 (for the wavy nature of the NML shown in Fig. 1b and c) and by 0.75 (for the ratio of coarsened Cu after Fig. 13) the total initial interfacial area of Cu nanolayers is found as 0.0792 m². Now, let us estimate the enthalpy part of the surface energy of solid Cu (= the maximum possible specific heat loss due to coarsening), similarly as it was done by Yakymovych et al [57], extrapolating the surface energy of the metal to T = 0 K, which equals about 2.50 J/m² (see Eq.10b in [8] and data from [39] and [58]). Multiplying this surface energy by the above found initial interface area, the maximum exothermic heat of −0.198 J follows. As compared to the above −0.857 J one can conclude that coarsening of Cu in our experiments can lead to maximum of about 23% of the measured heat release.

Therefore, some additional explanation is needed to rationalise the exothermic effect observed in Fig. 14. As was already discussed in relation with Fig. 8 the surface of the Cu crystals that appeared on the top of the NML at 450 °C is at least partly oxidised. The heat of oxidation in the temperature range of the exothermic peak in Fig. 14 is about −127 ± 10 kJ/mol-Cu for CuO and −61 ± 3 kJ/mol-Cu for Cu₂O [39]. The total amount of Cu on the top of the NML is the above-mentioned 132 mm² multiplied by 6.4 nm (the average thickness of each Cu nano-layer), by 200 (the number of Cu nano-layers), by 0.75 (from Fig. 13) and divided by 7.09 cm³/mol (the molar volume of Cu) = 1.79×10^-5 mol. Multiplying it by the above given possible range of −137 to −58 kJ/mol-Cu the resulting heat effect is −1.04 to −2.45 J. The missing exothermic heat after coarsening (−0.857 + 0.198 = −0.659 J) is 27–63% of the oxidation heat. The average crystal size of Cu from Fig. 6b is about 1 micron and it is approximately cubic in shape. The 27–63% of the amount of matter of a 1-micron cubic crystal takes its outer 10–28%, which corresponds to about 100–280-nm-thick surface oxide layer. However, this contradicts the above observation that the thickness of the surface oxide layer is surely below 11 nm. So, the oxidation heat of copper micro-crystals is at most −0.1 J. This leaves -0.857 + 0.198 + 0.1 = −0.559 J of additional exothermic heat. Therefore, coarsening and surface oxidation of Cu taken together are still not sufficient to explain the exothermic effect observed in Fig. 14. An additonal exothermic effect is connected with the oxidation of AlN to Al₂O₃ as proven above in Fig. 3. This is also confirmed by Fig. 15 proving that under our experimental conditions (temperature and oxygen/nitrogen partial pressure) the chemical reaction 2AlN + 1.5O₂ =Al₂O₃ + N₂ is shifted to the right. The standard heat of this reaction is about −507 ± 3 kJ/mol-AlN in the temperature range of the exothermic peak in Fig. 14. Suppose that the ceramic nano-layers are made fully of AlN. Then the initial maximum total amount of matter of AlN in the NML is calculated as 132 mm² (surface area of NML from one side) multiplied by 200 (number of nano-layers) and by 4.2 nm (thickness of one ceramic nano-layer) divided by 12.8 cm³/mol (the molar volume of AlN [59]) = 8.66 10^-6 mol. If this amount of AlN is multiplied by the above given heat of reaction (-507 kJ/mol), the maximum exothermic effect obtained from the oxidation of AlN is −4.39 kJ. Compared to the missing −0.524 J (see above), one can conclude that the oxidation of only 12 % of the maximum initial amount of AlN is sufficient to reproduce the exothermic heat found in Fig. 14.

Summarizing, the broad exothermic peak found in Fig. 14 (-0.857 J) is made of about −0.198 J (23 %) of coarsening heat, −0.10 J (12 %) of surface oxidation of the micron-sized Cu crystals and −0.557 J (65 %) of oxidation of AlN. These 3 processes explains why the broad exothermic peak in Fig. 14 contains 3 sub-peaks.

Now, let us discuss the large endothermic peak in Fig. 14, which is divided into two parts: into the first part below the macroscopic melting point of Cu (10.9 J/g * 0.153 g = 1.67 J) and into the second part above the same (27.4 J/g * 0.153 g = 4.19 J).

As follows from Fig. 14, the onset temperature of this large endothermic peak is 954 °C. However, it is lower than the temperature at which the surface oxide on Cu crystals will dissociate (= 975 °C, see Fig. 9, the cross section of line between the Cu₂O/Cu(s) line and the horizontal „p1” lines) and it is also lower than the temperature at which the sublimation of Cu starts (= 1010 °C, see Fig. 9, the intercept of the Cu(s)/Cu(g) line with the horizontal „p1” lines). Therefore, the endothermic process in the T-interval between 954 and 975 °C (i.e. the first small endothermic peak in Fig. 14) is much probably due to the melting of Cu nano-layers due to the melting point depression (MPD) of Cu [16]. The melting enthalpy of copper is 9.68 kJ/mol [39]. If this value is multiplied by the Cu-content still in the NML (= 1.79×10^-5 mol * 0.25/0.75 = 5.97 * 10^-6 mol), the endothermic heat of 0.058 J is obtained.

The second endothermic process takes place at and somewhat above 975 °C, when the surface oxide layer on Cu dissociates (see also Fig. 9). As the exothermic heat of Cu oxidation was found above as about −0.1 J, now its reverse value is found as about +0.1 J due to dissociation of Cu₂O.

The two first processes (premelting of Cu and dissociation of Cu₂O) are responsible for only about 0.058 + 0.1 = 0.158 J, which is only a small fraction (2.7 %) of the total endothermic heat found in Fig. 14 (1.67 + 4.19 = 5.86 J). Note that the reverse reaction Al₂O₃+ N₂= 2AlN + 1.5O₂ will not take place (see Fig. 15). The rest of the heat is taken by sublimation (at a higher temperature by melting/evaporation) of Cu (see Fig. 9). The sublimation heat of Cu in the T-interval of the first half of the endothermic peak in Fig. 14 is around +330 kJ/mol [39]. Multiplying this value by the amount of Cu on the top of the NML (1.79*10⁻⁵ mol) provides the endothermic heat of about 5.91 J, that covers the rest of the endothermic heat measured in Fig. 14: 5.86 − 0.158 = 5.70 J.