Monte Carlo simulation of order-disorder transition in refractory high entropy alloys: A data-driven approach

Abstract

High entropy alloys (HEAs) are a series of novel materials that demonstrate many exceptional mechanical properties. To understand the origin of these attractive properties, it is important to investigate the thermodynamics and elucidate the evolution of various chemical phases. In this work, we introduce a data-driven approach to construct the effective Hamiltonian and study the thermodynamics of HEAs through canonical Monte Carlo simulation. The main characteristic of our method is to use pairwise interactions between atoms as features and systematically improve the representativeness of the dataset using samples from Monte Carlo simulation. We find this method produces highly robust and accurate effective Hamiltonians that give less than 0.1 mRy test error for all the three refractory HEAs: MoNbTaW, MoNbTaVW, and MoNbTaTiW. Using replica exchange to speed up the MC simulation, we calculated the specific heats and short-range order parameters in a wide range of temperatures. For all the studied materials, we find there are two major order-disorder transitions occurring respectively at T 1 and T 2 , where T 1 is near room temperature but T 2 is much higher. We further demonstrate that the transition at T 1 is caused by W and Nb while the one at T 2 is caused by the other elements. By comparing with experiments, the results provide insight into the role of chemical ordering in the strength and ductility of HEAs.

The Sample Size Matters: To What Extent the Participant Reduction Affects the Outcomes of a Neuroscientific Research. A Case-Study in Neuromarketing Field

“…In fact, thanks to the increasing shared knowledge and recent scientific evidence produced by the neuroscientific community, behavioural neuroscience is experiencing an exponential growth in terms of applied research [ 13 , 14 , 15 ]. Recently, new terms have been coined, such as Neuroergonomics, Neuromarketing, Neuroaesthetics, and others, to include the new neuroscientific disciplines that aim at investigating neurophysiological correlates of humans’ behaviour at work [ 16 , 17 , 18 ], including driving a car [ 19 , 20 , 21 , 22 , 23 , 24 ], watching television [ 25 , 26 , 27 ], having a sensorial experience [ 28 , 29 , 30 ], and in any other activity of daily life. In the context of applied neurosciences, when physiological signals are acquired in real environments, several factors work against the ease of participant recruitment.…”

“…This number was deemed appropriate to assume the results were reliable, i.e., representative of the theorical population, in line with the scientific literature [32]. These subgroups were chosen since: (i) in the literature there is a large consensus considering [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] the optimal range of participants in neuroimaging studies [33]; (ii) in order to perform Analysis of Variance, the number of cases (i.e., 630) has to be much higher than the number of groups (i.e., five). The experimental task consisted of watching four TV spots with different lengths (30,30,20, and 15 s) during which electroencephalographic (EEG) signal and autonomic measures, i.e., heart rate (HR) and galvanic skin response (GSR), were acquired.…”

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

“…This method provides a full probabilistic description of Sobol' indices, whose distribution characterizes uncertainty in the sensitivity resulting from small data set size. The proposed method has been applied to many real‐world science and engineering problems, for example, material science (Bostanabad et al, 2018; X. Liu et al, 2021; Zhang, Shields, & TerMaath, 2020; Zhang et al, 2020), structural reliability (Sofi, Muscolino, & Giunta, 2020; Song, 2020; Sundar & Shields, 2019; C. Wang, Zhang, & Beer, 2018), failure and risk assessment (Guo, Yi, Fu, Huang, & Teng, 2019; Manouchehrynia, Abdullah, & Singh Karam Singh, 2020; Z. Wang & Jia, 2020), etc.…”

Emergence of machine learning in the development of high entropy alloy and their prospects in advanced engineering applications

“…The hydrogenation is an exothermic reaction and H bond with metal as a covalent bond, in which Ti and Sc lose an electron and Mo gain the electrons during absorption [86]. Another article shows Monte Carlo simulation of HEA to study the temperature-dependent chemical order of refractory metal (Mo-Nb-Ta-W) [87,88]. Similarly, the reverse Monte Carlo structure modelling was also used to study the local lattice distortion in three HEAs, namely, TiVNb, TiVZrNb and TiVZrNbHf.…”