Structural Phase Transitions by Design in Monolayer Alloys - ACS

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Structural Phase Transitions by Design in Monolayer Alloys Karel-Alexander N. Duerloo, and Evan J. Reed ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b04359 • Publication Date (Web): 08 Dec 2015 Downloaded from http://pubs.acs.org on December 12, 2015

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Mo1-xWxTe2 H phase

T’ phase

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WTe2

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WS2 MoSe2 WSe2 MoTe2

MoS2

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T'

3 2 1 0

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4 6 Frequency (THz)


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Lattice constant b / Å

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6.4 6.3 6.2 6.1 6 5.9 5.8 5.7 5.6 5.5 3.1

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MoTe2 WTe2

T' MoSe2 WSe2 MoS2 WS2

3.2 ACS Paragon 3.3Plus Environment 3.4 3.5 Lattice constant a / Å

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stable

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H 1

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H + T' MoTe2

W content

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H 2

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WTe2

MoTe2

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H

MoTe2

Mo

W

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WTe2

Te

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Structural Phase Transitions by Design in Monolayer Alloys Karel-Alexander N. Duerloo, and Evan J. Reed* Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, United States

ABSTRACT: Two-dimensional monolayer materials are a highly anomalous class of materials under vigorous exploration. Mo- and W-dichalcogenides are especially unusual two-dimensional materials because they exhibit at least three different monolayer crystal structures with strongly differing electronic properties. This intriguing yet poorly understood feature, which is not present in graphene, may support monolayer phase engineering, phase change memory and other applications. However, knowledge of the relevant phase boundaries and how to engineer them is lacking. Here we show using alloy models and state-of-the-art density functional theory calculations that alloyed MoTe2-WTe2 monolayers support structural phase transitions, with phase transition temperatures tunable over a large range from 0 to 933 K. We map temperaturecomposition phase diagrams of alloys between pure MoTe2 and pure WTe2, and benchmark our methods to analogous experiments on bulk materials. Our results suggest applications for two-dimensional materials as phase change materials that may provide scale, flexibility, and energy consumption advantages.

*

To whom correspondence should be addressed: Email: [email protected] Tel: [+1] (650) 723-2971 Fax: [+1] (650) 725-4034 URL: http://www.stanford.edu/group/evanreed Postal: 496 Lomita Mall, Stanford, CA 94305, USA 1 ACS Paragon Plus Environment

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Keywords: molybdenum ditelluride, phase transition, two-dimensional material, cluster expansion, phase diagram

The discovery of two-dimensional (2D) atomically thin materials1 has unleashed a wave of innovation and continues to present new challenges to our understanding of materials physics and chemistry. 2D materials are a diverse family of crystals ranging from elemental allotropes to complex compounds.1,2 One prominent group of compounds having a 2D crystalline form is the six-membered family of Mo- and W-dichalcogenides. The general formula for these compounds is MX2, where M = Mo or W and X = S, Se or Te. Notable applications for this monolayer family include nanoscale flexible electronics,3–6 hydrogen evolution catalysts,7,8 valleytronics9,10 and electromechanical devices.11–13 Mo- and W-dichalcogenides are especially unusual monolayer materials, because they can exist in several 2D phases.14 Each phase has a distinct crystal structure and set of physical properties. 2D phase engineering in Mo- and W-chalcogenides is of significant interest, in part because one monolayer phase is semiconducting (electronic band gaps between 1 and 2 eV)15 whereas the others have band gaps that are zero15 or only on the order of 10 meV.16

The relative stability of competing material phases is expected to be a function of degrees of freedom that include temperature, strain, defects, chemistry and charge. Thus far, intriguing mechanisms for chemical control of phase stability have been demonstrated for 2D materials and exfoliated layered materials. Lithium-based chemical exfoliation of bulk crystals has been shown to be a successful process for obtaining a

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metastable metallic phase of Mo- and W-chalcogenides.14,17,18 Lin et al. recently demonstrated19 an in-situ phase transition in MoS2 using an electron beam. Recent reports have been made of transformations between metallic and semiconducting phases of thin film MoTe2, as a function of the chemical tellurization rate of a Mo film.20 Finally, bulk MoTe2 is reported to undergo a semiconductor-to-metal phase transition at high temperature16,21 In a 2D device context, such a thermal mechanism of phase control may have significant advantages in capability and ease of implementation over counterparts requiring changes in chemistry or moving parts. This work will focus on temperature as a particularly attractive lever for two-dimensional phase transitions.

If well understood, the engineering of temperature-driven structural phase transitions between 2D crystals is of potentially high impact in the field of phase change memory (PCM) devices. Current PCM technology principally revolves around highly unusual bulk crystals that have phase transitions with high electrical conductivity or optical contrast at moderate transition temperatures.22 If this desirable combination of features were to be realized in a 2D material, PCM devices could also benefit from the mechanical flexibility and the reduced volume of 2D materials, which can reduce the energy required for switching, one of a number of key performance metrics for nonvolatile devices.

Chemically-induced structural phase transitions in 2D materials are reported to exhibit hysteresis and long lived metastable states in MoS214 and in WS2 persisting for at least five days,7 creating a rich landscape of phase engineering opportunities. Phase


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engineering has intriguing applications even in the static limit: for example, metallic regions of Mo- and W-chalcogenide monolayers have been associated with enhanced catalytic activity leading to hydrogen evolution,7 and local metallic regions have been shown to improve contact performance in MoS2.23

Results and Discussion

Figure 1a shows the two lowest-energy structural phases of MoS2, WS2, MoSe2, WSe2, MoTe2 and WTe2, which we will refer to as H and T’. Under ambient conditions, all six compounds except WTe2 are reported to exist in a layered bulk crystal structure composed of stacked H monolayers.24 Mo- and W-chalcogenide monolayers in the H structure are semiconductors with photon absorption gaps between 1 and 2 eV.4 The semimetallic24 T’ phase is found in WTe2 under ambient conditions,24 high-temperature MoTe2,25 and frequently as a metastable phase in chemically exfoliated14 and restacked26 monolayers. Recent work16 has reported 10 meV-scale band gap opening in few-layered

1 T’-MoTe2. H and T’ are approximately related by a displacement (vector − [0 1] in 3 Figure 1a) of all chalcogenide atoms on one side of the monolayer. The energy barrier for a displacive transition along such a trajectory is approximately 0.88 eV per formula unit, computed using a nudged elastic band approach.15 There also exists a highersymmetry metallic T phase (not shown in Figure 1a). Density functional theory (DFT) calculations indicate that this phase, at least in the absence of external stabilizing factors, is unstable and is considerably higher in energy than the broken-symmetry T’ phase15 for the Mo- and W-chalcogenide monolayers that we study here. Excess charges donated 4 ACS Paragon Plus Environment

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from a monolayer’s surroundings are believed to stabilize the T phase, particularly for sulfide monolayers.14,27–30 Computed energy differences between freely suspended charge-neutral T and T’ are 0.5 and 0.7 eV per formula unit of MoTe2 and WTe2, respectively.15

Figure 1b shows the DFT-based energy differences between the H and T’ monolayer phases, with each phase at its stress-free equilibrium lattice constants for all six pure MX2 compounds. The T’-H energy difference is correlated primarily with the chalcogenide species X, where X=Te leads to the smallest energy differences: 44 meV and -85 meV per MoTe2 or WTe2 formula unit, respectively. These data are consistent with experimental evidence that the bulk form of WTe2 is in the T’ phase, whereas all the other compounds shown crystallize in the semiconducting H phase.24 The phase energetics in Figure 1b establishes MoTe2 and WTe2 as the best candidates for accessible

H ↔ T phase transitions in these two-dimensional materials.

Temperature can control phase stability between competing solid phases when these have strongly differing vibrational spectra, each captured by the phonon density of states (PDOS). The vibrational free energy Fvib. for N formula units of MX2 is straightforward to compute under assumption of mode harmonicity:31 ) # 1 "ℏ . = PDOS ⋅ ℏ + ln 1 − ! $% & '( d. 2 *

Equation 1 5 ACS Paragon Plus Environment

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At their respective equilibrium lattice constants, each phase has its own zero-

stress Gibbs free energy: , = . + -* , composed of Fvib. and the energy U0 without vibrational effects. Gibbs free energies for H and T’ can thus be computed from the PDOS shown in Figure 1c. For freely-suspended H- and T’-MoTe2, we calculate that one would need to heat freely-suspended monolayer MoTe2 above 933 K in order for the T’ phase to have lower total Gibbs free energy than H under conditions of constant stress.

We hypothesize that H-T’ transition temperatures can be tuned to lower values closer to ambient conditions when using alloyed monolayers rather than pure compounds such as MoTe2. Here, alloying refers to substituting a fraction of one atomic species with another species within the same monolayer, as shown in Figure 2. We consider singlelayer alloys here, rather than stacks of multiple pure, unlike monolayers as are commonly studied.

The remainder of this Article will proceed as follows. As a first step, we rationalize Mo1-xWxTe2 (Figure 2) as a promising phase engineering alloy. We then develop generalized DFT-parameterized analytical models for microscopic alloy energetics, and for thermal free energy and thermal expansion. Both sets of models serve as the foundation for Gibbs and Helmholtz free energy landscapes, leading to the first realization of a thermal phase diagram for two-dimensional materials in a monolayer alloy composition space. We validate this monolayer Mo1-xWxTe2 phase diagram by independent calculations. Our modeling methods, which are fully described in the


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Methods section, are validated against a reported bulk, experimental phase transition temperature in pure MoTe2.

The general formula for the Mo- and W-dichalcogenide alloy system is Mo1xWxS2-2y-2zSe2yTe2z.

Several subsets of this monolayer alloy space have been investigated

and synthesized.32–38 We focus on a subspace 0 ≤ 0 ≤ 1, 2 = 0, 3 = 1 for three reasons.

First, WTe2 is a promising candidate for alloying since it is the only monolayer in the T’ phase at ambient conditions. Second, we seek to alloy materials with minimal difference in lattice constants because solid solution phases might be difficult to stabilize in the presence of strong impurity-impurity interactions or large local deformations around impurity sites. The impact of such effects is expected to be commensurate with the lattice constant mismatch of the monolayer compounds that participate in the alloy. Figure 3 shows that these monolayer compounds’ lattice constants15 are much more strongly correlated with the chalcogenide species than with the transition metal species. Thus, solid solution phases with WTe2 may be the most stable when alloying within the tellurides, i.e. Mo1-xWxTe2. Third, synthesis techniques for a binary alloy such as Mo1xWxTe2

are likely easier to develop than counterparts with more compositional degrees of

freedom. The synthesis of two-dimensional telluride materials is still a developing field. MoTe2 crystals can presently be grown,20,39,40 and support exfoliation of single monolayers and few-layer flakes.41,42

Bulk, three-dimensional Mo1-xWxTe2 alloys have previously been observed to exist in more than one structural phase, with the dominant phase or two-phase 7 ACS Paragon Plus Environment

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coexistence depending on the alloy’s compositional parameter x.43 Here we introduce Mo1-xWxTe2 alloys into the realm of monolayer materials, extending their phase diagram to a wide range of chemical compositions and temperatures. We will find that the chemical composition of these alloy monolayers allows tuning of transition temperature, a highly useful feature for enabling phase engineering and phase change memory applications in 2D materials.

We begin by investigating the thermodynamic stability of H-Mo1-xWxTe2 and T’Mo1-xWxTe2 monolayers by constructing a lattice energy model for the energy of microscopic alloy configurations. We subsequently parameterize this model by fitting to a large set of DFT calculations. The Methods section of this article describes this procedure in detail. We find that microscopic impurity-impurity interactions between neighboring W atoms are weakly repulsive, having interaction energies on the order of 1 meV. The relative weakness of these impurity-impurity interactions is expected to lead to deposition of a homogeneous, random pattern of W atoms at growth temperatures. Such a random pattern has been observed in earlier experiments on Mo1-xWxS2 monolayers.32

In this investigation of the thermodynamics of competing crystal structures, the Helmholtz free energy 4 5 6, 7, , 0 is the governing thermodynamic potential at fixed lattice constants (a,b), fixed temperature T and atomic concentration x of tungsten atoms. We obtain analytical expressions for alloy energy and temperature-dependent free energy using a mean-field model that is developed in the Methods section and Supporting Methods 1. We find that the mean-field free energy 489 per Mo1-xWxTe2 formula unit of

5


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a monolayer with structural phase P = {H, T } can be described using Equation 2, as a linear interpolation between the respective energies of pure MoTe2 and WTe2, plus a temperature-dependent entropic configurational term and a mean-field mixing energy term − > 5 0 1 − 0 : < =

1

5 489 = 1 − 0 ⋅ ? 5 0 = 0 + 0 ⋅ ? 5 0 = 1 − ABCDE. − > 5 0 1 − 0 2 Equation 2

Here the configurational entropy ABCDE. is defined as − F0 log 0 + 1 −

0 log 1 − 0 I. In the Methods section, we show that > J = 0.0252 eV and > NO Q = P

0.0156 eV. Equation 2 captures some temperature dependence through its −ABCDE term,

but does not yet contain the temperature-dependent free energy 4. due to ionic

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vibrations, as defined in Equation 1. Equation 3 provides an analytical expression for 4 5 6, 7, , 0 incorporating a vibrational contribution: 4 5 6, 7, , 0 = 1 − 0 4 < =

5

6, 7, , 0 = 0 + 04 5 6, 7, , 0 = 1 −

> 5 0 1 − 0 − ABCDE. . Equation 3

We use Equation 3 to generate 4 5 6, 7, , 0 for arbitrary values of x using DFT

calculations at opposite extremes of the alloying spectrum. Here the free energies 4

5

at

0 = 0 (pure MoTe2) and 0 = 1 (pure WTe2) are composed of a DFT-calculated energy without vibrational effects ?

5

and vibrational free energy 4. calculated using Equation

5


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1. We assume in Equation 3 that the composition dependence of the vibrational free energy 4. is a linear interpolation between its computed values at x = 0 and at x = 1. We

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show in Supporting Methods 1 that this assumption is accurate for our purposes.

The free energy in Equation 3 is appropriate for comparison between monolayer phases when both phases are constrained to exist with the same fixed set of lattice constants (a, b). This constraint may apply with strongly binding, high friction substrates that prevent the lattice constants from changing when the phase transformation occurs. This is an unusual constraint that is quite different from relevant constraints for bulk materials. Complementary to the Helmholtz free energy, Gibbs free energy governs stability between monolayer phases at the same stress state and different lattice constants (a, b). In a scenario where the monolayer only weakly interacts with its substrate, is free to slide on a substrate, or is freely suspended, lattice constants or area of the monolayer are free to change when the transition occurs, maintaining a state of constant stress which we take to be zero stress here. In this stress-free case the Gibbs free energy S 5 is the minimum of 4 5 over (a, b), i.e. S 5 , 0 = minV,W 4 5 6, 7, , 0 . When vibrational

effects are included, the unclamped lattice constants also depend on temperature through thermal expansion. Supporting Methods 1 describes the computation of S 5 in more detail. Given that > J and > NO Q are both positive, the computed Helmholtz and Gibbs P

free energies are both convex functions of x. Consequently, each single phase is stable in the sense that it does not segregate into W-rich and W-depleted versions of the same 10 ACS Paragon Plus Environment

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structural phase. However, phase stability is more complicated in the case of Mo1-xWxTe2 because there is more than one structural phase at play. Given some concentration x, either the H- or T’-phase may be thermodynamically unstable because the competing phase has a lower free energy. Alternatively, the most stable state of a Mo1-xWxTe2 monolayer might not be a single phase but rather a two-phase coexistence. We construct stable and metastable phase diagrams using the DFT-computed S 5 and 4 5 . Free energy landscapes can be constructed using S 5 or 4 5 , depending on the prevailing thermodynamic constraints. A schematic example of such a landscape is shown in Figure 4. Two types of thermodynamic phase diagrams can be extracted from this data. The first type is the stable or diffusional phase diagram that strictly follows the convex hull, including a two-phase regime following an energy-minimizing common tangent between both free energy curves. This convex hull is shown in Figure 4a. The common tangent between the H and T’ curves describes the free energy of a W-depleted H and W-rich T’ phase coexistence. Figure 2 shows a schematic example of such a twophase monolayer. This analysis makes the assumption that the two-phase monolayer consists of phase regions sufficiently large that the total interface energy between them is negligible. The actual size of these regions may depend on the interface energy and the constraint provided by the substrate, where small interfacial energies may allow twophase regimes on the nanoscale.

Because a two-phase regime requires diffusional redistribution of W atoms into a W-depleted H phase and a W-rich T’ phase, this scenario may be most likely observed at


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higher temperatures, and may be suppressed at sufficiently low temperatures.

The

timescale of long-range diffusion of W in solid phases also likely depends critically on the concentration of defects in the monolayer. On the other hand, the H-T’ structural transition requires no long-ranged motion of chalcogenide or metal atoms and therefore has the potential to be faster under most circumstances.

The second type of phase diagram, the metastable or diffusionless diagram, is valid when W diffusion is suppressed on the experimental timescale maintaining a homogeneous mixture of W and Mo atoms. In this case, the intersection of the singlephase energy curves marks the boundary between a single-phase H regime and a singlephase T’ regime. The metastable system follows the pink curve in Figure 4b, which is higher in energy than the stable curve following the two-phase common tangent. In this case the metastable system is in chemical disequilibrium, frozen in place by quenched W diffusion kinetics.

We generate composition-temperature phase diagrams for two mechanical conditions. The case that we explore first is that of fixed lattice constants. The lattice constants a0 and b0 are set to 3.555 Å and √3 ⋅3.555 Å respectively, representing approximately the tellurides’ H phase equilibrium lattice constants. The second set of phase diagrams apply in the zero-stress ensemble with thermal expansion. Figure 5 shows compositiontemperature phase diagrams for all four combinations of fixed lattice versus relaxed lattice conditions and stable versus metastable thermodynamics. We also re-compute these phase diagrams after including spin-orbit coupling (SOC) effects in the underlying


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non-vibrational energy ?

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, while retaining non-SOC calculated vibrations. Supporting

Methods 2 justify this hybrid SOC treatment. Figure 5 shows abundant potential for phase engineering experiments in monolayer alloys. The individual phase diagrams in Figure 5 intentionally cover a wide array of thermodynamic constraints to create confidence that phase transitions are an effect that is expected to be widely accessible in Mo1-xWxTe2 alloys, rather than localized to a highly specific set of experimental conditions.

The most significant impacts of the SOC are to shift the transition

temperature of pure MoTe2 down approximately 200 K under constant stress conditions (relaxed lattice case in Figure 5), and to shift the metastable case phase boundaries to W concentrations lower by up to 0.2. These changes are quantitative and have no qualitative impact on the main conclusions of this study.

In order to better understand the magnitude of errors associated with our approach in constructing free energy landscapes, we perform an additional set of calculations on a

large Mo14W4Te36 ( 0 = 2/9 ) computational cell. As with the Gibbs free energy calculation on pure compounds, we allow for thermal expansion. For both H and T’, we calculate S\ , 2/9 for a randomly chosen alloy configuration i (] = {1,2,3}). We

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extract nine approximate metastable transition temperatures \^ at which S\ N\^ , 2/

J

9Q = S^

NOP Q

N\^ , 2/9Q. These transition temperatures can be directly compared to the

metastable, relaxed lattice phase diagram in Figure 5. As Supporting Figure 2 shows, the actual \^ values fall within approximately 50 K of the predicted metastable phase boundary. An alternative way to regard this offset is that the predicted W concentration


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for a metastable transition at 400 K differs by approximately 0.02 from the actual concentration. These discrepancies are minor in comparison to the difference between the spin-orbit coupling and non-spin-orbit coupling diagrams. We continue our analysis of the 0 = 2/9 sample calculations, this time from an electronic perspective. Figure 6 shows the DFT-computed electronic density of single particle Kohn-Sham states (EDOS) around the Fermi level for one H and one T’ alloy configuration. The EDOS between different configurations of the same phase at 0 = 2/9

are found to be similar. As with pure MoTe2 and WTe2, the H and T’ phase differ in that H has a band gap whereas T’ has electronic states around the Fermi level. Thus, a phase transition between H and T’ alloy monolayers is expected to exhibit a large contrast in electronic properties, suggesting intriguing applications in an electronics and infrared context. The addition of W impurities does not appear to lead to any mid-gap dopant states at the semilocal exchange and correlation Kohn-Sham level of theory. The results in Figure 6 do not include SOC effects. The joint inclusion of SOC effects and hybrid exchange-correlation functionals has been reported elsewhere to predict a gap on the order of 10 meV in monolayer T’.16

In order to gauge the accuracy of Equation 1 parameterized by DFT calculations to predict thermal phase transitions, we also apply this technique to the reported thermal semiconductor-to-metal transition in bulk MoTe2 occurring at temperatures between 1093 K and 1153 K,21 and between 773 K and 1173 K for a spectrum of MoTe2 samples

ranging from Te-deficient to Te-rich.16 Our calculation predicts a bulk H → T transition 14 ACS Paragon Plus Environment

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at a temperature of 1103 K at zero pressure, not including SOC corrections (see Supporting Figure 3), consistent with these experimental numbers.16,21

This result

suggests that the particular set of approximations made in this work lead to reasonable agreement with experiments. The non-SOC calculations may be a better prediction of experimental numbers than the SOC calculations, although the approximately 200 K transition temperature difference between SOC and non-SOC monolayer calculations appears to be comparable to the uncertainty in some experimental measurements.16

A

cancellation of errors could play a role in the computed 1103 K transition temperature for bulk MoTe2, due to combined disregard for both SOC and anharmonic effects. Anharmonic contributions to vibrational free energy are not captured in Equation 1, but could play a role in the high-temperature regime at which pure MoTe2 transforms.

Thermodynamic variables other than temperature may also affect H-T’ phase transitions. The presence of charges, particularly in experiments with a chemical history, is also a potentially important factor given studied relationships between excess charge and the T phase.14,27–30

The observed difference between the computed bulk transition temperature of 1103 K and the suspended monolayer transition temperature of 933 K is modest, owing to weak phonon dispersion along the bulk out-of-plane axis. This difference suggests a range of approximately 200 K for tuning the phase boundary temperature with layer number. These results also suggest that growth of MoTe2 could initially occur in the T’ phase if the temperatures are sufficiently high, followed by a phase change to H upon


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cooling. Whether this vapor→T’→H sequence occurs in laboratory settings depends in part on substrate binding effects, which are not comprehensively modeled in this work. This indirect route to H phase growth process differs for other commonly grown transition metal dichalcogenides like MoS2, where growth occurs in the H phase.

Comparison of our monolayer phase diagram to experimental data on bulk Mo1xWxTe2

is possible for various values43 of x and is illustrated in Supporting Figure 4.

While the approximately 200 K difference between the transition temperatures in monolayer and bulk MoTe2 calculation cases suggest that this comparison should not be a perfect one, it is nevertheless expected to be qualitatively similar. We find that the concentrations at which this experimental work observed H, T’ and intermediate twophase regimes coincide roughly with the relaxed-lattice, non-SOC monolayer phase diagram of Figure 5. Furthermore, the limited occurrence of two-phase regimes in this experiment is qualitatively similar to the metastable phase diagram which assumes no W diffusion. The narrowness of the experimental two-phase regime suggests incomplete diffusional W equilibration on the timescales over which the reported experimental samples were cooled after growth.

The results presented so far provide a purely thermodynamic picture, but kinetic effects and diffusion timescales may also play an important role. For instance, kinetics will determine which of the stable and metastable phase diagrams of Figure 5 are relevant at the experimental timescale. Kinetic effects may also effectively stabilize metastable T’ in quenched and strongly undercooled scenarios. Prior nudged elastic band calculations15


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place the energy barrier of a coherent, displacive H→T’ transformation in monolayer MoTe2 at 0.88 eV per formula unit. This single number likely presents a greatly oversimplified picture of processes that will experimentally depend strongly on factors such as interface energies, substrate, temperature, strain and impurities. In laboratorytimescale experiments on bulk MoTe2, H → T′ transitions are experimentally reported to

occur at 1093 K to 1153 K,21 and the converse, exothermic T’ → H transition also occurs

in the absence of fast quenching between 773 and 1093 K.16,21 Bidirectional T’ ↔ H

phase transitions have also been reported in MoTe2 thin film growth experiments on 10minute timescales at growth temperatures.20 Differential scanning calorimetry

measurements are reported to observe T’ → H transitions in bulk WS2 on timescales on

the order of one minute at high temperatures.44 The above experiments support the

modeling methods and assumptions used here, while creating confidence that these phase transitions do in fact occur on relevant, laboratory timescales.

Conclusion The calculations we present significantly extend the available experimental phase diagram by showing that the transition temperature can be tuned over a large range in temperature by adjusting the alloy stoichiometry, a critical feature for a practical phase change material. One can envision using the computed monolayer phase diagrams in Figure 5 toward the design of growth and thermal processes aimed at obtaining a specific monolayer phase (or combination of phases). The large contrast in electronic properties between the H and T’ phases raises other intriguing technological possibilities. For example, these phase diagrams suggest that monolayer alloys could be used as electronic 17 ACS Paragon Plus Environment

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phase-change memory elements via a combination of temperature quenching and annealing steps, as is done in emerging GeSbTe phase-change memory technology. Monolayer phase change materials may be competitive with GeSbTe with respect to lower latent heat and potentially smaller volumes, potentially leading to lower energy consumption. For example, we compute that the latent heat released in a T’→ H transition of Mo14W4Te36 is approximately 3 meV/atom. The latent heat of Ge2Sb2Te5 is estimated to be 14 meV/atom.45 It is possible to speculate that lithographic techniques that excite localized portions of the monolayer could be used to engineer electronic properties of a phase-changing monolayer device, providing microscopically engineered patterns of H and T’ phases and phase boundaries, similar to the coherent H-T’ heterostructures demonstrated in chemically exfoliated MoS2.14

H-T’ phase transition temperatures in Mo1-xWxTe2 monolayers can be manipulated through W content, and the metastable phase transition can be tuned arbitrarily close to room temperature if desired. This feature may unlock other, nonthermal degrees of freedom that switch monolayer phase stability such as strain15, which we have previously studied for phase transition potential. The large range of tunability of transition temperatures may also render Mo1-xWxTe2 alloys competitive with metal-toinsulator phase change materials such as VO246, which are less amenable to phase boundary engineering with standard mean field electronic structure approaches due to their strongly correlated electronic nature and/or challenges with self interaction corrections.


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Methods Lattice gas model A Mo1-xWxTe2 monolayer will feature some microscopic distribution of Mo- and W- atoms on the transition metal sites (see Supporting Figure 1). Equation 4 gives the lattice gas approximation (or equivalently, low-order cluster expansion47) for the extensive energy of a H-phase monolayer under some microscopic configuration of Moand W-atoms:

J

J - J = ?* − b J ∑e \f< d\ + ?< ∑D.D. \g^ d\ d^ .

Equation 4 ?* , b J and ?
j avoiding the double counting of pairs. The lattice gas model applied to T’ includes second- and third-nearest neighbors that would have been firstnearest neighbors in the more symmetric H phase (see Supporting Figure 1):

-

OP

=

NOP Q ?*

−b

+ ?l

NOP Q

NOP Q

e

h d\ + ?< \f

Structural Phase Transitions by Design in Monolayer Alloys - ACS

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