TECHNICAL PAPER Applicability of c * Parameter on Glass Forming Ability of Zr-,Ti- ,Hf-(Cu–Ni)-based Metallic Glasses Anuj Khond 1 • Jatin Bhatt 1 • Ajeet K. Srivastav 1 Received: 30 July 2018 / Accepted: 6 September 2018 Ó The Indian Institute of Metals - IIM 2018 Abstract Bulk metallic glasses are considered as potential materials for engineering application due to the absence of long-range periodicity. The ability of material to be cast into amorphous phase is defined by the term called glass forming ability (GFA). In the present paper, GFA of Zr-, Hf- and Ti-based metallic glass have been studied based on well-established c * parameter. The c * parameter has been calculated for reported binary, ternary, quaternary and quinary Zr-, Hf- and Ti-based systems. The c * parameter increases with Zr, Hf and Ti content in Zr–Cu–Ni, Hf–Cu– Ni and Ti–Cu–Ni systems validating the confidence of parameter. These findings are well matched with existing literature in which 50–60 at.% Zr, Hf and Ti form amor- phous phase in Zr–Cu–Ni, Hf–Cu–Ni and Ti–Cu–Ni sys- tems, respectively. Hence, applicability of c * parameter has been discussed in context to Zr-, Hf-, and Ti-based sys- tems. The result shows that c * is an effective thermody- namic parameter to define the GFA in binary, ternary, quaternary and quinary Zr-, Hf- and Ti-based systems. Keywords Bulk metallic glass  Glass forming ability  Hf-based glass  c * parameter 1 Introduction In the recent past, more attention has been paid to bulk metallic glasses (BMGs) due to its superior physical and mechanical properties. BMGs exhibit high strength, good corrosion resistance, and excellent magnetic/electrical properties compared to the crystalline material [1–3]. Glass forming ability (GFA) of the alloys is mainly dependent on cooling rate and alloy composition. Critical cooling rate is the decisive parameter to determine the GFA but it is very difficult to measure experimentally [4]. Hence major importance has been given to improve the GFA by varying the composition among the constituent elements. In this regards, many criteria for GFA have been proposed [4–6]. Among the existing criteria, reduced glass transition tem- perature (T rg = T g /T l )[3], c parameter [c = T x /(T g ? T l )] [4], DT x =(T x - T g )[3], a =(T x /T l ) and b =(T x /T g ? T g / T l )[3] where T g is glass transition temperature, T l is liquids temperature and T x is crystallization temperature are widely used to define the GFA in metallic glasses. Inoue et al. [7] and Johnson [8] have proposed certain important criteria such as multicomponent alloy systems with three or more elements, atomic size difference should be more than 12% among the constituent elements, negative heat of mixing among the constituent element resulting in deep eutectic. These criteria have been successfully used in most of the glass forming systems for many decades. However, these experimental criteria are useful only when tempera- ture events (T x , T g , T l ) of the compositions forming metallic glasses are known. In other words, one cannot use these parameters to predict the GFA if glass forming composition is not known. Thermodynamic analysis is the effective way to obtain the glass forming composition in alloy systems. Vincent et al. [9] proposed the model to optimize the glass forming composition using thermodynamic parameters. They pro- posed the P HS and P HSS model for ternary and quaternary systems by calculating the product of enthalpy of mixing (DH mix ), mismatch entropy (DS r ) and configurational entropy (DS config ). The higher negative value of P HS or & Ajeet K. Srivastav srivastav.ajeet.kumar@gmail.com 1 Department of Metallurgical and Materials Engineering, V.N.I.T. Nagpur, Nagpur 440010, India 123 Trans Indian Inst Met https://doi.org/10.1007/s12666-018-1412-y