In the present investigation, thermodynamic and topological concepts have been used together to understand the formation of bulk metallic glasses. The article attempts to develop a parameter that combines chemical mixing enthalpy (ΔH chem), mismatch entropy normalized by Boltzmann constant (ΔSσ /kB), and configurational entropy (ΔS config/ R), which can be effectively used to identify the best bulk glass forming compositions in multicomponent systems. The ΔHchem for multicomponent systems has been calculated by extending the Miedema's macroscopic model, and ΔSσ/kB was obtained from Mansoori's approach. The iso-ΔHchem, iso-ΔSσ /kB, and iso-ΔSconfig/R contours have been developed. The product of ΔHchem and ΔSσ/kB in the ΔSconfig /R range of 0.9 to 1.0 can be correlated strongly to glass forming ability. This has been demonstrated in the case of the quaternary Cu-Zr-Ti-Ni bulk glass forming system to determine the bulk metallic glass forming compositions. Mechanical alloying is used to prepare the bulk amorphous powder at the compositions predicted by the model in order to validate the model. © The Minerals, Metals &amp; Materials Society and ASM International 2007.

Budaraju Srinivasa Murty

Department of Metallurgical and Materials Engineering

Boltzmann equation

enthalpy

entropy

Glass manufacture

Mechanical Alloying

CHEMICAL MIXING ENTHALPY

MANSOORI'S APPROACH

MULTICOMPONENT SYSTEMS

Metallic glass

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science

The available glass forming ability criteria have been examined by classifying them into four basic categories depending on critical temperatures, thermodynamic quantities, topological and kinetic aspects of glass forming alloys. A large number of glass forming alloys of widely varying natures and origin have been analysed with their experimentally measured properties to assess their glass forming ability. A novel approach using kinetic viscosity of glass forming alloys obtained by the Vogel-Fulcher-Tamman equation and the critical cooling rate calculated from the TTT diagram is demonstrated as an excellent universal glass forming ability criterion. Moreover, thermodynamic and topological modelling results through computation of a novel PHSS parameter for various alloy compositions spanning different alloy systems have rendered qualitative guidelines on propensity for glass formation in multicomponent alloy systems. Besides, the importance of kinetic interpretation of PHSS range observed for glass forming alloys is also elaborated. © 2016 Institute of Materials, Minerals and Mining.

Materials Science and Technology (United Kingdom)

Critical evaluation of glass forming ability criteria

Topological factors such as mismatch entropy and configurational entropy, along with thermodynamic entity such as enthalpy of chemical mixing, are found to control glass formation in metallic systems. Taking both these factors into consideration, a parameter called P HS was proposed to correlate glass forming ability successfully in the Cu-Zr-Ti system. The parameter P HS (=ΔH chem × ΔS σ /k B ) is a product of enthalpy of chemical mixing and mismatch entropy. Our study indicates that the more negative is the PHS value within the configurational entropy (ΔS config/R) range of 0.9 to 1.0, the higher is the stability of glassy phase resulting in a larger diameter of bulk metallic glass rods. Observed theoretical predictions are supported by experimental results in which the compositions with high negative P HS resulted in easy amorphous phase formation in comparison with less negative P HS compositions by mechanical alloying. This criterion was extended to Cu-Zr-Al and Cu-Zr-Ag systems as well, thus establishing a strong correlation between P HS and the glass forming ability of alloys. The role of size effect, probability of atomic arrangements, and heat of formation among constituent elements in obtaining a larger dimension bulk metallic glasses was addressed in this study. © 2013 The Minerals, Metals &amp; Materials Society and ASM International.

Thermodynamic basis for glass formation in Cu-Zr rich ternary systems and their synthesis by mechanical alloying

Formation of a glassy phase in metallic systems is controlled to large extent by the composition of the alloy. Alloying behavior can be qualitatively predicted from the knowledge of enthalpy of mixing and atomic size mismatch among elements involved in bonding. A more quantitative description of glass forming ability (GFA) can be obtained by using a parameter PHS [= ΔHC(ΔSσ/kB)], where ΔHC is the chemical enthalpy of mixing and ΔSσ/kB is entropy due to atomic size mismatch normalized by Boltzmann constant. Using this criterion, alloys with high GFA were identified in several ternary systems. However, PHS parameter was found to be insufficient to predict GFA in multicomponent systems. Present analysis indicates that the incorporation of configurational entropy into PHS parameter resulted in more quantitative description to explain higher GFA in multicomponent systems. This new GFA parameter is called PHSS (= PHS × ΔS C/R), where ΔSC/R is the configurational entropy normalized by universal gas constant. Using PHS and PHSS parameters, GFA predictions are done for Fe-Zr-B, Fe-Cr-Zr-B, Fe-Cr-Ni-Zr-B, Cu-Zr-Ag-Ti, Cu-Zr-Al-Y and Cu-Zr-Al-Be systems and an attempt has been made establish the suitability of this new GFA parameter to various quaternary and quinary alloy systems.

Transactions of the Indian Institute of Metals

Prediction of glass forming ability using thermodynamic parameters

Melt-spun ribbons of Fe99-x-y Zr x B y Cu1 alloys with x + y = 11 and x + y = 13 were prepared under similar experimental conditions and characterized for structure and soft magnetic properties. Substitution of Zr by B changes the structure of as-spun ribbons from completely amorphous to cellular bcc solid solution coexisting with the amorphous phase at intercellular regions and then to completely dendritic solid solution. The glass forming ability (GFA) of the Fe-Zr-B-Cu system, evaluated from thermodynamic properties such as enthalpy of mixing and mismatch entropy, is found to be in good agreement with the experimental observations. Annealing of all ribbons leads to the precipitation of nanocrystalline bcc α-Fe phase from both amorphous phase and already existing bcc solid solution. A window of alloy compositions that exhibit the best combination of soft magnetic properties (high saturation magnetization and low coercivity) was identified. © 2010 The Minerals, Metals &amp; Materials Society and ASM International.

Structure, properties, and glass forming ability of melt-spun Fe-Zr-B-Cu alloys with different Zr/B ratios

Prediction of bulk metallic glass (BMG) forming compositions has always been a challenge due to thermodynamic and kinetic constraints. In the present investigation, a parameter based on the enthalpy of chemical mixing (ΔHchem) and the mismatch entropy (ΔSσ/ kB) has been used to correlate with glass forming ability in some Zr based BMGs. The new thermodynamic parameter, PHS = ΔH chem × ΔSσ/kB, is found to have strong correlation with glass forming ability in the configurational entropy (ΔSconfig/R) range of 0.9-1.0. PHS has been calculated for compositions in Zr-Cu-Ag, Zr-Cu-Al, Zr-Cu-Ti and Zr-Cu-Ga ternary systems. It is observed that in all the systems studied, the best BMG composition (highest critical diameter (Zc) of glass formation) is the one that corresponds to the highest negative PHS value. Present approach using PHS could be road map to design new BMG forming compositions. © 2011 Elsevier B.V. All rights reserved.

Journal of Non-Crystalline Solids

Thermodynamic prediction of bulk metallic glass forming alloys in ternary Zr-Cu-X (X = Ag, Al, Ti, Ga) systems

Compositions with easy bulk metallic glass formation have been identified in quinary systems with the Gibbs-energy change between the amorphous and solid solution phases as the thermodynamic parameter. The Gibbs-energy change has been calculated with the help of Miedema, Miracle, mismatch entropy, and configurational entropy models. The best glass forming composition has been identified by drawing iso-Gibbs-energy change contours by representing quinary systems as pseudo-ternary ones. Attempts have been made to correlate the Gibbs-energy change with different existing glass forming criteria and it is found that the present thermodynamic parameter has good correlation with the reduced glass transition temperature. Further, encouraging correlations have been obtained between the energy required for amorphization during mechanical alloying to the Gibbs-energy change between the amorphous and solid solutions. © 2006 Elsevier B.V. All rights reserved.

Materials Science and Engineering A

Identification of compositions with highest glass forming ability in multicomponent systems by thermodynamic and topological approaches

Compositions with high glass forming ability have been identified in Zr-Cu-Al system with the help of a thermodynamic parameter, which takes into account the enthalpy of chemical mixing (ΔHchem), the mismatch entropy normalized by Boltzmann's constant (Sσ/kB) and the configurational entropy (Sconfig/R). The best bulk metallic glass forming composition is identified as the one at ΔHchem and Sσ/kB maxima in a specific range of Sconfig/R. A product of thermodynamic parameters (Δ Hchem × Sσ / kB) is found to have strong correlation with glass forming ability and can help to identify the exact composition that can form bulk metallic glass. © 2006 Elsevier Ltd. All rights reserved.

Intermetallics

Optimization of bulk metallic glass forming compositions in Zr-Cu-Al system by thermodynamic modeling

A new parameter has been proposed to assess the glass forming ability of liquids and its effectiveness is compared with the existing parameters. The new parameter (α = Tx/Tl), which incorporates both the factors of stability of the liquid (a low Tl) and the thermal stability of glass (a high Tx), has good correlation with the critical cooling rate for glass formation in a wide variety of glass forming alloys. This parameter can even be used for those glass forming alloys, which do not show a clear glass transition temperature. It has also been shown that the heating rate used during differential scanning calorimetry has negligible effect on the different glass forming parameters. © 2005 Elsevier B.V. All rights reserved.

Journal	Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science
ISSN	10735623
Open Access	No