Thermodynamic modeling of Zr-Ti-Cu-Ni-Be bulk metallic glass

Abstract

In the present thermodynamic model, the optimization of bulk metallic glass forming compositions in Zr-Ti-Cu-Ni-Be system using enthalpy of chemical mixing ('H chem ) as thermodynamic, mismatch entropy ('S V /k B ) as topological and configurational entropy ('S config /R) as statistical parameters were studied. The product of 'H chem and 'S V /k B which is termed as 'P HS in the 'S config /R range of 0.9 to 1.0 can be strongly correlated to glass forming ability. Using the contributions of 'P HS values of all ternary compositions possible in Zr-Ti-Cu-Ni-Be system, the final quinary composition is designed. Composition obtained from present model was found to closely match with compositions reported in literature.

Applications of an extended Miedema's model for ternary alloys

“…In order to study the lattice strain energies of solid solutions we have used the approach developed by Miracle and Senkov [24,25], and extended to ternary systems by Ray et al [8,26]. According to this approach, the lattice strain energy of a multicomponent system can be expressed as: (13) where E b in ij is the lattice strain energy of a binary i − j solid solution (i as the matrix species and j as the solute species).…”

“…A number of factors like the e/a ratio [30,31], lattice strain [8,9,24,26], formation enthalpy [8][9][10][11]26] and local geometry [8,[27][28][29] have been proposed to explain the phenomena. In this paper, we have focused on the thermodynamics of glass formation.…”

On Prediction of Amorphous Phase Forming Compositions in the Iron-Rich Fe-Zr-B Ternary System and Their Synthesis

“…The main advantage of this parameter is its applicability to multicomponent systems, which was missing in earlier predictive models. This parameter was found to correlate well with the GFAs of Zr-Cu-Al, [15] Cu-Zr-Ti, [16] Cu-Zr-Ti-Ni, [17] Zr-Ti-Cu-Ni-Be, [18] and Zr-Ti-Cu-NiAl [19] systems. However, this approach was not extended much to iron-based glass systems, which inherently possess low GFA.…”

Critical evaluation of glass forming ability criteria

“…where R is the universal gas constant, and x i is the molar fraction of element i. Bhatt et al 30,31,32,33 have shown that two parameters can be utilised to decide the amorphous forming ability of a particular alloy. Two compound parameters are formed from these two entropy terms, and they are as follows:…”

“…Different GFA criteria can be categorised into four basic classes as shown in Table 1. Category A consists of criteria depending on critical temperatures of glass forming alloys, category B shows the criteria depending on the thermodynamic parameters calculated based on Miedema's approach, [22][23][24][25][26][27][28] category C enlists the GFA criteria based on internal atomic structure and atomic arrangement of constituting elements in a glass forming alloy [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] and the category D suggests the criteria depending on the kinetic properties of the glassy materials. [45][46][47][48][49][50][51][52][53][54] Only those GFA criteria are listed where one criterion has been applied on various bulk metallic glass (BMG) forming systems and has been proven for its compatibility.…”