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Thermophysical properties of Zr–Cu–Al metallic glasses during crystallization
Journal of Non-Crystalline Solids 357 (2011) 126–131
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Journal of Non-Crystalline Solids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l
Thermophysical properties of Zr–Cu–Al metallic glasses during crystallization Hideaki Nagai a,⁎, Mikito Mamiya a, Takeshi Okutani b a Thin Film Processing Group, Advanced Manufacturing Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan b Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa 240-8501, Japan
a r t i c l e
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Article history: Received 22 February 2010 Received in revised form 27 August 2010 Keywords: Zr–Cu–Al metallic glass; Thermophysical properties; Hot-disk method; Crystallization; Heat treatment
a b s t r a c t The crystallization behavior of Zr–Cu–Al metallic glasses was studied using thermophysical property measurements. When the Zr content of Zr–Cu–Al metallic glass decreased from 65 at.% to 45 at.%, the thermal conductivity gradually increased and the maximum value obtained was the composition of Zr:Cu: Al = 50:39.3:10.7(at.%). These metallic glasses were not crystallized upon heat treatment below the glass transition temperature Tg, and the thermophysical properties of these metallic glasses were almost constant. In contrast, these metallic glasses started to crystallize upon heat treatment above Tg after a certain derived time, and their thermal conductivity increased with the crystallinity of the metallic glass. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Since the 1990s, investigations of multicomponent metallic alloys have led to the development of metallic glasses with high glass-forming ability [1,2]. Crystallization is prevented by quenching the molten metal from the liquid disordered state to the solid state. In particular, Zr-based metallic glasses are of great interest in engineering fields because of a large region of supercooled liquid [3] which is defined by the temperature interval between the glass transition temperature Tg and the crystallization temperature Tx, ΔTx (ΔTx = Tx − Tg), and by its low-cooling-rate fabrication (less than 103 K/s) as compared with general amorphous alloys ( above 104 K/s). Because of the applications of these metallic glasses, it is important to acquire full knowledge of their physical properties, such as the mechanical, electrical, magnetic, and thermal transport properties of the materials. Although the first three properties mentioned have been thoroughly investigated, there has been very little work on the thermal conductivity of metallic glasses because of the difficulty of making the accurate thermal conductivity measurements on typical thin samples (less than 50 μm) [4]. Some millimeter-thick Zr-based metallic glasses have been obtained as samples whose thermal conductivity can be measured by the laser flash method [5,6], but many metallic glasses cannot be measured by this method because of difficulty of obtaining uniform samples with millimeter thickness.
For measuring the thermal conductivity of thin samples, we focused on the hot-disk method developed by Gustafsson [7]. This method uses a transient plane source (TPS) element as both the heat source and the temperature sensor in a manner similar to the use of a thin wire in the hot-wire method. The TPS element of the hot-disk sensor is made of a thin metal foil and its conducting pattern is a double spiral. By using the hot-disk method, the thermal conductivity of both the insulating materials and the electrically conducting materials can be measured because each side of the thin metal foil is coated with a thin uniform insulating sheet. This method can be applied to thermal conductivity measurement of samples with bulk, thin-plate, or thin-film shapes by selecting the analytical model corresponding to the sample shape. Therefore, it is possible to measure the thermal conductivity of many thin metallic glasses. Moreover, this method can simultaneously measure the thermal diffusivity and specific heat per unit volume of the metallic glass samples. In this study, the thermal conductivity, thermal diffusivity and specific heat per unit volume of Zr–Cu–Al metallic glasses with different compositions were measured by the hot-disk method. In addition, the crystallization behavior of these metallic glasses was evaluated from the perspective of their thermophysical properties because of the establishment of optimum conditions for utilizing metallic glasses without crystallization. 2. Experimental methods 2.1. Principle of the hot-disk method
⁎ Corresponding author. Tel.: + 81 29 861 4404. E-mail address: [email protected] (H. Nagai). 0022-3093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2010.09.078
The normal experimental procedure for the hot-disk method is to pass a constant current through a hot-disk sensor and simultaneously
H. Nagai et al. / Journal of Non-Crystalline Solids 357 (2011) 126–131
record voltage changes derived from temperature changes in the sensor. When analyzing the behavior of a hot-disk sensor during a transient recording, it is convenient to express the time-dependent resistance [R(t)] using the following equation [8]: RðtÞ ¼ R0 f1 þ α½ΔTi þ ΔTðτÞg;
ð1Þ
where R0 is the resistance of the hot-disk sensor before the transient recording, α is the temperature coefficient of the resistance, ΔTi is a small temperature drop derived from heat loss transferred to the electrically insulating layer of the hot-disk sensor, and ΔT(τ) is the time-dependent temperature increase of the thin metal foil. The temperature increase is expressed in this equation as a function of only one variable, τ, which is defined as 1=2
τ ¼ ðt=θÞ
2
; θ ¼ d =κs ;
ð2Þ
where t is the time elapsed from the start of the transient heating, θ is the characteristic time, d is the radius of the hot-disk sensor, and κs is the thermal diffusivity of the sample. It is expected that ΔTi would be constant after a short initialization period of Δti, because the heat transferred to the sample through the insulating layer becomes constant due to the release of constant power from the thin metal foil, and Δti is estimated as 2
Δti ¼ δ =κi ;
ð3Þ
where δ is the thickness of the insulating layer and κi is the thermal diffusivity of the insulating layer. However, ΔTi only becomes constant after a much longer period than Δti because of inadequate thermal contact between the thin metal foil, the insulating layer and the sample, along with other factors (nonideal electrical components in the circuit, finite specific heat of the sensor, software and hardware delays between triggering the transient event and recording data, etc.). A “time correction” term, Δtcorr , is introduced to simplify these factors. The data points at the beginning of the transient recording at times less than Δtcorr are not used in the fitting of the analytical model of the hot-disk method because these data include the effects of the additional factors. ΔT(τ) is affected by the power output of the hot-disk sensor, the design parameters of the sensor, the thermal transport properties of the sample, and the shape of the sample. ΔT(τ) is given by the following equation for a disk-shaped sensor [7], from which the thermal conductivity and diffusivity can be obtained: −1 3=2 ΔTðτÞ ¼ P0 π dλ DðτÞ;
ð4Þ
where P0 is the total output power and λ is the thermal conductivity of the sample. The function D(τ) is a theoretical expression of the time-dependent temperature increase. The standard hot-disk method assumes that the hot-disk sensor is located in an infinite sample, and the function D(τ)std express as following equation, which models the conducting pattern of the disk-shaped sensor by assuming that the disk is made up of a number of concentric ring sources: m. DðτÞstd = ½mðm + 1Þ 2
2
τ
∫0 dσ
1 3 0 2 2 l +k lk 2 4 5: AI0 ∑ l ∑ k exp@ ×σ 2m2 σ 2 4m2 σ 2 l=1 k=1 m
ð5Þ
m
When the sample has a limited extension in the direction perpendicular to the sensor but is still considered infinite in the
127
plane of the sensor, that is, when the sample is slab sheet, the function D(τ)slab express as following equation: DðτÞslab
#) i2 h 2 = ½mðm + 1Þ ∫ dσ × σ 1 + 2 ∑ exp 2 0 σ r i=1 1 2 3 0 m m l2 + k 2 lk 4 5: @ A I0 × ∑ l ∑ k exp 2m2 σ 2 4m2 σ 2 l=1 k=1 2
(
τ
2
∞
"
ð5′Þ As h, the thickness of the slab sheet, tends to infinity, we obtain the same function as the one used in the standard hot-disk method, where the sample is considered infinite in all directions. This method of thermophysical property measurement of a slab sheet using Eq. (5′) is called the slab method. When the slab sheet samples are measured by the slab method, the outside surfaces of the slab sheets need to be insulated by a material with low thermal conductivity because heat loss should be kept low compared with the total output of power in the sensor during the transient recording. We substituted Eq. (4) into Eq. (1) and obtained Eq. (6). RðtÞ¼ R0 ½ð1 þ αΔTi Þ þ αP0 ðπ
3=2
1
dλÞ DðτÞ:
ð6Þ
When the characteristic time (θ) is equal to the value that is calculated from the radius of the hot-disk sensor and the thermal diffusivity of the sample by Eq. (2), a plot of the measured resistivity R (t) vs D(τ) will, according to Eq. (6), yield a straight line. However, D (τ) at each data recording time is calculated for any value of θ, and the correlation coefficients of the straight line fit of R(t) vs D(τ) are then calculated. The θ of the optimum straight line fit is used to estimate the thermal diffusivity of the sample [Eq. (2)], and the thermal conductivity is calculated from the slope of the fit. When the measurement time, measured from the start of transient heating, is close to the characteristic time (ideally 0.5 b t/θ b 1.0), the thermal diffusivity and thermal conductivity of the sample can be reliably measured. The thermal conductivity and thermal diffusivity of the sample are interrelated as follows. λ ¼ ρCp κs :
ð7Þ
Here, ρ is the density of the sample and Cp is its specific heat. The specific heat per unit volume (ρCp) can be calculated using the sample thermal diffusivity and thermal conductivity. The reproducibility of the thermal conductivity, thermal diffusivity and specific heat per unit volume measured by the slab method were ±2 %, ±5 % and ±3 %, respectively. 2.2. Preparation of Zr–Cu–Al metallic glasses Starting samples of Zr–Cu–Al alloy with different compositions were synthesized by arc-melting. Zr(99.9% pure), Cu(99.99% pure), and Al (99.99% pure) ingots were supplied by Rare Metallic Co., Ltd.. Zr–Cu–Al metallic glass with Zr:Cu:Al = 65:27.5:7.5 (at.%) was selected as a parent sample [9], and the Zr contents were changed with a constant ratio of Cu and Al[Cu:Al = 11:3 (in mole)]. The starting Zr–Cu–Al alloy ingot was cut into small blocks (approximately 0.75 g) for rapid solidification experiments. Fig. 1 schematically diagrams the rapid solidification experiment. Generally, the starting alloy of the metallic glass is melted in the quartz glass tube. Complete melting of the starting alloy is important to obtain metallic glass with an entirely amorphous structure, but it is difficult to confirm complete melting of the alloy in the quartz glass tube. Moreover, the Zr–Cu–Al alloy melt can easily react with the quartz glass making it difficult to premake the melt without oxygen contamination, which strongly affects the glass-forming ability and crystallization behavior of metallic glasses [10]. To solve these
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H. Nagai et al. / Journal of Non-Crystalline Solids 357 (2011) 126–131
but any shift of the composition due to the addition of tungsten was negligible. For example, 0.75 g of a starting sample block with Zr:Cu: Al = 65:32.5:7.5 (at.%) would be changed into one with Zr:Cu:Al: W = 64.8:32.4:7.5:0.3 (at.%) by adding 5 mg of tungsten. The dropped sample was rapidly solidified by the copper spin rotor, which rotated at about 5000 rpm. 2.3. Characterization of Zr–Cu–Al metallic glasses
Fig. 1. Schematic diagram of rapid solidification equipment for preparing of the metallic glass.
problems, the starting Zr–Cu–Al alloy block was tied with tungsten wire 0.1 mm in diameter and hung in the quartz glass tube of the equipment without contacting any oxide material to prevent contamination by oxygen coming from the crucible or nozzle. Argon gas (purity 99.9995%, oxygen content less than 0.2 ppm) was introduced into the equipment at a pressure of 1.0 × 105 Pa after the chamber had initially been pumped down to below 10− 2 Pa. Fig. 2 presents a typical temperature profile of the starting sample block during heating. A B-type thermocouple covered by quartz glass was attached to the starting sample block only for measuring the sample temperature and was specifically not inserted, during the preparation of the metallic glass in order to prevent oxygen contamination. At first, the starting sample block [Fig. 2(a)] was heated by moderate infrared heating, ultimately reaching about 1273 K, higher than the melting point of the Zr–Cu–Al alloys. At this time, the starting sample block was visually confirmed to be completely melted and still hanging by adhesion to the tungsten wire because of good wettability [Fig. 2(b)]. Introducing extra infrared heating quickly increased the temperature of the melted sample, which then dropped toward the cooling spin rotor at around 1850 K [Fig. 2(c)]. At this point, a piece of the tungsten wire (about 5 mg) was dissolved into the melted sample,
Fig. 2. Typical temperature profile of the starting block during heating.
The crystalline structure of the obtained samples was analyzed by X-ray diffraction (XRD; MAC Science M03XHF22). The exothermic and endothermic reactions associated with Tg and Tx were measured by differential scanning calorimetry (DSC; Rigaku DSC8270) at up to 1273 K in a vacuum. The heating rate was 10 K/min. The thermophysical properties of the samples were measured by the slab method. Fig. 3 schematically diagrams the sample plate setting for the slab method. The rather rough surfaces of the obtained samples were flattened to less than 1 μm of roughness by polishing in order to obtain good thermal contact between the sample and the hot-disk sensor. The hot-disk sensor was placed between two polished sheet samples of the similar thickness, and the outsides of the samples were covered with polystyrene foam to suppress heat loss. The resistivities of the polished samples were measured using the Van der Pauw method (Toyo Corp.; Resi Test 8340) to support later estimates of the electron contribution to the thermal conductivity. The polished samples were annealed in a vacuum at a temperature below Tg or between Tg and Tx. Their thermophysical properties were then measured by the slab method only after they had cooled down to room temperature because the hot-disk sensor and polystyrene foam used in this study can only be used at much lower temperature than the annealing temperature. The annealed samples were also analyzed by XRD. 3. Results 3.1. Thermophysical properties of Zr–Cu–Al metallic glasses Fig. 4 presents a photograph and XRD pattern of the solidified Zr65Cu27.5Al7.5 sample after spin rotor cooling. A disk-shape sample about 30 mm in diameter and 0.2 mm thick was obtained. The sample had a rough surface with a large whirling pattern and a small wave pattern. Because the high-speed spin rotor used as a cooling media exhibited a slight vibration, this rough surface might result from rapid solidification, with the shape of the melt deformed by rotation and vibration. To measure thermophysical properties of the obtained sample, the sample surface needed to be flat, as mentioned above. Therefore, the sample surface was polished, and a flat plate about 0.1 mm thick was obtained. The solidified sample was shown to be amorphous by XRD, as seen in Fig. 4, and the DSC result reveals that there was clear Tg point on the solidified sample, as mentioned below. Based on these results, we can say that a metallic glass plate could be synthesized by using spin rotor cooling. When melts with Zr content between 45 and 65 at.% were solidified by spin rotor cooling, metallic glasses with entirely amorphous phase and similar sample shapes could be obtained, but the solidified sample with 40 at.% Zr-content was a mixture of crystalline phase and amorphous phase. Table 1 lists the thermal conductivity, thermal diffusivity, and specific heat per unit volume of Zr–Cu–Al metallic glasses measured by the slab method as a function of Zr content for Zrx(Cu11Al3)(100 − x)/14 metallic glasses. Table 1 also provides reference data for similar compositions reported in the literature [6,11,12]. Our measured data were in good agreement with the reference data. The thermal conductivity and specific heat of Z50Cu39.3Al10.7 metallic glass had their maximum values in these compositions of metallic glasses.
H. Nagai et al. / Journal of Non-Crystalline Solids 357 (2011) 126–131
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Fig. 3. Schematic diagram of sample plate setting for the slab method.
3.2. Relationship between thermophysical properties and crystallization of Zr–Cu–Al metallic glasses by heat treatment Table 2 gives Tg, Tx, and ΔTx as a function of the Zr content for Zrx (Cu11Al3)(100 − x)/14 metallic glasses and provides reference data for similar compositions reported in the literature [9,13]. Tg and Tx of our sample decreased simply with Zr content, and ΔTx increased simply with Zr content. These tendencies of our sample with respect to Zr content were similar to those of the references, but our values differed from the reference values. Figs. 5 and 6 plot the thermal conductivity and specific heat of metallic glasses following heat treatment at 673 K and 698 K. The crystalline structure was also measured by XRD at each point of the thermophysical property measurements. With heat treatment at
673 K, the thermal conductivities and specific heats of the metallic glasses with 45, 50 and 55 at.% Zr-content were almost constant during the entire measurement time. The thermal conductivity of metallic glass with 60 at.% Zr-content was constant for the first few hours at this temperature, but after that the thermal conductivity increased and the metallic glass began to crystallize. However, the specific heat of this metallic glass was decreased by the heat treatment regardless of crystallization. The thermal conductivity of metallic glass with 65 at.% Zr-content increased quickly during just one hour of heat treatment. With heat treatment at 698 K, we measured the thermal conductivities and specific heats of only metallic glasses with 50 or 55 at.% Zr-content because the thermal conductivity of metallic glass with 45 at.% Zr-content was predicted to be constant following heat treatment at 698 K, close to Tg for this metallic glass, for 10 h. The thermal conductivity of metallic glass with 50 at.% Zr-content was constant for the first few hours at this temperature, but after that the thermal conductivity increased and the metallic glass began to crystallize. The specific heat of this metallic glass with a 1 h heat treatment was the same as that of the assynthesized metallic glass, but the specific heats of samples heattreated for between 2 h and 4 h were lower than that of the assynthesized sample, even though this metallic glass still had an amorphous structure and retained the same thermal conductivity. The thermal conductivity of metallic glass with 55 at.% Zr-content
Table 1 Thermophysical properties of Zr–Cu–Al metallic glass measured by hot-disk method at room temperature. Composition of metallic glass
Thermal conductivity (W/mK)
Thermal diffusivity (×10− 6 m2/s)
Specific heat per unit volume (× 106 J/m3K)
Remarks
Value Std. dev.⁎ Value Std. dev.⁎ Value Std. dev.⁎
Fig. 4. Typical photograph of the metallic glass solidified by spin rotor cooling and its XRD pattern.
Zr45Cu43.2Al11.8 Z50Cu39.3Al10.7 Zr55Cu35.4Al9.6 Zr60Cu31.4Al8.6 Zr65Cu32.5Al7.5 Zr50Cu40Al10 Zr55Cu35Al10 Zr55Cu30Ni5Al10 Zr55Cu45
5.11 6.20 5.53 5.54 5.23
0.24 0.10 0.22 0.11 0.19
5.02 5.88
*Std. dev.: Standard deviation.
2.65 2.55 2.38 2.35 2.76 2.3 2.1 2.2 2.41
0.16 0.11 0.14 0.17 0.17
1.94 2.43 2.33 2.36 1.90
2.42
0.20 0.09 0.18 0.12 0.18 Ref. Ref. Ref. Ref.
[11] [11] [6] [12]
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H. Nagai et al. / Journal of Non-Crystalline Solids 357 (2011) 126–131
Table 2 Compositional dependence of the glass transition temperature, crystallization temperature, and ΔTx. Composition of metallic glass
Glass transition temperature (Tg, K)
Crystallization temperature (Tx, K)
ΔTx(K)
Remarks
Zr45Cu43.2Al11.8 Z50Cu39.3Al10.7 Zr55Cu35.4Al9.6 Zr60Cu31.4Al8.6 Zr65Cu32.5Al7.5 Zr45Cu43Al12 Zr50Cu40Al10 Z55Cu35Al10 Zr65Cu32.5Al7.5 Zr65Cu32.5Al7.5 Zr45Cu43Al12 Zr50Cu40Al10 Z55Cu35Al10
690 685 668 635 625 690–699 670–679 650–659 649b 656 670–679 650–659 649b
756 758 741 716 710 760–769 740–749 730–739 729b 745 750–759 750 729b
66 73 73 81 85 60–69 70–79 70–79 60–69 89 70–79 N 80 70–79
Ribbon, Ref. [13] Ribbon, Ref. [13] Ribbon, Ref. [13] Ribbon, Ref. [13] Ribbon, Ref. [9] Bulk, Ref. [13] Bulk, Ref. [13] Bulk, Ref. [13]
increased quickly after only one hour of heat treatment, and the specific heats with heat treatment for 1 h or less were lower than that of the as-synthesized one.
4. Discussion 4.1. Thermophysical properties of Zr–Cu–Al metallic glasses
Fig. 6. Effect of heat treatment on thermal conductivities and specific heats of the metallic glasses. Heat treatment temperature: 698 K.
Table 3 lists the resistivity and thermal conductivity of Zr–Cu– Al metallic glasses with different Zr content. The thermal conduc-
: 45at%Zr,
7.0
λ ¼ λelectron þ λphonon ;
: 50at%Zr,
: 55at%Zr
6.0 5.0
3.0 2.5 2.0 1.5 0
2
4
6
8
Specific heat 6 3 per unit volume (10 J/m K)
Thermal conductivity (W/mK)
(1)Annealing below or close to Tg
10
Annealing time (h)
7.0 6.0 3.0
5.0
2.5 2.0 0
2
4
: 65at%Zr
6
8
10
1.5
Specific heat 6 3 per unit volume (10 J/m K)
Thermal conductivity (W/mK)
(2)Annealing above Tg
: 60at%Zr,
tivity of the material, λ, is the sum of the electron and phonon contributions:
Annealing time (h) Fig. 5. Effect of heat treatment on thermal conductivities and specific heats of the metallic glasses. Heat treatment temperature: 673 K.
ð8Þ
where λelectron is the electron thermal conductivity and λphonon is the phonon thermal conductivities. The electron contribution to the thermal conductivity can be estimated by the Wiedemann–Franz law: λelectron ¼ L × T=r;
ð9Þ
where L is the Lorenz number, which is 2.445 × 10− 8 W · Ω · K− 2 for a degenerate free-electron gas system; T is the temperature; and r is the resistivity. It was found that Z50Cu39.3Al10.7 metallic glass had a higher phonon contribution to the thermal conductivity because the electron contribution of the thermal conductivity of the metallic glasses was almost constant, independent of the composition of the metallic glasses. This composition is close to the ternary eutectic point of the Zr–Cu–Al alloy system [Zr:Cu:Al= 50:40:10 (at.%)] [14], and it has been reported that the atoms in Zr50Cu40Al10 metallic glass are closely packed compared with Zr70Cu20Al10 metallic glass [15]. Therefore, the higher thermal conductivity and specific heat of Z50Cu39.3Al10.7 metallic glass were considered to result in close packing of the constituent atoms. Table 3 Resistivity and thermal conductivity of Zr–Cu–Al metallic glasses at room temperature. Composition of metallic glass
Resistivity (10− 6 Ωm)
Thermal conductivity (W/mK) λ⁎
λelectron⁎⁎
λphonon⁎⁎⁎
Zr45Cu43.2Al11.8 Z50Cu39.3Al10.7 Zr55Cu35.4Al9.6 Zr60Cu31.4Al8.6 Zr65Cu32.5Al7.5
1.77 1.86 1.88 1.83 1.63
5.11 6.20 5.53 5.54 5.23
4.05 3.85 3.81 3.91 4.40
1.06 2.35 1.72 1.63 0.83
*λ= λelectron + λphonon.. **λelectron: Electron contribution to thermal conductivity. ***λphonon: Phonon contribution to thermal conductivity.
H. Nagai et al. / Journal of Non-Crystalline Solids 357 (2011) 126–131
4.2. Relationship between thermophysical properties and crystallization of Zr–Cu–Al metallic glasses after heat treatment Tg, Tx, and ΔTx of metallic glasses are useful factors for estimating the glass-forming ability and the stability of the glassy phase. However, Yokoyama et al. reported that splat-cooled and tilt-cast metallic glasses had different thermal properties based on DSC measurements [13], and we have reported that the cooling history of metallic glass is important for determining thermal properties based on DSC measurements [16]. From these reports, Tg, Tx, and ΔTx of metallic glasses are considered to depend on the cooling process as well as the sample composition. Therefore, the values of our sample in Table 2 were used to determine the annealing temperature for evaluating the crystallization of metallic glasses in this study. Based on the results of Table 2 and Figs. 5, 6, the relationship between the crystallization behavior and thermophysical properties of the metallic glass with respect to heat treatment appeared as follows; (1) The thermal conductivities and specific heats of the metallic glasses were constant with heat treatment below or close to Tg. (2) The thermal conductivities of the metallic glasses increased with heat treatment above Tg because of crystallization of the metallic glass. (3) The metallic glass with heat treatment crystallized more quickly if the heat treatment temperature was far from Tg. Therefore, the metallic glass crystallized above Tg, and the increase in thermal conductivity of the metallic glass caused it to crystallize. With heat treatment above Tg, the specific heats of the metallic glasses just before crystallization tended to be lower than that of the as-synthesized sample. At these points, each constituent element had been moving toward energetic equilibrium points for phase transformation from amorphous to crystalline. This clear decrease in the specific heat of the metallic glass might be the premonitory symptom for crystallization of the metallic glass. This matter will need to be investigated future.
131
5. Conclusions The thermophysical properties, such as the thermal conductivity, thermal diffusivity and specific heat, of Zr–Cu–Al metallic glasses with different compositions were measured using the hot-disk method at room temperature. When the Zr content of the Zr–Cu–Al metallic glass decreased from 65 at.% to 45 at.%, the thermal conductivity gradually increased, with the maximum value obtained with a composition of Zr:Cu:Al = 50:39.3:10.7(at.%) because of the close packing of the constituent atoms. These metallic glasses were not crystallized with heat treatment below Tg, and their thermophysical properties were almost constant. However, these metallic glasses began to crystallize with heat treatment above Tg, as the thermal conductivity increased with the progress of crystallization of the metallic glass.
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Journal of Non-Crystalline Solids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l
Thermophysical properties of Zr–Cu–Al metallic glasses during crystallization Hideaki Nagai a,⁎, Mikito Mamiya a, Takeshi Okutani b a Thin Film Processing Group, Advanced Manufacturing Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 5, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan b Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa 240-8501, Japan
a r t i c l e
i n f o
Article history: Received 22 February 2010 Received in revised form 27 August 2010 Keywords: Zr–Cu–Al metallic glass; Thermophysical properties; Hot-disk method; Crystallization; Heat treatment
a b s t r a c t The crystallization behavior of Zr–Cu–Al metallic glasses was studied using thermophysical property measurements. When the Zr content of Zr–Cu–Al metallic glass decreased from 65 at.% to 45 at.%, the thermal conductivity gradually increased and the maximum value obtained was the composition of Zr:Cu: Al = 50:39.3:10.7(at.%). These metallic glasses were not crystallized upon heat treatment below the glass transition temperature Tg, and the thermophysical properties of these metallic glasses were almost constant. In contrast, these metallic glasses started to crystallize upon heat treatment above Tg after a certain derived time, and their thermal conductivity increased with the crystallinity of the metallic glass. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Since the 1990s, investigations of multicomponent metallic alloys have led to the development of metallic glasses with high glass-forming ability [1,2]. Crystallization is prevented by quenching the molten metal from the liquid disordered state to the solid state. In particular, Zr-based metallic glasses are of great interest in engineering fields because of a large region of supercooled liquid [3] which is defined by the temperature interval between the glass transition temperature Tg and the crystallization temperature Tx, ΔTx (ΔTx = Tx − Tg), and by its low-cooling-rate fabrication (less than 103 K/s) as compared with general amorphous alloys ( above 104 K/s). Because of the applications of these metallic glasses, it is important to acquire full knowledge of their physical properties, such as the mechanical, electrical, magnetic, and thermal transport properties of the materials. Although the first three properties mentioned have been thoroughly investigated, there has been very little work on the thermal conductivity of metallic glasses because of the difficulty of making the accurate thermal conductivity measurements on typical thin samples (less than 50 μm) [4]. Some millimeter-thick Zr-based metallic glasses have been obtained as samples whose thermal conductivity can be measured by the laser flash method [5,6], but many metallic glasses cannot be measured by this method because of difficulty of obtaining uniform samples with millimeter thickness.
For measuring the thermal conductivity of thin samples, we focused on the hot-disk method developed by Gustafsson [7]. This method uses a transient plane source (TPS) element as both the heat source and the temperature sensor in a manner similar to the use of a thin wire in the hot-wire method. The TPS element of the hot-disk sensor is made of a thin metal foil and its conducting pattern is a double spiral. By using the hot-disk method, the thermal conductivity of both the insulating materials and the electrically conducting materials can be measured because each side of the thin metal foil is coated with a thin uniform insulating sheet. This method can be applied to thermal conductivity measurement of samples with bulk, thin-plate, or thin-film shapes by selecting the analytical model corresponding to the sample shape. Therefore, it is possible to measure the thermal conductivity of many thin metallic glasses. Moreover, this method can simultaneously measure the thermal diffusivity and specific heat per unit volume of the metallic glass samples. In this study, the thermal conductivity, thermal diffusivity and specific heat per unit volume of Zr–Cu–Al metallic glasses with different compositions were measured by the hot-disk method. In addition, the crystallization behavior of these metallic glasses was evaluated from the perspective of their thermophysical properties because of the establishment of optimum conditions for utilizing metallic glasses without crystallization. 2. Experimental methods 2.1. Principle of the hot-disk method
⁎ Corresponding author. Tel.: + 81 29 861 4404. E-mail address: [email protected] (H. Nagai). 0022-3093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2010.09.078
The normal experimental procedure for the hot-disk method is to pass a constant current through a hot-disk sensor and simultaneously
H. Nagai et al. / Journal of Non-Crystalline Solids 357 (2011) 126–131
record voltage changes derived from temperature changes in the sensor. When analyzing the behavior of a hot-disk sensor during a transient recording, it is convenient to express the time-dependent resistance [R(t)] using the following equation [8]: RðtÞ ¼ R0 f1 þ α½ΔTi þ ΔTðτÞg;
ð1Þ
where R0 is the resistance of the hot-disk sensor before the transient recording, α is the temperature coefficient of the resistance, ΔTi is a small temperature drop derived from heat loss transferred to the electrically insulating layer of the hot-disk sensor, and ΔT(τ) is the time-dependent temperature increase of the thin metal foil. The temperature increase is expressed in this equation as a function of only one variable, τ, which is defined as 1=2
τ ¼ ðt=θÞ
2
; θ ¼ d =κs ;
ð2Þ
where t is the time elapsed from the start of the transient heating, θ is the characteristic time, d is the radius of the hot-disk sensor, and κs is the thermal diffusivity of the sample. It is expected that ΔTi would be constant after a short initialization period of Δti, because the heat transferred to the sample through the insulating layer becomes constant due to the release of constant power from the thin metal foil, and Δti is estimated as 2
Δti ¼ δ =κi ;
ð3Þ
where δ is the thickness of the insulating layer and κi is the thermal diffusivity of the insulating layer. However, ΔTi only becomes constant after a much longer period than Δti because of inadequate thermal contact between the thin metal foil, the insulating layer and the sample, along with other factors (nonideal electrical components in the circuit, finite specific heat of the sensor, software and hardware delays between triggering the transient event and recording data, etc.). A “time correction” term, Δtcorr , is introduced to simplify these factors. The data points at the beginning of the transient recording at times less than Δtcorr are not used in the fitting of the analytical model of the hot-disk method because these data include the effects of the additional factors. ΔT(τ) is affected by the power output of the hot-disk sensor, the design parameters of the sensor, the thermal transport properties of the sample, and the shape of the sample. ΔT(τ) is given by the following equation for a disk-shaped sensor [7], from which the thermal conductivity and diffusivity can be obtained: −1 3=2 ΔTðτÞ ¼ P0 π dλ DðτÞ;
ð4Þ
where P0 is the total output power and λ is the thermal conductivity of the sample. The function D(τ) is a theoretical expression of the time-dependent temperature increase. The standard hot-disk method assumes that the hot-disk sensor is located in an infinite sample, and the function D(τ)std express as following equation, which models the conducting pattern of the disk-shaped sensor by assuming that the disk is made up of a number of concentric ring sources: m. DðτÞstd = ½mðm + 1Þ 2
2
τ
∫0 dσ
1 3 0 2 2 l +k lk 2 4 5: AI0 ∑ l ∑ k exp@ ×σ 2m2 σ 2 4m2 σ 2 l=1 k=1 m
ð5Þ
m
When the sample has a limited extension in the direction perpendicular to the sensor but is still considered infinite in the
127
plane of the sensor, that is, when the sample is slab sheet, the function D(τ)slab express as following equation: DðτÞslab
#) i2 h 2 = ½mðm + 1Þ ∫ dσ × σ 1 + 2 ∑ exp 2 0 σ r i=1 1 2 3 0 m m l2 + k 2 lk 4 5: @ A I0 × ∑ l ∑ k exp 2m2 σ 2 4m2 σ 2 l=1 k=1 2
(
τ
2
∞
"
ð5′Þ As h, the thickness of the slab sheet, tends to infinity, we obtain the same function as the one used in the standard hot-disk method, where the sample is considered infinite in all directions. This method of thermophysical property measurement of a slab sheet using Eq. (5′) is called the slab method. When the slab sheet samples are measured by the slab method, the outside surfaces of the slab sheets need to be insulated by a material with low thermal conductivity because heat loss should be kept low compared with the total output of power in the sensor during the transient recording. We substituted Eq. (4) into Eq. (1) and obtained Eq. (6). RðtÞ¼ R0 ½ð1 þ αΔTi Þ þ αP0 ðπ
3=2
1
dλÞ DðτÞ:
ð6Þ
When the characteristic time (θ) is equal to the value that is calculated from the radius of the hot-disk sensor and the thermal diffusivity of the sample by Eq. (2), a plot of the measured resistivity R (t) vs D(τ) will, according to Eq. (6), yield a straight line. However, D (τ) at each data recording time is calculated for any value of θ, and the correlation coefficients of the straight line fit of R(t) vs D(τ) are then calculated. The θ of the optimum straight line fit is used to estimate the thermal diffusivity of the sample [Eq. (2)], and the thermal conductivity is calculated from the slope of the fit. When the measurement time, measured from the start of transient heating, is close to the characteristic time (ideally 0.5 b t/θ b 1.0), the thermal diffusivity and thermal conductivity of the sample can be reliably measured. The thermal conductivity and thermal diffusivity of the sample are interrelated as follows. λ ¼ ρCp κs :
ð7Þ
Here, ρ is the density of the sample and Cp is its specific heat. The specific heat per unit volume (ρCp) can be calculated using the sample thermal diffusivity and thermal conductivity. The reproducibility of the thermal conductivity, thermal diffusivity and specific heat per unit volume measured by the slab method were ±2 %, ±5 % and ±3 %, respectively. 2.2. Preparation of Zr–Cu–Al metallic glasses Starting samples of Zr–Cu–Al alloy with different compositions were synthesized by arc-melting. Zr(99.9% pure), Cu(99.99% pure), and Al (99.99% pure) ingots were supplied by Rare Metallic Co., Ltd.. Zr–Cu–Al metallic glass with Zr:Cu:Al = 65:27.5:7.5 (at.%) was selected as a parent sample [9], and the Zr contents were changed with a constant ratio of Cu and Al[Cu:Al = 11:3 (in mole)]. The starting Zr–Cu–Al alloy ingot was cut into small blocks (approximately 0.75 g) for rapid solidification experiments. Fig. 1 schematically diagrams the rapid solidification experiment. Generally, the starting alloy of the metallic glass is melted in the quartz glass tube. Complete melting of the starting alloy is important to obtain metallic glass with an entirely amorphous structure, but it is difficult to confirm complete melting of the alloy in the quartz glass tube. Moreover, the Zr–Cu–Al alloy melt can easily react with the quartz glass making it difficult to premake the melt without oxygen contamination, which strongly affects the glass-forming ability and crystallization behavior of metallic glasses [10]. To solve these
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but any shift of the composition due to the addition of tungsten was negligible. For example, 0.75 g of a starting sample block with Zr:Cu: Al = 65:32.5:7.5 (at.%) would be changed into one with Zr:Cu:Al: W = 64.8:32.4:7.5:0.3 (at.%) by adding 5 mg of tungsten. The dropped sample was rapidly solidified by the copper spin rotor, which rotated at about 5000 rpm. 2.3. Characterization of Zr–Cu–Al metallic glasses
Fig. 1. Schematic diagram of rapid solidification equipment for preparing of the metallic glass.
problems, the starting Zr–Cu–Al alloy block was tied with tungsten wire 0.1 mm in diameter and hung in the quartz glass tube of the equipment without contacting any oxide material to prevent contamination by oxygen coming from the crucible or nozzle. Argon gas (purity 99.9995%, oxygen content less than 0.2 ppm) was introduced into the equipment at a pressure of 1.0 × 105 Pa after the chamber had initially been pumped down to below 10− 2 Pa. Fig. 2 presents a typical temperature profile of the starting sample block during heating. A B-type thermocouple covered by quartz glass was attached to the starting sample block only for measuring the sample temperature and was specifically not inserted, during the preparation of the metallic glass in order to prevent oxygen contamination. At first, the starting sample block [Fig. 2(a)] was heated by moderate infrared heating, ultimately reaching about 1273 K, higher than the melting point of the Zr–Cu–Al alloys. At this time, the starting sample block was visually confirmed to be completely melted and still hanging by adhesion to the tungsten wire because of good wettability [Fig. 2(b)]. Introducing extra infrared heating quickly increased the temperature of the melted sample, which then dropped toward the cooling spin rotor at around 1850 K [Fig. 2(c)]. At this point, a piece of the tungsten wire (about 5 mg) was dissolved into the melted sample,
Fig. 2. Typical temperature profile of the starting block during heating.
The crystalline structure of the obtained samples was analyzed by X-ray diffraction (XRD; MAC Science M03XHF22). The exothermic and endothermic reactions associated with Tg and Tx were measured by differential scanning calorimetry (DSC; Rigaku DSC8270) at up to 1273 K in a vacuum. The heating rate was 10 K/min. The thermophysical properties of the samples were measured by the slab method. Fig. 3 schematically diagrams the sample plate setting for the slab method. The rather rough surfaces of the obtained samples were flattened to less than 1 μm of roughness by polishing in order to obtain good thermal contact between the sample and the hot-disk sensor. The hot-disk sensor was placed between two polished sheet samples of the similar thickness, and the outsides of the samples were covered with polystyrene foam to suppress heat loss. The resistivities of the polished samples were measured using the Van der Pauw method (Toyo Corp.; Resi Test 8340) to support later estimates of the electron contribution to the thermal conductivity. The polished samples were annealed in a vacuum at a temperature below Tg or between Tg and Tx. Their thermophysical properties were then measured by the slab method only after they had cooled down to room temperature because the hot-disk sensor and polystyrene foam used in this study can only be used at much lower temperature than the annealing temperature. The annealed samples were also analyzed by XRD. 3. Results 3.1. Thermophysical properties of Zr–Cu–Al metallic glasses Fig. 4 presents a photograph and XRD pattern of the solidified Zr65Cu27.5Al7.5 sample after spin rotor cooling. A disk-shape sample about 30 mm in diameter and 0.2 mm thick was obtained. The sample had a rough surface with a large whirling pattern and a small wave pattern. Because the high-speed spin rotor used as a cooling media exhibited a slight vibration, this rough surface might result from rapid solidification, with the shape of the melt deformed by rotation and vibration. To measure thermophysical properties of the obtained sample, the sample surface needed to be flat, as mentioned above. Therefore, the sample surface was polished, and a flat plate about 0.1 mm thick was obtained. The solidified sample was shown to be amorphous by XRD, as seen in Fig. 4, and the DSC result reveals that there was clear Tg point on the solidified sample, as mentioned below. Based on these results, we can say that a metallic glass plate could be synthesized by using spin rotor cooling. When melts with Zr content between 45 and 65 at.% were solidified by spin rotor cooling, metallic glasses with entirely amorphous phase and similar sample shapes could be obtained, but the solidified sample with 40 at.% Zr-content was a mixture of crystalline phase and amorphous phase. Table 1 lists the thermal conductivity, thermal diffusivity, and specific heat per unit volume of Zr–Cu–Al metallic glasses measured by the slab method as a function of Zr content for Zrx(Cu11Al3)(100 − x)/14 metallic glasses. Table 1 also provides reference data for similar compositions reported in the literature [6,11,12]. Our measured data were in good agreement with the reference data. The thermal conductivity and specific heat of Z50Cu39.3Al10.7 metallic glass had their maximum values in these compositions of metallic glasses.
H. Nagai et al. / Journal of Non-Crystalline Solids 357 (2011) 126–131
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Fig. 3. Schematic diagram of sample plate setting for the slab method.
3.2. Relationship between thermophysical properties and crystallization of Zr–Cu–Al metallic glasses by heat treatment Table 2 gives Tg, Tx, and ΔTx as a function of the Zr content for Zrx (Cu11Al3)(100 − x)/14 metallic glasses and provides reference data for similar compositions reported in the literature [9,13]. Tg and Tx of our sample decreased simply with Zr content, and ΔTx increased simply with Zr content. These tendencies of our sample with respect to Zr content were similar to those of the references, but our values differed from the reference values. Figs. 5 and 6 plot the thermal conductivity and specific heat of metallic glasses following heat treatment at 673 K and 698 K. The crystalline structure was also measured by XRD at each point of the thermophysical property measurements. With heat treatment at
673 K, the thermal conductivities and specific heats of the metallic glasses with 45, 50 and 55 at.% Zr-content were almost constant during the entire measurement time. The thermal conductivity of metallic glass with 60 at.% Zr-content was constant for the first few hours at this temperature, but after that the thermal conductivity increased and the metallic glass began to crystallize. However, the specific heat of this metallic glass was decreased by the heat treatment regardless of crystallization. The thermal conductivity of metallic glass with 65 at.% Zr-content increased quickly during just one hour of heat treatment. With heat treatment at 698 K, we measured the thermal conductivities and specific heats of only metallic glasses with 50 or 55 at.% Zr-content because the thermal conductivity of metallic glass with 45 at.% Zr-content was predicted to be constant following heat treatment at 698 K, close to Tg for this metallic glass, for 10 h. The thermal conductivity of metallic glass with 50 at.% Zr-content was constant for the first few hours at this temperature, but after that the thermal conductivity increased and the metallic glass began to crystallize. The specific heat of this metallic glass with a 1 h heat treatment was the same as that of the assynthesized metallic glass, but the specific heats of samples heattreated for between 2 h and 4 h were lower than that of the assynthesized sample, even though this metallic glass still had an amorphous structure and retained the same thermal conductivity. The thermal conductivity of metallic glass with 55 at.% Zr-content
Table 1 Thermophysical properties of Zr–Cu–Al metallic glass measured by hot-disk method at room temperature. Composition of metallic glass
Thermal conductivity (W/mK)
Thermal diffusivity (×10− 6 m2/s)
Specific heat per unit volume (× 106 J/m3K)
Remarks
Value Std. dev.⁎ Value Std. dev.⁎ Value Std. dev.⁎
Fig. 4. Typical photograph of the metallic glass solidified by spin rotor cooling and its XRD pattern.
Zr45Cu43.2Al11.8 Z50Cu39.3Al10.7 Zr55Cu35.4Al9.6 Zr60Cu31.4Al8.6 Zr65Cu32.5Al7.5 Zr50Cu40Al10 Zr55Cu35Al10 Zr55Cu30Ni5Al10 Zr55Cu45
5.11 6.20 5.53 5.54 5.23
0.24 0.10 0.22 0.11 0.19
5.02 5.88
*Std. dev.: Standard deviation.
2.65 2.55 2.38 2.35 2.76 2.3 2.1 2.2 2.41
0.16 0.11 0.14 0.17 0.17
1.94 2.43 2.33 2.36 1.90
2.42
0.20 0.09 0.18 0.12 0.18 Ref. Ref. Ref. Ref.
[11] [11] [6] [12]
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H. Nagai et al. / Journal of Non-Crystalline Solids 357 (2011) 126–131
Table 2 Compositional dependence of the glass transition temperature, crystallization temperature, and ΔTx. Composition of metallic glass
Glass transition temperature (Tg, K)
Crystallization temperature (Tx, K)
ΔTx(K)
Remarks
Zr45Cu43.2Al11.8 Z50Cu39.3Al10.7 Zr55Cu35.4Al9.6 Zr60Cu31.4Al8.6 Zr65Cu32.5Al7.5 Zr45Cu43Al12 Zr50Cu40Al10 Z55Cu35Al10 Zr65Cu32.5Al7.5 Zr65Cu32.5Al7.5 Zr45Cu43Al12 Zr50Cu40Al10 Z55Cu35Al10
690 685 668 635 625 690–699 670–679 650–659 649b 656 670–679 650–659 649b
756 758 741 716 710 760–769 740–749 730–739 729b 745 750–759 750 729b
66 73 73 81 85 60–69 70–79 70–79 60–69 89 70–79 N 80 70–79
Ribbon, Ref. [13] Ribbon, Ref. [13] Ribbon, Ref. [13] Ribbon, Ref. [13] Ribbon, Ref. [9] Bulk, Ref. [13] Bulk, Ref. [13] Bulk, Ref. [13]
increased quickly after only one hour of heat treatment, and the specific heats with heat treatment for 1 h or less were lower than that of the as-synthesized one.
4. Discussion 4.1. Thermophysical properties of Zr–Cu–Al metallic glasses
Fig. 6. Effect of heat treatment on thermal conductivities and specific heats of the metallic glasses. Heat treatment temperature: 698 K.
Table 3 lists the resistivity and thermal conductivity of Zr–Cu– Al metallic glasses with different Zr content. The thermal conduc-
: 45at%Zr,
7.0
λ ¼ λelectron þ λphonon ;
: 50at%Zr,
: 55at%Zr
6.0 5.0
3.0 2.5 2.0 1.5 0
2
4
6
8
Specific heat 6 3 per unit volume (10 J/m K)
Thermal conductivity (W/mK)
(1)Annealing below or close to Tg
10
Annealing time (h)
7.0 6.0 3.0
5.0
2.5 2.0 0
2
4
: 65at%Zr
6
8
10
1.5
Specific heat 6 3 per unit volume (10 J/m K)
Thermal conductivity (W/mK)
(2)Annealing above Tg
: 60at%Zr,
tivity of the material, λ, is the sum of the electron and phonon contributions:
Annealing time (h) Fig. 5. Effect of heat treatment on thermal conductivities and specific heats of the metallic glasses. Heat treatment temperature: 673 K.
ð8Þ
where λelectron is the electron thermal conductivity and λphonon is the phonon thermal conductivities. The electron contribution to the thermal conductivity can be estimated by the Wiedemann–Franz law: λelectron ¼ L × T=r;
ð9Þ
where L is the Lorenz number, which is 2.445 × 10− 8 W · Ω · K− 2 for a degenerate free-electron gas system; T is the temperature; and r is the resistivity. It was found that Z50Cu39.3Al10.7 metallic glass had a higher phonon contribution to the thermal conductivity because the electron contribution of the thermal conductivity of the metallic glasses was almost constant, independent of the composition of the metallic glasses. This composition is close to the ternary eutectic point of the Zr–Cu–Al alloy system [Zr:Cu:Al= 50:40:10 (at.%)] [14], and it has been reported that the atoms in Zr50Cu40Al10 metallic glass are closely packed compared with Zr70Cu20Al10 metallic glass [15]. Therefore, the higher thermal conductivity and specific heat of Z50Cu39.3Al10.7 metallic glass were considered to result in close packing of the constituent atoms. Table 3 Resistivity and thermal conductivity of Zr–Cu–Al metallic glasses at room temperature. Composition of metallic glass
Resistivity (10− 6 Ωm)
Thermal conductivity (W/mK) λ⁎
λelectron⁎⁎
λphonon⁎⁎⁎
Zr45Cu43.2Al11.8 Z50Cu39.3Al10.7 Zr55Cu35.4Al9.6 Zr60Cu31.4Al8.6 Zr65Cu32.5Al7.5
1.77 1.86 1.88 1.83 1.63
5.11 6.20 5.53 5.54 5.23
4.05 3.85 3.81 3.91 4.40
1.06 2.35 1.72 1.63 0.83
*λ= λelectron + λphonon.. **λelectron: Electron contribution to thermal conductivity. ***λphonon: Phonon contribution to thermal conductivity.
H. Nagai et al. / Journal of Non-Crystalline Solids 357 (2011) 126–131
4.2. Relationship between thermophysical properties and crystallization of Zr–Cu–Al metallic glasses after heat treatment Tg, Tx, and ΔTx of metallic glasses are useful factors for estimating the glass-forming ability and the stability of the glassy phase. However, Yokoyama et al. reported that splat-cooled and tilt-cast metallic glasses had different thermal properties based on DSC measurements [13], and we have reported that the cooling history of metallic glass is important for determining thermal properties based on DSC measurements [16]. From these reports, Tg, Tx, and ΔTx of metallic glasses are considered to depend on the cooling process as well as the sample composition. Therefore, the values of our sample in Table 2 were used to determine the annealing temperature for evaluating the crystallization of metallic glasses in this study. Based on the results of Table 2 and Figs. 5, 6, the relationship between the crystallization behavior and thermophysical properties of the metallic glass with respect to heat treatment appeared as follows; (1) The thermal conductivities and specific heats of the metallic glasses were constant with heat treatment below or close to Tg. (2) The thermal conductivities of the metallic glasses increased with heat treatment above Tg because of crystallization of the metallic glass. (3) The metallic glass with heat treatment crystallized more quickly if the heat treatment temperature was far from Tg. Therefore, the metallic glass crystallized above Tg, and the increase in thermal conductivity of the metallic glass caused it to crystallize. With heat treatment above Tg, the specific heats of the metallic glasses just before crystallization tended to be lower than that of the as-synthesized sample. At these points, each constituent element had been moving toward energetic equilibrium points for phase transformation from amorphous to crystalline. This clear decrease in the specific heat of the metallic glass might be the premonitory symptom for crystallization of the metallic glass. This matter will need to be investigated future.
131
5. Conclusions The thermophysical properties, such as the thermal conductivity, thermal diffusivity and specific heat, of Zr–Cu–Al metallic glasses with different compositions were measured using the hot-disk method at room temperature. When the Zr content of the Zr–Cu–Al metallic glass decreased from 65 at.% to 45 at.%, the thermal conductivity gradually increased, with the maximum value obtained with a composition of Zr:Cu:Al = 50:39.3:10.7(at.%) because of the close packing of the constituent atoms. These metallic glasses were not crystallized with heat treatment below Tg, and their thermophysical properties were almost constant. However, these metallic glasses began to crystallize with heat treatment above Tg, as the thermal conductivity increased with the progress of crystallization of the metallic glass.
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