Suitability of binary oxides for molecular-beam epitaxy source materials: A comprehensive thermodynamic analysis

We have conducted a comprehensive thermodynamic analysis of the volatility of 128 binary oxides to evaluate their suitability as source materials for oxide molecular-beam epitaxy (MBE). 16 solid or liquid oxides are identified that evaporate nearly congruently from stable oxide sources to gas species: As2O3, B2O3, BaO, MoO3, OsO4, P2O5, PbO, PuO2, Rb2O, Re2O7, Sb2O3, SeO2, SnO, ThO2, Tl2O, and WO3. An additional 24 oxides could provide molecular beams with dominant gas species of CeO, Cs2O, DyO, ErO, Ga2O, GdO, GeO, HfO, HoO, In2O, LaO, LuO, NdO, PmO, PrO, PuO, ScO, SiO, SmO, TbO, Te2O2, U2O6, VO2, and YO2. The present findings are in close accord with available experimental results in the literature. For example, As2O3, B2O3, BaO, MoO3, PbO, Sb2O3, and WO3 are the only oxides in the ideal category that have been used in MBE. The remaining oxides deemed ideal for MBE awaiting experimental verification. We also consider two-phase mixtures as a route to achieve the desired congruent evaporation characteristic of an ideal MBE source. These include (Ga2O3 + Ga) to produce a molecular beam of Ga2O(g), (GeO2 + Ge) to produce GeO(g), (SiO2 + Si) to produce SiO(g), (SnO2 + Sn) to produce SnO(g), etc.; these suboxide sources enable suboxide MBE. Our analysis provides the vapor pressures of the gas species over the condensed phases of 128 binary oxides, which may be either solid or liquid depending on the melting temperature. © 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0013159., s

because of its clean, ultra-high vacuum environment allowing film synthesis to be monitored by a variety of techniques during growth as well as its notable absence of highly energetic species. These characteristics allow for the precise customization of thin films with very few impurities and minimal disorder. 15 When it comes to preparing materials that are highly sensitive to crystalline perfection, MBE achieves electrical transport characteristics surpassing all other thin film growth methods, making it the gold-standard technique for preparing oxide heterostructures. [16][17][18][19] MBE traditionally utilizes elemental molecular beams-one for each element in the compound being formed-that all impinge on the substrate to form the desired compound. 15 Challenges arise when this approach is applied to oxides. Consider trying to grow a layer of an oxide containing harder-to-oxidize elements on top of a layer that oxidizes easily and one does not want to overoxidize, as in the case for SrTiO 3 /Si or SrTiO 3 /GdTiO 3 . 20,21 Having an increased variety of molecular beams to choose from, for example, ones that deliver species already oxidized, could enhance the ability to make well-controlled heterostructures involving oxides by MBE.
For multicomponent materials such as oxides, one might be tempted to just evaporate the desired oxide directly. In general, such an approach does not work because when most oxides are heated, they do not simply evaporate as molecules with the same composition as the starting material, i.e., congruently. Instead, some of the constituents have higher vapor pressures and evaporate first; they evaporate incongruently. This leads to the composition of what is left behind changing, resulting in the partial pressures of the species that evaporate from a multicomponent source to change over time, making it useless for the controlled deposition of thin films. There are, however, some well-known exceptions to this rule. For example, SiO is known to evaporate congruently in vacuum as SiO molecules. [22][23][24] However, how many other exceptions are there among oxides? Answering this question is important for experimentalists seeking suitable source materials for the growth of oxides by MBE.
Stolyarova and Semenov 22 summarized the gas species emanating from Knudsen cells containing many different binary oxides. Complete data, however, showing the partial pressure of each gas species as a function of temperature are not available for many of these oxides, 22 limiting the usefulness of the information for MBE experimentalists. Lamoreaux et al. 25,26 conducted thermodynamic analyses on the evaporation behavior of the oxides of elements in groups 1, 2, and 12-14 under reducing conditions (O 2 partial pressure, P O 2 = 10 −10 Pa), oxidizing conditions (P O 2 = 2 × 10 4 Pa), and congruent evaporation conditions. By providing the partial pressures of the vapor species over the condensed oxides as a function of temperature, their results 25,26 are widely used to determine if an oxide will make a good MBE source material. Nonetheless, much of the periodic table remains to be filled in as data for many of the oxides of transition metals and rare-earth (RE) metals are missing from their studies. 25,26 This lack of knowledge motivates the present thermodynamic analyses in which we analyze the evaporation behavior of 128 binary oxides; see Table S1 in the supplementary material for a complete list.
In the present work, we perform thermodynamic calculations to comprehensively consider the suitability of binary oxides and two-phase mixtures as potential sources for oxide MBE. Most binary oxides are found to be unsuitable because upon heating, they decompose and evaporate a dominant species that contains either pure oxygen, which pollutes the vacuum environment, or the pure metal, which provides no benefit over using the pure metal directly. A few binary oxides are found that evaporate a metal oxide molecule in the vapor phase and are thus suitable for oxide MBE. Some of these are well appreciated and utilized, while others are new and await experimental verification. Several two-phase mixtures are also found to be suitable for oxide MBE.

II. METHODOLOGY
A. Thermodynamic analysis of evaporation for oxides Equilibrium calculations were performed using the SGTE substance database (SSUB5) 27 within the Thermo-Calc software 28 to assess the evaporation behavior of binary oxides, i.e., the gaseous species and their vapor pressures. For amorphous SiO(am), which is well-known to evaporate congruently, [22][23][24] its close chemical relative GeO(am), and compounds including PtO 2 , Pt 3 O 4 , and PtO, which are missing in the SSUB5 database, thermodynamic descriptions were added using the reported enthalpies (and entropies when available) of formation at 298.15 K for GeO(am), 29 SiO(am), 30 and the Pt-O compounds. 31 In calculating the evaporation behavior of oxides, the gas species with the highest partial pressure-which with the increasing temperature is the first to reach a vapor pressure of 10 −1 Pa-is described as the "dominant" species. The relevance of 10 −1 Pa for MBE is that this partial pressure at the source is typically used for thin film growth. [32][33][34] If two gas-phase species have the same concentration within a factor of 10, they are both considered dominant; this is the case for the binary oxides of CsO 2 , PbO, Rb 2 O, Sc 2 O 3 , TcO 2 , U 4 O 9 , and ZrO 2 .
In thermodynamic calculations, the components of the system are defined as the element of interest and O 2 with the number of moles of the non-oxygen element fixed to one, i.e., n(M) = 1 mol. It is worth mentioning that there are many oxygen-containing species in the gas phase such as O, O 2 , and O 3 . At equilibrium, there is only one independent partial pressure for the independent component O, which can be represented by P O 2 , or P O , or P O 3 , or the partial pressure of any O-containing species, and the partial pressures of other O-containing species are dependent variables and can be calculated. In other words, the number of independent partial pressures (or activity or chemical potential) equals the number of independent components in the system, and the partial pressures of other components (species) can be calculated, but they are not independent.
The partial pressure of O 2 is fixed at 10 −4 Pa, a typical oxygen background pressure in the growth of oxides by MBE, because at higher background pressures, hot filaments and other MBE components are damaged from oxidation and the fluxes from many elemental sources become unstable due to surface oxidation. 35,36 Calculations are made with the gas phase fixed at zero amount as this is considered to represent equilibrium evaporation from an MBE source; when the material evaporates from an MBE source into the open system of MBE, it does not return. It is worth noting that the total pressure in the system equals the vapor pressure of the condensed phases, which varies with temperature in equilibrium with the fixed gas phase and should not be set as a fixed equilibrium condition in thermodynamic calculations. Furthermore, another benefit in using the partial pressure of O 2 as a fixed equilibrium condition is that the oxygen content in the system is self-regulated by the phase stability of the system. This is an open system with respect to O 2 , and the amount of O 2 not only is different in different systems but also varies in the same system as the temperature is changed. An example of the macro file (i.e., the tcm file used by the Thermo-Calc software) to calculate the evaporation of a stable oxide source is provided in Table S3 in the supplementary material.
For metastable oxides in equilibrium with gas, the gas compositions are calculated under the same conditions (temperature, O 2 activity, and moles of the element) as those used for the stable oxide sources, but with all condensed phases removed except for the metastable oxide of interest. Two scenarios are possible when the oxide decomposes; these depend on the kinetics of the compound. If the solid oxide decomposes faster into a metal-oxygen containing gas phase than into another oxide or metal condensed phase, the metastable oxide is potentially useful as an oxide MBE source. If, on the other hand, the solid oxide decomposes faster into another condensed phase (oxide or pure element), O 2 gas will be produced and pollute the vacuum. An example of the macro file to calculate the evaporation of a metastable oxide source is provided in Table S3 in the supplementary material.
For the cases of gas species evaporated from a two-phase mixture of MmOn + M with an overall composition MxOy, the conditions for thermodynamic calculations are n(M) = 1 mol, n(O 2 ) = 0.5y/x mol, and the amount of gas phase is fixed at zero, while the partial pressure of O 2 is determined by the three-phase equilibrium of the two condensed phases and the gas phase. The pressure of the gas phase is much lower than the 10 −4 Pa typical oxygen background pressure used in the growth of oxides by MBE that is mentioned above due to the presence of the pure metal in equilibrium at low temperatures. Nevertheless, when the pure metal becomes metastable at high temperatures, the partial pressure of O 2 can increase significantly as shown in the discussion of Ga 2 O 3 and relevant to suboxide-MBE (S-MBE). An example of the macro file to calculate the evaporation of a two-phase mixture case is provided in Table S3 in the supplementary material.
These two types of calculations, i.e., the cases with the fixed partial pressure of O 2 vs the two-phase mixture, represent the two different thermodynamic constraints on the system, viz., an open system vs a closed system. Even though the MBE chamber is an open system, in practice because gas is exchanged between the MBE chamber and the surroundings via the input of gases and its departure through several vacuum pumps, it can behave like either an open or a closed system depending on the fluxes of metallic elements, the partial pressure of O 2 , and temperature as demonstrated in the discussion of the thermodynamics of MBE (TOMBE) diagram for ternary systems. 19 In the TOMBE diagram, O 2 partial pressure is plotted against temperature and the diagram is labeled with the stable phases with the gas phase always present. For a binary system, in the closed-system regions of the TOMBE diagram, two condensed phases and the gas phase are in equilibrium with one degree of freedom (independent number of potentials) based on the Gibbs phase rule. 37 This is the same situation as typical Ellingham diagrams, such as the two-phase mixture in the present work of two components, with the temperature being the independent potential and the chemical potentials being dependent potentials. Meanwhile in the open-system regions, one condensed phase and the gas phase are in equilibrium with two degrees of freedom. This is the case for a fixed partial pressure of the non-oxygen element with both the temperature and the chemical potential of O 2 being independent potentials in maintaining the two-phase equilibrium. For evaporation, both scenarios are useful as demonstrated in the present work, while for MBE growth of thin films, the open-system scenario with one condensed phase is ideal as demonstrated in the MBE growth of Sr 2 RuO 4 , SrRuO 3 , and CaRuO 3 epitaxial films. 17,19 B. Five scenarios of oxide source evaporation Four possible scenarios for the evaporation of oxide sources are shown in Fig. 1. These are each described in detail below, together with one additional possibility (scenario 5) consisting of the evaporation of mixtures of two condensed phases. Note that we ignore the complex reaction products in scenarios 2-4 for the sake of simplicity; for example, we ignore the possible products of new oxide + O 2 , or new oxide + M, or new oxide + additional oxide, or any combination of them other than the mentioned product MmOn. Scenario 1: Nearly congruent evaporation of metal-oxygen gas species [MxOy(s or ℓ) → MxOy(g); see S1 of Fig. 1]. Here, the letters s, ℓ, and g in the parentheses indicate solid, liquid, and gas phases, respectively. In congruent evaporation, the species that evaporates into the gas phase has the same stoichiometric ratio as the solid or liquid source from which it comes; see additional details in Sec. II C. Two attributes make congruent evaporation the best scenario for MBE sources: (i) when the oxide is heated in the crucible and evaporates, metal-oxygen containing gas species of known composition will traverse the MBE chamber and deposit onto the substrate, and (ii) the metal-oxygen gas species MxOy(g) has the same stoichiometric ratio as the source material MxOy(s or ℓ), so the composition of the source material will remain constant over time, making it easier to provide a stable flux of this molecular beam of known composition. Scenario 2: Incongruent evaporation of metal-oxygen gas species [MxOy(s or ℓ) → MmOn(g); see S2 of Fig. 1]. In incongruent evaporation, the species that evaporate have a different Four scenarios (S1-S4) possible during evaporation plus an additional scenario (S5) examined in the present work with a two-phase mixture of MxOy + M as a source. Note that this plot ignores the possibility of complex reaction products that form from the oxide source for the sake of simplicity.

ARTICLE
scitation.org/journal/apm overall stoichiometric ratio than the solid or liquid source from which they emanate. Like congruent evaporation, incongruent evaporation can work for the MBE process, but it is less ideal. Although metal-oxygen containing gas species will be deposited onto the substrate, the gas species coming off of the oxide source [MmOn(g)] has a different stoichiometric ratio than the source [MxOy(s or ℓ)]. This difference in chemistry will cause the source material composition to change over time, making it more difficult to control the flux and composition of the molecular beam. Scenario 3: Evaporation of oxygen species [MxOy(s or ℓ) → Oz(g); see S3 of Fig. 1]. For some oxides, oxygen species [Oz(g)] will be the dominant species in the vapor. The dominant evaporation of oxygen species from the metal-oxide source is undesirable for an MBE process. In oxide MBE, it is desired to control the oxidant species (often an activated species such as ozone or those emitted from an oxygen plasma) and its flux directly. Oxygen species [Oz(g)] coming from the metal-oxide sources effectively pollute the ultra-high vacuum and cause a loss of the independent control of growth parameters that is desired in MBE. can also be the dominant species given off by the oxide source.
Oxides that evaporate elemental metal species are also undesirable for MBE. Evaporation of the elemental metal causes the oxide source composition to become oxygen rich over time. In addition, using such an oxide source to generate a flux of metal species generally offers no advantage over the use of a pure metal source. Scenario 5: Two-phase mixture of MmOn + M as sources. In addition to the above four scenarios, we also examine one more scenario to produce gas species MxOy from a two-phase mixture MmOn + M with an overall composition MxOy. This scenario builds upon experimental work, showing that this is a viable approach. 38,39 C. Three criteria for a nearly ideal MBE source material Once the gas compositions emanating from the binary oxides are calculated, each binary oxide is evaluated against three criteria based on MBE chamber conditions necessary to produce highquality thin films. A binary oxide source is identified as the most ideal for oxide MBE if it meets all three of the following criteria: Criterion 1. The solid or liquid metal-oxide source is stable under the given conditions. Stable metal-oxide sources are ideal because they do not decompose and release oxygen, which would pollute the MBE vacuum. Some elements in the SSUB5 database 27 such as actinium, astatine, californium, curium, einsteinium, fermium, francium, radium, and protactinium do not have solid or liquid oxides, so these are disqualified. Oxides of some transition metal are disqualified because the stable phase under the given conditions is a pure metal in solid or liquid form. Examples include Ag(s), Au(ℓ), Co(s), Cu(s), Ir(s), Os(s), Pd(s), Rh(s), and Ru(s). A select few of the elements are stable as liquid oxides under the given conditions such as Bi 2 O 3 (ℓ), FeO(ℓ) (i.e., the liquid Fe-oxide phase or the slag phase), Nb 2 O5(ℓ), Rb 2 O(ℓ), Ta 2 O5(ℓ), and Ti 4 O7(ℓ). If an element is able to form a metastable oxide, the metastable oxide is investigated. For example, Ir(s) is the most stable phase under the given conditions, but iridium also forms IrO 2 . Hence, IrO 2 is investigated as a metastable source. Note that the liquid state of FeO(ℓ) is a slag phase with a mixture of all iron oxides (such as FeO, Fe 3 O 4 , and Fe 2 O 3 ) in arbitrary ratios. Usually, melting processes are accompanied by a change in the metal-oxygen stoichiometry to lower the Gibbs energy by mixing, but not in the solid state. Criterion 2. The oxygen-metal containing gas species is dominant. A metal-oxygen gas species [MxOy(g)] is ideal as it provides pre-oxidized metals with the known oxygen content to the growing film when it reaches the substrate. Binary oxides for which the dominant evaporant is the oxygen species or metal species are disqualified as MBE sources for not meeting this second criterion. Criterion 3. The oxide source evaporates nearly congruently. Congruent evaporation ensures that the oxide source provides a constant flux of the desired species at a fixed temperature. This third criterion distinguishes between the most ideal sources for MBE and those that are less ideal because they evaporate incongruently.
Note that for exact congruent evaporation, the composition of the source oxide (solid or liquid phase) and that of the gas phase evaporating from it must be identical. The ideal case is where only one species exists in the gas phase and that species has the same stoichiometric ratio as the solid or liquid MBE source from which it evaporated. This is rarely the case; usually, multiple species evaporate into the gas phase, and congruent evaporation occurs when the overall composition of the gas phase matches that of the solid or liquid MBE source from which it came. As a practical matter, exact congruent evaporation is not needed for a source to perform well in MBE. Sources with evaporation characteristics sufficiently close to exact congruent evaporation can be tolerated. In the present work, we define nearly congruent evaporation as the condition where the mole fraction difference for each component, such as O 2 , in the oxide source and in the gas phase is less than 0.01, i.e., |Δx(O 2 )| < 0.01, with where x(oxide, O 2 ) and x(gas, O 2 ) are the mole fractions of the component O 2 in the oxide source (s or ℓ) and in the gas phase, respectively. The same condition is also used to define what we mean by the nearly congruent evaporation of metastable oxide sources.

III. RESULTS AND DISCUSSION
In the SSUB5 database, 27 58 elements have stable solid oxides and 14 elements have metastable oxides under the given conditions. To make the present study more comprehensive, additional metastable oxides under the given conditions are included. The list of all evaluated 128 stable and metastable oxides and 17 elements under the given conditions is available in Table S1 in Table I. are examined, where the elements M considered are rare-earth elements and other elements of practical interest; see Table S2. Note that we do not plot phase stability as a function of temperature for these oxides. Instead, we note in Figs. 2 and 4 and each supplemental figure caption (Figs. S1-S81) the stable phases as a function of temperature for each system.

A. Ideal MBE sources
16 solid and liquid oxides meet the criteria to be classified as ideal MBE sources. These are As 2 O 3 , B 2 O 3 , BaO, MoO 3 , OsO 4 , P 2 O5, PbO, PuO 2 , Rb 2 O, Re 2 O7, Sb 2 O 3 , SeO 2 , SnO, ThO 2 , Tl 2 O, and WO 3 ; see Table I. Some of these oxides have been well studied in Knudsen cell evaporation experiments. Some of the identified oxide sources have been used to make thin films via various deposition methods, but only As 2 O 3 , B 2 O 3 , MoO 3 , PbO, Sb 2 O 3 , SeO 2 , and WO 3 have been used successfully for MBE growth as described in below. We discuss these oxides in Secs. III A 1-III A 13 in alphabetical order except for As 2 O 3 and SnO, which are discussed with Sb 2 O 3 in Sec. III A 9, and PuO 2 , which is discussed with ThO 2 in Sec. III A 11.  Table I.  Fig. 2), and thin films have been successfully fabricated using MBE, the high reactivity of B 2 O 3 with water to form H 3 BO 3 under ambient conditions precludes it from many practical applications. 42 Putkonen and Niinistö 42 applied a protective Al 2 O 3 capping layer using atomic layer deposition (ALD) to prevent the B 2 O 3 thin film from reacting. When patterned, however, the film immediately suffered degradation from the exposed B 2 O 3 edge. Proposed applications of B 2 O 3 thin films include transistors, ultra-wide bandgap amorphous oxide semiconductors, and optoelectronics when combined with other oxides. [43][44][45] Glassy thin films such as B 2 O 3 also have potential as electrolytes used in batteries, as electrochemical sensors, as supercapacitors, and as electrochromic sensors. 45

BaO(s) (Fig. S8)
The calculated evaporation behavior of BaO is shown in Fig. S8 along with that of BaO 2 ; see also Table I. It can be seen that the primary species evaporating from BaO 2 is BaO, so a BaO 2 source works the same as BaO. The dominant BaO species in the molecular beam is relevant to making high dielectric constant perovskites such as BaTiO 3 and (Ba, Sr)TiO 3 , which have applications in high-K (K is the dielectric constant) memory, 46 tunable dielectrics, 47,48 optoelectronics, [49][50][51] and fuel cells. 52,53 Another important bariumcontaining oxide is BaSnO 3 -a semiconductor with high mobility at room temperature-which offers tantalizing properties for transparent electronics. 10,11,54,55 Barium hexaferrites including BaFe 12 O 19 are ferrimagnetic insulators with excellent performance at high frequency. 5,[56][57][58] In addition to complex oxides containing barium, BaO thin films themselves have applications in high current density cathodes, thermionic energy converters, and optical devices. 59 BaO films have been grown by many groups using MBE with separate beams of barium and O 2 . 60-62 Less common, but nonetheless demonstrated, is the growth of BaO films using a BaO 2 source 63 or a BaO source. 64,65 A BaO source could prove particularly advantageous when it is desired to not introduce any excess oxygen, e.g., when growing BaO on silicon and it is ideal to have all of the barium oxidized, yet not to oxidize any of the silicon (which can easily occur if excess oxygen is present). 61 3 powder from an effusion cell onto a substrate held at 673 K-823 K and immersed in activated oxygen species from an oxygen plasma operating at P O 2 = 4 × 10 −4 Pa. MoO 3 molecular beams could be used as a route to grow SrMoO 3 thin films, which are being studied for use as transparent conductors because of their very high conductivity. 69,70 MoO 3 thin films are also used as electrochromic sensors and in lithium batteries. 71 4. OsO 4 (s, ℓ) (Fig. S48) Solid OsO 4 (s) is a stable phase at low temperature, T < 304 K. With the increasing temperature, liquid OsO 4 (ℓ) becomes stable in a narrow temperature range from 304 K to 314 K. Above 314 K, OsO 2 (s) is the stable phase and remains so up to 832 K where solid Os(s) becomes stable. Figure S48 shows that the dominant gas species is OsO 4 (g) at low temperatures, i.e., T < 1028 K in the plot of OsO 2 (s) as an oxide source as well as in the plot of OsO 4 (s) as an oxide source. These results indicate that OsO 4 (s, ℓ) is an ideal source for MBE oxide when T < 314 K at P O 2 = 10 −4 Pa; see also Table I.
The calculated evaporation behavior of solid P 2 O5 with an orthorhombic structure is shown in Fig. S47; see also the data in Table I. P 2 O5 has exciting uses as a bioactive thin film material to modify surface properties of biomedical devices, to increase corrosion resistance, or for osteogenic applications. 72 The P 2 O5 thin films are commonly fabricated using a sol-gel method instead of physical vapor deposition. Stolyarova and Semenov 22 recorded the congruent evaporation of P 4 O 10 to P 4 O 10 gas species from a P 2 O5(s) source at 500 K. No publication in the literature was found using P 2 O5 in an MBE process.
6. PbO(s) (Fig. S50) PbO(s) was shown by Lamoreaux et al. 26 to have dominant species Pb(g) under reducing conditions and PbO(g) under oxidizing conditions. Experiments by Lopatin et al. 73 found that the dominant gas species in PbO(s) evaporated at 900 K-1150 K are PbnOn(g), Pb(g), and O(g). The PbnOn(g) species comes from the congruent evaporation of nPbO(s) → PbnOn with n = 1-6; the Pb(g) and O(g) species come from a partial dissociation of PbO(s) → Pb(g) + 1 2 O 2 . The polymeric PbnOn gas species observed by Lopatin et al. 73 were also included in the evaporation analysis by Lamoreaux et al., 26 but these PbnOn gas species are not included in the SSUB5 database and can thus not be seen in Fig. S50. Although the present work does not take into account the PbnOn (n = 2-6) species, the yellow orthorhombic phase PbO_yellow is dominant below 1163 K under the conditions of our thermodynamic calculations (not shown), which agrees with Lopatin's assessment that PbO is dominant between 900 K and 1150 K.
The evaporation behavior of PbO_yellow in Fig. S50 disagrees with the analysis by Lamoreaux et al., 26 which shows Pb(g) to be dominant from 700 K to 1800 K at P O 2 = 10 −10 Pa. On the other hand, an experimental attempt at using PbO(s) as an MBE source in an MBE system with no added oxygen (and a chamber background pressure in the 10 −10 Pa range) found that PbO(s) decomposed into mainly Pb(g) with very little PbO(g), 74 which is consistent with ARTICLE scitation.org/journal/apm the expectations of Lamoreaux et al. 26 To see if the disagreement between our calculations and those of Lamoreaux et al. 26 is due to the difference in O 2 partial pressure conditions, we redid our calculations as a function of oxygen partial pressure for P O 2 from 10 −1 Pa to 10 −10 Pa. Figure 3 shows the temperatures at which Pb(g) becomes the dominant species in the gas phase as a function of P O 2 ; the temperature at which Pb(g) becomes dominant over PbO(g) decreases with decreasing P O 2 . At the pressure used by Lamoreaux et al., 26 P O 2 = 10 −10 Pa, the calculations show that the partial pressure of Pb(g) exceeds that of PbO(g) at 725 K, in good agreement with findings of Lamoreaux et al. 26 who found that this crossover occurs around 700 K at P O 2 = 10 −10 Pa. A PbO source was used by Rispens and Noheda to grow highquality PbTiO 3 films by MBE. 75 These authors found the use of PbO(s) advantageous over Pb(ℓ), which is consistent with the results from Fig. S50 where the dominant species in the gas phase at MBErelevant growth conditions is PbO. We note that based on the diagram by Lamoreaux et al., 26 PbO is not a good source to use for the growth of PbTiO 3 or other Pb-containing oxides by MBE. This points to the importance of the current comprehensive analysis at a fixed oxygen pressure (10 −4 Pa) that is relevant for oxide MBE and in the case of PbO dramatically changes the dominant species in the gas phase as shown in Fig. 3.  Table I.
At lower P O 2 (e.g., <10 −4 Pa), the vapor is Rb-rich compared to the Rb 2 O source. Although at these lower oxygen partial pressures it is not an ideal MBE source, it should still produce a molecular beam containing a significant fraction of pre-oxidized rubidium in the form of Rb 2 O. Rb 2 O has been used as an MBE source for the growth of superconducting (Bi, Rb)BaO 3 films by Hellman et al. 76 These authors noted that the Rb 2 O source showed signs of decomposition into a Rb-rich molecular beam, consistent with the present calculations at different P O 2 values (Fig. S56). They also mentioned that they did not observe any Rb oxide molecules by mass spectrometry. This is inconsistent with the present calculations with higher partial pressures of O 2 , in which significant Rb 2 O(g) in the gas phase is expected (see P O 2 = 10 −4 Pa and 10 −1 Pa in Fig. S56). A possible reason for this is the strong dependence of the Rb 2 O(g) partial pressure on the oxygen partial pressure. Our calculations are done at P O 2 = 10 −4 Pa (as well as 10 −1 Pa and 10 −7 Pa in the present case); at lower oxygen partial pressures, which are likely the conditions under which Hellman et al. 76 operated their mass spectrometer, Rb(g) becomes the dominant gas species.
8. Re 2 O 7 (s, ℓ) (Fig. S57) Through Knudsen cell studies, Skinner 77 found that Re 2 O7(s) evaporates congruently as Re 2 O7(g) at P O 2 = 2 × 10 −4 Pa and T = 404 K. Due to a small amount of O 2 that simultaneously vaporized, some residual ReO 3 (s) was left in the cell. The ions exhibiting the highest signal in Skinner's mass spectrometry study are in the following order: Re 2 O7, ReO 3 , ReO 2 , Re 2 O 6 , and Re 2 O5. In the present calculations ( Fig. S57 as well as Table I), Re 2 O7 is the dominant gas species followed by Re 2 O 6 , which shares the stoichiometric ratio of ReO 3 . To the best of our knowledge, Re 2 O7(s, ℓ) has not yet been used as an oxide source for MBE growth. Like B 2 O 3 , Re 2 O7 is very hygroscopic, which may limit its applications. 78 9. As 2 O 3 (ℓ) (Fig. S5), Sb 2 O 3 (ℓ) (Fig. S60), and SnO(ℓ) (Fig. S65) Figure S5 indicates liquid As 2 O 3 (ℓ) is a stable phase at higher temperatures (T > 677 K) transformed from solid As 2 O5(s). In the temperature range 677 K-1274 K, As 2 O 3 (ℓ) is a possible ideal MBE source with the dominant gas species of As 4 O 6 (g) at P O 2 = 10 −4 Pa; see also Table I. The behavior calculated for Sb 2 O 3 is analogous to that of As 2 O 3 . At higher temperatures (T > 997 K), liquid Sb 2 O 3 (ℓ) is a stable phase transformed from solid SbO 2 (s). Figure S60 as well as Table I shows that Sb 2 O 3 (ℓ) is also a possible ideal MBE source with the dominant gas species being Sb 4 O 6 (g) in the temperature range of 997 K-1429 K. Nearly congruent evaporation of Sb 2 O 3 (ℓ) is calculated to occur over the temperature range 997 K-1398 K at P O 2 = 10 −4 Pa.
Similar to As 2 O 3 (ℓ) and Sb 2 O 3 (ℓ), at higher temperatures (T > 1498 K), liquid SnO(ℓ) becomes a stable phase. Figure S65 as well as Table I  10. SeO 2 (s, ℓ) (Fig. S62) The calculated evaporation behavior of SeO 2 (s) is shown in Fig. S62 as well as Table I. The results indicate that the gaseous SeO 2 species is dominant when SeO 2 (s) is heated and agree well with Knudsen evaporation measurements between 360 K and 660 K. 22,79,80 Metal oxides including SeO 2 as well as SnO 2 , ZnO, TiO 2 , VO, and WO 3 are particularly good gas sensors because the electrical conductivity of the thin film changes with gas adsorption. 81 and SnO 2 with P O 2 = 5 × 10 −5 Pa. After deposition, the films were annealed in flowing oxygen at 400 ○ C. The specific evaporation behavior of SeO 2 and SnO 2 is not discussed by the authors, 82 but it is likely that SnOx species were in the vapor since SnOx species from an SnO 2 source were noted under similar evaporation conditions. 11 11. ThO 2 (s) (Fig. S71) and PuO 2 (s) (Fig. S55) In agreement with the present calculations ( Fig. S71 as well as Table I), the dominant gas species given off by a ThO 2 source in a Knudsen cell was shown to be ThO 2 (g). 22 The evaporation behavior of ThO 2 is, however, not well studied in the literature, and the use of ThO 2 source materials in MBE is not reported. Similar to ThO 2 (s), PuO 2 (s) has not been reported as an MBE source either. In addition, no Knudsen cell evaporation studies could be found for PuO 2 in the literature.

Tl 2 O(s, ℓ) (Fig. S73)
Tl 2 O was calculated by Lamoreaux et al. 26 to exhibit congruent evaporation behavior under reducing conditions. Tl 2 O is more stable than Tl 4 O 3 and Tl 2 O 3 at low oxygen partial pressures, which makes it ideal for the MBE vacuum environment. 26,83 Tl 2 O powder is widely available from commercial distributors but is quite toxic. One concern with Tl 2 O is its high reactivity with O 2 and many other elements at elevated temperatures. 83 Holstein 83 used an argon atmosphere to mitigate this issue and found the vapor pressure of Tl 2 O(g) over the Tl 2 O(s) source to be 29 Pa at 820 K, which agrees well with the evaporation behavior calculated in the present work ( Fig. S73 and Table I). Tl 2 O has been used in the growth of thin films of the high-temperature superconductors Tl-Ba-Ca-Cu-O and Tl-Pb-Sr-Ca-Cu-O, but no literature was found showing Tl 2 O(s, ℓ) used as a source material in MBE. 83 13. WO 3 (s) (Fig. S77) WO 3 (s) is described to vaporize polymerically like MoO 3 (s); 22 see Fig. S77 vs Fig. S41. A Knudsen cell evaporation study by Blackburn et al. 84 showed that (WO 3 ) 3 is the dominant vapor species. WO 2 is also a vapor species but is reported to decompose into (WO 3 ) 3 and W species. 84 The latter observation is not reflected in the present calculations ( Fig. S77 and Table I), since the partial pressures of WO 2 and W in the present calculations are many orders of magnitude lower than that of W 3 O 9 or any of the WxO 3x species. The results shown in Fig. S77 are consistent with a heated charge of WO 3 that provides a beam of W 3 O 9 as described in the Knudsen cell study of Blackburn et al. 84 Li et al. 85 used WO 3 powder as an MBE source to successfully grow WO 3 thin films for applications as a photocatalyst. In their experiments, WO 3 powder was evaporated from a high-temperature effusion cell and deposited as an epitaxial WO 3 film at a substrate temperature of 773 K in the presence of activated oxygen species from an oxygen plasma operating at P O 2 = 4 × 10 −4 Pa. 85

B. Stable solid oxide with incongruent evaporation
Having established which binary oxides evaporate nearly congruently, we next consider the possibility that a metastable binary oxide (if there were some way to produce it and constrain it from not decomposing in the solid state) would evaporate nearly congruently when heated. Table II summarizes the binary oxides that do not meet criterion 3 for nearly congruent evaporation (see Sec. II C) but evaporate incongruently instead. Such oxides are not ideal as the composition of the source will generally change over time as it becomes depleted in some component, but they might still be useful for MBE if they provide a desired gaseous species. In addition to considering the binary oxides in Table II, the species emanating from them with the highest partial pressure, i.e., the dominant gas species, were separately investigated as metastable sources to see if nearly congruent evaporation exists for those species. TcO 2 was also investigated but is omitted from the present work because it exhibits a decrease in vapor pressure with the increasing temperature in our calculations.
1. SnO 2 (Fig. S65) Figure S65 shows the calculated evaporation behavior of SnO 2 as a function of temperature, where the gaseous species SnO is dominant above 1128 K in equilibrium with solid SnO 2 (see also Table II). To provide MBE-relevant fluxes, the temperature of the SnO 2 source is about 1350 K-1400 K, so when an SnO 2 source is used in oxide MBE, SnO is indeed the dominant species in the gas phase. SnO 2 was first used as a source in oxide MBE to achieve n-type doping of Ga 2 O 3 with Sn 4+ . 86 More recently, it has been used to grow BaSnO 3 10,11 and SnO. 87 The La-doped BaSnO 3 films grown by MBE with an SnO 2 source exhibit the highest mobility 10,11 and the best transistor performance 55 achieved to date, demonstrating SnO 2 as a viable MBE source.
Because SnO(g) is the dominant evaporating species, the use of SnO 2 (s) as an MBE source also provides a possible route to grow Sn 2+ -containing compounds such as p-type semiconductors that are predicted to have high mobility including SnO, 87  Sn 2+ -containing materials. Furthermore, for the synthesis of antiperovskites such as Sr 3 SnO, it is preferable to have SnO arrive to the growth surface pre-oxidized and without any excess oxygen in order to avoid the undesired reaction of Sr 3 SnO with excess oxygen to form unwanted SrO. 92 Finally, the present work (Fig. S65) also indicates that SnO(s) can be a metastable source that nearly congruently evaporates as SnO.
Following the recent experimental work of Hoffmann et al., 39 we also examined the gas species for evaporation from a two-phase mixture of SnO 2 (s) + Sn(ℓ) that has an overall composition SnO. Figure 4 shows that SnO(g) is the dominant gas species, indicating that a mixture of SnO 2 (s) + Sn(ℓ) is also an ideal MBE source providing the nearly congruent evaporation of SnO; see a complete list of the two-phase mixtures examined in Table S2. As discussed in Sec. II A, the partial pressure of O 2 in the two-phase mixture is much lower than the typical MBE background value of 10 −4 Pa, e.g., its value for a two-phase mixture of SnO 2 (s) + Sn(ℓ) at 1200 K is about 10 −9 Pa. The partial pressures of O 2 and all other species in the gas phase are determined by the two-phase equilibrium and are independent of the relative amounts of SnO 2 (s) and Sn(ℓ) in the system. The use of equal amounts of SnO 2 (s) and Sn(ℓ) to give the nominal SnO composition of the source may simplify experimental control if SnO 2 (s) and Sn(ℓ) have similar evaporation rates. If the two condensed phases have very different evaporation kinetics, one may adjust the relative amounts of each phase in the two-phase mixture to provide the desired partial pressures in the MBE beam. Additional impacts of the metal-to-oxide ratio will be discussed in a forthcoming paper where the S-MBE method is more systematically examined. 93 2. Ga 2 O 3 (Fig. S27) The present calculations (Fig. S27) show that Ga 2 O 3 (s) provides a beam of Ga 2 O(g). This is in agreement with the experiments performed by Butt et al. 94 demonstrating that Ga 2 O is the dominant gas species over Ga 2 O 3 (s). We did not investigate the nearly congruent evaporation of Ga 2 O because Ga 2 O(s) is not available in the SSUB5 database 27 [note that Ga 2 O(s) is not a stable phase at 0 K according to first-principles calculations in the OQMD database]. 95 Ga 2 O 3 thin films have several applications, including gas sensing. Its large bandgap, ability to be doped with n-type carriers, relatively high mobility, and high Baliga figure of merit that is second only to diamond also attract tremendous interest for this semiconductor to be used for high-power electronics and ultraviolet (UV) detectors. 13 Another route to produce a molecular beam of Ga 2 O(g) is to use a mixture of Ga(ℓ) and Ga 2 O 3 (s) instead of the incongruent evaporation of Ga 2 O 3 (s). 38,39 Such an approach has the advantage that a much lower temperature is needed to provide the same flux of Ga 2 O(g) in the molecular beam from a Ga 2 O 3 (s) + Ga(ℓ) mixture compared to that from just Ga 2 O 3 (s), see Fig. S27 and Table S2 with the partial pressure of O 2 being 10 −22 Pa at 1000 K. A prior MBE work used an iridium crucible to contain Ga 2 O 3 (s) because of the reactivity of Ga 2 O 3 at high temperatures (in excess of 1900 K) needed to grow Ga 2 O 3 films by MBE from a pure Ga 2 O 3 (s) source. 101,102 This temperature is considerably higher than that expected from Fig. S27 to yield a Ga 2 O(g) partial pressure of 10 −1 Pa (∼1500 K is expected). Using a 5:1 mixture of Ga:Ga 2 O 3 decreases the temperature of the crucible, i.e., the temperature needed to reach the same vapor pressure of Ga 2 O(g), by about 500 ○ C. 38 A more recent MBE study shows similar temperature lowering for a 3.8:1 mixture of Ga:Ga 2 O 3 . 39 Exploiting molecular beams of suboxides such as Ga 2 O(g) to grow films of compounds such as Ga 2 O 3 (s) is a powerful alternative to conventional MBE with many advantages; this approach is termed suboxide-MBE (S-MBE). 93 3. TeO 2 (Fig. S70) TeO 2 thin films have applications as gamma radiation detectors due to their sensitivity to gamma radiation. Sudha et al. 103 thermally evaporated TeO 2 powder onto a glass substrate at 10 −3 Pa to form TeO 2 amorphous thin films for gas sensing; these amorphous films could be subsequently annealed to make them crystalline. The congruent evaporation behavior reported in Sudha et al.'s work 103 disagrees with the incongruent evaporation calculated in the present study of TeO 2 (s) sublimation to Te 2 O 2 (s) at 760 K-892 K, although TeO 2 (s) is the dominant gas species below 760 K (Fig. S70). Unfortunately, Sudha et al. 103 did not provide a temperature for the thermal evaporation of the TeO 2 powder to allow for comparison between their work and the present study. Additionally, Fig. S70 shows that the vapor pressures of Te 2 O 2 , TeO 2 , and Te 2 O 4 gas species decrease at temperatures above 913 K, while the vapor pressures of the other gas species continue to increase based on the present thermodynamic calculations. 27

Rare-earth (RE) oxides
The present calculations (see the figures in the supplementary material) indicate that the majority of the rare-earth oxides share a similar evaporation behavior that is described below. The majority are most stable in sesquioxide form and provide molecular beams of stoichiometric REO (RE = rare earth), making them incongruent evaporation sources for MBE. There are, however, a few exceptions where the gas-phase species with the highest partial pressure is RE or REO 2 : a. Lanthanides with 2+ valence (Fig. S24). EuO(s), SmO(s), and YbO(s) are known to be stable as RE 2+ ions in addition to their sesquioxide forms. EuO(s) is calculated to produce a beam of Eu metal when heated as is its sesquioxide counterpart, Eu 2 O 3 (s); see Fig. S24. Unfortunately, thermodynamic calculations for SmO(s) and YbO(s) as oxide MBE sources could not be performed because they are not included in the SSUB5 database. 27 Experimentally, YbO thin films have been grown by MBE, although using separate beams of ytterbium and O 2 to deposit YbO. 104 The same is true for the ARTICLE scitation.org/journal/apm growth of EuO by MBE: from separate beams of europium and O 2 . [105][106][107] b. Rare-earth sesquioxides. Many of these rare-earth sesquioxides have been investigated as high-K gate dielectrics for use in metal-oxide-semiconductor field-effect transistors (MOSFETs) because of their high dielectric constant, large bandgap, and thermodynamic stability in contact with silicon. [108][109][110][111][112] To investigate these rare-earth sesquioxides as a replacement for SiO 2 in MOSFETs, researchers have used MBE to deposit Sc 2 O 3 , Y 2 O 3 , La 2 O 3 , Pr 2 O 3 , Nd 2 O 3 , Gd 2 O 3 , and Lu 2 O 3 films on silicon from solid oxide sources of these same materials, i.e., from Sc 2 O 3 (s), 113 108,114,118 to Lu 2 O 3 (s). 108 The evaporation behavior of the majority of the sesquioxides proceeds as follows based on high-temperature Knudsen effusion mass spectrometry: 119 where 0 <  (Fig. S61), Y 2 O 3 (Fig. S78), La 2 O 3 (Fig. S36), Ce 2 O 3 (Fig. S14), Pr 2 O 3 (Fig. S53), Nd 2 O 3 (Fig. S44), Pm 2 O 3 (Fig. S52), Sm 2 O 3 (Fig. S64), Gd 2 O 3 (Fig. S28), Tb 2 O 3 (Fig. S68), Dy 2 O 3 (Fig. S21), Er 2 O 3 (Fig. S22), and Lu 2 O 3 (Fig. S38), our thermodynamic calculations indicate that all of these rare-earth sesquioxides should provide molecular beams of REO(g) when heated to a temperature where the dominant species in the gas phase has a vapor pressure of 10 −1 Pa, i.e., the vapor pressure needed for typical oxide MBE growth. Unfortunately, the temperatures needed according to our vapor pressure calculations are near the limit of effusion cells for many of these RE 2 O 3 (s) sources, making it appropriate to use an e-beam evaporator or laser thermal evaporator to produce REO(g) molecular beams with source longevity. 120 Stolyarova et al. 22,121 listed YO(g) as the dominant vapor constituent of thermally evaporated Y 2 O 3 (s). In the present calculations (Fig. S78), however, YO 2 (g) is shown to be the dominant gas species when a Y 2 O 3 source is heated in the temperature range of 1980 K < T < 2680 K, and YO(g) becomes the dominant vapor constituent when T > 2680 K. By omitting YO 2 (g), YO(g) will be the dominant vapor constituent when T > 2370 K (Fig. S78). From the present study of the Y-O system, we note that calculations that disagree with experiments could be because certain gas species are added or omitted from the oxide systems in the SSUB5 database. 27 This is also seen in other systems such as the Pb-O system where the PbnOn species are omitted from the SSUB5 database but included in the analysis by Lamoreaux et al. 26 ; see Sec. III A 5.
For Eu 2 O 3 (and EuO), the present calculations (Fig. S24) reveal that Eu 2 O 3 (s) and EuO(s) should evaporate as Eu(g), which offers no advantage in using oxide sources over elemental europium. The advantage of europium metal is that it can be melted into the crucible to provide a dense fill with good thermal contact to the crucible (and surrounding thermocouple). Elemental europium has been used in oxide MBE for the growth of EuTiO 3 122 and EuO. [105][106][107] For Tm 2 O 3 , no literature on the evaporation behavior of Tm 2 O 3 could be found to corroborate that Tm 2 O 3 evaporates as a gas of the elemental metal thulium. If this is the case, a Tm 2 O 3 source would offer no advantage over using elemental thulium metal as an MBE source (see Fig. S74).

C. Metastable solid oxide with nearly congruent evaporation
Table III summarizes the metastable oxides that evaporate nearly congruently based on the present calculations. Of these, the oxides IrO 2 , PtO 2 , and RuO 2 would give the most advantage because their stable counterparts are elemental metals (iridium, platinum, and ruthenium) meaning no other solid (or liquid) binary oxide sources are available to create molecular beams of these oxides. Similar to Table I, Table III also lists the temperature range for nearly congruent evaporation defined by |Δx(O 2 )| < 0.01; see Eq. (1).
The concern with using metastable oxides as source materials for MBE is that these compounds could decompose into more stable compounds and in the process pollute the MBE vacuum with O 2 species. For metastable oxides, there are two scenarios that can occur when the oxide is heated, which depend on the kinetics of the compound as discussed in Sec. II A. The kinetics of oxide decomposition is beyond the scope of the present work, but a literature search has been conducted for experimental evidence of the successful use of metastable oxides in MBE; the details are described below. Furthermore, the decomposition of RuO 2 has been studied in the present work by differential thermal analysis with simultaneous thermogravimetry (DTA/TG) to follow the decomposition process under conditions approaching those in the high-vacuum MBE environment.
1. Cs 2 O (Fig. S19) Figure S19 shows that Cs 2 O(s) is a metastable phase, but it evaporates nearly congruently in the temperature range of 705 K-1059 K due to the value of |Δx(O 2 )| < 0.01 [see Eq. (1)]; see Table III. 2. SiO (Fig. S63) and GeO (Fig. S29) From Table II, it can be seen that the evaporation of SiO 2 and GeO 2 is incongruent and provides molecular beams of SiO and GeO,

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scitation.org/journal/apm  Table I). e Thermodynamic calculations of ReO3(s) were performed at PO 2 = 10 −15 Pa where its gas phase is metastable, a requirement for our calculations under the constraint that the fixed gas phase has zero amount. This zero amount requirement is not satisfied for ReO3(s) at PO 2 = 10 −4 Pa.
respectively. Unfortunately, these latter monoxides are not in the SSUB5 database. 27 Amorphous SiO(am) is well-known to evaporate nearly congruently; [22][23][24] its thermodynamic properties 30 were added to the database in the present work. In addition, the enthalpy of formation of the amorphous GeO(am) 29 was also added. The fact that SiO(am) evaporates nearly congruently makes it of interest for synthesizing Si 2+ -based compounds in MBE, and GeO(am) behaves similarly to SiO(am) and could be a route to Ge 2+ -based compounds. Figure S63 illustrates the evaporation behavior of SiO(am) calculated at P O 2 = 10 −4 Pa, showing that SiO(am) gives off SiO 2 (g) species at low temperatures (below 1320 K) and SiO(g) species at higher temperatures (above 1320 K). Stoichiometric SiO has been found to evaporate from an SiO(am) source at temperatures in the vicinity of 1520 K in high vacuum (∼10 −6 Pa), 23,24 which is consistent with the results shown in Fig. S63. When the evaporation behavior of SiO(am) is calculated under a stronger vacuum such as P O 2 = 10 −15 Pa, the SiO gas species becomes dominant at lower temperatures (above 990 K) than it does in lower vacuum (e.g., 1320 K as mentioned above). Stolyarova and Semenov 22 indicated that SiO(am) evaporates congruently in a Knudsen cell experiment between 1175 K and 1410 K. This is confirmed by the present calculations. Should an interesting Si-containing multicomponent oxide warrant investigation, SiO(am) could be used to provide a molecular beam of SiO(g). One system that might be relevant is the growth of Si-doped Ga 2 O 3 , where the high oxidant pressures involved in the growth of Ga 2 O 3 result in the oxidation of the surface of the traditional Si(s) doping sources used in MBE. 34 This oxidation results in the flux emanating from a Si(s) source to change rapidly over time, impeding the use of silicon as a dopant in the growth of oxides by MBE.
The calculated evaporation from a two-phase mixture of SiO 2 + Si with an overall composition SiO (Fig. S63) indicates that SiO(g) is the dominant gas species in the temperature range of study (see also Table S2) in agreement with a recent report. 39 Similar to the Si-O case, GeO 2 (s) is the stable phase up to 872 K, beyond which GeO(am) becomes stable based on the SSUB5 database and the enthalpy of formation of GeO(am) from the literature; 29 see also the note in the figure caption of Fig. S29. GeO(g) is the dominant gas species when the solid/liquid source is GeO 2 (s), GeO(am), or a two-phase mixture of GeO 2 + Ge (see also Table S2). Our conclusions for the GeO 2 + Ge mixture are in good agreement with the thermodynamic calculations by Hoffmann et al. 39 3. IrO 2 , PtO 2 , and RuO 2 (Figs. S34, S54, and S59) IrO 2 (s) and RuO 2 (s) are of particular interest for oxide MBE because in elemental form, Ir(s) and Ru(s) sources have such low vapor pressures that today's MBE effusion cells are unable to evaporate them. Solid iridium and ruthenium can be evaporated by electron-beam evaporation sources, but the stability of the flux from an electron-beam evaporator is inferior to the flux stability provided by effusion cells. IrO 2 and RuO 2 are components of materials with a multitude of interesting properties and electronic structures due to the high spin-orbit coupling and electron correlations present in materials containing these constituents. Examples ARTICLE scitation.org/journal/apm include the unconventional superconductor Sr 2 RuO 4 , 123 the itinerant metamagnet Sr 3 Ru 2 O7, 124 features in the electronic structure of doped Sr 2 IrO 4 that are akin to the cuprate high-temperature superconductors, 125 the magnetically ordered Mott insulator Na 2 IrO 3 , 126 Weyl semimetals in the RE 2 Ir 2 O7 pyrochlores, 127 and heterostructures containing these materials that could, for example, host a twodimensional gas of magnetic monopoles. 128 MBE sources that provided stable fluxes of IrO 2 and RuO 2 could thus greatly enhance the ability of oxide MBE to create iridates and ruthenates that are customized with atomic-layer precision. IrO 2 and RuO 2 are commercially available powders, so it is important to investigate these oxides even though they are metastable under MBE deposition conditions. In the present calculations, metastable IrO 2 and RuO 2 are found to evaporate nearly congruently as shown in Figs. S34 and S59, respectively. IrO 2 and RuO 2 thin films have been fabricated using MBE; however, they were made using elemental iridium or ruthenium sources heated by an electron-beam evaporator with oxidation provided by a separate molecular beam of ozone. 129,130 No literature was found on the evaporation of RuO 2 or the use of RuO 2 as a source in oxide MBE.
The suitability of IrO 2 and RuO 2 to create molecular beams depends on the kinetics of their decomposition as discussed in Sec. II A. For example, IrO 2 could follow two scenarios when heated in the MBE crucible, The first scenario, Eq. (3), shows IrO 2 (s) decomposition into Ir(s) and O 2 (g), which would pollute the MBE chamber with oxygen species. The Ir(s) species would then evaporate with the partial pressures of the gas species shown in Fig. S34. If this first pathway is relevant, IrO 2 (s) as an MBE source offers no advantages (and many disadvantages) over an elemental Ir(s) source. In the second scenario, Eq. (4), as IrO 2 (s) is heated up, it evaporates IrO 2 (g) as shown in Fig. S34. These IrO 2 (g) species would be emitted as a molecular beam, which would travel to the substrate in the MBE chamber. In this latter case, the IrO 2 (g) species would be depleted at the surface of the IrO 2 (s) source as it evaporates. To restore equilibrium, the IrO 2 species would produce more IrO 2 (g). In this second scenario, the IrO 2 (s) species evaporates into IrO 2 (g) much faster than it decomposes; for oxide MBE, this would be the preferred kinetic pathway to make IrO 2 (s) a viable MBE source material. Another thing to consider is the energy required to break IrO 2 (s) into Ir(s) and O 2 (g). If the activation barrier is high, it would be much more likely for IrO 2 (s) to evaporate as IrO 2 , where only intermolecular bonds have to be broken. In addition to metastable IrO 2 and RuO 2 , the present calculations ( Fig. S54 and Table III) also indicate that metastable PtO 2 evaporates nearly congruently in the temperature range of 915 K-1156 K at P O 2 = 10 −4 Pa. As IrO 2 , PtO 2 , and RuO 2 share the chemical similarity of all being 4+ oxides of platinoids, we performed some preliminary experiments on one of these compounds, RuO 2 (s), and found that it decomposes before it evaporates. Specifically, our experiments indicate that when heated, RuO 2 (s) undergoes the reaction 2RuO 2 (s) → Ru 2 O 3 (s) + 1 / 2 O 2 (g). The predominant species that RuO 2 (s) gives off when heated is thus O 2 (g), making it not useful as an MBE source. Figure 5 shows two thermogravimetric (TG) measurements where RuO 2 (s) was heated under ambient pressure in an Ar/O 2 mixture or in nominally pure Ar with 99.9999%-99.999% purity, which results in the stated oxygen partial pressures. 131 Between room temperature and 773 K, the changes in the first TG step occur, corresponding to Δm/m = −5.7% (oxidizing atmosphere) or −6.0% (Ar). These observed mass changes would be consistent with the reaction 2RuO 2 (s) → Ru 2 O 3 (s) + 1 / 2 O 2 (g), where Δm/m of the condensed phases would be −6.0%. The decomposition of the remainder becomes significant above 1273 K-1370 K. Since Ru 2 O 3 (s) is not in the SSUB5 thermodynamic database, this reaction is not predicted by our thermodynamic calculations. Nonetheless, Ru 3+ is reported in halides, such as RuF 3 and RuCl 3 , as well as in the oxide LaRuO 3 . 132 4. NbO 2 (Fig. S43) NbO 2 has been shown to have NbO 2 species in the gas phase when evaporated from a Knudsen cell at 2050 K. 22 Having NbO 2 as the dominant species in the gas phase is expected regardless of whether evaporation occurs from metastable NbO 2 (s) or from the stable phase, Nb 2 O5(ℓ), at 2050 K. The present work ( Fig. S43 and Table III) predicts that (metastable) NbO 2 evaporates nearly congruently between 1768 K and 2283 K at P O 2 = 10 −4 Pa. NbO 2 has useful metal-to-insulator transition electronic properties motivating its growth by MBE. 133 NbO 2 (s) could be a viable source for the growth of NbO 2 thin films and is worth trying as an MBE source.

ReO 3 (Fig. S57)
ReO 3 (s) is a metastable phase in the Re-O system, and it is expected that it could evaporate nearly congruently. In our thermodynamic calculations using P O 2 = 10 −4 Pa, however, the gas phase does not satisfy the requirement of having zero amount. So we performed ancillary thermodynamic calculations of ReO 3 (s) at a very FIG. 5. Thermogravimetric (TG) curves of RuO 2 (s) heated in 71% O 2 + 29% Ar (blue curve) or in "pure" Ar (red curve). Here, P O 2 indicates the oxygen partial pressure in atm and Δm/m shows the mass change in the TG curves.

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scitation.org/journal/apm 6. TiO 2 (Fig. S72) TiO 2 has been shown to evolve TiO species when evaporated from a Knudsen cell at 1920 K. 22 This result is unexpected from our thermodynamic calculations. If the initial TiO 2 loaded into the Knudsen cell decomposes into the stable phase, on heating to 1920 K, it would be Ti 4 O7(s) and the dominant species evaporated at 1920 K would be TiO 2 (g). On the other hand, if TiO 2 loaded into the Knudsen cell remained in the metastable rutile polymorph at 1920 K, then the dominant species evaporated at 1920 K would also be TiO 2 (g). Our calculations only show TiO to be the dominant vapor species at temperatures above 2220 K for both anatase and rutile TiO 2 , which are both metastable at this temperature, at the 10 −4 Pa O 2 partial pressure of the present work; see Fig. S72 as well as Table III. 7. UO 3 (Fig. S75) Solid UO 3 (s) is a stable phase when T < 525 K; at higher temperatures, the solid U 3 O 8 (s) becomes stable (>525 K). Figure S75 shows that U 2 O 6 (g) is the dominant gas species at temperatures T > 517 K and P O 2 = 10 −4 Pa [O 2 (g) is dominant at T < 517 K]. Although U 2 O 6 (g) is the dominant species in the gas phase, the value of |Δx(O 2 )| > 0.01 [see Eq. (1)] in the temperature range of 517 K-525 K due to the nonnegligible concentration of other species in the gas phase. This disqualifies UO 3 (s) as an ideal MBE source from the definition of nearly congruent evaporation that we have used. It is worth mentioning that at an extremely low partial pressure of O 2 (g), such as P O 2 = 10 −15 Pa, it is possible to make |Δx(O 2 )| < 0.01 for UO 3 (s).
As a metastable phase, the present calculations show that UO 3 (s) evaporates nearly congruently in the temperature range of 544 K-1900 K at P O 2 = 10 −4 Pa; see Table III. Table IV shows the metastable oxide sources that exhibit incongruent evaporation. Based on the dominant species in the molecular beams from the stable sources that exhibit incongruent evaporation, these metastable oxides are calculated in the present work to see if they would exhibit nearly congruent evaporation. Unfortunately, they all exhibit incongruent evaporation as can be seen in the calculated figures in the supplementary material. Specifically, see Fig. S14 for the binary oxides containing cerium, Fig. S19 for those containing cesium, Fig. S50 for those containing lead, Fig. S53 for those containing praseodymium, Fig. S67 for those containing tantalum, and Fig. S68 for those containing terbium. These metastable incongruent evaporants offer no advantage over their stable incongruent evaporant counterparts and hence are not discussed further.

IV. SUMMARY
A comprehensive thermodynamic investigation regarding the evaporation behavior of 128 binary oxides has been performed to evaluate their suitability as MBE source materials. Based mainly on the SSUB5 database used in the present work, 27  a molecular beam of mainly SnO(g). Although they do not meet the third criterion to be ideal MBE sources (i.e., nearly congruent evaporation; see Sec. II C), some oxides that meet the first criterion (i.e., solid or liquid metal-oxide source that is stable under the given conditions; see Sec. II C) may also work as oxide MBE source materials, like SnO 2 does. The amorphous and metastable phase SiO(s) is known to evaporate before it decomposes, making it suitable as an MBE source. The same may be true for other metastable phases including amorphous GeO(s) and SnO(s). Finally, a likely route to achieve the desired nearly congruent evaporation characteristic of an ideal MBE source-a characteristic that keeps the fluxes of the species in the molecular beams constant, because the composition of the source itself is not changing over the life of the source-is to use a two-phase mixture. Potential MBE sources of this mixture type are, for example, (Al 2 O 3 + Al) to produce a molecular beam of Al 2 O(g), (Ce 2 O 3 + Ce) to produce CeO(g), (Ga 2 O 3 + Ga) to produce Ga 2 O(g), (GeO 2 + Ge) to produce GeO(g), (HfO 2 + Hf) to produce HfO(g), (In 2 O 3 + In) to produce In 2 O(g), (La 2 O 3 + La) to produce LaO(g), (Pr 2 O 3 + Pr) to produce PrO(g), (SiO 2 + Si) to produce SiO(g), (SnO 2 + Sn) to produce SnO(g), (Ta 2 O5 + Ta) to produce TaO 2 (g), and (ZrO 2 + Zr) to produce ZrO(g); see the 27 cases examined in Table S2. Our conclusions for two-phase mixtures are in agreement with the recent thermodynamic calculations by Hoffmann et al. 39 for Al 2 O(g), Ga 2 O(g), GeO(g), In 2 O(g), LaO(g), PrO(g), SiO(g), and SnO(g). Our predictions also identify four additional two-phase sources of interest for producing molecular beams of CeO(g), HfO(g), TaO 2 (g), and ZrO(g). Several trends are evident in the evaporation behavior of binary metal oxides. These are shown in Fig. 6. Alkali-metal oxides, alkaline-earth metal oxides, and some of the transition-metal oxides evaporate mainly elemental metal gas species and thus are not ideal for MBE. The rare-earth oxides and some of the transition metals surrounding them as well as the metalloid oxides exhibit incongruent evaporation. Oxides ideal for MBE are the column IVA oxides SiO, GeO, SnO, and PbO, although the first three of these are metastable (amorphous). In addition, there are disruptions to certain trends such as the evaporation of elemental metals from EuO, Tm 2 O 3 , and Yb 2 O 3 , which do not follow the incongruent evaporation trend of the other rare earths.

SUPPLEMENTARY MATERIAL
See the supplementary material for an alphabetical list of 128 solid and liquid oxides together with a list of 17 elements of which the most stable phase is not an oxide (Table S1), a list of 27 twophase mixtures of a solid (or liquid) of pure element M in combination with one of its binary oxides yielding an overall composition of MxOy (Table S2), three illustrative examples of macro files to perform some of the Thermo-Calc calculations presented (Table S3), and an alphabetical list of supplemental figures (Figs. S1-S81) showing the calculated partial pressures of gas species over the phase(s) of interest.