#  Synthetic space bricks from lunar and martian regolith via sintering

Nitin Gupta  Department of Mechanical Engineering, Indian Institute of
Science, Bangalore Vineet Dawara  Department of Mechanical Engineering, Indian
Institute of Science, Bangalore Aloke Kumar  Department of Mechanical
Engineering, Indian Institute of Science, Bangalore Koushik Viswanathan
<EMAIL_ADDRESS>Department of Mechanical Engineering, Indian Institute of
Science, Bangalore

###### Abstract

The prospect of establishing extra-terrestrial habitats using in situ resource
utilization (ISRU) constitutes a long-term goal of multiple space agencies
around the world. In this work, we investigate sintering as a potential route
for making building blocks—termed synthetic space bricks—using _in situ_
regolith material. By systematically investigating sintering parameters using
a numerical lattice model, coupled with experimental observations and post
sintering characterization, we propose a process protocol for two lunar—lunar
highland simulant (LHS) and lunar mare dust simulant (LMS)—and one martian
(martian global simulant, MGS) simulants. The resulting bricks demonstrate
compressive strengths of upto 45 MPa under uniaxial loading, depending on the
simulant used. These strengths are much greater than those typically mandated
for structural applications under reduced gravity. We infer microscale
sintering mechanisms at the individual particle level indirectly, by measuring
temporal evolution exponents of sample dimensions during sintering. For all
three simulants, volume diffusion appears to be the primary mechanism for
particle coalescence. Our results clearly make a strong case for the use of
sintering as a potentially scalable method for consolidating regolith into
brick-like structures for load-bearing applications in extra-terrestrial
settings.

#### Keywords:

Sintering; Space habitation; Extra terrestrial regolith; Synthetic space
bricks

## 1 Introduction

The prospect of establishing extra-terrestrial habitats continues to remain a
long-term goal of multiple space agencies around the world [1]. This field has
traditionally encompassed a wide variety of disciplines ranging from
biological effects on humans [2] to geology and civil engineering [3]. The
possibility of developing extra-terrestrial structures that can sustain both
extreme environments and be built with minimal raw materials has drawn
significant recent interest [4, 5]. The obvious option of exploiting intrinsic
features on the martian or lunar surface, for instance lava tubes [6, 7], is
fraught with fundamental difficulties such as potential structural collapse
and the occurrence of surface fissures. The alternative option of constructing
settlements with material sourced from earth is expected to incur significant
costs, rendering it practically unviable.

A recently emerging research paradigm— _in situ_ resource utilization or
ISRU—attempts to address this problem by developing technologies for
exploiting resources, primarily regolith and solar energy, available on the
martian or lunar surface [8, 9, 10]. To help seed research in this direction,
several artificial regolith simulants have been developed to mimic martian or
lunar soil corresponding to various known locations on mars and the moon,
respectively, based on corresponding spectroscopy and/or particle morphology
data [11, 12, 13, 14, 15, 16, 17, 18, 19]. These regolith simulants can be
consolidated to form load bearing structures for habitat applications using a
range of strategies, from exploiting biological routes [20, 21, 22, 23] to
employing concrete-mimicking processes [24, 25, 26] and polymer binders with
sintering [27, 28, 29].

Among these consolidation techniques, sintering-based routes have so far
yielded the most promising results when final part strength is the primary
requirement. Various sintering protocols that have hitherto been proposed
include microwave [30, 31, 32], spark plasma [33], cold-sintering [34] and
solar radiation [35, 36, 37]. The effects of various process parameters on
resulting consolidate strength have also been systematically investigated at
the macroscale, including the role of sintering temperature [38, 39], porosity
[40, 41], initial mineral compositions [42, 43] and the presence of glass-like
phases [44]. A summary of these sintering/consolidation techniques and the
resulting average compressive strength $(\sigma_{comp,avg})$ is presented in
table 1.

Consolidation technique | Temperature | Simulants | $\sigma_{comp,avg}$ | Ref.
---|---|---|---|---
| (∘C) | used | (MPa) |
Sintering | 1000-1100 | HUST-1, CAS-1 | 68 | [28]
Sintering & melting | 1000-1300 | JSC-2A | 31 | [29]
Hybrid microwave sintering | 1075-1125 | FJS-1 | 45 | [30]
Microwave sintering | 1200-1500 | MLS-1, JSC-1 | - | [31]
Microwave sintering | 1120 | KLS-1 | 37 | [32]
Spark Plasma sintering | 1050 | FJS-1 | 220 | [33]
Cold sintering | 250 | MGS-1 | 45 | [34]
Sintering | 1100-1200 | MGS-1, LMS-1 | 22-25 | [38]
Digital light | 1100-1150 | CLRS-2 | 56 - 312 | [39]
processing & sintering |  |  |  |
Sintering | 1200 | JSC-1 A, JSC-1AF, | 103 - 232 | [40]
|  | and JSC- 1AC |  |
Sintering | 1120 | JSC-1A | 84.6 - 218.8 | [41]
Sintering | 1070-1125 | JSC-1, DNA, MLS-1 | 98 - 152 | [45, 42]
Additive Manufacturing | 1200 | LHS-1 | 20 | [43]
& sintering |  |  |  |
Laser assisted sintering | 1400 | HIT-LRS | 68 | [44]
Solar Sintering |  | JSC-2A | 2.49 | [46]
and 3D printing |  |  |  |
Extrusion & sintering | 1050 | JSC-1A | 20 | [47]
Additive manufacturing | 1000 | EAC-1 | 5.4 | [48]
& sintering |  |  |  |
Brazing of SiC | 1400 | LRS, MRS | 21 - 27 | [44]
Laser assisted sintering | 1000-1100 | Quartz sand |  $\sigma_{tensile}$ = 9.28 | [49]
Electric current assisted | 700 | JSC-1A | 50 | [50]
sintering (ECAS) |  |  |  |
Table 1: List of various sintering strategies used to consoildate regolith
simulants, with reported average mechanical strength under uniaxial
compression.

On the microscale, mechanisms governing particle consolidation during the
sintering process are expected to be independent of the energy source utilized
and largely determined by the thermal fields thereby produced [51]. In this
context, the specialized sintering techniques introduced allow for varying
degrees of thermal control. Yet they cannot compare with furnace-based
sintering, perhaps one of the oldest methods for producing ceramics. Here
spatially uniform temperatures are _a priori_ the norm, given the lack of
directionality of a focused energy source. Consequently parts produced via
furnace sintering are expected to have uniform, isotropic properties; this
process is also inherently scalable, as has been amply demonstrated on earth.
An additional advantage of furnace sintering is that it enables more
systematic study of the role of microscopic mechanisms operative at much
smaller length scales without intervening spatial inhomogeneity effects.

The primary objectives of the present work are threefold—the first is to
develop a scalable experimental protocol for making consolidated regolith-
based bricks on both the lunar and martian surfaces by using a polymer-based
binder and furnace sintering. To this end, we work with two lunar
simulants—lumar highland simulant (LHS) and lunar mare dust simulant (LMS)—and
one martian simulant (martian global simulant, MGS). The second is to evaluate
the microscopic mechanisms based on the kinetics of the sintering process by
taking recourse to classical results in the ceramics literature. The third and
final task is to correlate the established processing protocol and operative
microscopic mechanisms with final part strength. Our manuscript is organized
as follows. We first discuss the strategy of brick manufacturing in Sec. 2.1,
and corresponding post-consolidation characterization (Sec. 2.2). A simple
numerical model is presented to determine heating parameters needed for
ensuring spatial homogeneity (Sec. 2.3). The primary results are described in
Sec.3, beginning with numerical estimation of minimum soaking time $t_{s}$
required (Sec. 3.1), followed by evaluation of mechanical properties (Sec.
3.2) and sintering mechanisms (Sec. 3.4). We present a discussion of our
results and provide concluding results in Sec. 4.

## 2 Materials and Methods

### 2.1 Protocol for single brick production via sintering

We use three types of soil simulants for our experiments—MGS (Martian global
simulant), LHS (Lunar highland simulant), and LMS (Lunar mare dust simulant),
procured from Exolith lab, Florida, USA [14, 15]; details of these simulants
are provided in Fig. S2 and Table 1 of supplementary material. The
experimental procedure for producing sintered parts is summarized in Fig. 1. A
PVA solution was prepared by mixing 5g of PVA (polyvinyl alcohol) powder
(molecular weight 1,15,000 from Loba chemie pvt ltd.) with 100 ml of DI water
and stirring at 90∘C for 1 hr, followed by stirring at room temperature for
10-12hr. This solution (15 ml) was then thoroughly mixed with 100g of simulant
and the mixture die cast in the form of a cubical block of approximately $\sim
18\times 18\times 18$ mm3 using a hydraulic press with 280-300 MPa compaction
pressure. The resulting compacted sample weighed around 14 grams; it was then
heated in a muffle furnace (Delta Power systems) for sintering.

Stages of the sintering cycle are shown in the form of a temperature vs. time
curve, see Fig. 1 (bottom left). In the first step, as-cast samples were
heated for 1 hour at 600∘C with a slow temperature ramp-up and ramp-down. This
stage removes any volatile matter from the bricks, along with the PVA binder
used to make the compacted part. The furnace was then brought back to room
temperature at the time marked B. The dimensions of the sample were measured
at this stage and are henceforth referred to as the intiial dimensions,
denoted $L_{i}$. Correspondingly, the sample weight at the end of this stage
typically reduced by $\sim$13-14% . At time B, the sample is referred to as a
green part.

The green part was then subject to the next heating stage (C to D) upto a peak
temperature of $T_{a}=1150^{\circ}$C with heating rate $c=5^{\circ}$C/min for
time $t_{f}$ (point C to E). Following this, the samples were soaked for
different times ($t_{s}$) ranging from 10 minutes to 480 minutes (point E to
F), and then cooled (point F to D) at a rate of 4∘C/min to obtain final brown
parts, which we term ‘synthetic space bricks’. The final dimensions $L_{f}$
were measured post recovery to room temperature; the sample weight was
typically found to reduce by $\sim$4% at this stage, compared to the green
part.

Figure 1: Schematic representation of the sintering process. Mixing of 5% PVA
in 100 ml of DI water mixture extra-terrestrial soil simulant within the ratio
of 0.15:1 w/w. The mixture is poured into a die and compacted using a
hydraulic press, followed by sintering in the furnace. The sintering cycle
represents the preparation of the green part (heating to 600∘C for 1 hr)
followed by the brown part (heating to $T_{a}$ for $t_{s}$ minutes).

### 2.2 Post-sintering characterization

Internal porosity of sintered bricks was evaluated using mercury intrusion
porosimetry (Pore Master), henceforth referred to as MIP. This technique uses
high pressure (35000 psi) to drive mercury into the pore spaces in order to
determine the pore size distribution ranging from sub-micrometer pores to a
few hundred micrometers. Compressive strength measurements were performed
using quasi-static displacement-controlled unaxial compression on a universal
testing machine (Instron-5697) with a 30 kN capacity load cell and loading
rate of 0.5 mm/min. Post-sintering microstructural examination was carried out
using FE-SEM (field emission-scanning electron microscopy)(Carl Zeiss,
Germany) with a BSD detector. When compared with other detectors, BSD
detectors offer better efficiency for in-lens detection with higher surface
sensitivity and, consequently, enhanced spatial resolution for resolving pore
and grain-level information. The SE detector is used to image particle fusion
post-sintering.

### 2.3 Numerical estimation of sintering time $t_{s}$

In order to establish the efficacy of the sintering process and, in
particular, to estimate the optimal sintering time necessary for the complete
part to reach the desired sintering temperature, we employed a numerical model
based on a disordered lattice network description [52, 53, 54, 55]. The basic
problem consists of estimating the interior temperature of a porous material
(here the consolidated green part) as a function of temperature ramp and hold
at the boundaries (here the furnace conditions). The ramp rate was fixe at
$5^{\circ}$ C/min and the temperature at $T_{a}=1150^{\circ}$C, see schematic
in Fig. 1. The lattice network model was then used to estimate the duration of
soaking so that the interior of the brick attained uniform temperature to
ensure homogeneous sintering. This step is necessary because the interior
temperature of the bricks cannot be experimentally monitored during any stage
of the process.

The configuration used for the simulations presented schematically in Fig. 2,
and consists of a regular triangular lattice network with unit spacing $a$.
The governing heat conduction equation for temperature ($T$) evolution with
time ($t$) in an isotropic homogeneous solid with thermal diffusivity $\alpha$
is

$\displaystyle\frac{\partial T}{\partial t}=\alpha\nabla^{2}T$ (1)

which, when discretized on this lattice takes the form [56]

$\displaystyle\frac{\partial T_{i}}{\partial
t}=\frac{2\alpha}{3a^{2}}\sum_{j}^{6}(T_{j}(t)-T_{i}(t))$ (2)

Thus, we can imagine our solid as a regular network of bonds with diffusivity
(unit square bond length) $\kappa_{ij}=2\alpha/3a^{2}$ and a temperature
difference of $(T_{j}-T_{i})$ applied across it, as described in Fig. 2. To
determine the dynamic evolution of temperature, we used forward finite
difference time discretization in Eq. 2, yielding an explicit numerical scheme

$\displaystyle T_{i}(t+\Delta t)=T_{i}(t)+\Delta
t\sum\kappa_{ij}\sum_{j}^{6}(T_{j}(t)-T_{i}(t))$ (3)

All material information is described by bond diffusivity $\kappa_{ij}$
between nodes $i,j$. In order to simulate the internal porosity in the green
part, we assume that pores are randomly distributed throughout the specimen,
which otherwise has uniform diffusivity. Experimentally consistent porosity
values $p$ were first obtained from MIP measurements (see Sec. 2.2),
correspondingly nodes were removed in the lattice to generate an equivalent
porosity in the network (see inset to Fig. 2). In this way, different
realizations of a porous lattice of a given gross porosity $p$ were generated.

Figure 2: Schematic of lattice network model comprised of triangular lattice
nodes and random pore network with porosity $p$. Voronoi polygons were first
generated in the triangular lattice with porosity $p$, shown as a zoomed image
in the inset. Solid is shown as a regular network of thermal resistors with
conductivity $\tilde{\sigma}$ = 2/3 and a temperature difference of
($\theta_{j}$-$\theta_{i}$) applied across the bond joining lattice nodes
$i,j$; $\tau$, $\Theta$ and $\tilde{c}$ represents non dimensional time,
temperature and heating rate, respectively. See text for description.

At $t=0$, the temperature at all the nodes was kept equal to room temperature
$T_{0}=30^{\circ}$C. For $t>0$, we assume the nodes on the outer four
boundaries of the specimen (orange color, labeled ABCD in schematic) to be at
the furnace temperature at all times, which was increased at a constant rate
($c$) from room temperature $T_{0}$ to $T_{a}=1150^{\circ}$C, and thereafter
maintained constant. Equation 3 was then solved on the porous lattice to
determine time needed when the interior to reach the outer furnace temperature
$T_{a}$. This provided the minimum time necessary $t_{s}$ for the sintering
process to occur homogeneously. Data is presented in the form of non-
dimensionalized temperature $\Theta=(T-T_{0})/(T_{a}-T_{0})$.

## 3 Results

We now describe the results of sintering experiments, beginning with optimal
soaking time estimation using the lattice network model described in Sec. 2.3.
We then present results of compression testing experiments and use length
measurements during sintering to infer microscale mechanisms operative during
sintering.

### 3.1 Porosity and soaking time $t_{s}$

Results of the numerical simulations introduced in Sec. 2.3 are first used to
estimate the minimum soaking time $t_{S}$ necessary for optimal sintering.
This is defined as the time taken for the entire network to reach the furnace
temperature. However, the porosity $p$ of the green part is an input for the
model; we obtain this from MIP measurements of test samples as described in
Sec. 2.2. For bricks sintered at $1150^{\circ}$C, mercury was infused at 35
kpsi pressure in MIP. The porosity was estimated to be $24.2\%$ and $20.3\%$
for soaking durations of 1 hour and 6 hours, respectively. As an upper bound,
we set $p=25\%$ for the initial network; in the results that follow,
temperature $T$ and time $t$ are normalized as

$\displaystyle\Theta=(T-T_{0})/(T_{a}-T_{0})\hskip 28.45274pt\text{and}\hskip
28.45274pt\tau=\alpha t/a^{2}$ (4)

Being an explicit scheme, we use a small timestep $\Delta\tau=0.1$ for
ensuring a stable solution. The lattice size was taken to be 200$\times$200,
corresponding to the 18$\times$18mm2 dimensions of the green brick; thermal
diffusivity of LHS samples was approximated to be 2.65$\times 10^{-8}$ m2/s
(diffusivities for most simulants are $\sim 10^{-8}$ ($m^{2}$/s)), see [57,
58].

The results of the numerical simulation are summarized in Fig. 3. Panel (a)
shows the temperature field in the porous network at time $t_{f}$ when the
furnace first reaches the peak or soaking temperature $\Theta=1$. A gradient
is clearly observed in the field, with $\Theta$ varying by nearly 0.05 from
the sample periphery to its interior. As the furnace temperature is held
constant at $T_{a}$ (corresponding to $\Theta=1$), the interior temperature
continues to rise; the time taken for it to reach $T_{a}$ everywhere inside is
set to be the minimum soaking time $t_{s}$. The corresponding thermal field is
shown in panel (b) of Fig. 3.

Figure 3: Non-dimensional temperature field in the porous lattice network
($p=25\%$) when the boundary first reaches the soaking temperature (panel a),
and when the interior reaches $\Theta=1$ (panel b). Panel c shows temperature
distribution ($\theta$) along the horizontal lines at the center for various
values of $\tau$ (marked). Thermal conductivity of LHS is 2.65$\times$10-8
m2/s, 200$\times$200 lattice size, heat ramping rate 5∘C/min

The corresponding temperature evolution along the horizontal midline of the
sample is shown in Fig. 3(c) . The heterogeneity of the bricks, majorly pores,
causes the fluctuations in the curve. When the heating begins from room
temperature $\Theta$ = 0 (point C, in sintering cycle of Fig. 1), the
temperature at all points in the mid of the y-axis is zero. During the
temperature ramp, the end temperatures are slowly raised to $\Theta$ = 1
(point E in sintering cycle, Fig. 1). Even after ramp is complete, the
boundaries are maintained at $T_{a}$, the temperature continues to rise until
it becomes uniform inside the sample (point $E$ to $\tilde{F}$).

Based on these simulations, we determine that for the present geometry (cubic,
18 mm side length), a green part requires a total time $t_{f}+t_{s}\sim 285$
min to reach uniform peak temperature $T_{a}$. Given that the furnace takes
$t_{f}=224$ min to reach $T_{a}$ from room temperature, the total time for
sintering is expected to be atleast $t_{s}$ $\sim$60 min. This corresponds to
the temperature profile curve $\tilde{F}$ in Fig. 3(c). While this value holds
specifically for LMS, all simulants used in the present study have similar
thermal diffusivity and porosity so that we take 60 minutes as the minimum
soaking time for furnace sintering for LHS, LMS and MGS samples.

### 3.2 Compressive strength of synthetic space bricks

The compressive strength $\sigma_{c}$ of sintered samples was measured using
unconfined uniaxial compression, as described in Sec. 2.2 and the results
summarized in Fig. 4. For sintering, peak temperature was maintained at
$T_{a}=1150^{\circ}$C since that is the maximum temperature at which both LMS
and MGS can undergo solid-state sintering, without melting of their
constituent components. Data in is compiled based on individual stress-strain
curves such as the ones shown in Fig. S1 of supplementary material. The
results are summarized for LHS, LMS and MGS in Fig. 4 in the form of blue,
green orange and green bars, respectively. The values here are those obtained
over 4 samples with corresponding error bars representing standard deviation.
The horizontal axis represents the soaking time $t_{s}$, and the red arrow
marks the cut-off at the minimum soaking time estimated from the previous
section, corresponding to curve $\tilde{F}$ in Fig. 3(c).

For $t_{s}=10$ min, MGS-based bricks exhibit a mean compressive strength of
23.9 MPa, while LMS and LHS-based bricks showed compressive strengths of 11.0
MPa and 5.1 MPa, respectively. Beyond the estimated minimum $t_{s}$ of 60 min,
significant strength increase was observed for all three cases, with MGS, LMS,
and LHS reaching 40.8 MPa, 33.9 MPa, and 11.4 MPa, respectively. This is a
clear sign of enhanced sintering due to homogeneous internal temperature.

Figure 4: Compressive strength of Synthetic space bricks from LHS (blue), LMS
(orange) and MGS (green) simulants as a function of sintering or soaking time.
$T_{a}=1150^{\circ}$C.

However, given that this condition provides only a lower bound for sintering
time $t_{S}$, we evaluated the strength at times $t_{S}$ upto 480 min, as
shown in Fig. 4. LMS showed the largest compressive strength (exceeding 40
MPa) at $t_{S}=360$ min, with a reduction in strength at higher $t_{S}$.
Likewise, the strength of MGS bricks appeared to saturate after $t_{S}=240$
min, reaching $\sim 35$ MPa. LMS bricks showed the lowest strength ($<20$ MPa)
throughout the tested $t_{S}$ range. The reason for the apparent reduction in
strength for $t_{s}>360$ min for all three cases is not clear, and could be
dependent on specific microscopic processes operative in each of the regolith
materials. Potential causes include grain growth and microcrack formation due
to thermal stress leading to enhanced susceptibility to fracture.

Figure 5: Fracture patterns accompanying failure of synthetic space bricks
under unconfined compression. Arrows point to cracks growing in the loading
direction. $T_{a}=1150^{\circ}$C, $t_{S}=360$ min.

In each compression test, the compressive strength was evaluated using the
maximum force measured during loading, _cf._ Fig. S1 of supplementary. At this
point, the bricks undergo compressive failure, leading to a significant
reduction in the force-displacement curve. This failure is mediatead by a
number of cracks that are commonly aligned in the loading direction, see Fig.
5. The three panels in this figure show LHS (left), LMS (middle) and MGS
(right) samples, respectively, at the point of failure. All of these samples
were sintered for $t_{s}=360$ min. In each case, the proliferation of multiple
cracks is clear (see at arrows), all nominally aligned with the loading
direction. Prior simulations of these fracture patterns have shown that the
most likely mechanism for this is pore and microcrack coalescence leading to
macroscopic cracks. These then grow in a direction parallel to the compression
axis due to the lack of any lateral confining pressure [55].

### 3.3 Post-sintering microstructure

Post-process SEM images of bricks show clear signs of sintering on the
microscale, see Fig. 6. Panel (a) shows a typical brick and the location at
which SEM images are taken; the yellow arrow represents compaction direction.
A small section was mechanically removed from the sample surface and gold-
coated for imaging. Data for LHS bricks is presented, corresponding images for
LMS and MGS appear qualitatively similar. BSD detector was used to obtain
these images.

Panels (b) and (c) show the surface after $t_{S}=60$ min (minimum $t_{S}$
estimated) and $t_{S}=360$ min, respectively. Temporal progress of the
sintering process is clear from these images—initially disparate regolith
particles first appear loosely bound after 60 min (panel (b)). They
demonstrate significantly enhanced cohesion after 360 min, with a few pores
evident between particles (panel (c)). A higher resolution image (inset, blue
box) shows that the individuality of particles is clearly no longer
discernible at this stage.

Figure 6: SEM micrographs showing the top layer of LHS-based bricks using BSD
detector. (a) Schematic of SEM micrograph location. Panels (b), (c) show
micrographs for $t_{S}$ = 60 min and 480 min, respectively, clearly
demonstrating enhanced sintering with $t_{S}$, and consistent with compressive
strength measurements. $T_{a}=1150^{\circ}$C.

These micrographs show how crucial it is to regulate the sintering parameters
to create a coherent structure, which ultimately affects the strength and
utility of the bricks. The micrographs for LMS and MGS also show a similar
trend, even though the overall strength is quite different in all three cases
(_cf._ Fig. 4). This largely similar microstructure is also perhaps
responsible for the similar crack patterns observed during failure of all
three regolith-sintered bricks (_cf._ Fig. 5).

### 3.4 Inferring microscale sintering mechanisms

We now turn our attention to the microscopic mechanisms underlying particle
sintering during the soaking stage. Extensive prior studies by the ceramics
community dating back to the 1950s have identified four primary candidate
mechanisms for the joining of two individual particles—viscous flow, atomic
evaporation and condensation, surface diffusion, and lattice diffusion. The
underlying assumptions here are that only 2-particle mechanisms are dominant
and that particles themselves are approximately spherical.

Identifying which of these mechanisms is operative in our bricks is
challenging due to the large poly-dispersity in particle size and shape as
well as the complex mineral compositions involved. A simple macroscale method
for inferring the dominant mechanism(s) involves measuring sample dimensions
during the soaking process as a function of $t_{S}$ [59, 60, 61, 62, 63, 64,
51, 33]. Reduction in dimension is approximately correlated with centre-to-
centre distance $\delta$ and neck radius $x$ between particles on the
microscale, see Fig. 7(a). In general, $x^{n}\sim t$, where the exponent $n$
is governed by which mechanism is operative. For viscous flow, evaporation
condensation, volume diffusion and surface diffusion, the value $n$ is 2,3,5
and 7, respectively.

Specifically,

$\Big{(}\dfrac{x}{r}\Big{)}^{n}=\text{At}\implies\log\Big{(}\dfrac{x}{r}\Big{)}=\log{(\chi)}=\dfrac{1}{n}\log(A)+m\log(t)$
(5)

where $A$ is a material-dependent constant. For the bricks, $x/r$ is obtained
approximately by measuring the percentage shrinkage in linear dimensions from
the green to the brown part [63].

$\text{shrinkage}=\dfrac{L_{i}-L_{f}}{L_{i}}=\dfrac{\Delta
L}{L_{i}}=\dfrac{\delta}{r}\approx\dfrac{x^{2}}{4r^{2}}=\dfrac{\chi^{2}}{4}$
(6)

where $2\delta$ is change in centre-to-centre distance between two spherical
particles under coalescence, and $r$ is the particle size.

In order to finally evaluate the exponent $n$, dimensions of the cubic green
and brown parts were measured using a vernier caliper at various locations and
averaged to get a mean linear dimension; the value of $\Delta L/L_{i}$ then
provided an estimate of $\chi$ from Eq. 6. The corresponding log($\chi$) vs.
log($t_{s}$) plot is shown in Fig. 7(b). The relationship appears to be nearly
linear, with slope equal to the inverse exponent $m=1/n$, see Eq. 5. We have
only used samples for which $t_{s}>60$ min in accordance with the estimate
obtained in Sec. 3.1. The error bars represent standard deviations over 4
successive measurements.

Figure 7: Mechanism of neck growth and particle coalescence in sintered
bricks. (a) Schematic representing two-particle model for calculating the
growth rate. Panel (b) presenets experimental observations of variation of
$\chi$ vs. $t_{S}$ on a log-log scale, note that
$\chi=\dfrac{x}{r}=2\sqrt{\dfrac{\Delta L}{L}}$. Panels (c) and (d) show SEM
micrographs (SE detector) of MGS and LHS, respectively with red arrows
indicating particle coalescence. Data in (b) is averaged over 4 samples,
$T_{a}=1150^{\circ}$C.

The approximated slopes from the curves in Fig. 7(b) correspond to $n=$ 4.4,
4.2, and 4.9 for LHS, LMS, and MGS, respectively, sintered at 1150∘C. These
values strongly suggest that volume diffusion ($n=5$) is the predominant
mechanism for sintering on the microscale. Corresponding SEM images (SE
detector) of MGS and LHS are shown in Fig. 7(c) and (d), respectively. The
coalescence of individual regolith particles appears quite clear (at arrows).
The extent to which other mechanisms (e.g., viscous flow) are operative
remains uncertain based on these investigations and certainly warrants further
study.

## 4 Discussion and Summary

Based on our investigations, it is clear that a significant difference in
compressive strength (unconfined) is to be expected between various regolith
simulants—LMS and MGS are comparable ($\sim 40$ MPa) while that of LHS is
nearly $60\%$ lower. It is entirely possible that the use of higher sintering
temperature may significantly alter this picture since fundamental chemical
changes are expected, given the soil composition. In fact, exploiting the
presence of increased glass basalt content in LHS appears to be a direct route
for enhancing sintering strength that we are presently pursuing.

As fundamental building blocks for habitat applications, the minimum strength
needed for sustaining their self weight is around 3 MPa (lunar) and 6 MPa
(martian), based on the lower gravity on the surface of the moon or mars,
respectively. The synthetic space bricks reported in our work have
significantly larger strength, making them more than suitable for these
applications, even if only partially sintered (_cf._ Fig. 4). As far as
deployability is concerned, the sintering technique is ideally suited to _in
situ_ resource utilization (ISRU) on extra terrestrial habitats since the
process can be scaled and completely automated. We believe that this large
strength and process scalability are fundamental advantages of the sintering
process, over other routes that have been proposed in the literature, see also
Table. 1.

For both the lunar and martian bricks, ultimate failure (under unconfined
compression) occurs via the propagation of multiple axis-aligned cracks. A
typical stress-strain curve for these bricks (se Fig. S1, supplementary
material) shows that they are essentially brittle with little plastic flow on
the macroscale. The growth of cracks occurs due to local stress
concentration—at either large pores or pre-existing microcracks—that can lead
to catastrophic failure at a size-dependent critical load. This behaviour was
also observed to be somewhat anisotropic, being different in the compaction
direction (initial green part production) vis-á-vis the transverse directions.
In general, pores, inclusions, and grain boundaries are examples of
microstructural flaws that may inherently operate as stress concentrators, and
provide locations for crack initiation and propagation.

Based on our results, it is to be expected that the peak temperature and
soaking time are the two primary contributors to final part strength. While
the increase in strength with $t_{S}$ is to be expected—longer soaking time
leads to better particle coalescence and hence, enhanced sintering—the
reduction in strength for $t_{S}>360$ min across all three materials is
noteworthy. This is quite likely due to the occurrence of large internal
pores, either driven by vacancy diffusion in the bulk or by thermal stresses.
However, little evidence of this was found in the compression test failure
mechanisms and this thus warrants further investigation. As mentioned in the
text, the occurrence of high glass basalt content (melting $\sim
1170^{\circ}$C) in LHS is likely to increase the strength in samples sintered
at higher temperature; we are presently actively investigating this
possibility.

In the context of sintering mechanisms, our results, based on classical
analyses commonplace in the ceramics community, indicate that volume diffusion
is the primary driver of particle coalescence. This is clear based on the
macroscopic measurements presented in Fig. 7, yet direct evidence of these
mechanisms is fundamentally challenging to obtain. The possibility of directly
observing individual particle coalescence at the grain level is complicated by
both the length-scales and high temperatures involved, not to mention the
complete lack of axisymmetry in the particles themselves. We believe that
coarse-grained granular dynamics simulations could be profitably employed to
address this question in more detail.

In summary, our work proposes a procedural protocol for fabricating synthetic
space bricks via sintering in extra-terrestrial settings using _in situ_
resource utilization. We have demonstrated the potential for using both lunar
and martian regolith simulants, with significant compressive strengths of
final sintered bricks. Process parameters were estimated using a numerical
model to evaluate time needed for uniform temperature in the interior of
porous green parts produced using a polymer binder. Based on these results,
compressive strength measurements were performed as a function of the
sintering time at a fixed temperature. Our results show that strengths of
$>40$ MPa are achievable with both lunar (LMS) and martian (MGS) simulants.
Strength resulting from particle coalescence was confirmed using both
compression testing and SEM imaging of consolidated samples. Based on linear
shrinkage, we inferred the primary microscopic sintering mechanism to be
volume diffusion in the bulk of individual particles in all three simulants.
Based on our results, the potential for using sintering to consolidate
regolith into bricks for structural applications has been clearly
demonstrated.

## Acknowledgments

The authors acknowledge Mr Bhupendra Chand and Prof Tejas Murthy, Civil
Engineering, IISc for extending the MIP facilities for conducting porosity
analysis.

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