Search

Breast cancer invasion into adipose tissue strongly influences disease progression and metastasis. The degree of cancer cell invasion into adipose tissue depends on both biochemical signaling and the mechanical properties of cancer cells, adipocytes, and other key components of adipose tissue. We model breast cancer invasion into adipose tissue using discrete element method simulations of active, cohesive spherical particles (cancer cells) invading into confluent packings of deformable polyhedra (adipocytes). We quantify the degree of invasion by calculating the interfacial area At between cancer cells and adipocytes. We determine the long-time value of At vs the activity and strength of the cohesion between cancer cells, as well as the mechanical properties of the adipocytes and extracellular matrix in which adipocytes are embedded. We show that the degree of invasion collapses onto a master curve as a function of the dimensionless energy scale Ec, which grows linearly with the cancer cell velocity persistence time and fluctuations, is inversely proportional to the system pressure, and is offset by the cancer cell cohesive energy. When E c > 1 , cancer cells will invade the adipose tissue, whereas for E c < 1 , cancer cells and adipocytes remain de-mixed. We also show that At decreases when the adipocytes are constrained by the ECM by an amount that depends on the spatial heterogeneity of the adipose tissue. [ABSTRACT FROM AUTHOR]

Micro- and nanoresonators have important applications including sensing, navigation, and biochemical detection. Their performance is quantified using the quality factor Q, which gives the ratio of the energy stored to the energy dissipated per cycle. Metallic glasses are a promising material class for micro- and nanoscale resonators since they are amorphous and can be fabricated precisely into complex shapes on these length scales. To understand the intrinsic dissipation mechanisms that ultimately limit large Q-values in metallic glasses, we perform molecular dynamics simulations to model metallic glass resonators subjected to bending vibrations at low temperatures. We calculate the power spectrum of the kinetic energy, redistribution of energy from the fundamental mode of vibration, and Q vs the kinetic energy per atom K of the excitation. In the harmonic and anharmonic response regimes where there are no atomic rearrangements, we find that Q → ∞ over the time periods we consider (since we do not consider coupling to the environment). We identify a characteristic Kr above which atomic rearrangements occur, and there is significant energy leakage from the fundamental mode to higher frequencies, causing finite Q. Thus, Kr is a critical parameter determining resonator performance. We show that Kr decreases as a power-law, Kr ∼ N−k, with increasing system size N, where k ≈ 1.3. We estimate the critical strain ⟨γr⟩∼ 10−8 for micrometer-sized resonators below which atomic rearrangements do not occur in the millikelvin temperature range, and thus, large Q-values can be obtained when they are operated below γr. We also find that Kr for amorphous resonators is comparable to that for resonators with crystalline order. [ABSTRACT FROM AUTHOR]

When a liquid is cooled well below its melting temperature at a rate that exceeds the critical cooling rate Rc, the crystalline state is bypassed and a metastable, amorphous glassy state forms instead. Rc (or the corresponding critical casting thickness dc) characterizes the glass-forming ability (GFA) of each material. While silica is an excellent glass-former with small Rc < 10-2 K/s, pure metals and most alloys are typically poor glass-formers with large Rc > 1010 K/s. Only in the past thirty years have bulk metallic glasses (BMGs) been identified with Rc approaching that for silica. Recent simulations have shown that simple, hard-sphere models are able to identify the atomic size ratio and number fraction regime where BMGs exist with critical cooling rates more than 13 orders of magnitude smaller than those for pure metals. However, there are a number of other features of interatomic potentials beyond hard-core interactions. How do these other features affect the glass-forming ability of BMGs? In this manuscript, we perform molecular dynamics simulations to determine how variations in the softness and non-additivity of the repulsive core and form of the interatomic pair potential at intermediate distances affect the GFA of binary alloys. These variations in the interatomic pair potential allow us to introduce geometric frustration and change the crystal phases that compete with glass formation. We also investigate the effect of tuning the strength of the many-body interactions from zero to the full embedded atom model on the GFA for pure metals. We then employ the full embedded atom model for binary BMGs and show that hard-core interactions play the dominant role in setting the GFA of alloys, while other features of the interatomic potential only change the GFA by one to two orders of magnitude. Despite their perturbative effect, understanding the detailed form of the intermetallic potential is important for designing BMGs with cm or greater casting thickness. [ABSTRACT FROM AUTHOR]

The likelihood that an undercooled liquid vitrifies or crystallizes depends on the cooling rate R. The critical cooling rate Rc, below which the liquid crystallizes upon cooling, characterizes the glass-forming ability (GFA) of the system. While pure metals are typically poor glass formers with Rc > 1012 K/s, specific multi-component alloys can form bulk metallic glasses (BMGs) even at cooling rates below R ~ 1 K/s. Conventional wisdom asserts that metal alloys with three or more components are better glass formers (with smaller Rc) than binary alloys. However, there is currently no theoretical framework that provides quantitative predictions for Rc for multi-component alloys. In this manuscript, we perform simulations of ternary hard-sphere systems, which have been shown to be accurate models for the glass-forming ability of BMGs, to understand the roles of geometric frustration and demixing in determining Rc. Specifically, we compress ternary hard sphere mixtures into jammed packings and measure the critical compression rate, below which the system crystallizes, as a function of the diameter ratios sB/sA and sC/sA and number fractions xA, xB, and xC. We find two distinct regimes for the GFA in parameter space for ternary hard spheres. When the diameter ratios are close to 1, such that the largest (A) and smallest (C) species are well-mixed, the GFA of ternary systems is no better than that of the optimal binary glass former. However, when sC/sA ≲ 0.8 is below the demixing threshold for binary systems, adding a third component B with sC < sB < sA increases the GFA of the system by preventing demixing of A and C. Analysis of the available data from experimental studies indicates that most ternary BMGs are below the binary demixing threshold with sC/sA < 0.8. [ABSTRACT FROM AUTHOR]

Bulk metallic glasses (BMGs) are amorphous alloys with desirable mechanical properties and processing capabilities. To date, the design of new BMGs has largely employed empirical rules and trial-and-error experimental approaches. Ab initio computational methods are currently prohibitively slow to be practically used in searching the vast space of possible atomic combinations for bulk glass formers. Here, we perform molecular dynamics simulations of a coarse-grained, anisotropic potential, which mimics interatomic covalent bonding, to measure the critical cooling rates for metal-metalloid alloys as a function of the atomic size ratio σS/σL and number fraction xS of the metalloid species. We show that the regime in the space of σS/σL and xS where well-mixed, optimal glass formers occur for patchy and LJ particle mixtures, coincides with that for experimentally observed metal-metalloid glass formers. Thus, our simple computational model provides the capability to perform combinatorial searches to identify novel glass-forming alloys. [ABSTRACT FROM AUTHOR]

Bulk metallic glasses (BMGs) are produced by rapidly thermally quenching supercooled liquid metal alloys below the glass transition temperature at rates much faster than the critical cooling rate Rc below which crystallization occurs. The glass-forming ability of BMGs increases with decreasing Rc, and thus good glass-formers possess small values of Rc. We perform molecular dynamics simulations of binary Lennard-Jones (LJ) mixtures to quantify how key parameters, such as the stoichiometry, particle size difference, attraction strength, and heat of mixing, influence the glass-formability of model BMGs. For binary LJ mixtures, we find that the best glass-forming mixtures possess atomic size ratios (small to large) less than 0.92 and stoichiometries near 50:50 by number. In addition, weaker attractive interactions between the smaller atoms facilitate glass formation, whereas negative heats of mixing (in the experimentally relevant regime) do not change Rc significantly. These results are tempered by the fact that the slowest cooling rates achieved in our simulations correspond to ∼1011 K/s, which is several orders of magnitude higher than Rc for typical BMGs. Despite this, our studies represent a first step in the development of computational methods for quantitatively predicting glass-formability. [ABSTRACT FROM AUTHOR]

When a liquid is cooled well below its melting temperature at a rate that exceeds the critical cooling rate Rc, the crystalline state is bypassed and a metastable, amorphous glassy state forms instead. Rc (or the corresponding critical casting thickness dc) characterizes the glass-forming ability (GFA) of each material. While silica is an excellent glass-former with small Rc < 10(-2) K/s, pure metals and most alloys are typically poor glass-formers with large Rc > 10(10) K/s. Only in the past thirty years have bulk metallic glasses (BMGs) been identified with Rc approaching that for silica. Recent simulations have shown that simple, hard-sphere models are able to identify the atomic size ratio and number fraction regime where BMGs exist with critical cooling rates more than 13 orders of magnitude smaller than those for pure metals. However, there are a number of other features of interatomic potentials beyond hard-core interactions. How do these other features affect the glass-forming ability of BMGs? In this manuscript, we perform molecular dynamics simulations to determine how variations in the softness and non-additivity of the repulsive core and form of the interatomic pair potential at intermediate distances affect the GFA of binary alloys. These variations in the interatomic pair potential allow us to introduce geometric frustration and change the crystal phases that compete with glass formation. We also investigate the effect of tuning the strength of the many-body interactions from zero to the full embedded atom model on the GFA for pure metals. We then employ the full embedded atom model for binary BMGs and show that hard-core interactions play the dominant role in setting the GFA of alloys, while other features of the interatomic potential only change the GFA by one to two orders of magnitude. Despite their perturbative effect, understanding the detailed form of the intermetallic potential is important for designing BMGs with cm or greater casting thickness.

The likelihood that an undercooled liquid vitrifies or crystallizes depends on the cooling rate R. The critical cooling rate R(c), below which the liquid crystallizes upon cooling, characterizes the glass-forming ability (GFA) of the system. While pure metals are typically poor glass formers with R(c)>10(12)K/s, specific multi-component alloys can form bulk metallic glasses (BMGs) even at cooling rates below R∼1 K/s. Conventional wisdom asserts that metal alloys with three or more components are better glass formers (with smaller R(c)) than binary alloys. However, there is currently no theoretical framework that provides quantitative predictions for R(c) for multi-component alloys. In this manuscript, we perform simulations of ternary hard-sphere systems, which have been shown to be accurate models for the glass-forming ability of BMGs, to understand the roles of geometric frustration and demixing in determining R(c). Specifically, we compress ternary hard sphere mixtures into jammed packings and measure the critical compression rate, below which the system crystallizes, as a function of the diameter ratios σ(B)/σ(A) and σ(C)/σ(A) and number fractions x(A), x(B), and x(C). We find two distinct regimes for the GFA in parameter space for ternary hard spheres. When the diameter ratios are close to 1, such that the largest (A) and smallest (C) species are well-mixed, the GFA of ternary systems is no better than that of the optimal binary glass former. However, when σ(C)/σ(A) ≲ 0.8 is below the demixing threshold for binary systems, adding a third component B with σ(C) < σ(B) < σ(A) increases the GFA of the system by preventing demixing of A and C. Analysis of the available data from experimental studies indicates that most ternary BMGs are below the binary demixing threshold with σ(C)/σ(A) < 0.8.

Bulk metallic glasses (BMGs) are amorphous alloys with desirable mechanical properties and processing capabilities. To date, the design of new BMGs has largely employed empirical rules and trial-and-error experimental approaches. Ab initio computational methods are currently prohibitively slow to be practically used in searching the vast space of possible atomic combinations for bulk glass formers. Here, we perform molecular dynamics simulations of a coarse-grained, anisotropic potential, which mimics interatomic covalent bonding, to measure the critical cooling rates for metal-metalloid alloys as a function of the atomic size ratio σS/σL and number fraction xS of the metalloid species. We show that the regime in the space of σS/σL and xS where well-mixed, optimal glass formers occur for patchy and LJ particle mixtures, coincides with that for experimentally observed metal-metalloid glass formers. Thus, our simple computational model provides the capability to perform combinatorial searches to identify novel glass-forming alloys.