Towards Informatics-Driven Design of Nuclear Waste Forms

Vinay I. Hegde,1 Miroslava Peterson,2 Sarah I. Allec,1 Xiaonan Lu,2
Thiruvillamalai Mahadevan,3 Thanh Nguyen,3 Jayani Kalahe,3 Jared Oshiro,2
Robert J. Seffens,2 Ethan K. Nickerson,2 Jincheng Du,3 Brian J. Riley,2 John
D. Vienna,2 James E. Saal1,***Corresponding author; email<EMAIL_ADDRESS>

1Citrine Informatics, Redwood City, CA 94063
2Pacific Northwest National Laboratory, Richland, WA 99352
3University of North Texas, Denton, TX 76203

Informatics-driven approaches, such as machine learning and sequential
experimental design, have shown the potential to drastically impact next-
generation materials discovery and design. In this perspective, we present a
few guiding principles for applying informatics-based methods towards the
design of novel nuclear waste forms. We advocate for adopting a system design
approach, and describe the effective usage of data-driven methods in every
stage of such a design process. We demonstrate how this approach can optimally
leverage physics-based simulations, machine learning surrogates, and
experimental synthesis and characterization, within a feedback-driven closed-
loop sequential learning framework. We discuss the importance of incorporating
domain knowledge into the representation of materials, the construction and
curation of datasets, the development of predictive property models, and the
design and execution of experiments. We illustrate the application of this
approach by successfully designing and validating Na- and Nd-containing
phosphate-based ceramic waste forms. Finally, we discuss open challenges in
such informatics-driven workflows and present an outlook for their widespread
application for the cleanup of nuclear wastes.

## 1 Introduction to Nuclear Waste Forms

The United States manages large volumes of nuclear wastes generated from
nuclear weapons production during World War II and the Cold War. These wastes
are primarily stored at US Department of Energy sites such as Hanford (near
Richland, Washington), Savannah River Site (near Aiken, South Carolina), Oak
Ridge National Laboratory (ORNL; in Oak Ridge, Tennessee), Los Alamos National
Laboratory (in Los Alamos, New Mexico), and the Idaho Nuclear Technical and
Engineering Center (near Idaho Falls, Idaho). These wastes range from solids
to sludges to liquids and contain, in broad terms, most of the elements from
the periodic table. In general, the most hazardous of these wastes are high-
level tank wastes at Hanford and Savannah River which will be vitrified into
borosilicate glass-based waste forms and buried in disposal facilities.

Recent increased interest in advanced nuclear power technologies has spurred
interest in advanced nuclear fuel cycles [1]. Some of those fuel cycles
include the generation of unique waste streams such as molten halide salts
containing fission and activation products that will need to be treated for
ultimate disposal [2, 3, 4, 5, 6]. Modern approaches that short circuit the
traditional inefficient Edisonian trial-and-error style of waste form
development and significantly accelerate the design of novel waste forms are
in great need.

In general, options for immobilizing entire salt wastes, i.e., without any
salt fraction partitioning, are limited. For such full-salt immobilization,
the few demonstrated waste form options include glass-bonded sodalite and
tellurite glasses [2, 7], all of which exhibit low salt loading.
Alternatively, rather than immobilizing the full-salt waste, the salt can be
partitioned into different constituents to make waste form fabrication and/or
partition recycling easier. One method for doing this is removing the halide
fraction and converting the resulting salt cations (e.g., M^m+) to other
chemistries (e.g., M2O, M3PO4) through a process called dehalogenation.

Dehalogenation can be accomplished through a variety of methods, including the
conversion of the halide salt cation in air to oxides [8, 9, 10], conversion
of halide salt cations to phosphates through reactions with NH4H2PO4 [11, 12,
13], (NH4)2HPO4 [12], or H3PO4 [14, 15], or converting fluoride-salt wastes to
a different fluoride-containing compound that is environmentally stable (water
insoluble), such as CaF2, for disposal [16]. Any halide-containing byproducts
from the dehalogenation process (e.g., H^37Cl, NH4^37Cl) can be captured and
recycled to produce new actinide halides or directly disposed (e.g., F). Since
the one of the key limiters of waste loading capacity of a waste form is the
halide fraction, the dehalogenated salt products (e.g., oxides, phosphates)
can be immobilized at much higher salt cation loadings than the full-salt
wastes prior to dehalogenation.

Different salt-based nuclear waste streams, such as alkali-based (e.g.,
Li/K/Na, Li/Be) and/or alkaline earth-based ones, can thus undergo a
dehalogenation process with the waste cations being converted to the same
anion-type compounds (e.g., oxides, phosphates). These compounds then be mixed
with glass-forming compounds to create a final waste form that meets all of
the necessary product criteria based on disposal requirements. Some of the
primary properties of interest for each waste composition are waste loading
(salt cation loading in wt%), chemical durability (e.g., aqueous solubility,
leach rates), processability/manufacturability (e.g., higher melt viscosity,
lower melt temperatures), mechanical durability (e.g., compressive strength),
and radiation/thermal stability under expected radiation fields in the final
product.

Historically, glass composition-property models have been developed to predict
the properties required for efficient processing and acceptable product
qualities of (mainly borosilicate) waste forms. These models have largely been
empirical fits of glass composition-property data using single metal oxide
concentrations as features. The model development process typically involved
the production and development of painstaking, time-consuming, and
empirically-created databases. There is an opportunity to leverage the large
amounts of data present in existing chemical, physical, and thermodynamic
databases to build machine learning (ML) models to predict the waste form
properties of interest for an entirely new class of waste forms, e.g.,
dehalogenated phosphate ceramics or glasses. Thus, the empirical data
collection process could be side-stepped entirely or be limited to incremental
efforts in the novel chemistries and/or processes where there exist no prior
data for the ML models to train on. Such an approach has the potential to
bring about a paradigm shift in the design of different types of novel waste
forms, including relatively simple single-phase systems (e.g., glasses,
single-phase ceramics) or more complex multiphase systems (e.g., glass-ceramic
hybrids, multiphase ceramics, and cermets).

## 2 AI/ML for Nuclear Waste Immobilization: Prior Art

Approaches utilizing artificial intelligence (AI) or machine learning (ML)
techniques have enabled significant advances in many materials science
problems, ranging from the prediction of complex materials properties (e.g.,
superconducting critical temperatures of complex oxides [17, 18], the casting
size of metallic glass alloys [19]) to the development of self-driving labs
[20, 21]. However, there remain certain families of materials and research
questions that have not benefited as extensively from AI/ML due to their
extreme complexity, of which designing new nuclear waste form materials is a
prime example. In the case of nuclear waste form design, difficulties in data-
driven approaches primarily arise from (1) a vast and complex design space (in
terms of chemistry, phase, microstructure, processing) that spans glasses,
ceramics, and glass-ceramic composites, and (2) a lack of sizeable legacy
datasets for several properties a waste form must possess to be considered
viable for disposal (e.g., chemical durability, radiation stability),
especially for classes of materials that have not been previously explored.
Further, due to the cost of performing experiments with nuclear materials and
the complexity of waste form compositions, experimental data acquisition is a
major bottleneck [22, 23, 24].

Nonetheless, there is a plethora of prior work on using AI/ML approaches to
model waste forms [25, 26], and we highlight a few recent reports below,
including both ceramic and glass based waste forms. In terms of radiation
effects, Pilania et al. [27] used ML to explore the physical factors
underlying amorphization resistance in pyrochlores (A2B2O7), which have been
extensively investigated for use in nuclear waste forms [28, 29, 30, 31, 32,
33, 34, 35, 36, 37] and have been incorporated into some variants of the
SYNROC waste form [38]. Here, an ML model was trained to predict the critical
amorphization temperature, Tc, from simple structural features and DFT
energetics. Another critical property for nuclear waste forms is chemical
durability, which is significantly reduced by nepheline (NaAlSiO4)
precipitation during vitrification of certain waste glasses. To address this
challenge, Sargin et al. [39] and Lu et al. [40] built ML models to predict
nepheline crystallization behavior from glass composition, comparing several
different algorithms and achieving a reasonable classification accuracy.
However, due to the data acquisition challenge for nuclear waste forms, we
note that the dataset sizes for the aforementioned models is relatively low
for ML (on the order of 100–1000 data points), which may limit
generalizability and extrapolability.

Similarly, several previous efforts focused on developing ML models for
predicting properties relevant for glass waste forms, including glass density
[41], viscosity [42], durability [43, 44, 45], glass transition temperature
[46], thermal expansion [47], mechanochemical wear [48], and Young’s modulus
[49]. While many of these models were trained to predict a single property on
a specific family of glasses (e.g., silicates), a recently developed multi-
task deep neural network model, GlassNet, has been trained predict 85 various
glass properties on the entire SciGlass database [50] with reasonable accuracy
on most of the modeled properties [51].

In addition to the direct modeling of waste form properties, the development
of neural network interatomic potentials (NNIPs) trained on first-principles
density functional theory (DFT) energetics of waste form-relevant systems has
made significant strides. For example, NNIPs have been applied to the modeling
of molten salts, enabling the accurate prediction of structural and dynamical
properties at normal operating conditions, high-temperature–pressure
conditions, and in the crystalline solid phase [52, 53]. Additionally,
Byggmästar et al. developed a Gaussian Approximation Potential (GAP) to study
radiation damage in W [54], and Ghosh et al. developed an NNIP to study Cs
incorporation into hollandite (A2B8O16) [55].

While significant advances have been made in applying AI/ML methods toward
modeling nuclear waste forms, approaches that utilize such methods for the
design of entirely novel waste forms are not well established. Some recent
works have explored the use of AI/ML to design optimal waste glass
compositions [56, 57], but a unified framework for an informatics-driven
design, especially in previously-unexplored chemistries encompassing ceramics,
glasses, and other types of waste forms is lacking.

In the following sections, we present a generally-applicable, closed-loop,
iterative design framework that effectively combines AI/ML approaches with
physics-based simulations and experiments to design novel waste forms. As a
topical use-case, we present the design of new phosphate-based ceramic waste
forms as part of an ongoing project under the Advanced Research Projects
Agency-Energy (ARPA-E) ONWARDS program, with the following initial target
properties: (1) >20% waste cation mass loading, (2) <400 cm3 waste form
volume/100 g salt, and (3) >30 MPa compressive strength. For each task in the
presented iterative design framework, we discuss available methods and tools,
and best practices to use them, with illustrative examples from the phosphate-
based waste form design problem. We also present a single end-to-end pass
(i.e., the first iteration) through the design process for the same problem,
resulting in successful synthesis of phosphate waste forms that satisfy all
the target criteria listed above.

## 3 A System Design View of Nuclear Waste Forms

A system design approach primarily uses the well-established processing-
structure-property-performance (PSPP) paradigm to understand the underlying
materials problem [58, 59]. Namely, the ways in which a material is
synthesized and processed (including the various steps and their respective
parameters and conditions) determines its structure, both on a microscopic
level (i.e., the phases that are formed, their atomistic structure, etc.) as
well as on a macroscopic level (i.e., the grain structure, level of porosity
and other defects, etc.). The overall structure of a material, in turn,
determines its properties, which, in turn, determine its performance in the
target application. This system design approach can be encapsulated in a so-
called “system design chart” where individual components of the PSPP systems
are connected by causal links or edges in the forward direction (i.e., from
processing to structure to properties to performance), which often capture
domain knowledge for the problem. Note that several processing steps can
affect multiple structural features of a material, and several structural
features can contribute to the properties of the overall material, and so on.
Drawing up a system design chart for the materials problem at hand should
therefore be the first step in any non-trivial materials design endeavor.

Figure 1:  A sample system design chart for nuclear waste form design.

An example system design chart for the recently-proposed phosphate glass waste
forms [12] is shown in Figure 1. Here, a typical processing step can involve
dehalogenation of the salt waste via reagents such as NH4H2PO4, followed by
melting with glass-forming chemicals (GFCs) such as Fe2O3, and eventual
quenching and/or slow cooling of the melt. The waste form resulting from such
a process can be crystalline, glassy, or a mixture of both, i.e., various
crystalline phases embedded in a glassy matrix. In addition, depending on
other processing steps such as sintering or hot isostatic pressing (HIP), the
waste form may have porosities ranging from 2% to 30%. The properties of
interest of the resulting waste forms can then be obtained by direct
experimental measurement during one of the processing steps (e.g., melting
temperature and viscosity during the melting step) or once the processing is
complete (e.g., waste salt cation loading, volume, and compressive strength of
the final solid waste form). Finally, within limitations of available
experimental facilities, the waste form can be tested to determine its actual
performance in near-operation conditions (e.g., chemical durability in aqueous
conditions).

## 4 A System Design-Informed Sequential Learning Framework

Sequential learning (or active learning) (SL) is an iterative approach for the
design of novel materials via data-driven models. A typical SL workflow
consists of the following iterative loop: (1) machine learning (ML) models are
trained on existing materials property data, (2) these ML models are then used
to make property predictions in an as-yet unexplored design space, (3) the ML
predictions, and uncertainties in such predictions, are used to identify the
most-promising candidate material(s) to evaluate next, (4) the objective
evaluation (via simulations and/or experiments) of the selected candidate(s)
is performed, and (5) the loop iterates to augment the training data with
results from the objective evaluations, retrain and/or refine the ML models,
make new candidate predictions, and so on. SL workflows have been previously
shown to significantly accelerate the discovery of new materials, ranging from
small molecules to catalysts to semiconductors and others [60, 61, 62, 63,
64], as well as to rapidly optimize manufacturing and processing parameters
[65, 66].

Figure 2:  A sample sequential learning driven workflow for the design of
novel waste forms, informed by the underlying system design chart.

The construction of such an SL workflow for the materials design problem at
hand can greatly benefit from being informed by the underlying system design
chart. An example of a system design-informed SL workflow for phosphate waste
forms is shown in Figure 2. An effective translation from the system design
chart to a closed-loop SL workflow requires: (1) an initial data generation or
collection effort upfront, ideally pertaining to the design spaces of
interest, (2) various aspects of processing, structure, and properties to be
adequately captured in the representation or schema used to store materials
data, (3) physics-based simulations or ML models that can predict both (a) the
mixture of phases and their structure in the final resulting waste forms based
on their initial compositions and relevant processing conditions, and (b) the
target waste form properties of interest, with robust uncertainty estimates,
and (5) a scheme to filter and rank candidates in the target design space that
takes into account model predictions and uncertainties, as well as any other
application-based constraints not previously accounted for. In each of the
above steps, incorporating domain knowledge and expertise can have a
significant impact on the effectiveness of the SL workflow; this is further
discussed in the context of each individual SL task below.

###  4.1 Dataset construction

The first step in an SL workflow is dataset construction. This can involve (1)
data collection from various sources such as existing materials databases,
published materials property datasets, and individual or small sets of data
scattered across literature, (2) data generation using relatively inexpensive
physics based simulations (see Section 4.2) and/or a small set of baseline
experimental measurements, and (3) data engineering of the collected and/or
generated data. The latter step encompasses data curation (e.g., outlier
removal, imputation of missing values), data fusion (e.g., combining data for
a given set of materials from different experimental measurements or
simulations), and other related post-processing.

What datasets should one construct for their effective use in waste form
design? The target datasets should be informed by the underlying system design
chart. That is, datasets should be constructed for the target materials
properties that correspond to the waste form performance criteria. This
identification of materials properties data that correlates with waste form
performance is non-trivial and requires significant domain knowledge
integration for extracting maximum utility. We provide a sample list of
openly-available datasets of materials properties and related performance
criteria in Table LABEL:tab:datasets, some of which were used for phosphate
waste form design in this work. Note that while a 1:1 correspondence between
materials property and performance metric is ideal (e.g., leach rate
[property] $\Rightarrow$ chemical durability [performance]), ML models can
leverage indirectly-related data (e.g., cohesive energy [property]
$\Leftrightarrow$ melt temperature [property] $\Rightarrow$ processability
[performance]) via approaches such as transfer learning [67, 68, 69, 70, 71,
72] (see Section 4.3).

Lastly, while the dataset construction task is often overlooked in favor of
exploring more sophisticated ML algorithms, improving data quality and
quantity is perhaps the most critical enabler of the eventual success of an
informatics-driven approach to materials design. A recent “renaissance”
towards data-centric AI (in contrast to model-centric AI) across several other
fields is ongoing [73, 74, 75].

###  4.2 Physics-based simulations

Physics-based simulations, such as those based on first-principles density
functional theory (DFT), molecular dynamics (MD), calculation of phase
diagrams (CALPHAD), and other approaches can be used to perform “computational
experiments”, at various time and length scales, that can both augment
datasets of materials properties as well as provide faster feedback within an
SL design loop. We discuss some of the more widely-used physics-based modeling
approaches below, with a focus on how they can be integrated within an SL
workflow.

####  4.2.1 Ab initio atomistic simulations

Ab initio density functional theory (DFT) and related methods can be used to
calculate a variety of properties of a material based only on its crystal
structure, including but not limited to formation energy, bulk density,
elastic moduli, electronic band structure and gap, and others. Due to some
underlying approximations in the approach (e.g., the exchange-correlation
functional in DFT), the accuracy of a DFT calculation can vary significantly
based on the target material/property and its applicability is often limited
to materials with unit cells consisting of not more than hundreds of atoms.
Nonetheless, these calculations are an invaluable tool to generate initial
training data for ML, validate ML-predicted properties of a waste form
candidate, improve the description of a waste form composition, etc. within an
SL workflow. As an example, below we highlight how a DFT-calculated property
(compound formation energy) can be used to estimate the ground state mixture
of phases from the overall composition of a waste melt, enabling ML property
predictions for those phases.

An analysis of the convex hull of compound formation energies as a function of
phase composition can be used to identify the thermodynamically stable phases
in a given chemical space [76, 77, 78, 79, 80]. Combined with linear
programming approaches, a convex hull of a chemical space can rapidly predict
compounds that are stable/synthesizable as well as the ground state mixture of
phases that can be expected to form under thermodynamic equilibrium conditions
at any given composition in that chemical space (see Figure 3a) [81].

The grand potential $\phi$ of a collection of phases in a chemical space is
given by

$\phi(\boldsymbol{x},\boldsymbol{\mu})=\sum_{i}x_{i}G_{i}-\sum_{j}\left(\mu_{j}\sum_{i}x_{i}C_{i,j}\right)$
(1)

where $x_{i}$ is the relative amount of phase $i$, $\mu_{j}$ is the chemical
potential of element $j$, and $C_{i,j}$ is the fraction of element $j$ in
phase $i$. The ground state mixture of phases (i.e., the $x_{i}$) can be
determined by minimizing $\phi$ with respect to $\vec{x}$ and $\vec{\mu}$,
provided the free energies $G_{i}$ and the list of stable phases in the
chemical system (the $C_{i,j}$ terms) are defined. Typically, tools such as
high-throughput DFT are used to calculate the energies of the various phases
in the chemical space of interest in a self-consistent fashion, and the phase
free energies are approximated by their respective 0 K formation energies.
Although using 0 K energies from a computational tool such as DFT ignores
finite-temperature effects, kinetic effects, and other factors, and can result
in differences between predictions and experimental observations (e.g., see
two slices of a DFT-computed Na-Fe-P-O convex hull in Figure 3b–c, where two
experimentally-reported phases, Na3Fe2(PO4)3 and Na6Fe3(PO4)4, are predicted
to be unstable), this approach is still invaluable for estimating ground state
mixture of phases with reasonable accuracy [82, 83], particularly for systems
that are not experimentally explored or fully described within the CALPHAD
approach (see Section 4.2.3).

Figure 3:  (a) The convex hull of formation energy in a model A-B system. Blue
circles indicate stable phases (“on the hull”), and red diamonds ($\langle
u\rangle$) indicate phases that are metastable or unstable (“above the hull”).
Under perfect thermodynamic equilibrium conditions, the unstable/metastable
phases will decompose into a mixture of stable phases. For example, AB is
predicted to decompose into a mixture of A3B + AB3, and its distance to the
convex hull (“EHD”) is an indicator of the thermodynamic drive for the
decomposition (or relatedly, likelihood of its experimental synthesis [82,
83]). (b, c) Slices of the convex hull computed using DFT-calculated formation
energies in the Na-Fe-P-O chemical system, with sodium and iron phosphate (3+
and 2+, respectively) end members.

####  4.2.2 Semi-empirical atomistic simulations

Interatomic potential based atomistic simulations, e.g., classical molecular
dynamics (MD) and Monte Carlo (MC) methods, are computationally much more
efficient and can deal with much larger systems (up to millions or billions of
atoms) and longer time scales (micro to milliseconds) than ab initio methods.
Such semi-empirical atomistic simulations have been successfully used to study
multicomponent glass structures, radiation effects in metals, ceramics and
glasses, and to study the effect of microstructure on mechanical properties
[84, 85, 86].

The fidelity of an MD simulation strongly depends on the type and quality of
the underlying interatomic potential (IAP), making the development of an IAP
and its parameterization a significant portion of the overall simulation
effort. For example, the development of IAPs for the modeling of borosilicate
glasses, a widely-used nuclear waste glass, has been a challenge due to the
strong dependence of boron coordination on thermal history and composition,
which in turn affects properties such as mechanical strength and corrosion
rate. However, recent efforts in IAP development have led to successful
simulations of borosilicate glasses across a wide range of compositions where
boron coordination is in good agreement with experimental observations [87,
88, 89]. Also, the development of efficient “reactive” potentials allow for
simulations of reactions of aqueous solution with glasses [90, 91, 92, 93,
94].

Further, these large-scale atomistic simulations enable so-called quantitative
structure-property relationship (QSPR) analysis, linking properties of a
material to its atomistic structural features. QSPR analysis has been applied
to a wide range of properties such as glass transition temperature,
dissolution rate, Young’s modulus, and hardness of glass materials,
correlating trends in these properties to descriptors derived from structural
features such as bond angles, bond energies, coordination numbers, network
connectivity (e.g., see Figure 4a for a visualization of a iron phosphate
glass, showing various $Q_{n}$ units, where $n$ is the number of bridging
oxygen atoms connected to network formers $Q$, Fe2O3 and P2O5) [95]. A simple
statistical model (e.g., linear or multilinear regression) can then be used to
identify relationships between such descriptors and the target property of
interest (e.g., see Figure 4b for an example of modeling Young’s modulus as a
linear function of a glass network strength descriptor, Fnet [96, 97]).

Figure 4:  (a) Visualization of part of the atomic structure of a sodium iron
phosphate glass with composition 5%Na2O-35%Fe2O3-60%P2O5, showing the various
$Q_{n}$ units in the glass network (where $n$ is the number of bridging oxygen
atoms (red spheres) connected to network formers, Fe2O3 and P2O5), and (b)
linear correlation between Young’s modulus and QSPR-based network strength
descriptor, Fnet, calculated using bond strength of diatomic cations (“BS-dc”)
and a multiplicative factor (“mx”) [96, 97]. The blue circles are MD-
calculated Young’s moduli values for various Na-Fe-P-O glass compositions (the
error bars indicate variance in the calculated moduli across different
structures at the same composition), and the solid black line shows a linear
fit with an $r^{2}$ score of 0.95.

####  4.2.3 Thermodynamic modeling

The Calculation of Phase Diagrams (CALPHAD) approach is a commonly used
thermodynamic formalism, along with related numerical methods, to assess phase
equilibria in materials under various conditions. Within the CALPHAD approach,
thermodynamic properties (e.g., Gibbs energy, specific heat) of phases in a
system are described using mathematical models with adjustable parameters,
which are then optimized by fitting to all available thermochemical
information about phases/sub-systems to arrive at a consistent description of
the multicomponent system of interest.

The CALPHAD method can be used to study the typically multicomponent,
multiphase nuclear waste materials, e.g., calculate phase diagrams of the
waste form systems (e.g., the Fe2O3-P2O5 iron phosphate system, shown in
Figure 5), equilibrium and non-equilibrium phase evolution during
solidification of a molten salt mixture, estimating transformation
temperatures between waste-relevant phases, waste salt or waste element
solubility limits, and so on.

While CALPHAD-based approaches can be used to study the behavior of waste-
relevant systems under non-ideal conditions (e.g., as a function of
temperature, pressure, chemical potential, pH), they are often limited by the
availability of fully-assessed thermodynamic databases for the systems of
interest. While ab initio methods can be used to calculate the properties
(e.g., formation energy) of novel phases from scratch, such data may suffer
from limitations related to “ideal conditions”, as discussed in Section 4.2.1.
For example, we compare the 0 K phase diagram calculated using DFT with that
from CALPHAD for the Fe2O3-P2O5 system in Figure 5. Note that two of the
experimentally observed phases, Fe3PO7 and Fe4(P2O7)3, described correctly by
CALPHAD are predicted to be metastable at 0 K by DFT. Further, for systems
with missing or partial CALPHAD assessments, there are no currently available
tools that enable a seamless integration of such ab initio data with existing
thermodynamic databases to extend their capabilities to the partially
assessed/unassessed system (e.g., the Na2O-Fe2O3-P2O5 system, discussed in
Section 4.5).

Figure 5:  The Fe2O3-P2O5 phase diagram (a) computed using the CALPHAD
approach (the liquidus curve is highlighted in solid green), and (b)
calculated using ab initio DFT (blue circles indicate “on the convex hull”
stable phases and red diamonds indicate “above the convex hull” 0 K metastable
phases).

###  4.3 Machine learning models

The various waste form-relevant property datasets described in Section 4.1 can
be used as input to train ML models that can predict those properties of novel
waste forms. While sizeable research efforts have gone into ML algorithms and
models for predicting materials properties, there are a few considerations to
keep in mind specifically towards their effective applicability in an SL
workflow for waste forms. First, the crystal structure of a novel waste form
is often unknown or yet to be characterized. Even though ML models that are
built using crystal structure-based descriptors as input show higher accuracy
in predicting materials properties [98], this information is often a priori
unavailable. Thus, ML models that can predict waste form properties purely
based on the melt composition alone tend to be of higher value than those that
require crystal structure as input. Several approaches have been developed to
generate physical descriptors based on chemical composition of a material
(“featurization”), e.g., Magpie [99], Deml [100], Matscholar [101], MEGNet
[102], including off-the-shelf software tools with implementations of such
approaches, e.g., matminer [103], that can be used to featurize waste form
compositions.

Second, the type of AI/ML model to build, e.g., based on ensemble approaches
such as random forests (RF) and gradient-boosted trees, or deep neural net
(NN) approaches such as ElemNet [104], Roost [105], CrabNet [106], depends on
the target property and the size of the available data. Tree-based models have
been shown to generally outperform deep learning models on tabular data,
especially for small-to-medium sized datasets typical of materials properties
(102–103 examples) [107]. While NN-based models are useful for certain larger
property datasets, e.g., CrabNet for predicting the formation energy, or
GlassNet to predict the glass transition temperature from an input
composition), we urge researchers to test “simpler” ML models using off-the-
shelf tools such as scikit-learn [108] and lolo [109], as these can often be
more interpretable and provide superior extrapolation performance [110].

Figure 6:  (a) An actual-vs-predicted parity plot for an ML model trained in
predict congruent melting temperatures of stoichiometric compounds, evaluated
using 5-fold random cross-validation. (b) Performance of the melting
temperature model in predicting liquidus temperatures of a waste form-relevant
target system (here, Fe2O3-P2O5). The dashed black lines represent “ground-
truth” liquidus temperatures from CALPHAD, and the blue circles are liquidus
values predicted by the melting temperature (Tm) model. The yellow-to-red
solid lines show predictions from an ML model that is trained on a dataset
with increasingly higher amounts of the target liquidus data (TL) in the
training set, tested on the held-out liquidus data. These results show that
the performance of the model, especially in the two deep eutectic-related
compositions of 40% and 60% P2O5 can be improved significantly augmenting the
training dataset with even a small sampling (10–20%) of the target design
space.

Third, we underline the importance of assessing the performance of ML models
using evaluation methods and metrics that are directly relevant to the task at
hand. Typically, ML model accuracies are reported using metrics such as r2
values or mean absolute errors (MAEs) evaluated in random cross-validation or
a random train/validation/test split of the available data, which can be
informative of within-distribution generalization but not of out-of-
distribution performance. For example, an ML model for predicting melt
temperatures trained on chemical composition based Magpie features [99] and a
dataset of congruent melting temperatures of stoichiometric compounds has a
reasonable accuracy (MAE of $\sim$200 K, consistent with prior work [111]) in
random cross-validation (Figure 6a). However, the model fails to capture the
liquidus temperature trends in a target design space of the Fe2O3-P2O5 system,
especially the two deep eutectic regions around 40% and 60% P2O5 content,
where the prediction errors are higher than 400–450 K (see Figure 6b). In
short, using a test strategy (e.g., leave-one-cluster-out [LOCO] cross-
validation for estimating extrapolative performance [18]) that is
representative of the actual environment that the ML model will be eventually
used in, is critical for a true assessment of its performance. Further, an
accurate evaluation of a model is crucial to improving it, e.g., overcoming
data scarcity with strategies such as transfer learning [67, 68, 69, 70, 72,
71] or prioritizing targeted data collection (see Figure 6b, which shows how
adding even a small fraction [10–20%] of data from the target design space of
Fe2O3-P2O5 enables the ML model to learn the liquidus curve more effectively
than from congruent melting temperatures alone).

Lastly, while most of the focus of ML-based modeling of materials properties
has been towards developing more accurate models, the efficacy of an ML model
within an SL workflow goes beyond simply the model accuracy [112]. In other
words, it is indeed possible to have performant SL workflows with lower-
accuracy ML models. Further, robust uncertainty estimates along with ML model
predictions are crucial not only to calibrate user confidence in the model
predictions but also for ranking and selecting candidates within an SL
workflow (see Section 4.4).

###  4.4 Candidate ranking and selection

Once ML models for target properties have been trained, the next task in the
SL workflow is to rank and select candidates in a target design space for
objective evaluation. The target design space is defined by the target
application, and can be identified by the underlying system design chart. As
discussed earlier (see Section 3), for phosphate-based nuclear waste forms,
the design space is often bound by the composition of the liquid melt, which
in turn is defined by the waste stream, the reagents used for dehalogenation,
glass-forming chemicals (GFCs), and other additives added during the
processing step. From a well-defined design space, candidates can be generated
via simple enumeration (e.g., a uniform grid of compositions within a Gibbs
triangle for a ternary design space). This enumerated list of candidates can
be further filtered down using domain knowledge and/or outputs of simulations
as an intermediate step.

As illustrative examples of phosphate-based waste form design, we generate
candidates in the ternary Na2O-Fe2O3-P2O5 and quaternary Na2O-Nd2O3-Fe2O3-P2O5
spaces (where Na/Nd are the waste cations, Fe2O3 acts as the GFC), using a
uniform grid spacing of 2.5% along each composition axis. We then apply a
combination of domain knowledge-informed rules as well as results from DFT
convex hull analysis to filter out candidate compositions with the following
characteristics (and are therefore unviable): (1) no salt cations in the
composition, (2) unreacted elements, unreacted waste salt, or no phosphates in
the ground state phase mixture predicted by the convex hull analysis, and (3)
ground state phase mixtures that contain binary alkali compounds (e.g.,
Na3PO4) that are known to be water soluble. The resulting filtered list of
viable candidate compositions is much smaller (see Figure 7).

All the relevant target properties for each viable candidate can then be
predicted using the previously trained ML models. The scoring of candidates,
and the identification of candidates to prioritize for experimental validation
and testing (the “acquisition function”), can be performed one of several ways
depending on the design problem. For the design of waste forms in particular,
it is desirable for the acquisition function to be: (1) multiobjective, to
simultaneously optimize several target properties such as mass loading, waste
form volume, compressive strength, and so on; (2) enable end users and domain
experts to weight the different targets or success criteria differently. For
example, Vienna and Kim [113] used a penalty-based approach to multiattribute
optimization of borosilicate glasses:

$P_{i}=\left\\{\begin{aligned}
w_{i}\left(\frac{T_{i}-Y_{i}}{T_{i}-L_{i,L}}\right)^{n}&\quad\text{if
$Y_{i}\leq T_{i}$}\\\
w_{i}\left(\frac{Y_{i}-T_{i}}{L_{i,U}-T_{i}}\right)^{n}&\quad\text{if
$Y_{i}>T_{i}$}\end{aligned}\right\\}$ (2)

where $P_{i}$ is penalty associated with the $i^{\rm th}$ property, $w_{i}$ is
the $i^{\rm th}$ property weighting parameter, $T_{i}$ is the $i^{\rm th}$
property target value, $Y_{i}$ is the $i^{\rm th}$ property predicted value,
and $L_{i,L}$ and $L_{i,U}$ are the lower and upper limit for property $i$.
For each formulation, an optimization is performed by minimizing the sum of
penalties for multiple properties; (3) able to leverage ML model predictions
as well as prediction uncertainties to score candidates. Acquisition functions
traditionally used for Bayesian optimization are well-suited for this purpose,
such as probability of improvement over a specified baseline, $a_{\rm
PI}(x)=\int_{x_{0}}^{\infty}\mathcal{N}[\mu(x),\sigma^{2}(x)]dx$, where $x$ is
the target variable to be maximized (e.g., bulk modulus), $x_{0}$ is the
current baseline performance, and $\mu(x)$ and $\sigma^{2}(x)$ are the
predicted value and uncertainty from the relevant ML model. For multiple
objectives, a scalarizing function that combines $a_{\rm PI}$ for all the
targets can be defined (e.g., simply a product of $a_{\rm PI}$ values for
uncorrelated targets).

Figure 7:  Candidate generation, ranking, and selection in two sample waste
form design spaces: (a) Na2O-Fe2O3-P2O5 and (b) Na2O-Nd2O3-Fe2O3-P2O5 (with a
constant 5 mol% Nd2O3). In both design spaces, a significant fraction of the
candidate compositions are filtered out: with no salt waste or phosphate
phases (open circles), with unreacted waste (dark grey filled circles), with
binary alkali phases (light grey filled hexagons). Viable candidate
compositions are shown as hexagons colored according to (a) salt cation
loading in wt%, and (b) a scaled score that quantifies the likelihood of
improvement simultaneously over all target metrics over reasonable baseline
values; in the latter panel, candidate compositions with salt cation loading
$>$20 wt% are shown as hexagons outlined in bold. The candidates selected for
experimental synthesis and validation from the two design spaces, (a) A2 and
(b) E1, E2, are annotated.

We demonstrate two different strategies for candidate selection in the two
example design spaces. For the Na2O-Fe2O3-P2O5 design space, we show a single-
objective optimization targeting salt cation loading in wt%, which can be
estimated from DFT-based convex hull analysis without the need for ML
surrogates. We choose a candidate composition from among the ones showing the
highest loading ($\sim$18%; higher than the state-of-the-art iron phosphate
glasses [114, 12, 6]) for validation (e.g., “A2” in Figure 7a). For the
Na2O-Nd2O3-Fe2O3-P2O5 design space, we show a multi-objective optimization
with the following three objectives as well as a hard constraint of salt
cation loading $>$20%: (1) minimizing melt temperatures ($<$1173 K, the lowest
liquidus temperature in the Fe2O3-P2O5 binary; see Figure 5a), (2) minimizing
the waste form volume to immobilize 100 g of salt ($<$100 cm3, lower than
state-of-the-art phosphate glass waste forms [114, 12, 6]), and (3) maximizing
bulk modulus ($>$48 GPa, the highest moduli reported for Fe2O3-P2O5 glasses
[115, 116]). We use the product of the individual $a_{\rm PI}$ scores (scaled
to lie within 0–1) as the aggregate metric, representing the likelihood of
improvement over all three targets simultaneously (note that the term
“likelihood” is used loosely, and is not exactly equivalent to the statistical
concept of likelihood), to rank candidates and choose the most promising ones
for experimental synthesis and validation (e.g., “E1” and “E2” in Figure 7b).

###  4.5 Experimental validation

The final task in a SL workflow is the validation of selected candidates, and
closing the loop by providing feedback for the refinement of next round of
predictions and candidate selection tasks. Ideally, the synthesis of the
target materials and any post-processing steps should mimic the final
production process as closely as possible, although this is not always
practical (e.g., an industrial process that is hard to replicate in a
laboratory). Similarly, the characterization of the synthesized materials and
measurement of properties should enable direct feedback into the earlier
prediction and selection tasks in the SL workflow; note that this is not
always possible, e.g., properties that are hard to measure experimentally,
mismatch in target performance metrics and properties for which there exists
data to train ML models.

Figure 8:  A2 candidate waste form: (a) picture of the as-quenched sample, (b)
Rietveld refinement of the diffraction pattern of the as-quenched sample.

Here, we synthesize the three selected candidate waste forms (A2, E1, and E2;
e.g., see Figure 8a for an image of a quenched sample) and perform post-
synthesis heat treatment to simulate a canister pour-and-cool for final
disposal (see Section 7.3 for details of the heat treatment profiles used). We
then characterize the heat-treated samples using X-ray diffraction (e.g., see
Figure 8b for Rietveld refinement for the as-quenched A2
candidate)—determining the phases in each sample and quantifying their
distribution (Table LABEL:tab:phases). We follow up with measurements of
candidate properties such as density (i.e., to validate storage volume
estimation) and compressive strength.

## 5 An End-to-End Workflow Run

To illustrate the end-to-end workflow of an informatics-driven framework, we
consolidate and present one full SL iteration for one of the candidate waste
forms discussed previously, E2, from the Na2O-Nd2O3-Fe2O3-P2O5 chemical space
(with Na2O and Nd2O3 from the waste stream, Fe2O3 added as a GFC, and P2O5
from the dehalogenation process).

We first generate an enumerated design space of potential candidates in the
quaternary space, as a uniform grid with 2.5 mol% spacing along each
composition axis, for a total of 12341 candidate compositions. For each
candidate composition, we then apply DFT convex hull analysis to predict the
ground state phase mixture, and apply domain knowledge filters to exclude
unviable compositions, as described in Section 4.4. The E2 candidate
(composition 37.5% Na2O + 5% Nd2O3 + 20% Fe2O3 + 37.5% P2O5 in mol%) passes
all the domain knowledge filters, and a mixture of {50% Na3Fe(PO4)2 + 21.43%
Na3Fe3(PO4)4 + 28.57% NdPO4} (mol%) is predicted to be the thermodynamic
ground state at its overall composition. We then estimate (a) the salt cation
loading (25.29 wt% of Na, Nd combined), (b) the waste form storage volume per
100 g of nominal waste salt (an equivalent amount of NaCl + NdCl3) as the the
mole fraction weighted DFT-calculated volume of the ground state phase mixture
(54.36 cm3), (c) target properties (e.g., melt temperature, bulk modulus)
using pretrained ML models. Note that the ML models used here are trained to
predict the properties of the individual phases in the mixture, and the
overall properties (and uncertainties) of the mixture are approximated as the
mole fraction-weighted mean. For the E2 candidate, e.g., the predicted bulk
modulus is $75.6\pm 20.1$, the predicted melt temperature is $1480.7\pm
229.3$. We calculate the probability of improvement for each property (e.g.,
$a_{\rm PI}(x={\rm bulk\;modulus})=\int_{\rm
48GPa}^{\infty}\mathcal{N}[\mu(x)=75.6,\sigma^{2}(x)=20.1]dx=0.91$) and
aggregate the individual scores into a cumulative likelihood of improvement
metric scaled to lie between 0 and 1 (see Figure 7b).

Figure 9:  Compressive strength of the E2 waste form (tested on two different
samples).

We then perform experimental synthesis and heat treatment for the target E2
composition, and characterize the phases present using X-ray diffraction (see
Table LABEL:tab:phases). We measure properties such as density (3.164 g/cm3,
and corresponding waste form volume) and compressive strength (38.3–40.2 GPa;
see Figure 9), with all properties surpassing the target performance criteria
listed at the end of Section 2. The characterization data and measured
properties are used to refine the outputs from the physics-based modeling
tasks, as well as to augment existing training data and retrain ML models for
the next SL iteration; these efforts will be reported in the future.

## 6 Discussion and Outlook

While such as informatics-driven workflows are powerful tools for accelerating
materials design in general, and waste form design in particular, some
challenges remain and we discuss a few salient ones below.

The prediction of the exact phases formed during synthesis (and their
respective distributions) given the overall composition and a set of
experimental conditions and post-processing steps remains an open question.
Analyses based on DFT convex hull and related thermodynamic stability
measures, while still extremely useful, suffer from limitations related to DFT
accuracy and ideal conditions (zero temperature and, often, ambient pressure).
As seen from Table LABEL:tab:phases, the mismatch between computational
predictions and experimental realization is large. Some phases that have been
reported experimentally are predicted to be 0 K unstable by DFT (e.g.,
Na2Fe3(PO4)3 found in both A2 and E1 candidates is predicted to be 60 meV/atom
above the convex hull of formation energy). Some other phases are excluded
from the DFT analyses due the nature of the problem set up; i.e., with the
overall melt modeled as a mixture of the corresponding oxides, certain
compounds with mixed elemental oxidation states (e.g., NaFe3(PO4)3 found in
the E2 candidate, with two nominal Fe^3+ and one nominal Fe^2+) or oxidation
states different from the one in the melt ingredient (e.g., NaFePO4 with Fe2+,
in contrast to the GFC additive Fe2O3 in the melt) are naturally excluded. The
latter problem can be mitigated by performing DFT convex hull analyses with
varying elemental chemical potential (e.g., $\mu_{\rm O}$) but increases the
computational expense and complexity of the task. While CALPHAD approaches can
consider effects of variables such as temperature and chemical potential is
calculating phase diagrams, they are severely limited by the lack of assessed
databases, especially for compositions relevant to phosphate-based waste forms
(e.g., current CALPHAD databases in FactSage do not include thermodynamic data
for any quaternary phases in the Na-Fe-P-O chemical space [resulting in the
mismatch for sample A2 in Table LABEL:tab:phases], and assessed databases for
the Na-Nd-Fe-P-O chemical space do not exist). Further, while recent work has
shown the possibility of predicting crystallization pathways from amorphous
matter using a combination of ab-initio methods and deep learning [117],
further efforts are needed to develop a holistic framework that fully bridges
the gap between computational design and experimental realization of
materials.

Another general challenge is the lack of large, well-curated datasets to train
ML models to predict several waste form-relevant properties of interest. For
example, properties such as compressive strength are not widely reported for a
large set of materials and are not trivial to calculate using ab-initio
techniques. Similarly, chemical durability measurements of ceramic waste forms
are scattered across the literature and no centralized curated dataset exists
(in contrast to traditional borosilicate glass-based waste forms, e.g.). While
some of these challenges may be mitigated by using domain knowledge
integration (DKI; see below) or using techniques such as transfer learning
[67, 68, 69, 70, 71, 72], we urge for investments into large-scale data
collection and curation of waste form properties that can benefit the
community as a whole.

For effective use of informatics-based approaches for the design of waste
forms, especially in the context of the above-mentioned challenges, it is
crucial to leverage DKI from experts in various parts of the SL workflow. Such
DKI can take many forms: (1) identifying data-abundant waste form properties
that are correlated with data-scarce performance metrics (e.g., cohesive
energy to inform chemical durability, viscosity and liquidus temperature to
inform processability, bulk modulus to compressive strength [as used in this
work]), (2) defining and constraining the design spaces of interest (e.g.,
identifying the correct target alkali and rare-earth waste cations, and any
potential pool of additives that can be used in waste form fabrication), (3)
filtering undesirable candidates (e.g., excluding candidate waste form
compositions that are expected to form water-soluble alkali phosphates), and
so on.

Overall, the proposed approach of using informatics-based approaches for waste
form design has the potential to drastically reshape the way that these types
of efforts are conducted across the world. The largest impact of this method,
in contrast to the Edisonian trial and error approach, is the potential to cut
the time required to find optimal solutions by an order of magnitude (or
more). Tapping into crystallographic databases, thermodynamic property
databases, phase diagrams, as well as other material property databases, this
informatics approach can be used to design waste forms containing anywhere
from high amorphous (glassy) phase fractions to high crystalline fractions as
well as mixtures thereof. Finally, we note that the opportunities afforded by
such approaches extend far past borosilicate and phosphate waste forms, and
these techniques can be used for optimize the processing history and
conditions to effectively fabricate the next generation of waste forms as well
as aiding eventual scale-up efforts for promising waste forms once so
identified. Some challenges related to bridging the gap between predictions
and laboratory realization of waste forms exist, but current approaches
already present avenues for significant acceleration of the design of novel
waste forms.

## 7 Methods

###  7.1 Thermodynamic analysis

All DFT-based convex hull analysis was performed using data openly available
from the Materials Project [118] and the pymatgen [119] software package.

All CALPHAD calculations were performed using the commercial FactSage software
[120] and associated databases.

###  7.2 Machine learning

All machine learning models reported in this work were built using the open-
source lolo [109] random forests library, using default hyperparameters,
trained on open datasets listed in Table LABEL:tab:datasets (i.e., those for
melting temperature and bulk modulus). The additional Fe2O3-P2O5 liquidus data
used in Figure 6 was calculated using FactSage, and the data is made
available.

###  7.3 Experimental synthesis and characterization

The raw reagents (i.e., Na2CO3 [Aldrich, 99.9% trace metals], Nd2O3, Fe2O3
[Baker, 100.4%], and NH4H2PO4 [Sigma Aldrich, $\geq$98.5%]) were batched using
an analytical balance (Mettler Toledo ME204). The reagents were then loaded
into 250 mL alumina crucibles (ACC3742, McDanel Advanced Ceramic Technologies)
with a Pt/10%Rh lid and melted in a high-temperature furnace (Deltech
Furnaces, Inc.) for 2 hour delay at 1250∘C, with a ramp heating rate of
5∘C/min, followed by quenching on an Inconel plate. The quenched materials
were ground to a fine particle size in a tungsten carbide milling chamber and
run through slow cooling process with an aliquot of the ground material within
a 10 mL alumina crucible (ACM3760, McDanel Advanced Ceramic Technologies).

Two custom heat treatment profiles were employed: “SC2” for samples A2 and E1,
and “SC1” for sample E2. SC2 included a ramp rate of 5∘C/min from room
temperature to 1250∘C, a dwell for 1 hour at 1250∘C, a $-5$∘C/min cooling to
500∘C, a reheat at 5∘C/min to 600∘C, a dwell for 12 hours, a ramp cool at
$-0.03$∘C/min to 465∘Cover the course of 75 hours, and ended with a $-1$∘C/min
ramp cooling rate. SC1 included a ramp rate of 5∘C/min from room temperature
to 1250∘Cat 5∘C/minute, held for 1 hour, ramp cooled at $-25$∘C/minute to
1000∘C, and then ramp cooled to room temperature at $-0.1^{\circ}$C/minute.
These custom heat treatments were designed to homogenize the melt at 1250∘C,
rapidly cool to above the glass transition temperature ($T_{g}$), reheat and
then cool slowly to initiate crystallization.

Once the samples were cooled, vertical slides were prepared using glycol
suspensions and a slow speed Buehler diamond saw. The samples were removed
from their alumina crucibles, ground in a tungsten carbide milling chamber to
a fine particle size and analyzed using X-ray diffraction. Then, a known
amount (5 mass%) CeO2 of a NIST Standard Reference Material (SRM-674b) was
added and ground for 30 additional seconds. Samples doped with CeO2 were run
with a Bruker D8 Advance diffractometer in a scan range of 5–90∘ 2$\theta$,
with a 0.01486∘ 2$\theta$ step angle, with 1 second dwells per step. The
diffraction patterns were analyzed using Bruker Topas (version 5) software
with PDF5+ International Centre for Diffraction Data (ICDD) and Inorganic
Crystal Structure Database (ICSD).

Compressive strength tests were run in duplicate on an Instron 5582 (ID
5582R1924) using a fixed rate of 0.1 mm/minute in accordance with ASTM
C1358-18. Samples were prepared in a 2:1 geometry of height:width using a
series of procedures from a diamond wire saw, a slow-speed diamond blade saw,
and polishing processes. The preferred sample geometry is a cylinder but
making cylinders from these samples proved difficult due to small sample size.
Thus, rectangular prisms were made that were on the order of $\sim$6 mm tall
by $\sim$3 mm wide. Samples were loaded until failure and the compressive
strength was reported as the maximum uniaxial compressive stress reached when
the material failed.

## Data Availability

All associated research data has been deposited into a repository on figshare
[121].

## Author Contributions

Conceptualization: VIH, JES, BJR, JDV, JD; Data curation: VIH, MP, SIA, XL,
JO, RJS, EKN, BJR, JDV, TM, JK, TN; Formal anaylsis: VIH, MP, JO, RJS, EKN,
BJR, JDV, TM, JK, TN; Funding acquisition: VIH, JES, BJR, JDV, JD;
Investigation: VIH, MP, JO, RJS, EKN, BJR, JD, TM, JK, TN; Methodology: VIH,
SIA, JES, MP, XL, RJS, EKN, BJR, JDV, TM, JK, TN; Project administration: JES,
JDV, JD; Resources: BJR, JDV, JD; Software: VIH, SIA; Supervision: JES, BJR,
JDV, JD; Validation: VIH, BJR, TM; Visualization: VIH, MP, BJR, JD, TM, JK,
TN; Writing – original draft: VIH, SIA, JES, MP, XL, BJR, JDV, JD, TM; Writing
– review and editing: all authors.

## Conflicts of Interest

There are no conflicts of interest to declare.

## Acknowledgments

The information, data, or work presented herein was funded in part by the
Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy,
under Award Number DE-AR0001613. The views and opinions of authors expressed
herein do not necessarily state or reflect those of the United States
Government or any agency thereof. Pacific Northwest National Laboratory (PNNL)
is operated by Battelle Memorial Institute for the DOE under contract DE-
AC05-76RL01830. The authors thank Anthony Guzman (PNNL), Irving L. Brown
(PNNL), and Timothy J. Roosendaal (PNNL) for help with preparing samples for
compressive strength, which proved to be quite challenging, and Jarrod V. Crum
(PNNL) for reviewing the manuscript.

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