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A topological model is proposed for metallic glass formation through destabilization of the host crystalline lattice by substitutional and/or interstitial solute elements. A solute element may partition between substitutional and interstitial sites and the model calculates relative site frequency as a function of the strain energy associated with e...
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... be placed on the surface of atom B; however, the number of the nearest neighbors A around each atom A still cannot exceed 5. On the other hand, in the range of 0.414 5/ R B/0.902, only four atoms A can be placed on the surface of atom B around each atom A. This considera- tion led to the following relation: The results of Eq. (15) are plotted in Fig. 3 along with the results from Egami's earlier estimate, Eq. (14). A discontinuous increase in N th of about 0.8 occurs at R 0/ 0.902. Egami's estimate provides a good match with current calculations below R 0/0.902, but it is lower than the current N th values by nearly unity above this transition. From Eq. (15), the critical relative ...
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... It was shown by the above authors [51] that the lattice parameter of the α-Fe solid solution increased with increasing milling time (Fig. 2). Incorporation of solute atoms into the Fe lattice introduces lattice distortion and once the threshold amount of lattice distortion has been achieved due to the size mismatch between the solvent and solute atoms, the crystalline lattice becomes destabilized and an amorphous phase is expected to form [62,63]. Since a crystalline phase had formed on continued milling, it was concluded that crystallization of the amorphous phase had occurred in the primary mode through formation of the primary-metal-based solid solution [7][8][9]. ...
... Additively to Inoue's rules [3] and some theoretical findings of D. Turnbull [4], all the existing approaches to quantify GFA of BMGs may be sorted into four (04) main categories [2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. ...
... BMGs with high GFA should contain different elements with, at least, three different atomic sizes (i.e. large, medium, and small) [5,22]. Consequently, structural (and topological) GFA criteria are related to the elements atomic size and its distribution, their electronegativity and the electron-to-atom ratio (fraction of solute atoms) that constitute the atomistic approach. ...
... Consequently, structural (and topological) GFA criteria are related to the elements atomic size and its distribution, their electronegativity and the electron-to-atom ratio (fraction of solute atoms) that constitute the atomistic approach. O. Senkov headed the discussion of a topological approach linked with the atomic size distribution (ASD) plots and the geometrical details of the different diameters of elements [22]. ...
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Abstract—In this theoretical contribution, authors propose a new glass-forming ability criterion: the vitrification
driving force for metallic glasses (VDFMGs) based on the phenomenological discussion of crystallization
driving force (CDF). The VDFMGs mathematical expression is the inverse one of CDF (Vitrification and
crystallization being opposite phenomena). Authors suggest confine its calculation in the temperature interval
ΔTl–g = (Tl – Tg) where the crystallization vs. vitrification competition takes place. A case study on various
metallic glasses systems revealed high statistical correlations with the cooling rate Rc, Trg, γ, γm, and k (selected
as most efficient GFA indicators) and demonstrates its obvious accurate aptitude to quantify the GFAMGs.
... To illustrate this, let us take the example of metallic glasses. Early models of glass formation in metallic systems considered only one factor (or feature) at a time, such as-formation enthalpy [31], configurational and mismatch entropy [32], lattice strain and strain energy [33], valence electron concentration [34] or even denserandom packing of atoms in solute-centered clusters [35,36]. Very few synergistic analytical models were proposed that could combine all of these factors [37,38]. ...
Multi-Principal Element Alloys (MPEAs) have brought a paradigm shift in the alloy design process and pose a significant challenge due to the astronomical and compositional space available for exploration. Since experimental and ab-initio methods are more suitable for targeted alloy design over a narrow composition range, data-driven methodologies have shown promise in the search for alloys with unique or improved properties. This chapter introduces the field of materials informatics by laying out the fundamentals of machine learning, i.e., the types of problems, dataset formulation, feature selection, and machine learning algorithms, as applied to materials science. It follows with a holistic review of the existing data-driven models targeted towards the prediction of phase selection, mechanical properties and ordering behaviour in MPEAs. It also discusses the methodology for the development of machine learning force fields that enable atomistic modelling of various phenomena, such as diffusion, phase transformations and mechanical deformation, in MPEAs.
... In the MG field, the search for a universal parameter to characterize the glass-forming ability (GFA) of each type of MGs has attracted much attention, as it may provide a crucial tool for understanding the origins of glass formation and for designing and developing new MGs [4]. At time of writing, the search for a GFA criterion has been underway for nearly a century, and several parameters have been developed based on thermodynamics, kinetics, atomic structure, volume/density, topological instability, phase diagram, and characteristic temperatures of the systems [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The direct parameters used to rank GFAs of alloys are their critical cooling rate, R c , and the critical glassy size d c of the sample, which are also used as the standard with which to evaluate the validity of other GFA parameters; however, accurate measurement of R c and d c is difficult to be realized, in particular, the quantities are not able to evaluate marginal glass-formers. ...
Based on the time-temperature-transformation interpretation, a new criterion for glass forming ability, Z = [(Tx-Tg)/(Tl-Tg)][(Tl–Tl(c))/(Tl-Tg)]0.556, is proposed, where Tg, Tx, Tl and Tl(c) respectively denote the glass transition temperature, the onset crystallization temperature upon heating, the liquidus temperature and the onset solidification temperature of the liquid upon cooling. The Z parameter jointly considers the stability of the liquid and the devitrification of glassy phases. A non-linear relationship between the parameter Z and the critical glassy size dc has been found to be log (dc)cal = 0.1392 + 17.0616Z - 41.985(Z)², showing stronger correlation than other earlier reported parameters. The advantage of using Z as a GFA parameter is that it roughly reflects the relative influences of the thermodynamics and kinetics of the systems on glass formation. In addition, the parameter describes the stability of liquid in the course of being quenched from above liquidus temperature.
... As shown in Fig. 2, since the Cu element is almost insoluble in the iron element in the early stage of annealing, it leads to component separation and the formation of Cu-rich clusters. Furthermore, the compositional fluctuations of elements in the matrix between clusters and α-Fe nucleation are induced [5]. During the nucleation process, the Si element in the matrix diffuses into α-Fe to form the BCC α-Fe(Si) phase. ...
... Series: Earth and Environmental Science 565 (2020) 012048 IOP Publishing doi:10.1088/1755-1315/565/1/012048 5 ...
... It can be determined in many different ways, including experimental and theoretical methods. [10][11][12][13] Thermodynamic approach utilizing semi-empirical Miedema's model [14][15][16][17] is used in the present paper to determine GFA of ternary Fe-Ni-TM alloys, where TM represent group V and VI transition metals. Z ...
The glass-forming ability (GFA) of Fe-Ni-TM alloys, where TM = V, Nb, Cr, Mo, was determined utilizing thermodynamic modeling. Enthalpies of formation of amorphous state were calculated and analyzed along with normalized mismatch entropy and glass-forming ability parameter. All thermodynamic quantities were qualitatively compared with enthalpies of formation of solid solution and experimental results. Due to the fact that FeNi-based amorphous ribbons are used nowadays in magnetoelastic sensors (MES), which can be used in biomedical or chemical applications, discussion is concentrated mainly on the substitution effect of group V and VI transition metals on the improvement of GFA. In this sense, group V elements are preferred, with Nb as the most promising candidate among all analyzed TM elements. This is a consequence of significant differences of potential and density of electrons at the boundary of Wigner–Seitz cell comparing to Fe and Ni, which in turn leads to more negative values of interfacial enthalpy and higher driving force for vitrification.
... Also few alternative approaches have been reported in the literature. The Inoue's empirical rule [3], deep eutectic based compositional design [22,23], structure and topologybased approach [24][25][26], data training of artificial neural network [27,28] are to name a few effort made to develop a strategy for compositional design.Also the thermodynamics based approach [29][30][31][32][33], cluster line based approach [34][35][36], molecular dynamics simulation based approach [37,38] and a golden mean analysis based approach [39] has been attempted to design the BMG compositions.However, these attempts have led to limited success due to one or other constraints. ...
This paper demonstrates how principal component analysis of multivariate BMG alloy data and the genetic programming of the extracted features in the form of principal components can be used to develop a meta-modeling scheme for GFA expression. The proposed GFA model can estimate the glass forming potential of an alloy from its composition data, unlike the characteristic temperature based glass forming ability expressions, consisting of T g , T x and T l. The BMG alloys have been described by means of generic attributes of the constituent elements and corresponding composition of the alloy yielding a multi-dimensional descriptor space for a 594 BMGs compiled from literature. The PCA model of the data base plausibly reduced the dimensionality into a two dimension in terms of two extracted features by first two principle components capturing the 82% of the data knowledge. Successively, these principle components are used to develop a constitutive model for glass forming ability using genetic programming. The combinatorial analysis of the meta-model for GFA expression is applied to the prediction of potential compositional zone in five different experimentally explored ternary systems. The predicted composition zones are discussed in the context of available experimental data in literature and the energy of formation of the stable phases in respective alloy systems.
... It was shown the topological instability of the lattice and the corresponding glass formation occurs when ε A V reaches a critical values of 0.054 [46,48]. According to Eq. (1), the calculated value of ε A V for ...
The effect of milling time on the microstructural evolution and magnetic properties of a new Fe-based amorphous/nanocrystalline powder produced via mechanical alloying (MA) has been investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), differential scanning calorimetry (DSC) and vibrating sample magnetometer (VSM). The Rietveld refined XRD results show that the weight fraction of the amorphous phase increases to about 94% after 120 h of milling and then decreases to about 89% by further milling to 150 h due to partial crystallization. The contribution of lattice strain to solid-state amorphization has been discussed in the frame work of the Egami's topological instability model. The DSC measurements demonstrate that the obtained glassy powders after 120 h of milling have a high thermal stability, according to their wide supercooled liquid region of 75 K. The magnetic measurements indicate that saturation magnetization decreases continuously up to 50 h and then slightly increases after 150 h of milling. Simultaneously, magnetic coercivity rapidly increases and then notably decreases with the milling process. In addition, it has been shown that an annealing treatment at 673 K can significantly improve the soft magnetic properties of 120 h milled powders through the reduction of coercivity from 2.72 kA/m to 1.38 kA/m.
... The preservation of a supercooled liquid structure depends substantially on two factors: the stability of the supercooled liquid, and the difficulty of crystallization. The characteristics of metallic liquid have been extensively studied that the composition of alloy with good GFA is roughly located at the composition of eutectic point [11,[14][15][16][17][18][19][20], where the liquid is relatively stable against others through optimal dense structural topology [21][22][23]. However, this criterion does not always work in practice, and the difficulty in actual implement increases along the increasing number of alloying elements. ...
A quantificational composition design protocol (CDP) of Fe-based bulk metallic glasses (BMGs) with excellent glass-forming ability (GFA) has been proposed on the basis of the thermodynamic calculations. The stability of liquid and the crystallization of solids were both evaluated from the perspective of atomic structure and local composition. The present protocol successfully associates the stability of liquid to the melting point of alloy and the difficulty of crystallization by considering the type and competition of potential equilibrated phases. Specifically, this protocol provided the selection criteria of phases and elements from the viewpoint of structure and composition fluctuations during nucleation for each phase, whose accuracy and effectiveness were experimentally verified.
... • the expected atomic concentrations and relative size ratios correspond well to conditions identified by Miracle and co-workers [12][13][14] to be most suitable for bulk metallic glass formation; ...
New BMGs exhibiting strong glass forming ability combined with high hardness have been developed based on the Pt-Si-B ternary system. The effects of partial substitution of platinum by transition metals of the group iron, cobalt, nickel, and copper, as well as the partial replacement of silicon by germanium on the melting temperature, Tm, the crystallization temperature, Tx, the glass transition temperature, Tg, and the hardness are investigated. Amongst the transition metals, nickel and copper were found to reduce the liquidus and the solidus temperatures of the Pt-Si-B near ternary eutectic composition, while cobalt and iron had no influence on the solidus temperature but raised the liquidus temperature significantly. Substitution of one fourth of platinum atoms by either nickel or copper increased the glass transition temperature by roughly 45 K and 65 K, respectively, with a concomitant increase in crystallization temperature of similar magnitude. For a series of alloys with the general formula (Pt0.75Cu0.25)66.6B24Si9.4-xGex, increasing substitution of silicon by germanium (x = 0 … 3) led to a significantly increased crystallization temperature essentially by shifting the first of typically two crystallization peaks to higher temperatures, while the Tg was slightly lowered as x increased. This resulted in a marked widening of the supercooled liquid region, ΔT. Within this alloying series a general trend of increased hardness with increased Tg was observed.
