Fig. 1. Bright field TEM image and selected area diffraction pattern of a Ti50Cu25Ni20Sn5 sample mechanically alloyed for 20 h

Động học kết tinh của hợp kim vô định hình Ti50Cu25Ni20Sn5 chế tạo bằng phương pháp nghiền cơ học

In this work, the crystallization kinetic parame- ters ofTi50Cu25Ni20Sn5 amorphous alloy were cal- culated to explain the details of nucleation and growth behaviors during crystallization process…

Crystallization kinetics of mechanically milled Ti50Cu25Ni20Sn5 amorphous alloy

Hanoi University of Science and Technology, Vietnam


Ngày nhận bài: 16/5/2018, Ngày duyệt đăng: 24/7/2018


The crystallization kinetics of mechanically milled Ti50Cu25Ni20Sn5 amorphous alloy was studied by DSC in isothermal mode. The Avrami exponent was determined from the Johnson-Mehl-Avrami equation and showed that at the first stage the crystallization mechanism is a three-dimensional diffusion-controlled nucleation and growth with increasing high nucleation rate. In the second stage, the local Avrami exponent decreases close to 2 with the increase of the crystalline volume fraction suggesting a reduction of nucleation rate. Crystals of the Ti2Ni and γCuTi intermetallic compounds are formed after crystallization process as reported before. The activation energy increas- es with increasing crystalline volume fraction.

Keywords: Crystallization kinetics, Ti50Cu25Ni20Sn5 amorphous alloy.


Động học tinh thể hóa bột hợp kim vô định hình Ti50Cu25Ni20Sn5 chế tạo từ phương pháp nghiền cơ học được nghiên cứu bằng phương pháp phân tích nhiệt lượng kế vi sai sử dụng chế độ đẳng nhiệt. Số mũ Avrami được xác định từ phương trình Johnson-Mehl-Avrami cho thấy ở giai đoạn đầu tiên quá trình kết tinh là sự tạo mầm và phát triển mầm theo cơ chế khuếch tán điều khiển theo ba chiều với tốc độ phát triển mầm cao. Trong giai đoạn thứ hai, số mũ Avrami cục bộ giảm xuống giá trị gần 2 với sự tăng của phần thể tích tinh thể cho thấy giảm tỷ lệ tạo mầm. Các tinh thể của hợp chất liên kim Ti2Ni và γ-CuTi đã được tạo thành sau quá trình kết tinh như đã thông báo trước đây. Năng lượng hoạt hóa tăng lên khi tăng tỷ phần thể tích tinh thể.

Từ khóa: Động học kết tinh, hợp kim vô định hình Ti50Cu25Ni20Sn5 .


The main advantages of Ti-based metallic glasses are high specific strength and excellent corrosion resistance [1-3]. Ti-rich glass metallic alloys exhibit the supercooled liquid region (SLR) during heating such as Ti-Cu-Ni alloy. However, SLR of this alloy is about 40 K corresponding to glass forming ability (GFA) not enough high for forming bulk amorphous alloys [4]. For increasing consolidation ability of this alloy, it is necessary to expand the SLR by addition of alloying elements. With a small amount of Sn replaced for Ni in Ti-Cu- Ni amorphous alloy, the tensile strength can be improved significantly as reported in [5]. Another effect on quality of bulk sample is thermal stability of glass metallic materials. It is well known that metallic glass materials are metastable and tend to crystallize during continuous heating. The crys- tallization mechanism, the structure and composition of the crystallization products depend on the initial chemical composition of the amorphous phase and its preparation method. The crystalliza- tion behavior of Ti-Ni-Cu and Ti-Ni-Cu-Sn amor- phous alloys has been studied recently [4, 6]. The addition of Sn to Ti50Ni25Cu25 alloy changes the shape of differential scanning calorimetry (DSC) traces from the single heat release to a double- step one, however the crystallization kinetics dur- ing crystallization process is unstudied. There are numerous reports on the crystallization kinetics of amorphous materials in non-isothermal or isother- mal modes. In the isothermal method, the sample is brought to a temperature above the glass transition temperature and the heat produced during the crystallization process at a constant tempera- ture is recorded as a function of time. Crystallization kinetics can be described by three kinetic parameters: the activation energy for crys- tallization (Ec), the Avrami exponent (n), and the frequency factor (ko) which reflects the character- istics of nucleation and growth processes.

In this work, the crystallization kinetic parame- ters ofTi50Cu25Ni20Sn5 amorphous alloy were cal- culated to explain the details of nucleation and growth behaviors during crystallization process.


Amorphous alloy powder with nominal com- positions  of  Ti50Cu25Ni20Sn5  was  synthesized via mechanical alloying [7]. A mixture of Ti, Cu, Ni and Sn element powders was milled in a planetary ball mill (P100, South Korea) using hard- ened steel vials and balls of 5 mm diameter. The rotation speed of the jar was 300 rpm and the ball to powder weight ratio was 20/1. The microstructure of the amorphous powder after 20 h of milling was studied by transmission electron microscopy (TEM) with a JEOL JEM-2100 micro- scope.  DSC  was  conducted  using  NETZSCH STA 409C to study isothermal crystallization kinetics of the amorphous alloy. The samples were heated up to the isothermal annealing tem- peratures (713-723 K) at a heating rate of 20 K/min, and then held for 40 min.



XRD pattern of theTi50Cu25Ni20Sn5 alloy after milling for 20 h showed a fully amorphous structure [8] and confirmed by TEM analysis as shown in Fig.1. A selected area diffraction pattern taken from this region shows a diffuse halo ring which is characteristic of the amorphous structure.

Fig. 2. Isothermal scans of 20 h MATi50Cu25Ni20Sn5 alloy

The DSC scan for the amorphousTi50Cu25Ni20Sn5 alloy mentioned in [7] showed an endothermic event of the glass transition with a SLR (Tx = Tx – Tg = 47 K) which is higher than that of Ti50Cu25Ni25 amorphous alloy [4]. Considering this thermodynamic effect, three different anneal- ing temperatures between Tg (glass transition temperature) and Tx1 (on-set crystallization tem- perature) were chosen: 713, 718 and 723 K to determine precipitation phases at different crystal- lization steps. The isothermal thermograms of amorphous alloy are shown in Fig. 2. Each DSC curve exhibits an incubation period followed by exothermic peaks which corresponds to the crys- tallization of the metallic glass. The incubation time decreases with the increase in isothermal anneal- ing temperature because atoms become more mobile at higher annealing temperatures, resulting in more energy fluctuation necessary for facilita ing long-range atomic ordering of large scale crys- tallization [9]. The crystalline volume fraction x at different annealing temperatures can be obtained by integrating the isothermal DSC curves as plot- ted in Fig. 3. All the curves exhibit sigmoid type. At higher annealing temperature, the curve becomes steeper  that  means  the  crystallization  process gets faster. Amorphous structure of milled powders transferred to crystalline structure completely after 40 min for sample annealed at 713 K.

Fig. 3. Transformed fraction ofTi50Cu25Ni20Sn5 alloy as a function of the time

The isothermal crystallization kinetics of the amorphous alloys can be described by Johnson- Mehl-Avrami (JMAK) equation as [10]:

where x is the crystalline volume fraction (%), τ is the incubation time (the time interval between the sample reaching the isothermal temperature and the initiation of crystallization), n is the Avrami exponent, and k is the crystallization rate constant which is influenced by the annealing temperature and can be determined by Arrhenius relation [11]:

where ko is a constant, and Ec is the local acti- vation  energy  for  crystallization. From  equation (1), the values of k and n can be determined by the following equation:

Fig. 4. JMA plots of ln[-ln(1-x(t))] versus ln(t-τ)
at different annealing temperatures
By plotting ln[-ln(1-x(t))] against ln(t-τ) will get the n values from the slope of curves, as shown in Fig. 4. It is found that the slope of curve mainly keeps nearly constant in the whole crystallization process, which indicates that the nucleation and growth of intermetallic phases  have  the  similar way in the crystallization process. The local Avrami exponent n(x) was used to investigate the nucle- ation and growth behavior of metallic glass during crystallization process [12]:

Fig. 5. Local Avrami exponent n(x) versus crys- talline volume fraction x at different annealing temperatures

Fig. 5 shows local Avrami exponent n(x) versus the crystallization fraction x. The local Avrami exponent n as a function of the crystalline volume fraction was considered in the range (10 < x < 90) due to the error at lower and higher crystalline vol- ume fractions [13]. The n(x) curves for three differ- ent annealing temperatures are in the same ten- dency by increasing the n value first and then decreasing it. At the high annealing temperatures of 718 and 723 K, the n(x) value increase from 3.8 and 4.1 to 4.2, respectively at the first stage (10 ≤ x ≤20), reveals that the crystallization mechanism is a three-dimensional diffusion-controlled nucleation and growth with increasing high nucleation rate [14]. At the second stage, the local Avrami exponent decreases close to 2 with the increase of the crystalline fraction (20 ≤ x ≤ 90). The n(x) val- ues decreased gently, suggesting a reduction of nucleation rate. The n(x) values (40 < x < 60) at annealing temperature of 718 K were slightly higher than that at 723 and 713 K, which implied that the nucleation rate was higher. Although the mech- anism of nucleation and growth remained unchanged, the nucleation rate decreased rapidly at higher temperatures. When x approached approximately 82 %, the local Avrami exponents at different temperatures have lowest value. This might indicate that the nucleation rate is minimum. The maximal reduction of n(x) was achieved at 723 K. The value of n(x) was 1.8 when x was around 82 %, reflecting that the nucleation rate was equal to zero. For diffusion-controlled growth, the range 1.5 < n < 2.5 reflects growth of particles with decreasing nucleation rate [15]. As discussed above, n(x) increased with increasing isothermal annealing  temperature  and  the  nucleation  rate was slowed down; the crystallization was changed from nucleation to growth gradually. Therefore, the annealing should be carried out at lower tempera- ture nearby Tx1. Meanwhile, the annealing time should be correspondingly shortened when the temperature increases.

To further characterize the sensitivity of the crystallization rate to temperature, activation energy Ec(x) of crystallization was evaluated based on Arrhenius equation:

where t(x) is the time-consuming consistent with x, to is a time constant, Ec(x) is the local acti- vation energy, R is the universal gas constant, and T is the isothermal temperature. The plot of ln t(x) against 1/(RT) yields a straight line with a slope of Ec(x). Then the relationship between the local activation energy Ec(x) and crystalline volume fraction was formulated in Fig. 6. Ec(x) increased with increasing the crystalline volume fraction, which could be classified as three ranges: x < 20 %, 20 % < x < 80 % and x > 80 %. In the first range with x < 20 %, the lower activation energy means a low energy barrier of crystallization.

Fig. 6. Activation energy Ec as function of crystallization volume fraction x for glass metallicTi50Cu25Ni20Sn5 alloy

Once the crystallization was initiated, the activation energy was increased rapidly. Ec(x) was increased linearity in the second range with 20 % < x < 80 %, implying that the crystallization proceeded stably in this region. When x > 80 % in the last range, the ener- gy barrier increased sharply. It was known that the amorphous structure was in a metastable high energy state. During the crystallization of theTi50Cu25Ni20Sn5 glassy alloy, crystals of the Ti2Ni and γCuTi intermetallic compounds may be formed after annealing at 755 K as reported [8]. It became more difficult for the following crystallization in the residual amorphous matrix. Hence, the crystalliza- tion slowed down in the final range, the nucleation was limited by growth process gradually. It can be seen that with increase of x, Ec(x) decreases for Ti50Cu25Ni25 [4], while in this work, Ec(x) increas- es when increasing crystalline volume fraction forTi50Cu25Ni20Sn5 alloy. This indicates that the addition of Sn makes the atomic diffusion in the crys- tallization process more difficult and decreases the crystallization rate, leading to a significant stability of glass phase.


The crystallization process of amorphous Ti50Cu25Ni20Sn5 alloy was investigated with DSC. Isothermal thermograms of amorphous alloy at dif- ferent annealing temperatures of 713, 718 and 723 K exhibits an incubation period followed by exothermic peaks which corresponds to the crys- tallization of the metallic glass. The crystallization mechanism at the first stage of crystallization process is a three-dimensional diffusion-controlled nucleation and growth with increasing high nucleation rate. In the second stage, the local Avrami exponent in the range of 1.5 < n < 2.5 reflects growth  of  particles  with  decreasing  nucleation rate. Sn addition into Ti-Cu-Ni alloy improved sig- nificantly the GFA due to reducing the atomic dif- fusion during crystallization process.


The authors would like to thank Prof. Ji-Soon Kim for financial support and allowing to finish this work in Lab. for Nano-Particulate Materials Processing, University of Ulsan.


  1. Inoue, A., et al., Ti-based amorphous alloys with a wide supercooled liquid region. Materials Letters, 1994, 19(3), p. 131-135.
  2. Kishimura, H. and H. Matsumoto, Fabrication of Ti-Cu-Ni-Al amorphous alloys by mechanical alloying and mechanical milling. Journal of Alloys and Compounds, 2011, 509(12), p. 4386-4389.
  3. Louzguine, D.V. and A. Inoue, Nanocrystallization of Ti-Ni-Cu-Sn amorphous alloy. Scripta Materialia, 2000, 43(4), p. 371-376.
  4. Chang, S.-H., S.-K. Wu, and H. Kimura, Crystallization Kinetics of Ti50Ni25Cu25 Melt-Spun Amorphous Ribbons. Materials Transactions, 2006. 47(10), p. 2489-2492.
  5. Zhang, T. and A. Inoue, Thermal and Mechanical properties of Ti-Ni-Cu-Sn amorphous alloys with a wide supercooled liquid region before crystallization. Materials Transactions, 1998, 39(10), p. 1001-1006.
  6. Kim, Y.-C., W.T. Kim, and D.-H. Kim, Glass Forming Ability and Crystallization Behavior in Amorphous Ti50Cu32-xNi15Sn3Bex (x = 0, 1, 3, 7) Alloys. Materials Transactions, 2002, 43(5), p. 1243-12437.
  7. Choi, P.P., et al.,Ti50Cu25Ni20Sn5 bulk metallic glass fabricated by powder consolidation. Materials Letters, 2007, 61(23), p. 4591-4594.
  8. Oanh, N.T.H., et al., Thermal Stability of Amorphous Ti-Cu-Ni-Sn Prepared by Mechanical Alloying. Materials Science Forum, 2007, 534-536, p. 233-236.
  9. Zhang, L.-C., J. Xu, and J. Eckert, Thermal stability and crystallization kinetics of mechanically alloyed TiC⁄Ti-based metallic glass matrix composite. Journal of Applied Physics, 2006, 100(3), p. 033514.
  10. Gao, W.-l., et al., Isothermal crystallization kinetics of ball-milled amorphous Al-Ni-Zr alloy. Acta Physica Sinica (Overseas Edition), 1995, 4(2), p. 113-117.
  11. Sahoo, K.L., V. Rao, and A. Mitra, Crystallization Kinetics in an Amorphous Al-Ni-Mm-Fe Alloy. Materials Transactions, 2003, 44(6), p. 1075-1080.
  12. Yang, Y.J., et al., Crystallization kinetics of a bulk amorphous Cu-Ti-Zr-Ni alloy investigated by differential scanning calorimetry. Journal of Alloys and Compounds, 2006, 415(1), p. 106-110.
  13. Mohammadi Rahvard, M., M. Tamizifar, and S.M.A. Boutorabi, The effect of Ag addition on the non- isothermal crystallization kinetics and fragility of Zr56Co28Al16 bulk metallic glass. Journal of Non-Crystalline Solids, 2018, 481, p. 74-84.
  14. Gong, P., K. Yao, and S. Zhao, Cu-alloying effect on crystallization kinetics of Ti41Zr25Be28Fe6 bulk metallic glass. Journal of Thermal Analysis and Calorimetry, 2015, 121(2), p. 697-704.
  15. Wang, R.W., et al., Nanocrystallization kinetics of amorphous Fe73.5Cu1Nb3−xMoxSi13.5B9 (x=1, 2, 3) alloys. Physica B: Condensed Matter, 2010, 405(17), p. 3555-3559.

Leave a Reply

Your email address will not be published. Required fields are marked *