Structural transformations driven by local disorder at interfaces

Yanyan Liang, Grisell Díaz Leines, Ralf Drautz, and Jutta Rogal

Phys. Rev. Materials 8, 033402 – Published 14 March 2024

Abstract

Despite the fundamental importance of solid-solid transformations in many technologies, the microscopic mechanisms remain poorly understood. Here we explore the atomistic mechanisms at the migrating interface during solid-solid phase transformations between the topologically closed-packed A15 and body-centred cubic phase in tungsten. The high energy barriers and slow dynamics associated with this transformation require the application of enhanced molecular sampling approaches. To this end, we performed metadynamics simulations in combination with a path collective variable derived from a machine-learning classification of local structural environments, which allows the system to freely sample the complex interface structure. A disordered region of varying width forming at the migrating interface is identified as a key physical descriptor of the transformation mechanisms, facilitating the atomic shuffling and rearrangement necessary for structural transformations. Furthermore, this can directly be linked to the differences in interface mobility for distinct orientation relationships as well as the formation of interfacial ledges during the migration along low-mobility directions.

Received 30 October 2023
Accepted 27 February 2024

DOI:https://doi.org/10.1103/PhysRevMaterials.8.033402

Physics Subject Headings (PhySH)

Crystal growth Crystal orientation Crystal phenomena Crystal structure Phase transitions by order Specific phase transitions

Elemental metals Interfaces Solid-solid interfaces

Machine learning Molecular dynamics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yanyan Liang ^1,*, Grisell Díaz Leines ², Ralf Drautz ¹, and Jutta Rogal ^3,4

¹ICAMS, Ruhr-Universität Bochum, 44801 Bochum, Germany
²European Bioinformatics Institute (EMBL- EBI), Wellcome Genome Campus, Hinxton, Cambridge CB10 1SD, United Kingdom
³Department of Chemistry, New York University, New York, New York 10003, USA
⁴Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany

^*yanyan.liang@rub.de

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Issue

Vol. 8, Iss. 3 — March 2024

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Images

Figure 1
Illustration of (a) the path collective variable $f (Y (r))$ and (b) the distance function $z (Y (r))$ (multiplied by 30) together with the path (red line) in the $Y^{bcc} - Y^{A15}$ space. There are 10 equidistant points along the path, starting at $Y_{1} = {Y^{bcc} : 0.15, Y^{A15} : 0.55}$ and ending at $Y_{10} = {Y^{bcc} : 0.60, Y^{A15} : 0.10}$ . Representative configurations are shown for the two end points of the path. In these configurations, bcc atoms are shown in blue, A15 in red, and disorder in gray.
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Figure 2
Illustration of supercells with interfaces for different orientation relationships. (a) ${[001]}_{bcc} ∥ {[001]}_{A15}$ , (b) ${[110]}_{bcc} ∥ {[110]}_{A15}$ , and (c) ${[210]}_{bcc} ∥ {[210]}_{A15}$ . Gray atoms represent the interface, where the left- and right-end gray atoms are fixed so only one interface (the middle one) is mobile in simulations. A15 is colored in red and bcc in blue.
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Figure 3
(a) Average path density in the $Y^{bcc} - Y^{A15}$ space together with the predefined path (red). The color gradient corresponds to an increase in density from light to dark. (b) Average free-energy profile along the path collective variable. (c) Average amount of disordered interface projected on the path collective variable. The shaded area indicates the standard deviation in $Y^{dis}$ . (d) Representative configurations at energy minima A and C, and transition state B. A15 phase is colored in red, bcc in blue, and disorder in gray, respectively. The dashed lines mark the boundary of the disordered interface between A15 and bcc. When the system is in the free energy minima, it has well defined crystalline layers with minimum amount of disorder at the interface; at the transition state, the width of the disordered region increases to facilitate the migration. From A to C, approximately four layers of A15 are transformed into bcc along the [001] direction.
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Figure 4
Average path density with the predefined (a) linear and (b) bumpy path (red) in the $Y^{bcc} - Y^{A15}$ space. (c) and (d) Free energy profiles along the path collective variable for the (c) linear path after $t = 781$ ns and (d) the bumpy path after $t = 1554$ ns. The average amount of disorder along the path collective variable is shown for the (e) linear and (f) bumpy path.
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Figure 5
(a) Average interface velocity as a function of temperature and (b) Arrhenius plot of interface migration rate vs the inverse temperature for different orientation relationships. Each point in the average velocity is calculated from a minimum of 100 values in ten MD runs at every temperature.
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Figure 6
A15 $\to bcc$ transformations for ${[110]}_{bcc} ∥ {[110]}_{A15}$ interfaces. (a) Average path density together with the predefined linear path (red) in the $Y^{bcc} - Y^{A15}$ space; (b) average free energy profile; (c) amount of disorder at the interface projected along the path collective variable; the black solid line represents the average amount of disorder, the gray shaded area represents the standard deviation. (d) Representative configurations for different states along the free-energy profile. A15 is colored in red, bcc in blue, and disorder in gray, respectively. The dashed lines in the configurations indicate interfacial ledge formation in the [100] direction.
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